%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW334+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 12:25:58 EDT 2023

% Result   : Theorem 45.15s 43.99s
% Output   : Proof 45.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW334+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n002.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 23:01:34 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 45.15/43.99  
% 45.15/43.99  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.15/43.99  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.15/43.99  %-----------------------------------------------------
% 45.15/43.99  ncf(matrix, plain, [(51638 ^ _2056441) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_na), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(v_x)), hAPP(c_Com_Ocom_OBODY, v_x)), v_Q(v_x)))], !, (49825 ^ _775828) ^ [_1777151, _1777153, _1777155] : [class_Orderings_Olinorder(_1777151), c_List_Olinorder__class_Osorted(_1777151, _1777153), -(c_List_Olinorder__class_Osorted(_1777151, hAPP(hAPP(c_List_Otake(_1777151), _1777155), _1777153)))], (1370 ^ _775828) ^ [_795571, _795573] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_795571)), _795573 = _795571, class_Groups_Oordered__ab__semigroup__add__imp__le(_795573)], (51452 ^ _775828) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (16979 ^ _775828) ^ [_1065424, _1065426, _1065428] : [class_Rings_Ocomm__semiring__1(_1065424), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065424), _1065426), hAPP(hAPP(c_Power_Opower__class_Opower(_1065424), _1065426), _1065428)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1065424), _1065426), hAPP(c_Nat_OSuc, _1065428)))], (10001 ^ _775828) ^ [_937389, _937391, _937393, _937395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937389, tc_HOL_Obool)), _937391), _937393)), hBOOL(hAPP(hAPP(c_member(_937389), _937395), _937391)), -(hBOOL(hAPP(hAPP(c_member(_937389), _937395), _937393)))], (2030 ^ _775828) ^ [_805412, _805414] : [_805414 = _805412, -(c_Int_Osucc(_805414) = c_Int_Osucc(_805412))], (34759 ^ _775828) ^ [_1424381, _1424383, _1424385] : [class_Orderings_Olinorder(_1424381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424381), _1424383)), -(_1424383 = c_Orderings_Obot__class_Obot(tc_fun(_1424381, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424381), _1424385)), -(_1424385 = c_Orderings_Obot__class_Obot(tc_fun(_1424381, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424381, tc_HOL_Obool)), _1424383), _1424385) = c_Orderings_Obot__class_Obot(tc_fun(_1424381, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1424381, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424381, tc_HOL_Obool)), _1424383), _1424385)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424381), c_Big__Operators_Olinorder__class_OMax(_1424381, _1424383)), c_Big__Operators_Olinorder__class_OMax(_1424381, _1424385)))], (17011 ^ _775828) ^ [_1066172, _1066174, _1066176] : [class_Int_Onumber__ring(_1066172), class_Rings_Olinordered__idom(_1066172), 17018 ^ _775828 : [(17025 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1066174), _1066176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066172), hAPP(c_Int_Onumber__class_Onumber__of(_1066172), _1066174)), hAPP(c_Int_Onumber__class_Onumber__of(_1066172), _1066176))))], (17019 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066172), hAPP(c_Int_Onumber__class_Onumber__of(_1066172), _1066174)), hAPP(c_Int_Onumber__class_Onumber__of(_1066172), _1066176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1066174), _1066176)))]]], (51466 ^ _775828) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (27373 ^ _775828) ^ [_1261553, _1261555, _1261557, _1261559] : [hBOOL(hAPP(hAPP(c_member(_1261555), _1261559), hAPP(c_Relation_ORange(_1261553, _1261555), _1261557))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1261553, _1261555, hAPP(hAPP(c_COMBC(_1261553, tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_fun(_1261555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261555, tc_fun(tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_fun(_1261555, tc_HOL_Obool)), _1261553), c_COMBC(_1261555, tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261555, tc_prod(_1261553, _1261555)), tc_fun(_1261555, tc_fun(tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_HOL_Obool)), _1261553), hAPP(c_COMBB(tc_prod(_1261553, _1261555), tc_fun(tc_fun(tc_prod(_1261553, _1261555), tc_HOL_Obool), tc_HOL_Obool), _1261555), c_member(tc_prod(_1261553, _1261555)))), c_Product__Type_OPair(_1261553, _1261555)))), _1261557)), _1261559)))], (24278 ^ _775828) ^ [_1201644, _1201646] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1201644)), hAPP(c_Nat_OSuc, _1201646)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1201644), _1201646)))], (30880 ^ _775828) ^ [_1340773] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1340773)), -(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))), _1340773)), c_FunDef_Omax__weak)))], (50722 ^ _775828) ^ [_1797068] : [c_List_Onat__list(_1797068), -(c_List_Oembed__list(c_List_Oreturn__list(_1797068)) = _1797068)], (19122 ^ _775828) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (39036 ^ _775828) ^ [_1518966, _1518968, _1518970, _1518972] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518966), _1518968)), 39039 ^ _775828 : [(39046 ^ _775828) ^ [] : [hAPP(c_Finite__Set_Ocard(_1518970), hAPP(c_Set_Oimage(_1518966, _1518970, _1518972), _1518968)) = hAPP(c_Finite__Set_Ocard(_1518966), _1518968), -(c_Fun_Oinj__on(_1518966, _1518970, _1518972, _1518968))], (39040 ^ _775828) ^ [] : [c_Fun_Oinj__on(_1518966, _1518970, _1518972, _1518968), -(hAPP(c_Finite__Set_Ocard(_1518970), hAPP(c_Set_Oimage(_1518966, _1518970, _1518972), _1518968)) = hAPP(c_Finite__Set_Ocard(_1518966), _1518968))]]], (45527 ^ _775828) ^ [_1673307, _1673309, _1673311, _1673313, _1673315, _1673317, _1673319] : [c_Map_Omap__comp(_1673307, _1673309, _1673311, _1673313, _1673315, _1673317) = hAPP(c_Option_Ooption_OSome(_1673309), _1673319), 45531 ^ _775828 : [(45534 ^ _775828) ^ [] : [-(hAPP(_1673313, 45530 ^ [_1673307, _1673309, _1673311, _1673313, _1673315, _1673317, _1673319]) = hAPP(c_Option_Ooption_OSome(_1673309), _1673319))], (45532 ^ _775828) ^ [] : [-(hAPP(_1673315, _1673317) = hAPP(c_Option_Ooption_OSome(_1673307), 45530 ^ [_1673307, _1673309, _1673311, _1673313, _1673315, _1673317, _1673319]))]]], (46822 ^ _775828) ^ [_1707303] : [46824 ^ _775828 : [(46827 ^ _775828) ^ [] : [46823 ^ [_1707303] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46825 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46823 ^ [_1707303]), hAPP(c_List_Oset(tc_Nat_Onat), _1707303))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1707303) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31607 ^ _775828) ^ [_1357748, _1357750] : [-(c_Transitive__Closure_Otrancl(_1357748, c_Transitive__Closure_Ortrancl(_1357748, _1357750)) = c_Transitive__Closure_Ortrancl(_1357748, _1357750))], (43876 ^ _775828) ^ [_1633886, _1633888, _1633890] : [class_Orderings_Olinorder(_1633886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633886), _1633888)), -(hBOOL(hAPP(hAPP(c_member(_1633886), _1633890), _1633888))), -(c_Big__Operators_Olinorder__class_OMin(_1633886, hAPP(hAPP(c_Set_Oinsert(_1633886), _1633890), _1633888)) = hAPP(hAPP(c_Finite__Set_Ofold(_1633886, _1633886, c_Orderings_Oord__class_Omin(_1633886)), _1633890), _1633888))], (19698 ^ _775828) ^ [_1114253] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1114253)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114253))))], (39670 ^ _775828) ^ [_1534744, _1534746, _1534748, _1534750, _1534752, _1534754] : [hBOOL(hAPP(hAPP(c_member(_1534744), _1534746), _1534748)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534744, tc_fun(_1534750, tc_HOL_Obool)), _1534748), hAPP(hAPP(c_COMBB(tc_fun(_1534750, tc_HOL_Obool), tc_fun(_1534750, tc_HOL_Obool), _1534744), hAPP(c_Set_Oinsert(_1534750), _1534752)), _1534754)) = hAPP(hAPP(c_Set_Oinsert(_1534750), _1534752), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534744, tc_fun(_1534750, tc_HOL_Obool)), _1534748), _1534754)))], (23678 ^ _775828) ^ [_1190486, _1190488, _1190490, _1190492] : [class_Orderings_Olinorder(_1190486), 23681 ^ _775828 : [(23690 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190486), _1190488), _1190490)), _1190492))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), _1190488), _1190492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), _1190490), _1190492))], (23682 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190486), _1190488), _1190490)), _1190492)), 23685 ^ _775828 : [(23688 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), _1190490), _1190492)))], (23686 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190486), _1190488), _1190492)))]]]]], (51304 ^ _775828) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (47729 ^ _775828) ^ [_1728809, _1728811, _1728813, _1728815] : [-(c_List_Osublist(_1728809, hAPP(hAPP(c_List_Olist_OCons(_1728809), _1728811), _1728813), _1728815) = hAPP(hAPP(c_List_Oappend(_1728809), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1728809)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1728815)), hAPP(hAPP(c_List_Olist_OCons(_1728809), _1728811), c_List_Olist_ONil(_1728809))), c_List_Olist_ONil(_1728809))), c_List_Osublist(_1728809, _1728813, 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)), _1728815)))))], (50425 ^ _775828) ^ [_1789413, _1789415, _1789417, _1789419] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789413)), _1789415) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789417)), _1789419), -(hAPP(hAPP(c_List_Ozip(_1789413, _1789417), hAPP(c_List_Orev(_1789413), _1789415)), hAPP(c_List_Orev(_1789417), _1789419)) = hAPP(c_List_Orev(tc_prod(_1789413, _1789417)), hAPP(hAPP(c_List_Ozip(_1789413, _1789417), _1789415), _1789419)))], (14391 ^ _775828) ^ [_1016629, _1016631] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1016629, _1016631))), -(hBOOL(hAPP(c_Com_OWT, _1016631)))], (44952 ^ _775828) ^ [_1660437, _1660439] : [class_Complete__Lattice_Ocomplete__lattice(_1660437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660437), _1660439)), -(_1660439 = c_Orderings_Obot__class_Obot(tc_fun(_1660437, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1660437, _1660439) = c_Complete__Lattice_OSup__class_OSup(_1660437, _1660439))], (27379 ^ _775828) ^ [_1261910, _1261912, _1261914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1261910, _1261910)), _1261912), c_Relation_OId__on(_1261910, _1261914))), 27383 ^ _775828 : [(27386 ^ _775828) ^ [] : [-(_1261912 = hAPP(hAPP(c_Product__Type_OPair(_1261910, _1261910), 27382 ^ [_1261910, _1261912, _1261914]), 27382 ^ [_1261910, _1261912, _1261914]))], (27384 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261910), 27382 ^ [_1261910, _1261912, _1261914]), _1261914)))]]], (27599 ^ _775828) ^ [_1266425, _1266427, _1266429, _1266431, _1266433, _1266435] : [-(hBOOL(hAPP(hAPP(c_member(_1266425), _1266427), c_SetInterval_Oord_OatLeastLessThan(_1266425, _1266429, _1266431, _1266433, _1266435)))), hBOOL(hAPP(hAPP(_1266429, _1266433), _1266427)), hBOOL(hAPP(hAPP(_1266431, _1266427), _1266435))], (4054 ^ _775828) ^ [_837700, _837702] : [_837702 = _837700, -(c_HOL_OEx(_837702) = c_HOL_OEx(_837700))], (32733 ^ _775828) ^ [_1381048, _1381050, _1381052, _1381054] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1381048, _1381050)), c_Sum__Type_OPlus(_1381048, _1381050, _1381052, _1381054)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381048), _1381052)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381050), _1381054))], (4914 ^ _775828) ^ [_850934, _850936, _850938, _850940, _850942, _850944, _850946, _850948, _850950, _850952] : [-(c_Map_Omap__upds(_850952, _850948, _850944, _850940, _850936) = c_Map_Omap__upds(_850950, _850946, _850942, _850938, _850934)), _850952 = _850950, _850948 = _850946, _850944 = _850942, _850940 = _850938, _850936 = _850934], (25547 ^ _775828) ^ [_1227510, _1227512, _1227514, _1227516] : [class_Rings_Ocomm__semiring__1(_1227510), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227510), _1227512), _1227514)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227510), _1227512), _1227516)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227510), _1227512), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1227510), _1227514), _1227516))))], (33829 ^ _775828) ^ [_1404460, _1404462, _1404464] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404460, tc_HOL_Obool)), _1404462), _1404464) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404460, tc_HOL_Obool)), _1404464), _1404462))], (39311 ^ _775828) ^ [_1525133, _1525135, _1525137] : [-(c_Fun_Oinj__on(tc_prod(_1525133, _1525135), tc_prod(_1525135, _1525133), hAPP(c_Product__Type_Oprod_Oprod__case(_1525133, _1525135, tc_prod(_1525135, _1525133)), hAPP(c_COMBC(_1525135, _1525133, tc_prod(_1525135, _1525133)), c_Product__Type_OPair(_1525135, _1525133))), _1525137))], (11813 ^ _775828) ^ [_970105, _970107, _970109] : [class_Rings_Osemiring__1(_970105), hBOOL(hAPP(hAPP(c_member(_970105), _970107), c_Nat_Osemiring__1__class_ONats(_970105))), hBOOL(hAPP(hAPP(c_member(_970105), _970109), c_Nat_Osemiring__1__class_ONats(_970105))), -(hBOOL(hAPP(hAPP(c_member(_970105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970105), _970107), _970109)), c_Nat_Osemiring__1__class_ONats(_970105))))], (36827 ^ _775828) ^ [_1467717, _1467719, _1467721, _1467723, _1467725] : [c_Finite__Set_Ofolding__one__idem(_1467717, _1467719, _1467721), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467717), _1467723)), -(_1467723 = c_Orderings_Obot__class_Obot(tc_fun(_1467717, tc_HOL_Obool))), -(hAPP(_1467721, hAPP(hAPP(c_Set_Oinsert(_1467717), _1467725), _1467723)) = hAPP(hAPP(_1467719, _1467725), hAPP(_1467721, _1467723)))], (13534 ^ _775828) ^ [_1000652, _1000654, _1000656, _1000658, _1000660] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1000652, _1000654, _1000656)), _1000658), _1000660))), 13535 ^ _775828 : [(13542 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1000652, _1000658))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000656), _1000658), _1000660))], (13536 ^ _775828) ^ [] : [hBOOL(hAPP(_1000652, _1000658)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000654), _1000658), _1000660))]]], (39590 ^ _775828) ^ [_1532061, _1532063, _1532065, _1532067] : [39592 ^ _775828 : [(39595 ^ _775828) ^ [] : [hAPP(_1532067, 39591 ^ [_1532061, _1532063, _1532065, _1532067]) = c_Orderings_Obot__class_Obot(tc_fun(_1532061, tc_HOL_Obool))], (39593 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532063), 39591 ^ [_1532061, _1532063, _1532065, _1532067]), _1532065)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1532061, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532063, tc_fun(_1532061, tc_HOL_Obool)), _1532065), _1532067))], (41578 ^ _775828) ^ [_1580594, _1580596, _1580598, _1580600] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1580594, _1580596), _1580598), _1580600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580594, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), _1580598), hAPP(hAPP(c_COMBS(_1580594, tc_fun(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580596, tc_HOL_Obool), tc_fun(tc_fun(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), _1580594), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), _1580600)), hAPP(hAPP(c_COMBC(_1580594, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1580596, tc_fun(tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), _1580594), c_COMBC(_1580596, tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1580596, tc_prod(_1580594, _1580596)), tc_fun(_1580596, tc_fun(tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))), _1580594), hAPP(c_COMBB(tc_prod(_1580594, _1580596), tc_fun(tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool), tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool)), _1580596), c_Set_Oinsert(tc_prod(_1580594, _1580596)))), c_Product__Type_OPair(_1580594, _1580596)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1580594, _1580596), tc_HOL_Obool))))))], (50947 ^ _775828) ^ [_1801465, _1801467, _1801469] : [-(c_List_OdropWhile(_1801465, _1801467, _1801469) = hAPP(hAPP(c_List_Odrop(_1801465), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801465)), c_List_OtakeWhile(_1801465, _1801467, _1801469))), _1801469))], (3444 ^ _775828) ^ [_828051, _828053] : [_828053 = _828051, -(c_Nitpick_Onum(_828053) = c_Nitpick_Onum(_828051))], (44876 ^ _775828) ^ [_1658669, _1658671] : [class_Complete__Lattice_Ocomplete__lattice(_1658669), -(c_Complete__Lattice_OSup__class_OSup(_1658669, hAPP(hAPP(c_Set_Oinsert(_1658669), _1658671), c_Orderings_Obot__class_Obot(tc_fun(_1658669, tc_HOL_Obool)))) = _1658671)], (23606 ^ _775828) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (17531 ^ _775828) ^ [_1075969, _1075971] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075969)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075971)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1075969), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1075971))))], (33278 ^ _775828) ^ [_1392228, _1392230, _1392232, _1392234, _1392236] : [class_Groups_Ocomm__monoid__mult(_1392228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392230), _1392232)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392230, _1392228), _1392234), hAPP(hAPP(c_Set_Oinsert(_1392230), _1392236), _1392232)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392228), hAPP(_1392234, _1392236)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392230, _1392228), _1392234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392230, tc_HOL_Obool)), _1392232), hAPP(hAPP(c_Set_Oinsert(_1392230), _1392236), c_Orderings_Obot__class_Obot(tc_fun(_1392230, tc_HOL_Obool)))))))], (20440 ^ _775828) ^ [_1127061, _1127063] : [class_Rings_Ocomm__semiring__1(_1127061), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127061), _1127063), _1127063) = hAPP(hAPP(c_Power_Opower__class_Opower(_1127061), _1127063), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (50666 ^ _775828) ^ [_1795911, _1795913, _1795915] : [class_Orderings_Olinorder(_1795911), c_List_Olinorder__class_Osorted(_1795911, _1795913), -(c_List_Olinorder__class_Osorted(_1795911, c_List_OtakeWhile(_1795911, _1795915, _1795913)))], (10662 ^ _775828) ^ [_949855, _949857, _949859, _949861, _949863] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_949855), 10665 ^ _775828 : [(10666 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949857), _949859)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949861), _949863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949857), _949863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949861), _949859)), -(_949857 = _949861), -(_949859 = _949863)], (10676 ^ _775828) ^ [] : [10677 ^ _775828 : [(10680 ^ _775828) ^ [] : [_949859 = _949863], (10678 ^ _775828) ^ [] : [_949857 = _949861]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949857), _949859)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949861), _949863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949857), _949863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949855), _949861), _949859)))]]], (11582 ^ _775828) ^ [_966273, _966275] : [class_Rings_Oring__1__no__zero__divisors(_966273), 11585 ^ _775828 : [(11586 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966273), _966275), _966275) = c_Groups_Oone__class_Oone(_966273), -(_966275 = c_Groups_Oone__class_Oone(_966273)), -(_966275 = hAPP(c_Groups_Ouminus__class_Ouminus(_966273), c_Groups_Oone__class_Oone(_966273)))], (11596 ^ _775828) ^ [] : [11597 ^ _775828 : [(11600 ^ _775828) ^ [] : [_966275 = hAPP(c_Groups_Ouminus__class_Ouminus(_966273), c_Groups_Oone__class_Oone(_966273))], (11598 ^ _775828) ^ [] : [_966275 = c_Groups_Oone__class_Oone(_966273)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966273), _966275), _966275) = c_Groups_Oone__class_Oone(_966273))]]], (18773 ^ _775828) ^ [_1098537, _1098539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098537), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098539), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1098537, _1098539) = 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), _1098537), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098539)))))], (35151 ^ _775828) ^ [_1434443, _1434445, _1434447, _1434449, _1434451] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1434443, _1434445, _1434447), _1434449), _1434451), c_Orderings_Obot__class_Obot(tc_fun(_1434445, tc_HOL_Obool))) = _1434451)], (25313 ^ _775828) ^ [_1222317, _1222319] : [_1222317 = _1222319, -(hAPP(c_Code__Numeral_Oof__nat, _1222317) = hAPP(c_Code__Numeral_Oof__nat, _1222319))], (1020 ^ _775828) ^ [_791196, _791198] : [-(class_Rings_Oring__no__zero__divisors(_791196)), _791198 = _791196, class_Rings_Oring__no__zero__divisors(_791198)], (39339 ^ _775828) ^ [_1525740, _1525742, _1525744, _1525746, _1525748] : [c_Fun_Oinj__on(_1525740, _1525742, _1525744, _1525746), hBOOL(hAPP(hAPP(c_member(_1525740), _1525748), _1525746)), -(hAPP(c_Fun_Othe__inv__into(_1525740, _1525742, _1525746, _1525744), hAPP(_1525744, _1525748)) = _1525748)], (28287 ^ _775828) ^ [_1283218, _1283220, _1283222, _1283224] : [class_Lattices_Olattice(_1283218), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283218), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283218), _1283220), _1283222)), _1283224) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283218), _1283220), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283218), _1283222), _1283224)))], (47916 ^ _775828) ^ [_1733347, _1733349, _1733351, _1733353] : [_1733351 = _1733353, -(hAPP(hAPP(c_List_Oappend(_1733347), _1733349), _1733351) = hAPP(hAPP(c_List_Oappend(_1733347), _1733349), _1733353))], (5807 ^ _775828) ^ [_868390, _868392] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_868390, _868392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14421 ^ _775828) ^ [_1017327, _1017329, _1017331, _1017333, _1017335] : [c_Com_Ocom_OWhile(_1017327, _1017329) = c_Com_Ocom_OLocal(_1017331, _1017333, _1017335)], (24573 ^ _775828) ^ [_1207403, _1207405, _1207407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1207403, _1207403), tc_HOL_Obool)), _1207405), _1207407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1207403, tc_HOL_Obool)), c_Wellfounded_Oacc(_1207403, _1207407)), c_Wellfounded_Oacc(_1207403, _1207405))))], (35627 ^ _775828) ^ [_1444860, _1444862, _1444864, _1444866, _1444868] : [class_Orderings_Olinorder(_1444860), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444860, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1444860, _1444862, _1444864)), c_SetInterval_Oord__class_OatLeastAtMost(_1444860, _1444866, _1444868)) = c_SetInterval_Oord__class_OatLeastAtMost(_1444860, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1444860), _1444862), _1444866), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1444860), _1444864), _1444868)))], (3780 ^ _775828) ^ [_833251, _833253] : [_833253 = _833251, -(c_Equiv__Relations_Oquotient(_833253) = c_Equiv__Relations_Oquotient(_833251))], (20680 ^ _775828) ^ [_1131163, _1131165, _1131167] : [class_Rings_Olinordered__idom(_1131163), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131163), c_Groups_Ozero__class_Ozero(_1131163)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131163), hAPP(hAPP(c_Power_Opower__class_Opower(_1131163), _1131165), 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(_1131163), _1131167), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (28541 ^ _775828) ^ [_1288457, _1288459, _1288461] : [class_Lattices_Osemilattice__sup(_1288457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288457), _1288459), _1288461)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288457), _1288459), _1288461) = _1288461)], (28477 ^ _775828) ^ [_1287356, _1287358, _1287360] : [class_Lattices_Osemilattice__sup(_1287356), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287356), _1287358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287356), _1287360), _1287358))))], (51504 ^ _775828) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (14425 ^ _775828) ^ [_1017436, _1017438, _1017440, _1017442] : [c_Com_Ocom_OSemi(_1017436, _1017438) = c_Com_Ocom_OWhile(_1017440, _1017442)], (34275 ^ _775828) ^ [_1413944, _1413946, _1413948] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413944, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413944, tc_HOL_Obool)), _1413946), _1413948)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413944, tc_HOL_Obool)), _1413946), _1413948)) = _1413946)], (29657 ^ _775828) ^ [_1314157, _1314159] : [-(hAPP(c_Set_OCollect(_1314157), hAPP(c_fequal, _1314159)) = hAPP(hAPP(c_Set_Oinsert(_1314157), _1314159), c_Orderings_Obot__class_Obot(tc_fun(_1314157, tc_HOL_Obool))))], (43586 ^ _775828) ^ [_1628097, _1628099, _1628101, _1628103] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1628097, _1628099, _1628101), _1628103), c_Orderings_Obot__class_Obot(tc_fun(_1628097, tc_HOL_Obool))) = _1628103)], (27841 ^ _775828) ^ [_1273649, _1273651, _1273653] : [c_Wellfounded_Owf(_1273649, _1273651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1273649, _1273649), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1273649, _1273649, _1273649), _1273651), _1273653)), _1273651)), -(c_FunDef_Oreduction__pair(_1273649, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1273649, _1273649), tc_HOL_Obool), tc_fun(tc_prod(_1273649, _1273649), tc_HOL_Obool)), _1273651), _1273653)))], (45729 ^ _775828) ^ [_1678095, _1678097, _1678099, _1678101, _1678103, _1678105, _1678107] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1678095), tc_Option_Ooption(_1678097), _1678099, hAPP(c_Option_Omap(_1678095, _1678097), _1678101)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1678099, tc_Option_Ooption(_1678095)), _1678103), _1678105), hAPP(c_Option_Ooption_OSome(_1678095), _1678107))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1678099, tc_Option_Ooption(_1678097)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1678095), tc_Option_Ooption(_1678097), _1678099, hAPP(c_Option_Omap(_1678095, _1678097), _1678101)), _1678103)), _1678105), hAPP(c_Option_Ooption_OSome(_1678097), hAPP(_1678101, _1678107))))], (41442 ^ _775828) ^ [_1577542, _1577544, _1577546, _1577548, _1577550, _1577552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577542, _1577544), tc_HOL_Obool)), _1577546), hAPP(hAPP(c_Product__Type_OSigma(_1577542, _1577544), _1577548), hAPP(c_COMBK(tc_fun(_1577544, tc_HOL_Obool), _1577542), _1577550)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1577544, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1577542, _1577544, _1577546), _1577552)), _1577550)))], (50870 ^ _775828) ^ [_1800010, _1800012, _1800014, _1800016] : [hBOOL(hAPP(_1800010, _1800012)), -(c_List_OdropWhile(_1800014, _1800010, hAPP(hAPP(c_List_Olist_OCons(_1800014), _1800012), _1800016)) = c_List_OdropWhile(_1800014, _1800010, _1800016))], (40081 ^ _775828) ^ [_1544269, _1544271] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1544269, _1544271)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1544269, _1544271), tc_HOL_Obool)))), 40084 ^ _775828 : [(40087 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544271), c_Orderings_Otop__class_Otop(tc_fun(_1544271, tc_HOL_Obool)))))], (40085 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544269), c_Orderings_Otop__class_Otop(tc_fun(_1544269, tc_HOL_Obool)))))]]], (31641 ^ _775828) ^ [_1358516, _1358518, _1358520, _1358522, _1358524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1358516, _1358516)), hAPP(hAPP(c_Product__Type_OPair(_1358516, _1358516), _1358518), _1358520)), c_Transitive__Closure_Ortrancl(_1358516, _1358522))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1358516, _1358516)), hAPP(hAPP(c_Product__Type_OPair(_1358516, _1358516), _1358520), _1358524)), c_Transitive__Closure_Ortrancl(_1358516, _1358522))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1358516, _1358516)), hAPP(hAPP(c_Product__Type_OPair(_1358516, _1358516), _1358518), _1358524)), c_Transitive__Closure_Ortrancl(_1358516, _1358522))))], (44830 ^ _775828) ^ [_1657698, _1657700, _1657702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1657698, tc_HOL_Obool), tc_HOL_Obool)), _1657700), _1657702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657698, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657698, tc_HOL_Obool), _1657702)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657698, tc_HOL_Obool), _1657700))))], (12385 ^ _775828) ^ [_980193, _980195, _980197] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980193), _980195)), _980197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980193), _980197)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980195), _980197)))], (31553 ^ _775828) ^ [_1356531, _1356533, _1356535] : [hAPP(c_Finite__Set_Ocard(_1356531), _1356533) = hAPP(c_Nat_OSuc, _1356535), 31558 ^ _775828 : [(31561 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1356531), 31556 ^ [_1356531, _1356533, _1356535]), 31557 ^ [_1356531, _1356533, _1356535]))], (31563 ^ _775828) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1356531), 31557 ^ [_1356531, _1356533, _1356535]) = _1356535)], (31565 ^ _775828) ^ [] : [_1356535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(31557 ^ [_1356531, _1356533, _1356535] = c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool)))], (31559 ^ _775828) ^ [] : [-(_1356533 = hAPP(hAPP(c_Set_Oinsert(_1356531), 31556 ^ [_1356531, _1356533, _1356535]), 31557 ^ [_1356531, _1356533, _1356535]))]]], (46414 ^ _775828) ^ [_1696012, _1696014, _1696016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1696012, _1696012), tc_HOL_Obool)), _1696014), _1696016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1696012), tc_List_Olist(_1696012)), tc_HOL_Obool)), c_List_Olistrel(_1696012, _1696014)), c_List_Olistrel(_1696012, _1696016))))], (16000 ^ _775828) ^ [_1046686, _1046688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1046686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046688), _1046686)), _1046688)))], (42077 ^ _775828) ^ [_1592289, _1592291, _1592293, _1592295, _1592297, _1592299, _1592301] : [-(hAPP(c_Product__Type_Osnd(_1592289, _1592291), hAPP(c_Product__Type_Omap__pair(_1592293, _1592289, _1592295, _1592291, _1592297, _1592299), _1592301)) = hAPP(_1592299, hAPP(c_Product__Type_Osnd(_1592293, _1592295), _1592301)))], (44663 ^ _775828) ^ [_1654094, _1654096, _1654098, _1654100] : [-(hAPP(c_Set_Oimage(_1654094, _1654096, _1654098), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654094, tc_HOL_Obool), _1654100)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654094, tc_HOL_Obool), tc_fun(_1654096, tc_HOL_Obool)), _1654100), c_Set_Oimage(_1654094, _1654096, _1654098)))], (14792 ^ _775828) ^ [_1023279, _1023281, _1023283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023279), _1023281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023283), 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), _1023281), _1023283)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023279), _1023283))))], (11014 ^ _775828) ^ [_956017, _956019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956017), _956019)), 11017 ^ _775828 : [(11020 ^ _775828) ^ [] : [_956017 = _956019], (11018 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956017), _956019)))]]], (9141 ^ _775828) ^ [_921997, _921999] : [class_Rings_Oring__1(_921997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921999)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921997), hAPP(c_Int_Onat, _921999)) = hAPP(c_Int_Oring__1__class_Oof__int(_921997), _921999))], (41364 ^ _775828) ^ [_1575357, _1575359, _1575361, _1575363, _1575365] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575357, _1575359), _1575361), hAPP(hAPP(c_COMBS(_1575357, tc_fun(_1575359, tc_HOL_Obool), tc_fun(_1575359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575359, tc_HOL_Obool), tc_fun(tc_fun(_1575359, tc_HOL_Obool), tc_fun(_1575359, tc_HOL_Obool)), _1575357), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575359, tc_HOL_Obool))), _1575363)), _1575365)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575357, _1575359), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575357, _1575359), _1575361), _1575363)), hAPP(hAPP(c_Product__Type_OSigma(_1575357, _1575359), _1575361), _1575365)))], (12477 ^ _775828) ^ [_981682] : [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)), _981682)), _981682) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30377 ^ _775828) ^ [_1330855, _1330857, _1330859] : [30378 ^ _775828 : [(30381 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330855), hAPP(c_Set_OCollect(_1330855), _1330859)))], (30379 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330855), hAPP(c_Set_OCollect(_1330855), _1330857)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330855), hAPP(c_Set_OCollect(_1330855), hAPP(hAPP(c_COMBS(_1330855, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1330855), c_fconj), _1330857)), _1330859)))))], (7747 ^ _775828) ^ [_899516, _899518] : [class_Rings_Olinordered__idom(_899516), 7750 ^ _775828 : [(7757 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899516), _899518), c_Groups_Ozero__class_Ozero(_899516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899516), _899518), hAPP(c_Groups_Ouminus__class_Ouminus(_899516), _899518))))], (7751 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899516), _899518), hAPP(c_Groups_Ouminus__class_Ouminus(_899516), _899518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899516), _899518), c_Groups_Ozero__class_Ozero(_899516))))]]], (50910 ^ _775828) ^ [_1800680, _1800682, _1800684] : [50912 ^ _775828 : [(50915 ^ _775828) ^ [] : [hBOOL(hAPP(_1800682, 50911 ^ [_1800680, _1800682, _1800684]))], (50913 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800680), 50911 ^ [_1800680, _1800682, _1800684]), hAPP(c_List_Oset(_1800680), _1800684))))]], -(c_List_OdropWhile(_1800680, _1800682, _1800684) = c_List_Olist_ONil(_1800680))], (7255 ^ _775828) ^ [_891425, _891427, _891429, _891431] : [class_Rings_Olinordered__ring__strict(_891425), 7258 ^ _775828 : [(7273 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891425), _891427), _891429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891425), _891431), _891429)))), 7274 ^ _775828 : [(7281 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891429), c_Groups_Ozero__class_Ozero(_891425))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891431), _891427))], (7275 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), c_Groups_Ozero__class_Ozero(_891425)), _891429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891427), _891431))]]], (7259 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891425), _891427), _891429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891425), _891431), _891429))), 7264 ^ _775828 : [(7267 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891427), _891431)))], (7265 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), c_Groups_Ozero__class_Ozero(_891425)), _891429)))]], 7268 ^ _775828 : [(7271 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891431), _891427)))], (7269 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891425), _891429), c_Groups_Ozero__class_Ozero(_891425))))]]]]], (13680 ^ _775828) ^ [_1003608, _1003610, _1003612, _1003614, _1003616] : [c_Com_Ocom_OSemi(_1003608, _1003610) = c_Com_Ocom_OCall(_1003612, _1003614, _1003616)], (1140 ^ _775828) ^ [_792696, _792698] : [-(class_Int_Oring__char__0(_792696)), _792698 = _792696, class_Int_Oring__char__0(_792698)], (21204 ^ _775828) ^ [_1143111] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143111) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1143111)))], (48199 ^ _775828) ^ [_1740122, _1740124, _1740126, _1740128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740122), tc_List_Olist(_1740122))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740122), tc_List_Olist(_1740122)), _1740124), _1740126)), c_List_Olistrel1(_1740122, _1740128))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740122)), _1740124) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740122)), _1740126))], (41362 ^ _775828) ^ [_1575247, _1575249, _1575251, _1575253, _1575255] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575247, _1575249), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575247, tc_HOL_Obool)), _1575251), _1575253)), hAPP(c_COMBK(tc_fun(_1575249, tc_HOL_Obool), _1575247), _1575255)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575247, _1575249), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575247, _1575249), _1575251), hAPP(c_COMBK(tc_fun(_1575249, tc_HOL_Obool), _1575247), _1575255))), hAPP(hAPP(c_Product__Type_OSigma(_1575247, _1575249), _1575253), hAPP(c_COMBK(tc_fun(_1575249, tc_HOL_Obool), _1575247), _1575255))))], (8861 ^ _775828) ^ [_917627, _917629, _917631] : [class_Orderings_Opreorder(_917627), 8864 ^ _775828 : [(8873 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917627), _917629), _917631))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917627), _917629), _917631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917627), _917631), _917629)))], (8865 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917627), _917629), _917631)), 8868 ^ _775828 : [(8871 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917627), _917631), _917629))], (8869 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917627), _917629), _917631)))]]]]], (24404 ^ _775828) ^ [_1204356] : [c_Code__Numeral_OSuc__code__numeral(_1204356) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (13334 ^ _775828) ^ [_996757, _996759, _996761, _996763] : [class_Divides_Osemiring__div(_996757), -(c_Divides_Odiv__class_Omod(_996757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996757), _996759), _996761), _996763) = c_Divides_Odiv__class_Omod(_996757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996757), c_Divides_Odiv__class_Omod(_996757, _996759, _996763)), _996761), _996763))], (6745 ^ _775828) ^ [_882816] : [6746 ^ _775828 : [(6747 ^ _775828) ^ [_882864] : [hAPP(c_Com_Obody, _882816) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _882864)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882816))))], (7675 ^ _775828) ^ [_898384] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _898384) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12869 ^ _775828) ^ [_988159, _988161, _988163, _988165, _988167, _988169] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _988159), _988161)), _988163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _988165), _988167)), _988169), 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), _988165), _988167)), _988169)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988163), _988159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988165), _988159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988167), _988161)))], (51354 ^ _775828) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (31265 ^ _775828) ^ [_1350478, _1350480, _1350482] : [class_Orderings_Olinorder(_1350478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350478), _1350480)), -(_1350482 = c_Orderings_Obot__class_Obot(tc_fun(_1350478, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350478, tc_HOL_Obool)), _1350482), _1350480)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1350478), c_Big__Operators_Olattice_OInf__fin(_1350478, c_Orderings_Oord__class_Omin(_1350478), _1350482)), c_Big__Operators_Olattice_OInf__fin(_1350478, c_Orderings_Oord__class_Omin(_1350478), _1350480)) = c_Big__Operators_Olattice_OInf__fin(_1350478, c_Orderings_Oord__class_Omin(_1350478), _1350480))], (48876 ^ _775828) ^ [_1756320, _1756322, _1756324] : [class_Orderings_Olinorder(_1756320), -(c_Big__Operators_Olinorder__class_OMax(_1756320, hAPP(c_List_Oset(_1756320), hAPP(hAPP(c_List_Olist_OCons(_1756320), _1756322), _1756324))) = hAPP(c_List_Ofoldl(_1756320, _1756320, c_Orderings_Oord__class_Omax(_1756320), _1756322), _1756324))], (51632 ^ _775828) ^ [_1809843] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1809843), v_Procs)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, v_na, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(_1809843)), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1809843))), v_Q(_1809843))))], (27507 ^ _775828) ^ [_1264567, _1264569, _1264571] : [_1264569 = _1264571, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1264567, _1264567)), hAPP(hAPP(c_Product__Type_OPair(_1264567, _1264567), _1264569), _1264571)), c_Relation_OId(_1264567))))], (15012 ^ _775828) ^ [_1027510, _1027512] : [-(_1027510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15015 ^ _775828 : [(15022 ^ _775828) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1027512, _1027510) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1027510)) = 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), _1027512), _1027510))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15016 ^ _775828) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1027512, _1027510) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1027510)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027512), _1027510)))]]], (8633 ^ _775828) ^ [_914327, _914329, _914331, _914333] : [class_Orderings_Oorder(_914327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914327), _914329), _914331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914327), _914333), _914329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914327), _914333), _914331)))], (28098 ^ _775828) ^ [_1279378, _1279380, _1279382] : [c_Wellfounded_OwfP(_1279378, _1279380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279378, tc_fun(_1279378, tc_HOL_Obool))), _1279382), _1279380)), -(c_Wellfounded_OwfP(_1279378, _1279382))], (24561 ^ _775828) ^ [_1207251] : [c_Nat__Transfer_Ois__nat(_1207251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207251)))], (45757 ^ _775828) ^ [_1678751, _1678753, _1678755, _1678757, _1678759, _1678761] : [-(hBOOL(hAPP(hAPP(c_member(_1678751), _1678753), hAPP(c_List_Oset(_1678751), _1678755)))), -(hAPP(hAPP(c_List_Omap(_1678751, _1678757), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1678751, _1678757), _1678759), _1678753), _1678761)), _1678755) = hAPP(hAPP(c_List_Omap(_1678751, _1678757), _1678759), _1678755))], (21648 ^ _775828) ^ [_1150725, _1150727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150725)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150727))), -(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(_1150727))), 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), _1150725)), c_Int_Onat))))))], (51512 ^ _775828) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (5786 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21384 ^ _775828) ^ [_1146221, _1146223] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1146221))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1146223)), hAPP(c_Int_Onat, _1146221)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1146223), _1146221)), 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)))], (36345 ^ _775828) ^ [_1458221, _1458223, _1458225, _1458227] : [class_Orderings_Olinorder(_1458221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458221), _1458223), _1458225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458221), _1458225), _1458227)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458221, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458221, _1458223), _1458225)), c_SetInterval_Oord__class_OatLeastAtMost(_1458221, _1458225, _1458227)) = c_SetInterval_Oord__class_OatLeastAtMost(_1458221, _1458223, _1458227))], (16705 ^ _775828) ^ [_1060381, _1060383] : [class_Int_Onumber__ring(_1060381), -(hAPP(c_Int_Onumber__class_Onumber__of(_1060381), _1060383) = hAPP(c_Int_Oring__1__class_Oof__int(_1060381), _1060383))], (51310 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (48359 ^ _775828) ^ [_1744992, _1744994] : [-(hAPP(c_List_Orotate1(_1744992), _1744994) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1744992), _1744992, c_List_Olist_ONil(_1744992), hAPP(hAPP(c_COMBB(tc_List_Olist(_1744992), tc_fun(tc_List_Olist(_1744992), tc_List_Olist(_1744992)), _1744992), hAPP(c_COMBC(tc_List_Olist(_1744992), tc_List_Olist(_1744992), tc_List_Olist(_1744992)), c_List_Oappend(_1744992))), hAPP(hAPP(c_COMBC(_1744992, tc_List_Olist(_1744992), tc_List_Olist(_1744992)), c_List_Olist_OCons(_1744992)), c_List_Olist_ONil(_1744992)))), _1744994))], (50306 ^ _775828) ^ [_1786753, _1786755] : [50308 ^ _775828 : [(50311 ^ _775828) ^ [] : [50307 ^ [_1786753, _1786755] = c_List_Olist_ONil(_1786753)], (50309 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1786753)), 50307 ^ [_1786753, _1786755]), hAPP(c_List_Oset(tc_List_Olist(_1786753)), _1786755))))]], -(c_List_Oconcat(_1786753, _1786755) = c_List_Olist_ONil(_1786753))], (11795 ^ _775828) ^ [_969763, _969765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969763), _969765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969763)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969765))))], (8497 ^ _775828) ^ [_912263] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _912263)), -(hAPP(c_Int_Onat, _912263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1160 ^ _775828) ^ [_792946, _792948] : [-(class_Groups_Osgn__if(_792946)), _792948 = _792946, class_Groups_Osgn__if(_792948)], (45436 ^ _775828) ^ [_1670891, _1670893, _1670895, _1670897] : [-(c_Map_Omap__add(_1670891, _1670893, _1670895, c_Map_Omap__of(_1670891, _1670893, _1670897)) = c_List_Ofoldr(tc_prod(_1670891, _1670893), tc_fun(_1670891, tc_Option_Ooption(_1670893)), hAPP(c_Product__Type_Oprod_Oprod__case(_1670891, _1670893, tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), hAPP(hAPP(c_COMBC(_1670891, tc_fun(_1670893, tc_Option_Ooption(_1670893)), tc_fun(_1670893, tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1670893), tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), tc_fun(tc_fun(_1670893, tc_Option_Ooption(_1670893)), tc_fun(_1670893, tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893))))), _1670891), c_COMBB(tc_Option_Ooption(_1670893), tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893))), _1670893)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(tc_Option_Ooption(_1670893), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), tc_fun(tc_Option_Ooption(_1670893), tc_fun(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), _1670891), c_COMBC(tc_fun(_1670891, tc_Option_Ooption(_1670893)), tc_Option_Ooption(_1670893), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), hAPP(c_COMBC(tc_fun(_1670891, tc_Option_Ooption(_1670893)), _1670891, tc_fun(tc_Option_Ooption(_1670893), tc_fun(_1670891, tc_Option_Ooption(_1670893)))), c_Fun_Ofun__upd(_1670891, tc_Option_Ooption(_1670893)))))), c_Option_Ooption_OSome(_1670893))), _1670897, _1670895))], (10580 ^ _775828) ^ [_948151, _948153, _948155, _948157] : [class_Groups_Oordered__cancel__ab__semigroup__add(_948151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948151), _948153), _948155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948151), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948151), _948153), _948157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948151), _948155), _948157))))], (28729 ^ _775828) ^ [_1292314, _1292316, _1292318] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1292314, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292314, tc_HOL_Obool)), _1292316), _1292318)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292314, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1292314, tc_HOL_Obool)), _1292316)), _1292318))], (46031 ^ _775828) ^ [_1684891, _1684893, _1684895, _1684897, _1684899, _1684901, _1684903, _1684905] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1684891, _1684893), _1684895), _1684897), hAPP(hAPP(c_List_Ozip(_1684891, _1684893), hAPP(hAPP(c_List_Omap(_1684899, _1684891), _1684901), _1684903)), _1684905)) = hAPP(hAPP(c_List_Omap(tc_prod(_1684899, _1684893), _1684895), hAPP(c_Product__Type_Oprod_Oprod__case(_1684899, _1684893, _1684895), hAPP(hAPP(c_COMBB(tc_fun(_1684893, tc_prod(_1684891, _1684893)), tc_fun(_1684893, _1684895), _1684899), hAPP(c_COMBB(tc_prod(_1684891, _1684893), _1684895, _1684893), _1684897)), hAPP(hAPP(c_COMBB(_1684891, tc_fun(_1684893, tc_prod(_1684891, _1684893)), _1684899), c_Product__Type_OPair(_1684891, _1684893)), _1684901)))), hAPP(hAPP(c_List_Ozip(_1684899, _1684893), _1684903), _1684905)))], (12407 ^ _775828) ^ [_980565] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980565), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _980565)], (39660 ^ _775828) ^ [_1534553, _1534555, _1534557, _1534559, _1534561] : [class_Complete__Lattice_Ocomplete__lattice(_1534553), hBOOL(hAPP(hAPP(c_member(_1534555), _1534557), _1534559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534553), hAPP(_1534561, _1534557)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534555, _1534553), _1534559), _1534561))))], (50011 ^ _775828) ^ [_1780203, _1780205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1780203), _1780205)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1780203, _1780205)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1780205), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (19080 ^ _775828) ^ [_1104479] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104479), 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), _1104479)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1104479)))], (40135 ^ _775828) ^ [_1545337, _1545339, _1545341] : [class_Lattices_Obounded__lattice__top(_1545337), 40138 ^ _775828 : [(40147 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545337), _1545339), _1545341) = c_Orderings_Otop__class_Otop(_1545337)), _1545339 = c_Orderings_Otop__class_Otop(_1545337), _1545341 = c_Orderings_Otop__class_Otop(_1545337)], (40139 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545337), _1545339), _1545341) = c_Orderings_Otop__class_Otop(_1545337), 40142 ^ _775828 : [(40145 ^ _775828) ^ [] : [-(_1545341 = c_Orderings_Otop__class_Otop(_1545337))], (40143 ^ _775828) ^ [] : [-(_1545339 = c_Orderings_Otop__class_Otop(_1545337))]]]]], (27226 ^ _775828) ^ [_1257584, _1257586, _1257588] : [hBOOL(hAPP(hAPP(c_member(_1257584), _1257586), hAPP(c_Set_OCollect(_1257584), _1257588))), -(hBOOL(hAPP(_1257588, _1257586)))], (50110 ^ _775828) ^ [_1782163, _1782165, _1782167] : [class_Orderings_Olinorder(_1782163), hBOOL(hAPP(hAPP(c_member(_1782163), _1782165), hAPP(c_List_Oset(_1782163), _1782167))), c_List_Olinorder__class_Osorted(_1782163, _1782167), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1782163, _1782163, c_COMBI(_1782163)), _1782165), c_List_Oremove1(_1782163, _1782165, _1782167)) = _1782167)], (18597 ^ _775828) ^ [_1095459, _1095461] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1095459), hAPP(hAPP(c_Power_Opower__class_Opower(_1095459), hAPP(c_Int_Onumber__class_Onumber__of(_1095459), c_Int_OMin)), _1095461)) = c_Groups_Oone__class_Oone(_1095459)), class_Int_Onumber__ring(_1095459), class_Rings_Olinordered__idom(_1095459)], (19922 ^ _775828) ^ [_1117766, _1117768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1117766)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1117768)), _1117766) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117768), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117766), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (7221 ^ _775828) ^ [_890819, _890821, _890823, _890825] : [class_Rings_Olinordered__ring__strict(_890819), 7224 ^ _775828 : [(7239 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890819), _890821), _890823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890819), _890821), _890825)))), 7240 ^ _775828 : [(7247 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890821), c_Groups_Ozero__class_Ozero(_890819))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890825), _890823))], (7241 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), c_Groups_Ozero__class_Ozero(_890819)), _890821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890823), _890825))]]], (7225 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890819), _890821), _890823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890819), _890821), _890825))), 7230 ^ _775828 : [(7233 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890823), _890825)))], (7231 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), c_Groups_Ozero__class_Ozero(_890819)), _890821)))]], 7234 ^ _775828 : [(7237 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890825), _890823)))], (7235 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890819), _890821), c_Groups_Ozero__class_Ozero(_890819))))]]]]], (1050 ^ _775828) ^ [_791571, _791573] : [-(class_Rings_Oordered__ring__abs(_791571)), _791573 = _791571, class_Rings_Oordered__ring__abs(_791573)], (25319 ^ _775828) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (25479 ^ _775828) ^ [_1225367, _1225369, _1225371, _1225373, _1225375] : [-(_1225367 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1225369, _1225371, _1225373, _1225375), _1225367) = c_Lazy__Sequence_Ohb__bind(_1225369, _1225371, hAPP(_1225373, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1225367), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1225369, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1225371))), _1225375), _1225367)))], (33408 ^ _775828) ^ [_1395360, _1395362, _1395364, _1395366, _1395368] : [-(c_Map_Orestrict__map(_1395360, _1395362, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1395360, tc_Option_Ooption(_1395362)), _1395364), _1395366), hAPP(c_Option_Ooption_OSome(_1395362), _1395368)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1395360, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1395360), _1395366), c_Orderings_Obot__class_Obot(tc_fun(_1395360, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1395360, _1395362, _1395364, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1395360, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1395360), _1395366), c_Orderings_Obot__class_Obot(tc_fun(_1395360, tc_HOL_Obool))))))], (5587 ^ _775828) ^ [_864364] : [hAPP(c_Nat_OSuc, _864364) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49279 ^ _775828) ^ [_1765236, _1765238, _1765240] : [hBOOL(hAPP(hAPP(c_member(_1765236), _1765238), hAPP(c_List_Oset(_1765236), c_List_Obutlast(_1765236, _1765240)))), -(hBOOL(hAPP(hAPP(c_member(_1765236), _1765238), hAPP(c_List_Oset(_1765236), _1765240))))], (33835 ^ _775828) ^ [_1404642, _1404644, _1404646, _1404648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404642, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404642, tc_HOL_Obool)), _1404644), _1404646)), _1404648) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404642, tc_HOL_Obool)), _1404644), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404642, tc_HOL_Obool)), _1404646), _1404648)))], (45955 ^ _775828) ^ [_1683238, _1683240, _1683242] : [-(hBOOL(hAPP(hAPP(c_member(_1683238), _1683240), hAPP(c_List_Oset(_1683238), _1683242)))), -(c_List_Oremove1(_1683238, _1683240, _1683242) = _1683242)], (29821 ^ _775828) ^ [_1317815, _1317817, _1317819, _1317821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1317815, tc_HOL_Obool)), _1317817), hAPP(hAPP(c_Set_Oinsert(_1317815), _1317819), _1317821))), 29824 ^ _775828 : [(29831 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317815), _1317819), _1317821))), 29834 ^ _775828 : [(29841 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317815), _1317819), _1317817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317815, tc_HOL_Obool)), _1317817), _1317821)))], (29835 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1317815), _1317819), _1317817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1317815, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317815, tc_HOL_Obool)), _1317817), hAPP(hAPP(c_Set_Oinsert(_1317815), _1317819), c_Orderings_Obot__class_Obot(tc_fun(_1317815, tc_HOL_Obool))))), _1317821)))]]], (29825 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1317815), _1317819), _1317821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1317815, tc_HOL_Obool)), _1317817), _1317821)))]]], (25074 ^ _775828) ^ [_1218260, _1218262] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218260)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218262))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1218260), _1218262)))], (6466 ^ _775828) ^ [_878666, _878668, _878670, _878672] : [class_Orderings_Opreorder(_878666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878666), _878668), _878670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878666), _878670), _878672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878666), _878668), _878672)))], (50760 ^ _775828) ^ [_1797743, _1797745] : [_1797745 = c_List_Olist_ONil(_1797743), -(c_List_Oremdups(_1797743, _1797745) = c_List_Olist_ONil(_1797743))], (45614 ^ _775828) ^ [_1675228, _1675230] : [-(hAPP(hAPP(c_List_Omap(_1675228, _1675228), c_COMBI(_1675228)), _1675230) = _1675230)], (5767 ^ _775828) ^ [_867759, _867761, _867763] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_867759), _867761), _867763)), -(c_Natural_Oevaln(_867759, _867761, 5770 ^ [_867759, _867761, _867763], _867763))], (3322 ^ _775828) ^ [_826102, _826104, _826106, _826108] : [-(c_Relation_OId__on(_826108, _826104) = c_Relation_OId__on(_826106, _826102)), _826108 = _826106, _826104 = _826102], (15126 ^ _775828) ^ [_1029653, _1029655] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029653), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029655), _1029653)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029655), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029655, _1029653)))], (19916 ^ _775828) ^ [_1117645, _1117647] : [class_Int_Onumber__ring(_1117645), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117645), c_Groups_Oone__class_Oone(_1117645)), hAPP(c_Int_Onumber__class_Onumber__of(_1117645), _1117647)) = hAPP(c_Int_Onumber__class_Onumber__of(_1117645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1117647)))], (29993 ^ _775828) ^ [_1322543, _1322545] : [_1322543 = _1322545, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1322543, _1322545) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1322543), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (48309 ^ _775828) ^ [_1743424, _1743426, _1743428, _1743430, _1743432, _1743434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1743424, _1743424)), hAPP(hAPP(c_Product__Type_OPair(_1743424, _1743424), _1743426), _1743428)), c_Transitive__Closure_Ortrancl(_1743424, _1743430))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743424), tc_List_Olist(_1743424))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743424), tc_List_Olist(_1743424)), _1743432), _1743434)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1743424), c_List_Olistrel1(_1743424, _1743430)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743424), tc_List_Olist(_1743424))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743424), tc_List_Olist(_1743424)), hAPP(hAPP(c_List_Olist_OCons(_1743424), _1743426), _1743432)), hAPP(hAPP(c_List_Olist_OCons(_1743424), _1743428), _1743434))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1743424), c_List_Olistrel1(_1743424, _1743430)))))], (44425 ^ _775828) ^ [_1648162, _1648164, _1648166, _1648168, _1648170] : [_1648162 = c_Orderings_Obot__class_Obot(tc_fun(_1648164, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648164, tc_fun(_1648166, tc_HOL_Obool)), _1648162), hAPP(hAPP(c_COMBC(_1648164, tc_fun(_1648166, tc_HOL_Obool), tc_fun(_1648166, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648166, tc_HOL_Obool), tc_fun(tc_fun(_1648166, tc_HOL_Obool), tc_fun(_1648166, tc_HOL_Obool)), _1648164), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648166, tc_HOL_Obool))), _1648168)), _1648170)) = c_Orderings_Otop__class_Otop(tc_fun(_1648166, tc_HOL_Obool)))], (10436 ^ _775828) ^ [_945695, _945697, _945699, _945701] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_945695), 10439 ^ _775828 : [(10446 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945695), _945697), _945701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945695), _945697), _945699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945695), _945701), _945699))))], (10440 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945695), _945697), _945699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945695), _945701), _945699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945695), _945697), _945701)))]]], (41889 ^ _775828) ^ [_1587574, _1587576] : [-(hAPP(c_Fun_Oid(_1587574), _1587576) = _1587576)], (30245 ^ _775828) ^ [_1327145] : [-(_1327145 = 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)), _1327145), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (25080 ^ _775828) ^ [_1218386, _1218388] : [_1218386 = _1218388, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218386) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218388))], (38808 ^ _775828) ^ [_1514575, _1514577, _1514579, _1514581, _1514583] : [c_Fun_Oinj__on(_1514575, _1514577, _1514579, _1514581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1514575, tc_HOL_Obool)), _1514583), _1514581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1514577, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514575, _1514577, _1514579), _1514583)), hAPP(c_Set_Oimage(_1514575, _1514577, _1514579), _1514581))))], (15474 ^ _775828) ^ [_1036100, _1036102, _1036104] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036100), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036102, _1036104)), _1036104) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036100), _1036102), _1036104))], (38526 ^ _775828) ^ [_1508325, _1508327, _1508329, _1508331, _1508333, _1508335] : [hBOOL(hAPP(hAPP(c_member(_1508325), _1508327), _1508329)), -(hAPP(c_Fun_Ooverride__on(_1508325, _1508331, _1508333, _1508335, _1508329), _1508327) = hAPP(_1508335, _1508327))], (27771 ^ _775828) ^ [_1270447, _1270449, _1270451] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1270447, _1270447, _1270449), c_Relation_OId(_1270447)), _1270451) = _1270451)], (16625 ^ _775828) ^ [_1058730, _1058732, _1058734, _1058736] : [hBOOL(hAPP(hAPP(c_member(_1058730), _1058732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058730, tc_HOL_Obool)), _1058734), _1058736))), -(hBOOL(hAPP(hAPP(c_member(_1058730), _1058732), _1058734)))], (44389 ^ _775828) ^ [_1646699, _1646701, _1646703, _1646705, _1646707] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646699, tc_fun(_1646701, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1646699, tc_HOL_Obool)), _1646703), _1646705)), _1646707) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646701, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646699, tc_fun(_1646701, tc_HOL_Obool)), _1646703), _1646707)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646699, tc_fun(_1646701, tc_HOL_Obool)), _1646705), _1646707)))], (22584 ^ _775828) ^ [_1168756, _1168758, _1168760] : [class_Fields_Olinordered__field(_1168756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168756), c_Groups_Ozero__class_Ozero(_1168756)), _1168758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168756), c_Groups_Ozero__class_Ozero(_1168756)), _1168760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168756), c_Groups_Ozero__class_Ozero(_1168756)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168756), _1168758), _1168760))))], (40195 ^ _775828) ^ [] : [-(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))], (41977 ^ _775828) ^ [_1589810, _1589812, _1589814, _1589816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589810), _1589812)), 41983 ^ _775828 : [(41986 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589814), hAPP(_1589816, 41982 ^ [_1589810, _1589812, _1589814, _1589816])))], (41984 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589810), 41982 ^ [_1589810, _1589812, _1589814, _1589816]), _1589812)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1589810, _1589814)), hAPP(hAPP(c_Product__Type_OSigma(_1589810, _1589814), _1589812), _1589816)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1589810, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1589814, tc_HOL_Obool), tc_Nat_Onat, _1589810), c_Finite__Set_Ocard(_1589814)), _1589816)), _1589812))], (6765 ^ _775828) ^ [_883072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883072)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29102 ^ _775828) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (26543 ^ _775828) ^ [_1244617, _1244619, _1244621, _1244623] : [class_Rings_Ocomm__ring(_1244617), class_Rings_Odvd(_1244617), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244617), _1244619), _1244621)), 26554 ^ _775828 : [(26561 ^ _775828) ^ [_1245043, _1245045] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244617), _1244619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244617), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1244617), _1245045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244617), _1245043), _1244621))), _1244623))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244617), _1244619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244617), _1245045), _1244623))))], (26555 ^ _775828) ^ [_1244870, _1244872] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244617), _1244619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244617), _1244872), _1244623))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244617), _1244619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244617), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1244617), _1244872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244617), _1244870), _1244621))), _1244623))))]]], (17569 ^ _775828) ^ [_1076576, _1076578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076576)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076576), _1076578)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1076576)), _1076578))], (41990 ^ _775828) ^ [_1590147, _1590149] : [class_Groups_Oab__semigroup__mult(_1590147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590147), _1590149)), -(_1590149 = c_Orderings_Obot__class_Obot(tc_fun(_1590147, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1590147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1590147), 42003 ^ [_1590147, _1590149]), 42004 ^ [_1590147, _1590149])), hAPP(hAPP(c_Set_Oinsert(_1590147), 42003 ^ [_1590147, _1590149]), hAPP(hAPP(c_Set_Oinsert(_1590147), 42004 ^ [_1590147, _1590149]), c_Orderings_Obot__class_Obot(tc_fun(_1590147, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1590147), hAPP(c_Finite__Set_Ofold1(_1590147, c_Groups_Otimes__class_Otimes(_1590147)), _1590149)), _1590149)))], (25001 ^ _775828) ^ [_1216414, _1216416, _1216418, _1216420, _1216422] : [hBOOL(hAPP(hAPP(c_member(_1216414), _1216416), hAPP(c_Set_Oimage(_1216418, _1216414, _1216420), _1216422))), 25005 ^ _775828 : [(25008 ^ _775828) ^ [] : [-(_1216416 = hAPP(_1216420, 25004 ^ [_1216414, _1216416, _1216418, _1216420, _1216422]))], (25006 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1216418), 25004 ^ [_1216414, _1216416, _1216418, _1216420, _1216422]), _1216422)))]]], (49016 ^ _775828) ^ [_1759832, _1759834, _1759836] : [49018 ^ _775828 : [(49021 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1759832), 49017 ^ [_1759832, _1759834, _1759836]), _1759836))], (49019 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759832), 49017 ^ [_1759832, _1759834, _1759836]), hAPP(c_List_Oset(_1759832), _1759834))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759832)), _1759834), c_List_Olists(_1759832, _1759836))))], (24867 ^ _775828) ^ [_1213664, _1213666] : [-(c_Nitpick_Ouminus__frac(_1213664, _1213666) = c_Nitpick_OAbs__Frac(_1213664, 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(_1213664), _1213666))), hAPP(c_Nitpick_Odenom(_1213664), _1213666))))], (18613 ^ _775828) ^ [_1095709, _1095711, _1095713, _1095715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1095709), _1095711)), -(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), _1095709), _1095713)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1095711), _1095715))), c_FunDef_Opair__less)))], (29573 ^ _775828) ^ [_1312486, _1312488, _1312490, _1312492] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312486, tc_HOL_Obool)), _1312488), hAPP(hAPP(c_Set_Oinsert(_1312486), _1312490), _1312492)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312486, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312486, tc_HOL_Obool)), _1312488), hAPP(hAPP(c_Set_Oinsert(_1312486), _1312490), c_Orderings_Obot__class_Obot(tc_fun(_1312486, tc_HOL_Obool))))), _1312492))], (15798 ^ _775828) ^ [_1042281, _1042283, _1042285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042281), _1042283)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042285), _1042283)), _1042281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042285), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042283), _1042281)))], (31231 ^ _775828) ^ [_1349925, _1349927] : [class_Orderings_Olinorder(_1349925), -(c_Big__Operators_Olattice_OSup__fin(_1349925, c_Orderings_Oord__class_Omax(_1349925), hAPP(hAPP(c_Set_Oinsert(_1349925), _1349927), c_Orderings_Obot__class_Obot(tc_fun(_1349925, tc_HOL_Obool)))) = _1349927)], (7379 ^ _775828) ^ [_893512, _893514, _893516] : [hAPP(c_Option_Ooption_OSome(_893512), _893514) = hAPP(c_Option_Ooption_OSome(_893512), _893516), -(_893514 = _893516)], (31865 ^ _775828) ^ [_1364025, _1364027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1364025), _1364027)), -(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), _1364025), _1364027)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (24995 ^ _775828) ^ [_1216259, _1216261, _1216263, _1216265, _1216267] : [hBOOL(hAPP(hAPP(c_member(_1216259), _1216261), _1216263)), -(hBOOL(hAPP(hAPP(c_member(_1216265), hAPP(_1216267, _1216261)), hAPP(c_Set_Oimage(_1216259, _1216265, _1216267), _1216263))))], (5028 ^ _775828) ^ [_852747, _852749] : [_852749 = _852747, -(c_Finite__Set_Ocard(_852749) = c_Finite__Set_Ocard(_852747))], (8661 ^ _775828) ^ [_914793, _914795, _914797, _914799] : [class_Orderings_Oorder(_914793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914793), _914795), _914797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914793), _914799), _914795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914793), _914799), _914797)))], (20268 ^ _775828) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (49556 ^ _775828) ^ [_1771971, _1771973] : [-(c_Random_Opick(_1771971, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1771971), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1771971, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1771971, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1771971)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1771973)) = c_Random_Opick(_1771971, _1771973))], (27316 ^ _775828) ^ [_1259976, _1259978, _1259980, _1259982] : [_1259976 = _1259978, hBOOL(hAPP(hAPP(c_member(_1259980), _1259976), _1259982)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1259980, _1259980)), hAPP(hAPP(c_Product__Type_OPair(_1259980, _1259980), _1259976), _1259978)), c_Relation_OId__on(_1259980, _1259982))))], (10838 ^ _775828) ^ [_953077, _953079, _953081, _953083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953077), _953079)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953081), _953079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953077), _953083), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953081), _953083)))], (38964 ^ _775828) ^ [_1517564, _1517566, _1517568, _1517570] : [-(_1517564 = c_Orderings_Obot__class_Obot(tc_fun(_1517566, tc_HOL_Obool))), 38967 ^ _775828 : [(38968 ^ _775828) ^ [] : [-(hAPP(c_Set_Oimage(_1517568, _1517566, 38975 ^ [_1517564, _1517566, _1517568, _1517570]), _1517570) = _1517564), 38969 ^ _775828 : [(38970 ^ _775828) ^ [_1517705] : [c_Fun_Oinj__on(_1517566, _1517568, _1517705, _1517564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517568, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1517566, _1517568, _1517705), _1517564)), _1517570))]]], (38979 ^ _775828) ^ [] : [38980 ^ _775828 : [(38981 ^ _775828) ^ [_1517897] : [hAPP(c_Set_Oimage(_1517568, _1517566, _1517897), _1517570) = _1517564]], 38983 ^ _775828 : [(38986 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517568, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1517566, _1517568, 38982 ^ [_1517564, _1517566, _1517568, _1517570]), _1517564)), _1517570)))], (38984 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1517566, _1517568, 38982 ^ [_1517564, _1517566, _1517568, _1517570], _1517564))]]]]], (46614 ^ _775828) ^ [_1701521, _1701523, _1701525] : [-(c_List_Oset__Cons(_1701521, _1701523, _1701525) = hAPP(c_Set_OCollect(tc_List_Olist(_1701521)), hAPP(hAPP(c_COMBB(tc_fun(_1701521, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1701521)), c_HOL_OEx(_1701521)), hAPP(hAPP(c_COMBB(tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_fun(_1701521, tc_HOL_Obool), tc_List_Olist(_1701521)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_HOL_Obool, _1701521), c_HOL_OEx(tc_List_Olist(_1701521)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701521), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1701521, tc_fun(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), tc_fun(tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), tc_List_Olist(_1701521)), c_COMBS(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1701521, tc_fun(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), tc_List_Olist(_1701521)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701521), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), _1701521), c_COMBS(tc_List_Olist(_1701521), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1701521)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1701521), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1701521)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701521), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_List_Olist(_1701521))), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1701521), tc_List_Olist(_1701521)), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_fun(tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_List_Olist(_1701521))), tc_fun(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool))), tc_List_Olist(_1701521)), c_COMBB(tc_fun(tc_List_Olist(_1701521), tc_List_Olist(_1701521)), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), _1701521)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1701521), tc_List_Olist(_1701521)), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), tc_List_Olist(_1701521)), c_COMBB(tc_List_Olist(_1701521), tc_HOL_Obool, tc_List_Olist(_1701521))), c_fequal))), c_List_Olist_OCons(_1701521)))))), hAPP(hAPP(c_COMBC(_1701521, tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool)), _1701521), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1701521))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1701521), c_fconj), hAPP(hAPP(c_COMBC(_1701521, tc_fun(_1701521, tc_HOL_Obool), tc_HOL_Obool), c_member(_1701521)), _1701523)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1701521), tc_fun(tc_List_Olist(_1701521), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1701521))), _1701525)))))))], (1580 ^ _775828) ^ [_798196, _798198] : [-(class_Rings_Ocomm__semiring(_798196)), _798198 = _798196, class_Rings_Ocomm__semiring(_798198)], (44353 ^ _775828) ^ [_1645954, _1645956, _1645958, _1645960, _1645962] : [_1645954 = c_Orderings_Obot__class_Obot(tc_fun(_1645956, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645958, tc_HOL_Obool)), _1645960), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645956, tc_fun(_1645958, tc_HOL_Obool)), _1645954), _1645962)) = _1645960)], (2090 ^ _775828) ^ [_806330, _806332, _806334, _806336] : [-(c_Divides_Odivmod__int__rel(_806336, _806332) = c_Divides_Odivmod__int__rel(_806334, _806330)), _806336 = _806334, _806332 = _806330], (21110 ^ _775828) ^ [_1141171, _1141173, _1141175] : [21112 ^ _775828 : [(21115 ^ _775828) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1141171, _1141173), 21111 ^ [_1141171, _1141173, _1141175]))], (21113 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1141173, 21111 ^ [_1141171, _1141173, _1141175]), _1141175)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1141171, _1141173), _1141175)))], (23248 ^ _775828) ^ [_1180770, _1180772, _1180774] : [class_Fields_Olinordered__field(_1180770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180770), _1180772), _1180774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180770), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180770), _1180772), _1180774)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180770), c_Groups_Oone__class_Oone(_1180770)), c_Groups_Oone__class_Oone(_1180770)))), _1180774)))], (35251 ^ _775828) ^ [_1436729, _1436731, _1436733, _1436735, _1436737, _1436739, _1436741] : [c_Big__Operators_Ocomm__monoid__big(_1436729, _1436731, _1436733, _1436735, _1436737), 35254 ^ _775828 : [(35261 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436731), _1436739))), -(hAPP(hAPP(_1436737, _1436741), _1436739) = _1436735)], (35255 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436731), _1436739)), -(hAPP(hAPP(_1436737, _1436741), _1436739) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436729, _1436731, _1436733), _1436741), _1436735), _1436739))]]], (38377 ^ _775828) ^ [_1504788, _1504790] : [38378 ^ _775828 : [(38379 ^ _775828) ^ [_1504852, _1504854] : [_1504790 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1504788, _1504852), 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)), _1504854)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1504788), _1504790)))], (51574 ^ _775828) ^ [_1809089, _1809091] : [hBOOL(_1809089), -(hBOOL(hAPP(hAPP(c_fdisj, _1809089), _1809091)))], (7041 ^ _775828) ^ [_887465, _887467, _887469, _887471] : [class_Rings_Olinordered__comm__semiring__strict(_887465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887465), _887467), _887469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887465), c_Groups_Ozero__class_Ozero(_887465)), _887471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_887465), _887471), _887467)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_887465), _887471), _887469))))], (41220 ^ _775828) ^ [_1571353, _1571355, _1571357] : [class_Groups_Oab__semigroup__mult(_1571353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571353), _1571355)), -(_1571355 = c_Orderings_Obot__class_Obot(tc_fun(_1571353, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571353), _1571357)), -(_1571357 = c_Orderings_Obot__class_Obot(tc_fun(_1571353, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1571353, tc_HOL_Obool)), _1571355), _1571357) = c_Orderings_Obot__class_Obot(tc_fun(_1571353, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1571353, c_Groups_Otimes__class_Otimes(_1571353)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571353, tc_HOL_Obool)), _1571355), _1571357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1571353), hAPP(c_Finite__Set_Ofold1(_1571353, c_Groups_Otimes__class_Otimes(_1571353)), _1571355)), hAPP(c_Finite__Set_Ofold1(_1571353, c_Groups_Otimes__class_Otimes(_1571353)), _1571357)))], (10832 ^ _775828) ^ [_952966, _952968, _952970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952966), _952968)), _952970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _952966), _952970)))], (22516 ^ _775828) ^ [_1167576, _1167578, _1167580] : [class_Fields_Olinordered__field__inverse__zero(_1167576), 22519 ^ _775828 : [(22534 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167576), _1167578), _1167580)))), 22535 ^ _775828 : [(22542 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), _1167578), c_Groups_Ozero__class_Ozero(_1167576))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), _1167580), c_Groups_Ozero__class_Ozero(_1167576)))], (22536 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), _1167578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), _1167580))]]], (22520 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167576), _1167578), _1167580))), 22525 ^ _775828 : [(22528 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), _1167580)))], (22526 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), c_Groups_Ozero__class_Ozero(_1167576)), _1167578)))]], 22529 ^ _775828 : [(22532 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), _1167580), c_Groups_Ozero__class_Ozero(_1167576))))], (22530 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167576), _1167578), c_Groups_Ozero__class_Ozero(_1167576))))]]]]], (24368 ^ _775828) ^ [_1203443, _1203445, _1203447, _1203449, _1203451, _1203453, _1203455] : [-(hAPP(c_Product__Type_Oapsnd(_1203443, _1203445, _1203447, _1203449), hAPP(c_Product__Type_Oapfst(_1203451, _1203447, _1203443, _1203453), _1203455)) = hAPP(hAPP(c_Product__Type_OPair(_1203447, _1203445), hAPP(_1203453, hAPP(c_Product__Type_Ofst(_1203451, _1203443), _1203455))), hAPP(_1203449, hAPP(c_Product__Type_Osnd(_1203451, _1203443), _1203455))))], (51138 ^ _775828) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (45204 ^ _775828) ^ [_1666002, _1666004, _1666006, _1666008, _1666010, _1666012, _1666014, _1666016] : [c_Finite__Set_Ofolding__image__simple__idem(_1666002, _1666004, _1666006, _1666008, _1666010, _1666012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1666004), _1666014)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1666004), _1666016)), -(hAPP(_1666012, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1666004, tc_HOL_Obool)), _1666014), _1666016)) = hAPP(hAPP(_1666006, hAPP(_1666012, _1666014)), hAPP(_1666012, _1666016)))], (10294 ^ _775828) ^ [_942841, _942843, _942845, _942847] : [class_Rings_Ocomm__semiring__1(_942841), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942841), _942843), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942841), _942845), _942847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942841), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942841), _942843), _942845)), _942847))], (24152 ^ _775828) ^ [_1198759, _1198761, _1198763] : [class_Orderings_Olinorder(_1198759), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198759), _1198761), _1198763) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198759), _1198763), _1198761))], (28699 ^ _775828) ^ [_1291646, _1291648] : [c_Wellfounded_Oacyclic(_1291646, hAPP(c_Relation_Oconverse(_1291646, _1291646), _1291648)), -(c_Wellfounded_Oacyclic(_1291646, _1291648))], (46013 ^ _775828) ^ [_1684338, _1684340, _1684342, _1684344] : [hBOOL(hAPP(c_List_Odistinct(_1684338), _1684340)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1684342, _1684338)), hAPP(hAPP(c_List_Ozip(_1684342, _1684338), _1684344), _1684340))))], (45248 ^ _775828) ^ [_1666894, _1666896, _1666898, _1666900, _1666902, _1666904, _1666906, _1666908] : [c_Finite__Set_Ofolding__image__simple__idem(_1666894, _1666896, _1666898, _1666900, _1666902, _1666904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1666896), _1666906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1666896, tc_HOL_Obool)), _1666908), _1666906)), -(hAPP(hAPP(_1666898, hAPP(_1666904, _1666908)), hAPP(_1666904, _1666906)) = hAPP(_1666904, _1666906))], (20686 ^ _775828) ^ [_1131306, _1131308, _1131310] : [class_Rings_Olinordered__idom(_1131306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131306), hAPP(hAPP(c_Power_Opower__class_Opower(_1131306), _1131308), 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(_1131306), _1131310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1131306)))], (44990 ^ _775828) ^ [_1660966, _1660968, _1660970, _1660972, _1660974, _1660976, _1660978, _1660980] : [c_Fun_Oinj__on(_1660966, _1660968, _1660970, _1660972), 44996 ^ _775828 : [(44999 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660966, tc_HOL_Obool)), hAPP(_1660978, 44995 ^ [_1660966, _1660968, _1660970, _1660972, _1660974, _1660976, _1660978, _1660980])), _1660972))], (44997 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660974), 44995 ^ [_1660966, _1660968, _1660970, _1660972, _1660974, _1660976, _1660978, _1660980]), _1660976)))]], hBOOL(hAPP(hAPP(c_member(_1660974), _1660980), _1660976)), -(hAPP(c_Set_Oimage(_1660966, _1660968, _1660970), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660974, tc_fun(_1660966, tc_HOL_Obool)), _1660976), _1660978)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660974, tc_fun(_1660968, tc_HOL_Obool)), _1660976), hAPP(hAPP(c_COMBB(tc_fun(_1660966, tc_HOL_Obool), tc_fun(_1660968, tc_HOL_Obool), _1660974), c_Set_Oimage(_1660966, _1660968, _1660970)), _1660978)))], (33943 ^ _775828) ^ [_1407261, _1407263, _1407265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407261, tc_HOL_Obool)), _1407263), _1407265)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407261, tc_HOL_Obool)), _1407265), _1407263) = _1407263)], (49893 ^ _775828) ^ [_1778171, _1778173] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1778171, _1778173)))], (33713 ^ _775828) ^ [_1401963, _1401965, _1401967, _1401969] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401963, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401963, tc_HOL_Obool)), _1401965), _1401967)), _1401969) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401963, tc_HOL_Obool)), _1401965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401963, tc_HOL_Obool)), _1401967), _1401969)))], (3222 ^ _775828) ^ [_824532, _824534] : [_824534 = _824532, -(c_Rings_Oinverse__class_Odivide(_824534) = c_Rings_Oinverse__class_Odivide(_824532))], (21926 ^ _775828) ^ [_1156258, _1156260, _1156262, _1156264] : [class_Fields_Ofield(_1156258), -(_1156260 = c_Groups_Ozero__class_Ozero(_1156258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1156262), _1156264)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156258), _1156260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1156264), _1156262)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156258), hAPP(hAPP(c_Power_Opower__class_Opower(_1156258), _1156260), _1156264)), hAPP(hAPP(c_Power_Opower__class_Opower(_1156258), _1156260), _1156262)))], (51238 ^ _775828) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51192 ^ _775828) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (19584 ^ _775828) ^ [_1112454] : [c_Int_OBit1(_1112454) = c_Int_OMin, -(_1112454 = c_Int_OMin)], (28411 ^ _775828) ^ [_1285975, _1285977, _1285979, _1285981, _1285983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285975, tc_HOL_Obool)), _1285977), _1285979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285975, tc_HOL_Obool)), _1285981), _1285983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285975, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285975, tc_HOL_Obool)), _1285977), _1285981)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285975, tc_HOL_Obool)), _1285979), _1285983))))], (1740 ^ _775828) ^ [_800196, _800198] : [-(class_Int_Onumber(_800196)), _800198 = _800196, class_Int_Onumber(_800198)], (30768 ^ _775828) ^ [_1338578, _1338580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1338578, _1338578)), _1338580)), c_Wellfounded_Oacyclic(_1338578, _1338580), -(c_Wellfounded_Owf(_1338578, hAPP(c_Relation_Oconverse(_1338578, _1338578), _1338580)))], (35971 ^ _775828) ^ [_1451353, _1451355, _1451357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451353)), 35974 ^ _775828 : [(35975 ^ _775828) ^ [_1451487] : [35977 ^ _775828 : [(35983 ^ _775828) ^ [] : [-(_1451487 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35979 ^ [_1451353, _1451355, _1451357, _1451487]), 35976 ^ [_1451353, _1451355, _1451357, _1451487]))], (35981 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35979 ^ [_1451353, _1451355, _1451357, _1451487]), _1451355)))], (35978 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35976 ^ [_1451353, _1451355, _1451357, _1451487]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451353))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451487), _1451357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1451487), _1451353)), _1451357)))]]], (46456 ^ _775828) ^ [_1697724, _1697726, _1697728, _1697730, _1697732, _1697734] : [-(c_List_Ofoldr(_1697724, _1697726, _1697728, hAPP(hAPP(c_List_Olist_OCons(_1697724), _1697730), _1697732), _1697734) = hAPP(hAPP(_1697728, _1697730), c_List_Ofoldr(_1697724, _1697726, _1697728, _1697732, _1697734)))], (40824 ^ _775828) ^ [_1561071, _1561073, _1561075, _1561077, _1561079] : [hBOOL(hAPP(hAPP(c_member(_1561071), _1561073), hAPP(c_Set_Ovimage(_1561071, _1561075, _1561077), _1561079))), -(hBOOL(hAPP(hAPP(c_member(_1561075), hAPP(_1561077, _1561073)), _1561079)))], (19610 ^ _775828) ^ [_1112796] : [-(c_Int_Osucc(c_Int_Opred(_1112796)) = _1112796)], (11715 ^ _775828) ^ [_968348, _968350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968348), hAPP(c_Nat_OSuc, _968350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968348), _968350)))], (18353 ^ _775828) ^ [_1091423, _1091425, _1091427] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091423, _1091423), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091425), _1091427))), -(_1091423 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1091425 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21094 ^ _775828) ^ [_1140786, _1140788, _1140790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140786, tc_HOL_Obool)), _1140788), _1140790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140786, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1140786, tc_fun(_1140786, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140786)), _1140788)), hAPP(hAPP(c_COMBC(_1140786, tc_fun(_1140786, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140786)), _1140790))))], (34119 ^ _775828) ^ [_1410492, _1410494, _1410496] : [class_Lattices_Olattice(_1410492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410492), _1410494)), -(_1410494 = c_Orderings_Obot__class_Obot(tc_fun(_1410492, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410492), _1410496)), -(_1410496 = c_Orderings_Obot__class_Obot(tc_fun(_1410492, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410492, tc_HOL_Obool)), _1410494), _1410496) = c_Orderings_Obot__class_Obot(tc_fun(_1410492, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1410492, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410492, tc_HOL_Obool)), _1410494), _1410496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410492), c_Big__Operators_Olattice__class_OInf__fin(_1410492, _1410494)), c_Big__Operators_Olattice__class_OInf__fin(_1410492, _1410496)))], (5790 ^ _775828) ^ [_868125, _868127, _868129] : [class_Rings_Osemiring__1(_868125), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_868125, _868127, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _868129) = _868129)], (28818 ^ _775828) ^ [_1294295, _1294297, _1294299] : [hBOOL(hAPP(_1294295, _1294297)), -(hBOOL(hAPP(_1294295, c_Hilbert__Choice_OEps(_1294299, _1294295))))], (34891 ^ _775828) ^ [_1426940, _1426942, _1426944] : [c_Wellfounded_Owf(_1426940, _1426942), c_Wellfounded_Owf(_1426940, _1426944), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426940, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1426940, _1426940), _1426942)), hAPP(c_Relation_ORange(_1426940, _1426940), _1426944)) = c_Orderings_Obot__class_Obot(tc_fun(_1426940, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1426940, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1426940, _1426940), tc_HOL_Obool)), _1426942), _1426944)))], (25661 ^ _775828) ^ [_1229476, _1229478, _1229480] : [class_Rings_Ocomm__ring__1(_1229476), 25664 ^ _775828 : [(25671 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229476), _1229478), _1229480)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229476), _1229478), hAPP(c_Groups_Ouminus__class_Ouminus(_1229476), _1229480))))], (25665 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229476), _1229478), hAPP(c_Groups_Ouminus__class_Ouminus(_1229476), _1229480))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229476), _1229478), _1229480)))]]], (48371 ^ _775828) ^ [_1745413, _1745415] : [hAPP(c_List_Orotate1(_1745413), _1745415) = c_List_Olist_ONil(_1745413), -(_1745415 = c_List_Olist_ONil(_1745413))], (39468 ^ _775828) ^ [_1529426, _1529428, _1529430, _1529432, _1529434] : [class_Complete__Lattice_Ocomplete__lattice(_1529426), 39471 ^ _775828 : [(39472 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1529426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529428, _1529426), _1529430), _1529432)), _1529434)), 39475 ^ _775828 : [(39476 ^ _775828) ^ [_1529607] : [hBOOL(hAPP(hAPP(c_member(_1529428), _1529607), _1529430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1529426), hAPP(_1529432, _1529607)), _1529434)))]]], (39482 ^ _775828) ^ [] : [39484 ^ _775828 : [(39487 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1529426), hAPP(_1529432, 39483 ^ [_1529426, _1529428, _1529430, _1529432, _1529434])), _1529434))], (39485 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529428), 39483 ^ [_1529426, _1529428, _1529430, _1529432, _1529434]), _1529430)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1529426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529428, _1529426), _1529430), _1529432)), _1529434)))]]], (42307 ^ _775828) ^ [_1597439] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1597439), c_Int_OInteg)), -(_1597439 = hAPP(c_Int_ORep__Integ, 42310 ^ [_1597439]))], (46786 ^ _775828) ^ [_1706563, _1706565, _1706567, _1706569] : [class_Groups_Ocomm__monoid__add(_1706563), 46789 ^ _775828 : [(46796 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1706565), _1706567))), -(c_Nitpick_Osetsum_H(_1706565, _1706563, _1706569, _1706567) = c_Groups_Ozero__class_Ozero(_1706563))], (46790 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1706565), _1706567)), -(c_Nitpick_Osetsum_H(_1706565, _1706563, _1706569, _1706567) = hAPP(c_List_Omonoid__add__class_Olistsum(_1706563), hAPP(hAPP(c_List_Omap(_1706565, _1706563), _1706569), c_Hilbert__Choice_OEps(tc_List_Olist(_1706565), hAPP(hAPP(c_COMBS(tc_List_Olist(_1706565), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1706565)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706565), tc_fun(_1706565, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1706565, tc_HOL_Obool), tc_fun(tc_fun(_1706565, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1706565)), c_fequal), c_List_Oset(_1706565))), _1706567))), c_List_Odistinct(_1706565))))))]]], (39417 ^ _775828) ^ [_1527701, _1527703, _1527705, _1527707, _1527709] : [39419 ^ _775828 : [(39422 ^ _775828) ^ [] : [hBOOL(hAPP(_1527709, 39418 ^ [_1527701, _1527703, _1527705, _1527707, _1527709]))], (39420 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527701), 39418 ^ [_1527701, _1527703, _1527705, _1527707, _1527709]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527703, tc_fun(_1527701, tc_HOL_Obool)), _1527705), _1527707))))]], 39423 ^ _775828 : [(39424 ^ _775828) ^ [_1527923] : [hBOOL(hAPP(hAPP(c_member(_1527703), _1527923), _1527705)), 39427 ^ _775828 : [(39428 ^ _775828) ^ [_1528020] : [hBOOL(hAPP(hAPP(c_member(_1527701), _1528020), hAPP(_1527707, _1527923))), -(hBOOL(hAPP(_1527709, _1528020)))]]]]], (41324 ^ _775828) ^ [_1574085, _1574087, _1574089, _1574091, _1574093] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1574085, _1574087), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574085, tc_HOL_Obool)), _1574089), _1574091)), _1574093) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574085, _1574087), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1574085, _1574087), _1574089), _1574093)), hAPP(hAPP(c_Product__Type_OSigma(_1574085, _1574087), _1574091), _1574093)))], (35463 ^ _775828) ^ [_1442091, _1442093] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442091, _1442093))))], (14255 ^ _775828) ^ [_1014096, _1014098] : [class_Divides_Osemiring__div(_1014096), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014096), _1014098), c_Groups_Oone__class_Oone(_1014096)) = _1014098)], (1270 ^ _775828) ^ [_794321, _794323] : [-(class_Lattices_Osemilattice__inf(_794321)), _794323 = _794321, class_Lattices_Osemilattice__inf(_794323)], (11703 ^ _775828) ^ [_968129, _968131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968129), _968131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968129)), _968131)))], (41127 ^ _775828) ^ [_1568498, _1568500, _1568502, _1568504] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1568498), _1568500)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1568498), _1568502)), -(_1568502 = c_Orderings_Obot__class_Obot(tc_fun(_1568498, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1568498, tc_HOL_Obool), tc_fun(_1568498, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1568498, tc_HOL_Obool), tc_fun(_1568498, tc_HOL_Obool)), _1568500), _1568502)), c_Wellfounded_Omax__ext(_1568498, _1568504)))), 41141 ^ _775828 : [(41144 ^ _775828) ^ [_1568903] : [hBOOL(hAPP(hAPP(c_member(_1568498), _1568903), _1568502)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568498, _1568498)), hAPP(hAPP(c_Product__Type_OPair(_1568498, _1568498), 41140 ^ [_1568498, _1568500, _1568502, _1568504]), _1568903)), _1568504))], (41142 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568498), 41140 ^ [_1568498, _1568500, _1568502, _1568504]), _1568500)))]]], (13352 ^ _775828) ^ [_997178, _997180, _997182, _997184] : [class_Divides_Osemiring__div(_997178), -(c_Divides_Odiv__class_Omod(_997178, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997178), _997180), _997182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997178), _997184), _997182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997178), c_Divides_Odiv__class_Omod(_997178, _997180, _997184)), _997182))], (36173 ^ _775828) ^ [_1455107, _1455109, _1455111, _1455113, _1455115] : [class_Orderings_Olinorder(_1455107), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455107, _1455109), _1455111) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455107, _1455113), _1455115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455107), _1455109), _1455111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455107), _1455113), _1455115)), -(_1455111 = _1455115)], (48269 ^ _775828) ^ [_1742400, _1742402, _1742404, _1742406, _1742408, _1742410] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742400), tc_List_Olist(_1742400))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742400), tc_List_Olist(_1742400)), hAPP(hAPP(c_List_Olist_OCons(_1742400), _1742402), _1742404)), hAPP(hAPP(c_List_Olist_OCons(_1742400), _1742406), _1742408))), c_List_Olistrel1(_1742400, _1742410)))), 48270 ^ _775828 : [(48277 ^ _775828) ^ [] : [_1742402 = _1742406, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742400), tc_List_Olist(_1742400))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742400), tc_List_Olist(_1742400)), _1742404), _1742408)), c_List_Olistrel1(_1742400, _1742410)))], (48271 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1742400, _1742400)), hAPP(hAPP(c_Product__Type_OPair(_1742400, _1742400), _1742402), _1742406)), _1742410)), _1742404 = _1742408]]], (32193 ^ _775828) ^ [_1370852, _1370854, _1370856] : [class_Orderings_Olinorder(_1370852), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1370852, tc_HOL_Obool)), _1370854), _1370856)), -(_1370854 = c_Orderings_Obot__class_Obot(tc_fun(_1370852, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370852), _1370856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370852), c_Big__Operators_Olinorder__class_OMin(_1370852, _1370856)), c_Big__Operators_Olinorder__class_OMin(_1370852, _1370854))))], (33378 ^ _775828) ^ [_1394491, _1394493, _1394495, _1394497, _1394499] : [hAPP(_1394491, _1394493) = hAPP(c_Option_Ooption_OSome(_1394495), _1394497), -(hBOOL(hAPP(hAPP(c_member(_1394495), _1394497), c_Map_Oran(_1394499, _1394495, _1394491))))], (12343 ^ _775828) ^ [_979412, _979414, _979416, _979418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979412, tc_HOL_Obool)), _979414), _979416)), hBOOL(hAPP(_979414, _979418)), -(hBOOL(hAPP(_979416, _979418)))], (38031 ^ _775828) ^ [_1497020, _1497022, _1497024] : [class_Orderings_Oord(_1497020), 38034 ^ _775828 : [(38041 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497020), _1497024), _1497022)), -(hBOOL(hAPP(hAPP(c_member(_1497020), _1497022), hAPP(c_SetInterval_Oord__class_OatLeast(_1497020), _1497024))))], (38035 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1497020), _1497022), hAPP(c_SetInterval_Oord__class_OatLeast(_1497020), _1497024))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497020), _1497024), _1497022)))]]], (21356 ^ _775828) ^ [_1145589, _1145591, _1145593, _1145595] : [class_Fields_Ofield(_1145589), -(_1145591 = c_Groups_Ozero__class_Ozero(_1145589)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145589), _1145593), _1145591)), _1145595) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145589), hAPP(hAPP(c_Power_Opower__class_Opower(_1145589), _1145593), _1145595)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145589), _1145591), _1145595)))], (46498 ^ _775828) ^ [_1698600, _1698602, _1698604, _1698606, _1698608, _1698610] : [hBOOL(hAPP(hAPP(_1698600, _1698602), _1698604)), c_List_Olistrelp(_1698606, _1698600, _1698608, _1698610), -(c_List_Olistrelp(_1698606, _1698600, hAPP(hAPP(c_List_Olist_OCons(_1698606), _1698602), _1698608), hAPP(hAPP(c_List_Olist_OCons(_1698606), _1698604), _1698610)))], (10590 ^ _775828) ^ [_948346, _948348, _948350, _948352] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_948346), 10593 ^ _775828 : [(10600 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948346), _948350), _948352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948346), _948348), _948350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948346), _948348), _948352))))], (10594 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948346), _948348), _948350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948346), _948348), _948352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948346), _948350), _948352)))]]], (14261 ^ _775828) ^ [_1014212, _1014214, _1014216, _1014218] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014212, _1014214), _1014216, _1014218, _1014216), hBOOL(hAPP(_1014212, _1014216)), 14269 ^ _775828 : [(14272 ^ _775828) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014212, _1014214), 14268 ^ [_1014212, _1014214, _1014216, _1014218], _1014218, _1014216))], (14270 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_1014214, _1014216, _1014218, 14268 ^ [_1014212, _1014214, _1014216, _1014218]))]]], (42065 ^ _775828) ^ [_1591898, _1591900, _1591902, _1591904, _1591906, _1591908, _1591910, _1591912, _1591914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591898, _1591900)), hAPP(hAPP(c_Product__Type_OPair(_1591898, _1591900), _1591902), _1591904)), _1591906)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591908, _1591910)), hAPP(hAPP(c_Product__Type_OPair(_1591908, _1591910), hAPP(_1591912, _1591902)), hAPP(_1591914, _1591904))), hAPP(c_Set_Oimage(tc_prod(_1591898, _1591900), tc_prod(_1591908, _1591910), c_Product__Type_Omap__pair(_1591898, _1591908, _1591900, _1591910, _1591912, _1591914)), _1591906))))], (23522 ^ _775828) ^ [_1187111, _1187113] : [-(_1187111 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23525 ^ _775828 : [(23532 ^ _775828) ^ [] : [-(_1187113 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1187111, _1187113) = 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, _1187113))), 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, _1187111)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1187113))), c_Divides_Opdivmod(_1187111, _1187113)), 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), _1187113))))), c_Divides_Opdivmod(_1187111, _1187113)))))], (23526 ^ _775828) ^ [] : [_1187113 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1187111, _1187113) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187111))]]], (20940 ^ _775828) ^ [_1136050, _1136052] : [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), _1136050))), 20943 ^ _775828 : [(20950 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136052)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136050)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136052), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136050)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136050)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136052), 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), _1136050)))))], (20944 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136052)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136050))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136052), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136050)) = 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), _1136052)))]]], (5100 ^ _775828) ^ [_853843, _853845, _853847, _853849, _853851, _853853, _853855, _853857] : [-(c_Fun_Ocomp(_853857, _853853, _853849, _853845) = c_Fun_Ocomp(_853855, _853851, _853847, _853843)), _853857 = _853855, _853853 = _853851, _853849 = _853847, _853845 = _853843], (50782 ^ _775828) ^ [_1798084, _1798086] : [hBOOL(hAPP(c_List_Odistinct(_1798084), _1798086)), -(c_List_Oremdups(_1798084, _1798086) = _1798086)], (14193 ^ _775828) ^ [_1013080, _1013082, _1013084] : [-(hBOOL(hAPP(_1013080, _1013082))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1013080, _1013084)), _1013082), _1013082)))], (43942 ^ _775828) ^ [_1635134, _1635136, _1635138, _1635140, _1635142, _1635144, _1635146] : [c_Finite__Set_Ofun__left__comm(_1635134, _1635136, _1635138), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1635134, _1635136, _1635138, _1635140, _1635142), _1635144)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1635134, _1635136, _1635138, _1635140, _1635142), _1635146)), -(_1635146 = _1635144)], (24024 ^ _775828) ^ [_1196465, _1196467, _1196469, _1196471] : [class_Orderings_Olinorder(_1196465), 24027 ^ _775828 : [(24036 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196465), _1196467), _1196469)), _1196471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), _1196467), _1196471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), _1196469), _1196471))], (24028 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196465), _1196467), _1196469)), _1196471)), 24031 ^ _775828 : [(24034 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), _1196469), _1196471)))], (24032 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196465), _1196467), _1196471)))]]]]], (46538 ^ _775828) ^ [_1699443, _1699445, _1699447] : [hBOOL(hAPP(c_List_Odistinct(_1699443), hAPP(hAPP(c_List_Olist_OCons(_1699443), _1699445), _1699447))), 46541 ^ _775828 : [(46544 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1699443), _1699447)))], (46542 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1699443), _1699445), hAPP(c_List_Oset(_1699443), _1699447)))]]], (33761 ^ _775828) ^ [_1402945, _1402947, _1402949] : [class_Lattices_Osemilattice__inf(_1402945), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402945), _1402947), _1402949) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402945), _1402949), _1402947))], (41370 ^ _775828) ^ [_1575614, _1575616, _1575618, _1575620, _1575622] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575614, _1575616), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1575614, tc_HOL_Obool)), _1575618), _1575620)), hAPP(c_COMBK(tc_fun(_1575616, tc_HOL_Obool), _1575614), _1575622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575614, _1575616), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575614, _1575616), _1575618), hAPP(c_COMBK(tc_fun(_1575616, tc_HOL_Obool), _1575614), _1575622))), hAPP(hAPP(c_Product__Type_OSigma(_1575614, _1575616), _1575620), hAPP(c_COMBK(tc_fun(_1575616, tc_HOL_Obool), _1575614), _1575622))))], (11544 ^ _775828) ^ [_965617] : [class_Rings_Olinordered__semidom(_965617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965617), c_Groups_Ozero__class_Ozero(_965617)), c_Groups_Oone__class_Oone(_965617))))], (2718 ^ _775828) ^ [_816272, _816274, _816276, _816278, _816280, _816282, _816284, _816286] : [-(c_New__DSequence_Opos__decr__bind(_816286, _816282, _816278, _816274) = c_New__DSequence_Opos__decr__bind(_816284, _816280, _816276, _816272)), _816286 = _816284, _816282 = _816280, _816278 = _816276, _816274 = _816272], (44966 ^ _775828) ^ [_1660609, _1660611, _1660613] : [class_Complete__Lattice_Ocomplete__lattice(_1660609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660609), _1660611)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1660609), _1660613), c_Complete__Lattice_OInf__class_OInf(_1660609, _1660611)) = hAPP(hAPP(c_Finite__Set_Ofold(_1660609, _1660609, c_Lattices_Osemilattice__inf__class_Oinf(_1660609)), _1660613), _1660611))], (7111 ^ _775828) ^ [_888782, _888784, _888786, _888788] : [class_Rings_Olinordered__ring__strict(_888782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888782), _888784), c_Groups_Ozero__class_Ozero(_888782))), 7118 ^ _775828 : [(7125 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888782), _888788), _888786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888782), _888784), _888786)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888782), _888784), _888788))))], (7119 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888782), _888784), _888786)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888782), _888784), _888788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888782), _888788), _888786)))]]], (39309 ^ _775828) ^ [_1525049, _1525051, _1525053, _1525055, _1525057, _1525059] : [-(hAPP(c_Relation_OImage(_1525049, _1525051, _1525053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525055, tc_fun(_1525049, tc_HOL_Obool)), _1525057), _1525059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525055, tc_fun(_1525051, tc_HOL_Obool)), _1525057), hAPP(hAPP(c_COMBB(tc_fun(_1525049, tc_HOL_Obool), tc_fun(_1525051, tc_HOL_Obool), _1525055), c_Relation_OImage(_1525049, _1525051, _1525053)), _1525059)))], (49606 ^ _775828) ^ [_1773233, _1773235, _1773237, _1773239, _1773241] : [class_Orderings_Olinorder(_1773233), c_List_Olinorder__class_Osorted(_1773233, hAPP(hAPP(c_List_Omap(_1773235, _1773233), _1773237), _1773239)), -(c_List_Olinorder__class_Osorted(_1773233, hAPP(hAPP(c_List_Omap(_1773235, _1773233), _1773237), hAPP(c_List_Ofilter(_1773235, _1773241), _1773239))))], (42081 ^ _775828) ^ [_1592390, _1592392, _1592394, _1592396] : [-(c_Product__Type_Oapsnd(_1592390, _1592392, _1592394, _1592396) = c_Product__Type_Omap__pair(_1592394, _1592394, _1592390, _1592392, c_Fun_Oid(_1592394), _1592396))], (31917 ^ _775828) ^ [_1365906, _1365908, _1365910] : [class_Orderings_Oorder(_1365906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365906), _1365908), _1365910)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1365906, _1365910, _1365908) = c_Orderings_Obot__class_Obot(tc_fun(_1365906, tc_HOL_Obool)))], (36885 ^ _775828) ^ [_1469112, _1469114, _1469116, _1469118] : [class_Groups_Oordered__ab__group__add__abs(_1469112), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469112), c_Groups_Ozero__class_Ozero(_1469112)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469114, _1469112), hAPP(hAPP(c_COMBB(_1469112, _1469112, _1469114), c_Groups_Oabs__class_Oabs(_1469112)), _1469116)), _1469118))))], (15124 ^ _775828) ^ [_1029606, _1029608] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029606, _1029608) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029606), _1029608)), _1029608)))], (9199 ^ _775828) ^ [_922928, _922930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922928), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _922928), _922930)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _922928))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _922930))))], (2672 ^ _775828) ^ [_815449, _815451, _815453, _815455] : [-(c_Code__Numeral_Onat__of__aux(_815455, _815451) = c_Code__Numeral_Onat__of__aux(_815453, _815449)), _815455 = _815453, _815451 = _815449], (49100 ^ _775828) ^ [_1761780, _1761782, _1761784] : [-(_1761780 = c_List_Olist_ONil(_1761782)), -(c_List_Olast(_1761782, hAPP(hAPP(c_List_Olist_OCons(_1761782), _1761784), _1761780)) = c_List_Olast(_1761782, _1761780))], (12079 ^ _775828) ^ [_974975, _974977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _974975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _974977)), 12086 ^ _775828 : [(12093 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974975), _974977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _974975)), hAPP(c_Int_Onat, _974977))))], (12087 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _974975)), hAPP(c_Int_Onat, _974977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974975), _974977)))]]], (44635 ^ _775828) ^ [_1653116, _1653118, _1653120, _1653122] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653116, tc_HOL_Obool), hAPP(c_Set_Oimage(_1653118, tc_fun(_1653116, tc_HOL_Obool), _1653120), _1653122)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653118, tc_fun(_1653116, tc_HOL_Obool)), _1653122), _1653120))], (6586 ^ _775828) ^ [_880547, _880549, _880551] : [class_Orderings_Opreorder(_880547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880547), _880549), _880551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880547), _880551), _880549))], (48635 ^ _775828) ^ [_1751478, _1751480] : [-(_1751478 = c_List_Olist_ONil(_1751480)), -(hAPP(c_List_Ohd(_1751480), _1751478) = hAPP(hAPP(c_List_Onth(_1751480), _1751478), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23876 ^ _775828) ^ [_1193916, _1193918, _1193920, _1193922] : [class_Orderings_Olinorder(_1193916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193916), _1193918), _1193920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193916), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193916), _1193922), _1193918)), _1193920)))], (32879 ^ _775828) ^ [_1383932, _1383934, _1383936, _1383938, _1383940] : [hAPP(_1383936, _1383938) = _1383940, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383932, _1383934), _1383936), _1383938), _1383940) = _1383936)], (43848 ^ _775828) ^ [_1633458, _1633460, _1633462] : [class_Lattices_Olattice(_1633458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633458), _1633460)), -(hBOOL(hAPP(hAPP(c_member(_1633458), _1633462), _1633460))), -(c_Big__Operators_Olattice__class_OSup__fin(_1633458, hAPP(hAPP(c_Set_Oinsert(_1633458), _1633462), _1633460)) = hAPP(hAPP(c_Finite__Set_Ofold(_1633458, _1633458, c_Lattices_Osemilattice__sup__class_Osup(_1633458)), _1633462), _1633460))], (36673 ^ _775828) ^ [_1464946, _1464948, _1464950, _1464952, _1464954] : [c_Finite__Set_Ofolding__one__idem(_1464946, _1464948, _1464950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464946), _1464952)), -(_1464952 = c_Orderings_Obot__class_Obot(tc_fun(_1464946, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464946), _1464954)), -(_1464954 = c_Orderings_Obot__class_Obot(tc_fun(_1464946, tc_HOL_Obool))), -(hAPP(_1464950, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464946, tc_HOL_Obool)), _1464952), _1464954)) = hAPP(hAPP(_1464948, hAPP(_1464950, _1464952)), hAPP(_1464950, _1464954)))], (19740 ^ _775828) ^ [_1114902] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1114902) = c_Int_Opred(_1114902))], (20756 ^ _775828) ^ [_1132829] : [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, _1132829, 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, _1132829, 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))], (43110 ^ _775828) ^ [_1616521, _1616523, _1616525, _1616527, _1616529, _1616531] : [c_Finite__Set_Ofolding(_1616521, _1616523, _1616525, _1616527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616521), _1616529)), -(hAPP(_1616527, hAPP(hAPP(c_Set_Oinsert(_1616521), _1616531), _1616529)) = hAPP(c_Fun_Ocomp(_1616523, _1616523, _1616523, hAPP(_1616527, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616521, tc_HOL_Obool)), _1616529), hAPP(hAPP(c_Set_Oinsert(_1616521), _1616531), c_Orderings_Obot__class_Obot(tc_fun(_1616521, tc_HOL_Obool)))))), hAPP(_1616525, _1616531)))], (25337 ^ _775828) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48825 ^ _775828) ^ [_1755301, _1755303] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1755301), _1755303) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1755301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48831 ^ _775828 : [(48834 ^ _775828) ^ [] : [48830 ^ [_1755301, _1755303] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48832 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 48830 ^ [_1755301, _1755303]), hAPP(c_List_Oset(tc_Nat_Onat), _1755303))))]]], (44172 ^ _775828) ^ [_1640120, _1640122, _1640124, _1640126, _1640128, _1640130] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640120, tc_fun(_1640122, tc_fun(_1640124, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1640120, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_fun(_1640122, tc_fun(_1640124, tc_HOL_Obool)), _1640120), hAPP(c_COMBC(_1640122, tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_fun(_1640124, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640124, tc_fun(tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_fun(_1640124, tc_HOL_Obool)), _1640122), c_COMBC(_1640124, tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640124, tc_prod(_1640122, _1640124)), tc_fun(_1640124, tc_fun(tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_HOL_Obool)), _1640122), hAPP(c_COMBB(tc_prod(_1640122, _1640124), tc_fun(tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool), tc_HOL_Obool), _1640124), c_member(tc_prod(_1640122, _1640124)))), c_Product__Type_OPair(_1640122, _1640124))))), _1640126)), _1640128), _1640130)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640122, _1640124)), hAPP(hAPP(c_Product__Type_OPair(_1640122, _1640124), _1640128), _1640130)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640120, tc_fun(tc_prod(_1640122, _1640124), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1640120, tc_HOL_Obool))), _1640126))))], (42079 ^ _775828) ^ [_1592349, _1592351] : [-(c_Product__Type_Omap__pair(_1592349, _1592349, _1592351, _1592351, c_COMBI(_1592349), c_COMBI(_1592351)) = c_Fun_Oid(tc_prod(_1592349, _1592351)))], (18129 ^ _775828) ^ [_1086926, _1086928, _1086930, _1086932, _1086934] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1086926, _1086928), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1086930), _1086932))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086934)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1086926, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086928), _1086934)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1086930), _1086934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086928), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1086930, _1086934))), _1086932)))))], (47825 ^ _775828) ^ [_1731025, _1731027, _1731029, _1731031] : [-(hAPP(hAPP(c_List_Onth(_1731025), hAPP(hAPP(c_List_Oappend(_1731025), _1731027), hAPP(hAPP(c_List_Olist_OCons(_1731025), _1731029), _1731031))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731025)), _1731027)) = _1731029)], (51294 ^ _775828) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (4 ^ _775828) ^ [_775878, _775880] : [_775880 = _775878, -(_775878 = _775880)], (40457 ^ _775828) ^ [_1551614, _1551616, _1551618, _1551620, _1551622] : [c_Fun_Oinj__on(_1551614, _1551616, _1551618, c_Orderings_Otop__class_Otop(tc_fun(_1551614, tc_HOL_Obool))), 40460 ^ _775828 : [(40467 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551614, tc_HOL_Obool)), _1551620), _1551622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551616, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551614, _1551616, _1551618), _1551620)), hAPP(c_Set_Oimage(_1551614, _1551616, _1551618), _1551622))))], (40461 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551616, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551614, _1551616, _1551618), _1551620)), hAPP(c_Set_Oimage(_1551614, _1551616, _1551618), _1551622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551614, tc_HOL_Obool)), _1551620), _1551622)))]]], (2120 ^ _775828) ^ [_806777, _806779, _806781, _806783] : [-(c_Divides_Opdivmod(_806783, _806779) = c_Divides_Opdivmod(_806781, _806777)), _806783 = _806781, _806779 = _806777], (27810 ^ _775828) ^ [_1271470, _1271472, _1271474, _1271476] : [hBOOL(hAPP(c_Predicate_ODomainP(_1271470, _1271472, hAPP(hAPP(c_COMBC(_1271470, tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_fun(_1271472, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271472, tc_fun(tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_fun(_1271472, tc_HOL_Obool)), _1271470), c_COMBC(_1271472, tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271472, tc_prod(_1271470, _1271472)), tc_fun(_1271472, tc_fun(tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_HOL_Obool)), _1271470), hAPP(c_COMBB(tc_prod(_1271470, _1271472), tc_fun(tc_fun(tc_prod(_1271470, _1271472), tc_HOL_Obool), tc_HOL_Obool), _1271472), c_member(tc_prod(_1271470, _1271472)))), c_Product__Type_OPair(_1271470, _1271472)))), _1271474)), _1271476)), -(hBOOL(hAPP(hAPP(c_member(_1271470), _1271476), hAPP(c_Relation_ODomain(_1271470, _1271472), _1271474))))], (24384 ^ _775828) ^ [_1203782, _1203784, _1203786, _1203788, _1203790, _1203792] : [-(hAPP(c_Product__Type_Oapfst(_1203782, _1203784, _1203786, _1203788), hAPP(hAPP(c_Product__Type_OPair(_1203782, _1203786), _1203790), _1203792)) = hAPP(hAPP(c_Product__Type_OPair(_1203784, _1203786), hAPP(_1203788, _1203790)), _1203792))], (8486 ^ _775828) ^ [_912084] : [-(hBOOL(hAPP(_912084, 8493 ^ [_912084]))), 8487 ^ _775828 : [(8488 ^ _775828) ^ [_912136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912136)), hBOOL(hAPP(_912084, hAPP(c_Int_Onat, _912136)))]]], (30243 ^ _775828) ^ [_1327115] : [-(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)), _1327115), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (25343 ^ _775828) ^ [_1222855, _1222857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1222855)), hAPP(c_Code__Numeral_Oof__nat, _1222857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222855), _1222857)))], (41924 ^ _775828) ^ [_1588213, _1588215, _1588217, _1588219] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588215, _1588213), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1588213, tc_prod(_1588215, _1588213), 41920 ^ [_1588213, _1588215, _1588217, _1588219]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588215, tc_fun(_1588213, tc_HOL_Obool)), _1588217), _1588219))), hAPP(hAPP(c_Product__Type_OSigma(_1588215, _1588213), _1588217), _1588219))))], (45655 ^ _775828) ^ [_1676279, _1676281] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1676279), hAPP(c_List_Oset(_1676279), _1676281))))], (42810 ^ _775828) ^ [_1609626, _1609628, _1609630, _1609632, _1609634, _1609636] : [-(hAPP(c_Set_Oimage(_1609626, _1609628, hAPP(c_Fun_Ocomp(_1609630, _1609628, _1609626, _1609632), _1609634)), _1609636) = hAPP(c_Set_Oimage(_1609630, _1609628, _1609632), hAPP(c_Set_Oimage(_1609626, _1609630, _1609634), _1609636)))], (16571 ^ _775828) ^ [_1057584, _1057586, _1057588] : [class_Groups_Oordered__ab__group__add__abs(_1057584), -(hAPP(c_Groups_Oabs__class_Oabs(_1057584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057584), hAPP(c_Groups_Oabs__class_Oabs(_1057584), _1057586)), hAPP(c_Groups_Oabs__class_Oabs(_1057584), _1057588))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057584), hAPP(c_Groups_Oabs__class_Oabs(_1057584), _1057586)), hAPP(c_Groups_Oabs__class_Oabs(_1057584), _1057588)))], (51356 ^ _775828) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51346 ^ _775828) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (29903 ^ _775828) ^ [_1319716, _1319718, _1319720, _1319722, _1319724] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1319716, _1319718, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1319716)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1319716), hAPP(hAPP(c_COMBC(_1319716, 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)), _1319716), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1319720)), 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), _1319722)), _1319724))), c_Com_Ocom_OAss(_1319722, _1319724)), _1319720)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1319716), tc_HOL_Obool)))))], (44095 ^ _775828) ^ [_1638154, _1638156, _1638158, _1638160, _1638162, _1638164] : [hBOOL(hAPP(hAPP(c_member(_1638154), _1638156), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638158, tc_fun(_1638154, tc_HOL_Obool)), _1638160), _1638162))), -(hBOOL(hAPP(hAPP(c_member(_1638154), _1638156), hAPP(_1638162, _1638164)))), hBOOL(hAPP(hAPP(c_member(_1638158), _1638164), _1638160))], (26986 ^ _775828) ^ [_1252609, _1252611] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252609), _1252611)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252609)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252611))))], (1410 ^ _775828) ^ [_796071, _796073] : [-(class_Groups_Oordered__ab__semigroup__add(_796071)), _796073 = _796071, class_Groups_Oordered__ab__semigroup__add(_796073)], (10258 ^ _775828) ^ [_942035, _942037, _942039] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942035), _942037) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942035), _942039), -(_942037 = _942039)], (2312 ^ _775828) ^ [_809669, _809671, _809673, _809675, _809677, _809679] : [-(c_Nitpick_Otimes__frac(_809679, _809675, _809671) = c_Nitpick_Otimes__frac(_809677, _809673, _809669)), _809679 = _809677, _809675 = _809673, _809671 = _809669], (36437 ^ _775828) ^ [_1460167, _1460169, _1460171] : [class_Orderings_Olinorder(_1460167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460167), _1460169), _1460171)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460167, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1460167), _1460169), c_Orderings_Obot__class_Obot(tc_fun(_1460167, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1460167, _1460169, _1460171)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460167, _1460169), _1460171))], (29967 ^ _775828) ^ [_1321911] : [-(c_Transitive__Closure_Otrancl(_1321911, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1321911, _1321911), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1321911, _1321911), tc_HOL_Obool)))], (18751 ^ _775828) ^ [_1098122, _1098124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098124), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1098122, _1098124) = 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), _1098122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098124)))))], (10480 ^ _775828) ^ [_946433, _946435] : [class_Groups_Olinordered__ab__group__add(_946433), 10483 ^ _775828 : [(10490 ^ _775828) ^ [] : [_946435 = c_Groups_Ozero__class_Ozero(_946433), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946433), _946435), _946435) = c_Groups_Ozero__class_Ozero(_946433))], (10484 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946433), _946435), _946435) = c_Groups_Ozero__class_Ozero(_946433), -(_946435 = c_Groups_Ozero__class_Ozero(_946433))]]], (40179 ^ _775828) ^ [_1546076, _1546078] : [class_Orderings_Otop(_1546076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1546076), _1546078), c_Orderings_Otop__class_Otop(_1546076))))], (10354 ^ _775828) ^ [_944101] : [class_Rings_Olinordered__semidom(_944101), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944101), c_Groups_Ozero__class_Ozero(_944101)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944101), c_Groups_Oone__class_Oone(_944101)), c_Groups_Oone__class_Oone(_944101)))))], (43249 ^ _775828) ^ [_1619767, _1619769, _1619771, _1619773] : [-(c_New__Random__Sequence_Opos__map(_1619767, _1619769, _1619771, _1619773) = c_New__Random__Sequence_Opos__bind(_1619767, _1619769, _1619773, hAPP(c_Fun_Ocomp(_1619769, 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(_1619769))))), _1619767, c_New__Random__Sequence_Opos__single(_1619769)), _1619771)))], (48765 ^ _775828) ^ [_1754015, _1754017, _1754019, _1754021, _1754023] : [-(c_List_Olist_Olist__size(_1754015, _1754017, hAPP(hAPP(c_List_Omap(_1754019, _1754015), _1754021), _1754023)) = c_List_Olist_Olist__size(_1754019, hAPP(c_Fun_Ocomp(_1754015, tc_Nat_Onat, _1754019, _1754017), _1754021), _1754023))], (31859 ^ _775828) ^ [_1363920, _1363922] : [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), _1363920), _1363922)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1363920), _1363922)))], (42912 ^ _775828) ^ [_1611828, _1611830, _1611832, _1611834, _1611836, _1611838] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1611828, _1611830), _1611830, tc_prod(_1611832, _1611834), c_Product__Type_Osnd(_1611828, _1611830)), c_Product__Type_Omap__pair(_1611832, _1611828, _1611834, _1611830, _1611836, _1611838)) = hAPP(c_Fun_Ocomp(_1611834, _1611830, tc_prod(_1611832, _1611834), _1611838), c_Product__Type_Osnd(_1611832, _1611834)))], (44254 ^ _775828) ^ [_1643031, _1643033, _1643035, _1643037, _1643039, _1643041] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643031, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1643033, _1643031, _1643035), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643037, tc_fun(_1643033, tc_HOL_Obool)), _1643039), _1643041))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643037, tc_fun(_1643031, tc_HOL_Obool)), _1643039), hAPP(hAPP(c_COMBB(tc_fun(_1643033, tc_HOL_Obool), tc_fun(_1643031, tc_HOL_Obool), _1643037), c_Relation_OImage(_1643033, _1643031, _1643035)), _1643041)))))], (10876 ^ _775828) ^ [_953812, _953814, _953816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953812), _953814)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953812), _953816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953814), _953816)))], (43218 ^ _775828) ^ [_1619052, _1619054, _1619056, _1619058, _1619060, _1619062] : [c_Finite__Set_Ofolding__idem(_1619052, _1619054, _1619056, _1619058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619052), _1619060)), -(hAPP(_1619058, hAPP(hAPP(c_Set_Oinsert(_1619052), _1619062), _1619060)) = hAPP(c_Fun_Ocomp(_1619054, _1619054, _1619054, hAPP(_1619058, _1619060)), hAPP(_1619056, _1619062)))], (16162 ^ _775828) ^ [_1050084, _1050086, _1050088, _1050090, _1050092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050084), _1050086)), -(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), _1050086), _1050088)), _1050090)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050084), _1050088)), _1050092)) = 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), _1050086), _1050084)), _1050088)), _1050090)), _1050092))], (42055 ^ _775828) ^ [_1591613, _1591615, _1591617, _1591619, _1591621, _1591623] : [hAPP(c_Set_Oimage(_1591613, _1591615, _1591617), c_Orderings_Otop__class_Otop(tc_fun(_1591613, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1591615, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1591619, _1591621, _1591623), c_Orderings_Otop__class_Otop(tc_fun(_1591619, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1591621, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1591613, _1591619), tc_prod(_1591615, _1591621), c_Product__Type_Omap__pair(_1591613, _1591615, _1591619, _1591621, _1591617, _1591623)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1591613, _1591619), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1591615, _1591621), tc_HOL_Obool)))], (30153 ^ _775828) ^ [_1325513, _1325515] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325513, _1325515) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325513), _1325515))], (11092 ^ _775828) ^ [_957465, _957467, _957469, _957471, _957473] : [c_Natural_Oevaln(_957465, _957467, _957469, _957471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957469), _957473)), -(c_Natural_Oevaln(_957465, _957467, _957473, _957471))], (40123 ^ _775828) ^ [_1545147, _1545149] : [class_Lattices_Obounded__lattice__top(_1545147), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545147), c_Orderings_Otop__class_Otop(_1545147)), _1545149) = _1545149)], (17551 ^ _775828) ^ [_1076278, _1076280] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076278) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076280), 17554 ^ _775828 : [(17557 ^ _775828) ^ [] : [-(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), _1076280))))], (17555 ^ _775828) ^ [] : [-(_1076278 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076280)))]]], (27475 ^ _775828) ^ [_1263909] : [-(hAPP(c_Relation_Oconverse(_1263909, _1263909), c_Relation_OId(_1263909)) = c_Relation_OId(_1263909))], (51140 ^ _775828) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (20132 ^ _775828) ^ [_1121667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1121667)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121667), c_Int_OPls)))], (50399 ^ _775828) ^ [_1788909, _1788911, _1788913] : [_1788911 = _1788913, -(hAPP(c_List_Orev(_1788909), _1788911) = hAPP(c_List_Orev(_1788909), _1788913))], (41472 ^ _775828) ^ [_1578312, _1578314, _1578316, _1578318] : [_1578312 = c_Orderings_Obot__class_Obot(tc_fun(_1578314, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1578316, _1578314), _1578316, c_Product__Type_Ofst(_1578316, _1578314)), hAPP(hAPP(c_Product__Type_OSigma(_1578316, _1578314), _1578318), hAPP(c_COMBK(tc_fun(_1578314, tc_HOL_Obool), _1578316), _1578312))) = c_Orderings_Obot__class_Obot(tc_fun(_1578316, tc_HOL_Obool)))], (44377 ^ _775828) ^ [_1646473, _1646475, _1646477, _1646479] : [class_Complete__Lattice_Ocomplete__lattice(_1646473), -(_1646475 = c_Orderings_Obot__class_Obot(tc_fun(_1646477, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646477, _1646473), _1646475), hAPP(c_COMBK(_1646473, _1646477), _1646479)) = _1646479)], (9803 ^ _775828) ^ [_933866, _933868, _933870, _933872, _933874] : [class_Rings_Olinordered__semiring__strict(_933866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933866), _933868), _933870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933866), _933872), _933874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933866), c_Groups_Ozero__class_Ozero(_933866)), _933868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933866), c_Groups_Ozero__class_Ozero(_933866)), _933872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933866), _933868), _933872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933866), _933870), _933874))))], (49616 ^ _775828) ^ [_1773420, _1773422, _1773424, _1773426, _1773428] : [class_Orderings_Olinorder(_1773420), -(c_List_Olinorder__class_Osorted(_1773420, hAPP(hAPP(c_List_Omap(_1773422, _1773420), _1773424), hAPP(c_List_Ofilter(_1773422, hAPP(hAPP(c_COMBC(_1773422, _1773420, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1773420, tc_fun(_1773420, tc_HOL_Obool), _1773422), c_fequal), _1773424)), hAPP(_1773426, _1773428))), _1773428))))], (29605 ^ _775828) ^ [_1313246, _1313248] : [hAPP(c_Set_OCollect(_1313246), _1313248) = c_Orderings_Obot__class_Obot(tc_fun(_1313246, tc_HOL_Obool)), 29608 ^ _775828 : [(29609 ^ _775828) ^ [_1313331] : [hBOOL(hAPP(_1313248, _1313331))]]], (22376 ^ _775828) ^ [_1164902, _1164904, _1164906, _1164908, _1164910, _1164912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1164902, tc_fun(_1164904, tc_HOL_Obool))), _1164906), _1164908)), hBOOL(hAPP(hAPP(_1164906, _1164910), _1164912)), -(hBOOL(hAPP(hAPP(_1164908, _1164910), _1164912)))], (36587 ^ _775828) ^ [_1463294] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1463294)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1463294)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1463294)))], (20396 ^ _775828) ^ [_1126346, _1126348] : [class_Int_Onumber__ring(_1126346), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126346), hAPP(c_Int_Onumber__class_Onumber__of(_1126346), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1126348) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126346), _1126348), _1126348))], (50603 ^ _775828) ^ [_1794634, _1794636, _1794638, _1794640, _1794642] : [-(c_List_OtakeWhile(_1794634, _1794636, hAPP(hAPP(c_List_Omap(_1794638, _1794634), _1794640), _1794642)) = hAPP(hAPP(c_List_Omap(_1794638, _1794634), _1794640), c_List_OtakeWhile(_1794638, hAPP(c_Fun_Ocomp(_1794634, tc_HOL_Obool, _1794638, _1794636), _1794640), _1794642)))], (36519 ^ _775828) ^ [_1461899, _1461901] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1461899), _1461901)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1461901), _1461899)))], (29281 ^ _775828) ^ [_1306856, _1306858] : [-(hAPP(c_Relation_ORange(_1306856, _1306858), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1306856, _1306858), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1306858, tc_HOL_Obool)))], (34601 ^ _775828) ^ [_1421172, _1421174, _1421176] : [class_Lattices_Olattice(_1421172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421172), _1421174)), 34608 ^ _775828 : [(34615 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421172, tc_HOL_Obool)), _1421174), hAPP(hAPP(c_Set_Oinsert(_1421172), _1421176), c_Orderings_Obot__class_Obot(tc_fun(_1421172, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1421172, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1421172, hAPP(hAPP(c_Set_Oinsert(_1421172), _1421176), _1421174)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421172), _1421176), c_Big__Operators_Olattice__class_OInf__fin(_1421172, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421172, tc_HOL_Obool)), _1421174), hAPP(hAPP(c_Set_Oinsert(_1421172), _1421176), c_Orderings_Obot__class_Obot(tc_fun(_1421172, tc_HOL_Obool)))))))], (34609 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421172, tc_HOL_Obool)), _1421174), hAPP(hAPP(c_Set_Oinsert(_1421172), _1421176), c_Orderings_Obot__class_Obot(tc_fun(_1421172, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1421172, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1421172, hAPP(hAPP(c_Set_Oinsert(_1421172), _1421176), _1421174)) = _1421176)]]], (40349 ^ _775828) ^ 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_1305332)), hAPP(hAPP(c_Product__Type_OPair(_1305332, _1305332), _1305334), _1305336)), _1305338)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305332, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1305332), _1305334), hAPP(hAPP(c_Set_Oinsert(_1305332), _1305336), c_Orderings_Obot__class_Obot(tc_fun(_1305332, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1305332), _1305338)))], (51132 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (15786 ^ _775828) ^ [_1042007, _1042009, _1042011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042007), _1042009)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042009), _1042011)), _1042007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042009), _1042007)), _1042011))], (19010 ^ _775828) ^ [_1103083, _1103085, _1103087, _1103089] : [-(_1103083 = _1103085), hAPP(c_Product__Type_Ofst(_1103087, _1103089), _1103083) = hAPP(c_Product__Type_Ofst(_1103087, _1103089), _1103085), hAPP(c_Product__Type_Osnd(_1103087, _1103089), _1103083) = hAPP(c_Product__Type_Osnd(_1103087, _1103089), _1103085)], (19190 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (47097 ^ _775828) ^ [_1713974, _1713976, _1713978, _1713980] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713974), tc_List_Olist(_1713974))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713974), tc_List_Olist(_1713974)), _1713976), _1713978)), c_List_Olex(_1713974, _1713980))), 47100 ^ _775828 : [(47103 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713974)), _1713976) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713974)), _1713978))], (47101 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713974), tc_List_Olist(_1713974))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713974), tc_List_Olist(_1713974)), _1713976), _1713978)), c_List_Olexord(_1713974, _1713980))))]]], (21220 ^ _775828) ^ [_1143488, _1143490] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1143488), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1143490))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1143488), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143490))), 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))))], (35469 ^ _775828) ^ [_1442210, _1442212] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442210, _1442212) = 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), _1442210), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1442212))))], (28195 ^ _775828) ^ [_1281337, _1281339, _1281341, _1281343] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281337, tc_HOL_Obool)), _1281339), _1281341)), _1281343) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281337, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281337, tc_HOL_Obool)), _1281339), _1281343)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281337, tc_HOL_Obool)), _1281341), _1281343)))], (16477 ^ _775828) ^ [_1056152, _1056154, _1056156] : [class_Int_Onumber__ring(_1056152), class_Int_Oring__char__0(_1056152), 16484 ^ _775828 : [(16491 ^ _775828) ^ [] : [_1056154 = _1056156, -(hAPP(c_Int_Onumber__class_Onumber__of(_1056152), _1056154) = hAPP(c_Int_Onumber__class_Onumber__of(_1056152), _1056156))], (16485 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1056152), _1056154) = hAPP(c_Int_Onumber__class_Onumber__of(_1056152), _1056156), -(_1056154 = _1056156)]]], (5751 ^ _775828) ^ [_867477, _867479, _867481, _867483] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_867477), _867479), _867481)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_867477), _867479), _867483)), -(_867483 = _867481)], (7725 ^ _775828) ^ [_899084, _899086, _899088] : [7726 ^ _775828 : [(7729 ^ _775828) ^ [] : [_899086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7727 ^ _775828) ^ [] : [_899084 = _899088]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _899084), _899086) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _899088), _899086))], (7289 ^ _775828) ^ [_892031, _892033] : [class_Rings_Olinordered__ring(_892031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_892031), _892033), _892033)), c_Groups_Ozero__class_Ozero(_892031)))], (49550 ^ _775828) ^ [_1771731] : [-(c_List_Otranspose(_1771731, c_List_Olist_ONil(tc_List_Olist(_1771731))) = c_List_Olist_ONil(tc_List_Olist(_1771731)))], (12315 ^ _775828) ^ [_978901, _978903, _978905, _978907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978901, tc_HOL_Obool)), _978903), _978905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978901, tc_HOL_Obool)), _978905), _978907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978901, tc_HOL_Obool)), _978903), _978907)))], (31831 ^ _775828) ^ [_1363237, _1363239, _1363241, _1363243] : [-(c_Wellfounded_Owf(_1363237, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1363237, _1363237)), hAPP(hAPP(c_Product__Type_OPair(_1363237, _1363237), _1363239), _1363241)), _1363243))), c_Wellfounded_Owf(_1363237, _1363243), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1363237, _1363237)), hAPP(hAPP(c_Product__Type_OPair(_1363237, _1363237), _1363241), _1363239)), c_Transitive__Closure_Ortrancl(_1363237, _1363243))))], (44190 ^ _775828) ^ [_1641332, _1641334, _1641336, _1641338] : [hBOOL(hAPP(hAPP(c_member(_1641334), _1641338), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641332, tc_fun(_1641334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1641332, tc_HOL_Obool))), _1641336))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641332, tc_fun(_1641334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1641332, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1641334, tc_HOL_Obool), tc_fun(_1641334, tc_HOL_Obool), _1641332), hAPP(c_COMBC(_1641334, tc_fun(_1641334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1641334))), _1641336)), _1641338)))], (39636 ^ _775828) ^ [_1533663, _1533665, _1533667, _1533669, _1533671] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533663, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533665, tc_fun(_1533663, tc_HOL_Obool)), _1533667), _1533669)), _1533671) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533665, tc_fun(_1533663, tc_HOL_Obool)), _1533667), hAPP(hAPP(c_COMBC(_1533665, tc_fun(_1533663, tc_HOL_Obool), tc_fun(_1533663, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533663, tc_HOL_Obool), tc_fun(tc_fun(_1533663, tc_HOL_Obool), tc_fun(_1533663, tc_HOL_Obool)), _1533665), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533663, tc_HOL_Obool))), _1533669)), _1533671)))], (13182 ^ _775828) ^ [_993924, _993926, _993928, _993930, _993932] : [c_Com_Ocom_OLocal(_993924, _993926, _993928) = c_Com_Ocom_OSemi(_993930, _993932)], (36871 ^ _775828) ^ [_1468545, _1468547, _1468549] : [-(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), _1468545)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1468547))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468549))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468549), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468545), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1468549), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1468547)))))], (49558 ^ _775828) ^ [_1772034, _1772036, _1772038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1772036))), c_List_Otranspose(_1772036, _1772038)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1772036)), c_List_Otranspose(_1772036, _1772038)), _1772034) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1772036), _1772036), hAPP(hAPP(c_COMBC(tc_List_Olist(_1772036), tc_Nat_Onat, _1772036), c_List_Onth(_1772036)), _1772034)), hAPP(c_List_Ofilter(tc_List_Olist(_1772036), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1772036)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772034)), c_Nat_Osize__class_Osize(tc_List_Olist(_1772036)))), _1772038)))], (44936 ^ _775828) ^ [_1660111, _1660113, _1660115] : [class_Complete__Lattice_Ocomplete__lattice(_1660111), -(c_Complete__Lattice_OInf__class_OInf(_1660111, hAPP(hAPP(c_Set_Oinsert(_1660111), _1660113), hAPP(hAPP(c_Set_Oinsert(_1660111), _1660115), c_Orderings_Obot__class_Obot(tc_fun(_1660111, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1660111), _1660113), _1660115))], (14626 ^ _775828) ^ [_1020598, _1020600] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1020598), _1020600) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14627 ^ _775828 : [(14636 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020598), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020600), _1020598))], (14630 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020598), _1020600))], (14628 ^ _775828) ^ [] : [_1020600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (34715 ^ _775828) ^ [_1423556, _1423558, _1423560] : [class_Orderings_Olinorder(_1423556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423556), _1423558)), -(_1423558 = c_Orderings_Obot__class_Obot(tc_fun(_1423556, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423556), _1423560)), -(_1423560 = c_Orderings_Obot__class_Obot(tc_fun(_1423556, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423556, tc_HOL_Obool)), _1423558), _1423560) = c_Orderings_Obot__class_Obot(tc_fun(_1423556, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1423556, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423556, tc_HOL_Obool)), _1423558), _1423560)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1423556), c_Big__Operators_Olinorder__class_OMin(_1423556, _1423558)), c_Big__Operators_Olinorder__class_OMin(_1423556, _1423560)))], (14602 ^ _775828) ^ [_1020247, _1020249, _1020251] : [class_Divides_Osemiring__div(_1020247), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020247), c_Divides_Odiv__class_Omod(_1020247, _1020249, _1020251)), _1020251) = c_Groups_Ozero__class_Ozero(_1020247))], (29533 ^ _775828) ^ [_1311663, _1311665, _1311667] : [c_Orderings_Obot__class_Obot(tc_fun(_1311663, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1311663), _1311665), _1311667)], (41424 ^ _775828) ^ [_1577047, _1577049, _1577051, _1577053] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1577047, _1577049)), hAPP(hAPP(c_Product__Type_OSigma(_1577047, _1577049), hAPP(hAPP(c_Set_Oinsert(_1577047), _1577051), c_Orderings_Obot__class_Obot(tc_fun(_1577047, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1577049, tc_HOL_Obool), _1577047), _1577053))) = hAPP(c_Finite__Set_Ocard(_1577049), _1577053))], (44413 ^ _775828) ^ [_1647770, _1647772, _1647774, _1647776, _1647778] : [class_Complete__Lattice_Ocomplete__lattice(_1647770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647772, tc_HOL_Obool)), _1647774), _1647776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1647770), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647772, _1647770), _1647776), _1647778)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647772, _1647770), _1647774), _1647778))))], (24608 ^ _775828) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (27272 ^ _775828) ^ [_1258801] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1258801) = 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), _1258801), c_Int_Onat)))))], (23560 ^ _775828) ^ [_1187918, _1187920, _1187922, _1187924, _1187926] : [hBOOL(hAPP(hAPP(_1187918, _1187920), _1187922)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1187924, _1187926, tc_HOL_Obool), _1187918), hAPP(hAPP(c_Product__Type_OPair(_1187924, _1187926), _1187920), _1187922))))], (42387 ^ _775828) ^ [_1598978, _1598980, _1598982, _1598984] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1598978), _1598980))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598982), hAPP(c_Set_Oimage(_1598978, _1598982, _1598984), _1598980))), 42395 ^ _775828 : [(42398 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1598978), hAPP(c_Set_OCollect(_1598978), hAPP(hAPP(c_COMBS(_1598978, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1598978), c_fconj), hAPP(hAPP(c_COMBC(_1598978, tc_fun(_1598978, tc_HOL_Obool), tc_HOL_Obool), c_member(_1598978)), _1598980))), hAPP(hAPP(c_COMBC(_1598978, _1598982, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1598982, tc_fun(_1598982, tc_HOL_Obool), _1598978), c_fequal), _1598984)), hAPP(_1598984, 42394 ^ [_1598978, _1598980, _1598982, _1598984]))))))], (42396 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598978), 42394 ^ [_1598978, _1598980, _1598982, _1598984]), _1598980)))]]], (26760 ^ _775828) ^ [_1248718, _1248720, _1248722, _1248724] : [class_Orderings_Oorder(_1248718), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1248718, 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)))), _1248720), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248718), hAPP(_1248720, _1248722)), hAPP(_1248720, _1248724)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248722), _1248724)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1248724), _1248722)))], (12913 ^ _775828) ^ [_989019, _989021, _989023, _989025, _989027, _989029] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989019), _989021)), _989023) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989025), _989027)), _989029), 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), _989025), _989027)), _989029))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _989029), _989025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989023)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989025), _989019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989021), _989027)))], (2024 ^ _775828) ^ [_805327, _805329] : [_805329 = _805327, -(c_Nat_Osemiring__1__class_ONats(_805329) = c_Nat_Osemiring__1__class_ONats(_805327))], (23016 ^ _775828) ^ [_1176428, _1176430, _1176432, _1176434] : [class_Fields_Olinordered__field(_1176428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176428), c_Groups_Ozero__class_Ozero(_1176428)), _1176430)), 23023 ^ _775828 : [(23030 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176428), _1176432), _1176430)), _1176434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176428), _1176432), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176428), _1176434), _1176430))))], (23024 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176428), _1176432), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176428), _1176434), _1176430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176428), _1176432), _1176430)), _1176434)))]]], (28723 ^ _775828) ^ [_1292171, _1292173, _1292175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292171, tc_HOL_Obool)), _1292173), _1292175)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292171, tc_HOL_Obool)), _1292173), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292171, tc_HOL_Obool)), _1292175), _1292173)) = _1292175)], (39762 ^ _775828) ^ [_1537069, _1537071, _1537073, _1537075, _1537077] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537069, tc_fun(_1537071, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1537069), _1537073), _1537075)), _1537077) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537071, tc_HOL_Obool)), hAPP(_1537077, _1537073)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537069, tc_fun(_1537071, tc_HOL_Obool)), _1537075), _1537077)))], (29379 ^ _775828) ^ [_1308608, _1308610, _1308612] : [hBOOL(hAPP(hAPP(c_member(_1308608), _1308610), _1308612)), -(hAPP(hAPP(c_Set_Oinsert(_1308608), _1308610), _1308612) = _1308612)], (46019 ^ _775828) ^ [_1684459, _1684461, _1684463, _1684465] : [hBOOL(hAPP(c_List_Odistinct(_1684459), _1684461)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1684459, _1684463)), hAPP(hAPP(c_List_Ozip(_1684459, _1684463), _1684461), _1684465))))], (18545 ^ _775828) ^ [_1094754] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1094754) = 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)))], (23474 ^ _775828) ^ [_1186029, _1186031, _1186033, _1186035, _1186037] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186029, _1186031, _1186033), _1186035), _1186037) = hAPP(hAPP(_1186035, hAPP(c_Product__Type_Ofst(_1186029, _1186031), _1186037)), hAPP(c_Product__Type_Osnd(_1186029, _1186031), _1186037)))], (49106 ^ _775828) ^ [_1761834, _1761836, _1761838] : [_1761834 = c_List_Olist_ONil(_1761836), -(c_List_Olast(_1761836, hAPP(hAPP(c_List_Olist_OCons(_1761836), _1761838), _1761834)) = _1761838)], (29589 ^ _775828) ^ [_1312866, _1312868] : [-(hAPP(c_Relation_ODomain(_1312866, _1312868), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1312866, _1312868), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1312866, tc_HOL_Obool)))], (50445 ^ _775828) ^ [_1789737, _1789739] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1789737), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1789737))), c_List_Otranspose(_1789737, _1789739)))))], (12741 ^ _775828) ^ [_986174, _986176] : [class_Rings_Olinordered__idom(_986174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986174), c_Groups_Ozero__class_Ozero(_986174)), _986176)), -(c_Groups_Osgn__class_Osgn(_986174, _986176) = c_Groups_Oone__class_Oone(_986174))], (33831 ^ _775828) ^ [_1404509, _1404511, _1404513] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404509, tc_HOL_Obool)), _1404511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404509, tc_HOL_Obool)), _1404511), _1404513)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404509, tc_HOL_Obool)), _1404511), _1404513))], (41334 ^ _775828) ^ [_1574484, _1574486, _1574488] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1574484, _1574486), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1574484, _1574486), _1574488), hAPP(c_COMBK(tc_fun(_1574486, tc_HOL_Obool), _1574484), c_Orderings_Otop__class_Otop(tc_fun(_1574486, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1574484, _1574486), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1574484, tc_HOL_Obool)), _1574488)), hAPP(c_COMBK(tc_fun(_1574486, tc_HOL_Obool), _1574484), c_Orderings_Otop__class_Otop(tc_fun(_1574486, tc_HOL_Obool)))))], (40935 ^ _775828) ^ [_1563695, _1563697, _1563699, _1563701, _1563703, _1563705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563695, _1563695)), hAPP(hAPP(c_Product__Type_OPair(_1563695, _1563695), _1563697), _1563699)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1563695, _1563695), tc_HOL_Obool), _1563701), _1563703))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563695, _1563695)), hAPP(hAPP(c_Product__Type_OPair(_1563695, _1563695), _1563699), _1563705)), _1563703)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563695, _1563695)), hAPP(hAPP(c_Product__Type_OPair(_1563695, _1563695), _1563697), _1563705)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1563695, _1563695), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1563701)), _1563703))))], (4794 ^ _775828) ^ [_849074, _849076, _849078, _849080] : [-(c_List_Olist__update(_849080, _849076) = c_List_Olist__update(_849078, _849074)), _849080 = _849078, _849076 = _849074], (19388 ^ _775828) ^ [_1109091] : [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), _1109091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1109091)))], (49479 ^ _775828) ^ [_1769471, _1769473, _1769475] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1769471, tc_HOL_Obool)), hAPP(c_List_Oset(_1769471), _1769473)), hAPP(hAPP(c_Set_Oinsert(_1769471), _1769475), c_Orderings_Obot__class_Obot(tc_fun(_1769471, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1769471), hAPP(c_List_Ofilter(_1769471, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1769471), c_fNot), hAPP(hAPP(c_COMBC(_1769471, _1769471, tc_HOL_Obool), c_fequal), _1769475))), _1769473)))], (49726 ^ _775828) ^ [_1775499, _1775501, _1775503, _1775505] : [class_Orderings_Olinorder(_1775499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1775499), _1775501), _1775503)), c_List_Olinorder__class_Osorted(_1775499, hAPP(hAPP(c_List_Olist_OCons(_1775499), _1775503), _1775505)), -(c_List_Olinorder__class_Osorted(_1775499, hAPP(hAPP(c_List_Olist_OCons(_1775499), _1775501), hAPP(hAPP(c_List_Olist_OCons(_1775499), _1775503), _1775505))))], (9739 ^ _775828) ^ [_932636, _932638, _932640, _932642] : [class_Rings_Olinordered__semiring(_932636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932636), _932638), _932640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932636), _932638), _932642))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932636), c_Groups_Ozero__class_Ozero(_932636)), _932638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932636), _932640), _932642)))], (29427 ^ _775828) ^ [_1309599, _1309601, _1309603] : [class_Orderings_Obot(_1309599), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1309601, _1309599)), _1309603) = c_Orderings_Obot__class_Obot(_1309599))], (42786 ^ _775828) ^ [_1609007, _1609009, _1609011, _1609013, _1609015, _1609017, _1609019] : [hAPP(c_Fun_Ocomp(_1609007, _1609009, _1609011, _1609013), _1609015) = _1609017, -(hAPP(_1609013, hAPP(_1609015, _1609019)) = hAPP(_1609017, _1609019))], (38998 ^ _775828) ^ [_1518201, _1518203, _1518205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518201), _1518203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518201, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1518201, _1518201, _1518205), _1518203)), _1518203)), c_Fun_Oinj__on(_1518201, _1518201, _1518205, _1518203), -(hAPP(c_Set_Oimage(_1518201, _1518201, _1518205), _1518203) = _1518203)], (35725 ^ _775828) ^ [_1446644, _1446646, _1446648] : [class_Orderings_Olinorder(_1446644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446644), _1446646), _1446648)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446644, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1446644), _1446646), c_Orderings_Obot__class_Obot(tc_fun(_1446644, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1446644, _1446646, _1446648)) = c_SetInterval_Oord__class_OatLeastAtMost(_1446644, _1446646, _1446648))], (36511 ^ _775828) ^ [_1461748] : [-(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)), _1461748))))], (23554 ^ _775828) ^ [_1187747, _1187749, _1187751, _1187753, _1187755, _1187757, _1187759] : [hBOOL(hAPP(hAPP(c_member(_1187747), _1187749), hAPP(hAPP(_1187751, _1187753), _1187755))), -(hBOOL(hAPP(hAPP(c_member(_1187747), _1187749), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1187757, _1187759, tc_fun(_1187747, tc_HOL_Obool)), _1187751), hAPP(hAPP(c_Product__Type_OPair(_1187757, _1187759), _1187753), _1187755)))))], (27066 ^ _775828) ^ [_1254045, _1254047] : [-(_1254045 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254047), _1254045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254047)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254045))))], (45824 ^ _775828) ^ [_1680171, _1680173, _1680175] : [hBOOL(hAPP(c_List_Odistinct(_1680171), hAPP(hAPP(c_List_Omap(tc_prod(_1680171, _1680173), _1680171), c_Product__Type_Ofst(_1680171, _1680173)), _1680175))), -(c_Map_Oran(_1680171, _1680173, c_Map_Omap__of(_1680171, _1680173, _1680175)) = hAPP(c_Set_Oimage(tc_prod(_1680171, _1680173), _1680173, c_Product__Type_Osnd(_1680171, _1680173)), hAPP(c_List_Oset(tc_prod(_1680171, _1680173)), _1680175)))], (23584 ^ _775828) ^ [_1188456, _1188458, _1188460, _1188462, _1188464, _1188466] : [-(hAPP(c_Product__Type_Oapsnd(_1188456, _1188458, _1188460, _1188462), hAPP(hAPP(c_Product__Type_OPair(_1188460, _1188456), _1188464), _1188466)) = hAPP(hAPP(c_Product__Type_OPair(_1188460, _1188458), _1188464), hAPP(_1188462, _1188466)))], (17773 ^ _775828) ^ [_1080221, _1080223, _1080225, _1080227] : [class_Rings_Olinordered__semidom(_1080221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080221), _1080223), _1080225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080221), c_Groups_Ozero__class_Ozero(_1080221)), _1080223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080221), hAPP(hAPP(c_Power_Opower__class_Opower(_1080221), _1080223), _1080227)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080221), _1080225), _1080227))))], (13781 ^ _775828) ^ [_1005361, _1005363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005361), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13784 ^ _775828 : [(13787 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005361), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005363, _1005361))))], (13785 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005363, _1005361)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40804 ^ _775828) ^ [_1560600, _1560602, _1560604] : [-(hAPP(c_Set_Ovimage(_1560600, _1560602, _1560604), c_Orderings_Otop__class_Otop(tc_fun(_1560602, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560600, tc_HOL_Obool)))], (36395 ^ _775828) ^ [_1459366, _1459368, _1459370] : [class_Groups_Oordered__ab__group__add(_1459366), -(hAPP(c_Set_Oimage(_1459366, _1459366, c_Groups_Ouminus__class_Ouminus(_1459366)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1459366, _1459368, _1459370)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459366, hAPP(c_Groups_Ouminus__class_Ouminus(_1459366), _1459370)), hAPP(c_Groups_Ouminus__class_Ouminus(_1459366), _1459368)))], (39387 ^ _775828) ^ [_1526752, _1526754, _1526756, _1526758, _1526760] : [c_Fun_Oinj__on(_1526752, _1526754, _1526756, _1526758), hBOOL(hAPP(hAPP(c_member(_1526754), _1526760), hAPP(c_Set_Oimage(_1526752, _1526754, _1526756), _1526758))), -(hAPP(_1526756, hAPP(c_Fun_Othe__inv__into(_1526752, _1526754, _1526758, _1526756), _1526760)) = _1526760)], (21642 ^ _775828) ^ [_1150577, _1150579] : [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(_1150577))), 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)), _1150579)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150577)), hAPP(c_Nat_OSuc, _1150579))))], (22884 ^ _775828) ^ [_1174012, _1174014, _1174016] : [class_Fields_Olinordered__field(_1174012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174012), _1174014), c_Groups_Ozero__class_Ozero(_1174012))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174012), c_Groups_Ozero__class_Ozero(_1174012)), _1174016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174012), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174012), _1174014), _1174016)), c_Groups_Ozero__class_Ozero(_1174012))))], (22196 ^ _775828) ^ [_1161607, _1161609] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161607), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161609)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161607)) = 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), _1161609), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161607)))), 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)))], (11939 ^ _775828) ^ [_972377, _972379, _972381] : [class_Rings_Olinordered__ring(_972377), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972377), c_Groups_Ozero__class_Ozero(_972377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972377), _972379), _972379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972377), _972381), _972381)))))], (51474 ^ _775828) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (47711 ^ _775828) ^ [_1728203, _1728205, _1728207, _1728209, _1728211, _1728213] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728203)), _1728205) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728207)), _1728209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728203, tc_HOL_Obool)), hAPP(c_List_Oset(_1728203), _1728205)), _1728211)), -(c_Map_Orestrict__map(_1728203, _1728207, c_Map_Omap__upds(_1728203, _1728207, _1728213, _1728205, _1728209), _1728211) = c_Map_Omap__upds(_1728203, _1728207, c_Map_Orestrict__map(_1728203, _1728207, _1728213, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1728203, tc_HOL_Obool)), _1728211), hAPP(c_List_Oset(_1728203), _1728205))), _1728205, _1728209))], (9767 ^ _775828) ^ [_933174, _933176, _933178, _933180] : [class_Rings_Olinordered__semiring(_933174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933174), _933176), _933178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933174), _933180), _933178))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933174), c_Groups_Ozero__class_Ozero(_933174)), _933178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933174), _933176), _933180)))], (25287 ^ _775828) ^ [_1221903, _1221905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1221903), _1221905)), -(c_Quickcheck_Obeyond(_1221903, _1221905) = _1221905)], (21366 ^ _775828) ^ [_1145767, _1145769, _1145771] : [class_Fields_Ofield__inverse__zero(_1145767), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145767), c_Groups_Oone__class_Oone(_1145767)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145767), _1145769), _1145771)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1145767), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145767), c_Groups_Oone__class_Oone(_1145767)), _1145769)), _1145771))], (15340 ^ _775828) ^ [_1033630] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1033630) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3646 ^ _775828) ^ [_831256, _831258] : [_831258 = _831256, -(c_New__Random__Sequence_Oneg__single(_831258) = c_New__Random__Sequence_Oneg__single(_831256))], (30505 ^ _775828) ^ [_1333252] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1333252)), -(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)), _1333252))))], (38302 ^ _775828) ^ [_1503242, _1503244] : [class_Orderings_Olinorder(_1503242), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1503242, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1503242), _1503244)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503242), _1503244))], (24088 ^ _775828) ^ [_1197583, _1197585, _1197587, _1197589] : [class_Orderings_Olinorder(_1197583), 24091 ^ _775828 : [(24092 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197583), _1197585), _1197587)), _1197589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), _1197585), _1197589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), _1197587), _1197589)))], (24102 ^ _775828) ^ [] : [24103 ^ _775828 : [(24106 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), _1197587), _1197589))], (24104 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), _1197585), _1197589))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197583), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197583), _1197585), _1197587)), _1197589)))]]], (16789 ^ _775828) ^ [_1061782, _1061784] : [class_Groups_Oordered__ab__group__add__abs(_1061782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061782), c_Groups_Ozero__class_Ozero(_1061782)), _1061784)), -(hAPP(c_Groups_Oabs__class_Oabs(_1061782), _1061784) = _1061784)], (43329 ^ _775828) ^ [_1622310, _1622312, _1622314, _1622316, _1622318, _1622320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622310, tc_HOL_Obool)), _1622312), _1622314)), 43335 ^ _775828 : [(43338 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622316, tc_HOL_Obool)), hAPP(_1622318, 43334 ^ [_1622310, _1622312, _1622314, _1622316, _1622318, _1622320])), hAPP(_1622320, 43334 ^ [_1622310, _1622312, _1622314, _1622316, _1622318, _1622320])))], (43336 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622310), 43334 ^ [_1622310, _1622312, _1622314, _1622316, _1622318, _1622320]), _1622312)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1622310, _1622316), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1622310, _1622316), _1622312), _1622318)), hAPP(hAPP(c_Product__Type_OSigma(_1622310, _1622316), _1622314), _1622320))))], (6135 ^ _775828) ^ [_873335] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _873335)], (10045 ^ _775828) ^ [_938347] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938347), _938347)))], (9015 ^ _775828) ^ [_920044, _920046] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _920044), _920046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _920044), _920046)), -(_920044 = _920046)], (30844 ^ _775828) ^ [_1340008, _1340010, _1340012] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340008), _1340010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1340008, tc_HOL_Obool)), _1340012), _1340010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1340008), _1340012)), hAPP(c_Finite__Set_Ocard(_1340008), _1340010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1340008, tc_HOL_Obool)), _1340012), _1340010)))], (15504 ^ _775828) ^ [_1036604, _1036606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1036604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1036604), _1036606)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036606), _1036604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1036606)), hAPP(c_Int_Onat, _1036604)))], (28000 ^ _775828) ^ [_1276598, _1276600, _1276602, _1276604] : [28001 ^ _775828 : [(28002 ^ _775828) ^ [_1276652] : [hBOOL(hAPP(hAPP(_1276602, _1276604), _1276652))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1276598, _1276600, _1276602), _1276604)))], (25443 ^ _775828) ^ [_1224596, _1224598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1224596), _1224598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224596)), hAPP(c_Code__Numeral_Onat__of, _1224598))))], (5186 ^ _775828) ^ [_855160, _855162] : [_855162 = _855160, -(c_List_Omonoid__add__class_Olistsum(_855162) = c_List_Omonoid__add__class_Olistsum(_855160))], (45795 ^ _775828) ^ [_1679716, _1679718, _1679720, _1679722] : [-(hBOOL(hAPP(hAPP(c_member(_1679716), _1679722), hAPP(c_Set_Oimage(tc_prod(_1679716, _1679718), _1679716, c_Product__Type_Ofst(_1679716, _1679718)), hAPP(c_List_Oset(tc_prod(_1679716, _1679718)), _1679720))))), -(hAPP(c_Map_Omap__of(_1679716, _1679718, _1679720), _1679722) = c_Option_Ooption_ONone(_1679718))], (7397 ^ _775828) ^ [_893807, _893809] : [class_Rings_Ocomm__semiring__1(_893807), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_893807), c_Groups_Ozero__class_Ozero(_893807)), _893809) = c_Groups_Ozero__class_Ozero(_893807))], (3672 ^ _775828) ^ [_831639, _831641, _831643, _831645] : [-(c_Transitive__Closure_Otrancl(_831645, _831641) = c_Transitive__Closure_Otrancl(_831643, _831639)), _831645 = _831643, _831641 = _831639], (11068 ^ _775828) ^ [_957047] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _957047) = _957047)], (26231 ^ _775828) ^ [_1238940, _1238942, _1238944, _1238946] : [class_Rings_Ocomm__semiring__1(_1238940), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238940), _1238942), _1238944)), _1238946)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238940), _1238944), _1238946)))], (45618 ^ _775828) ^ [_1675331, _1675333, _1675335, _1675337, _1675339] : [-(c_Map_Omap__comp(_1675331, _1675333, _1675335, _1675337, hAPP(c_COMBK(tc_Option_Ooption(_1675331), _1675335), c_Option_Ooption_ONone(_1675331)), _1675339) = c_Option_Ooption_ONone(_1675333))], (29312 ^ _775828) ^ [_1307458, _1307460] : [29313 ^ _775828 : [(29314 ^ _775828) ^ [_1307511] : [hBOOL(hAPP(hAPP(c_member(_1307458), _1307511), _1307460))]], _1307460 = c_Orderings_Obot__class_Obot(tc_fun(_1307458, tc_HOL_Obool))], (22550 ^ _775828) ^ [_1168166, _1168168, _1168170] : [class_Fields_Olinordered__field__inverse__zero(_1168166), 22553 ^ _775828 : [(22568 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168166), _1168168), _1168170)), c_Groups_Ozero__class_Ozero(_1168166)))), 22569 ^ _775828 : [(22576 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), _1168168), c_Groups_Ozero__class_Ozero(_1168166))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), c_Groups_Ozero__class_Ozero(_1168166)), _1168170))], (22570 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), c_Groups_Ozero__class_Ozero(_1168166)), _1168168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), _1168170), c_Groups_Ozero__class_Ozero(_1168166)))]]], (22554 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168166), _1168168), _1168170)), c_Groups_Ozero__class_Ozero(_1168166))), 22559 ^ _775828 : [(22562 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), _1168170), c_Groups_Ozero__class_Ozero(_1168166))))], (22560 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), c_Groups_Ozero__class_Ozero(_1168166)), _1168168)))]], 22563 ^ _775828 : [(22566 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), c_Groups_Ozero__class_Ozero(_1168166)), _1168170)))], (22564 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168166), _1168168), c_Groups_Ozero__class_Ozero(_1168166))))]]]]], (12487 ^ _775828) ^ [_981899, _981901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981899), _981901)), -(_981901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981899), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12490 ^ [_981899, _981901])))], (27645 ^ _775828) ^ [_1267359, _1267361, _1267363, _1267365] : [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), _1267359, _1267361)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267363, _1267365))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267359), _1267361)), 27652 ^ _775828 : [(27655 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267361), _1267365)))], (27653 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267363), _1267359)))]]], (24511 ^ _775828) ^ [_1206581] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206581)))], (13650 ^ _775828) ^ [_1002898, _1002900] : [hBOOL(hAPP(c_Com_OWT, _1002898)), hBOOL(hAPP(c_Com_OWT, _1002900)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_1002898, _1002900))))], (40899 ^ _775828) ^ [_1562983, _1562985, _1562987, _1562989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562983), _1562985)), c_Fun_Oinj__on(_1562987, _1562983, _1562989, c_Orderings_Otop__class_Otop(tc_fun(_1562987, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1562987), hAPP(c_Set_Ovimage(_1562987, _1562983, _1562989), _1562985))))], (38063 ^ _775828) ^ [_1497580, _1497582, _1497584, _1497586, _1497588, _1497590] : [hBOOL(hAPP(hAPP(c_member(_1497580), _1497582), _1497584)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1497580, _1497586)), hAPP(hAPP(c_Product__Type_OPair(_1497580, _1497586), _1497582), _1497588)), _1497590)), -(hBOOL(hAPP(hAPP(c_member(_1497586), _1497588), hAPP(c_Relation_OImage(_1497580, _1497586, _1497590), _1497584))))], (49461 ^ _775828) ^ [_1769016, _1769018, _1769020, _1769022, _1769024] : [-(hAPP(c_List_Ofilter(_1769016, _1769018), hAPP(hAPP(c_List_Omap(_1769020, _1769016), _1769022), _1769024)) = hAPP(hAPP(c_List_Omap(_1769020, _1769016), _1769022), hAPP(c_List_Ofilter(_1769020, hAPP(c_Fun_Ocomp(_1769016, tc_HOL_Obool, _1769020, _1769018), _1769022)), _1769024)))], (24861 ^ _775828) ^ [_1213609, _1213611, _1213613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1213609), _1213611))), -(c_Random_Ominus__shift(_1213613, _1213609, _1213611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1213609), _1213611))], (36585 ^ _775828) ^ [_1463262] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1463262)) = hAPP(c_Nat_OSuc, _1463262))], (14274 ^ _775828) ^ [_1014426, _1014428, _1014430, _1014432] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014426, _1014428), _1014430, _1014432, _1014430)), 14275 ^ _775828 : [(14278 ^ _775828) ^ [_1014513] : [c_Natural_Oevaln(_1014428, _1014430, _1014432, _1014513), c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014426, _1014428), _1014513, _1014432, _1014430)], (14276 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1014426, _1014430)))]]], (40189 ^ _775828) ^ [_1546256, _1546258, _1546260] : [class_Orderings_Otop(_1546256), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1546258, _1546256)), _1546260) = c_Orderings_Otop__class_Otop(_1546256))], (4408 ^ _775828) ^ [_843137, _843139] : [_843139 = _843137, -(c_Orderings_Otop__class_Otop(_843139) = c_Orderings_Otop__class_Otop(_843137))], (11232 ^ _775828) ^ [_960124, _960126, _960128, _960130] : [class_Groups_Oordered__comm__monoid__add(_960124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960124), c_Groups_Ozero__class_Ozero(_960124)), _960126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960124), _960128), _960130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960124), _960128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960124), _960130), _960126))))], (48415 ^ _775828) ^ [_1746305, _1746307, _1746309, _1746311] : [-(hAPP(hAPP(c_List_Odrop(_1746305), _1746307), hAPP(hAPP(c_List_Odrop(_1746305), _1746309), _1746311)) = hAPP(hAPP(c_List_Odrop(_1746305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746307), _1746309)), _1746311))], (48675 ^ _775828) ^ [_1752121, _1752123, _1752125] : [-(hAPP(c_List_Oset(_1752121), hAPP(c_List_Orotate(_1752121, _1752123), _1752125)) = hAPP(c_List_Oset(_1752121), _1752125))], (45560 ^ _775828) ^ [_1674055, _1674057, _1674059, _1674061, _1674063, _1674065] : [-(hAPP(hAPP(c_List_Omap(_1674055, _1674057), _1674059), hAPP(hAPP(c_List_Omap(_1674061, _1674055), _1674063), _1674065)) = hAPP(hAPP(c_List_Omap(_1674061, _1674057), hAPP(c_Fun_Ocomp(_1674055, _1674057, _1674061, _1674059), _1674063)), _1674065))], (13789 ^ _775828) ^ [_1005510, _1005512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005510), 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, _1005512, _1005510)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18363 ^ _775828) ^ [_1091539, _1091541, _1091543, _1091545] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091539, _1091541), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091543), _1091545))), -(_1091541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1091539, _1091541) = _1091545)], (11751 ^ _775828) ^ [_968977, _968979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968977), _968979)), 11754 ^ _775828 : [(11761 ^ _775828) ^ [] : [_968979 = _968977, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968979), hAPP(c_Nat_OSuc, _968977))))], (11755 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968979), hAPP(c_Nat_OSuc, _968977))), -(_968979 = _968977)]]], (26109 ^ _775828) ^ [_1236782, _1236784] : [class_Rings_Ocomm__semiring__1(_1236782), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236782), c_Groups_Ozero__class_Ozero(_1236782)), _1236784)), -(_1236784 = c_Groups_Ozero__class_Ozero(_1236782))], (14445 ^ _775828) ^ [_1017745, _1017747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017747)), -(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), _1017745), _1017747))))], (30019 ^ _775828) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (31895 ^ _775828) ^ [_1365282, _1365284, _1365286] : [class_Lattices_Odistrib__lattice(_1365282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365282), _1365284)), -(_1365284 = 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hAPP(hAPP(c_COMBB(tc_fun(_1365282, tc_HOL_Obool), tc_fun(tc_fun(_1365282, _1365282), tc_fun(_1365282, tc_HOL_Obool)), _1365282), c_COMBB(_1365282, tc_HOL_Obool, _1365282)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1365282), _1365286))))), hAPP(hAPP(c_COMBC(_1365282, tc_fun(_1365282, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365282)), _1365284))))))], (18273 ^ _775828) ^ [_1089853, _1089855] : [-(c_Divides_Opdivmod(_1089853, _1089855) = 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), _1089853)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1089855))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1089853), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1089855))))], (36055 ^ _775828) ^ [_1452950, _1452952, _1452954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452950)), 36058 ^ _775828 : [(36059 ^ _775828) ^ [_1453084] : [36061 ^ _775828 : [(36067 ^ _775828) ^ [] : [-(_1453084 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36063 ^ [_1452950, _1452952, _1452954, _1453084]), 36060 ^ [_1452950, _1452952, _1452954, _1453084]))], (36065 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36063 ^ [_1452950, _1452952, _1452954, _1453084]), _1452952)))], (36062 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36060 ^ [_1452950, _1452952, _1452954, _1453084]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452950))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453084), _1452954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1453084), _1452950)), _1452954)))]]], (4424 ^ _775828) ^ [_843371, _843373, _843375, _843377] : [-(c_List_Olistrel1(_843377, _843373) = c_List_Olistrel1(_843375, _843371)), _843377 = _843375, _843373 = _843371], (18499 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6943 ^ _775828) ^ [_885872, _885874, _885876] : [class_Rings_Osemiring__1(_885872), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _885874), _885876)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885872), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885872), _885874)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885872), _885876)))], (41869 ^ _775828) ^ [_1586128, _1586130, _1586132, _1586134, _1586136, _1586138, _1586140] : [class_Rings_Osemiring__0(_1586128), c_Fun_Oinj__on(tc_prod(_1586130, _1586132), _1586128, hAPP(c_Product__Type_Oprod_Oprod__case(_1586130, _1586132, _1586128), hAPP(hAPP(c_COMBC(_1586130, tc_fun(_1586132, _1586128), tc_fun(_1586132, _1586128)), hAPP(hAPP(c_COMBB(tc_fun(_1586128, _1586128), tc_fun(tc_fun(_1586132, 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tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1586128), hAPP(c_COMBB(tc_fun(_1586132, tc_HOL_Obool), tc_fun(_1586132, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1586130), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1586132), c_fconj))), hAPP(hAPP(c_COMBC(_1586128, tc_fun(_1586130, tc_fun(_1586132, _1586128)), tc_fun(_1586130, tc_fun(_1586132, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1586132, _1586128), tc_fun(_1586132, tc_HOL_Obool)), tc_fun(tc_fun(_1586130, tc_fun(_1586132, _1586128)), tc_fun(_1586130, tc_fun(_1586132, tc_HOL_Obool))), _1586128), c_COMBB(tc_fun(_1586132, _1586128), tc_fun(_1586132, tc_HOL_Obool), _1586130)), hAPP(hAPP(c_COMBB(tc_fun(_1586128, tc_HOL_Obool), tc_fun(tc_fun(_1586132, _1586128), tc_fun(_1586132, tc_HOL_Obool)), _1586128), c_COMBB(_1586128, tc_HOL_Obool, _1586132)), c_fequal))), hAPP(hAPP(c_COMBC(_1586130, tc_fun(_1586132, _1586128), tc_fun(_1586132, _1586128)), hAPP(hAPP(c_COMBB(tc_fun(_1586128, _1586128), tc_fun(tc_fun(_1586132, _1586128), tc_fun(_1586132, _1586128)), _1586130), c_COMBB(_1586128, _1586128, _1586132)), hAPP(hAPP(c_COMBB(_1586128, tc_fun(_1586128, _1586128), _1586130), c_Groups_Otimes__class_Otimes(_1586128)), _1586134))), _1586136)))))), hAPP(hAPP(c_COMBC(_1586130, tc_fun(_1586132, tc_HOL_Obool), tc_fun(_1586132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1586132, tc_HOL_Obool), tc_fun(_1586132, tc_HOL_Obool)), _1586130), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1586132)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1586130), c_fconj), hAPP(hAPP(c_COMBC(_1586130, tc_fun(_1586130, tc_HOL_Obool), tc_HOL_Obool), c_member(_1586130)), _1586138)))), hAPP(hAPP(c_COMBC(_1586132, tc_fun(_1586132, tc_HOL_Obool), tc_HOL_Obool), c_member(_1586132)), _1586140))))))))], (37156 ^ _775828) ^ [_1475542, _1475544, _1475546, _1475548, _1475550] : [class_Groups_Oab__group__add(_1475542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1475544), _1475546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1475546), _1475548)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1475542), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475542), _1475550), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475544), _1475548))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475542), _1475550), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475544), _1475546))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475542), _1475550), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475546), _1475548)))], (3930 ^ _775828) ^ [_835698, _835700, _835702, _835704] : [-(c_List_Olenlex(_835704, _835700) = c_List_Olenlex(_835702, _835698)), _835704 = _835702, _835700 = _835698], (22420 ^ _775828) ^ [_1165858, _1165860, _1165862, _1165864] : [class_Fields_Olinordered__field__inverse__zero(_1165858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165858), _1165860), _1165862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165858), _1165864), c_Groups_Ozero__class_Ozero(_1165858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165858), _1165862), _1165864)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165858), _1165860), _1165864))))], (16853 ^ _775828) ^ [_1063036, _1063038, _1063040] : [class_Groups_Oordered__ab__group__add__abs(_1063036), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063036), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063036), hAPP(c_Groups_Oabs__class_Oabs(_1063036), _1063038)), hAPP(c_Groups_Oabs__class_Oabs(_1063036), _1063040))), hAPP(c_Groups_Oabs__class_Oabs(_1063036), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063036), _1063040), _1063038)))))], (30784 ^ _775828) ^ [_1338848, _1338850, _1338852] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338848), _1338850)), 30787 ^ _775828 : [(30794 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338848), _1338852), _1338850))), -(hAPP(c_Finite__Set_Ocard(_1338848), hAPP(hAPP(c_Set_Oinsert(_1338848), _1338852), _1338850)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1338848), _1338850)))], (30788 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338848), _1338852), _1338850)), -(hAPP(c_Finite__Set_Ocard(_1338848), hAPP(hAPP(c_Set_Oinsert(_1338848), _1338852), _1338850)) = hAPP(c_Finite__Set_Ocard(_1338848), _1338850))]]], (49118 ^ _775828) ^ [_1762056, _1762058, _1762060] : [-(_1762056 = c_List_Olist_ONil(_1762058)), -(c_List_Olast(_1762058, hAPP(hAPP(c_List_Oappend(_1762058), _1762060), _1762056)) = c_List_Olast(_1762058, _1762056))], (6522 ^ _775828) ^ [_879556, _879558, _879560, _879562] : [class_Orderings_Oord(_879556), _879558 = _879560, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879556), _879560), _879562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879556), _879558), _879562)))], (43198 ^ _775828) ^ [_1618666, _1618668, _1618670, _1618672, _1618674] : [c_Finite__Set_Ofolding__idem(_1618666, _1618668, _1618670, _1618672), -(hAPP(c_Fun_Ocomp(_1618668, _1618668, _1618668, hAPP(_1618670, _1618674)), hAPP(_1618670, _1618674)) = hAPP(_1618670, _1618674))], (14522 ^ _775828) ^ [_1018943] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018943), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22790 ^ _775828) ^ [_1172233, _1172235, _1172237] : [class_Fields_Olinordered__field(_1172233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172233), c_Groups_Ozero__class_Ozero(_1172233)), _1172235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172233), c_Groups_Ozero__class_Ozero(_1172233)), _1172237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172233), c_Groups_Ozero__class_Ozero(_1172233)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172233), _1172235), _1172237))))], (51312 ^ _775828) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (49094 ^ _775828) ^ [_1761728, _1761730, _1761732] : [-(_1761728 = c_List_Olist_ONil(_1761730)), -(c_List_Olast(_1761730, hAPP(hAPP(c_List_Olist_OCons(_1761730), _1761732), _1761728)) = c_List_Olast(_1761730, _1761728))], (19200 ^ _775828) ^ [_1106085, _1106087] : [class_Int_Onumber__ring(_1106085), 19203 ^ _775828 : [(19210 ^ _775828) ^ [] : [c_Int_Oiszero(_1106085, hAPP(c_Int_Onumber__class_Onumber__of(_1106085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1106087)))), -(c_Groups_Ozero__class_Ozero(_1106085) = hAPP(c_Int_Onumber__class_Onumber__of(_1106085), _1106087))], (19204 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_1106085) = hAPP(c_Int_Onumber__class_Onumber__of(_1106085), _1106087), -(c_Int_Oiszero(_1106085, hAPP(c_Int_Onumber__class_Onumber__of(_1106085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1106087)))))]]], (10376 ^ _775828) ^ [_944532, _944534, _944536, _944538] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_944532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944532), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944532), _944534), _944536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944532), _944538), _944536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944532), _944534), _944538)))], (28908 ^ _775828) ^ [_1298285, _1298287] : [c_Wellfounded_Owf(_1298285, _1298287), 28911 ^ _775828 : [(28912 ^ _775828) ^ [_1298417] : [28913 ^ _775828 : [(28914 ^ _775828) ^ [_1298522] : [hBOOL(hAPP(hAPP(c_member(_1298285), _1298522), _1298417))]], 28916 ^ _775828 : [(28919 ^ _775828) ^ [_1298644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1298285, _1298285)), hAPP(hAPP(c_Product__Type_OPair(_1298285, _1298285), _1298644), 28915 ^ [_1298285, _1298287, _1298417])), _1298287)), hBOOL(hAPP(hAPP(c_member(_1298285), _1298644), _1298417))], (28917 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298285), 28915 ^ [_1298285, _1298287, _1298417]), _1298417)))]]]]], (24406 ^ _775828) ^ [_1204390] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1204390)], (33899 ^ _775828) ^ [_1405922, _1405924, _1405926, _1405928] : [class_Lattices_Odistrib__lattice(_1405922), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405922), _1405924), _1405926)), _1405928) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405922), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405922), _1405924), _1405928)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405922), _1405926), _1405928)))], (19812 ^ _775828) ^ [] : [-(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)))))], (7445 ^ _775828) ^ [_894666, _894668, _894670] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894666), _894668)), _894670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894668), _894670)))], (37598 ^ _775828) ^ [_1486693, _1486695] : [class_Rings_Ocomm__semiring__1(_1486693), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1486693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1486693), c_Groups_Oone__class_Oone(_1486693)), c_Groups_Oone__class_Oone(_1486693))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486693), c_Nat_Osemiring__1__class_Oof__nat(_1486693)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1486695))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1486693), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1486693), _1486695)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1486693), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1486693), _1486695)), c_Groups_Oone__class_Oone(_1486693))))], (24200 ^ _775828) ^ [_1199729, _1199731, _1199733, _1199735] : [class_Orderings_Olinorder(_1199729), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199729), _1199731), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199729), _1199733), _1199735)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199729), _1199733), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199729), _1199731), _1199735)))], (32839 ^ _775828) ^ [_1383229, _1383231, _1383233, _1383235, _1383237] : [hAPP(_1383229, _1383231) = _1383233, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383235, _1383237), _1383229), _1383231), _1383233) = _1383229)], (44305 ^ _775828) ^ [_1644577, _1644579, _1644581, _1644583, _1644585] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644577, tc_fun(_1644579, tc_HOL_Obool)), _1644581), hAPP(hAPP(c_COMBC(_1644577, tc_fun(_1644579, tc_HOL_Obool), 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tc_fun(_1533772, tc_HOL_Obool)), _1533776), hAPP(hAPP(c_COMBB(tc_fun(_1533780, tc_fun(_1533772, tc_HOL_Obool)), tc_fun(_1533772, tc_HOL_Obool), _1533774), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533780, tc_fun(_1533772, tc_HOL_Obool)), _1533782)), hAPP(hAPP(c_COMBC(_1533774, tc_fun(_1533780, tc_fun(_1533772, tc_HOL_Obool)), tc_fun(_1533780, tc_fun(_1533772, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1533772, tc_HOL_Obool), tc_fun(_1533772, tc_HOL_Obool)), tc_fun(tc_fun(_1533780, tc_fun(_1533772, tc_HOL_Obool)), tc_fun(_1533780, tc_fun(_1533772, tc_HOL_Obool))), _1533774), c_COMBB(tc_fun(_1533772, tc_HOL_Obool), tc_fun(_1533772, tc_HOL_Obool), _1533780)), hAPP(hAPP(c_COMBB(tc_fun(_1533772, tc_HOL_Obool), tc_fun(tc_fun(_1533772, tc_HOL_Obool), tc_fun(_1533772, tc_HOL_Obool)), _1533774), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533772, tc_HOL_Obool))), _1533778))), _1533784))))], (20658 ^ _775828) ^ [_1130767, _1130769, _1130771] : [class_Rings_Olinordered__idom(_1130767), 20661 ^ _775828 : [(20670 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130767), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130767), hAPP(hAPP(c_Power_Opower__class_Opower(_1130767), _1130769), 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(_1130767), _1130771), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1130767)))), _1130769 = c_Groups_Ozero__class_Ozero(_1130767), _1130771 = c_Groups_Ozero__class_Ozero(_1130767)], (20662 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130767), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130767), hAPP(hAPP(c_Power_Opower__class_Opower(_1130767), _1130769), 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(_1130767), _1130771), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1130767))), 20665 ^ _775828 : [(20668 ^ _775828) ^ [] : [-(_1130771 = c_Groups_Ozero__class_Ozero(_1130767))], (20666 ^ _775828) ^ [] : [-(_1130769 = c_Groups_Ozero__class_Ozero(_1130767))]]]]], (23794 ^ _775828) ^ [_1192538, _1192540, _1192542, _1192544] : [class_Orderings_Olinorder(_1192538), 23797 ^ _775828 : [(23798 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192538), _1192542), _1192544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), _1192542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), _1192544)))], (23808 ^ _775828) ^ [] : [23809 ^ _775828 : [(23812 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), _1192544))], (23810 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), _1192542))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192538), _1192540), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192538), _1192542), _1192544))))]]], (6125 ^ _775828) ^ [_873146, _873148, _873150, _873152] : [c_Com_Ocom_OCall(_873146, _873148, _873150) = hAPP(c_Com_Ocom_OBODY, _873152)], (5440 ^ _775828) ^ [_858923, _858925, _858927, _858929] : [-(hAPP(_858929, _858925) = hAPP(_858927, _858923)), _858929 = _858927, _858925 = _858923], (9941 ^ _775828) ^ [] : [-(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))))], (24116 ^ _775828) ^ [_1198091, _1198093, _1198095, _1198097] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1198091), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198091), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198091), _1198093), _1198095)), _1198097) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198091), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198091), _1198093), _1198097)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198091), _1198095), _1198097)))], (29989 ^ _775828) ^ [_1322433, _1322435, _1322437, _1322439] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1322433, _1322435, _1322437), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322433, _1322435), tc_HOL_Obool))), _1322439) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322433, _1322437), tc_HOL_Obool)))], (28006 ^ _775828) ^ [_1276716] : [class_Orderings_Owellorder(_1276716), -(c_Wellfounded_Owf(_1276716, hAPP(c_Set_OCollect(tc_prod(_1276716, _1276716)), hAPP(c_Product__Type_Oprod_Oprod__case(_1276716, _1276716, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1276716)))))], (42738 ^ _775828) ^ [_1607778, _1607780, _1607782, _1607784, _1607786, _1607788] : [c_Fun_Oinj__on(_1607778, _1607780, hAPP(c_Fun_Ocomp(_1607782, _1607780, _1607778, _1607784), _1607786), _1607788), -(c_Fun_Oinj__on(_1607778, _1607782, _1607786, _1607788))], (9029 ^ _775828) ^ [_920259, _920261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _920259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _920261)), 9036 ^ _775828 : [(9043 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _920259), _920261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _920259)), hAPP(c_Int_Onat, _920261))))], (9037 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _920259)), hAPP(c_Int_Onat, _920261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _920259), _920261)))]]], (29875 ^ _775828) ^ [_1319045, _1319047, _1319049, _1319051] : [-(hBOOL(hAPP(hAPP(c_member(_1319045), _1319047), _1319049))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319045, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1319045), _1319047), _1319051)), _1319049) = hAPP(hAPP(c_Set_Oinsert(_1319045), _1319047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319045, tc_HOL_Obool)), _1319051), _1319049)))], (9649 ^ _775828) ^ [_931005, _931007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _931005)), hAPP(c_Int_Onat, _931007))), 9652 ^ _775828 : [(9655 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _931005), _931007)))], (9653 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _931007)))]]], (6793 ^ _775828) ^ [_883449, _883451] : [_883449 = _883451, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883449) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883451))], (30528 ^ _775828) ^ [_1333627] : [30530 ^ _775828 : [(30533 ^ _775828) ^ [_1333737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30529 ^ [_1333627, _1333737]), _1333737))], (30531 ^ _775828) ^ [_1333703] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30529 ^ [_1333627, _1333703]), _1333627)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1333627)))], (24942 ^ _775828) ^ [_1215000, _1215002, _1215004, _1215006, _1215008, _1215010, _1215012] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1215000, _1215002)), hAPP(hAPP(c_Product__Type_OPair(_1215000, _1215002), _1215004), _1215006)), _1215008)), -(hBOOL(hAPP(hAPP(c_member(_1215010), hAPP(hAPP(_1215012, _1215004), _1215006)), hAPP(c_Set_Oimage(tc_prod(_1215000, _1215002), _1215010, hAPP(c_Product__Type_Oprod_Oprod__case(_1215000, _1215002, _1215010), _1215012)), _1215008))))], (32499 ^ _775828) ^ [_1376520, _1376522, _1376524] : [class_Lattices_Olattice(_1376520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376520), _1376522)), hBOOL(hAPP(hAPP(c_member(_1376520), _1376524), _1376522)), 32510 ^ _775828 : [(32517 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376520, tc_HOL_Obool)), _1376522), hAPP(hAPP(c_Set_Oinsert(_1376520), _1376524), c_Orderings_Obot__class_Obot(tc_fun(_1376520, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1376520, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1376520, _1376522) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1376520), _1376524), c_Big__Operators_Olattice__class_OSup__fin(_1376520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376520, tc_HOL_Obool)), _1376522), hAPP(hAPP(c_Set_Oinsert(_1376520), _1376524), c_Orderings_Obot__class_Obot(tc_fun(_1376520, tc_HOL_Obool)))))))], (32511 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376520, tc_HOL_Obool)), _1376522), hAPP(hAPP(c_Set_Oinsert(_1376520), _1376524), c_Orderings_Obot__class_Obot(tc_fun(_1376520, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1376520, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1376520, _1376522) = _1376524)]]], (40869 ^ _775828) ^ [_1562244, _1562246, _1562248, _1562250, _1562252] : [hAPP(_1562250, _1562246) = _1562252, -(hBOOL(hAPP(hAPP(c_member(_1562244), _1562246), hAPP(c_Set_Ovimage(_1562244, _1562248, _1562250), hAPP(hAPP(c_Set_Oinsert(_1562248), _1562252), c_Orderings_Obot__class_Obot(tc_fun(_1562248, tc_HOL_Obool)))))))], (28499 ^ _775828) ^ [_1287719, _1287721, _1287723, _1287725] : [class_Lattices_Osemilattice__sup(_1287719), 28502 ^ _775828 : [(28511 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287719), _1287721), _1287723)), _1287725))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), _1287721), _1287725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), _1287723), _1287725))], (28503 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287719), _1287721), _1287723)), _1287725)), 28506 ^ _775828 : [(28509 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), _1287723), _1287725)))], (28507 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287719), _1287721), _1287725)))]]]]], (26667 ^ _775828) ^ [_1247198, _1247200] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247198), _1247200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247198), _1247200)))], (3296 ^ _775828) ^ [_825711, _825713] : [_825713 = _825711, -(c_Nat_Ofunpow(_825713) = c_Nat_Ofunpow(_825711))], (51540 ^ _775828) ^ [_1808665] : [hBOOL(hAPP(c_fNot, _1808665)), hBOOL(_1808665)], (9081 ^ _775828) ^ [_921040, _921042] : [-(_921040 = hAPP(c_Int_Onat, _921042)), 9084 ^ _775828 : [(9087 ^ _775828) ^ [] : [_921042 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921040)], (9085 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921042)))]], 9088 ^ _775828 : [(9091 ^ _775828) ^ [] : [_921040 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9089 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921042))]]], (31635 ^ _775828) ^ [_1358367, _1358369, _1358371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358367, _1358367), tc_HOL_Obool)), _1358369), c_Transitive__Closure_Ortrancl(_1358367, _1358371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358367, _1358367), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1358367, _1358369)), c_Transitive__Closure_Ortrancl(_1358367, _1358371))))], (8160 ^ _775828) ^ [_907021, _907023, _907025] : [-(hBOOL(hAPP(hAPP(c_member(_907021), _907023), _907025))), -(hBOOL(hAPP(hAPP(c_member(_907021), _907023), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_907021, tc_HOL_Obool)), _907025))))], (33603 ^ _775828) ^ [_1399511, _1399513, _1399515] : [33604 ^ _775828 : [(33607 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399511), _1399515))], (33605 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399511), _1399513))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1399511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399511, tc_HOL_Obool)), _1399513), _1399515))))], (41312 ^ _775828) ^ [_1573557, _1573559, _1573561] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1573557, _1573559), _1573561), hAPP(c_COMBK(tc_fun(_1573559, tc_HOL_Obool), _1573557), c_Orderings_Obot__class_Obot(tc_fun(_1573559, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1573557, _1573559), tc_HOL_Obool)))], (15344 ^ _775828) ^ [_1033699, _1033701, _1033703] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1033699)), _1033701)), hAPP(c_Nat_OSuc, _1033703)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033699), _1033701)), _1033703))], (8468 ^ _775828) ^ [_911763] : [8470 ^ _775828 : [(8473 ^ _775828) ^ [] : [hBOOL(hAPP(_911763, hAPP(c_Int_Onat, 8469 ^ [_911763])))], (8471 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8469 ^ [_911763])))]], 8474 ^ _775828 : [(8475 ^ _775828) ^ [_911896] : [-(hBOOL(hAPP(_911763, _911896)))]]], (49975 ^ _775828) ^ [_1779557, _1779559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779557)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779559))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779557), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779559)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779557)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779557)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779559))))], (43390 ^ _775828) ^ [_1623783, _1623785, _1623787, _1623789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1623783, tc_HOL_Obool), tc_fun(_1623783, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1623783, tc_HOL_Obool), tc_fun(_1623783, tc_HOL_Obool)), _1623785), _1623787)), c_Wellfounded_Omax__ext(_1623783, _1623789))), 43393 ^ _775828 : [(43396 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1623783), _1623787)))], (43398 ^ _775828) ^ [] : [_1623787 = c_Orderings_Obot__class_Obot(tc_fun(_1623783, tc_HOL_Obool))], (43400 ^ _775828) ^ [_1624077] : [hBOOL(hAPP(hAPP(c_member(_1623783), _1624077), _1623785)), 43404 ^ _775828 : [(43407 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623783, _1623783)), hAPP(hAPP(c_Product__Type_OPair(_1623783, _1623783), _1624077), 43403 ^ [_1623783, _1623785, _1623787, _1623789, _1624077])), _1623789)))], (43405 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623783), 43403 ^ [_1623783, _1623785, _1623787, _1623789, _1624077]), _1623787)))]]], (43394 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1623783), _1623785)))]]], (50287 ^ _775828) ^ [_1786341, _1786343] : [50289 ^ _775828 : [(50292 ^ _775828) ^ [] : [50288 ^ [_1786341, _1786343] = c_List_Olist_ONil(_1786341)], (50290 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1786341)), 50288 ^ [_1786341, _1786343]), hAPP(c_List_Oset(tc_List_Olist(_1786341)), _1786343))))]], -(c_List_Olist_ONil(_1786341) = c_List_Oconcat(_1786341, _1786343))], (46654 ^ _775828) ^ [_1703146, _1703148, _1703150] : [hBOOL(hAPP(c_List_Odistinct(_1703146), _1703148)), -(hBOOL(hAPP(c_List_Odistinct(_1703146), c_List_Osublist(_1703146, _1703148, _1703150))))], (12237 ^ _775828) ^ [_977516, _977518] : [class_Rings_Olinordered__idom(_977516), hBOOL(hAPP(hAPP(c_member(_977516), _977518), c_Int_Oring__1__class_OInts(_977516))), 12244 ^ _775828 : [(12251 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977516), _977518), c_Groups_Ozero__class_Ozero(_977516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977516), c_Groups_Oone__class_Oone(_977516)), _977518)), _977518)), c_Groups_Ozero__class_Ozero(_977516))))], (12245 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977516), c_Groups_Oone__class_Oone(_977516)), _977518)), _977518)), c_Groups_Ozero__class_Ozero(_977516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977516), _977518), c_Groups_Ozero__class_Ozero(_977516))))]]], (960 ^ _775828) ^ [_790446, _790448] : [-(class_Lattices_Obounded__lattice(_790446)), _790448 = _790446, class_Lattices_Obounded__lattice(_790448)], (32529 ^ _775828) ^ [_1377133, _1377135, _1377137] : [class_Lattices_Olattice(_1377133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377133), _1377135)), hBOOL(hAPP(hAPP(c_member(_1377133), _1377137), _1377135)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1377133), _1377137), c_Big__Operators_Olattice__class_OSup__fin(_1377133, _1377135)) = c_Big__Operators_Olattice__class_OSup__fin(_1377133, _1377135))], (42956 ^ _775828) ^ [_1613003, _1613005, _1613007, _1613009, _1613011] : [c_Hoare__Mirabelle_Ohoare__derivs(_1613003, _1613005, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1613003)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1613003), c_Hoare__Mirabelle_Opeek__and(_1613003, _1613007, _1613009)), _1613011), _1613007)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1613003), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1613003, _1613005, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1613003)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1613003), _1613007), c_Com_Ocom_OWhile(_1613009, _1613011)), c_Hoare__Mirabelle_Opeek__and(_1613003, _1613007, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1613009)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1613003), tc_HOL_Obool)))))], (15554 ^ _775828) ^ [_1037556, _1037558, _1037560] : [class_Groups_Oordered__ab__group__add(_1037556), 15557 ^ _775828 : [(15564 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037556), _1037558), _1037560)), c_Groups_Ozero__class_Ozero(_1037556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037556), _1037558), _1037560)))], (15558 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037556), _1037558), _1037560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037556), _1037558), _1037560)), c_Groups_Ozero__class_Ozero(_1037556))))]]], (15440 ^ _775828) ^ [_1035364, _1035366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035364), _1035366)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035366), _1035364)) = _1035364)], (15296 ^ _775828) ^ [_1032783, _1032785, _1032787, _1032789] : [class_Divides_Oring__div(_1032783), -(c_Divides_Odiv__class_Omod(_1032783, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032783), _1032785), _1032787), _1032789) = c_Divides_Odiv__class_Omod(_1032783, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032783), c_Divides_Odiv__class_Omod(_1032783, _1032785, _1032789)), c_Divides_Odiv__class_Omod(_1032783, _1032787, _1032789)), _1032789))], (49112 ^ _775828) ^ [_1761951, _1761953, _1761955] : [_1761951 = c_List_Olist_ONil(_1761953), -(c_List_Olast(_1761953, hAPP(hAPP(c_List_Oappend(_1761953), _1761955), _1761951)) = c_List_Olast(_1761953, _1761955))], (20156 ^ _775828) ^ [_1122101, _1122103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1122101)), c_Int_OBit1(_1122103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122101), _1122103)))], (47387 ^ _775828) ^ [_1721213, _1721215, _1721217, _1721219] : [_1721215 = c_List_Olist_ONil(_1721213), -(hAPP(hAPP(c_List_Olist__update(_1721213, _1721215), _1721217), _1721219) = c_List_Olist_ONil(_1721213))], (30085 ^ _775828) ^ [_1324140, _1324142] : [30086 ^ _775828 : [(30089 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1324142), _1324140))], (30087 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1324140), _1324142)))]], -(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)))), _1324140, _1324142) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30864 ^ _775828) ^ [_1340450, _1340452, _1340454] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340450), _1340452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1340450), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340450, tc_HOL_Obool)), _1340452), hAPP(hAPP(c_Set_Oinsert(_1340450), _1340454), c_Orderings_Obot__class_Obot(tc_fun(_1340450, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1340450), _1340452))))], (44455 ^ _775828) ^ [_1648974, _1648976, _1648978, _1648980, _1648982] : [-(_1648974 = c_Orderings_Obot__class_Obot(tc_fun(_1648976, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648978, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648976, tc_fun(_1648978, tc_HOL_Obool)), _1648974), _1648980)), _1648982) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648976, tc_fun(_1648978, tc_HOL_Obool)), _1648974), hAPP(hAPP(c_COMBC(_1648976, tc_fun(_1648978, tc_HOL_Obool), tc_fun(_1648978, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648978, tc_HOL_Obool), tc_fun(tc_fun(_1648978, tc_HOL_Obool), tc_fun(_1648978, tc_HOL_Obool)), _1648976), c_Groups_Ominus__class_Ominus(tc_fun(_1648978, tc_HOL_Obool))), _1648980)), _1648982)))], (5676 ^ _775828) ^ [_866115, _866117, _866119, _866121, _866123] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_866115, _866117, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866115), _866119), _866121), _866123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20224 ^ _775828) ^ [_1123309, _1123311] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1123309)), c_Int_OBit0(_1123311)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123309), _1123311)))], (14660 ^ _775828) ^ [_1021134, _1021136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021134)), 14663 ^ _775828 : [(14670 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021134), _1021136)), -(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), _1021136), _1021134))))], (14664 ^ _775828) ^ [] : [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), _1021136), _1021134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021134), _1021136)))]]], (27028 ^ _775828) ^ [_1253378, _1253380] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253378), _1253380)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1253380), _1253378)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253380)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253378)))], (47089 ^ _775828) ^ [_1713676, _1713678] : [class_Groups_Ocomm__monoid__add(_1713676), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1713676), _1713678) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1713676), hAPP(c_List_Onth(_1713676), _1713678)), 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(_1713676)), _1713678))))], (34061 ^ _775828) ^ [_1409343, _1409345, _1409347, _1409349] : [class_Lattices_Osemilattice__inf(_1409343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409343), _1409345), _1409347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409343), _1409345), _1409349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409343), _1409345), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409343), _1409347), _1409349))))], (39884 ^ _775828) ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775] : [c_Equiv__Relations_Oequiv(_1539763, _1539765, _1539767), c_Equiv__Relations_Ocongruent(_1539763, tc_fun(_1539769, tc_HOL_Obool), _1539767, _1539771), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539763, tc_fun(_1539769, tc_HOL_Obool)), _1539773), _1539771) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539763, tc_fun(_1539769, tc_HOL_Obool)), _1539775), _1539771), hBOOL(hAPP(hAPP(c_member(tc_fun(_1539763, tc_HOL_Obool)), _1539773), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1539763), _1539765), _1539767))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1539763, tc_HOL_Obool)), _1539775), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1539763), _1539765), _1539767))), 39906 ^ _775828 : [(39910 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539763), 39908 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775]), _1539765)))], (39912 ^ _775828) ^ [] : [-(hAPP(_1539771, 39905 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775]) = hAPP(_1539771, 39908 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775]))], (39914 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539763, _1539763)), hAPP(hAPP(c_Product__Type_OPair(_1539763, _1539763), 39905 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775]), 39908 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775])), _1539767))], (39907 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539763), 39905 ^ [_1539763, _1539765, _1539767, _1539769, _1539771, _1539773, _1539775]), _1539765)))]], -(_1539773 = _1539775)], (6508 ^ _775828) ^ [_879337, _879339, _879341, _879343] : [class_Orderings_Oorder(_879337), _879339 = _879341, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879337), _879343), _879341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879337), _879343), _879339)))], (31781 ^ _775828) ^ [_1362133, _1362135] : [-(c_Transitive__Closure_Otrancl(_1362133, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1362133, _1362133), tc_HOL_Obool)), _1362135), c_Relation_OId(_1362133))) = c_Transitive__Closure_Ortrancl(_1362133, _1362135))], (41246 ^ _775828) ^ [_1571860, _1571862, _1571864, _1571866, _1571868, _1571870] : [hBOOL(hAPP(hAPP(c_member(_1571860), _1571862), _1571864)), hBOOL(hAPP(hAPP(c_member(_1571866), _1571868), hAPP(_1571870, _1571862))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571860, _1571866)), hAPP(hAPP(c_Product__Type_OPair(_1571860, _1571866), _1571862), _1571868)), hAPP(hAPP(c_Product__Type_OSigma(_1571860, _1571866), _1571864), _1571870))))], (20362 ^ _775828) ^ [_1125716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1125716)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125716), c_Int_OMin)))], (20506 ^ _775828) ^ [_1128228, _1128230, _1128232] : [class_Rings_Olinordered__semidom(_1128228), hAPP(hAPP(c_Power_Opower__class_Opower(_1128228), _1128230), 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(_1128228), _1128232), 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(_1128228), c_Groups_Ozero__class_Ozero(_1128228)), _1128230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128228), c_Groups_Ozero__class_Ozero(_1128228)), _1128232)), -(_1128230 = _1128232)], (1570 ^ _775828) ^ [_798071, _798073] : [-(class_Divides_Osemiring__div(_798071)), _798073 = _798071, class_Divides_Osemiring__div(_798073)], (40205 ^ _775828) ^ [_1546531, _1546533, _1546535] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1546531, _1546533, c_Orderings_Obot__class_Obot(tc_fun(_1546531, tc_HOL_Obool))), _1546535))], (27254 ^ _775828) ^ [_1258456, _1258458, _1258460] : [-(hAPP(c_Relation_Oconverse(_1258456, _1258458), hAPP(c_Relation_Oconverse(_1258458, _1258456), _1258460)) = _1258460)], (48721 ^ _775828) ^ [_1753092] : [-(c_List_Orotate(_1753092, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1753092)))], (31661 ^ _775828) ^ [_1359056, _1359058, _1359060, _1359062, _1359064] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1359056, _1359056)), hAPP(hAPP(c_Product__Type_OPair(_1359056, _1359056), _1359058), _1359060)), _1359062)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1359056, _1359056)), hAPP(hAPP(c_Product__Type_OPair(_1359056, _1359056), _1359060), _1359064)), c_Transitive__Closure_Ortrancl(_1359056, _1359062))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1359056, _1359056)), hAPP(hAPP(c_Product__Type_OPair(_1359056, _1359056), _1359058), _1359064)), c_Transitive__Closure_Ortrancl(_1359056, _1359062))))], (51620 ^ _775828) ^ [_1809641] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _1809641), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, v_na, _1809641))], (13630 ^ _775828) ^ [_1002586, _1002588, _1002590] : [c_Com_Ocom_OLocal(_1002586, _1002588, _1002590) = c_Com_Ocom_OSKIP], (20204 ^ _775828) ^ [_1122939, _1122941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1122939)), c_Int_OBit0(_1122941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122939), _1122941)))], (10126 ^ _775828) ^ [_939731, _939733, _939735, _939737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939731), _939733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939735), _939737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939731), _939735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939733), _939737))))], (14477 ^ _775828) ^ [_1018256, _1018258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018256), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14480 ^ _775828 : [(14487 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018258), _1018256)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14481 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018258), _1018256)), 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)), _1018258)))]]], (15872 ^ _775828) ^ [_1043710, _1043712, _1043714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043710), _1043712)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043714), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043712), _1043710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043714), _1043710)), _1043712))], (30985 ^ _775828) ^ [_1343583, _1343585, _1343587, _1343589, _1343591, _1343593, _1343595, _1343597] : [c_Finite__Set_Ofolding__image__simple(_1343583, _1343585, _1343587, _1343589, _1343591, _1343593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343585), _1343595)), hBOOL(hAPP(hAPP(c_member(_1343585), _1343597), _1343595)), -(hAPP(_1343593, _1343595) = hAPP(hAPP(_1343587, hAPP(_1343591, _1343597)), hAPP(_1343593, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343585, tc_HOL_Obool)), _1343595), hAPP(hAPP(c_Set_Oinsert(_1343585), _1343597), c_Orderings_Obot__class_Obot(tc_fun(_1343585, tc_HOL_Obool)))))))], (34333 ^ _775828) ^ [_1415376, _1415378, _1415380] : [class_Lattices_Olattice(_1415376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415376), _1415378)), hBOOL(hAPP(hAPP(c_member(_1415376), _1415380), _1415378)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415376), _1415380), c_Big__Operators_Olattice__class_OSup__fin(_1415376, _1415378)) = _1415380)], (30105 ^ _775828) ^ [_1324484, _1324486] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1324484), _1324486)), -(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)))), _1324486, _1324484) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29909 ^ _775828) ^ [_1319961] : [-(c_Option_Oset(_1319961, c_Option_Ooption_ONone(_1319961)) = c_Orderings_Obot__class_Obot(tc_fun(_1319961, tc_HOL_Obool)))], (15656 ^ _775828) ^ [_1039637, _1039639, _1039641] : [_1039637 = 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), _1039637), _1039639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039637), _1039641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51342 ^ _775828) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (32743 ^ _775828) ^ [_1381227, _1381229, _1381231, _1381233] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381227), _1381229)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381231), _1381233)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1381227, _1381231)), c_Sum__Type_OPlus(_1381227, _1381231, _1381229, _1381233))))], (13138 ^ _775828) ^ [_993087, _993089, _993091, _993093, _993095] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_993087), _993089), _993091)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_993093), _993091), _993095)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_993087, _993093)), _993089), _993095)))], (13346 ^ _775828) ^ [_997035, _997037, _997039, _997041] : [class_Divides_Osemiring__div(_997035), -(c_Divides_Odiv__class_Omod(_997035, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997035), _997037), _997039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997035), _997037), _997041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997035), _997037), c_Divides_Odiv__class_Omod(_997035, _997039, _997041)))], (51218 ^ _775828) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (48689 ^ _775828) ^ [_1752394, _1752396] : [hBOOL(hAPP(c_List_Odistinct(_1752394), _1752396)), -(hBOOL(hAPP(c_List_Odistinct(_1752394), hAPP(c_List_Otl(_1752394), _1752396))))], (47053 ^ _775828) ^ [_1712905, _1712907, _1712909] : [-(hBOOL(hAPP(hAPP(c_member(_1712905), _1712907), hAPP(c_List_Oset(_1712905), _1712909)))), 47054 ^ _775828 : [(47055 ^ _775828) ^ [_1712979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712905)), _1712909))), hAPP(hAPP(c_List_Onth(_1712905), _1712909), _1712979) = _1712907]]], (18113 ^ _775828) ^ [_1086516, _1086518, _1086520, _1086522, _1086524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1086516, _1086518)), hAPP(hAPP(c_Product__Type_OPair(_1086516, _1086518), _1086522), _1086524)), _1086520)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1086516, _1086518, _1086520), _1086522), _1086524)))], (17271 ^ _775828) ^ [_1071229, _1071231, _1071233] : [class_Int_Onumber__ring(_1071229), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071229), hAPP(c_Groups_Ouminus__class_Ouminus(_1071229), hAPP(c_Int_Onumber__class_Onumber__of(_1071229), _1071231))), _1071233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071229), hAPP(c_Int_Onumber__class_Onumber__of(_1071229), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071231))), _1071233))], (22668 ^ _775828) ^ [_1170314, _1170316, _1170318, _1170320, _1170322] : [class_Fields_Ofield(_1170314), -(_1170316 = c_Groups_Ozero__class_Ozero(_1170314)), -(_1170318 = c_Groups_Ozero__class_Ozero(_1170314)), 22679 ^ _775828 : [(22686 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170314), _1170320), _1170318) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170314), _1170322), _1170316), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170314), _1170320), _1170316) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170314), _1170322), _1170318))], (22680 ^ _775828) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170314), _1170320), _1170316) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170314), _1170322), _1170318), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170314), _1170320), _1170318) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170314), _1170322), _1170316))]]], (24272 ^ _775828) ^ [_1201505, _1201507, _1201509] : [class_Groups_Olinordered__ab__group__add(_1201505), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1201505), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201505), _1201507), _1201509)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201505), hAPP(c_Groups_Ouminus__class_Ouminus(_1201505), _1201507)), hAPP(c_Groups_Ouminus__class_Ouminus(_1201505), _1201509)))], (25086 ^ _775828) ^ [_1218471, _1218473] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218471) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218473), -(_1218471 = _1218473)], (2298 ^ _775828) ^ [_809448, _809450, _809452, _809454, _809456, _809458] : [-(c_Product__Type_Ointernal__split(_809458, _809454, _809450) = c_Product__Type_Ointernal__split(_809456, _809452, _809448)), _809458 = _809456, _809454 = _809452, _809450 = _809448], (5707 ^ _775828) ^ [_866767, _866769, _866771] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _866767))), _866769), _866771)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _866767)), _866769), _866771)))], (19596 ^ _775828) ^ [_1112622] : [c_Int_OMin = c_Int_OBit1(_1112622), -(c_Int_OMin = _1112622)], (2232 ^ _775828) ^ [_808469, _808471] : [_808471 = _808469, -(c_Nitpick_Oone__frac(_808471) = c_Nitpick_Oone__frac(_808469))], (1150 ^ _775828) ^ [_792821, _792823] : [-(class_Int_Onumber__ring(_792821)), _792823 = _792821, class_Int_Onumber__ring(_792823)], (13230 ^ _775828) ^ [_994803, _994805, _994807, _994809, _994811, _994813] : [c_Com_Ocom_OLocal(_994803, _994805, _994807) = c_Com_Ocom_OLocal(_994809, _994811, _994813), 13233 ^ _775828 : [(13238 ^ _775828) ^ [] : [-(_994807 = _994813)], (13236 ^ _775828) ^ [] : [-(_994805 = _994811)], (13234 ^ _775828) ^ [] : [-(_994803 = _994809)]]], (18547 ^ _775828) ^ [_1094780] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1094780, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40089 ^ _775828) ^ [_1544434, _1544436] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1544434, _1544436)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1544434, _1544436), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544434), c_Orderings_Otop__class_Otop(tc_fun(_1544434, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544436), c_Orderings_Otop__class_Otop(tc_fun(_1544436, tc_HOL_Obool))))], (1730 ^ _775828) ^ [_800071, _800073] : [-(class_Groups_Ozero(_800071)), _800073 = _800071, class_Groups_Ozero(_800073)], (51470 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (13813 ^ _775828) ^ [_1005903, _1005905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 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hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364183), c_fconj))), hAPP(hAPP(c_COMBC(_1364183, tc_fun(_1364183, tc_fun(_1364183, _1364183)), tc_fun(_1364183, tc_fun(_1364183, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1364183, _1364183), tc_fun(_1364183, tc_HOL_Obool)), tc_fun(tc_fun(_1364183, tc_fun(_1364183, _1364183)), tc_fun(_1364183, tc_fun(_1364183, tc_HOL_Obool))), _1364183), c_COMBB(tc_fun(_1364183, _1364183), tc_fun(_1364183, tc_HOL_Obool), _1364183)), hAPP(hAPP(c_COMBB(tc_fun(_1364183, tc_HOL_Obool), tc_fun(tc_fun(_1364183, _1364183), tc_fun(_1364183, tc_HOL_Obool)), _1364183), c_COMBB(_1364183, tc_HOL_Obool, _1364183)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1364183)))))), hAPP(hAPP(c_COMBC(_1364183, tc_fun(_1364183, tc_HOL_Obool), tc_fun(_1364183, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1364183, tc_HOL_Obool), tc_fun(_1364183, tc_HOL_Obool)), _1364183), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1364183)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364183), c_fconj), hAPP(hAPP(c_COMBC(_1364183, tc_fun(_1364183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364183)), _1364185)))), hAPP(hAPP(c_COMBC(_1364183, tc_fun(_1364183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364183)), _1364187))))))))], (17739 ^ _775828) ^ [_1079661, _1079663, _1079665] : [class_Rings_Olinordered__idom(_1079661), -(hAPP(c_Groups_Oabs__class_Oabs(_1079661), hAPP(hAPP(c_Power_Opower__class_Opower(_1079661), _1079663), _1079665)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079661), hAPP(c_Groups_Oabs__class_Oabs(_1079661), _1079663)), _1079665))], (43754 ^ _775828) ^ [_1631593, _1631595, _1631597] : [class_Lattices_Olattice(_1631593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631593), _1631595)), -(c_Big__Operators_Olattice__class_OInf__fin(_1631593, hAPP(hAPP(c_Set_Oinsert(_1631593), _1631597), _1631595)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631593, _1631593, c_Lattices_Osemilattice__inf__class_Oinf(_1631593)), _1631597), _1631595))], (46265 ^ _775828) ^ [_1691187, _1691189] : [-(c_List_Olenlex(_1691187, _1691189) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1691187)), tc_List_Olist(_1691187)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1691187), c_Wellfounded_Oless__than, c_List_Olex(_1691187, _1691189))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1691187), tc_List_Olist(_1691187), tc_prod(tc_Nat_Onat, tc_List_Olist(_1691187))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1691187), tc_prod(tc_Nat_Onat, tc_List_Olist(_1691187))), tc_List_Olist(_1691187)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1691187))), c_Nat_Osize__class_Osize(tc_List_Olist(_1691187)))), c_COMBI(tc_List_Olist(_1691187)))))], (51246 ^ _775828) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (12285 ^ _775828) ^ [_978387, _978389, _978391] : [_978387 = _978389, 12288 ^ _775828 : [(12291 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978391, tc_HOL_Obool)), _978389), _978387)))], (12289 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978391, tc_HOL_Obool)), _978387), _978389)))]]], (14644 ^ _775828) ^ [_1020893, _1020895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020893)), 14647 ^ _775828 : [(14654 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020895)), -(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), _1020895), _1020893))))], (14648 ^ _775828) ^ [] : [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), _1020895), _1020893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020895)))]]], (39290 ^ _775828) ^ [_1524637, _1524639, _1524641, _1524643, _1524645] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524637, tc_fun(_1524639, tc_HOL_Obool)), _1524641), _1524643), _1524645)), 39294 ^ _775828 : [(39297 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1524643, 39293 ^ [_1524637, _1524639, _1524641, _1524643, _1524645]), _1524645)))], (39295 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524637), 39293 ^ [_1524637, _1524639, _1524641, _1524643, _1524645]), _1524641)))]]], (35619 ^ _775828) ^ [_1444684, _1444686, _1444688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444684, tc_HOL_Obool)), _1444686), _1444688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1444684, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1444684, _1444686)), c_Predicate_OPowp(_1444684, _1444688))))], (6480 ^ 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hAPP(c_Nat_OSuc, _872386)), hAPP(c_Nat_OSuc, _872388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872386), _872388)))], (25491 ^ _775828) ^ [_1225567, _1225569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225567), _1225569)), -(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), _1225567), _1225569)), c_Wellfounded_Oless__than)))], (36563 ^ _775828) ^ [_1462927] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1462927) = 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), _1462927))))], (40357 ^ _775828) ^ [] : [-(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)))], (43608 ^ _775828) ^ [_1628606, _1628608, _1628610, _1628612] : [class_Lattices_Osemilattice__inf(_1628606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628606), _1628608)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628606, _1628606, c_Lattices_Osemilattice__inf__class_Oinf(_1628606)), _1628610), hAPP(hAPP(c_Set_Oinsert(_1628606), _1628612), _1628608)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1628606), _1628612), hAPP(hAPP(c_Finite__Set_Ofold(_1628606, _1628606, c_Lattices_Osemilattice__inf__class_Oinf(_1628606)), _1628610), _1628608)))], (33737 ^ _775828) ^ [_1402545, _1402547] : [class_Lattices_Osemilattice__inf(_1402545), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402545), _1402547), _1402547) = _1402547)], (48395 ^ _775828) ^ [_1745920, _1745922, _1745924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745920, tc_HOL_Obool)), hAPP(c_List_Oset(_1745920), hAPP(hAPP(c_List_Odrop(_1745920), _1745922), _1745924))), hAPP(c_List_Oset(_1745920), _1745924))))], (47303 ^ _775828) ^ [_1719304] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719304)), c_List_Olist_ONil(_1719304)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18143 ^ _775828) ^ [_1087242, _1087244] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087242))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087242)), _1087244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1087244))], (11550 ^ _775828) ^ [_965712] : [class_Rings_Olinordered__semidom(_965712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965712), c_Groups_Oone__class_Oone(_965712)), c_Groups_Ozero__class_Ozero(_965712)))], (46919 ^ _775828) ^ [_1709671, _1709673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709671), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1709673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1709673), _1709671)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1709673))))], (5963 ^ _775828) ^ [_870645, _870647, _870649, _870651, _870653] : [c_Com_Ocom_OCall(_870645, _870647, _870649) = c_Com_Ocom_OAss(_870651, _870653)], (5993 ^ _775828) ^ [_871145, _871147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871145), _871147)), _871147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5670 ^ _775828) ^ [_866016, _866018, _866020] : [hBOOL(hAPP(_866020, _866018)), -(hBOOL(hAPP(hAPP(c_member(_866016), _866018), _866020)))], (18761 ^ _775828) ^ [_1098303, _1098305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098303), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098305), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1098303), _1098305) = 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), _1098303), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098305)))))], (3462 ^ _775828) ^ [_828306, _828308, _828310, _828312, _828314, _828316] : [-(c_Com_Ocom_OCond(_828316, _828312, _828308) = c_Com_Ocom_OCond(_828314, _828310, _828306)), _828316 = _828314, _828312 = _828310, _828308 = _828306], (35427 ^ _775828) ^ [_1441301, _1441303, _1441305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1441301), _1441303)), hBOOL(hAPP(_1441305, _1441303)), 35438 ^ _775828 : [(35441 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441301), 35436 ^ [_1441301, _1441303, _1441305]), 35437 ^ [_1441301, _1441303, _1441305])))], (35443 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1441305, 35437 ^ [_1441301, _1441303, _1441305])))], (35445 ^ _775828) ^ [] : [hBOOL(hAPP(_1441305, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1441301, tc_HOL_Obool)), 35437 ^ [_1441301, _1441303, _1441305]), hAPP(hAPP(c_Set_Oinsert(_1441301), 35436 ^ [_1441301, _1441303, _1441305]), c_Orderings_Obot__class_Obot(tc_fun(_1441301, tc_HOL_Obool))))))], (35439 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1441301), 35437 ^ [_1441301, _1441303, _1441305])))]], -(hBOOL(hAPP(_1441305, c_Orderings_Obot__class_Obot(tc_fun(_1441301, tc_HOL_Obool)))))], (14826 ^ _775828) ^ [_1023908, _1023910, _1023912] : [-(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), _1023908), _1023910)), _1023910)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023908, _1023910))), _1023912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023908), _1023912))], (38948 ^ _775828) ^ [_1517275, _1517277, _1517279, _1517281] : [c_Fun_Oinj__on(_1517275, _1517277, _1517279, _1517281), -(hAPP(c_Finite__Set_Ocard(_1517277), hAPP(c_Set_Oimage(_1517275, _1517277, _1517279), _1517281)) = hAPP(c_Finite__Set_Ocard(_1517275), _1517281))], (7501 ^ _775828) ^ [_895535] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _895535)) = _895535)], (15302 ^ _775828) ^ [_1032926, _1032928, _1032930, _1032932, _1032934, _1032936] : [class_Divides_Oring__div(_1032926), c_Divides_Odiv__class_Omod(_1032926, _1032928, _1032930) = c_Divides_Odiv__class_Omod(_1032926, _1032932, _1032930), c_Divides_Odiv__class_Omod(_1032926, _1032934, _1032930) = c_Divides_Odiv__class_Omod(_1032926, _1032936, _1032930), -(c_Divides_Odiv__class_Omod(_1032926, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032926), _1032928), _1032934), _1032930) = c_Divides_Odiv__class_Omod(_1032926, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032926), _1032932), _1032936), _1032930))], (27851 ^ _775828) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (41338 ^ _775828) ^ [_1574668, _1574670, _1574672, _1574674, _1574676, _1574678] : [hBOOL(hAPP(hAPP(c_member(_1574668), _1574670), _1574672)), 41341 ^ _775828 : [(41348 ^ _775828) ^ [] : [_1574676 = _1574678, -(hAPP(hAPP(c_Product__Type_OSigma(_1574674, _1574668), _1574676), hAPP(c_COMBK(tc_fun(_1574668, tc_HOL_Obool), _1574674), _1574672)) = hAPP(hAPP(c_Product__Type_OSigma(_1574674, _1574668), _1574678), hAPP(c_COMBK(tc_fun(_1574668, tc_HOL_Obool), _1574674), _1574672)))], (41342 ^ _775828) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1574674, _1574668), _1574676), hAPP(c_COMBK(tc_fun(_1574668, tc_HOL_Obool), _1574674), _1574672)) = hAPP(hAPP(c_Product__Type_OSigma(_1574674, _1574668), _1574678), hAPP(c_COMBK(tc_fun(_1574668, tc_HOL_Obool), _1574674), _1574672)), -(_1574676 = _1574678)]]], (19302 ^ _775828) ^ [_1107757] : [class_Int_Onumber__ring(_1107757), c_Int_Oiszero(_1107757, hAPP(c_Int_Onumber__class_Onumber__of(_1107757), c_Int_OMin))], (2288 ^ _775828) ^ [_809299, _809301, _809303, _809305] : [-(c_Nitpick_Oint__lcm(_809305, _809301) = c_Nitpick_Oint__lcm(_809303, _809299)), _809305 = _809303, _809301 = _809299], (3652 ^ _775828) ^ [_831341, _831343, _831345, _831347] : [-(c_New__DSequence_Oneg__single(_831347, _831343) = c_New__DSequence_Oneg__single(_831345, _831341)), _831347 = _831345, _831343 = _831341], (45576 ^ _775828) ^ [_1674456, _1674458, _1674460] : [c_Fun_Oinj__on(tc_List_Olist(_1674456), tc_List_Olist(_1674458), hAPP(c_List_Omap(_1674456, _1674458), _1674460), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674456), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1674456, _1674458, _1674460, c_Orderings_Otop__class_Otop(tc_fun(_1674456, tc_HOL_Obool))))], (23628 ^ _775828) ^ [_1189394, _1189396] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1189394)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1189396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1189396))), 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), _1189394)), c_Int_Onat)))))], (48489 ^ _775828) ^ [_1748095, _1748097, _1748099, _1748101] : [-(_1748095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1748097), _1748095), hAPP(hAPP(c_List_Olist_OCons(_1748097), _1748099), _1748101)) = hAPP(hAPP(c_List_Odrop(_1748097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1748095), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1748101))], (41778 ^ _775828) ^ [_1584486, _1584488, _1584490] : [class_Orderings_Olinorder(_1584486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584486), _1584488)), -(_1584488 = c_Orderings_Obot__class_Obot(tc_fun(_1584486, tc_HOL_Obool))), 41789 ^ _775828 : [(41790 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1584486), _1584490), hAPP(c_Finite__Set_Ofold1(_1584486, c_Orderings_Oord__class_Omin(_1584486)), _1584488))), 41793 ^ _775828 : [(41794 ^ _775828) ^ [_1584779] : [hBOOL(hAPP(hAPP(c_member(_1584486), _1584779), _1584488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1584486), _1584490), _1584779)))]]], (41800 ^ _775828) ^ [] : [41802 ^ _775828 : [(41805 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1584486), _1584490), 41801 ^ [_1584486, _1584488, _1584490]))], (41803 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1584486), 41801 ^ [_1584486, _1584488, _1584490]), _1584488)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1584486), _1584490), hAPP(c_Finite__Set_Ofold1(_1584486, c_Orderings_Oord__class_Omin(_1584486)), _1584488))))]]], (51296 ^ _775828) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (9131 ^ _775828) ^ [_921818, _921820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921820)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _921818)), hAPP(c_Int_Onat, _921820)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _921818), _921820)))], (39738 ^ _775828) ^ [_1536440, _1536442, _1536444, _1536446, _1536448] : [_1536440 = c_Orderings_Obot__class_Obot(tc_fun(_1536442, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536442, tc_fun(_1536444, tc_HOL_Obool)), _1536440), hAPP(hAPP(c_COMBC(_1536442, tc_fun(_1536444, tc_HOL_Obool), tc_fun(_1536444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536444, tc_HOL_Obool), tc_fun(tc_fun(_1536444, tc_HOL_Obool), tc_fun(_1536444, tc_HOL_Obool)), _1536442), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536444, tc_HOL_Obool))), _1536446)), _1536448)) = c_Orderings_Obot__class_Obot(tc_fun(_1536444, tc_HOL_Obool)))], (21372 ^ _775828) ^ [_1145916, _1145918, _1145920] : [class_Int_Onumber__ring(_1145916), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145916), hAPP(c_Int_Onumber__class_Onumber__of(_1145916), _1145918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1145920))) = hAPP(hAPP(c_HOL_OLet(_1145916, _1145916), hAPP(hAPP(c_Power_Opower__class_Opower(_1145916), hAPP(c_Int_Onumber__class_Onumber__of(_1145916), _1145918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145920))), hAPP(hAPP(c_COMBS(_1145916, _1145916, _1145916), c_Groups_Otimes__class_Otimes(_1145916)), c_COMBI(_1145916))))], (5176 ^ _775828) ^ [_855011, _855013, _855015, _855017] : [-(c_List_Ofilter(_855017, _855013) = c_List_Ofilter(_855015, _855011)), _855017 = _855015, _855013 = _855011], (38720 ^ _775828) ^ [_1512588, _1512590, _1512592, _1512594] : [hBOOL(hAPP(hAPP(c_member(_1512588), _1512590), _1512592)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1512588, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1512588, _1512588, _1512594), hAPP(hAPP(c_Set_Oinsert(_1512588), _1512590), c_Orderings_Obot__class_Obot(tc_fun(_1512588, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512588), _1512592), _1512594))))], (18025 ^ _775828) ^ [_1084773, _1084775, _1084777, _1084779] : [class_Rings_Olinordered__semidom(_1084773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084773), c_Groups_Oone__class_Oone(_1084773)), _1084775)), 18032 ^ _775828 : [(18039 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084777), _1084779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084773), hAPP(hAPP(c_Power_Opower__class_Opower(_1084773), _1084775), _1084777)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084773), _1084775), _1084779))))], (18033 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084773), hAPP(hAPP(c_Power_Opower__class_Opower(_1084773), _1084775), _1084777)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084773), _1084775), _1084779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084777), _1084779)))]]], (34241 ^ _775828) ^ [_1413032, _1413034, _1413036, _1413038] : [hBOOL(hAPP(hAPP(c_member(_1413032), _1413034), _1413036)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413032, tc_HOL_Obool)), _1413036), hAPP(hAPP(c_Set_Oinsert(_1413032), _1413034), _1413038)) = hAPP(hAPP(c_Set_Oinsert(_1413032), _1413034), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413032, tc_HOL_Obool)), _1413036), _1413038)))], (26345 ^ _775828) ^ [_1240931, _1240933, _1240935] : [class_Divides_Osemiring__div(_1240931), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240931), _1240933), _1240935)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240931), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240931), _1240935), _1240933)), _1240933) = _1240935)], (12789 ^ _775828) ^ [_986947] : [-(_986947 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12792 ^ _775828 : [(12799 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986947))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _986947) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12793 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986947)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _986947) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (11945 ^ _775828) ^ [_972520, _972522, _972524] : [class_Rings_Olinordered__ring(_972520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972520), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972520), _972522), _972522)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972520), _972524), _972524))), c_Groups_Ozero__class_Ozero(_972520)))], (9979 ^ _775828) ^ [_937070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _937070)), -(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, _937070))))], (24206 ^ _775828) ^ [_1199872, _1199874, _1199876, _1199878] : [class_Orderings_Olinorder(_1199872), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199872), _1199874), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199872), _1199876), _1199878)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199872), _1199876), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199872), _1199874), _1199878)))], (11562 ^ _775828) ^ [_965903, _965905, _965907] : [class_Rings_Olinordered__semidom(_965903), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965903), c_Groups_Oone__class_Oone(_965903)), _965905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965903), c_Groups_Oone__class_Oone(_965903)), _965907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965903), c_Groups_Oone__class_Oone(_965903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965903), _965905), _965907))))], (51176 ^ _775828) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (47000 ^ _775828) ^ [_1711689, _1711691] : [47002 ^ _775828 : [(47006 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47004 ^ [_1711689, _1711691]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711689)), _1711691))))], (47008 ^ _775828) ^ [] : [47001 ^ [_1711689, _1711691] = 47004 ^ [_1711689, _1711691]], (47010 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1711689), _1711691), 47001 ^ [_1711689, _1711691]) = hAPP(hAPP(c_List_Onth(_1711689), _1711691), 47004 ^ [_1711689, _1711691]))], (47003 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47001 ^ [_1711689, _1711691]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711689)), _1711691))))]], -(hBOOL(hAPP(c_List_Odistinct(_1711689), _1711691)))], (26365 ^ _775828) ^ [_1241321, _1241323, _1241325, _1241327, _1241329] : [class_Divides_Osemiring__div(_1241321), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241321), _1241323), _1241325)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241321), _1241327), _1241329)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241321), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241321), _1241325), _1241323)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241321), _1241329), _1241327)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241321), _1241325), _1241329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241321), _1241323), _1241327)))], (30708 ^ _775828) ^ [_1337442, _1337444] : [30709 ^ _775828 : [(30712 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337442), _1337444)))], (30710 ^ _775828) ^ [] : [_1337444 = c_Orderings_Obot__class_Obot(tc_fun(_1337442, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1337442), _1337444) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12283 ^ _775828) ^ [_978334, _978336] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978334, tc_HOL_Obool)), _978336), _978336)))], (47355 ^ _775828) ^ [_1720607, _1720609, _1720611] : [c_List_Olist_ONil(_1720607) = hAPP(hAPP(c_List_Olist_OCons(_1720607), _1720609), _1720611)], (14001 ^ _775828) ^ [_1009424, _1009426, _1009428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009424), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14004 ^ _775828 : [(14005 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1009426, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1009428), _1009424)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1009428, _1009424))), 14008 ^ _775828 : [(14009 ^ _775828) ^ [_1009634, _1009636] : [-(hBOOL(hAPP(hAPP(_1009426, _1009636), _1009634))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009424), _1009634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1009634), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1009428 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009424), _1009636)), _1009634)]]], (14023 ^ _775828) ^ [] : [14026 ^ _775828 : [(14029 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14025 ^ [_1009424, _1009426, _1009428]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14031 ^ _775828) ^ [] : [-(_1009428 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009424), 14024 ^ [_1009424, _1009426, _1009428])), 14025 ^ [_1009424, _1009426, _1009428]))], (14033 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1009426, 14024 ^ [_1009424, _1009426, _1009428]), 14025 ^ [_1009424, _1009426, _1009428]))], (14027 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009424), 14025 ^ [_1009424, _1009426, _1009428])))]], -(hBOOL(hAPP(hAPP(_1009426, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1009428), _1009424)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1009428, _1009424))))]]], (33717 ^ _775828) ^ [_1402120, _1402122, _1402124, _1402126] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402120, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402120, tc_HOL_Obool)), _1402122), _1402124)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402120, tc_HOL_Obool)), _1402126), _1402124)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402120, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402120, tc_HOL_Obool)), _1402122), _1402124)), _1402126))], (24176 ^ _775828) ^ [_1199211, _1199213, _1199215] : [class_Orderings_Olinorder(_1199211), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199211), _1199213), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199211), _1199213), _1199215)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199211), _1199213), _1199215))], (6666 ^ _775828) ^ [_881566, _881568, _881570] : [class_Rings_Osemiring__1(_881566), hBOOL(hAPP(hAPP(c_member(_881566), _881568), c_Nat_Osemiring__1__class_ONats(_881566))), hBOOL(hAPP(_881570, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_881566), 6675 ^ [_881566, _881568, _881570]))), -(hBOOL(hAPP(_881570, _881568)))], (49375 ^ _775828) ^ [_1767344, _1767346] : [-(hAPP(c_List_Ofilter(_1767344, _1767346), c_List_Olist_ONil(_1767344)) = c_List_Olist_ONil(_1767344))], (26171 ^ _775828) ^ [_1237860, _1237862, _1237864] : [class_Rings_Ocomm__semiring__1(_1237860), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237860), _1237862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237860), _1237864), _1237862))))], (19940 ^ _775828) ^ [_1118159, _1118161] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1118159), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118161)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1118159), 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)))), _1118161)))], (30357 ^ _775828) ^ [_1330484] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330484), c_Orderings_Obot__class_Obot(tc_fun(_1330484, tc_HOL_Obool)))))], (1890 ^ _775828) ^ [_803184, _803186, _803188, _803190] : [-(c_Int_Onat__aux(_803190, _803186) = c_Int_Onat__aux(_803188, _803184)), _803190 = _803188, _803186 = _803184], (36851 ^ _775828) ^ [_1468128, _1468130, _1468132, _1468134, _1468136] : [c_Finite__Set_Ofolding__one__idem(_1468128, _1468130, _1468132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468128), _1468134)), -(_1468136 = c_Orderings_Obot__class_Obot(tc_fun(_1468128, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468128, tc_HOL_Obool)), _1468136), _1468134)), -(hAPP(hAPP(_1468130, hAPP(_1468132, _1468136)), hAPP(_1468132, _1468134)) = hAPP(_1468132, _1468134))], (50405 ^ _775828) ^ [_1789028, _1789030, _1789032] : [hAPP(c_List_Orev(_1789028), _1789030) = _1789032, -(_1789030 = hAPP(c_List_Orev(_1789028), _1789032))], (23700 ^ _775828) ^ [_1190866, _1190868, _1190870, _1190872] : [class_Orderings_Olinorder(_1190866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190866), _1190868), _1190870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190866), _1190868), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190866), _1190870), _1190872))))], (44240 ^ _775828) ^ [_1642669, _1642671, _1642673, _1642675] : [-(_1642669 = c_Orderings_Obot__class_Obot(tc_fun(_1642671, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642671, tc_fun(_1642673, tc_HOL_Obool)), _1642669), hAPP(c_COMBK(tc_fun(_1642673, tc_HOL_Obool), _1642671), _1642675)) = _1642675)], (36926 ^ _775828) ^ [_1469935, _1469937, _1469939, _1469941, _1469943, _1469945] : [class_Groups_Ocomm__monoid__add(_1469935), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469937, _1469935), hAPP(hAPP(c_COMBC(_1469937, tc_fun(_1469939, tc_HOL_Obool), _1469935), hAPP(hAPP(c_COMBB(tc_fun(_1469939, _1469935), tc_fun(tc_fun(_1469939, tc_HOL_Obool), _1469935), _1469937), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469939, _1469935)), _1469941)), _1469943)), _1469945) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469939, _1469935), hAPP(hAPP(c_COMBC(_1469939, tc_fun(_1469937, tc_HOL_Obool), _1469935), hAPP(hAPP(c_COMBB(tc_fun(_1469937, _1469935), tc_fun(tc_fun(_1469937, tc_HOL_Obool), _1469935), _1469939), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469937, _1469935)), hAPP(c_COMBC(_1469937, _1469939, _1469935), _1469941))), _1469945)), _1469943))], (46001 ^ _775828) ^ [_1684088, _1684090, _1684092, _1684094, _1684096] : [hBOOL(hAPP(hAPP(c_member(_1684088), _1684090), hAPP(c_List_Oset(_1684088), _1684092))), -(hAPP(c_Map_Omap__of(_1684088, _1684094, hAPP(hAPP(c_List_Ozip(_1684088, _1684094), _1684092), hAPP(hAPP(c_List_Omap(_1684088, _1684094), _1684096), _1684092))), _1684090) = hAPP(c_Option_Ooption_OSome(_1684094), hAPP(_1684096, _1684090)))], (3138 ^ _775828) ^ [_823166, _823168, _823170, _823172, _823174, _823176, _823178, _823180, _823182, _823184] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_823184, _823180, _823176, _823172, _823168) = c_SetInterval_Oord_OgreaterThanAtMost(_823182, _823178, _823174, _823170, _823166)), _823184 = _823182, _823180 = _823178, _823176 = _823174, _823172 = _823170, _823168 = _823166], (30999 ^ _775828) ^ [_1343908, _1343910, _1343912, _1343914, _1343916] : [c_Finite__Set_Ofolding__one(_1343908, _1343910, _1343912), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343908), _1343914)), hBOOL(hAPP(hAPP(c_member(_1343908), _1343916), _1343914)), 31010 ^ _775828 : [(31017 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343908, tc_HOL_Obool)), _1343914), hAPP(hAPP(c_Set_Oinsert(_1343908), _1343916), c_Orderings_Obot__class_Obot(tc_fun(_1343908, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1343908, tc_HOL_Obool))), -(hAPP(_1343912, _1343914) = hAPP(hAPP(_1343910, _1343916), hAPP(_1343912, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343908, tc_HOL_Obool)), _1343914), hAPP(hAPP(c_Set_Oinsert(_1343908), _1343916), c_Orderings_Obot__class_Obot(tc_fun(_1343908, tc_HOL_Obool)))))))], (31011 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343908, tc_HOL_Obool)), _1343914), hAPP(hAPP(c_Set_Oinsert(_1343908), _1343916), c_Orderings_Obot__class_Obot(tc_fun(_1343908, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1343908, tc_HOL_Obool)), -(hAPP(_1343912, _1343914) = _1343916)]]], (35693 ^ _775828) ^ [_1446055, _1446057, _1446059, _1446061] : [class_Orderings_Oorder(_1446055), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446055, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1446055, _1446057, _1446059)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1446055, _1446059, _1446061)) = c_Orderings_Obot__class_Obot(tc_fun(_1446055, tc_HOL_Obool)))], (51332 ^ _775828) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (3636 ^ _775828) ^ [_831107, _831109, _831111, _831113] : [-(c_Lazy__Sequence_Osingle(_831113, _831109) = c_Lazy__Sequence_Osingle(_831111, _831107)), _831113 = _831111, _831109 = _831107], (45084 ^ _775828) ^ [_1663451, _1663453, _1663455] : [45086 ^ _775828 : [(45089 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663451, tc_HOL_Obool)), 45085 ^ [_1663451, _1663453, _1663455]), _1663455))], (45087 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1663451, tc_HOL_Obool)), 45085 ^ [_1663451, _1663453, _1663455]), _1663453)))]], -(_1663453 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1663451, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663451, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663451, tc_HOL_Obool), _1663453)), _1663455)))], (31681 ^ _775828) ^ [_1359589, _1359591] : [-(c_Transitive__Closure_Otrancl(_1359589, _1359591) = hAPP(hAPP(c_Relation_Orel__comp(_1359589, _1359589, _1359589), c_Transitive__Closure_Ortrancl(_1359589, _1359591)), _1359591))], (3346 ^ _775828) ^ [_826472, _826474] : [_826474 = _826472, -(c_Relation_OId(_826474) = c_Relation_OId(_826472))], (46927 ^ _775828) ^ [_1709847, _1709849, _1709851, _1709853] : [-(hAPP(hAPP(c_List_Onth(_1709847), hAPP(hAPP(c_List_Olist_OCons(_1709847), _1709849), _1709851)), hAPP(c_Nat_OSuc, _1709853)) = hAPP(hAPP(c_List_Onth(_1709847), _1709851), _1709853))], (27310 ^ _775828) ^ [_1259829, _1259831, _1259833, _1259835, _1259837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1259829, _1259831)), hAPP(hAPP(c_Product__Type_OPair(_1259829, _1259831), _1259833), _1259835)), _1259837)), -(hBOOL(hAPP(hAPP(c_member(_1259831), _1259835), hAPP(c_Relation_ORange(_1259829, _1259831), _1259837))))], (10336 ^ _775828) ^ [_943792] : [class_Rings_Osemiring__1(_943792), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_943792), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_943792))], (17423 ^ _775828) ^ [_1074226, _1074228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074226)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1074226), _1074228)))], (4998 ^ _775828) ^ [_852292, _852294, _852296, _852298] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_852298, _852294) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_852296, _852292)), _852298 = _852296, _852294 = _852292], (16737 ^ _775828) ^ [_1060942, _1060944] : [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), _1060942)), _1060944))), _1060942 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1060944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47693 ^ _775828) ^ [_1727778, _1727780, _1727782, _1727784, _1727786, _1727788, _1727790] : [-(c_Map_Omap__upds(_1727778, _1727780, _1727782, hAPP(hAPP(c_List_Olist_OCons(_1727778), _1727784), _1727786), hAPP(hAPP(c_List_Olist_OCons(_1727780), _1727788), _1727790)) = c_Map_Omap__upds(_1727778, _1727780, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1727778, tc_Option_Ooption(_1727780)), _1727782), _1727784), hAPP(c_Option_Ooption_OSome(_1727780), _1727788)), _1727786, _1727790))], (29531 ^ _775828) ^ [_1311608, _1311610, _1311612] : [hAPP(hAPP(c_Set_Oinsert(_1311608), _1311610), _1311612) = c_Orderings_Obot__class_Obot(tc_fun(_1311608, tc_HOL_Obool))], (10820 ^ _775828) ^ [_952748, _952750] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952748), _952750) = _952748, -(_952750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47515 ^ _775828) ^ [_1723561, _1723563] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723561), tc_List_Olist(_1723561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723561), tc_List_Olist(_1723561)), c_List_Olist_ONil(_1723561)), c_List_Olist_ONil(_1723561))), c_List_Olistrel(_1723561, _1723563))))], (36309 ^ _775828) ^ [_1457465, _1457467, _1457469, _1457471] : [class_Orderings_Olinorder(_1457465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457465), _1457467), _1457469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457465), _1457469), _1457471)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1457465, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457465, _1457467), _1457469)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457465, _1457469), _1457471)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457465, _1457467), _1457471))], (19624 ^ _775828) ^ [_1113043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1113043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1113043)))], (47749 ^ _775828) ^ [_1729336, _1729338, _1729340, _1729342, _1729344] : [hAPP(hAPP(c_List_Olist_OCons(_1729336), _1729338), _1729340) = hAPP(hAPP(c_List_Oappend(_1729336), _1729342), _1729344), 47754 ^ _775828 : [(47757 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1729336), _1729338), _1729340) = _1729344)], (47755 ^ _775828) ^ [] : [-(_1729342 = c_List_Olist_ONil(_1729336))]], 47759 ^ _775828 : [(47762 ^ _775828) ^ [] : [-(_1729340 = hAPP(hAPP(c_List_Oappend(_1729336), 47758 ^ [_1729336, _1729338, _1729340, _1729342, _1729344]), _1729344))], (47760 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1729336), _1729338), 47758 ^ [_1729336, _1729338, _1729340, _1729342, _1729344]) = _1729342)]]], (47127 ^ _775828) ^ [_1714941, _1714943, _1714945, _1714947] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714941), tc_List_Olist(_1714941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714941), tc_List_Olist(_1714941)), _1714943), _1714945)), c_List_Olistrel(_1714941, _1714947)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714941)), _1714943) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714941)), _1714945), 47133 ^ _775828 : [(47136 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714941, _1714941)), hAPP(hAPP(c_Product__Type_OPair(_1714941, _1714941), hAPP(hAPP(c_List_Onth(_1714941), _1714943), 47132 ^ [_1714941, _1714943, _1714945, _1714947])), hAPP(hAPP(c_List_Onth(_1714941), _1714945), 47132 ^ [_1714941, _1714943, _1714945, _1714947]))), _1714947))], (47134 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47132 ^ [_1714941, _1714943, _1714945, _1714947]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714941)), _1714943))))]]], (50251 ^ _775828) ^ [_1785682] : [-(c_List_Oconcat(_1785682, c_List_Olist_ONil(tc_List_Olist(_1785682))) = c_List_Olist_ONil(_1785682))], (45789 ^ _775828) ^ [_1679566, _1679568, _1679570, _1679572] : [hAPP(c_Map_Omap__of(_1679566, _1679568, _1679570), _1679572) = c_Option_Ooption_ONone(_1679568), hBOOL(hAPP(hAPP(c_member(_1679566), _1679572), hAPP(c_Set_Oimage(tc_prod(_1679566, _1679568), _1679566, c_Product__Type_Ofst(_1679566, _1679568)), hAPP(c_List_Oset(tc_prod(_1679566, _1679568)), _1679570))))], (6416 ^ _775828) ^ [_877938, _877940, _877942] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_877938, _877940, _877942))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _877940))))], (10070 ^ _775828) ^ [_938743, _938745, _938747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938743), _938745)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938743), _938747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938745), _938747)))], (38502 ^ _775828) ^ [_1507871, _1507873, _1507875, _1507877, _1507879, _1507881] : [-(hBOOL(hAPP(hAPP(c_member(_1507871), _1507873), _1507875))), -(hAPP(c_Fun_Ooverride__on(_1507871, _1507877, _1507879, _1507881, _1507875), _1507873) = hAPP(_1507879, _1507873))], (19526 ^ _775828) ^ [_1111395, _1111397] : [_1111395 = _1111397, -(c_Int_OBit1(_1111395) = c_Int_OBit1(_1111397))], (2178 ^ _775828) ^ [_807636, _807638, _807640, _807642] : [-(c_Orderings_Oord_Omax(_807642, _807638) = c_Orderings_Oord_Omax(_807640, _807636)), _807642 = _807640, _807638 = _807636], (9065 ^ _775828) ^ [_920848, _920850] : [_920848 = hAPP(c_Int_Onat, _920850), 9068 ^ _775828 : [(9075 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _920850))), -(_920848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9069 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _920850)), -(_920850 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920848))]]], (20762 ^ _775828) ^ [_1132920] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1132920, 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, _1132920, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (2084 ^ _775828) ^ [_806245, _806247] : [_806247 = _806245, -(c_Divides_Oadjust(_806247) = c_Divides_Oadjust(_806245))], (49704 ^ _775828) ^ [_1775113, _1775115, _1775117, _1775119] : [class_Orderings_Olinorder(_1775113), 49707 ^ _775828 : [(49716 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1775113, hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775115), hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775117), _1775119)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1775113), _1775115), _1775117)), c_List_Olinorder__class_Osorted(_1775113, hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775117), _1775119))], (49708 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1775113, hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775115), hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775117), _1775119))), 49711 ^ _775828 : [(49714 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1775113, hAPP(hAPP(c_List_Olist_OCons(_1775113), _1775117), _1775119)))], (49712 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1775113), _1775115), _1775117)))]]]]], (41152 ^ _775828) ^ [_1569129, _1569131, _1569133, _1569135, _1569137, _1569139] : [c_Hoare__Mirabelle_Ohoare__derivs(_1569129, _1569131, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1569129)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1569129), _1569133), _1569135), _1569137)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1569129), tc_HOL_Obool)))), 41159 ^ _775828 : [(41162 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1569139, 41157 ^ [_1569129, _1569131, _1569133, _1569135, _1569137, _1569139]), 41158 ^ [_1569129, _1569131, _1569133, _1569135, _1569137, _1569139]))], (41160 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1569137, 41157 ^ [_1569129, _1569131, _1569133, _1569135, _1569137, _1569139]), 41158 ^ [_1569129, _1569131, _1569133, _1569135, _1569137, _1569139])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1569129, _1569131, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1569129)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1569129), _1569133), _1569135), _1569139)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1569129), tc_HOL_Obool)))))], (24455 ^ _775828) ^ [_1205252, _1205254, _1205256, _1205258] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1205252, _1205254, _1205256, c_Code__Numeral_OSuc__code__numeral(_1205258)) = hAPP(_1205256, _1205258))], (16190 ^ _775828) ^ [_1050778, _1050780] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050778, _1050780) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050778, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050780)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050778, _1050780)), _1050780))], (4240 ^ _775828) ^ [_840631, _840633] : [_840633 = _840631, -(c_List_Orotate1(_840633) = c_List_Orotate1(_840631))], (44248 ^ _775828) ^ [_1642786, _1642788, _1642790, _1642792, _1642794] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642786, tc_fun(_1642788, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1642786), _1642790), _1642792)), _1642794) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642788, tc_HOL_Obool)), hAPP(_1642794, _1642790)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642786, tc_fun(_1642788, tc_HOL_Obool)), _1642792), _1642794)))], (17559 ^ _775828) ^ [_1076411, _1076413] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076411) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076413)), _1076411 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076413)), 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), _1076413)))], (17069 ^ _775828) ^ [_1067253, _1067255, _1067257] : [class_Int_Onumber__ring(_1067253), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067253), hAPP(c_Int_Onumber__class_Onumber__of(_1067253), _1067255)), hAPP(c_Int_Onumber__class_Onumber__of(_1067253), _1067257)) = hAPP(c_Int_Onumber__class_Onumber__of(_1067253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067255), _1067257)))], (51168 ^ _775828) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (19582 ^ _775828) ^ [_1112417] : [c_Int_OPls = c_Int_OBit1(_1112417)], (42976 ^ _775828) ^ [_1613543, _1613545, _1613547, _1613549, _1613551, _1613553, _1613555, _1613557] : [c_Finite__Set_Ofolding__image(_1613543, _1613545, _1613547, _1613549, _1613551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613545), _1613553)), c_Fun_Oinj__on(_1613545, _1613545, _1613555, _1613553), -(hAPP(hAPP(_1613551, _1613557), hAPP(c_Set_Oimage(_1613545, _1613545, _1613555), _1613553)) = hAPP(hAPP(_1613551, hAPP(c_Fun_Ocomp(_1613545, _1613543, _1613545, _1613557), _1613555)), _1613553))], (43028 ^ _775828) ^ [_1614795, _1614797, _1614799, _1614801, _1614803, _1614805, _1614807, _1614809] : [c_Finite__Set_Ofolding(_1614795, _1614797, _1614799, _1614801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614795), _1614803)), -(hAPP(c_Fun_Ocomp(_1614797, _1614797, _1614805, hAPP(_1614799, _1614807)), hAPP(c_Fun_Ocomp(_1614797, _1614797, _1614805, hAPP(_1614801, _1614803)), _1614809)) = hAPP(c_Fun_Ocomp(_1614797, _1614797, _1614805, hAPP(_1614801, _1614803)), hAPP(c_Fun_Ocomp(_1614797, _1614797, _1614805, hAPP(_1614799, _1614807)), _1614809)))], (16425 ^ _775828) ^ [_1055156] : [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), _1055156))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055156) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055156)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (7187 ^ _775828) ^ [_890183, _890185, _890187] : [class_Rings_Olinordered__semiring__strict(_890183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890183), c_Groups_Ozero__class_Ozero(_890183)), _890185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890183), c_Groups_Ozero__class_Ozero(_890183)), _890187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890183), c_Groups_Ozero__class_Ozero(_890183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890183), _890185), _890187))))], (48455 ^ _775828) ^ [_1747252, _1747254, _1747256, _1747258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1747252), _1747254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747256, tc_HOL_Obool)), hAPP(c_List_Oset(_1747256), hAPP(hAPP(c_List_Odrop(_1747256), _1747254), _1747258))), hAPP(c_List_Oset(_1747256), hAPP(hAPP(c_List_Odrop(_1747256), _1747252), _1747258)))))], (35245 ^ _775828) ^ [_1436682, _1436684] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436682), _1436684))), -(hAPP(c_Finite__Set_Ocard(_1436682), _1436684) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16613 ^ _775828) ^ [_1058493, _1058495] : [class_Rings_Olinordered__idom(_1058493), -(hAPP(c_Groups_Oabs__class_Oabs(_1058493), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058493), _1058495)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058493), _1058495))], (29905 ^ _775828) ^ [_1319808, _1319810, _1319812, _1319814, _1319816] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1319808, _1319810, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1319808)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1319808), hAPP(hAPP(c_COMBC(_1319808, 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)), _1319808), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1319812)), 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), _1319814)), _1319816))), c_Com_Ocom_OAss(_1319814, _1319816)), _1319812)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1319808), tc_HOL_Obool)))))], (19826 ^ _775828) ^ [] : [-(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)))))], (48882 ^ _775828) ^ [_1756449, _1756451, _1756453] : [class_Orderings_Olinorder(_1756449), -(c_Big__Operators_Olattice_OInf__fin(_1756449, c_Orderings_Oord__class_Omin(_1756449), hAPP(c_List_Oset(_1756449), hAPP(hAPP(c_List_Olist_OCons(_1756449), _1756451), _1756453))) = hAPP(c_List_Ofoldl(_1756449, _1756449, c_Orderings_Oord__class_Omin(_1756449), _1756451), _1756453))], (32629 ^ _775828) ^ [_1378662, _1378664, _1378666] : [class_Lattices_Olattice(_1378662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378662), _1378664)), 32636 ^ _775828 : [(32643 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378662, tc_HOL_Obool)), _1378664), hAPP(hAPP(c_Set_Oinsert(_1378662), _1378666), c_Orderings_Obot__class_Obot(tc_fun(_1378662, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1378662, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1378662, hAPP(hAPP(c_Set_Oinsert(_1378662), _1378666), _1378664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1378662), _1378666), c_Big__Operators_Olattice__class_OSup__fin(_1378662, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378662, tc_HOL_Obool)), _1378664), hAPP(hAPP(c_Set_Oinsert(_1378662), _1378666), c_Orderings_Obot__class_Obot(tc_fun(_1378662, tc_HOL_Obool)))))))], (32637 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378662, tc_HOL_Obool)), _1378664), hAPP(hAPP(c_Set_Oinsert(_1378662), _1378666), c_Orderings_Obot__class_Obot(tc_fun(_1378662, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1378662, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1378662, hAPP(hAPP(c_Set_Oinsert(_1378662), _1378666), _1378664)) = _1378666)]]], (21666 ^ _775828) ^ [_1151163, _1151165] : [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(_1151163))), 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)), _1151165)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151163)), hAPP(c_Nat_OSuc, _1151165))))], (40606 ^ _775828) ^ [_1556464, _1556466, _1556468, _1556470] : [c_Equiv__Relations_Oequivp(_1556464, _1556466), hBOOL(hAPP(hAPP(_1556466, _1556468), _1556470)), -(hBOOL(hAPP(hAPP(_1556466, _1556470), _1556468)))], (25423 ^ _775828) ^ [_1224231] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1224231)) = _1224231)], (42920 ^ _775828) ^ [] : [-(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))], (50742 ^ _775828) ^ [_1797461, _1797463] : [c_List_Olist_ONil(_1797461) = c_List_Oremdups(_1797461, _1797463), -(_1797463 = c_List_Olist_ONil(_1797461))], (6919 ^ _775828) ^ [_885437, _885439, _885441] : [class_Int_Oring__char__0(_885437), 6922 ^ _775828 : [(6929 ^ _775828) ^ [] : [_885439 = _885441, -(hAPP(c_Int_Oring__1__class_Oof__int(_885437), _885439) = hAPP(c_Int_Oring__1__class_Oof__int(_885437), _885441))], (6923 ^ _775828) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_885437), _885439) = hAPP(c_Int_Oring__1__class_Oof__int(_885437), _885441), -(_885439 = _885441)]]], (50453 ^ _775828) ^ [_1789988, _1789990, _1789992, _1789994] : [-(c_List_Otranspose(_1789988, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1789988)), hAPP(hAPP(c_List_Olist_OCons(_1789988), _1789990), _1789992)), _1789994)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1789988)), hAPP(hAPP(c_List_Olist_OCons(_1789988), _1789990), c_List_Oconcat(_1789988, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1789988), tc_List_Olist(_1789988)), c_List_Olist_Olist__case(tc_List_Olist(_1789988), _1789988, c_List_Olist_ONil(_1789988), hAPP(hAPP(c_COMBB(tc_List_Olist(_1789988), tc_fun(tc_List_Olist(_1789988), tc_List_Olist(_1789988)), _1789988), c_COMBK(tc_List_Olist(_1789988), tc_List_Olist(_1789988))), hAPP(hAPP(c_COMBC(_1789988, tc_List_Olist(_1789988), tc_List_Olist(_1789988)), c_List_Olist_OCons(_1789988)), c_List_Olist_ONil(_1789988))))), _1789994)))), c_List_Otranspose(_1789988, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1789988)), _1789992), c_List_Oconcat(tc_List_Olist(_1789988), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1789988), tc_List_Olist(tc_List_Olist(_1789988))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1789988)), _1789988, c_List_Olist_ONil(tc_List_Olist(_1789988)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1789988), tc_List_Olist(tc_List_Olist(_1789988))), _1789988), hAPP(hAPP(c_COMBC(tc_List_Olist(_1789988), tc_List_Olist(tc_List_Olist(_1789988)), tc_List_Olist(tc_List_Olist(_1789988))), c_List_Olist_OCons(tc_List_Olist(_1789988))), c_List_Olist_ONil(tc_List_Olist(_1789988)))))), _1789994))))))], (28335 ^ _775828) ^ [_1284352, _1284354, _1284356, _1284358] : [28349 ^ _775828 : [(28352 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1284358, 28348 ^ [_1284352, _1284354, _1284356, _1284358])))], (28350 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1284352), 28348 ^ [_1284352, _1284354, _1284356, _1284358]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284352, tc_HOL_Obool)), _1284354), _1284356))))]], 28336 ^ _775828 : [(28343 ^ _775828) ^ [_1284561] : [hBOOL(hAPP(hAPP(c_member(_1284352), _1284561), _1284356)), hBOOL(hAPP(_1284358, _1284561))], (28337 ^ _775828) ^ [_1284465] : [hBOOL(hAPP(hAPP(c_member(_1284352), _1284465), _1284354)), hBOOL(hAPP(_1284358, _1284465))]]], (14385 ^ _775828) ^ [_1016523, _1016525] : [hBOOL(hAPP(c_Com_OWT, _1016523)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1016525, _1016523))))], (29084 ^ _775828) ^ [_1302297, _1302299, _1302301, _1302303] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302297, _1302297)), hAPP(hAPP(c_Product__Type_OPair(_1302297, _1302297), _1302299), _1302301)), hAPP(c_Relation_Oconverse(_1302297, _1302297), c_Transitive__Closure_Otrancl(_1302297, _1302303)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302297, _1302297)), hAPP(hAPP(c_Product__Type_OPair(_1302297, _1302297), _1302299), _1302301)), c_Transitive__Closure_Otrancl(_1302297, hAPP(c_Relation_Oconverse(_1302297, _1302297), _1302303)))))], (47253 ^ _775828) ^ [_1718474, _1718476, _1718478] : [-(hAPP(hAPP(c_List_Olist__update(_1718474, _1718476), _1718478), hAPP(hAPP(c_List_Onth(_1718474), _1718476), _1718478)) = _1718476)], (36125 ^ _775828) ^ [_1454319, _1454321, _1454323, _1454325, _1454327] : [class_Orderings_Olinorder(_1454319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454319), _1454321), _1454323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454319), _1454325), _1454327)), 36136 ^ _775828 : [(36145 ^ _775828) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454319, _1454321), _1454323) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454319, _1454325), _1454327)), _1454321 = _1454325, _1454323 = _1454327], (36137 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454319, _1454321), _1454323) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454319, _1454325), _1454327), 36140 ^ _775828 : [(36143 ^ _775828) ^ [] : [-(_1454323 = _1454327)], (36141 ^ _775828) ^ [] : [-(_1454321 = _1454325)]]]]], (46889 ^ _775828) ^ [_1708631, _1708633, _1708635, _1708637, _1708639, _1708641] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708631), tc_List_Olist(_1708631))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708631), tc_List_Olist(_1708631)), hAPP(hAPP(c_List_Olist_OCons(_1708631), _1708633), _1708635)), hAPP(hAPP(c_List_Olist_OCons(_1708631), _1708637), _1708639))), c_List_Olexord(_1708631, _1708641)))), 46890 ^ _775828 : [(46893 ^ _775828) ^ [] : [_1708633 = _1708637, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708631), tc_List_Olist(_1708631))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708631), tc_List_Olist(_1708631)), _1708635), _1708639)), c_List_Olexord(_1708631, _1708641)))], (46891 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1708631, _1708631)), hAPP(hAPP(c_Product__Type_OPair(_1708631, _1708631), _1708633), _1708637)), _1708641))]]], (15446 ^ _775828) ^ [_1035475, _1035477, _1035479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035475), _1035477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035475), _1035479)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035477), _1035479))))], (11104 ^ _775828) ^ [_957648, _957650, _957652, _957654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957648, tc_HOL_Obool)), _957650), _957652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957648, tc_HOL_Obool)), _957652), _957654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957648, tc_HOL_Obool)), _957650), _957654)))], (40499 ^ _775828) ^ [_1552684, _1552686, _1552688, _1552690] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1552684, _1552686, hAPP(hAPP(c_Set_Oinsert(_1552684), _1552688), c_Orderings_Obot__class_Obot(tc_fun(_1552684, tc_HOL_Obool)))), _1552690)), -(_1552688 = _1552690)], (47291 ^ _775828) ^ [_1719116, _1719118] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719116)), _1719118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1719118 = c_List_Olist_ONil(_1719116))], (49035 ^ _775828) ^ [_1760323, _1760325, _1760327, _1760329] : [49036 ^ _775828 : [(49037 ^ _775828) ^ [_1760420, _1760422] : [_1760323 = hAPP(hAPP(c_List_Olist_OCons(_1760325), _1760422), _1760420)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760325), tc_List_Olist(_1760325))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760325), tc_List_Olist(_1760325)), _1760327), hAPP(hAPP(c_List_Oappend(_1760325), _1760327), _1760323))), c_List_Olexord(_1760325, _1760329))))], (10756 ^ _775828) ^ [_951591, _951593, _951595] : [class_Groups_Ogroup__add(_951591), -(hAPP(c_Groups_Ouminus__class_Ouminus(_951591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951591), _951593), _951595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951591), hAPP(c_Groups_Ouminus__class_Ouminus(_951591), _951595)), hAPP(c_Groups_Ouminus__class_Ouminus(_951591), _951593)))], (19562 ^ _775828) ^ [_1112044, _1112046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112044), _1112046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1112044)), c_Int_OBit1(_1112046))))], (16340 ^ _775828) ^ [_1053561, _1053563] : [_1053561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053561), _1053563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3542 ^ _775828) ^ [_829584, _829586, _829588, _829590, _829592, _829594, _829596, _829598] : [-(c_New__Random__Sequence_Opos__map(_829598, _829594, _829590, _829586) = c_New__Random__Sequence_Opos__map(_829596, _829592, _829588, _829584)), _829598 = _829596, _829594 = _829592, _829590 = _829588, _829586 = _829584], (3250 ^ _775828) ^ [_825006, _825008, _825010, _825012] : [-(c_Set_Othe__elem(_825012, _825008) = c_Set_Othe__elem(_825010, _825006)), _825012 = _825010, _825008 = _825006], (18945 ^ _775828) ^ [_1101768, _1101770, _1101772] : [hBOOL(hAPP(_1101768, 18946 ^ [_1101768, _1101770, _1101772])), 18949 ^ _775828 : [(18950 ^ _775828) ^ [_1101879, _1101881] : [-(hBOOL(hAPP(_1101768, hAPP(hAPP(c_Product__Type_OPair(_1101770, _1101772), _1101881), _1101879))))]]], (16210 ^ _775828) ^ [_1051045, _1051047] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051045), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1051047), _1051045)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1051047), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1051047, _1051045)))], (29769 ^ _775828) ^ [_1316574, _1316576, _1316578] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1316574, _1316576, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316574)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316574), _1316578), c_Com_Ocom_OSKIP), _1316578)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316574), tc_HOL_Obool)))))], (38852 ^ _775828) ^ [_1515615, _1515617, _1515619, _1515621, _1515623, _1515625] : [c_Fun_Oinj__on(_1515615, _1515617, _1515619, _1515621), hAPP(_1515619, _1515623) = hAPP(_1515619, _1515625), hBOOL(hAPP(hAPP(c_member(_1515615), _1515623), _1515621)), hBOOL(hAPP(hAPP(c_member(_1515615), _1515625), _1515621)), -(_1515623 = _1515625)], (47952 ^ _775828) ^ [_1734116, _1734118, _1734120, _1734122] : [-(hAPP(hAPP(c_List_Onth(_1734116), hAPP(hAPP(c_List_Oappend(_1734116), _1734118), _1734120)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734116)), _1734118)), _1734122)) = hAPP(hAPP(c_List_Onth(_1734116), _1734120), _1734122))], (10274 ^ _775828) ^ [_942341, _942343] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942341), _942343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942343), _942341))], (1560 ^ _775828) ^ [_797946, _797948] : [-(class_Groups_Osemigroup__add(_797946)), _797948 = _797946, class_Groups_Osemigroup__add(_797948)], (20378 ^ _775828) ^ [_1125978, _1125980] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1125978)), c_Int_OBit1(_1125980)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1125978)), _1125980)))], (36819 ^ _775828) ^ [_1467536] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1467536)) = 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), _1467536))))], (39764 ^ _775828) ^ [_1537146] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1537146) = 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, _1537146)), 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))))))))], (14125 ^ _775828) ^ [_1012004, _1012006, _1012008, _1012010] : [_1012004 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012006), _1012008)), _1012010), -(_1012006 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012004), _1012006) = _1012008), 14132 ^ _775828 : [(14135 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012010), _1012006))], (14133 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012006)))]], 14140 ^ _775828 : [(14143 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012006), _1012010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012010), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14141 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012006))]]], (14249 ^ _775828) ^ [_1013997, _1013999] : [class_Divides_Osemiring__div(_1013997), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1013997), c_Groups_Ozero__class_Ozero(_1013997)), _1013999) = c_Groups_Ozero__class_Ozero(_1013997))], (44661 ^ _775828) ^ [_1654004, _1654006, _1654008, _1654010] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1654004, _1654006), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654004, tc_HOL_Obool), _1654008)), _1654010) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654004, tc_HOL_Obool), tc_fun(tc_prod(_1654004, _1654006), tc_HOL_Obool)), _1654008), hAPP(hAPP(c_COMBC(tc_fun(_1654004, tc_HOL_Obool), tc_fun(_1654004, tc_fun(_1654006, tc_HOL_Obool)), tc_fun(tc_prod(_1654004, _1654006), tc_HOL_Obool)), c_Product__Type_OSigma(_1654004, _1654006)), _1654010)))], (34785 ^ _775828) ^ [_1424858, _1424860, _1424862] : [class_Orderings_Olinorder(_1424858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424858), _1424860)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424858), _1424862)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424858, tc_HOL_Obool)), _1424860), _1424862) = c_Orderings_Obot__class_Obot(tc_fun(_1424858, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424858), c_Big__Operators_Olinorder__class_OMax(_1424858, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424858, tc_HOL_Obool)), _1424860), _1424862))), c_Big__Operators_Olinorder__class_OMax(_1424858, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424858, tc_HOL_Obool)), _1424860), _1424862))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424858), c_Big__Operators_Olinorder__class_OMax(_1424858, _1424860)), c_Big__Operators_Olinorder__class_OMax(_1424858, _1424862)))], (32996 ^ _775828) ^ [_1386535, _1386537, _1386539, _1386541] : [class_Rings_Ocomm__semiring__1(_1386535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386537), _1386539)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386537, _1386535), _1386541), _1386539) = c_Groups_Ozero__class_Ozero(_1386535)), 33005 ^ _775828 : [(33006 ^ _775828) ^ [_1386716] : [hBOOL(hAPP(hAPP(c_member(_1386537), _1386716), _1386539)), hAPP(_1386541, _1386716) = c_Groups_Ozero__class_Ozero(_1386535)]]], (50421 ^ _775828) ^ [_1789316, _1789318, _1789320, _1789322, _1789324] : [-(hAPP(c_List_Ofoldl(_1789316, _1789318, _1789320, _1789322), _1789324) = c_List_Ofoldr(_1789318, _1789316, hAPP(c_COMBC(_1789316, _1789318, _1789316), _1789320), hAPP(c_List_Orev(_1789318), _1789324), _1789322))], (25985 ^ _775828) ^ [_1234739, _1234741] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234739), _1234741))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234739), _1234741)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234741), _1234739)))], (40692 ^ _775828) ^ [_1557983, _1557985, _1557987, _1557989, _1557991, _1557993] : [c_Typedef_Otype__definition(_1557983, _1557985, _1557987, _1557989, _1557991), -(hBOOL(hAPP(hAPP(c_member(_1557985), hAPP(_1557987, _1557993)), _1557991)))], (28175 ^ _775828) ^ [_1280803, _1280805, _1280807, _1280809] : [hBOOL(hAPP(hAPP(c_member(_1280803), _1280805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280803, tc_HOL_Obool)), _1280807), _1280809))), -(hBOOL(hAPP(hAPP(c_member(_1280803), _1280805), _1280807))), -(hBOOL(hAPP(hAPP(c_member(_1280803), _1280805), _1280809)))], (44151 ^ _775828) ^ [_1639493, _1639495, _1639497, _1639499, _1639501] : [44153 ^ _775828 : [(44156 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1639493), _1639495), hAPP(_1639501, 44152 ^ [_1639493, _1639495, _1639497, _1639499, _1639501])))], (44154 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1639497), 44152 ^ [_1639493, _1639495, _1639497, _1639499, _1639501]), _1639499)))]], -(hBOOL(hAPP(hAPP(c_member(_1639493), _1639495), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639497, tc_fun(_1639493, tc_HOL_Obool)), _1639499), _1639501))))], (14405 ^ _775828) ^ [_1016872, _1016874, _1016876] : [hAPP(c_Com_Ocom_OBODY, _1016872) = c_Com_Ocom_OWhile(_1016874, _1016876)], (20414 ^ _775828) ^ [_1126687, _1126689] : [class_Rings_Oring__1__no__zero__divisors(_1126687), 20417 ^ _775828 : [(20424 ^ _775828) ^ [] : [_1126689 = c_Groups_Ozero__class_Ozero(_1126687), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126687), _1126689), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1126687))], (20418 ^ _775828) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1126687), _1126689), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1126687), -(_1126689 = c_Groups_Ozero__class_Ozero(_1126687))]]], (32131 ^ _775828) ^ [_1369855, _1369857] : [class_Orderings_Olinorder(_1369855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369855), _1369857)), -(_1369857 = c_Orderings_Obot__class_Obot(tc_fun(_1369855, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1369855), c_Big__Operators_Olinorder__class_OMin(_1369855, _1369857)), _1369857)))], (46740 ^ _775828) ^ [_1705389, _1705391] : [-(c_Random_Oselect__weight(_1705389, _1705391) = 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(_1705389, 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, _1705389), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1705389)), _1705391)))), hAPP(hAPP(c_COMBB(_1705389, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1705389, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1705389, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1705389, _1705391))))], (24835 ^ _775828) ^ [_1212990, _1212992, _1212994, _1212996, _1212998, _1213000, _1213002] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1212990, _1212992, _1212994, _1212996), _1212998), _1213000), _1213002) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1212992, _1212994, _1212996), _1213000), hAPP(_1212998, _1213002)))], (37987 ^ _775828) ^ [_1496046, _1496048, _1496050] : [class_Orderings_Olinorder(_1496046), 37990 ^ _775828 : [(37997 ^ _775828) ^ [] : [_1496048 = _1496050, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1496046), _1496048) = hAPP(c_SetInterval_Oord__class_OatLeast(_1496046), _1496050))], (37991 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1496046), _1496048) = hAPP(c_SetInterval_Oord__class_OatLeast(_1496046), _1496050), -(_1496048 = _1496050)]]], (23204 ^ _775828) ^ [_1179989, _1179991, _1179993, _1179995] : [class_Fields_Ofield__inverse__zero(_1179989), -(_1179991 = c_Groups_Ozero__class_Ozero(_1179989)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179989), _1179993), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179989), _1179995), _1179991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179989), _1179995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179989), _1179993), _1179991))), _1179991))], (19772 ^ _775828) ^ [_1115463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1115463)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115463), c_Int_OPls)))], (29074 ^ _775828) ^ [_1302077, _1302079, _1302081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302077, _1302077)), _1302079), _1302081)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302077, _1302077)), _1302079), c_Transitive__Closure_Otrancl(_1302077, _1302081))))], (27669 ^ _775828) ^ [_1267833, _1267835, _1267837, _1267839] : [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), _1267833, _1267835)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267837, _1267839))), 27672 ^ _775828 : [(27673 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267833), _1267835)), 27676 ^ _775828 : [(27681 ^ _775828) ^ [] : [27682 ^ _775828 : [(27685 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267833), _1267837))], (27683 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267837), _1267833)))]], 27686 ^ _775828 : [(27689 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267839), _1267835))], (27687 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267835), _1267839)))]]], (27679 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267835), _1267839)))], (27677 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267837), _1267833)))]]], (27691 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267837), _1267839)))]]], (26958 ^ _775828) ^ [_1252026, _1252028, _1252030, _1252032, _1252034] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252026), _1252028)), 26961 ^ _775828 : [(26968 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1252034), _1252028))), _1252032))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252030), _1252032))))], (26962 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252030), _1252032))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1252034), _1252028))), _1252032))))]]], (20064 ^ _775828) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (50365 ^ _775828) ^ [_1788208, _1788210, _1788212] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1788208), tc_List_Olist(_1788208), c_List_Oappend(_1788208), _1788210), _1788212) = hAPP(hAPP(c_List_Oappend(_1788208), _1788210), c_List_Oconcat(_1788208, _1788212)))], (19272 ^ _775828) ^ [_1107241, _1107243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107243)))), 19275 ^ _775828 : [(19278 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1107243))], (19276 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107241), _1107243)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107241), _1107243))], (36261 ^ _775828) ^ [_1456734, _1456736, _1456738] : [class_Orderings_Oorder(_1456734), 36264 ^ _775828 : [(36271 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456734), _1456736), _1456738))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456734, _1456736), _1456738) = c_Orderings_Obot__class_Obot(tc_fun(_1456734, tc_HOL_Obool)))], (36265 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456734, _1456736), _1456738) = c_Orderings_Obot__class_Obot(tc_fun(_1456734, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456734), _1456736), _1456738))]]], (50231 ^ _775828) ^ [_1785039, _1785041, _1785043] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785039), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1785039))), _1785041))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1785039))), _1785041))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785039), _1785039), hAPP(hAPP(c_COMBC(tc_List_Olist(_1785039), tc_Nat_Onat, _1785039), c_List_Onth(_1785039)), _1785043)), hAPP(c_List_Ofilter(tc_List_Olist(_1785039), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1785039)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785043)), c_Nat_Osize__class_Osize(tc_List_Olist(_1785039)))), c_List_Otranspose(_1785039, _1785041))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1785039)), _1785041), _1785043))], (11709 ^ _775828) ^ [_968228, _968230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968228)), _968230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968228), _968230)))], (1090 ^ _775828) ^ [_792071, _792073] : [-(class_Rings_Oordered__ring(_792071)), _792073 = _792071, class_Rings_Oordered__ring(_792073)], (27270 ^ _775828) ^ [_1258760] : [-(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)))), _1258760)) = 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), _1258760), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (35197 ^ _775828) ^ [_1435477, _1435479, _1435481, _1435483] : [class_Groups_Ocomm__monoid__mult(_1435477), 35200 ^ _775828 : [(35207 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1435479), _1435481))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1435479, _1435477), _1435483), _1435481) = c_Groups_Oone__class_Oone(_1435477))], (35201 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435479), _1435481)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1435479, _1435477), _1435483), _1435481) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435477, _1435479, c_Groups_Otimes__class_Otimes(_1435477)), _1435483), c_Groups_Oone__class_Oone(_1435477)), _1435481))]]], (17697 ^ _775828) ^ [_1078801, _1078803, _1078805] : [class_Rings_Oring__1__no__zero__divisors(_1078801), -(_1078803 = c_Groups_Ozero__class_Ozero(_1078801)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078801), _1078803), _1078805) = c_Groups_Ozero__class_Ozero(_1078801)], (18875 ^ _775828) ^ [_1100515, _1100517] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1100515), _1100517) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1100515, _1100517)))], (29159 ^ _775828) ^ [_1304317, _1304319] : [hBOOL(hAPP(hAPP(c_member(_1304317), _1304319), c_Orderings_Obot__class_Obot(tc_fun(_1304317, tc_HOL_Obool))))], (43255 ^ _775828) ^ [_1619943, _1619945, _1619947] : [-(hAPP(c_New__DSequence_Opos__single(_1619943, _1619945), _1619947) = c_Lazy__Sequence_Osingle(_1619943, _1619945))], (32371 ^ _775828) ^ [_1373680, _1373682, _1373684] : [class_Orderings_Olinorder(_1373680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373680), _1373682)), 32378 ^ _775828 : [(32385 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373680, tc_HOL_Obool)), _1373682), hAPP(hAPP(c_Set_Oinsert(_1373680), _1373684), c_Orderings_Obot__class_Obot(tc_fun(_1373680, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373680, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1373680, hAPP(hAPP(c_Set_Oinsert(_1373680), _1373684), _1373682)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1373680), _1373684), c_Big__Operators_Olinorder__class_OMin(_1373680, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373680, tc_HOL_Obool)), _1373682), hAPP(hAPP(c_Set_Oinsert(_1373680), _1373684), c_Orderings_Obot__class_Obot(tc_fun(_1373680, tc_HOL_Obool)))))))], (32379 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373680, tc_HOL_Obool)), _1373682), hAPP(hAPP(c_Set_Oinsert(_1373680), _1373684), c_Orderings_Obot__class_Obot(tc_fun(_1373680, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373680, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1373680, hAPP(hAPP(c_Set_Oinsert(_1373680), _1373684), _1373682)) = _1373684)]]], (16515 ^ _775828) ^ [_1056717, _1056719] : [-(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), _1056717)), _1056719))))], (27004 ^ _775828) ^ [_1252954, _1252956, _1252958] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1252954, _1252956) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1252958, _1252956), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252956), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1252954), _1252958))))], (50333 ^ _775828) ^ [_1787361, _1787363, _1787365] : [_1787365 = hAPP(hAPP(c_List_Olist_OCons(_1787361), _1787363), c_List_Olist_ONil(_1787361)), -(hAPP(hAPP(c_List_Olist_OCons(_1787361), _1787363), c_List_Olist_ONil(_1787361)) = hAPP(c_List_Orev(_1787361), _1787365))], (36017 ^ _775828) ^ [_1452256, _1452258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452256)), 36026 ^ _775828 : [(36029 ^ _775828) ^ [] : [hBOOL(hAPP(_1452258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36022 ^ [_1452256, _1452258]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36023 ^ [_1452256, _1452258]), _1452256))))], (36027 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1452258, 36022 ^ [_1452256, _1452258])))]], 36030 ^ _775828 : [(36033 ^ _775828) ^ [] : [hBOOL(hAPP(_1452258, 36022 ^ [_1452256, _1452258]))], (36031 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1452258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36022 ^ [_1452256, _1452258]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36023 ^ [_1452256, _1452258]), _1452256)))))]], 36034 ^ _775828 : [(36044 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1452258, 36051 ^ [_1452256, _1452258]))), 36045 ^ _775828 : [(36046 ^ _775828) ^ [_1452803] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1452803), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452256))), hBOOL(hAPP(_1452258, _1452803))]]], (36035 ^ _775828) ^ [] : [36036 ^ _775828 : [(36037 ^ _775828) ^ [_1452688] : [hBOOL(hAPP(_1452258, _1452688))]], 36039 ^ _775828 : [(36042 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1452258, 36038 ^ [_1452256, _1452258])))], (36040 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36038 ^ [_1452256, _1452258]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452256))))]]]]], (44838 ^ _775828) ^ [_1657889, _1657891, _1657893] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657889, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1657889, tc_HOL_Obool), tc_HOL_Obool)), _1657891), _1657893)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657889, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657889, tc_HOL_Obool), _1657891)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657889, tc_HOL_Obool), _1657893)))], (11124 ^ _775828) ^ [_958042, _958044, _958046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958042, tc_HOL_Obool)), _958044), _958046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958042, tc_HOL_Obool)), _958044), _958046)))], (47211 ^ _775828) ^ [_1717437, _1717439, _1717441, _1717443] : [-(hAPP(hAPP(c_List_Otake(_1717437), _1717439), hAPP(hAPP(c_List_Otake(_1717437), _1717441), _1717443)) = hAPP(hAPP(c_List_Otake(_1717437), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1717439), _1717441)), _1717443))], (12522 ^ _775828) ^ [_982478] : [-(hAPP(c_Nat_OSuc, _982478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _982478))], (6348 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (30031 ^ _775828) ^ [_1323168, _1323170] : [30032 ^ _775828 : [(30035 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323170), _1323168))], (30033 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323168), _1323170)))]], -(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)))), _1323168, _1323170))], (18149 ^ _775828) ^ [_1087353, _1087355] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087353)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087353)), _1087355)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1087353))), _1087355))], (4608 ^ _775828) ^ [_846189, _846191, _846193, _846195] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_846195, _846191) = c_SetInterval_Oord__class_OatLeastLessThan(_846193, _846189)), _846195 = _846193, _846191 = _846189], (33955 ^ _775828) ^ [_1407503, _1407505, _1407507] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407503, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407503, tc_HOL_Obool)), _1407505), _1407507)), _1407507)))], (48713 ^ _775828) ^ [_1752867, _1752869] : [-(c_List_Orotate(_1752867, _1752869) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1752867), tc_List_Olist(_1752867)), _1752869), c_List_Orotate1(_1752867)))], (31035 ^ _775828) ^ [_1344654, _1344656, _1344658, _1344660, _1344662, _1344664, _1344666, _1344668] : [c_Finite__Set_Ofolding__image__simple(_1344654, _1344656, _1344658, _1344660, _1344662, _1344664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344656), _1344666)), -(hBOOL(hAPP(hAPP(c_member(_1344656), _1344668), _1344666))), -(hAPP(_1344664, hAPP(hAPP(c_Set_Oinsert(_1344656), _1344668), _1344666)) = hAPP(hAPP(_1344658, hAPP(_1344662, _1344668)), hAPP(_1344664, _1344666)))], (27930 ^ _775828) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (51154 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (40622 ^ _775828) ^ [_1556725, _1556727] : [c_Equiv__Relations_Oequivp(_1556725, _1556727), 40625 ^ _775828 : [(40632 ^ _775828) ^ [_1556918, _1556920] : [hAPP(_1556727, _1556920) = hAPP(_1556727, _1556918), -(hBOOL(hAPP(hAPP(_1556727, _1556920), _1556918)))], (40626 ^ _775828) ^ [_1556819, _1556821] : [hBOOL(hAPP(hAPP(_1556727, _1556821), _1556819)), -(hAPP(_1556727, _1556821) = hAPP(_1556727, _1556819))]]], (38166 ^ _775828) ^ [_1499988, _1499990] : [class_Groups_Oordered__ab__group__add(_1499988), -(hAPP(c_Set_Oimage(_1499988, _1499988, c_Groups_Ouminus__class_Ouminus(_1499988)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499988), _1499990)) = hAPP(c_SetInterval_Oord__class_OatMost(_1499988), hAPP(c_Groups_Ouminus__class_Ouminus(_1499988), _1499990)))], (12365 ^ _775828) ^ [_979809] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _979809) = _979809)], (35613 ^ _775828) ^ [_1444551, _1444553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1444551), hAPP(c_Nat_OSuc, _1444553))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1444551, hAPP(c_Nat_OSuc, _1444553)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1444553)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1444551, _1444553)))], (4676 ^ _775828) ^ [_847267, _847269, _847271, _847273, _847275, _847277] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_847277, _847273, _847269) = c_SetInterval_Oord__class_OgreaterThanAtMost(_847275, _847271, _847267)), _847277 = _847275, _847273 = _847271, _847269 = _847267], (13686 ^ _775828) ^ [_1003757, _1003759] : [c_Com_Ocom_OSemi(_1003757, _1003759) = c_Com_Ocom_OSKIP], (19538 ^ _775828) ^ [_1111598, _1111600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111598), _1111600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111598)), c_Int_OBit1(_1111600))))], (16689 ^ _775828) ^ [_1060141, _1060143] : [class_Int_Onumber__ring(_1060141), 16692 ^ _775828 : [(16699 ^ _775828) ^ [] : [-(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), _1060143)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060141), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060143)) = c_Groups_Ozero__class_Ozero(_1060141))], (16693 ^ _775828) ^ [] : [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), _1060143))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060141), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060143)) = hAPP(c_Int_Onumber__class_Onumber__of(_1060141), _1060143))]]], (21306 ^ _775828) ^ [_1144877, _1144879] : [class_Rings_Odivision__ring(_1144877), -(_1144879 = c_Groups_Ozero__class_Ozero(_1144877)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144877), _1144879), _1144879) = c_Groups_Oone__class_Oone(_1144877))], (45218 ^ _775828) ^ [_1666295, _1666297, _1666299, _1666301, _1666303, _1666305, _1666307] : [c_Finite__Set_Ofolding__image__simple__idem(_1666295, _1666297, _1666299, _1666301, _1666303, _1666305), -(hAPP(hAPP(_1666299, _1666307), _1666307) = _1666307)], (45731 ^ _775828) ^ [_1678207, _1678209, _1678211, _1678213, _1678215] : [c_Fun_Oinj__on(_1678207, _1678209, _1678211, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1678207, tc_HOL_Obool)), hAPP(c_List_Oset(_1678207), _1678213)), hAPP(c_List_Oset(_1678207), _1678215))), 45734 ^ _775828 : [(45741 ^ _775828) ^ [] : [_1678213 = _1678215, -(hAPP(hAPP(c_List_Omap(_1678207, _1678209), _1678211), _1678213) = hAPP(hAPP(c_List_Omap(_1678207, _1678209), _1678211), _1678215))], (45735 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Omap(_1678207, _1678209), _1678211), _1678213) = hAPP(hAPP(c_List_Omap(_1678207, _1678209), _1678211), _1678215), -(_1678213 = _1678215)]]], (51608 ^ _775828) ^ [_1809484, _1809486] : [hBOOL(hAPP(hAPP(c_fimplies, _1809484), _1809486)), hBOOL(_1809484), -(hBOOL(_1809486))], (8565 ^ _775828) ^ [_913256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _913256), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _913256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30567 ^ _775828) ^ [_1334410, _1334412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334410, _1334410)), c_Transitive__Closure_Otrancl(_1334410, _1334412))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334410, _1334410)), _1334412)))], (46434 ^ _775828) ^ [_1697235, _1697237, _1697239, _1697241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697235)), _1697237)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697235)), _1697239))), _1697237 = hAPP(hAPP(c_List_Olist_OCons(_1697235), _1697241), _1697239)], (16449 ^ _775828) ^ [_1055661, _1055663, _1055665, _1055667] : [hBOOL(hAPP(hAPP(c_member(_1055661), _1055663), _1055665)), -(hBOOL(hAPP(hAPP(c_member(_1055661), _1055663), _1055667))), -(hBOOL(hAPP(hAPP(c_member(_1055661), _1055663), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055661, tc_HOL_Obool)), _1055665), _1055667))))], (39349 ^ _775828) ^ [_1525921, _1525923, _1525925, _1525927] : [c_Fun_Oinj__on(_1525921, _1525923, _1525925, _1525927), -(c_Fun_Oinj__on(_1525923, _1525921, c_Fun_Othe__inv__into(_1525921, _1525923, _1525927, _1525925), hAPP(c_Set_Oimage(_1525921, _1525923, _1525925), _1525927)))], (5780 ^ _775828) ^ [_867978, _867980, _867982, _867984] : [class_Rings_Osemiring__1(_867978), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_867978, _867980, hAPP(c_Nat_OSuc, _867982), _867984) = c_Nat_Osemiring__1__class_Oof__nat__aux(_867978, _867980, _867982, hAPP(_867980, _867984)))], (38350 ^ _775828) ^ [_1504223, _1504225, _1504227] : [class_Orderings_Olinorder(_1504223), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504223), _1504225), _1504227)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1504223, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1504223, _1504225, _1504227)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1504223), _1504227)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1504223), _1504225))], (18968 ^ _775828) ^ [_1102263, _1102265, _1102267, _1102269, _1102271, _1102273] : [-(hAPP(hAPP(c_Product__Type_OPair(_1102263, _1102265), _1102267), _1102269) = hAPP(hAPP(c_Product__Type_OPair(_1102263, _1102265), _1102271), _1102273)), _1102267 = _1102271, _1102269 = _1102273], (40447 ^ _775828) ^ [_1551419, _1551421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551419), c_Orderings_Otop__class_Otop(tc_fun(_1551419, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1551419, _1551419, _1551421), c_Orderings_Otop__class_Otop(tc_fun(_1551419, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551419, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1551419, _1551419, _1551421, c_Orderings_Otop__class_Otop(tc_fun(_1551419, tc_HOL_Obool))))], (1884 ^ _775828) ^ [_803099, _803101] : [_803101 = _803099, -(c_HOL_Obool_Obool__size(_803101) = c_HOL_Obool_Obool__size(_803099))], (51090 ^ _775828) ^ [_1804139, _1804141] : [class_Orderings_Otop(_1804139), -(class_Orderings_Otop(tc_fun(_1804141, _1804139)))], (12333 ^ _775828) ^ [_979247, _979249, _979251, _979253] : [hBOOL(hAPP(_979247, _979249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979251, tc_HOL_Obool)), _979247), _979253)), -(hBOOL(hAPP(_979253, _979249)))], (36813 ^ _775828) ^ [_1467405, _1467407, _1467409] : [class_Orderings_Oorder(_1467405), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467405, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1467405), _1467407)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1467405, _1467407), _1467409)) = c_Orderings_Obot__class_Obot(tc_fun(_1467405, tc_HOL_Obool)))], (48571 ^ _775828) ^ [_1750177, _1750179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750177)), _1750179)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1750177), _1750179) = _1750179)], (20078 ^ _775828) ^ [_1120766] : [c_Int_OBit0(_1120766) = c_Int_OPls, -(_1120766 = c_Int_OPls)], (49698 ^ _775828) ^ [_1774970, _1774972, _1774974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774970), _1774972)), -(c_List_Oupt(_1774970, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774972), _1774974)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1774970, _1774972)), c_List_Oupt(_1774972, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774972), _1774974))))], (28681 ^ _775828) ^ [_1291322, _1291324, _1291326] : [-(hAPP(c_Set_OCollect(_1291322), hAPP(hAPP(c_COMBS(_1291322, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1291322), c_fdisj), _1291324)), _1291326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291322, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1291322), _1291324)), hAPP(c_Set_OCollect(_1291322), _1291326)))], (43082 ^ _775828) ^ [_1615960, _1615962, _1615964, _1615966, _1615968, _1615970] : [c_Finite__Set_Ofolding(_1615960, _1615962, _1615964, _1615966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615960), _1615968)), -(hBOOL(hAPP(hAPP(c_member(_1615960), _1615970), _1615968))), -(hAPP(_1615966, hAPP(hAPP(c_Set_Oinsert(_1615960), _1615970), _1615968)) = hAPP(c_Fun_Ocomp(_1615962, _1615962, _1615962, hAPP(_1615966, _1615968)), hAPP(_1615964, _1615970)))], (18960 ^ _775828) ^ [_1102120, _1102122, _1102124, _1102126, _1102128, _1102130] : [hAPP(hAPP(c_Product__Type_OPair(_1102120, _1102122), _1102124), _1102126) = hAPP(hAPP(c_Product__Type_OPair(_1102120, _1102122), _1102128), _1102130), 18963 ^ _775828 : [(18966 ^ _775828) ^ [] : [-(_1102126 = _1102130)], (18964 ^ _775828) ^ [] : [-(_1102124 = _1102128)]]], (31449 ^ _775828) ^ [_1353820, _1353822, _1353824] : [class_Orderings_Olinorder(_1353820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353820), _1353822)), hBOOL(hAPP(hAPP(c_member(_1353820), _1353824), _1353822)), 31460 ^ _775828 : [(31467 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353820, tc_HOL_Obool)), _1353822), hAPP(hAPP(c_Set_Oinsert(_1353820), _1353824), c_Orderings_Obot__class_Obot(tc_fun(_1353820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353820, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1353820, c_Orderings_Oord__class_Omin(_1353820), _1353822) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1353820), _1353824), c_Big__Operators_Olattice_OInf__fin(_1353820, c_Orderings_Oord__class_Omin(_1353820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353820, tc_HOL_Obool)), _1353822), hAPP(hAPP(c_Set_Oinsert(_1353820), _1353824), c_Orderings_Obot__class_Obot(tc_fun(_1353820, tc_HOL_Obool)))))))], (31461 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353820, tc_HOL_Obool)), _1353822), hAPP(hAPP(c_Set_Oinsert(_1353820), _1353824), c_Orderings_Obot__class_Obot(tc_fun(_1353820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353820, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1353820, c_Orderings_Oord__class_Omin(_1353820), _1353822) = _1353824)]]], (48864 ^ _775828) ^ [_1756062, _1756064, _1756066] : [class_Lattices_Olattice(_1756062), -(c_Big__Operators_Olattice__class_OInf__fin(_1756062, hAPP(c_List_Oset(_1756062), hAPP(hAPP(c_List_Olist_OCons(_1756062), _1756064), _1756066))) = hAPP(c_List_Ofoldl(_1756062, _1756062, c_Lattices_Osemilattice__inf__class_Oinf(_1756062), _1756064), _1756066))], (1170 ^ _775828) ^ [_793071, _793073] : [-(class_Groups_Oabs__if(_793071)), _793073 = _793071, class_Groups_Oabs__if(_793073)], (23552 ^ _775828) ^ [_1187714] : [-(c_Hoare__Mirabelle_OMGT(_1187714) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1187714), c_Natural_Oevalc(_1187714)))], (29953 ^ _775828) ^ [_1321623, _1321625, _1321627, _1321629, _1321631, _1321633, _1321635] : [hBOOL(hAPP(hAPP(c_member(_1321623), _1321625), _1321627)), c_Nitpick_Ofold__graph_H(_1321623, _1321629, _1321631, _1321633, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321623, tc_HOL_Obool)), _1321627), hAPP(hAPP(c_Set_Oinsert(_1321623), _1321625), c_Orderings_Obot__class_Obot(tc_fun(_1321623, tc_HOL_Obool)))), _1321635), -(c_Nitpick_Ofold__graph_H(_1321623, _1321629, _1321631, _1321633, _1321627, hAPP(hAPP(_1321631, _1321625), _1321635)))], (10556 ^ _775828) ^ [_947685, _947687, _947689, _947691, _947693] : [class_Groups_Oordered__cancel__ab__semigroup__add(_947685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947685), _947687), _947689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947685), _947691), _947693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947685), _947687), _947691)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947685), _947689), _947693))))], (47305 ^ _775828) ^ [_1719336, _1719338, _1719340, _1719342] : [-(hAPP(hAPP(c_List_Otake(_1719336), _1719338), hAPP(hAPP(c_List_Olist_OCons(_1719336), _1719340), _1719342)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1719336), c_List_Olist_ONil(_1719336), hAPP(hAPP(c_COMBB(tc_List_Olist(_1719336), tc_List_Olist(_1719336), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1719336), _1719340)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1719336), tc_List_Olist(_1719336)), c_List_Otake(_1719336)), _1719342)), _1719338))], (42224 ^ _775828) ^ [_1595688, _1595690, _1595692] : [c_Relation_Orefl__on(_1595688, _1595690, _1595692), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1595688, _1595688), tc_HOL_Obool)), _1595692), hAPP(hAPP(c_Relation_Orel__comp(_1595688, _1595688, _1595688), hAPP(c_Relation_Oconverse(_1595688, _1595688), _1595692)), _1595692))))], (18505 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (25411 ^ _775828) ^ [_1224055, _1224057] : [hAPP(c_Code__Numeral_Onat__of, _1224055) = hAPP(c_Code__Numeral_Onat__of, _1224057), -(_1224055 = _1224057)], (14732 ^ _775828) ^ [_1022271, _1022273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022271), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14735 ^ _775828 : [(14742 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022273), 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), _1022273), _1022271))))], (14736 ^ _775828) ^ [] : [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), _1022273), _1022271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022273), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29911 ^ _775828) ^ [_1320009, _1320011] : [c_Option_Oset(_1320009, _1320011) = c_Orderings_Obot__class_Obot(tc_fun(_1320009, tc_HOL_Obool)), -(_1320011 = c_Option_Ooption_ONone(_1320009))], (18197 ^ _775828) ^ [_1088179, _1088181, _1088183] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088179, _1088181), _1088183)), -(c_Divides_Odivmod__nat(_1088179, _1088181) = _1088183)], (29717 ^ _775828) ^ [_1315596] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1315596, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1315596), hAPP(c_COMBK(tc_HOL_Obool, _1315596), c_fFalse)))], (35131 ^ _775828) ^ [_1434004, _1434006, _1434008, _1434010, _1434012, _1434014] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434004, tc_fun(_1434006, tc_HOL_Obool))), _1434008), _1434010), _1434012), _1434014)), 35134 ^ _775828 : [(35137 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1434010, _1434012), _1434014)))], (35135 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1434008, _1434012), _1434014)))]]], (38454 ^ _775828) ^ [_1506714, _1506716, _1506718, _1506720, _1506722] : [-(_1506714 = c_Option_Ooption_ONone(_1506716)), -(c_Map_Odom(_1506718, _1506716, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1506718, tc_Option_Ooption(_1506716)), _1506720), _1506722), _1506714)) = hAPP(hAPP(c_Set_Oinsert(_1506718), _1506722), c_Map_Odom(_1506718, _1506716, _1506720)))], (49469 ^ _775828) ^ [_1769297, _1769299, _1769301, _1769303] : [hBOOL(hAPP(hAPP(c_member(_1769297), _1769299), hAPP(c_List_Oset(_1769297), _1769301))), -(hBOOL(hAPP(_1769303, _1769299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769297)), hAPP(c_List_Ofilter(_1769297, _1769303), _1769301))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769297)), _1769301))))], (26241 ^ _775828) ^ [_1239119, _1239121, _1239123, _1239125] : [class_Rings_Oidom(_1239119), 26244 ^ _775828 : [(26245 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239119), _1239121), _1239123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239119), _1239121), _1239125))), -(_1239121 = c_Groups_Ozero__class_Ozero(_1239119)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239119), _1239123), _1239125)))], (26255 ^ _775828) ^ [] : [26256 ^ _775828 : [(26259 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239119), _1239123), _1239125))], (26257 ^ _775828) ^ [] : [_1239121 = c_Groups_Ozero__class_Ozero(_1239119)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239119), _1239121), _1239123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239119), _1239121), _1239125))))]]], (33675 ^ _775828) ^ [_1401021, _1401023, _1401025, _1401027] : [hBOOL(hAPP(hAPP(c_member(_1401021), _1401027), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401021, tc_HOL_Obool)), _1401023), _1401025))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401021, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1401021, tc_fun(_1401021, tc_HOL_Obool), tc_HOL_Obool), c_member(_1401021)), _1401023)), hAPP(hAPP(c_COMBC(_1401021, tc_fun(_1401021, tc_HOL_Obool), tc_HOL_Obool), c_member(_1401021)), _1401025)), _1401027)))], (10800 ^ _775828) ^ [_952450] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952450), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _952450)], (25217 ^ _775828) ^ [_1220759, _1220761] : [c_Nat__Transfer_Onat__set(_1220759), c_Nat__Transfer_Onat__set(_1220761), 25224 ^ _775828 : [(25231 ^ _775828) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1220759) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1220761), -(_1220759 = _1220761)], (25225 ^ _775828) ^ [] : [_1220759 = _1220761, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1220759) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1220761))]]], (18789 ^ _775828) ^ [_1098841, _1098843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098841), 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)), _1098843)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1098841), _1098843) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1098841, _1098843)))], (14159 ^ _775828) ^ [_1012547, _1012549, _1012551, _1012553] : [-(hBOOL(hAPP(_1012547, _1012549))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1012547, _1012551), _1012549, _1012553, _1012549))], (27816 ^ _775828) ^ [_1271821, _1271823, _1271825, _1271827] : [hBOOL(hAPP(hAPP(c_member(_1271821), _1271827), hAPP(c_Relation_ODomain(_1271821, _1271823), _1271825))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1271821, _1271823, hAPP(hAPP(c_COMBC(_1271821, tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_fun(_1271823, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271823, tc_fun(tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_fun(_1271823, tc_HOL_Obool)), _1271821), c_COMBC(_1271823, tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271823, tc_prod(_1271821, _1271823)), tc_fun(_1271823, tc_fun(tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_HOL_Obool)), _1271821), hAPP(c_COMBB(tc_prod(_1271821, _1271823), tc_fun(tc_fun(tc_prod(_1271821, _1271823), tc_HOL_Obool), tc_HOL_Obool), _1271823), c_member(tc_prod(_1271821, _1271823)))), c_Product__Type_OPair(_1271821, _1271823)))), _1271825)), _1271827)))], (46508 ^ _775828) ^ [_1698795, _1698797, _1698799, _1698801, _1698803] : [-(hAPP(hAPP(c_List_Omap(_1698795, _1698797), _1698799), hAPP(hAPP(c_List_Olist_OCons(_1698795), _1698801), _1698803)) = hAPP(hAPP(c_List_Olist_OCons(_1698797), hAPP(_1698799, _1698801)), hAPP(hAPP(c_List_Omap(_1698795, _1698797), _1698799), _1698803)))], (10922 ^ _775828) ^ [_954584, _954586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954584), _954586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954584), hAPP(c_Nat_OSuc, _954586))))], (20482 ^ _775828) ^ [] : [-(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)))))], (13006 ^ _775828) ^ [_990774, _990776] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_990774, _990776)) = 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), _990774)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _990776))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10980 ^ _775828) ^ [_955535, _955537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955535), _955537)), -(_955535 = _955537), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955535), _955537)))], (12649 ^ _775828) ^ [_984574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984574), 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)), _984574)), _984574)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16146 ^ _775828) ^ [_1049723, _1049725, _1049727, _1049729, _1049731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049723), _1049725)), 16149 ^ _775828 : [(16156 ^ _775828) ^ [] : [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), _1049725), _1049723)), _1049727)), _1049729) = _1049731, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049725), _1049727)), _1049729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049723), _1049727)), _1049731))], (16150 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049725), _1049727)), _1049729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049723), _1049727)), _1049731), -(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), _1049725), _1049723)), _1049727)), _1049729) = _1049731)]]], (24218 ^ _775828) ^ [_1200158, _1200160, _1200162, _1200164] : [class_Orderings_Olinorder(_1200158), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200158), _1200160), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200158), _1200162), _1200164)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200158), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200158), _1200160), _1200162)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200158), _1200160), _1200164)))], (25525 ^ _775828) ^ [_1227152] : [-(c_Wellfounded_Omeasure(_1227152) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1227152), c_Wellfounded_Oless__than))], (32827 ^ _775828) ^ [_1383056, _1383058, _1383060, _1383062, _1383064, _1383066] : [_1383056 = _1383058, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383060, _1383062), _1383064), _1383058), _1383066), _1383056) = _1383066)], (17691 ^ _775828) ^ [_1078731, _1078733] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078731)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078731)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078733)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078731)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078733))))], (39407 ^ _775828) ^ [_1527164, _1527166, _1527168, _1527170] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1527164, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527166, tc_fun(tc_fun(_1527164, tc_HOL_Obool), tc_HOL_Obool)), _1527168), hAPP(hAPP(c_COMBB(tc_fun(_1527164, tc_HOL_Obool), tc_fun(tc_fun(_1527164, tc_HOL_Obool), tc_HOL_Obool), _1527166), c_Set_OPow(_1527164)), _1527170))), hAPP(c_Set_OPow(_1527164), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527166, tc_fun(_1527164, tc_HOL_Obool)), _1527168), _1527170)))))], (29445 ^ _775828) ^ [_1309942, _1309944, _1309946, _1309948, _1309950] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1309942, _1309944, _1309946), _1309948), _1309950)), -(hBOOL(hAPP(hAPP(_1309946, _1309950), _1309948)))], (13316 ^ _775828) ^ [_996404, _996406, _996408] : [class_Divides_Osemiring__div(_996404), -(c_Divides_Odiv__class_Omod(_996404, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996404), _996406), _996408), _996406) = c_Divides_Odiv__class_Omod(_996404, _996408, _996406))], (18243 ^ _775828) ^ [_1089149, _1089151, _1089153, _1089155, _1089157] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1089149, _1089151), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1089153), _1089155))), -(_1089151 = 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)), _1089157)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1089149, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089151), _1089157)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1089153), _1089157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089151), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1089153, _1089157))), _1089155)))))], (29971 ^ _775828) ^ [_1321992, _1321994, _1321996, _1321998] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1321992, tc_fun(_1321994, tc_HOL_Obool))), _1321996), _1321998)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1321992, _1321994)), hAPP(hAPP(c_Product__Type_OPair(_1321992, _1321994), _1321996), _1321998)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1321992, _1321994), tc_HOL_Obool)))))], (48988 ^ _775828) ^ [_1759189, _1759191, _1759193, _1759195] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759189)), hAPP(hAPP(c_List_Olist_OCons(_1759189), _1759191), _1759193)), c_List_Olists(_1759189, _1759195))), 48991 ^ _775828 : [(48994 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759189)), _1759193), c_List_Olists(_1759189, _1759195))))], (48992 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759189), _1759191), _1759195)))]]], (11320 ^ _775828) ^ [_961639, _961641] : [class_Groups_Olinordered__ab__group__add(_961639), 11323 ^ _775828 : [(11330 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961639), c_Groups_Ozero__class_Ozero(_961639)), _961641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961639), c_Groups_Ozero__class_Ozero(_961639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961639), _961641), _961641))))], (11324 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961639), c_Groups_Ozero__class_Ozero(_961639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961639), _961641), _961641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961639), c_Groups_Ozero__class_Ozero(_961639)), _961641)))]]], (38194 ^ _775828) ^ [] : [-(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))))))], (9585 ^ _775828) ^ [_929930] : [-(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), _929930))))], (10049 ^ _775828) ^ [_938411, _938413] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938411), _938413))))], (15346 ^ _775828) ^ [_1033756, _1033758, _1033760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033756), _1033758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033756), _1033760)), _1033758)))], (45277 ^ _775828) ^ [_1667577, _1667579, _1667581] : [hBOOL(hAPP(hAPP(c_member(_1667577), _1667579), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667577, tc_HOL_Obool), _1667581))), 45281 ^ _775828 : [(45284 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1667577, tc_HOL_Obool)), 45280 ^ [_1667577, _1667579, _1667581]), _1667581)))], (45282 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667577), _1667579), 45280 ^ [_1667577, _1667579, _1667581])))]]], (44215 ^ _775828) ^ [_1642058, _1642060, _1642062, _1642064] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642058, tc_fun(_1642060, tc_HOL_Obool)), _1642062), _1642064) = c_Orderings_Otop__class_Otop(tc_fun(_1642060, tc_HOL_Obool)), 44218 ^ _775828 : [(44219 ^ _775828) ^ [_1642174] : [hBOOL(hAPP(hAPP(c_member(_1642058), _1642174), _1642062)), -(hAPP(_1642064, _1642174) = c_Orderings_Otop__class_Otop(tc_fun(_1642060, tc_HOL_Obool)))]]], (3426 ^ _775828) ^ [_827750, _827752, _827754, _827756, _827758, _827760, _827762, _827764] : [-(c_Fun_Othe__inv__into(_827764, _827760, _827756, _827752) = c_Fun_Othe__inv__into(_827762, _827758, _827754, _827750)), _827764 = _827762, _827760 = _827758, _827756 = _827754, _827752 = _827750], (6716 ^ _775828) ^ [_882382, _882384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882382), _882384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882382)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882384))))], (44589 ^ _775828) ^ [_1651810, _1651812, _1651814, _1651816] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1651810, tc_HOL_Obool), tc_fun(_1651812, tc_HOL_Obool)), _1651814), hAPP(hAPP(c_COMBC(tc_fun(_1651810, tc_HOL_Obool), tc_fun(_1651810, tc_fun(_1651812, tc_HOL_Obool)), tc_fun(_1651812, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651810, tc_fun(_1651812, tc_HOL_Obool))), _1651816)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651810, tc_fun(_1651812, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1651810, tc_HOL_Obool), _1651814)), _1651816))], (12045 ^ _775828) ^ [_974353, _974355, _974357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974353), _974355)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974357), _974355))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _974355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974353), _974357)))], (7795 ^ _775828) ^ [_900326, _900328] : [class_Groups_Oordered__ab__group__add(_900326), 7798 ^ _775828 : [(7805 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900326), _900328), c_Groups_Ozero__class_Ozero(_900326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900326), c_Groups_Ozero__class_Ozero(_900326)), hAPP(c_Groups_Ouminus__class_Ouminus(_900326), _900328))))], (7799 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900326), c_Groups_Ozero__class_Ozero(_900326)), hAPP(c_Groups_Ouminus__class_Ouminus(_900326), _900328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900326), _900328), c_Groups_Ozero__class_Ozero(_900326))))]]], (29421 ^ _775828) ^ [_1309446, _1309448, _1309450, _1309452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309446, tc_HOL_Obool)), _1309448), _1309450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309446, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1309446), _1309452), _1309448)), hAPP(hAPP(c_Set_Oinsert(_1309446), _1309452), _1309450))))], (27136 ^ _775828) ^ [_1255251, _1255253] : [class_Orderings_Oorder(_1255251), 27143 ^ _775828 : [(27148 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255251), hAPP(_1255253, 27141 ^ [_1255251, _1255253])), hAPP(_1255253, 27142 ^ [_1255251, _1255253])))], (27146 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27142 ^ [_1255251, _1255253]), 27141 ^ [_1255251, _1255253]))], (27144 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27141 ^ [_1255251, _1255253]), 27142 ^ [_1255251, _1255253])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1255251, 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)))), _1255253))], (47631 ^ _775828) ^ [_1725836, _1725838, _1725840, _1725842, _1725844] : [-(_1725836 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1725838, _1725840, _1725842, _1725836), _1725844) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1725840), _1725838), tc_prod(_1725840, _1725838), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725840), _1725838), c_List_Olist_ONil(_1725840)), _1725844), hAPP(c_Product__Type_Oprod_Oprod__case(_1725840, _1725838, tc_prod(tc_List_Olist(_1725840), _1725838)), hAPP(hAPP(c_COMBC(_1725840, tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838)), tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1725840), _1725838), tc_prod(tc_List_Olist(_1725840), _1725838)), tc_fun(tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838)), tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838))), _1725840), c_COMBB(tc_prod(tc_List_Olist(_1725840), _1725838), tc_prod(tc_List_Olist(_1725840), _1725838), _1725838)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1725840), tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838))), tc_fun(tc_prod(tc_List_Olist(_1725840), _1725838), tc_prod(tc_List_Olist(_1725840), _1725838)), _1725840), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1725840), _1725838, tc_prod(tc_List_Olist(_1725840), _1725838))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1725840), tc_List_Olist(_1725840)), tc_fun(tc_List_Olist(_1725840), tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838))), _1725840), hAPP(c_COMBB(tc_List_Olist(_1725840), tc_fun(_1725838, tc_prod(tc_List_Olist(_1725840), _1725838)), tc_List_Olist(_1725840)), c_Product__Type_OPair(tc_List_Olist(_1725840), _1725838))), c_List_Olist_OCons(_1725840))))), c_Lazy__Sequence_Oanamorph(_1725838, _1725840, _1725842, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1725836), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1725842, _1725844)))], (5519 ^ _775828) ^ [_863131, _863133, _863135, _863137, _863139, _863141] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_863131, _863133, _863135, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_863131), _863137), _863139), _863141)) = hAPP(hAPP(hAPP(_863135, _863137), _863139), _863141))], (21138 ^ _775828) ^ [_1141747, _1141749, _1141751, _1141753] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1141747, _1141749), _1141751)), hBOOL(hAPP(hAPP(_1141749, _1141753), _1141751)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1141747, _1141749), _1141753)))], (42119 ^ _775828) ^ [_1593359, _1593361, _1593363, _1593365, _1593367, _1593369, _1593371, _1593373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593359, _1593361)), _1593363), hAPP(c_Set_Oimage(tc_prod(_1593365, _1593367), tc_prod(_1593359, _1593361), c_Product__Type_Omap__pair(_1593365, _1593359, _1593367, _1593361, _1593369, _1593371)), _1593373))), 42124 ^ _775828 : [(42127 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593365, _1593367)), hAPP(hAPP(c_Product__Type_OPair(_1593365, _1593367), 42122 ^ [_1593359, _1593361, _1593363, _1593365, _1593367, _1593369, _1593371, _1593373]), 42123 ^ [_1593359, _1593361, _1593363, _1593365, _1593367, _1593369, _1593371, _1593373])), _1593373)))], (42125 ^ _775828) ^ [] : [-(_1593363 = hAPP(hAPP(c_Product__Type_OPair(_1593359, _1593361), hAPP(_1593369, 42122 ^ [_1593359, _1593361, _1593363, _1593365, _1593367, _1593369, _1593371, _1593373])), hAPP(_1593371, 42123 ^ [_1593359, _1593361, _1593363, _1593365, _1593367, _1593369, _1593371, _1593373])))]]], (38148 ^ _775828) ^ [_1499595, _1499597, _1499599, _1499601] : [class_Orderings_Olinorder(_1499595), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499595, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1499595, _1499597, _1499599)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499595), _1499601)) = c_SetInterval_Oord__class_OatLeastAtMost(_1499595, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1499595), _1499597), _1499601), _1499599))], (35349 ^ _775828) ^ [_1439111, _1439113] : [hAPP(c_Set_OPow(_1439111), _1439113) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1439111, tc_HOL_Obool), tc_HOL_Obool))], (1310 ^ _775828) ^ [_794821, _794823] : [-(class_Orderings_Otop(_794821)), _794823 = _794821, class_Orderings_Otop(_794823)], (14455 ^ _775828) ^ [_1017898, _1017900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1017898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017900, _1017898)), _1017898)))], (13694 ^ _775828) ^ [_1003890, _1003892, _1003894] : [class_Divides_Osemiring__div(_1003890), -(c_Divides_Odiv__class_Omod(_1003890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003890), _1003892), _1003894), _1003892) = c_Groups_Ozero__class_Ozero(_1003890))], (25375 ^ _775828) ^ [_1223472] : [-(_1223472 = 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, _1223472)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1223472))))], (1430 ^ _775828) ^ [_796321, _796323] : [-(class_Groups_Ocancel__ab__semigroup__add(_796321)), _796323 = _796321, class_Groups_Ocancel__ab__semigroup__add(_796323)], (15708 ^ _775828) ^ [_1040601, _1040603] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1040601)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1040603)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040601), _1040603)))], (29197 ^ _775828) ^ [_1305078, _1305080, _1305082] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305078, tc_HOL_Obool)), _1305080), _1305082) = c_Orderings_Obot__class_Obot(tc_fun(_1305078, tc_HOL_Obool))), _1305080 = c_Orderings_Obot__class_Obot(tc_fun(_1305078, tc_HOL_Obool)), _1305082 = c_Orderings_Obot__class_Obot(tc_fun(_1305078, tc_HOL_Obool))], (19946 ^ _775828) ^ [_1118324] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1118324)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35039 ^ _775828) ^ [_1430854, _1430856] : [c_Nat__Transfer_Onat__set(_1430854), c_Nat__Transfer_Onat__set(_1430856), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1430854), _1430856) = 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), _1430854)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1430856))))], (41448 ^ _775828) ^ [_1577723, _1577725, _1577727, _1577729] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577723, _1577725)), hAPP(hAPP(c_Product__Type_OSigma(_1577723, _1577725), _1577727), hAPP(c_COMBK(tc_fun(_1577725, tc_HOL_Obool), _1577723), _1577729)))), -(_1577727 = c_Orderings_Obot__class_Obot(tc_fun(_1577723, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577725), _1577729)))], (36513 ^ _775828) ^ [_1461776, _1461778] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1461776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461778), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1461776, _1461778))], (7677 ^ _775828) ^ [_898410] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898410), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39918 ^ _775828) ^ [_1540733, _1540735, _1540737, _1540739, _1540741, _1540743, _1540745, _1540747, _1540749, _1540751, _1540753] : [c_Equiv__Relations_Oequiv(_1540733, _1540735, _1540737), c_Equiv__Relations_Oequiv(_1540739, _1540741, _1540743), c_Equiv__Relations_Ocongruent2(_1540733, _1540739, tc_fun(_1540745, tc_HOL_Obool), _1540737, _1540743, _1540747), hBOOL(hAPP(hAPP(c_member(tc_fun(_1540733, tc_HOL_Obool)), _1540749), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1540733), _1540735), _1540737))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1540739, tc_HOL_Obool)), _1540751), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1540739), _1540741), _1540743))), 39940 ^ _775828 : [(39946 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1540745, tc_HOL_Obool)), hAPP(hAPP(_1540747, 39939 ^ [_1540733, _1540735, _1540737, _1540739, _1540741, _1540743, _1540745, _1540747, _1540749, _1540751, _1540753]), 39942 ^ [_1540733, _1540735, _1540737, _1540739, _1540741, _1540743, _1540745, _1540747, _1540749, _1540751, _1540753])), _1540753))], (39944 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540739), 39942 ^ [_1540733, _1540735, _1540737, _1540739, _1540741, _1540743, _1540745, _1540747, _1540749, _1540751, _1540753]), _1540741)))], (39941 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540733), 39939 ^ [_1540733, _1540735, _1540737, _1540739, _1540741, _1540743, _1540745, _1540747, _1540749, _1540751, _1540753]), _1540735)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1540745, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1540733, tc_fun(_1540745, tc_HOL_Obool)), _1540749), hAPP(hAPP(c_COMBB(tc_fun(_1540739, tc_fun(_1540745, tc_HOL_Obool)), tc_fun(_1540745, tc_HOL_Obool), _1540733), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1540739, tc_fun(_1540745, tc_HOL_Obool)), _1540751)), _1540747))), _1540753)))], (5336 ^ _775828) ^ [_857367, _857369] : [_857369 = _857367, -(tc_Option_Ooption(_857369) = tc_Option_Ooption(_857367))], (9587 ^ _775828) ^ [_929970] : [-(hBOOL(hAPP(_929970, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9594 ^ [_929970])))), 9588 ^ _775828 : [(9589 ^ _775828) ^ [_930022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930022)), hBOOL(hAPP(_929970, _930022))]]], (9049 ^ _775828) ^ [_920574, _920576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _920574)), 9052 ^ _775828 : [(9059 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _920574), _920576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _920574)), hAPP(c_Int_Onat, _920576))))], (9053 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _920574)), hAPP(c_Int_Onat, _920576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _920574), _920576)))]]], (39676 ^ _775828) ^ [_1534949, _1534951, _1534953, _1534955, _1534957] : [hBOOL(hAPP(hAPP(c_member(_1534949), _1534951), _1534953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1534955, tc_HOL_Obool)), hAPP(_1534957, _1534951)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534949, tc_fun(_1534955, tc_HOL_Obool)), _1534953), _1534957))))], (5428 ^ _775828) ^ [_858753, _858755] : [_858755 = _858753, -(c_Hoare__Mirabelle_Otriple_Otriple(_858755) = c_Hoare__Mirabelle_Otriple_Otriple(_858753))], (50581 ^ _775828) ^ [_1794000, _1794002, _1794004, _1794006] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1794000), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1794000))), _1794002))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794004), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1794000))), c_List_Otranspose(_1794000, _1794002)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794006), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1794000))), hAPP(c_List_Ofilter(tc_List_Olist(_1794000), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1794000)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794004)), c_Nat_Osize__class_Osize(tc_List_Olist(_1794000)))), _1794002)))), -(hAPP(hAPP(c_List_Onth(_1794000), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1794000)), c_List_Otranspose(_1794000, _1794002)), _1794004)), _1794006) = hAPP(hAPP(c_List_Onth(_1794000), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1794000)), _1794002), _1794006)), _1794004))], (16124 ^ _775828) ^ [_1049131, _1049133, _1049135, _1049137, _1049139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049131), _1049133)), -(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), _1049131), _1049135)), _1049137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049133), _1049135)), _1049139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049137), 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), _1049133), _1049131)), _1049135)), _1049139)))], (37729 ^ _775828) ^ [_1490059, _1490061, _1490063, _1490065, _1490067] : [class_Groups_Ocomm__monoid__add(_1490059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490061), _1490063)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490061), _1490065)), 37743 ^ _775828 : [(37746 ^ _775828) ^ [] : [hAPP(_1490067, 37742 ^ [_1490059, _1490061, _1490063, _1490065, _1490067]) = c_Groups_Ozero__class_Ozero(_1490059)], (37744 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490061), 37742 ^ [_1490059, _1490061, _1490063, _1490065, _1490067]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490061, tc_HOL_Obool)), _1490063), _1490065))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490061, _1490059), _1490067), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490061, tc_HOL_Obool)), _1490063), _1490065)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1490059), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490061, _1490059), _1490067), _1490063)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490061, _1490059), _1490067), _1490065)))], (39462 ^ _775828) ^ [_1529116, _1529118, _1529120, _1529122, _1529124, _1529126] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529116, tc_fun(_1529118, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529120, tc_fun(_1529116, tc_HOL_Obool)), _1529122), _1529124)), _1529126) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529120, tc_fun(_1529118, tc_HOL_Obool)), _1529122), hAPP(hAPP(c_COMBC(_1529120, tc_fun(_1529116, tc_fun(_1529118, tc_HOL_Obool)), tc_fun(_1529118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529116, tc_HOL_Obool), tc_fun(tc_fun(_1529116, tc_fun(_1529118, tc_HOL_Obool)), tc_fun(_1529118, tc_HOL_Obool)), _1529120), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529116, tc_fun(_1529118, tc_HOL_Obool))), _1529124)), _1529126)))], (18861 ^ _775828) ^ [_1100234, 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c_Groups_Ozero__class_Ozero(_892774))], (43351 ^ _775828) ^ [_1622961, _1622963, _1622965, _1622967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622961, _1622961)), hAPP(hAPP(c_Product__Type_OPair(_1622961, _1622961), _1622963), _1622965)), c_Transitive__Closure_Otrancl(_1622961, _1622967))), 43355 ^ _775828 : [(43358 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622961, _1622961)), hAPP(hAPP(c_Product__Type_OPair(_1622961, _1622961), 43354 ^ [_1622961, _1622963, _1622965, _1622967]), _1622965)), c_Transitive__Closure_Ortrancl(_1622961, _1622967))))], (43356 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622961, _1622961)), hAPP(hAPP(c_Product__Type_OPair(_1622961, _1622961), _1622963), 43354 ^ [_1622961, _1622963, _1622965, _1622967])), _1622967)))]]], (22640 ^ _775828) ^ [_1169776, _1169778, _1169780, _1169782] : [class_Fields_Olinordered__field(_1169776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169776), _1169778), _1169780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169776), c_Groups_Ozero__class_Ozero(_1169776)), _1169782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169776), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169776), _1169778), _1169782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169776), _1169780), _1169782))))], (47353 ^ _775828) ^ [_1720555, _1720557, _1720559] : [hAPP(hAPP(c_List_Olist_OCons(_1720555), _1720557), _1720559) = c_List_Olist_ONil(_1720555)], (24236 ^ _775828) ^ [_1200619, _1200621, _1200623, _1200625] : [class_Orderings_Olinorder(_1200619), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200619), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200619), _1200621), _1200623)), _1200625) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200619), _1200621), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200619), _1200623), _1200625)))], (8883 ^ _775828) ^ [_917984, _917986, _917988] : [class_Orderings_Oorder(_917984), 8886 ^ _775828 : [(8895 ^ _775828) ^ [] : 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hAPP(c_SetInterval_Oord__class_OatLeast(_1499738), _1499742)) = c_Orderings_Obot__class_Obot(tc_fun(_1499738, tc_HOL_Obool)))], (35173 ^ _775828) ^ [_1435004, _1435006, _1435008, _1435010, _1435012, _1435014] : [class_Groups_Oab__semigroup__mult(_1435004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435006), _1435008)), -(hBOOL(hAPP(hAPP(c_member(_1435006), _1435010), _1435008))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435004, _1435006, c_Groups_Otimes__class_Otimes(_1435004)), _1435012), _1435014), hAPP(hAPP(c_Set_Oinsert(_1435006), _1435010), _1435008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435004), hAPP(_1435012, _1435010)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435004, _1435006, c_Groups_Otimes__class_Otimes(_1435004)), _1435012), _1435014), _1435008)))], (49965 ^ _775828) ^ [_1779361, _1779363, _1779365, _1779367, _1779369] : [class_Orderings_Olinorder(_1779361), c_List_Olinorder__class_Osorted(_1779361, hAPP(hAPP(c_List_Omap(_1779363, _1779361), _1779365), _1779367)), -(c_List_Olinorder__class_Osorted(_1779361, hAPP(hAPP(c_List_Omap(_1779363, _1779361), _1779365), c_List_Olinorder__class_Oinsort__insert__key(_1779363, _1779361, _1779365, _1779369, _1779367))))], (23104 ^ _775828) ^ [_1178109, _1178111, _1178113, _1178115] : [class_Fields_Olinordered__field(_1178109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178109), _1178111), c_Groups_Ozero__class_Ozero(_1178109))), 23111 ^ _775828 : [(23118 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178109), _1178115), _1178111)), _1178113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178109), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178109), _1178113), _1178111)), _1178115)))], (23112 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178109), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178109), _1178113), _1178111)), _1178115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178109), _1178115), _1178111)), _1178113)))]]], (50296 ^ _775828) ^ [_1786547, _1786549] : [c_List_Oconcat(_1786547, _1786549) = c_List_Olist_ONil(_1786547), 50299 ^ _775828 : [(50300 ^ _775828) ^ [_1786638] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1786547)), _1786638), hAPP(c_List_Oset(tc_List_Olist(_1786547)), _1786549))), -(_1786638 = c_List_Olist_ONil(_1786547))]]], (40517 ^ _775828) ^ [_1553121, _1553123] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1553121, 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(_1553121, tc_HOL_Obool)), tc_fun(_1553121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1553121, tc_HOL_Obool)), tc_fun(_1553121, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1553121, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1553123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1553121, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1553123))], (41560 ^ _775828) ^ [_1579860, _1579862, _1579864, _1579866, _1579868, _1579870] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1579860, _1579862), hAPP(hAPP(c_Set_Oinsert(_1579860), _1579864), _1579866)), hAPP(c_COMBK(tc_fun(_1579862, tc_HOL_Obool), _1579860), hAPP(hAPP(c_Set_Oinsert(_1579862), _1579868), _1579870))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579860, _1579862)), hAPP(hAPP(c_Product__Type_OPair(_1579860, _1579862), _1579864), _1579868)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579860, _1579862), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1579860, _1579862), _1579866), hAPP(c_COMBK(tc_fun(_1579862, tc_HOL_Obool), _1579860), hAPP(hAPP(c_Set_Oinsert(_1579862), _1579868), _1579870)))), hAPP(hAPP(c_Product__Type_OSigma(_1579860, _1579862), hAPP(hAPP(c_Set_Oinsert(_1579860), _1579864), _1579866)), hAPP(c_COMBK(tc_fun(_1579862, tc_HOL_Obool), _1579860), _1579870)))))], (46131 ^ _775828) ^ [_1687808, _1687810, _1687812, _1687814, _1687816, _1687818] : [class_Orderings_Olinorder(_1687808), -(hAPP(_1687810, _1687812) = hAPP(_1687810, _1687814)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687816, _1687808, _1687810), _1687814), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687816, _1687808, _1687810), _1687812), _1687818)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687816, _1687808, _1687810), _1687812), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687816, _1687808, _1687810), _1687814), _1687818)))], (47639 ^ _775828) ^ [_1726178, _1726180, _1726182, _1726184, _1726186] : [-(hAPP(hAPP(c_List_Ozip(_1726178, _1726180), hAPP(hAPP(c_List_Olist_OCons(_1726178), _1726182), _1726184)), _1726186) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1726178, _1726180)), _1726180, c_List_Olist_ONil(tc_prod(_1726178, _1726180)), hAPP(hAPP(c_COMBC(_1726180, tc_fun(tc_List_Olist(_1726180), tc_List_Olist(tc_prod(_1726178, _1726180))), tc_fun(tc_List_Olist(_1726180), tc_List_Olist(tc_prod(_1726178, _1726180)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1726178, _1726180)), tc_List_Olist(tc_prod(_1726178, _1726180))), tc_fun(tc_fun(tc_List_Olist(_1726180), tc_List_Olist(tc_prod(_1726178, _1726180))), tc_fun(tc_List_Olist(_1726180), tc_List_Olist(tc_prod(_1726178, _1726180)))), _1726180), c_COMBB(tc_List_Olist(tc_prod(_1726178, _1726180)), tc_List_Olist(tc_prod(_1726178, _1726180)), tc_List_Olist(_1726180))), hAPP(hAPP(c_COMBB(tc_prod(_1726178, _1726180), tc_fun(tc_List_Olist(tc_prod(_1726178, _1726180)), tc_List_Olist(tc_prod(_1726178, _1726180))), _1726180), c_List_Olist_OCons(tc_prod(_1726178, _1726180))), hAPP(c_Product__Type_OPair(_1726178, _1726180), _1726182)))), hAPP(c_List_Ozip(_1726178, _1726180), _1726184))), _1726186))], (47419 ^ _775828) ^ [_1721766] : [-(hAPP(c_List_Oset(_1721766), c_List_Olist_ONil(_1721766)) = c_Orderings_Obot__class_Obot(tc_fun(_1721766, tc_HOL_Obool)))], (49811 ^ _775828) ^ [_1776949, _1776951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776949), _1776951)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1776949, _1776951)) = _1776949)], (42530 ^ _775828) ^ [_1602839, _1602841, _1602843] : [hBOOL(hAPP(c_Predicate_OPowp(_1602839, _1602841), _1602843)), 42533 ^ _775828 : [(42534 ^ _775828) ^ [_1602923] : [hBOOL(hAPP(hAPP(c_member(_1602839), _1602923), _1602843)), -(hBOOL(hAPP(_1602841, _1602923)))]]], (19532 ^ _775828) ^ [_1111497, _1111499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111497)), c_Int_OBit1(_1111499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111497), _1111499)))], (31211 ^ _775828) ^ [_1349565, _1349567, _1349569] : [class_Orderings_Olinorder(_1349565), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349565), _1349567)), hBOOL(hAPP(hAPP(c_member(_1349565), _1349569), _1349567)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349565), _1349569), c_Big__Operators_Olattice_OSup__fin(_1349565, c_Orderings_Oord__class_Omax(_1349565), _1349567)) = c_Big__Operators_Olattice_OSup__fin(_1349565, c_Orderings_Oord__class_Omax(_1349565), _1349567))], (13678 ^ _775828) ^ [_1003552, _1003554, _1003556, _1003558] : [c_Com_Ocom_OSemi(_1003552, _1003554) = c_Com_Ocom_OAss(_1003556, _1003558)], (42408 ^ _775828) ^ [_1599579, _1599581, _1599583, _1599585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1599579, _1599581), tc_HOL_Obool)), _1599583), _1599585)), c_Relation_Osingle__valued(_1599579, _1599581, _1599585), -(c_Relation_Osingle__valued(_1599579, _1599581, _1599583))], (12451 ^ _775828) ^ [_981202, _981204, _981206] : [class_Rings_Olinordered__idom(_981202), -(c_Groups_Osgn__class_Osgn(_981202, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981202), _981204), _981206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981202), c_Groups_Osgn__class_Osgn(_981202, _981204)), c_Groups_Osgn__class_Osgn(_981202, _981206)))], (5965 ^ _775828) ^ [_870698, _870700, _870702] : [c_Com_Ocom_OCall(_870698, _870700, _870702) = c_Com_Ocom_OSKIP], (48996 ^ _775828) ^ [_1759370, _1759372, _1759374, _1759376] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759370)), hAPP(hAPP(c_List_Olist_OCons(_1759370), _1759372), _1759374)), c_List_Olists(_1759370, _1759376)))), hBOOL(hAPP(hAPP(c_member(_1759370), _1759372), _1759376)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759370)), _1759374), c_List_Olists(_1759370, _1759376)))], (32833 ^ _775828) ^ [_1383165, _1383167, _1383169, _1383171, _1383173, _1383175] : [-(_1383165 = _1383167), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383169, _1383171), _1383173), _1383167), _1383175), _1383165) = hAPP(_1383173, _1383165))], (4084 ^ _775828) ^ [_838171, _838173, _838175, _838177] : [-(c_List_Olex(_838177, _838173) = c_List_Olex(_838175, _838171)), _838177 = _838175, _838173 = _838171], (7145 ^ _775828) ^ [_889418, _889420, _889422] : [class_Rings_Olinordered__semiring__strict(_889418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889418), c_Groups_Ozero__class_Ozero(_889418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_889418), _889420), _889422))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889418), c_Groups_Ozero__class_Ozero(_889418)), _889420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889418), c_Groups_Ozero__class_Ozero(_889418)), _889422)))], (48054 ^ _775828) ^ [_1736080, _1736082, _1736084] : [hBOOL(hAPP(c_List_Odistinct(_1736080), hAPP(hAPP(c_List_Oappend(_1736080), _1736082), _1736084))), 48057 ^ _775828 : [(48062 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1736080, tc_HOL_Obool)), hAPP(c_List_Oset(_1736080), _1736082)), hAPP(c_List_Oset(_1736080), _1736084)) = c_Orderings_Obot__class_Obot(tc_fun(_1736080, tc_HOL_Obool)))], (48060 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1736080), _1736084)))], (48058 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1736080), _1736082)))]]], (27829 ^ _775828) ^ [_1272373, _1272375, _1272377, _1272379, _1272381, _1272383, _1272385] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1272373, _1272375, _1272377, hAPP(hAPP(c_COMBC(_1272373, tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_fun(_1272375, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1272375, tc_fun(tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_fun(_1272375, tc_HOL_Obool)), _1272373), c_COMBC(_1272375, tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1272375, tc_prod(_1272373, _1272375)), tc_fun(_1272375, tc_fun(tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_HOL_Obool)), _1272373), hAPP(c_COMBB(tc_prod(_1272373, _1272375), tc_fun(tc_fun(tc_prod(_1272373, _1272375), tc_HOL_Obool), tc_HOL_Obool), _1272375), c_member(tc_prod(_1272373, _1272375)))), c_Product__Type_OPair(_1272373, _1272375)))), _1272379), hAPP(hAPP(c_COMBC(_1272375, tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_fun(_1272377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1272377, tc_fun(tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_fun(_1272377, tc_HOL_Obool)), _1272375), c_COMBC(_1272377, tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1272377, tc_prod(_1272375, _1272377)), tc_fun(_1272377, tc_fun(tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_HOL_Obool)), _1272375), hAPP(c_COMBB(tc_prod(_1272375, _1272377), tc_fun(tc_fun(tc_prod(_1272375, _1272377), tc_HOL_Obool), tc_HOL_Obool), _1272377), c_member(tc_prod(_1272375, _1272377)))), c_Product__Type_OPair(_1272375, _1272377)))), _1272381)), _1272383), _1272385)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1272373, _1272377)), hAPP(hAPP(c_Product__Type_OPair(_1272373, _1272377), _1272383), _1272385)), hAPP(hAPP(c_Relation_Orel__comp(_1272373, _1272375, _1272377), _1272379), _1272381))))], (17471 ^ _775828) ^ [_1075033, _1075035] : [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), _1075033), _1075035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075033))), -(_1075035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5591 ^ _775828) ^ [_864434] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _864434)], (37170 ^ _775828) ^ [_1475865, _1475867] : [hAPP(_1475865, 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), _1475865), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1475867)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1475865), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1475867)))], (24302 ^ _775828) ^ [_1202164, _1202166, _1202168] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202164), _1202166)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202168), _1202166)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1202164), _1202168)), _1202166))], (44691 ^ _775828) ^ [_1654930] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654930, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1654930, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1654930, tc_HOL_Obool)))], (47529 ^ _775828) ^ [_1723998, _1724000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1723998), _1724000)), -(c_List_Oupto(_1723998, _1724000) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1723998), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1723998), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1724000)))], (29899 ^ _775828) ^ [_1319546, _1319548, _1319550] : [-(hAPP(hAPP(c_Set_Oinsert(_1319546), _1319548), _1319550) = hAPP(c_Set_OCollect(_1319546), hAPP(hAPP(c_COMBS(_1319546, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1319546), c_fdisj), hAPP(hAPP(c_COMBC(_1319546, _1319546, tc_HOL_Obool), c_fequal), _1319548))), hAPP(hAPP(c_COMBC(_1319546, tc_fun(_1319546, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319546)), _1319550))))], (19964 ^ _775828) ^ [_1118668, _1118670] : [-(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), _1118668)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1118670)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1118668))) = 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), _1118670)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118668)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47095 ^ _775828) ^ [_1713809, _1713811, _1713813] : [-(hAPP(c_List_Oset(_1713809), c_List_Osublist(_1713809, _1713811, _1713813)) = hAPP(c_Set_OCollect(_1713809), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1713809), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1713809, 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)), _1713809), 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)), _1713809), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1713809, tc_fun(tc_Nat_Onat, _1713809), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1713809, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1713809), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1713809), c_COMBB(_1713809, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1713809), _1713811))))), 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(_1713809)), _1713811)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1713813))))))], (21222 ^ _775828) ^ [_1143539, _1143541, _1143543, _1143545] : [class_Rings_Odivision__ring(_1143539), -(_1143541 = c_Groups_Ozero__class_Ozero(_1143539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143539), _1143543), _1143541) = _1143545, -(_1143543 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143539), _1143545), _1143541))], (29353 ^ _775828) ^ [_1308138, _1308140, _1308142, _1308144] : [-(hBOOL(hAPP(hAPP(c_member(_1308138), _1308140), _1308142))), -(hBOOL(hAPP(hAPP(c_member(_1308138), _1308140), _1308144))), 29360 ^ _775828 : [(29367 ^ _775828) ^ [] : [_1308142 = _1308144, -(hAPP(hAPP(c_Set_Oinsert(_1308138), _1308140), _1308142) = hAPP(hAPP(c_Set_Oinsert(_1308138), _1308140), _1308144))], (29361 ^ _775828) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1308138), _1308140), _1308142) = hAPP(hAPP(c_Set_Oinsert(_1308138), _1308140), _1308144), -(_1308142 = _1308144)]]], (23828 ^ _775828) ^ [_1193101, _1193103, _1193105] : [class_Orderings_Olinorder(_1193101), 23831 ^ _775828 : [(23838 ^ _775828) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193101), _1193103), _1193105) = _1193103, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193101), _1193103), _1193105)))], (23832 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193101), _1193103), _1193105)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193101), _1193103), _1193105) = _1193103)]]], (18107 ^ _775828) ^ [_1086381, _1086383, _1086385, _1086387, _1086389] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1086381, _1086383, _1086385), _1086387), _1086389)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1086381, _1086383)), hAPP(hAPP(c_Product__Type_OPair(_1086381, _1086383), _1086387), _1086389)), _1086385)))], (14340 ^ _775828) ^ [_1015632, _1015634, _1015636, _1015638] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1015632, _1015634)), _1015636), _1015638))), 14341 ^ _775828 : [(14348 ^ _775828) ^ [] : [hBOOL(hAPP(_1015632, _1015636)), 14351 ^ _775828 : [(14352 ^ _775828) ^ [_1015851] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1015634), _1015636), _1015851)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1015632, _1015634)), _1015851), _1015638))]]], (14342 ^ _775828) ^ [] : [_1015638 = _1015636, -(hBOOL(hAPP(_1015632, _1015636)))]]], (48838 ^ _775828) ^ [_1755527, _1755529] : [-(c_List_Olist_Olist__size(_1755527, _1755529, c_List_Olist_ONil(_1755527)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24394 ^ _775828) ^ [_1204074, _1204076, _1204078, _1204080, _1204082, _1204084] : [hAPP(_1204080, hAPP(c_Product__Type_Ofst(_1204074, _1204078), _1204082)) = hAPP(_1204084, hAPP(c_Product__Type_Ofst(_1204074, _1204078), _1204082)), -(hAPP(c_Product__Type_Oapfst(_1204074, _1204076, _1204078, _1204080), _1204082) = hAPP(c_Product__Type_Oapfst(_1204074, _1204076, _1204078, _1204084), _1204082))], (19674 ^ _775828) ^ [_1113861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1113861)))], (47853 ^ _775828) ^ [_1731774, _1731776, _1731778, _1731780] : [-(hBOOL(hAPP(hAPP(c_member(_1731774), _1731776), hAPP(c_List_Oset(_1731774), _1731778)))), -(c_List_Oremove1(_1731774, _1731776, hAPP(hAPP(c_List_Oappend(_1731774), _1731778), _1731780)) = hAPP(hAPP(c_List_Oappend(_1731774), _1731778), c_List_Oremove1(_1731774, _1731776, _1731780)))], (34075 ^ _775828) ^ [_1409592, _1409594, _1409596, _1409598] : [class_Lattices_Osemilattice__inf(_1409592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409592), _1409594), _1409596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409592), _1409594), _1409598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409592), _1409594), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409592), _1409596), _1409598))))], (38126 ^ _775828) ^ [_1499122, _1499124, _1499126] : [class_Orderings_Olinorder(_1499122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499122), _1499124), _1499126)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499122, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1499122, _1499124), _1499126)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499122), _1499126)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1499122), _1499124))], (39720 ^ _775828) ^ [_1536036, _1536038, _1536040, _1536042, _1536044] : [-(_1536036 = c_Orderings_Obot__class_Obot(tc_fun(_1536038, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536040, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536038, tc_fun(_1536040, tc_HOL_Obool)), _1536036), _1536042)), _1536044) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536038, tc_fun(_1536040, tc_HOL_Obool)), _1536036), hAPP(hAPP(c_COMBC(_1536038, tc_fun(_1536040, tc_HOL_Obool), tc_fun(_1536040, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536040, tc_HOL_Obool), tc_fun(tc_fun(_1536040, tc_HOL_Obool), tc_fun(_1536040, tc_HOL_Obool)), _1536038), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536040, tc_HOL_Obool))), _1536042)), _1536044)))], (49319 ^ _775828) ^ [_1766109, _1766111] : [-(c_List_Obutlast(_1766109, _1766111) = hAPP(hAPP(c_List_Otake(_1766109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766109)), _1766111)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1766111))], (41360 ^ _775828) ^ [_1575164, _1575166, _1575168, _1575170, _1575172] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575164, _1575166), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575164, tc_HOL_Obool)), _1575168), _1575170)), _1575172) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575164, _1575166), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575164, _1575166), _1575168), _1575172)), hAPP(hAPP(c_Product__Type_OSigma(_1575164, _1575166), _1575170), _1575172)))], (38538 ^ _775828) ^ [_1508507, _1508509, _1508511, _1508513, _1508515] : [c_Equiv__Relations_Oequiv(_1508507, _1508509, _1508511), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508507, _1508507)), hAPP(hAPP(c_Product__Type_OPair(_1508507, _1508507), _1508513), _1508515)), _1508511)), -(hAPP(c_Relation_OImage(_1508507, _1508507, _1508511), hAPP(hAPP(c_Set_Oinsert(_1508507), _1508513), c_Orderings_Obot__class_Obot(tc_fun(_1508507, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508507, _1508507, _1508511), hAPP(hAPP(c_Set_Oinsert(_1508507), _1508515), c_Orderings_Obot__class_Obot(tc_fun(_1508507, tc_HOL_Obool)))))], (19890 ^ _775828) ^ [_1117213, _1117215] : [class_Int_Onumber__ring(_1117213), class_Rings_Olinordered__idom(_1117213), 19897 ^ _775828 : [(19904 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1117215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117213), c_Groups_Oone__class_Oone(_1117213)), hAPP(c_Int_Onumber__class_Onumber__of(_1117213), _1117215))))], (19898 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117213), c_Groups_Oone__class_Oone(_1117213)), hAPP(c_Int_Onumber__class_Onumber__of(_1117213), _1117215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1117215)))]]], (51488 ^ _775828) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (47399 ^ _775828) ^ [_1721456, _1721458, _1721460, _1721462, _1721464, _1721466] : [-(_1721456 = _1721458), -(hAPP(hAPP(c_List_Olist__update(_1721460, hAPP(hAPP(c_List_Olist__update(_1721460, _1721462), _1721456), _1721464)), _1721458), _1721466) = hAPP(hAPP(c_List_Olist__update(_1721460, hAPP(hAPP(c_List_Olist__update(_1721460, _1721462), _1721458), _1721466)), _1721456), _1721464))], (11739 ^ _775828) ^ [_968771, _968773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968771), _968773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968771), hAPP(c_Nat_OSuc, _968773))))], (6150 ^ _775828) ^ [_873576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873576), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_873576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41841 ^ _775828) ^ [_1585637, _1585639, _1585641] : [class_Orderings_Olinorder(_1585637), -(_1585639 = c_Orderings_Obot__class_Obot(tc_fun(_1585637, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1585637, tc_HOL_Obool)), _1585639), _1585641)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585637), _1585641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1585637), hAPP(c_Finite__Set_Ofold1(_1585637, c_Orderings_Oord__class_Omin(_1585637)), _1585641)), hAPP(c_Finite__Set_Ofold1(_1585637, c_Orderings_Oord__class_Omin(_1585637)), _1585639))))], (15322 ^ _775828) ^ [_1033332, _1033334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1033332), _1033334)), _1033332)))], (3536 ^ _775828) ^ [_829499, _829501] : [_829501 = _829499, -(c_Random__Sequence_Osingle(_829501) = c_Random__Sequence_Osingle(_829499))], (15618 ^ _775828) ^ [_1038916, _1038918] : [class_Groups_Ogroup__add(_1038916), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038916), c_Groups_Ozero__class_Ozero(_1038916)), _1038918) = hAPP(c_Groups_Ouminus__class_Ouminus(_1038916), _1038918))], (45667 ^ _775828) ^ [_1676581, _1676583, _1676585, _1676587, _1676589] : [45669 ^ _775828 : [(45672 ^ _775828) ^ [] : [hAPP(_1676585, 45668 ^ [_1676581, _1676583, _1676585, _1676587, _1676589]) = hAPP(_1676589, 45668 ^ [_1676581, _1676583, _1676585, _1676587, _1676589])], (45670 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676581), 45668 ^ [_1676581, _1676583, _1676585, _1676587, _1676589]), hAPP(c_List_Oset(_1676581), _1676587))))]], -(hAPP(hAPP(c_List_Omap(_1676581, _1676583), _1676585), _1676587) = hAPP(hAPP(c_List_Omap(_1676581, _1676583), _1676589), _1676587))], (50033 ^ _775828) ^ [_1780652, _1780654] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1780652, _1780654) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1780652, hAPP(c_Nat_OSuc, _1780654))))], (39802 ^ _775828) ^ [_1538068, _1538070, _1538072, _1538074, _1538076, _1538078, _1538080, _1538082] : [hBOOL(hAPP(hAPP(c_member(_1538068), _1538070), _1538072)), hBOOL(hAPP(hAPP(hAPP(_1538074, _1538070), _1538076), _1538078)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1538068, tc_fun(_1538080, tc_fun(_1538082, tc_HOL_Obool))), _1538072), _1538074), _1538076), _1538078)))], (50640 ^ _775828) ^ [_1795494, _1795496, _1795498] : [-(c_List_OtakeWhile(_1795494, _1795496, _1795498) = hAPP(hAPP(c_List_Otake(_1795494), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795494)), c_List_OtakeWhile(_1795494, _1795496, _1795498))), _1795498))], (18119 ^ _775828) ^ [_1086657, _1086659, _1086661, _1086663, _1086665] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1086657, _1086659), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1086661), _1086663))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086659)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086665), _1086657), _1086659), 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), _1086665), _1086661)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086665), _1086663)), _1086659))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086665), _1086663), _1086659)))))], (42263 ^ _775828) ^ [_1596561, _1596563, _1596565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1596561), _1596563)), 42269 ^ _775828 : [(42272 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1596565, 42268 ^ [_1596561, _1596563, _1596565])))], (42270 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1596561), 42268 ^ [_1596561, _1596563, _1596565]), _1596563)))]], -(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(_1596561, tc_Nat_Onat), _1596565), _1596563))))], (12099 ^ _775828) ^ [_975302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _975302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975302)))], (50327 ^ _775828) ^ [_1787236, _1787238, _1787240] : [hAPP(hAPP(c_List_Olist_OCons(_1787236), _1787238), c_List_Olist_ONil(_1787236)) = hAPP(c_List_Orev(_1787236), _1787240), -(_1787240 = hAPP(hAPP(c_List_Olist_OCons(_1787236), _1787238), c_List_Olist_ONil(_1787236)))], (3486 ^ _775828) ^ [_828676, _828678, _828680, _828682, _828684, _828686] : [-(c_Hoare__Mirabelle_Opeek__and(_828686, _828682, _828678) = c_Hoare__Mirabelle_Opeek__and(_828684, _828680, _828676)), _828686 = _828684, _828682 = _828680, _828678 = _828676], (10276 ^ _775828) ^ [_942378, _942380, _942382, _942384, _942386] : [class_Rings_Ocomm__semiring__1(_942378), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), _942380), _942382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), _942384), _942386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), _942380), _942384)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942378), _942382), _942386)))], (30391 ^ _775828) ^ [_1331223] : [-(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)), _1331223)))))], (51434 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (42296 ^ _775828) ^ [_1597257, _1597259] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1597257), c_Int_OInteg)), hBOOL(hAPP(_1597259, hAPP(c_Int_ORep__Integ, 42301 ^ [_1597257, _1597259]))), -(hBOOL(hAPP(_1597259, _1597257)))], (27016 ^ _775828) ^ [_1253198] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253198), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253198) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (44942 ^ _775828) ^ [_1660252, _1660254, _1660256] : [class_Complete__Lattice_Ocomplete__lattice(_1660252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660252), _1660254)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1660252), _1660256), c_Complete__Lattice_OSup__class_OSup(_1660252, _1660254)) = hAPP(hAPP(c_Finite__Set_Ofold(_1660252, _1660252, c_Lattices_Osemilattice__sup__class_Osup(_1660252)), _1660256), _1660254))], (5066 ^ _775828) ^ [_853354, _853356, _853358, _853360] : [-(c_List_Oremdups(_853360, _853356) = c_List_Oremdups(_853358, _853354)), _853360 = _853358, _853356 = _853354], (37574 ^ _775828) ^ [_1486166, _1486168, _1486170, _1486172, _1486174] : [class_Rings_Oring(_1486166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486168), _1486170)), hBOOL(hAPP(hAPP(c_member(_1486168), _1486172), _1486170)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1486168, _1486166), _1486174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486168, tc_HOL_Obool)), _1486170), hAPP(hAPP(c_Set_Oinsert(_1486168), _1486172), c_Orderings_Obot__class_Obot(tc_fun(_1486168, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1486166), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1486168, _1486166), _1486174), _1486170)), hAPP(_1486174, _1486172)))], (45305 ^ _775828) ^ [_1668164, _1668166, _1668168, _1668170, _1668172, _1668174] : [-(c_Map_Omap__add(_1668164, _1668166, _1668168, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1668164, tc_Option_Ooption(_1668166)), _1668170), _1668172), hAPP(c_Option_Ooption_OSome(_1668166), _1668174))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1668164, tc_Option_Ooption(_1668166)), c_Map_Omap__add(_1668164, _1668166, _1668168, _1668170)), _1668172), hAPP(c_Option_Ooption_OSome(_1668166), _1668174)))], (20120 ^ _775828) ^ [_1121483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1121483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1121483)))], (32259 ^ _775828) ^ [_1371929, _1371931, _1371933] : [class_Orderings_Olinorder(_1371929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371929), _1371931)), -(_1371933 = c_Orderings_Obot__class_Obot(tc_fun(_1371929, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371929, tc_HOL_Obool)), _1371933), _1371931)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371929), c_Big__Operators_Olinorder__class_OMax(_1371929, _1371933)), c_Big__Operators_Olinorder__class_OMax(_1371929, _1371931)) = c_Big__Operators_Olinorder__class_OMax(_1371929, _1371931))], (30293 ^ _775828) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (45985 ^ _775828) ^ [_1683760, _1683762, _1683764] : [hBOOL(hAPP(c_List_Odistinct(_1683760), _1683762)), -(hBOOL(hAPP(c_List_Odistinct(_1683760), c_List_Oremove1(_1683760, _1683764, _1683762))))], (11006 ^ _775828) ^ [_955865, _955867] : [11007 ^ _775828 : [(11010 ^ _775828) ^ [] : [_955865 = _955867], (11008 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955865), _955867))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955865), _955867)))], (24893 ^ _775828) ^ [_1214224, _1214226, _1214228, _1214230, _1214232] : [_1214224 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1214226, _1214228, _1214224, _1214230), _1214232) = hAPP(c_Product__Type_OPair(_1214226, _1214228), _1214232))], (13084 ^ _775828) ^ [_992138, _992140, _992142, _992144, _992146, _992148] : [-(hBOOL(hAPP(_992138, _992140))), c_Natural_Oevaln(_992142, _992140, _992144, _992146), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_992138, _992148, _992142), _992140, _992144, _992146))], (42756 ^ _775828) ^ [_1608164, _1608166, _1608168, _1608170, _1608172, _1608174, _1608176] : [-(hAPP(c_Product__Type_Oapfst(_1608164, _1608166, _1608168, _1608170), hAPP(c_Product__Type_Oapfst(_1608172, _1608164, _1608168, _1608174), _1608176)) = hAPP(c_Product__Type_Oapfst(_1608172, _1608166, _1608168, hAPP(c_Fun_Ocomp(_1608164, _1608166, _1608172, _1608170), _1608174)), _1608176))], (21746 ^ _775828) ^ [_1152786, _1152788, _1152790, _1152792] : [class_Fields_Olinordered__field__inverse__zero(_1152786), class_Int_Onumber(_1152786), 21753 ^ _775828 : [(21754 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152786), _1152788), _1152790)), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792))), 21757 ^ _775828 : [(21764 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), _1152790))), 21767 ^ _775828 : [(21774 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152790), c_Groups_Ozero__class_Ozero(_1152786)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792))))], (21768 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152790), c_Groups_Ozero__class_Ozero(_1152786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152786), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)), _1152790)), _1152788)))]]], (21758 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), _1152790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152786), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)), _1152790))))]]], (21780 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152786), _1152788), _1152790)), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)))), 21783 ^ _775828 : [(21786 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152786), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)), _1152790)))], (21784 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), _1152790)))]], 21787 ^ _775828 : [(21790 ^ _775828) ^ [] : [21791 ^ _775828 : [(21794 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152786), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)), _1152790)), _1152788))], (21792 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152790), c_Groups_Ozero__class_Ozero(_1152786))))]], 21795 ^ _775828 : [(21798 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), hAPP(c_Int_Onumber__class_Onumber__of(_1152786), _1152792)))], (21796 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), _1152790), c_Groups_Ozero__class_Ozero(_1152786)))]]], (21788 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152786), c_Groups_Ozero__class_Ozero(_1152786)), _1152790))]]]]], (24352 ^ _775828) ^ [_1203189, _1203191] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1203189)), _1203191) = 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), _1203189)), _1203191))], (6710 ^ _775828) ^ [_882277, _882279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882277)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882277), _882279)))], (39247 ^ _775828) ^ [_1523780, _1523782] : [-(c_Fun_Oinj__on(_1523780, tc_Option_Ooption(_1523780), c_Option_Ooption_OSome(_1523780), _1523782))], (30828 ^ _775828) ^ [_1339622, _1339624, _1339626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339622), _1339624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339622, tc_HOL_Obool)), _1339624), _1339626)), -(hAPP(c_Finite__Set_Ocard(_1339622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339622, tc_HOL_Obool)), _1339626), _1339624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1339622), _1339626)), hAPP(c_Finite__Set_Ocard(_1339622), _1339624)))], (15672 ^ _775828) ^ [_1039961, _1039963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1039961), _1039963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1039961), _1039963)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27627 ^ _775828) ^ [_1267002, _1267004, _1267006, _1267008, _1267010] : [hBOOL(hAPP(hAPP(c_member(_1267002), _1267004), c_SetInterval_Oord_OatLeastAtMost(_1267002, _1267006, _1267008, _1267010))), 27630 ^ _775828 : [(27633 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1267006, _1267004), _1267010)))], (27631 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1267006, _1267008), _1267004)))]]], (7441 ^ _775828) ^ [_894587, _894589] : [-(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, _894587)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894589))))], (17461 ^ _775828) ^ [_1074837, _1074839, _1074841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1074837), _1074839)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1074837), _1074841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074839), _1074841)))], (2742 ^ _775828) ^ [_816658, _816660, _816662, _816664, _816666, _816668, _816670, _816672] : [-(c_Lazy__Sequence_Obind(_816672, _816668, _816664, _816660) = c_Lazy__Sequence_Obind(_816670, _816666, _816662, _816658)), _816672 = _816670, _816668 = _816666, _816664 = _816662, _816660 = _816658], (33394 ^ _775828) ^ [_1394989, _1394991, _1394993, _1394995, _1394997, _1394999] : [-(hBOOL(hAPP(hAPP(c_member(_1394989), _1394991), _1394993))), -(c_Map_Orestrict__map(_1394989, _1394995, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394989, tc_Option_Ooption(_1394995)), _1394997), _1394991), _1394999), _1394993) = c_Map_Orestrict__map(_1394989, _1394995, _1394997, _1394993))], (970 ^ _775828) ^ [_790571, _790573] : [-(class_Rings_Olinordered__semiring__1__strict(_790571)), _790573 = _790571, class_Rings_Olinordered__semiring__1__strict(_790573)], (51408 ^ _775828) ^ [_1807186, _1807188] : [-(class_Finite__Set_Ofinite(tc_prod(_1807186, _1807188))), class_Finite__Set_Ofinite(_1807186), class_Finite__Set_Ofinite(_1807188)], (50702 ^ _775828) ^ [_1796624, _1796626] : [-(_1796624 = c_List_Olist_ONil(_1796626)), hBOOL(hAPP(c_List_Odistinct(_1796626), _1796624)), -(c_List_OtakeWhile(_1796626, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1796626), c_fNot), hAPP(hAPP(c_COMBC(_1796626, _1796626, tc_HOL_Obool), c_fequal), c_List_Olast(_1796626, _1796624))), _1796624) = c_List_Obutlast(_1796626, _1796624))], (51442 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (44065 ^ _775828) ^ [_1637539, _1637541, _1637543, _1637545, _1637547, _1637549] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637539, tc_fun(_1637541, tc_HOL_Obool)), _1637543), _1637545), _1637547)), -(hBOOL(hAPP(hAPP(_1637545, _1637549), _1637547))), hBOOL(hAPP(hAPP(c_member(_1637539), _1637549), _1637543))], (30543 ^ _775828) ^ 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hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158235), _1158239), _1158241))), 22033 ^ _775828 : [(22040 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158235), c_Groups_Ozero__class_Ozero(_1158235)), _1158241))), 22043 ^ _775828 : [(22050 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158235), _1158241), c_Groups_Ozero__class_Ozero(_1158235)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158235), hAPP(c_Int_Onumber__class_Onumber__of(_1158235), _1158237)), c_Groups_Ozero__class_Ozero(_1158235))))], (22044 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158235), _1158241), c_Groups_Ozero__class_Ozero(_1158235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158235), _1158239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158235), hAPP(c_Int_Onumber__class_Onumber__of(_1158235), _1158237)), _1158241))))]]], (22034 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158235), c_Groups_Ozero__class_Ozero(_1158235)), _1158241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158235), hAPP(c_Int_Onumber__class_Onumber__of(_1158235), _1158237)), _1158241)), _1158239)))]]], (22056 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158235), hAPP(c_Int_Onumber__class_Onumber__of(_1158235), _1158237)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158235), _1158239), _1158241)))), 22059 ^ _775828 : [(22062 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158235), hAPP(c_Int_Onumber__class_Onumber__of(_1158235), _1158237)), _1158241)), _1158239))], (22060 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158235), c_Groups_Ozero__class_Ozero(_1158235)), _1158241)))]], 22063 ^ _775828 : [(22066 ^ _775828) ^ [] : [22067 ^ _775828 : [(22070 ^ _775828) ^ [] : 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c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651990, tc_HOL_Obool), _1651994)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1651990, tc_HOL_Obool), tc_fun(_1651990, tc_HOL_Obool)), _1651994), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1651990, tc_HOL_Obool)), _1651992)))], (33701 ^ _775828) ^ [_1401676, _1401678, _1401680, _1401682] : [-(hBOOL(hAPP(hAPP(c_member(_1401676), _1401678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401676, tc_HOL_Obool)), _1401680), _1401682)))), hBOOL(hAPP(hAPP(c_member(_1401676), _1401678), _1401680)), hBOOL(hAPP(hAPP(c_member(_1401676), _1401678), _1401682))], (4278 ^ _775828) ^ [_841184, _841186, _841188, _841190] : [-(c_Complete__Lattice_OInf__class_OInf(_841190, _841186) = c_Complete__Lattice_OInf__class_OInf(_841188, _841184)), _841190 = _841188, _841186 = _841184], (48443 ^ _775828) ^ [_1747008, _1747010, _1747012] : [hAPP(hAPP(c_List_Odrop(_1747008), _1747010), _1747012) = 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-(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349318), _1349322), c_Big__Operators_Olattice_OInf__fin(_1349318, c_Orderings_Oord__class_Omin(_1349318), _1349320)) = c_Big__Operators_Olattice_OInf__fin(_1349318, c_Orderings_Oord__class_Omin(_1349318), _1349320))], (17533 ^ _775828) ^ [_1076018] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076018))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076018) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33613 ^ _775828) ^ [_1399749, _1399751, _1399753] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399749, tc_HOL_Obool)), _1399751), _1399753) = c_Orderings_Obot__class_Obot(tc_fun(_1399749, tc_HOL_Obool)), 33616 ^ _775828 : [(33617 ^ _775828) ^ [_1399873] : [hBOOL(hAPP(hAPP(c_member(_1399749), _1399873), _1399751)), 33620 ^ _775828 : [(33621 ^ _775828) ^ [_1399963] : [hBOOL(hAPP(hAPP(c_member(_1399749), _1399963), _1399753)), _1399873 = _1399963]]]]], (31671 ^ _775828) ^ 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066753), hAPP(c_Int_Onumber__class_Onumber__of(_1066753), _1066755)), hAPP(c_Int_Onumber__class_Onumber__of(_1066753), _1066757))))], (17051 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066753), hAPP(c_Int_Onumber__class_Onumber__of(_1066753), _1066755)), hAPP(c_Int_Onumber__class_Onumber__of(_1066753), _1066757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066755), _1066757)))]]], (42214 ^ _775828) ^ [_1595493, _1595495, _1595497, _1595499, _1595501] : [c_Relation_Orefl__on(_1595493, _1595495, _1595497), hBOOL(hAPP(hAPP(c_member(tc_prod(_1595493, _1595493)), hAPP(hAPP(c_Product__Type_OPair(_1595493, _1595493), _1595499), _1595501)), _1595497)), -(hBOOL(hAPP(hAPP(c_member(_1595493), _1595501), _1595495)))], (47521 ^ _775828) ^ [_1723783, _1723785, _1723787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723783), tc_List_Olist(_1723783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723783), tc_List_Olist(_1723783)), _1723785), c_List_Olist_ONil(_1723783))), c_List_Olex(_1723783, _1723787)))], (21148 ^ _775828) ^ [] : [-(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))], (6344 ^ _775828) ^ [_876707, _876709] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_876707, _876709))))], (18863 ^ _775828) ^ [_1100282, _1100284, _1100286] : [-(_1100282 = hAPP(hAPP(c_Product__Type_OPair(_1100284, _1100286), hAPP(c_Product__Type_Ofst(_1100284, _1100286), _1100282)), hAPP(c_Product__Type_Osnd(_1100284, _1100286), _1100282)))], (49568 ^ _775828) ^ [_1772464, _1772466, _1772468, _1772470, _1772472] : [class_Orderings_Olinorder(_1772464), hBOOL(hAPP(hAPP(c_member(_1772466), _1772468), hAPP(c_List_Oset(_1772466), _1772470))), c_List_Olinorder__class_Osorted(_1772464, hAPP(hAPP(c_List_Omap(_1772466, _1772464), _1772472), _1772470)), hAPP(c_List_Ohd(_1772466), hAPP(c_List_Ofilter(_1772466, hAPP(hAPP(c_COMBB(_1772464, tc_HOL_Obool, _1772466), hAPP(c_fequal, hAPP(_1772472, _1772468))), _1772472)), _1772470)) = _1772468, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1772466, _1772464, _1772472), _1772468), c_List_Oremove1(_1772466, _1772468, _1772470)) = _1772470)], (49253 ^ _775828) ^ [_1764823, _1764825, _1764827, _1764829] : [-(hAPP(hAPP(c_List_Omap(_1764823, _1764825), _1764827), c_List_Obutlast(_1764823, _1764829)) = c_List_Obutlast(_1764825, hAPP(hAPP(c_List_Omap(_1764823, _1764825), _1764827), _1764829)))], (28459 ^ _775828) ^ [_1287035, _1287037, _1287039] : [class_Lattices_Olattice(_1287035), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287035), _1287037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287035), _1287037), _1287039))))], (10342 ^ _775828) ^ [_943879, _943881, _943883] : [class_Rings_Oring__1(_943879), -(hAPP(c_Int_Oring__1__class_Oof__int(_943879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _943881), _943883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943879), hAPP(c_Int_Oring__1__class_Oof__int(_943879), _943881)), hAPP(c_Int_Oring__1__class_Oof__int(_943879), _943883)))], (16016 ^ _775828) ^ [_1046954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046954)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046954), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1046954)], (37330 ^ _775828) ^ [_1479831, _1479833, _1479835, _1479837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1479831), _1479833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479831, tc_HOL_Obool)), _1479833), _1479835)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479831, tc_Nat_Onat), _1479837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479831, tc_HOL_Obool)), _1479835), _1479833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479831, tc_Nat_Onat), _1479837), _1479835)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479831, tc_Nat_Onat), _1479837), _1479833)))], (29725 ^ _775828) ^ [_1315728, _1315730, _1315732] : [class_Lattices_Obounded__lattice__bot(_1315728), 29728 ^ _775828 : [(29737 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1315728), _1315730), _1315732) = c_Orderings_Obot__class_Obot(_1315728)), _1315730 = c_Orderings_Obot__class_Obot(_1315728), _1315732 = c_Orderings_Obot__class_Obot(_1315728)], (29729 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1315728), _1315730), _1315732) = c_Orderings_Obot__class_Obot(_1315728), 29732 ^ _775828 : [(29735 ^ _775828) ^ [] : [-(_1315732 = c_Orderings_Obot__class_Obot(_1315728))], (29733 ^ _775828) ^ [] : [-(_1315730 = c_Orderings_Obot__class_Obot(_1315728))]]]]], (20 ^ _775828) ^ [_776088, _776090, _776092, _776094] : [-(c_Option_Ois__none(_776092, _776088)), c_Option_Ois__none(_776094, _776090), _776094 = _776092, _776090 = _776088], (18719 ^ _775828) ^ [_1097480, _1097482, _1097484, _1097486] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1097480), _1097486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1097484), _1097482), -(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), _1097480), _1097482)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1097484), _1097486))), c_Int_Ointrel)))], (19692 ^ _775828) ^ [_1114140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114140), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114140)), c_Int_OMin)))], (11775 ^ _775828) ^ [_969357, _969359, _969361] : [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, _969357)), _969359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969357)), _969361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969359), _969361)))], (34371 ^ _775828) ^ [_1416233, _1416235, _1416237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1416233, _1416233), tc_HOL_Obool)), _1416235), _1416237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1416233, _1416233), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1416233, _1416233, _1416233), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1416233, _1416233), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1416233, _1416235)), _1416237)), _1416235)), _1416237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1416233, _1416233), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1416233, _1416235)), _1416237)))], (49997 ^ _775828) ^ [_1779962, _1779964, _1779966, _1779968] : [-(c_List_Oupt(_1779962, _1779964) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1779966), _1779968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1779962), _1779964)), _1779962 = _1779966, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1779962), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1779964) = _1779968], (41883 ^ _775828) ^ [_1587481, _1587483] : [-(hAPP(c_Set_Ovimage(_1587481, _1587481, c_Fun_Oid(_1587481)), _1587483) = _1587483)], (15908 ^ _775828) ^ [_1044408, _1044410, _1044412, _1044414, _1044416, _1044418] : [class_Rings_Oordered__ring(_1044408), 15911 ^ _775828 : [(15918 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044408), _1044414), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044408), _1044416), _1044410)), _1044412)), _1044418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), _1044410), _1044412)), _1044414)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), _1044416), _1044412)), _1044418))))], (15912 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), _1044410), _1044412)), _1044414)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), _1044416), _1044412)), _1044418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044408), _1044414), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044408), _1044416), _1044410)), _1044412)), _1044418))))]]], (46314 ^ _775828) ^ [_1692540, _1692542, _1692544, _1692546, _1692548] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692540)), _1692542) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692544)), _1692546), 46317 ^ _775828 : [(46325 ^ _775828) ^ [] : [46326 ^ _775828 : [(46327 ^ _775828) ^ [_1692828] : [hAPP(c_Map_Omap__of(_1692540, _1692544, hAPP(hAPP(c_List_Ozip(_1692540, _1692544), _1692542), _1692546)), _1692548) = hAPP(c_Option_Ooption_OSome(_1692544), _1692828)]], -(hBOOL(hAPP(hAPP(c_member(_1692540), _1692548), hAPP(c_List_Oset(_1692540), _1692542))))], (46318 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1692540), _1692548), hAPP(c_List_Oset(_1692540), _1692542))), -(hAPP(c_Map_Omap__of(_1692540, _1692544, hAPP(hAPP(c_List_Ozip(_1692540, _1692544), _1692542), _1692546)), _1692548) = hAPP(c_Option_Ooption_OSome(_1692544), 46321 ^ [_1692540, _1692542, _1692544, _1692546, _1692548]))]]], (43744 ^ _775828) ^ [_1631408, _1631410, _1631412] : [class_Lattices_Olattice(_1631408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631408), _1631410)), -(c_Big__Operators_Olattice__class_OSup__fin(_1631408, hAPP(hAPP(c_Set_Oinsert(_1631408), _1631412), _1631410)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631408, _1631408, c_Lattices_Osemilattice__sup__class_Osup(_1631408)), _1631412), _1631410))], (51206 ^ _775828) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (46027 ^ _775828) ^ [_1684644, _1684646, _1684648] : [-(hAPP(hAPP(c_List_Ozip(_1684644, _1684646), hAPP(hAPP(c_List_Omap(tc_prod(_1684644, _1684646), _1684644), c_Product__Type_Ofst(_1684644, _1684646)), _1684648)), hAPP(hAPP(c_List_Omap(tc_prod(_1684644, _1684646), _1684646), c_Product__Type_Osnd(_1684644, _1684646)), _1684648)) = _1684648)], (51380 ^ _775828) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (32913 ^ _775828) ^ [_1384824, _1384826, _1384828, _1384830, _1384832] : [class_Groups_Ocomm__monoid__mult(_1384824), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384826, _1384824), hAPP(hAPP(c_COMBS(_1384826, _1384824, _1384824), hAPP(hAPP(c_COMBB(_1384824, tc_fun(_1384824, _1384824), _1384826), c_Groups_Otimes__class_Otimes(_1384824)), _1384828)), _1384830)), _1384832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384824), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384826, _1384824), _1384828), _1384832)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384826, _1384824), _1384830), _1384832)))], (17685 ^ _775828) ^ [_1078626, _1078628] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078626))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078626)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078628)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19450 ^ _775828) ^ [_1110129, _1110131, _1110133] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110129), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110129)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110131)), _1110133)) = 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), _1110129), _1110131))), _1110133))], (29689 ^ _775828) ^ [_1314904, _1314906, _1314908, _1314910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314904, tc_HOL_Obool)), _1314906), hAPP(hAPP(c_Set_Oinsert(_1314904), _1314908), _1314910)))), 29692 ^ _775828 : [(29695 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314904, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314904, tc_HOL_Obool)), _1314906), hAPP(hAPP(c_Set_Oinsert(_1314904), _1314908), c_Orderings_Obot__class_Obot(tc_fun(_1314904, tc_HOL_Obool))))), _1314910))], (29693 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1314904), _1314908), _1314906)))]], 29696 ^ _775828 : [(29699 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314904, tc_HOL_Obool)), _1314906), _1314910))], (29697 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1314904), _1314908), _1314906))]]], (25507 ^ _775828) ^ [_1226027, _1226029, _1226031] : [-(c_Wellfounded_Omlex__prod(_1226027, _1226029, _1226031) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1226027), _1226027), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1226027, c_Wellfounded_Oless__than, _1226031)), hAPP(hAPP(c_COMBS(_1226027, _1226027, tc_prod(tc_Nat_Onat, _1226027)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1226027, tc_prod(tc_Nat_Onat, _1226027)), _1226027), c_Product__Type_OPair(tc_Nat_Onat, _1226027)), _1226029)), c_COMBI(_1226027))))], (45419 ^ _775828) ^ [_1670505, _1670507, _1670509, _1670511] : [class_Rings_Olinordered__semidom(_1670505), 45425 ^ _775828 : [(45428 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670505), c_Groups_Ozero__class_Ozero(_1670505)), hAPP(_1670511, 45424 ^ [_1670505, _1670507, _1670509, _1670511])))], (45426 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670507), 45424 ^ [_1670505, _1670507, _1670509, _1670511]), _1670509)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670505), c_Groups_Ozero__class_Ozero(_1670505)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1670507, _1670505), _1670511), _1670509))))], (31685 ^ _775828) ^ [_1359707] : [-(c_Transitive__Closure_Ortrancl(_1359707, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1359707, _1359707), tc_HOL_Obool))) = c_Relation_OId(_1359707))], (10848 ^ _775828) ^ [_953258, _953260, _953262, _953264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953258), _953260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953262), _953264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953258), _953262)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953260), _953264))))], (51536 ^ _775828) ^ [] : [hBOOL(c_fFalse)], (7983 ^ _775828) ^ [_903703, _903705, _903707, _903709] : [class_Rings_Ocomm__semiring__1(_903703), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903703), _903705), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903703), _903707), _903709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903703), _903705), _903707)), _903709))], (43192 ^ _775828) ^ [_1618509, _1618511, _1618513, _1618515, _1618517, _1618519, _1618521] : [c_Finite__Set_Ofolding__idem(_1618509, _1618511, _1618513, _1618515), -(hAPP(c_Fun_Ocomp(_1618511, _1618511, _1618517, hAPP(_1618513, _1618519)), hAPP(c_Fun_Ocomp(_1618511, _1618511, _1618517, hAPP(_1618513, _1618519)), _1618521)) = hAPP(c_Fun_Ocomp(_1618511, _1618511, _1618517, hAPP(_1618513, _1618519)), _1618521))], (19444 ^ _775828) ^ [_1110010, _1110012, _1110014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110010), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110012)), _1110014)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44820 ^ _775828) ^ [_1657476, _1657478, _1657480] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1657476, tc_HOL_Obool)), _1657478), _1657480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657476, tc_HOL_Obool)), _1657478), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657476, tc_HOL_Obool), _1657480))))], (17063 ^ _775828) ^ [_1067084, _1067086, _1067088, _1067090] : [class_Int_Onumber__ring(_1067084), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067084), hAPP(c_Int_Onumber__class_Onumber__of(_1067084), _1067086)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067084), hAPP(c_Int_Onumber__class_Onumber__of(_1067084), _1067088)), _1067090)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067084), hAPP(c_Int_Onumber__class_Onumber__of(_1067084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067086), _1067088))), _1067090))], (48747 ^ _775828) ^ [_1753588, _1753590, _1753592] : [-(hAPP(c_List_Orotate(_1753588, _1753590), _1753592) = hAPP(hAPP(c_List_Oappend(_1753588), hAPP(hAPP(c_List_Odrop(_1753588), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1753590, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753588)), _1753592))), _1753592)), hAPP(hAPP(c_List_Otake(_1753588), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1753590, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753588)), _1753592))), _1753592)))], (29929 ^ _775828) ^ [_1320466, _1320468, _1320470, _1320472, _1320474] : [c_Hoare__Mirabelle_Ohoare__derivs(_1320466, _1320468, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1320466)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1320466), _1320470), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1320472))), _1320474)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1320466), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1320466, _1320468, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1320466)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1320466), _1320470), hAPP(c_Com_Ocom_OBODY, _1320472)), _1320474)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1320466), tc_HOL_Obool)))))], (47565 ^ _775828) ^ [_1724571, _1724573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724571)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724573))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724571), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724573)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724571)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724571)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724573))))], (5082 ^ _775828) ^ [_853588, _853590] : [_853590 = _853588, -(c_List_Oembed__list(_853590) = c_List_Oembed__list(_853588))], (32687 ^ _775828) ^ [_1380043, _1380045, _1380047, _1380049, _1380051, _1380053, _1380055] : [-(c_Nitpick_Ofold__graph_H(_1380043, _1380045, _1380047, _1380049, _1380051, hAPP(hAPP(_1380047, _1380053), _1380055))), 32688 ^ _775828 : [(32695 ^ _775828) ^ [_1380272, _1380274] : [hAPP(hAPP(_1380047, _1380053), _1380055) = hAPP(hAPP(_1380047, _1380274), _1380272), hBOOL(hAPP(hAPP(c_member(_1380043), _1380274), _1380051)), c_Nitpick_Ofold__graph_H(_1380043, _1380045, _1380047, _1380049, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1380043, tc_HOL_Obool)), _1380051), hAPP(hAPP(c_Set_Oinsert(_1380043), _1380274), c_Orderings_Obot__class_Obot(tc_fun(_1380043, tc_HOL_Obool)))), _1380272)], (32689 ^ _775828) ^ [] : [_1380051 = c_Orderings_Obot__class_Obot(tc_fun(_1380043, tc_HOL_Obool)), hAPP(hAPP(_1380047, _1380053), _1380055) = _1380049]]], (36243 ^ _775828) ^ [_1456414, _1456416] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1456414), hAPP(c_Nat_OSuc, _1456416)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1456414, _1456416))], (36651 ^ _775828) ^ [_1464521, _1464523, _1464525] : [class_Orderings_Oorder(_1464521), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1464521), _1464523)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1464521, _1464523, _1464525)) = c_Orderings_Obot__class_Obot(tc_fun(_1464521, tc_HOL_Obool)))], (49692 ^ _775828) ^ [_1774841, _1774843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774841), _1774843)), -(c_List_Oupt(_1774841, hAPP(c_Nat_OSuc, _1774843)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1774841, _1774843)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1774843), c_List_Olist_ONil(tc_Nat_Onat))))], (27591 ^ _775828) ^ [_1266272, _1266274, _1266276, _1266278, _1266280, _1266282] : [hBOOL(hAPP(hAPP(c_member(_1266272), _1266274), c_SetInterval_Oord_OatLeastLessThan(_1266272, _1266276, _1266278, _1266280, _1266282))), 27594 ^ _775828 : [(27597 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1266278, _1266274), _1266282)))], (27595 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1266276, _1266280), _1266274)))]]], (38586 ^ _775828) ^ [_1509649, _1509651, _1509653, _1509655, _1509657] : [c_Equiv__Relations_Oequiv(_1509649, _1509651, _1509653), 38589 ^ _775828 : [(38600 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509649, _1509649)), hAPP(hAPP(c_Product__Type_OPair(_1509649, _1509649), _1509655), _1509657)), _1509653))), hAPP(c_Relation_OImage(_1509649, _1509649, _1509653), hAPP(hAPP(c_Set_Oinsert(_1509649), _1509655), c_Orderings_Obot__class_Obot(tc_fun(_1509649, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509649, _1509649, _1509653), hAPP(hAPP(c_Set_Oinsert(_1509649), _1509657), c_Orderings_Obot__class_Obot(tc_fun(_1509649, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1509649), _1509655), _1509651)), hBOOL(hAPP(hAPP(c_member(_1509649), _1509657), _1509651))], (38590 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509649, _1509649)), hAPP(hAPP(c_Product__Type_OPair(_1509649, _1509649), _1509655), _1509657)), _1509653)), 38593 ^ _775828 : [(38598 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509649), _1509657), _1509651)))], (38596 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509649), _1509655), _1509651)))], (38594 ^ _775828) ^ [] : [-(hAPP(c_Relation_OImage(_1509649, _1509649, _1509653), hAPP(hAPP(c_Set_Oinsert(_1509649), _1509655), c_Orderings_Obot__class_Obot(tc_fun(_1509649, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509649, _1509649, _1509653), hAPP(hAPP(c_Set_Oinsert(_1509649), _1509657), c_Orderings_Obot__class_Obot(tc_fun(_1509649, tc_HOL_Obool)))))]]]]], (50017 ^ _775828) ^ [_1780314, _1780316, _1780318, _1780320, _1780322, _1780324] : [class_Orderings_Olinorder(_1780314), c_List_Olinorder__class_Osorted(_1780314, hAPP(hAPP(c_List_Omap(_1780316, _1780314), _1780318), _1780320)), hBOOL(hAPP(_1780322, _1780324)), -(hAPP(c_List_Ofilter(_1780316, _1780322), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1780316, _1780314, _1780318), _1780324), _1780320)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1780316, _1780314, _1780318), _1780324), hAPP(c_List_Ofilter(_1780316, _1780322), _1780320)))], (48701 ^ _775828) ^ [_1752668, _1752670, _1752672] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752668)), hAPP(c_List_Orotate(_1752668, _1752670), _1752672)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752668)), _1752672))], (5805 ^ _775828) ^ [_868357, _868359, _868361] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_868357, _868359, _868361)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47393 ^ _775828) ^ [_1721322, _1721324, _1721326] : [-(hAPP(hAPP(c_List_Olist__update(_1721322, c_List_Olist_ONil(_1721322)), _1721324), _1721326) = c_List_Olist_ONil(_1721322))], (45884 ^ _775828) ^ [_1681694, _1681696, _1681698, _1681700, _1681702] : [hBOOL(hAPP(c_List_Odistinct(_1681694), hAPP(hAPP(c_List_Omap(tc_prod(_1681694, _1681696), _1681694), c_Product__Type_Ofst(_1681694, _1681696)), _1681698))), 45887 ^ _775828 : [(45894 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681694, _1681696)), hAPP(hAPP(c_Product__Type_OPair(_1681694, _1681696), _1681700), _1681702)), hAPP(c_List_Oset(tc_prod(_1681694, _1681696)), _1681698))), -(hAPP(c_Map_Omap__of(_1681694, _1681696, _1681698), _1681700) = hAPP(c_Option_Ooption_OSome(_1681696), _1681702))], (45888 ^ _775828) ^ [] : [hAPP(c_Map_Omap__of(_1681694, _1681696, _1681698), _1681700) = hAPP(c_Option_Ooption_OSome(_1681696), _1681702), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681694, _1681696)), hAPP(hAPP(c_Product__Type_OPair(_1681694, _1681696), _1681700), _1681702)), hAPP(c_List_Oset(tc_prod(_1681694, _1681696)), _1681698))))]]], (44549 ^ _775828) ^ [_1651011, _1651013] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1651011), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651011, tc_HOL_Obool), _1651013)))), 44550 ^ _775828 : [(44551 ^ _775828) ^ [_1651075] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1651011, tc_HOL_Obool)), _1651075), _1651013)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1651011), _1651075))]]], (31429 ^ _775828) ^ [_1353332, _1353334, _1353336] : [class_Orderings_Olinorder(_1353332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353332), _1353334)), 31436 ^ _775828 : [(31443 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353332, tc_HOL_Obool)), _1353334), hAPP(hAPP(c_Set_Oinsert(_1353332), _1353336), c_Orderings_Obot__class_Obot(tc_fun(_1353332, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353332, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1353332, c_Orderings_Oord__class_Omax(_1353332), hAPP(hAPP(c_Set_Oinsert(_1353332), _1353336), _1353334)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353332), _1353336), c_Big__Operators_Olattice_OSup__fin(_1353332, c_Orderings_Oord__class_Omax(_1353332), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353332, tc_HOL_Obool)), _1353334), hAPP(hAPP(c_Set_Oinsert(_1353332), _1353336), c_Orderings_Obot__class_Obot(tc_fun(_1353332, tc_HOL_Obool)))))))], (31437 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353332, tc_HOL_Obool)), _1353334), hAPP(hAPP(c_Set_Oinsert(_1353332), _1353336), c_Orderings_Obot__class_Obot(tc_fun(_1353332, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353332, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1353332, c_Orderings_Oord__class_Omax(_1353332), hAPP(hAPP(c_Set_Oinsert(_1353332), _1353336), _1353334)) = _1353336)]]], (48397 ^ _775828) ^ [_1745990, _1745992] : [hBOOL(hAPP(c_List_Odistinct(_1745990), hAPP(c_List_Orotate1(_1745990), _1745992))), -(hBOOL(hAPP(c_List_Odistinct(_1745990), _1745992)))], (46700 ^ _775828) ^ [_1704347, _1704349, _1704351, _1704353, _1704355] : [class_Rings_Osemiring__0(_1704347), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704347), hAPP(hAPP(c_List_Omap(_1704349, _1704347), hAPP(hAPP(c_COMBC(_1704349, _1704347, _1704347), hAPP(hAPP(c_COMBB(_1704347, tc_fun(_1704347, _1704347), _1704349), c_Groups_Otimes__class_Otimes(_1704347)), _1704351)), _1704353)), _1704355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1704347), hAPP(c_List_Omonoid__add__class_Olistsum(_1704347), hAPP(hAPP(c_List_Omap(_1704349, _1704347), _1704351), _1704355))), _1704353))], (9555 ^ _775828) ^ [_929428, _929430] : [class_Groups_Olinordered__ab__group__add(_929428), 9558 ^ _775828 : [(9565 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929428), c_Groups_Ozero__class_Ozero(_929428)), _929430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929428), hAPP(c_Groups_Ouminus__class_Ouminus(_929428), _929430)), _929430)))], (9559 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929428), hAPP(c_Groups_Ouminus__class_Ouminus(_929428), _929430)), _929430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929428), c_Groups_Ozero__class_Ozero(_929428)), _929430)))]]], (39950 ^ _775828) ^ [_1541735, _1541737, _1541739, _1541741, _1541743, _1541745, _1541747] : [c_Equiv__Relations_Oequiv(_1541735, _1541737, _1541739), c_Equiv__Relations_Ocongruent(_1541735, tc_fun(_1541741, tc_HOL_Obool), _1541739, _1541743), hBOOL(hAPP(hAPP(c_member(tc_fun(_1541735, tc_HOL_Obool)), _1541745), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1541735), _1541737), _1541739))), 39964 ^ _775828 : [(39967 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1541741, tc_HOL_Obool)), hAPP(_1541743, 39963 ^ [_1541735, _1541737, _1541739, _1541741, _1541743, _1541745, _1541747])), _1541747))], (39965 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541735), 39963 ^ [_1541735, _1541737, _1541739, _1541741, _1541743, _1541745, _1541747]), _1541737)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1541741, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541735, tc_fun(_1541741, tc_HOL_Obool)), _1541745), _1541743)), _1541747)))], (15284 ^ _775828) ^ [_1032513, _1032515, _1032517, _1032519] : [class_Divides_Oring__div(_1032513), -(c_Divides_Odiv__class_Omod(_1032513, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032513), _1032515), _1032517), _1032519) = c_Divides_Odiv__class_Omod(_1032513, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032513), _1032515), c_Divides_Odiv__class_Omod(_1032513, _1032517, _1032519)), _1032519))], (13609 ^ _775828) ^ [_1002129, _1002131, _1002133, _1002135] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_1002129, _1002131)), _1002133), _1002135)), 13613 ^ _775828 : [(13616 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1002131), 13612 ^ [_1002129, _1002131, _1002133, _1002135]), _1002135)))], (13614 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1002129), _1002133), 13612 ^ [_1002129, _1002131, _1002133, _1002135])))]]], (45110 ^ _775828) ^ [_1664004, _1664006, _1664008, _1664010, _1664012, _1664014, _1664016] : [c_Finite__Set_Ofun__left__comm(_1664004, _1664006, _1664008), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1664004, _1664006, _1664008, _1664010, hAPP(hAPP(c_Set_Oinsert(_1664004), _1664012), _1664014)), _1664016)), -(hBOOL(hAPP(hAPP(c_member(_1664004), _1664012), _1664014))), 45122 ^ _775828 : [(45125 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1664004, _1664006, _1664008, _1664010, _1664014), 45121 ^ [_1664004, _1664006, _1664008, _1664010, _1664012, _1664014, _1664016])))], (45123 ^ _775828) ^ [] : [-(_1664016 = hAPP(hAPP(_1664008, _1664012), 45121 ^ [_1664004, _1664006, _1664008, _1664010, _1664012, _1664014, _1664016]))]]], (12500 ^ _775828) ^ [_982147, _982149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982147), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _982149), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982147), _982149))), -(_982147 = _982149)], (46510 ^ _775828) ^ [_1698878, _1698880, _1698882, _1698884] : [_1698878 = _1698880, -(c_List_Oremove1(_1698882, _1698878, hAPP(hAPP(c_List_Olist_OCons(_1698882), _1698880), _1698884)) = _1698884)], (7655 ^ _775828) ^ [_897979, _897981, _897983] : [class_Rings_Oring(_897979), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897979), hAPP(c_Groups_Ouminus__class_Ouminus(_897979), _897981)), _897983) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897979), _897981), hAPP(c_Groups_Ouminus__class_Ouminus(_897979), _897983)))], (4308 ^ _775828) ^ [_841631, _841633, _841635, _841637] : [-(c_Big__Operators_Olinorder__class_OMin(_841637, _841633) = c_Big__Operators_Olinorder__class_OMin(_841635, _841631)), _841637 = _841635, _841633 = _841631], (40764 ^ _775828) ^ [_1559551, _1559553, _1559555, _1559557] : [-(hAPP(hAPP(c_Nat_Ocompow(_1559551, _1559551), _1559553), hAPP(hAPP(c_Nat_Ocompow(_1559551, _1559551), _1559555), _1559557)) = hAPP(hAPP(c_Nat_Ocompow(_1559551, _1559551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1559555), _1559553)), _1559557))], (19184 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17247 ^ _775828) ^ [_1070826] : [_1070826 = 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), _1070826)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (50055 ^ _775828) ^ [_1781139, _1781141] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1781139, _1781141) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1781139), hAPP(c_Nat_OSuc, _1781141))))], (39756 ^ _775828) ^ [_1536961, _1536963, _1536965, _1536967, _1536969] : [-(_1536961 = c_Orderings_Obot__class_Obot(tc_fun(_1536963, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536963, tc_fun(_1536965, tc_HOL_Obool)), _1536961), hAPP(hAPP(c_COMBB(tc_fun(_1536965, tc_HOL_Obool), tc_fun(_1536965, tc_HOL_Obool), _1536963), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536965, tc_HOL_Obool)), _1536967)), _1536969)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536965, tc_HOL_Obool)), _1536967), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536963, tc_fun(_1536965, tc_HOL_Obool)), _1536961), _1536969)))], (44924 ^ _775828) ^ [_1659736, _1659738, _1659740] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1659736, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659736, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1659736, tc_HOL_Obool), tc_HOL_Obool)), _1659738), _1659740))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659736, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659736, tc_HOL_Obool), _1659738)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659736, tc_HOL_Obool), _1659740)))))], (6911 ^ _775828) ^ [_885265, _885267, _885269] : [class_Rings_Oring__1(_885265), -(hAPP(c_Int_Oring__1__class_Oof__int(_885265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885267), _885269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885265), hAPP(c_Int_Oring__1__class_Oof__int(_885265), _885267)), hAPP(c_Int_Oring__1__class_Oof__int(_885265), _885269)))], (45472 ^ _775828) ^ [_1671744, _1671746, _1671748, _1671750] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1671746, _1671744)), _1671748), _1671750) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1671746), hAPP(hAPP(c_COMBC(_1671746, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1671744, 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))), _1671746), c_Smallcheck_Osmall__class_Osmall(_1671744)), hAPP(hAPP(c_COMBB(tc_fun(_1671744, tc_prod(_1671746, _1671744)), tc_fun(_1671744, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1671746), hAPP(c_COMBB(tc_prod(_1671746, _1671744), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1671744), _1671748)), c_Product__Type_OPair(_1671746, _1671744)))), _1671750)), _1671750)), class_Smallcheck_Osmall(_1671744), class_Smallcheck_Osmall(_1671746)], (5803 ^ _775828) ^ [_868323, _868325, _868327] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_868323, _868325, _868327)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17215 ^ _775828) ^ [_1070322, _1070324] : [class_Groups_Oabs__if(_1070322), 17218 ^ _775828 : [(17225 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070322), _1070324), c_Groups_Ozero__class_Ozero(_1070322)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1070322), _1070324) = _1070324)], (17219 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070322), _1070324), c_Groups_Ozero__class_Ozero(_1070322))), -(hAPP(c_Groups_Oabs__class_Oabs(_1070322), _1070324) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070322), _1070324))]]], (36323 ^ _775828) ^ [_1457742, _1457744, _1457746, _1457748] : [class_Orderings_Olinorder(_1457742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457742), _1457744), _1457746)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1457742, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457742, _1457744), _1457748)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457742, _1457744), _1457746)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457742, _1457746), _1457748))], (41520 ^ _775828) ^ [_1579220, _1579222] : [class_Orderings_Olinorder(_1579220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579220), _1579222)), -(c_Big__Operators_Olinorder__class_OMin(_1579220, _1579222) = hAPP(c_Finite__Set_Ofold1(_1579220, c_Orderings_Oord__class_Omin(_1579220)), _1579222))], (27346 ^ _775828) ^ [_1260584, _1260586] : [-(hAPP(c_Relation_Oconverse(_1260584, _1260584), c_Relation_OId__on(_1260584, _1260586)) = c_Relation_OId__on(_1260584, _1260586))], (33340 ^ _775828) ^ [_1393795, _1393797, _1393799, _1393801, _1393803] : [-(hBOOL(hAPP(hAPP(c_member(_1393795), _1393797), _1393799))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1393795, tc_Option_Ooption(_1393801)), c_Map_Orestrict__map(_1393795, _1393801, _1393803, _1393799)), _1393797), c_Option_Ooption_ONone(_1393801)) = c_Map_Orestrict__map(_1393795, _1393801, _1393803, _1393799))], (25128 ^ _775828) ^ [_1219385, _1219387] : [c_Nat__Transfer_Onat__set(_1219385), c_Nat__Transfer_Onat__set(_1219387), 25135 ^ _775828 : [(25142 ^ _775828) ^ [] : [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), _1219385)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1219385), _1219387)))], (25136 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1219385), _1219387)), -(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), _1219385)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219387))))]]], (35055 ^ _775828) ^ [_1431705, _1431707, _1431709, _1431711, _1431713, _1431715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1431705, _1431707)), hAPP(hAPP(c_Product__Type_OPair(_1431705, _1431707), _1431713), _1431715)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool)), _1431709), _1431711))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431705, tc_fun(_1431707, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1431705, tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_fun(_1431707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431707, tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_fun(_1431707, tc_HOL_Obool)), _1431705), c_COMBC(_1431707, tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431707, tc_prod(_1431705, _1431707)), tc_fun(_1431707, tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), _1431705), hAPP(c_COMBB(tc_prod(_1431705, _1431707), tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool), _1431707), c_member(tc_prod(_1431705, _1431707)))), c_Product__Type_OPair(_1431705, _1431707)))), _1431709)), hAPP(hAPP(c_COMBC(_1431705, tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_fun(_1431707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431707, tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_fun(_1431707, tc_HOL_Obool)), _1431705), c_COMBC(_1431707, tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431707, tc_prod(_1431705, _1431707)), tc_fun(_1431707, tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool)), _1431705), hAPP(c_COMBB(tc_prod(_1431705, _1431707), tc_fun(tc_fun(tc_prod(_1431705, _1431707), tc_HOL_Obool), tc_HOL_Obool), _1431707), c_member(tc_prod(_1431705, _1431707)))), c_Product__Type_OPair(_1431705, _1431707)))), _1431711)), _1431713), _1431715)))], (51618 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_x), v_Procs)))], (51146 ^ _775828) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (35145 ^ _775828) ^ [_1434310, _1434312, _1434314, _1434316, _1434318, _1434320] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434310, tc_fun(_1434312, tc_HOL_Obool))), _1434314), _1434316), _1434318), _1434320)), -(hBOOL(hAPP(hAPP(_1434316, _1434318), _1434320)))], (14534 ^ _775828) ^ [_1019205, _1019207] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019205, _1019207)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019205), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019207)))], (51012 ^ _775828) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (28059 ^ _775828) ^ [_1278278, _1278280] : [c_Wellfounded_Owf(_1278278, hAPP(c_Set_OCollect(tc_prod(_1278278, _1278278)), hAPP(c_Product__Type_Oprod_Oprod__case(_1278278, _1278278, tc_HOL_Obool), _1278280))), -(c_Wellfounded_OwfP(_1278278, _1278280))], (20356 ^ _775828) ^ [_1125615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1125615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1125615))))], (25855 ^ _775828) ^ [_1232661, _1232663] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232661), _1232663)), 25860 ^ _775828 : [(25863 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232663), _1232661))], (25861 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232661), _1232663)))]], -(_1232661 = _1232663)], (49586 ^ _775828) ^ [_1772843, _1772845, _1772847] : [-(c_List_Osublist(_1772843, _1772845, _1772847) = hAPP(hAPP(c_List_Omap(tc_prod(_1772843, tc_Nat_Onat), _1772843), c_Product__Type_Ofst(_1772843, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1772843, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1772843, 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(_1772843, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1772843, tc_Nat_Onat))), _1772847)), hAPP(hAPP(c_List_Ozip(_1772843, tc_Nat_Onat), _1772845), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772843)), _1772845))))))], (1240 ^ _775828) ^ [_793946, _793948] : [-(class_Lattices_Obounded__lattice__top(_793946)), _793948 = _793946, class_Lattices_Obounded__lattice__top(_793948)], (36938 ^ _775828) ^ [_1470357, _1470359, _1470361] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470357, tc_Nat_Onat), _1470359), _1470361) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470357, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1470357), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1470359)), _1470361)))], (48437 ^ _775828) ^ [_1746867, _1746869, _1746871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746867)), _1746869)), _1746871)), -(hAPP(hAPP(c_List_Odrop(_1746867), _1746871), _1746869) = c_List_Olist_ONil(_1746867))], (19802 ^ _775828) ^ [_1115897] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1115897)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1115897)))], (4268 ^ _775828) ^ [_841035, _841037, _841039, _841041] : [-(c_Complete__Lattice_OSup__class_OSup(_841041, _841037) = c_Complete__Lattice_OSup__class_OSup(_841039, _841035)), _841041 = _841039, _841037 = _841035], (51516 ^ _775828) ^ [_1808248, _1808250, _1808252, _1808254] : [-(hAPP(hAPP(c_COMBK(_1808248, _1808250), _1808252), _1808254) = _1808252)], (15624 ^ _775828) ^ [_1039021, _1039023, _1039025] : [class_Groups_Ogroup__add(_1039021), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039021), _1039023), hAPP(c_Groups_Ouminus__class_Ouminus(_1039021), _1039025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039021), _1039023), _1039025))], (10890 ^ _775828) ^ [_954116, _954118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954116), _954118)), _954116))], (37944 ^ _775828) ^ [_1495172, _1495174] : [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)), _1495172), 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)), _1495174), 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)), _1495172), _1495174)), c_Int_Ointrel)))], (42257 ^ _775828) ^ [_1596472, _1596474, _1596476] : [c_Predicate_Oreflp(_1596472, _1596474), -(hBOOL(hAPP(hAPP(_1596474, _1596476), _1596476)))], (8703 ^ _775828) ^ [_915433, _915435, _915437] : [class_Orderings_Oorder(_915433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915433), _915435), _915437)), -(_915435 = _915437), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915433), _915435), _915437)))], (34982 ^ _775828) ^ [_1429646, _1429648, _1429650, _1429652, _1429654] : [class_Fields_Ofield(_1429646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429648), _1429650)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429648), _1429652)), 34996 ^ _775828 : [(34999 ^ 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hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429648, tc_HOL_Obool)), _1429650), _1429652))))], (1080 ^ _775828) ^ [_791946, _791948] : [-(class_Groups_Oab__group__add(_791946)), _791948 = _791946, class_Groups_Oab__group__add(_791948)], (24938 ^ _775828) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (40271 ^ _775828) ^ [_1547807, _1547809] : [-(hAPP(c_Relation_ORange(_1547807, _1547807), c_Transitive__Closure_Ortrancl(_1547807, _1547809)) = c_Orderings_Otop__class_Otop(tc_fun(_1547807, tc_HOL_Obool)))], (46458 ^ _775828) ^ [_1697798, _1697800, _1697802] : [_1697798 = hAPP(hAPP(c_List_Olist_OCons(_1697800), _1697802), _1697798)], (29907 ^ _775828) ^ [_1319900, _1319902, _1319904] : [-(hAPP(hAPP(c_Set_Oinsert(_1319900), _1319902), _1319904) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319900, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1319900), hAPP(hAPP(c_COMBC(_1319900, _1319900, tc_HOL_Obool), c_fequal), _1319902))), _1319904))], (40863 ^ _775828) ^ [_1562105, _1562107, _1562109, _1562111, _1562113] : [hBOOL(hAPP(hAPP(c_member(_1562105), _1562107), hAPP(c_Set_Ovimage(_1562105, _1562109, _1562111), hAPP(hAPP(c_Set_Oinsert(_1562109), _1562113), c_Orderings_Obot__class_Obot(tc_fun(_1562109, tc_HOL_Obool)))))), -(hAPP(_1562111, _1562107) = _1562113)], (41510 ^ _775828) ^ [_1579063, _1579065] : [class_Lattices_Olattice(_1579063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579063), _1579065)), -(c_Big__Operators_Olattice__class_OInf__fin(_1579063, _1579065) = hAPP(c_Finite__Set_Ofold1(_1579063, c_Lattices_Osemilattice__inf__class_Oinf(_1579063)), _1579065))], (33014 ^ _775828) ^ [_1386865, _1386867, _1386869] : [class_Groups_Ocomm__monoid__mult(_1386865), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386867, _1386865), _1386869), c_Orderings_Obot__class_Obot(tc_fun(_1386867, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1386865))], (49150 ^ _775828) ^ [_1762426, _1762428, _1762430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762428)), _1762430))), -(c_List_Olast(_1762428, hAPP(hAPP(c_List_Odrop(_1762428), _1762426), _1762430)) = c_List_Olast(_1762428, _1762430))], (8583 ^ _775828) ^ [_913499, _913501] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913499) = _913501, 8586 ^ _775828 : [(8589 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913501)))], (8587 ^ _775828) ^ [] : [-(_913499 = hAPP(c_Int_Onat, _913501))]]], (16869 ^ _775828) ^ [_1063368, _1063370, _1063372] : [class_Groups_Oordered__ab__group__add__abs(_1063368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063368), _1063370), _1063372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063368), hAPP(c_Groups_Ouminus__class_Ouminus(_1063368), _1063370)), _1063372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063368), hAPP(c_Groups_Oabs__class_Oabs(_1063368), _1063370)), _1063372)))], (40227 ^ _775828) ^ [_1546980, _1546982, _1546984, _1546986, _1546988] : [c_Fun_Oinj__on(_1546980, _1546982, _1546984, c_Orderings_Otop__class_Otop(tc_fun(_1546980, tc_HOL_Obool))), 40230 ^ _775828 : [(40237 ^ _775828) ^ [] : [_1546986 = _1546988, -(hAPP(c_Set_Oimage(_1546980, _1546982, _1546984), _1546986) = hAPP(c_Set_Oimage(_1546980, _1546982, _1546984), _1546988))], (40231 ^ _775828) ^ [] : [hAPP(c_Set_Oimage(_1546980, _1546982, _1546984), _1546986) = hAPP(c_Set_Oimage(_1546980, _1546982, _1546984), _1546988), -(_1546986 = _1546988)]]], (50660 ^ _775828) ^ [_1795853, _1795855, _1795857, _1795859] : [-(hBOOL(hAPP(_1795853, _1795855))), -(c_List_OtakeWhile(_1795857, _1795853, hAPP(hAPP(c_List_Olist_OCons(_1795857), _1795855), _1795859)) = c_List_Olist_ONil(_1795857))], (28749 ^ _775828) ^ [_1292993, _1292995, _1292997] : [c_Wellfounded_Owf(_1292993, _1292995), c_Wellfounded_Owf(_1292993, _1292997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1292993, _1292993), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1292993, _1292993, _1292993), _1292995), _1292997)), _1292995)), -(c_Wellfounded_Owf(_1292993, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292993, _1292993), tc_HOL_Obool)), _1292995), _1292997)))], (4288 ^ _775828) ^ [_841333, _841335, _841337, _841339] : [-(c_Big__Operators_Olattice__class_OSup__fin(_841339, _841335) = c_Big__Operators_Olattice__class_OSup__fin(_841337, _841333)), _841339 = _841337, _841335 = _841333], (3722 ^ _775828) ^ [_832392, _832394] : [_832394 = _832392, -(c_Set_OBall(_832394) = c_Set_OBall(_832392))], (27802 ^ _775828) ^ [_1271190, _1271192, _1271194, _1271196] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271190, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271190, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1271190, 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hAPP(hAPP(_1596824, 42281 ^ [_1596822, _1596824, _1596826, _1596828, _1596830]), 42282 ^ [_1596822, _1596824, _1596826, _1596828, _1596830])) = hAPP(hAPP(_1596824, hAPP(_1596828, 42281 ^ [_1596822, _1596824, _1596826, _1596828, _1596830])), hAPP(_1596828, 42282 ^ [_1596822, _1596824, _1596826, _1596828, _1596830])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596822), _1596830)), -(_1596830 = c_Orderings_Obot__class_Obot(tc_fun(_1596822, tc_HOL_Obool))), -(hAPP(_1596828, hAPP(_1596826, _1596830)) = hAPP(_1596826, hAPP(c_Set_Oimage(_1596822, _1596822, _1596828), _1596830)))], (27893 ^ _775828) ^ [_1274578, _1274580] : [c_Wellfounded_Owf(_1274578, hAPP(hAPP(c_Relation_Orel__comp(_1274578, _1274578, _1274578), _1274580), _1274580)), -(c_Wellfounded_Owf(_1274578, _1274580))], (2036 ^ _775828) ^ [_805497, _805499, _805501, _805503] : [-(c_Divides_OnegDivAlg(_805503, _805499) = c_Divides_OnegDivAlg(_805501, _805497)), _805503 = _805501, _805499 = _805497], (42339 ^ _775828) ^ [_1598167, _1598169, _1598171, _1598173, _1598175] : [c_Finite__Set_Ofun__left__comm__idem(_1598167, _1598169, _1598171), -(hAPP(hAPP(_1598171, _1598173), hAPP(hAPP(_1598171, _1598173), _1598175)) = hAPP(hAPP(_1598171, _1598173), _1598175))], (10750 ^ _775828) ^ [_951472, _951474, _951476] : [class_Groups_Ogroup__add(_951472), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951472), _951474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951472), hAPP(c_Groups_Ouminus__class_Ouminus(_951472), _951474)), _951476)) = _951476)], (48962 ^ _775828) ^ [_1758556] : [-(c_List_Olists(_1758556, c_Orderings_Otop__class_Otop(tc_fun(_1758556, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1758556), tc_HOL_Obool)))], (10400 ^ _775828) ^ [_944998, _945000, _945002, _945004] : [class_Groups_Oordered__ab__semigroup__add(_944998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944998), _945000), _945002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944998), _945004), _945000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944998), _945004), _945002))))], (19102 ^ _775828) ^ [_1104814] : [class_Int_Onumber__ring(_1104814), -(c_Int_Oiszero(_1104814, hAPP(c_Int_Onumber__class_Onumber__of(_1104814), c_Int_OPls)))], (19144 ^ _775828) ^ [_1105344] : [class_Rings_Osemiring__1(_1105344), -(c_Int_Oiszero(_1105344, c_Groups_Ozero__class_Ozero(_1105344)))], (8799 ^ _775828) ^ [_916786, _916788, _916790] : [class_Orderings_Olinorder(_916786), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916786), _916788), _916790))), 8806 ^ _775828 : [(8813 ^ _775828) ^ [] : [_916788 = _916790, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916786), _916788), _916790)))], (8807 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916786), _916788), _916790)), -(_916788 = _916790)]]], (18517 ^ _775828) ^ [_1094304, _1094306] : [class_Int_Onumber__ring(_1094304), 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_1114348))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1114348)))))], (41166 ^ _775828) ^ [_1569558, _1569560, _1569562, _1569564, _1569566, _1569568] : [c_Hoare__Mirabelle_Ohoare__derivs(_1569558, _1569560, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1569558)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1569558), _1569562), _1569564), _1569566)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1569558), tc_HOL_Obool)))), 41173 ^ _775828 : [(41176 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1569562, 41171 ^ [_1569558, _1569560, _1569562, _1569564, _1569566, _1569568]), 41172 ^ [_1569558, _1569560, _1569562, _1569564, _1569566, _1569568]))], (41174 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1569568, 41171 ^ [_1569558, _1569560, _1569562, _1569564, _1569566, _1569568]), 41172 ^ [_1569558, _1569560, _1569562, _1569564, _1569566, _1569568])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1569558, _1569560, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1569558)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1569558), _1569568), _1569564), _1569566)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1569558), tc_HOL_Obool)))))], (28925 ^ _775828) ^ [_1298804, _1298806] : [-(c_Wellfounded_Owf(_1298804, _1298806)), 28928 ^ _775828 : [(28931 ^ _775828) ^ [_1299024] : [hBOOL(hAPP(hAPP(c_member(_1298804), _1299024), 28926 ^ [_1298804, _1298806])), 28935 ^ _775828 : [(28938 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298804), 28934 ^ [_1298804, _1298806, _1299024]), 28926 ^ [_1298804, _1298806])))], (28936 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1298804, _1298804)), hAPP(hAPP(c_Product__Type_OPair(_1298804, _1298804), 28934 ^ [_1298804, _1298806, _1299024]), _1299024)), _1298806)))]]], (28929 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298804), 28927 ^ [_1298804, _1298806]), 28926 ^ [_1298804, _1298806])))]]], (36365 ^ _775828) ^ [_1458651, _1458653, _1458655, _1458657] : [class_Orderings_Oorder(_1458651), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458651, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458651, _1458653), _1458655)), c_SetInterval_Oord__class_OatLeastAtMost(_1458651, _1458655, _1458657)) = c_Orderings_Obot__class_Obot(tc_fun(_1458651, tc_HOL_Obool)))], (36745 ^ _775828) ^ [_1466089, _1466091, _1466093] : [class_Orderings_Olinorder(_1466089), 36748 ^ _775828 : [(36755 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1466089), _1466091), _1466093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466089, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466089), _1466091)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466089), _1466093))))], (36749 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466089, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466089), _1466091)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466089), _1466093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1466089), _1466091), _1466093)))]]], (7811 ^ _775828) ^ [_900615, _900617] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _900615)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _900617), 7814 ^ _775828 : [(7817 ^ _775828) ^ [] : [-(_900617 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7815 ^ _775828) ^ [] : [-(_900615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27473 ^ _775828) ^ [_1263780] : [-(c_Relation_OId(_1263780) = hAPP(c_Set_OCollect(tc_prod(_1263780, _1263780)), hAPP(hAPP(c_COMBB(tc_fun(_1263780, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1263780, _1263780)), c_HOL_OEx(_1263780)), hAPP(hAPP(c_COMBC(tc_prod(_1263780, _1263780), tc_fun(_1263780, tc_prod(_1263780, _1263780)), tc_fun(_1263780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1263780, _1263780), tc_HOL_Obool), tc_fun(tc_fun(_1263780, tc_prod(_1263780, _1263780)), tc_fun(_1263780, tc_HOL_Obool)), tc_prod(_1263780, _1263780)), c_COMBB(tc_prod(_1263780, _1263780), tc_HOL_Obool, _1263780)), c_fequal)), hAPP(hAPP(c_COMBS(_1263780, _1263780, tc_prod(_1263780, _1263780)), c_Product__Type_OPair(_1263780, _1263780)), c_COMBI(_1263780))))))], (29469 ^ _775828) ^ [_1310406, _1310408, _1310410] : [-(c_Predicate_Oconversep(_1310406, _1310408, c_Predicate_Oconversep(_1310408, _1310406, _1310410)) = _1310410)], (34169 ^ _775828) ^ [_1411490, _1411492, _1411494, _1411496] : [class_Lattices_Olattice(_1411490), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411490), _1411492), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411490), _1411494), _1411496))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411490), _1411492), _1411494)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411490), _1411492), _1411496)))))], (8963 ^ _775828) ^ [_919139, _919141, _919143] : [class_Groups_Oordered__ab__group__add(_919139), 8966 ^ _775828 : [(8973 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919139), hAPP(c_Groups_Ouminus__class_Ouminus(_919139), _919143)), _919141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919139), hAPP(c_Groups_Ouminus__class_Ouminus(_919139), _919141)), _919143)))], (8967 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919139), hAPP(c_Groups_Ouminus__class_Ouminus(_919139), _919141)), _919143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919139), hAPP(c_Groups_Ouminus__class_Ouminus(_919139), _919143)), _919141)))]]], (14712 ^ _775828) ^ [_1021951, _1021953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021953), 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), _1021951), _1021953)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25118 ^ _775828) ^ [_1219133, _1219135, _1219137] : [-(c_Random__Sequence_Oempty(_1219133, _1219135, _1219137) = 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(_1219133)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1219133)))], (51196 ^ _775828) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (35467 ^ _775828) ^ [_1442153, _1442155, _1442157] : [-(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)), _1442153)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442155, _1442157)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442155), _1442153), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442157), _1442153)))], (42099 ^ _775828) ^ [_1592941, _1592943, _1592945, _1592947] : [c_Wellfounded_Owf(_1592941, _1592943), c_Fun_Oinj__on(_1592941, _1592945, _1592947, c_Orderings_Otop__class_Otop(tc_fun(_1592941, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1592945, hAPP(c_Set_Oimage(tc_prod(_1592941, _1592941), tc_prod(_1592945, _1592945), c_Product__Type_Omap__pair(_1592941, _1592945, _1592941, _1592945, _1592947, _1592947)), _1592943)))], (48110 ^ _775828) ^ [_1737449, _1737451, _1737453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737449), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737451)), _1737453))), -(hAPP(hAPP(c_List_Otake(_1737451), hAPP(c_Nat_OSuc, _1737449)), _1737453) = hAPP(hAPP(c_List_Oappend(_1737451), hAPP(hAPP(c_List_Otake(_1737451), _1737449), _1737453)), hAPP(hAPP(c_List_Olist_OCons(_1737451), hAPP(hAPP(c_List_Onth(_1737451), _1737453), _1737449)), c_List_Olist_ONil(_1737451))))], (40269 ^ _775828) ^ [_1547768, _1547770] : [-(hAPP(c_Relation_ODomain(_1547768, _1547768), c_Transitive__Closure_Ortrancl(_1547768, _1547770)) = c_Orderings_Otop__class_Otop(tc_fun(_1547768, tc_HOL_Obool)))], (30818 ^ _775828) ^ [_1339456, _1339458] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1339456), _1339458)))), -(_1339458 = c_Orderings_Obot__class_Obot(tc_fun(_1339456, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339456), _1339458))], (38460 ^ _775828) ^ [_1506790, _1506792, _1506794, _1506796, _1506798] : [-(c_Map_Odom(_1506790, _1506792, c_Fun_Ooverride__on(_1506790, tc_Option_Ooption(_1506792), _1506794, _1506796, _1506798)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506790, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506790, tc_HOL_Obool)), c_Map_Odom(_1506790, _1506792, _1506794)), hAPP(c_Set_OCollect(_1506790), hAPP(hAPP(c_COMBC(_1506790, tc_fun(_1506790, tc_HOL_Obool), tc_HOL_Obool), c_member(_1506790)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506790, tc_HOL_Obool)), _1506798), c_Map_Odom(_1506790, _1506792, _1506796)))))), hAPP(c_Set_OCollect(_1506790), hAPP(hAPP(c_COMBC(_1506790, tc_fun(_1506790, tc_HOL_Obool), tc_HOL_Obool), c_member(_1506790)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506790, tc_HOL_Obool)), _1506798), c_Map_Odom(_1506790, _1506792, _1506796))))))], (45224 ^ _775828) ^ [_1666402, _1666404, _1666406, _1666408, _1666410, _1666412, _1666414, _1666416] : [c_Finite__Set_Ofolding__image__simple__idem(_1666402, _1666404, _1666406, _1666408, _1666410, _1666412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1666404), _1666414)), hBOOL(hAPP(hAPP(c_member(_1666404), _1666416), _1666414)), -(hAPP(hAPP(_1666406, hAPP(_1666410, _1666416)), hAPP(_1666412, _1666414)) = hAPP(_1666412, _1666414))], (40768 ^ _775828) ^ [_1559684, _1559686] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1559684, _1559684), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1559686) = _1559686)], (31609 ^ _775828) ^ [_1357782, _1357784] : [-(c_Transitive__Closure_Ortrancl(_1357782, c_Transitive__Closure_Ortrancl(_1357782, _1357784)) = c_Transitive__Closure_Ortrancl(_1357782, _1357784))], (9689 ^ _775828) ^ [_931686, _931688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931686)), _931688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931686), hAPP(c_Int_Onat, _931688))))], (48705 ^ _775828) ^ [_1752765, _1752767, _1752769] : [-(hAPP(c_List_Otl(_1752765), hAPP(hAPP(c_List_Olist_OCons(_1752765), _1752767), _1752769)) = _1752769)], (2542 ^ _775828) ^ [_813300, _813302, _813304, _813306] : [-(tc_Nitpick_Opair__box(_813306, _813302) = tc_Nitpick_Opair__box(_813304, _813300)), _813306 = _813304, _813302 = _813300], (29231 ^ _775828) ^ [_1305848, _1305850, _1305852, _1305854] : [_1305854 = c_Orderings_Obot__class_Obot(tc_fun(_1305850, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1305848, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1305850, _1305848, _1305852), _1305854))], (11380 ^ _775828) ^ [_962747, _962749, _962751, _962753] : [class_Rings_Olinordered__semidom(_962747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962747), c_Groups_Ozero__class_Ozero(_962747)), _962749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962747), _962751), _962753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962747), _962751), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962747), _962749), _962753))))], (15466 ^ _775828) ^ [_1035872, _1035874, _1035876] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1035874), _1035876)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035872), _1035874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035872), _1035876)))], (25299 ^ _775828) ^ [_1222036, _1222038, _1222040, _1222042, _1222044, _1222046] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1222036, _1222038, _1222040, _1222042), _1222044), _1222046) = hAPP(_1222042, hAPP(hAPP(c_Product__Type_OPair(_1222036, _1222038), _1222044), _1222046)))], (51518 ^ _775828) ^ [_1808286, _1808288, _1808290, _1808292, _1808294, _1808296] : [-(hAPP(hAPP(hAPP(c_COMBB(_1808286, _1808288, _1808290), _1808292), _1808294), _1808296) = hAPP(_1808292, hAPP(_1808294, _1808296)))], (286 ^ _775828) ^ [_779965, _779967] : [-(c_Nitpick_Ounknown(_779965)), _779967 = _779965, c_Nitpick_Ounknown(_779967)], (50569 ^ _775828) ^ [_1793539, _1793541, _1793543] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1793539), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1793539))), _1793541))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1793543), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1793539))), _1793541))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1793539))), hAPP(c_List_Ofilter(tc_List_Olist(_1793539), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1793539)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1793543)), c_Nat_Osize__class_Osize(tc_List_Olist(_1793539)))), c_List_Otranspose(_1793539, _1793541))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793539)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1793539)), _1793541), _1793543)))], (33026 ^ _775828) ^ [_1387083, _1387085, _1387087, _1387089] : [class_Groups_Ocomm__monoid__mult(_1387083), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1387085), _1387087))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387085, _1387083), _1387089), _1387087) = c_Groups_Oone__class_Oone(_1387083))], (11050 ^ _775828) ^ [_956704, _956706, _956708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956704), _956706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956708), _956704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956708), _956706))))], (47297 ^ _775828) ^ [_1719207, _1719209] : [_1719209 = c_List_Olist_ONil(_1719207), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719207)), _1719209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39788 ^ _775828) ^ [_1537767, _1537769, _1537771, _1537773, _1537775, _1537777] : [c_Equiv__Relations_Oequiv(_1537767, _1537769, _1537771), c_Equiv__Relations_Ocongruent(_1537767, tc_fun(_1537773, tc_HOL_Obool), _1537771, _1537775), hBOOL(hAPP(hAPP(c_member(_1537767), _1537777), _1537769)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537767, tc_fun(_1537773, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1537767, _1537767, _1537771), hAPP(hAPP(c_Set_Oinsert(_1537767), _1537777), c_Orderings_Obot__class_Obot(tc_fun(_1537767, tc_HOL_Obool))))), _1537775) = hAPP(_1537775, _1537777))], (22898 ^ _775828) ^ [_1174267, _1174269, _1174271] : [class_Fields_Olinordered__field(_1174267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174267), _1174269), c_Groups_Ozero__class_Ozero(_1174267))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174267), _1174271), c_Groups_Ozero__class_Ozero(_1174267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174267), c_Groups_Ozero__class_Ozero(_1174267)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174267), _1174269), _1174271))))], (42071 ^ _775828) ^ [_1592117, _1592119, _1592121, _1592123, _1592125, _1592127, _1592129, _1592131] : [-(hAPP(c_Product__Type_Omap__pair(_1592117, _1592119, _1592121, _1592123, _1592125, _1592127), hAPP(hAPP(c_Product__Type_OPair(_1592117, _1592121), _1592129), _1592131)) = hAPP(hAPP(c_Product__Type_OPair(_1592119, _1592123), hAPP(_1592125, _1592129)), hAPP(_1592127, _1592131)))], (28431 ^ _775828) ^ [_1286439, _1286441, _1286443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286439, tc_HOL_Obool)), _1286441), _1286443)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286439, tc_HOL_Obool)), _1286443), _1286441) = _1286443)], (49443 ^ _775828) ^ [_1768599, _1768601, _1768603] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768599)), hAPP(c_List_Ofilter(_1768599, _1768601), _1768603))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768599)), hAPP(c_List_Ofilter(_1768599, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768599), c_fNot), _1768601)), _1768603))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768599)), _1768603))], (30261 ^ _775828) ^ [] : [-(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)))))], (47357 ^ _775828) ^ [_1720644, _1720646, _1720648, _1720650] : [-(hAPP(hAPP(c_List_Olist__update(_1720644, hAPP(hAPP(c_List_Olist_OCons(_1720644), _1720646), _1720648)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1720650) = hAPP(hAPP(c_List_Olist_OCons(_1720644), _1720650), _1720648))], (20244 ^ _775828) ^ [_1123655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1123655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1123655))))], (36972 ^ _775828) ^ [_1471508, _1471510, _1471512, _1471514, _1471516] : [class_Groups_Oab__group__add(_1471508), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471510, _1471508), hAPP(hAPP(c_COMBS(_1471510, _1471508, _1471508), hAPP(hAPP(c_COMBB(_1471508, tc_fun(_1471508, _1471508), _1471510), c_Groups_Ominus__class_Ominus(_1471508)), _1471512)), _1471514)), _1471516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1471508), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471510, _1471508), _1471512), _1471516)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471510, _1471508), _1471514), _1471516)))], (21180 ^ _775828) ^ [_1142569, _1142571, _1142573, _1142575] : [class_Rings_Odivision__ring(_1142569), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142569), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142569), _1142571), _1142573)), _1142575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142569), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142569), _1142571), _1142575)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142569), _1142573), _1142575)))], (43008 ^ _775828) ^ [_1614321, _1614323, _1614325, _1614327, _1614329, _1614331, _1614333, _1614335] : [c_Finite__Set_Ofolding__image(_1614321, _1614323, _1614325, _1614327, _1614329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614323), _1614331)), -(hAPP(hAPP(_1614329, hAPP(hAPP(c_COMBS(_1614323, _1614321, _1614321), hAPP(hAPP(c_COMBB(_1614321, tc_fun(_1614321, _1614321), _1614323), _1614325), _1614333)), _1614335)), _1614331) = hAPP(hAPP(_1614325, hAPP(hAPP(_1614329, _1614333), _1614331)), hAPP(hAPP(_1614329, _1614335), _1614331)))], (19668 ^ _775828) ^ [_1113760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1113760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113760))))], (8076 ^ _775828) ^ [_905585, _905587] : [class_Rings_Oring__1(_905585), 8079 ^ _775828 : [(8086 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _905587), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_905585), _905587) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905585), hAPP(c_Int_Onat, _905587)))], (8080 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _905587), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_905585), _905587) = hAPP(c_Groups_Ouminus__class_Ouminus(_905585), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905585), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _905587)))))]]], (11044 ^ _775828) ^ [_956581, _956583, _956585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956581), _956583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956581), _956585)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956583), _956585))))], (12534 ^ _775828) ^ [] : [-(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)))], (40383 ^ _775828) ^ [_1550057, _1550059] : [class_Lattices_Oboolean__algebra(_1550057), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1550057), hAPP(c_Groups_Ouminus__class_Ouminus(_1550057), _1550059)), _1550059) = c_Orderings_Otop__class_Otop(_1550057))], (24422 ^ _775828) ^ [_1204648] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1204648)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1204648)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38248 ^ _775828) ^ [_1502330, _1502332, _1502334] : [class_Orderings_Olinorder(_1502330), 38251 ^ _775828 : [(38258 ^ _775828) ^ [] : [_1502332 = _1502334, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502330), _1502332) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502330), _1502334))], (38252 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502330), _1502332) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502330), _1502334), -(_1502332 = _1502334)]]], (6027 ^ _775828) ^ [_871595, _871597, _871599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871595), _871597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871597), _871599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _871595)), _871599)))], (51596 ^ _775828) ^ [_1809357, _1809359] : [-(hBOOL(_1809357)), -(hBOOL(hAPP(hAPP(c_fimplies, _1809357), _1809359)))], (34269 ^ _775828) ^ [_1413753, _1413755, _1413757, _1413759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413753, tc_HOL_Obool)), _1413759), _1413755)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413753, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413753, tc_HOL_Obool)), _1413755), _1413757)), _1413759) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413753, tc_HOL_Obool)), _1413755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413753, tc_HOL_Obool)), _1413757), _1413759)))], (2268 ^ _775828) ^ [_809001, _809003, _809005, _809007] : [-(c_Random_Olog(_809007, _809003) = c_Random_Olog(_809005, _809001)), _809007 = _809005, _809003 = _809001], (47910 ^ _775828) ^ [_1733238, _1733240, _1733242, _1733244] : [hAPP(hAPP(c_List_Oappend(_1733238), _1733240), _1733242) = hAPP(hAPP(c_List_Oappend(_1733238), _1733240), _1733244), -(_1733242 = _1733244)], (18952 ^ _775828) ^ [_1101915, _1101917, _1101919] : [hBOOL(hAPP(_1101915, hAPP(hAPP(c_Product__Type_OPair(_1101917, _1101919), 18953 ^ [_1101915, _1101917, _1101919]), 18954 ^ [_1101915, _1101917, _1101919]))), 18957 ^ _775828 : [(18958 ^ _775828) ^ [_1102062] : [-(hBOOL(hAPP(_1101915, _1102062)))]]], (17001 ^ _775828) ^ [_1065929, _1065931, _1065933, _1065935] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065929), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065929), _1065931), _1065933)), hAPP(c_Int_Onumber__class_Onumber__of(_1065929), _1065935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065929), _1065931), hAPP(c_Int_Onumber__class_Onumber__of(_1065929), _1065935))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065929), _1065933), hAPP(c_Int_Onumber__class_Onumber__of(_1065929), _1065935)))), class_Int_Onumber(_1065929), class_Rings_Oring(_1065929)], (31803 ^ _775828) ^ [_1362579, _1362581, _1362583, _1362585] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362579, _1362579)), hAPP(hAPP(c_Product__Type_OPair(_1362579, _1362579), _1362581), _1362583)), c_Transitive__Closure_Ortrancl(_1362579, _1362585))), hBOOL(hAPP(hAPP(c_member(_1362579), _1362583), c_Wellfounded_Oacc(_1362579, _1362585))), -(hBOOL(hAPP(hAPP(c_member(_1362579), _1362581), c_Wellfounded_Oacc(_1362579, _1362585))))], (40331 ^ _775828) ^ [_1549156] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1549156)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (24066 ^ _775828) ^ [_1197203, _1197205, _1197207, _1197209] : [class_Orderings_Olinorder(_1197203), 24069 ^ _775828 : [(24078 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197203), _1197207), _1197209)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), _1197207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), _1197209))], (24070 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197203), _1197207), _1197209))), 24073 ^ _775828 : [(24076 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), _1197209)))], (24074 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197203), _1197205), _1197207)))]]]]], (44407 ^ _775828) ^ [_1647524, _1647526, _1647528, _1647530] : [-(hAPP(c_Set_OCollect(_1647524), hAPP(hAPP(c_COMBB(tc_fun(_1647526, tc_HOL_Obool), tc_HOL_Obool, _1647524), c_HOL_OAll(_1647526)), hAPP(hAPP(c_COMBB(tc_fun(_1647526, tc_HOL_Obool), tc_fun(_1647526, tc_HOL_Obool), _1647524), hAPP(c_COMBS(_1647526, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1647526), c_fimplies), hAPP(hAPP(c_COMBC(_1647526, tc_fun(_1647526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647526)), _1647528)))), _1647530))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647526, tc_fun(_1647524, tc_HOL_Obool)), _1647528), hAPP(hAPP(c_COMBB(tc_fun(_1647524, tc_HOL_Obool), tc_fun(_1647524, tc_HOL_Obool), _1647526), c_Set_OCollect(_1647524)), hAPP(c_COMBC(_1647524, _1647526, tc_HOL_Obool), _1647530))))], (20924 ^ _775828) ^ [_1135810, _1135812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135810)), 20927 ^ _775828 : [(20934 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135812), _1135810))), -(c_Divides_OposDivAlg(_1135812, _1135810) = hAPP(c_Divides_Oadjust(_1135810), c_Divides_OposDivAlg(_1135812, 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)))), _1135810))))], (20928 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135812), _1135810)), -(c_Divides_OposDivAlg(_1135812, _1135810) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135812))]]], (45854 ^ _775828) ^ [_1681014, _1681016, _1681018, _1681020] : [hBOOL(hAPP(c_List_Odistinct(_1681014), hAPP(hAPP(c_List_Omap(tc_prod(_1681014, _1681016), _1681014), c_Product__Type_Ofst(_1681014, _1681016)), _1681018))), hBOOL(hAPP(c_List_Odistinct(_1681014), hAPP(hAPP(c_List_Omap(tc_prod(_1681014, _1681016), _1681014), c_Product__Type_Ofst(_1681014, _1681016)), _1681020))), 45861 ^ _775828 : [(45868 ^ _775828) ^ [] : [hAPP(c_List_Oset(tc_prod(_1681014, _1681016)), _1681018) = hAPP(c_List_Oset(tc_prod(_1681014, _1681016)), _1681020), -(c_Map_Omap__of(_1681014, _1681016, _1681018) = c_Map_Omap__of(_1681014, _1681016, _1681020))], (45862 ^ _775828) ^ [] : [c_Map_Omap__of(_1681014, _1681016, _1681018) = c_Map_Omap__of(_1681014, _1681016, _1681020), -(hAPP(c_List_Oset(tc_prod(_1681014, _1681016)), _1681018) = hAPP(c_List_Oset(tc_prod(_1681014, _1681016)), _1681020))]]], (47185 ^ _775828) ^ [_1716868, _1716870, _1716872, _1716874] : [hBOOL(hAPP(hAPP(c_member(_1716868), _1716870), hAPP(c_List_Oset(_1716868), hAPP(hAPP(c_List_Otake(_1716868), _1716872), _1716874)))), -(hBOOL(hAPP(hAPP(c_member(_1716868), _1716870), hAPP(c_List_Oset(_1716868), _1716874))))], (31571 ^ _775828) ^ [_1356949, _1356951, _1356953] : [-(hAPP(c_Finite__Set_Ocard(_1356949), _1356951) = hAPP(c_Nat_OSuc, _1356953)), 31572 ^ _775828 : [(31573 ^ _775828) ^ [_1357049, _1357051] : [_1356951 = hAPP(hAPP(c_Set_Oinsert(_1356949), _1357051), _1357049), -(hBOOL(hAPP(hAPP(c_member(_1356949), _1357051), _1357049))), hAPP(c_Finite__Set_Ocard(_1356949), _1357049) = _1356953, 31584 ^ _775828 : [(31587 ^ _775828) ^ [] : [_1357049 = c_Orderings_Obot__class_Obot(tc_fun(_1356949, tc_HOL_Obool))], (31585 ^ _775828) ^ [] : [-(_1356953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (37919 ^ _775828) ^ [_1494626, _1494628, _1494630, _1494632, _1494634] : [class_Groups_Ocomm__monoid__add(_1494626), class_Groups_Oordered__cancel__ab__semigroup__add(_1494626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494628), _1494630)), -(_1494630 = c_Orderings_Obot__class_Obot(tc_fun(_1494628, tc_HOL_Obool))), 37937 ^ _775828 : [(37940 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1494626), hAPP(_1494632, 37936 ^ [_1494626, _1494628, _1494630, _1494632, _1494634])), hAPP(_1494634, 37936 ^ [_1494626, _1494628, _1494630, _1494632, _1494634])))], (37938 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494628), 37936 ^ [_1494626, _1494628, _1494630, _1494632, _1494634]), _1494630)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1494626), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494628, _1494626), _1494632), _1494630)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494628, _1494626), _1494634), _1494630))))], (50478 ^ _775828) ^ [_1791032, _1791034, _1791036] : [50480 ^ _775828 : [(50483 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1791032), tc_List_Olist(_1791032), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1791032), tc_fun(tc_List_Olist(_1791032), tc_Nat_Onat), tc_fun(tc_List_Olist(_1791032), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1791032), tc_Nat_Onat), tc_fun(tc_List_Olist(_1791032), tc_HOL_Obool)), tc_List_Olist(_1791032)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1791032))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1791032)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1791032))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1791032)))), 50479 ^ [_1791032, _1791034, _1791036]))], (50481 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1791032), tc_List_Olist(_1791032))), 50479 ^ [_1791032, _1791034, _1791036]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1791032), tc_List_Olist(_1791032))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1791032), tc_List_Olist(_1791032)), _1791034), _1791036)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1791032))), _1791034) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1791032))), _1791036), 50488 ^ _775828 : [(50495 ^ _775828) ^ [] : [_1791034 = _1791036, -(c_List_Oconcat(_1791032, _1791034) = c_List_Oconcat(_1791032, _1791036))], (50489 ^ _775828) ^ [] : [c_List_Oconcat(_1791032, _1791034) = c_List_Oconcat(_1791032, _1791036), -(_1791034 = _1791036)]]], (1290 ^ _775828) ^ [_794571, _794573] : [-(class_Lattices_Oboolean__algebra(_794571)), _794573 = _794571, class_Lattices_Oboolean__algebra(_794573)], (10156 ^ _775828) ^ [_940295, _940297] : [class_Rings_Olinordered__semidom(_940295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940295), _940297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940295), _940297), c_Groups_Oone__class_Oone(_940295)))))], (22342 ^ _775828) ^ [_1164252, _1164254, _1164256, _1164258] : [class_Fields_Olinordered__field(_1164252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164252), c_Groups_Ozero__class_Ozero(_1164252)), _1164254)), 22349 ^ _775828 : [(22356 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164252), _1164256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164252), _1164258), _1164254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164252), _1164256), _1164254)), _1164258)))], (22350 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164252), _1164256), _1164254)), _1164258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164252), _1164256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164252), _1164258), _1164254))))]]], (4538 ^ _775828) ^ [_845114, _845116, _845118, _845120] : [-(c_Random_Opick(_845120, _845116) = c_Random_Opick(_845118, _845114)), _845120 = _845118, _845116 = _845114], (12201 ^ _775828) ^ [_976864, _976866] : [-(c_Int_Onat__aux(_976864, _976866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _976864)), _976866))], (51472 ^ _775828) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (38690 ^ _775828) ^ [_1512030, _1512032, _1512034] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512030), _1512032), _1512034) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1512030, tc_HOL_Obool), tc_HOL_Obool)), -(_1512032 = c_Orderings_Obot__class_Obot(tc_fun(_1512030, tc_HOL_Obool)))], (43956 ^ _775828) ^ [_1635379, _1635381, _1635383, _1635385, _1635387] : [c_Finite__Set_Ofun__left__comm(_1635379, _1635381, _1635383), -(c_Finite__Set_Ofun__left__comm(_1635385, _1635381, hAPP(hAPP(c_COMBB(_1635379, tc_fun(_1635381, _1635381), _1635385), _1635383), _1635387)))], (44539 ^ _775828) ^ [_1650842, _1650844] : [class_Complete__Lattice_Ocomplete__lattice(_1650842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650842), _1650844)), -(c_Complete__Lattice_OSup__class_OSup(_1650842, _1650844) = hAPP(hAPP(c_Finite__Set_Ofold(_1650842, _1650842, c_Lattices_Osemilattice__sup__class_Osup(_1650842)), c_Orderings_Obot__class_Obot(_1650842)), _1650844))], (22626 ^ _775828) ^ [_1169521, _1169523, _1169525] : [class_Fields_Olinordered__field(_1169521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169521), _1169523), c_Groups_Ozero__class_Ozero(_1169521))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169521), _1169525), c_Groups_Ozero__class_Ozero(_1169521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169521), c_Groups_Ozero__class_Ozero(_1169521)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169521), _1169523), _1169525))))], (23578 ^ _775828) ^ [_1188305, _1188307, _1188309, _1188311, _1188313, _1188315, _1188317] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188305, _1188307, tc_fun(_1188309, tc_HOL_Obool)), _1188311), hAPP(hAPP(c_Product__Type_OPair(_1188305, _1188307), _1188313), _1188315)), _1188317)), -(hBOOL(hAPP(hAPP(hAPP(_1188311, _1188313), _1188315), _1188317)))], (26838 ^ _775828) ^ [_1250009, _1250011] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250009), _1250011)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1250009)), _1250011)))], (39566 ^ _775828) ^ [_1531548, _1531550, _1531552, _1531554] : [_1531548 = c_Orderings_Obot__class_Obot(tc_fun(_1531550, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531550, tc_fun(_1531552, tc_HOL_Obool)), _1531548), hAPP(c_COMBK(tc_fun(_1531552, tc_HOL_Obool), _1531550), _1531554)) = c_Orderings_Obot__class_Obot(tc_fun(_1531552, tc_HOL_Obool)))], (18495 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (15738 ^ _775828) ^ [_1041170, _1041172, _1041174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041170), _1041174)), _1041172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041170), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041172), _1041174))))], (51004 ^ _775828) ^ [_1802944, _1802946, _1802948, _1802950] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1802944)), _1802946), hAPP(c_List_Oset(tc_List_Olist(_1802944)), c_Enum_On__lists(_1802944, _1802948, _1802950)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802944)), _1802946) = _1802948)], (27885 ^ _775828) ^ [_1274440, _1274442] : [-(c_Wellfounded_Owf(_1274440, hAPP(c_Wellfounded_Omeasure(_1274440), _1274442)))], (28669 ^ _775828) ^ [_1290918, _1290920, _1290922, _1290924] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290918, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1290918, tc_fun(_1290918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1290918)), _1290920)), hAPP(hAPP(c_COMBC(_1290918, tc_fun(_1290918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1290918)), _1290922)), _1290924)), -(hBOOL(hAPP(hAPP(c_member(_1290918), _1290924), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290918, tc_HOL_Obool)), _1290920), _1290922))))], (38784 ^ _775828) ^ [_1513996, _1513998, _1514000] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513996), _1513998)), c_Fun_Oinj__on(_1513996, tc_fun(tc_fun(_1513996, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1513996, tc_fun(tc_prod(_1513996, _1513996), tc_HOL_Obool), tc_fun(tc_fun(_1513996, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513996, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1513996, _1513996), tc_HOL_Obool), tc_fun(tc_fun(_1513996, tc_HOL_Obool), tc_HOL_Obool)), _1513996), c_Equiv__Relations_Oquotient(_1513996)), hAPP(hAPP(c_COMBC(_1513996, tc_fun(_1513996, tc_HOL_Obool), tc_fun(_1513996, tc_HOL_Obool)), c_Set_Oinsert(_1513996)), c_Orderings_Obot__class_Obot(tc_fun(_1513996, tc_HOL_Obool))))), _1514000), _1513998), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1513996, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513996), _1513998), _1514000)) = hAPP(c_Finite__Set_Ocard(_1513996), _1513998))], (27693 ^ _775828) ^ [_1268295, _1268297, _1268299, _1268301] : [-(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), _1268295, _1268297)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268299, _1268301)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268299), _1268301)), 27696 ^ _775828 : [(27699 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268299), _1268295)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268297), _1268301)), 27706 ^ _775828 : [(27713 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268297), _1268301)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268301), _1268297)))], (27707 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268299), _1268295)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268295), _1268299)))]]], (27697 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1268295), _1268297)))]]], (44309 ^ _775828) ^ [_1644776, _1644778, _1644780, _1644782, _1644784] : [class_Complete__Lattice_Ocomplete__lattice(_1644776), 44312 ^ _775828 : [(44313 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644776), _1644778), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644780, _1644776), _1644782), _1644784))), 44316 ^ _775828 : [(44317 ^ _775828) ^ [_1644957] : [hBOOL(hAPP(hAPP(c_member(_1644780), _1644957), _1644782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644776), _1644778), hAPP(_1644784, _1644957))))]]], (44323 ^ _775828) ^ [] : [44325 ^ _775828 : [(44328 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644776), _1644778), hAPP(_1644784, 44324 ^ [_1644776, _1644778, _1644780, _1644782, _1644784])))], (44326 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644780), 44324 ^ [_1644776, _1644778, _1644780, _1644782, _1644784]), _1644782)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644776), _1644778), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644780, _1644776), _1644782), _1644784))))]]], (10100 ^ _775828) ^ [_939296, _939298, _939300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939296), _939298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939296), _939300)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939298), _939300))))], (45345 ^ _775828) ^ [_1668994, _1668996, _1668998] : [-(c_Map_Omap__add(_1668994, _1668996, _1668998, hAPP(c_COMBK(tc_Option_Ooption(_1668996), _1668994), c_Option_Ooption_ONone(_1668996))) = _1668998)], (39191 ^ _775828) ^ [_1522299, _1522301, _1522303, _1522305] : [c_Fun_Oinj__on(_1522299, tc_fun(tc_fun(_1522299, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1522299, tc_fun(tc_prod(_1522299, _1522299), tc_HOL_Obool), tc_fun(tc_fun(_1522299, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522299, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1522299, _1522299), tc_HOL_Obool), tc_fun(tc_fun(_1522299, tc_HOL_Obool), tc_HOL_Obool)), _1522299), c_Equiv__Relations_Oquotient(_1522299)), hAPP(hAPP(c_COMBC(_1522299, tc_fun(_1522299, tc_HOL_Obool), tc_fun(_1522299, tc_HOL_Obool)), c_Set_Oinsert(_1522299)), c_Orderings_Obot__class_Obot(tc_fun(_1522299, tc_HOL_Obool))))), _1522301), _1522303), hBOOL(hAPP(hAPP(c_member(_1522299), _1522305), _1522303)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1522299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522299, tc_HOL_Obool)), _1522303), hAPP(hAPP(c_Set_Oinsert(_1522299), _1522305), c_Orderings_Obot__class_Obot(tc_fun(_1522299, tc_HOL_Obool))))), _1522301) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1522299, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1522299), _1522303), _1522301)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1522299), hAPP(hAPP(c_Set_Oinsert(_1522299), _1522305), c_Orderings_Obot__class_Obot(tc_fun(_1522299, tc_HOL_Obool)))), _1522301)))], (11875 ^ _775828) ^ [_971218, _971220, _971222, _971224] : [class_Groups_Oordered__comm__monoid__add(_971218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971218), c_Groups_Ozero__class_Ozero(_971218)), _971220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971218), _971222), _971224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971218), _971222), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971218), _971220), _971224))))], (40023 ^ _775828) ^ [_1543340, _1543342] : [-(hBOOL(hAPP(hAPP(c_member(_1543340), _1543342), c_Orderings_Otop__class_Otop(tc_fun(_1543340, tc_HOL_Obool)))))], (18275 ^ _775828) ^ [_1089909, _1089911, _1089913, _1089915, _1089917] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1089909, _1089911), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1089913), _1089915))), -(_1089911 = 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), _1089917), _1089909), _1089911), 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), _1089917), _1089913)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089917), _1089915)), _1089911))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089917), _1089915), _1089911)))))], (18231 ^ _775828) ^ [_1088849, _1088851, _1088853, _1088855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1088849, _1088849)), hAPP(hAPP(c_Product__Type_OPair(_1088849, _1088849), _1088851), _1088853)), hAPP(c_Wellfounded_Omeasure(_1088849), _1088855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1088855, _1088851)), hAPP(_1088855, _1088853))))], (45916 ^ _775828) ^ [_1682454, _1682456] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1682454, _1682456) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1682454), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1682456), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (1390 ^ _775828) ^ [_795821, _795823] : [-(class_Groups_Olinordered__ab__semigroup__add(_795821)), _795823 = _795821, class_Groups_Olinordered__ab__semigroup__add(_795823)], (51010 ^ _775828) ^ [_1803079] : [-(c_Enum_Osublists(_1803079, c_List_Olist_ONil(_1803079)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803079)), c_List_Olist_ONil(_1803079)), c_List_Olist_ONil(tc_List_Olist(_1803079))))], (38234 ^ _775828) ^ [_1502037] : [-(_1502037 = 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), 38231 ^ [_1502037]), 38232 ^ [_1502037])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (48942 ^ _775828) ^ [_1758176, _1758178, _1758180] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758176)), _1758178), c_Wellfounded_Oacc(tc_List_Olist(_1758176), c_List_Olistrel1(_1758176, _1758180)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758176)), _1758178), c_List_Olists(_1758176, c_Wellfounded_Oacc(_1758176, _1758180)))))], (39826 ^ _775828) ^ [_1538511, _1538513, _1538515, _1538517, _1538519, _1538521, _1538523, _1538525] : [c_Equiv__Relations_Oequiv(_1538511, _1538513, _1538515), c_Equiv__Relations_Ocongruent2(_1538511, _1538517, _1538519, _1538515, _1538521, _1538523), hBOOL(hAPP(hAPP(c_member(_1538511), _1538525), _1538513)), -(c_Equiv__Relations_Ocongruent(_1538517, _1538519, _1538521, hAPP(_1538523, _1538525)))], (19114 ^ _775828) ^ [_1104957] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1104957), c_Int_OPls) = _1104957)], (5288 ^ _775828) ^ [_856665, _856667, _856669, _856671] : [-(c_Enum_Osublists(_856671, _856667) = c_Enum_Osublists(_856669, _856665)), _856671 = _856669, _856667 = _856665], (25867 ^ _775828) ^ [_1232855, _1232857] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232855), _1232857)), -(_1232855 = _1232857), 25874 ^ _775828 : [(25877 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232857), _1232855))], (25875 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232855), _1232857)))]]], (36942 ^ _775828) ^ [_1470473, _1470475, _1470477, _1470479] : [class_Rings_Osemiring__1(_1470473), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1470473), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470475, tc_Nat_Onat), _1470477), _1470479)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470475, _1470473), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1470473, _1470475), c_Nat_Osemiring__1__class_Oof__nat(_1470473)), _1470477)), _1470479))], (7689 ^ _775828) ^ [_898552, _898554] : [7690 ^ _775828 : [(7693 ^ _775828) ^ [] : [_898554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7691 ^ _775828) ^ [] : [_898552 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898552), _898554) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5048 ^ _775828) ^ [_853053, _853055, _853057, _853059, _853061, _853063, _853065, _853067] : [-(c_List_Ofoldl(_853067, _853063, _853059, _853055) = c_List_Ofoldl(_853065, _853061, _853057, _853053)), _853067 = _853065, _853063 = _853061, _853059 = _853057, _853055 = _853053], (23500 ^ _775828) ^ [_1186664, _1186666] : [-(_1186664 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23503 ^ _775828 : [(23510 ^ _775828) ^ [] : [-(_1186666 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1186664, _1186666) = 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, _1186666))), 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)), _1186666)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186664))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186666), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186664), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1186664, _1186666)), 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), _1186666))))), c_Divides_Opdivmod(_1186664, _1186666)))))], (23504 ^ _775828) ^ [] : [_1186666 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1186664, _1186666) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186664))]]], (51364 ^ _775828) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (11576 ^ _775828) ^ [_966158, _966160] : [class_Rings_Ocomm__ring__1(_966158), -(hAPP(c_Groups_Ouminus__class_Ouminus(_966158), _966160) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966158), hAPP(c_Groups_Ouminus__class_Ouminus(_966158), c_Groups_Oone__class_Oone(_966158))), _966160))], (49309 ^ _775828) ^ [_1765872, _1765874, _1765876] : [-(c_List_Obutlast(_1765872, hAPP(hAPP(c_List_Oappend(_1765872), _1765874), hAPP(hAPP(c_List_Olist_OCons(_1765872), _1765876), c_List_Olist_ONil(_1765872)))) = _1765874)], (28065 ^ _775828) ^ [_1278402, _1278404] : [c_Wellfounded_OwfP(_1278402, hAPP(hAPP(c_COMBC(_1278402, tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_fun(_1278402, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278402, tc_fun(tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_fun(_1278402, tc_HOL_Obool)), _1278402), c_COMBC(_1278402, tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278402, tc_prod(_1278402, _1278402)), tc_fun(_1278402, tc_fun(tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_HOL_Obool)), _1278402), hAPP(c_COMBB(tc_prod(_1278402, _1278402), tc_fun(tc_fun(tc_prod(_1278402, _1278402), tc_HOL_Obool), tc_HOL_Obool), _1278402), c_member(tc_prod(_1278402, _1278402)))), c_Product__Type_OPair(_1278402, _1278402)))), _1278404)), -(c_Wellfounded_Owf(_1278402, _1278404))], (39313 ^ _775828) ^ [_1525190, _1525192, _1525194, _1525196, _1525198, _1525200, _1525202] : [-(hBOOL(hAPP(hAPP(c_member(_1525190), _1525192), _1525194))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1525190, _1525196, _1525198, _1525200, _1525194), _1525202)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1525190, _1525196, _1525198, _1525200, hAPP(hAPP(c_Set_Oinsert(_1525190), _1525192), _1525194)), hAPP(hAPP(_1525198, _1525192), _1525202))))], (14892 ^ _775828) ^ [_1025233, _1025235, _1025237, _1025239] : [class_Divides_Osemiring__div(_1025233), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025233), _1025235), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025233), _1025237), _1025235))), c_Divides_Odiv__class_Omod(_1025233, _1025237, _1025235))), _1025239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025233), _1025237), _1025239))], (40009 ^ _775828) ^ [_1543105, _1543107, _1543109] : [class_Lattices_Oboolean__algebra(_1543105), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1543105), _1543107), _1543109) = c_Orderings_Obot__class_Obot(_1543105), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1543105), _1543107), _1543109) = c_Orderings_Otop__class_Otop(_1543105), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1543105), _1543107) = _1543109)], (21290 ^ _775828) ^ [_1144655, _1144657] : [class_Rings_Odivision__ring__inverse__zero(_1144655), 21293 ^ _775828 : [(21300 ^ _775828) ^ [] : [-(_1144657 = c_Groups_Ozero__class_Ozero(_1144655)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144655), _1144657), _1144657) = c_Groups_Oone__class_Oone(_1144655))], (21294 ^ _775828) ^ [] : [_1144657 = c_Groups_Ozero__class_Ozero(_1144655), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144655), _1144657), _1144657) = c_Groups_Ozero__class_Ozero(_1144655))]]], (50676 ^ _775828) ^ [_1796050, _1796052] : [-(c_List_OtakeWhile(_1796050, _1796052, c_List_Olist_ONil(_1796050)) = c_List_Olist_ONil(_1796050))], (38676 ^ _775828) ^ [_1511708, _1511710] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511708), c_Orderings_Obot__class_Obot(tc_fun(_1511708, tc_HOL_Obool))), _1511710) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1511708, tc_HOL_Obool), tc_HOL_Obool)))], (50654 ^ _775828) ^ [_1795726, _1795728, _1795730, _1795732] : [hBOOL(hAPP(_1795726, _1795728)), -(c_List_OtakeWhile(_1795730, _1795726, hAPP(hAPP(c_List_Olist_OCons(_1795730), _1795728), _1795732)) = hAPP(hAPP(c_List_Olist_OCons(_1795730), _1795728), c_List_OtakeWhile(_1795730, _1795726, _1795732)))], (39990 ^ _775828) ^ [_1542747, _1542749, _1542751, _1542753, _1542755] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1542747, _1542747, _1542749, _1542751, _1542753), _1542755)), -(hBOOL(hAPP(hAPP(c_member(_1542747), _1542751), _1542753))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1542747, _1542749, hAPP(hAPP(c_Set_Oinsert(_1542747), _1542751), _1542753)), _1542755)))], (49764 ^ _775828) ^ [_1776139, _1776141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1776139), _1776141)), -(c_List_Oupt(_1776141, _1776139) = c_List_Olist_ONil(tc_Nat_Onat))], (28840 ^ _775828) ^ [_1294652, _1294654] : [-(hAPP(c_Relation_OField(_1294652), hAPP(c_Relation_Oconverse(_1294652, _1294652), _1294654)) = hAPP(c_Relation_OField(_1294652), _1294654))], (49267 ^ _775828) ^ [_1765069, _1765071, _1765073] : [_1765069 = c_List_Olist_ONil(_1765071), -(c_List_Obutlast(_1765071, hAPP(hAPP(c_List_Olist_OCons(_1765071), _1765073), _1765069)) = c_List_Olist_ONil(_1765071))], (4444 ^ _775828) ^ [_843669, _843671, _843673, _843675] : [-(c_List_Olists(_843675, _843671) = c_List_Olists(_843673, _843669)), _843675 = _843673, _843671 = _843669], (27471 ^ _775828) ^ [_1263734, _1263736] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263734, _1263734)), hAPP(hAPP(c_Product__Type_OPair(_1263734, _1263734), _1263736), _1263736)), c_Relation_OId(_1263734))))], (40187 ^ _775828) ^ [_1546217] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1546217, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1546217), hAPP(c_COMBK(tc_HOL_Obool, _1546217), c_fTrue)))], (31683 ^ _775828) ^ [_1359630, _1359632, _1359634] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1359630, _1359630), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1359630, _1359630), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1359630, _1359632)), c_Transitive__Closure_Ortrancl(_1359630, _1359634))), c_Transitive__Closure_Ortrancl(_1359630, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1359630, _1359630), tc_HOL_Obool)), _1359632), _1359634)))))], (48683 ^ _775828) ^ [_1752285, _1752287, _1752289] : [hBOOL(hAPP(c_List_Odistinct(_1752285), _1752289)), -(hBOOL(hAPP(c_List_Odistinct(_1752285), hAPP(c_List_Orotate(_1752285, _1752287), _1752289))))], (33655 ^ _775828) ^ [_1400514, _1400516, _1400518] : [-(hAPP(c_Set_OCollect(_1400514), hAPP(hAPP(c_COMBS(_1400514, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1400514), c_fconj), _1400516)), _1400518)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400514, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1400514), _1400516)), hAPP(c_Set_OCollect(_1400514), _1400518)))], (12357 ^ _775828) ^ [_979679, _979681] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979679), _979681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979681), _979679))], (17481 ^ _775828) ^ [_1075139, _1075141] : [17482 ^ _775828 : [(17485 ^ _775828) ^ [] : [_1075141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17483 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075139))]], -(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), _1075139), _1075141))))], (32851 ^ _775828) ^ [_1383396, _1383398, _1383400, _1383402, _1383404, _1383406, _1383408] : [-(_1383396 = _1383398), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383400, _1383402), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383400, _1383402), _1383404), _1383396), _1383406)), _1383398), _1383408) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383400, _1383402), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383400, _1383402), _1383404), _1383398), _1383408)), _1383396), _1383406))], (48593 ^ _775828) ^ [_1750893, _1750895, _1750897] : [-(_1750893 = c_List_Olist_ONil(_1750895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750897), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750895)), _1750893))), -(hAPP(c_List_Ohd(_1750895), hAPP(hAPP(c_List_Odrop(_1750895), _1750897), _1750893)) = hAPP(hAPP(c_List_Onth(_1750895), _1750893), _1750897))], (13795 ^ _775828) ^ [_1005615, _1005617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005615), _1005617)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005615, _1005617) = _1005615)], (16053 ^ _775828) ^ [_1047656, _1047658, _1047660] : [hBOOL(hAPP(_1047656, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047658), _1047660))), 16056 ^ _775828 : [(16063 ^ _775828) ^ [_1047847] : [_1047658 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047660), _1047847), -(hBOOL(hAPP(_1047656, _1047847)))], (16057 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047658), _1047660)), -(hBOOL(hAPP(_1047656, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (25148 ^ _775828) ^ [_1219688, _1219690] : [c_Nat__Transfer_Onat__set(_1219688), c_Nat__Transfer_Onat__set(_1219690), 25155 ^ _775828 : [(25162 ^ _775828) ^ [] : [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), _1219688)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1219688), _1219690)))], (25156 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1219688), _1219690)), -(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), _1219688)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219690))))]]], (45442 ^ _775828) ^ [_1671253, _1671255, _1671257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1671253), _1671255)), -(c_Smallcheck_Osmall_H(_1671257, _1671253, _1671255) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (43638 ^ _775828) ^ [_1629275, _1629277, _1629279, _1629281, _1629283, _1629285] : [c_Finite__Set_Ofun__left__comm__idem(_1629275, _1629277, _1629279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629275), _1629281)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1629275, _1629277, _1629279), _1629283), hAPP(hAPP(c_Set_Oinsert(_1629275), _1629285), _1629281)) = hAPP(hAPP(_1629279, _1629285), hAPP(hAPP(c_Finite__Set_Ofold(_1629275, _1629277, _1629279), _1629283), _1629281)))], (39702 ^ _775828) ^ [_1535630, _1535632, _1535634, _1535636, _1535638] : [_1535630 = c_Orderings_Obot__class_Obot(tc_fun(_1535632, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1535634), _1535636), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535632, tc_fun(_1535634, tc_HOL_Obool)), _1535630), _1535638)) = hAPP(hAPP(c_Set_Oinsert(_1535634), _1535636), c_Orderings_Obot__class_Obot(tc_fun(_1535634, tc_HOL_Obool))))], (19982 ^ _775828) ^ [_1119042, _1119044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119042)), -(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)))), _1119044))), 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)))), _1119042)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1119044), _1119042))], (15866 ^ _775828) ^ [_1043585, _1043587, _1043589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043585), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043589), _1043587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043585), _1043587)), _1043589)))], (28896 ^ _775828) ^ [_1298054, _1298056] : [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), _1298054), _1298056)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1298054), _1298056)))], (27433 ^ _775828) ^ [_1263029, _1263031] : [-(c_Relation_Oirrefl(_1263029, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1263029, _1263029), tc_HOL_Obool)), _1263031), c_Relation_OId(_1263029))))], (30287 ^ _775828) ^ [_1328323, _1328325] : [c_Wellfounded_Owf(_1328323, _1328325), -(c_Wellfounded_Owf(tc_fun(_1328323, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1328323, _1328325)))], (36940 ^ _775828) ^ [_1470415, _1470417, _1470419] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470415, tc_Nat_Onat), _1470417), _1470419)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470415, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1470415), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1470417)), _1470419))], (46235 ^ _775828) ^ [_1690062, _1690064, _1690066] : [hBOOL(hAPP(hAPP(c_member(_1690062), _1690064), hAPP(c_List_Oset(_1690062), _1690066))), -(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(_1690062)), _1690066))))], (48888 ^ _775828) ^ [_1756584, _1756586, _1756588] : [class_Orderings_Olinorder(_1756584), -(c_Big__Operators_Olattice_OSup__fin(_1756584, c_Orderings_Oord__class_Omax(_1756584), hAPP(c_List_Oset(_1756584), hAPP(hAPP(c_List_Olist_OCons(_1756584), _1756586), _1756588))) = hAPP(c_List_Ofoldl(_1756584, _1756584, c_Orderings_Oord__class_Omax(_1756584), _1756586), _1756588))], (20238 ^ _775828) ^ [_1123572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1123572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1123572)))], (36339 ^ _775828) ^ [_1458084, _1458086] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1458084)), _1458086) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1458084, _1458086))], (47946 ^ _775828) ^ [_1733977, _1733979, _1733981] : [class_Groups_Omonoid__add(_1733977), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1733977), hAPP(hAPP(c_List_Oappend(_1733977), _1733979), _1733981)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1733977), hAPP(c_List_Omonoid__add__class_Olistsum(_1733977), _1733979)), hAPP(c_List_Omonoid__add__class_Olistsum(_1733977), _1733981)))], (15906 ^ _775828) ^ [_1044365, _1044367] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044365), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044367)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044365), _1044367)))], (7673 ^ _775828) ^ [] : [-(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))], (11042 ^ _775828) ^ [_956541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956541), _956541)))))], (47577 ^ _775828) ^ [_1724784, _1724786, _1724788] : [-(_1724784 = c_List_Olist_ONil(_1724786)), -(hBOOL(hAPP(hAPP(c_member(_1724786), hAPP(c_Product__Type_Ofst(_1724786, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1724786, _1724784), _1724788))), hAPP(c_List_Oset(_1724786), _1724784))))], (3560 ^ _775828) ^ [_829885, _829887, _829889, _829891, _829893, _829895, _829897, _829899] : [-(c_New__Random__Sequence_Opos__bind(_829899, _829895, _829891, _829887) = c_New__Random__Sequence_Opos__bind(_829897, _829893, _829889, _829885)), _829899 = _829897, _829895 = _829893, _829891 = _829889, _829887 = _829885], (11034 ^ _775828) ^ [_956322, _956324, _956326] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956324), _956326)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956322), _956324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956322), _956326)))], (24140 ^ _775828) ^ [_1198541, _1198543, _1198545] : [class_Orderings_Olinorder(_1198541), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198541), _1198543), _1198545) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198541), _1198545), _1198543))], (20402 ^ _775828) ^ [_1126463, _1126465] : [class_Int_Onumber__ring(_1126463), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126463), _1126465), hAPP(c_Int_Onumber__class_Onumber__of(_1126463), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126463), _1126465), _1126465))], (8186 ^ _775828) ^ [_907353, _907355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907353), _907355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907355), _907353)), -(_907353 = _907355)], (43178 ^ _775828) ^ [_1618238, _1618240, _1618242, _1618244, _1618246, _1618248] : [c_Finite__Set_Ofolding__idem(_1618238, _1618240, _1618242, _1618244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618238), _1618246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618238, tc_HOL_Obool)), _1618248), _1618246)), -(hAPP(c_Fun_Ocomp(_1618240, _1618240, _1618240, hAPP(_1618244, _1618246)), hAPP(_1618244, _1618248)) = hAPP(_1618244, _1618246))], (23056 ^ _775828) ^ [_1177190, _1177192, _1177194, _1177196] : [class_Fields_Olinordered__field(_1177190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177190), c_Groups_Ozero__class_Ozero(_1177190)), _1177192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177190), _1177194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177190), _1177196), _1177192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177190), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177190), _1177194), _1177192)), _1177196)))], (20914 ^ _775828) ^ [_1135741, _1135743] : [-(c_Divides_OposDivAlg(_1135741, _1135743) = hAPP(c_Divides_Oadjust(_1135743), c_Divides_OposDivAlg(_1135741, 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)))), _1135743)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135741), _1135743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135743), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17231 ^ _775828) ^ [_1070562, _1070564] : [class_Groups_Oordered__ab__group__add__abs(_1070562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070562), _1070564), c_Groups_Ozero__class_Ozero(_1070562))), -(hAPP(c_Groups_Oabs__class_Oabs(_1070562), _1070564) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070562), _1070564))], (40129 ^ _775828) ^ [_1545242, _1545244] : [class_Lattices_Obounded__lattice__top(_1545242), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545242), _1545244), c_Orderings_Otop__class_Otop(_1545242)) = _1545244)], (40061 ^ _775828) ^ [_1543891] : [class_Finite__Set_Ofinite(_1543891), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543891), c_Orderings_Otop__class_Otop(tc_fun(_1543891, tc_HOL_Obool)))))], (34555 ^ _775828) ^ [_1420271, _1420273, _1420275, _1420277, _1420279, _1420281, _1420283, _1420285] : [c_Finite__Set_Ofolding__image__simple(_1420271, _1420273, _1420275, _1420277, _1420279, _1420281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420273), _1420283)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420273), _1420285)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420273, tc_HOL_Obool)), _1420283), _1420285) = c_Orderings_Obot__class_Obot(tc_fun(_1420273, tc_HOL_Obool)), -(hAPP(_1420281, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420273, tc_HOL_Obool)), _1420283), _1420285)) = hAPP(hAPP(_1420275, hAPP(_1420281, _1420283)), hAPP(_1420281, _1420285)))], (24499 ^ _775828) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (47197 ^ _775828) ^ [_1717152, _1717154, _1717156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717152, tc_HOL_Obool)), hAPP(c_List_Oset(_1717152), hAPP(hAPP(c_List_Otake(_1717152), _1717154), _1717156))), hAPP(c_List_Oset(_1717152), _1717156))))], (24829 ^ _775828) ^ [_1212766, _1212768, _1212770, _1212772, _1212774, _1212776, _1212778, _1212780, _1212782] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212766, _1212768, _1212770, _1212772), hAPP(hAPP(c_Product__Type_Oscomp(_1212766, _1212774, _1212776, tc_prod(_1212768, _1212770)), _1212778), _1212780)), _1212782) = hAPP(hAPP(c_Product__Type_Oscomp(_1212766, _1212774, _1212776, _1212772), _1212778), hAPP(hAPP(c_COMBC(_1212774, tc_fun(_1212768, tc_fun(_1212770, _1212772)), tc_fun(_1212776, _1212772)), hAPP(hAPP(c_COMBB(tc_fun(_1212776, tc_prod(_1212768, _1212770)), tc_fun(tc_fun(_1212768, tc_fun(_1212770, _1212772)), tc_fun(_1212776, _1212772)), _1212774), c_Product__Type_Oscomp(_1212776, _1212768, _1212770, _1212772)), _1212780)), _1212782)))], (41376 ^ _775828) ^ [_1575900, _1575902, _1575904, _1575906, _1575908, _1575910] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575900, _1575902)), hAPP(hAPP(c_Product__Type_OPair(_1575900, _1575902), _1575904), _1575906)), hAPP(hAPP(c_Product__Type_OSigma(_1575900, _1575902), _1575908), _1575910))), 41379 ^ _775828 : [(41382 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575902), _1575906), hAPP(_1575910, _1575904))))], (41380 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575900), _1575904), _1575908)))]]], (42914 ^ _775828) ^ [_1611899, _1611901, _1611903, _1611905, _1611907, _1611909] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611899, tc_fun(_1611901, tc_HOL_Obool)), _1611903), hAPP(c_Fun_Ocomp(_1611905, tc_fun(_1611901, tc_HOL_Obool), _1611899, _1611907), _1611909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611905, tc_fun(_1611901, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1611899, _1611905, _1611909), _1611903)), _1611907))], (42505 ^ _775828) ^ [_1602011, _1602013, _1602015] : [-(c_Relation_Orefl__on(_1602011, _1602013, _1602015)), 42509 ^ _775828 : [(42512 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1602011, _1602011, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1602011, tc_fun(_1602011, tc_HOL_Obool), tc_fun(_1602011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1602011, tc_HOL_Obool), tc_fun(_1602011, tc_HOL_Obool)), _1602011), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1602011)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1602011), c_fconj), hAPP(hAPP(c_COMBC(_1602011, tc_fun(_1602011, tc_HOL_Obool), tc_HOL_Obool), c_member(_1602011)), _1602013)))), hAPP(hAPP(c_COMBC(_1602011, tc_fun(_1602011, tc_HOL_Obool), tc_HOL_Obool), c_member(_1602011)), _1602013))), 42508 ^ [_1602011, _1602013, _1602015]))], (42510 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602011, _1602011)), 42508 ^ [_1602011, _1602013, _1602015]), _1602015)))]], 42514 ^ _775828 : [(42517 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602011, _1602011)), hAPP(hAPP(c_Product__Type_OPair(_1602011, _1602011), 42513 ^ [_1602011, _1602013, _1602015]), 42513 ^ [_1602011, _1602013, _1602015])), _1602015))], (42515 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602011), 42513 ^ [_1602011, _1602013, _1602015]), _1602013)))]]], (47509 ^ _775828) ^ [_1723422, _1723424, _1723426, _1723428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723422), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723424)), _1723426))), -(hAPP(hAPP(c_List_Onth(_1723424), hAPP(hAPP(c_List_Olist__update(_1723424, _1723426), _1723422), _1723428)), _1723422) = _1723428)], (47427 ^ _775828) ^ [_1721913, _1721915] : [_1721915 = c_List_Olist_ONil(_1721913), -(c_Orderings_Obot__class_Obot(tc_fun(_1721913, tc_HOL_Obool)) = hAPP(c_List_Oset(_1721913), _1721915))], (47847 ^ _775828) ^ [_1731627, _1731629, _1731631, _1731633] : [hBOOL(hAPP(hAPP(c_member(_1731627), _1731629), hAPP(c_List_Oset(_1731627), _1731631))), -(c_List_Oremove1(_1731627, _1731629, hAPP(hAPP(c_List_Oappend(_1731627), _1731631), _1731633)) = hAPP(hAPP(c_List_Oappend(_1731627), c_List_Oremove1(_1731627, _1731629, _1731631)), _1731633))], (43072 ^ _775828) ^ [_1615759, _1615761, _1615763, _1615765, _1615767, _1615769, _1615771] : [c_Finite__Set_Ofolding__image(_1615759, _1615761, _1615763, _1615765, _1615767), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615761), _1615769)), -(hAPP(hAPP(_1615767, _1615771), _1615769) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1615759, _1615761, _1615763), _1615771), _1615765), _1615769))], (40818 ^ _775828) ^ [_1560938, _1560940, _1560942, _1560944, _1560946] : [hBOOL(hAPP(hAPP(c_member(_1560942), hAPP(_1560944, _1560940)), _1560946)), -(hBOOL(hAPP(hAPP(c_member(_1560938), _1560940), hAPP(c_Set_Ovimage(_1560938, _1560942, _1560944), _1560946))))], (12667 ^ _775828) ^ [_984912, _984914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984912), _984914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984914), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (25020 ^ _775828) ^ [_1216816, _1216818, _1216820, _1216822, _1216824] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216816, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216816, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1216818, _1216816, _1216820), _1216822)), hAPP(c_Set_Oimage(_1216818, _1216816, _1216820), _1216824))), hAPP(c_Set_Oimage(_1216818, _1216816, _1216820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216818, tc_HOL_Obool)), _1216822), _1216824)))))], (50339 ^ _775828) ^ [_1787492, _1787494, _1787496] : [-(c_List_Oconcat(_1787492, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1787492)), _1787494), _1787496)) = hAPP(hAPP(c_List_Oappend(_1787492), _1787494), c_List_Oconcat(_1787492, _1787496)))], (38174 ^ _775828) ^ [_1500179, _1500181, _1500183, _1500185, _1500187] : [hBOOL(hAPP(hAPP(c_member(_1500179), _1500181), hAPP(c_Relation_OImage(_1500183, _1500179, _1500185), hAPP(hAPP(c_Set_Oinsert(_1500183), _1500187), c_Orderings_Obot__class_Obot(tc_fun(_1500183, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500183, _1500179)), hAPP(hAPP(c_Product__Type_OPair(_1500183, _1500179), _1500187), _1500181)), _1500185)))], (25361 ^ _775828) ^ [_1223214, _1223216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1223214)), hAPP(c_Code__Numeral_Oof__nat, _1223216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223214), _1223216)))], (27567 ^ _775828) ^ [_1265757, _1265759, _1265761, _1265763] : [hBOOL(hAPP(hAPP(_1265761, _1265763), _1265759)), -(hBOOL(hAPP(hAPP(c_member(_1265757), _1265759), c_SetInterval_Oord_OatLeast(_1265757, _1265761, _1265763))))], (10958 ^ _775828) ^ [_955209, _955211] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955209), _955211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955211)), _955209)))], (3002 ^ _775828) ^ [_820948, _820950] : [_820950 = _820948, -(c_Int_Oint__ge__less__than(_820950) = c_Int_Oint__ge__less__than(_820948))], (46454 ^ _775828) ^ [_1697671, _1697673, _1697675] : [-(hAPP(c_List_Oset(_1697671), hAPP(hAPP(c_List_Olist_OCons(_1697671), _1697673), _1697675)) = hAPP(hAPP(c_Set_Oinsert(_1697671), _1697673), hAPP(c_List_Oset(_1697671), _1697675)))], (13272 ^ _775828) ^ [_995438, _995440, _995442, _995444, _995446, _995448] : [class_Divides_Osemiring__div(_995438), c_Divides_Odiv__class_Omod(_995438, _995440, _995442) = c_Divides_Odiv__class_Omod(_995438, _995444, _995442), c_Divides_Odiv__class_Omod(_995438, _995446, _995442) = c_Divides_Odiv__class_Omod(_995438, _995448, _995442), -(c_Divides_Odiv__class_Omod(_995438, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995438), _995440), _995446), _995442) = c_Divides_Odiv__class_Omod(_995438, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995438), _995444), _995448), _995442))], (11364 ^ _775828) ^ [_962464, _962466] : [class_Rings_Olinordered__idom(_962464), 11367 ^ _775828 : [(11374 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962464), _962466), c_Groups_Ozero__class_Ozero(_962464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962464), _962466), _962466)), c_Groups_Ozero__class_Ozero(_962464))))], (11368 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962464), _962466), _962466)), c_Groups_Ozero__class_Ozero(_962464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962464), _962466), c_Groups_Ozero__class_Ozero(_962464))))]]], (21214 ^ _775828) ^ [_1143317, _1143319, _1143321] : [class_Int_Onumber__ring(_1143317), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1143317), _1143319), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1143321))) = hAPP(hAPP(c_HOL_OLet(_1143317, _1143317), hAPP(hAPP(c_Power_Opower__class_Opower(_1143317), _1143319), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143321))), hAPP(hAPP(c_COMBS(_1143317, _1143317, _1143317), c_Groups_Otimes__class_Otimes(_1143317)), c_COMBI(_1143317))))], (13008 ^ _775828) ^ [_990823, _990825, _990827] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_990823, _990825, _990827)) = 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(_990825)), c_Com_Ocom_Ocom__size(_990827))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30021 ^ _775828) ^ [_1323007, _1323009] : [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)))), _1323007, _1323009), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323007), _1323009)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323009), _1323007)))], (10714 ^ _775828) ^ [_950878, _950880] : [class_Rings_Ocomm__semiring__1(_950878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950878), _950880), c_Groups_Oone__class_Oone(_950878)) = _950880)], (17967 ^ _775828) ^ [_1083780, _1083782] : [class_Power_Opower(_1083780), class_Rings_Osemiring__0(_1083780), 17974 ^ _775828 : [(17981 ^ _775828) ^ [] : [-(_1083782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1083780), c_Groups_Ozero__class_Ozero(_1083780)), _1083782) = c_Groups_Ozero__class_Ozero(_1083780))], (17975 ^ _775828) ^ [] : [_1083782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1083780), c_Groups_Ozero__class_Ozero(_1083780)), _1083782) = c_Groups_Oone__class_Oone(_1083780))]]], (34929 ^ _775828) ^ [_1427717, _1427719, _1427721] : [class_Lattices_Odistrib__lattice(_1427717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427717), _1427719)), -(_1427719 = c_Orderings_Obot__class_Obot(tc_fun(_1427717, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427717), _1427721)), -(_1427721 = c_Orderings_Obot__class_Obot(tc_fun(_1427717, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427717), c_Big__Operators_Olattice__class_OSup__fin(_1427717, _1427719)), c_Big__Operators_Olattice__class_OSup__fin(_1427717, _1427721)) = c_Big__Operators_Olattice__class_OSup__fin(_1427717, hAPP(c_Set_OCollect(_1427717), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_HOL_Obool), tc_HOL_Obool, _1427717), c_HOL_OEx(_1427717)), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool)), tc_fun(_1427717, tc_HOL_Obool), _1427717), hAPP(c_COMBB(tc_fun(_1427717, tc_HOL_Obool), tc_HOL_Obool, _1427717), c_HOL_OEx(_1427717))), hAPP(hAPP(c_COMBC(_1427717, tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool)), tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_fun(tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool))), tc_fun(tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool)), tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool))), _1427717), c_COMBS(_1427717, tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_fun(_1427717, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1427717, tc_fun(tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool))), _1427717), hAPP(c_COMBB(tc_fun(_1427717, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool)), _1427717), c_COMBS(_1427717, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool)), tc_fun(_1427717, tc_fun(_1427717, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1427717), hAPP(c_COMBB(tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1427717), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1427717), c_fconj))), hAPP(hAPP(c_COMBC(_1427717, tc_fun(_1427717, tc_fun(_1427717, _1427717)), tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1427717, _1427717), tc_fun(_1427717, tc_HOL_Obool)), tc_fun(tc_fun(_1427717, tc_fun(_1427717, _1427717)), tc_fun(_1427717, tc_fun(_1427717, tc_HOL_Obool))), _1427717), c_COMBB(tc_fun(_1427717, _1427717), tc_fun(_1427717, tc_HOL_Obool), _1427717)), hAPP(hAPP(c_COMBB(tc_fun(_1427717, tc_HOL_Obool), tc_fun(tc_fun(_1427717, _1427717), tc_fun(_1427717, tc_HOL_Obool)), _1427717), c_COMBB(_1427717, tc_HOL_Obool, _1427717)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1427717)))))), hAPP(hAPP(c_COMBC(_1427717, tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1427717, tc_HOL_Obool), tc_fun(_1427717, tc_HOL_Obool)), _1427717), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1427717)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1427717), c_fconj), hAPP(hAPP(c_COMBC(_1427717, tc_fun(_1427717, tc_HOL_Obool), tc_HOL_Obool), c_member(_1427717)), _1427719)))), hAPP(hAPP(c_COMBC(_1427717, tc_fun(_1427717, tc_HOL_Obool), tc_HOL_Obool), c_member(_1427717)), _1427721))))))))], (32117 ^ _775828) ^ [_1369675, _1369677] : [class_Orderings_Olinorder(_1369675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369675), _1369677)), -(_1369677 = c_Orderings_Obot__class_Obot(tc_fun(_1369675, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1369675), c_Big__Operators_Olinorder__class_OMax(_1369675, _1369677)), _1369677)))], (13186 ^ _775828) ^ [_994051, _994053, _994055, _994057, _994059, _994061] : [c_Com_Ocom_OLocal(_994051, _994053, _994055) = c_Com_Ocom_OCond(_994057, _994059, _994061)], (25545 ^ _775828) ^ [_1227485] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1227485)))], (50830 ^ _775828) ^ [_1798952, _1798954, _1798956, _1798958, _1798960] : [c_Finite__Set_Ofun__left__comm(_1798952, _1798954, _1798956), -(hAPP(hAPP(c_Finite__Set_Ofold(_1798952, _1798954, _1798956), _1798958), hAPP(c_List_Oset(_1798952), _1798960)) = hAPP(c_List_Ofoldl(_1798954, _1798952, hAPP(c_COMBC(_1798952, _1798954, _1798954), _1798956), _1798958), c_List_Oremdups(_1798952, _1798960)))], (14698 ^ _775828) ^ [_1021712, _1021714, _1021716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021714), _1021716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021712), _1021716)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021712), _1021714))))], (50688 ^ _775828) ^ [_1796241, _1796243, _1796245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796241)), c_List_OtakeWhile(_1796241, _1796243, _1796245))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796241)), _1796245))), hBOOL(hAPP(_1796243, hAPP(hAPP(c_List_Onth(_1796241), _1796245), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796241)), c_List_OtakeWhile(_1796241, _1796243, _1796245)))))], (7439 ^ _775828) ^ [_894550] : [-(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, _894550)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13684 ^ _775828) ^ [_1003717, _1003719] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_1003717, _1003719)], (48483 ^ _775828) ^ [_1747972, _1747974, _1747976, _1747978] : [_1747972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1747974), _1747972), hAPP(hAPP(c_List_Olist_OCons(_1747974), _1747976), _1747978)) = hAPP(hAPP(c_List_Olist_OCons(_1747974), _1747976), _1747978))], (42690 ^ _775828) ^ [_1606698, _1606700, _1606702, _1606704, _1606706, _1606708, _1606710, _1606712, _1606714, _1606716, _1606718] : [-(hAPP(c_Product__Type_Omap__pair(_1606698, _1606700, _1606702, _1606704, _1606706, _1606708), hAPP(c_Product__Type_Omap__pair(_1606710, _1606698, _1606712, _1606702, _1606714, _1606716), _1606718)) = hAPP(c_Product__Type_Omap__pair(_1606710, _1606700, _1606712, _1606704, hAPP(c_Fun_Ocomp(_1606698, _1606700, _1606710, _1606706), _1606714), hAPP(c_Fun_Ocomp(_1606702, _1606704, _1606712, _1606708), _1606716)), _1606718))], (40909 ^ _775828) ^ [_1563164, _1563166, _1563168, _1563170] : [c_Fun_Oinj__on(_1563164, _1563166, _1563168, c_Orderings_Otop__class_Otop(tc_fun(_1563164, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1563164, _1563166, _1563168), hAPP(c_Set_Oimage(_1563164, _1563166, _1563168), _1563170)) = _1563170)], (18285 ^ _775828) ^ [_1090164, _1090166, _1090168, _1090170, _1090172, _1090174, _1090176, _1090178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1090164, _1090166), tc_prod(_1090164, _1090166))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1090164, _1090166), tc_prod(_1090164, _1090166)), hAPP(hAPP(c_Product__Type_OPair(_1090164, _1090166), _1090168), _1090170)), hAPP(hAPP(c_Product__Type_OPair(_1090164, _1090166), _1090172), _1090174))), c_Wellfounded_Olex__prod(_1090164, _1090166, _1090176, _1090178))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1090164, _1090164)), hAPP(hAPP(c_Product__Type_OPair(_1090164, _1090164), _1090168), _1090172)), _1090176))), 18292 ^ _775828 : [(18295 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1090166, _1090166)), hAPP(hAPP(c_Product__Type_OPair(_1090166, _1090166), _1090170), _1090174)), _1090178)))], (18293 ^ _775828) ^ [] : [-(_1090168 = _1090172)]]], (20768 ^ _775828) ^ [_1133017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1133017)), -(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), _1133017), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29673 ^ _775828) ^ [_1314572, _1314574, _1314576, _1314578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314572, tc_HOL_Obool)), _1314574), hAPP(hAPP(c_Set_Oinsert(_1314572), _1314576), _1314578))), 29676 ^ _775828 : [(29683 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1314572), _1314576), _1314574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314572, tc_HOL_Obool)), _1314574), _1314578)))], (29677 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1314572), _1314576), _1314574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314572, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314572, tc_HOL_Obool)), _1314574), hAPP(hAPP(c_Set_Oinsert(_1314572), _1314576), c_Orderings_Obot__class_Obot(tc_fun(_1314572, tc_HOL_Obool))))), _1314578)))]]], (11510 ^ _775828) ^ [_965055, _965057] : [class_Groups_Ogroup__add(_965055), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965055), hAPP(c_Groups_Ouminus__class_Ouminus(_965055), _965057)), _965057) = c_Groups_Ozero__class_Ozero(_965055))], (6408 ^ _775828) ^ [_877770, _877772, _877774] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_877770, _877772)), _877774), hAPP(hAPP(hAPP(c_Natural_Oupdate, _877774), _877770), hAPP(_877772, _877774)))))], (51038 ^ _775828) ^ [_1803457, _1803459] : [class_Lattices_Olattice(_1803457), -(class_Lattices_Osemilattice__sup(tc_fun(_1803459, _1803457)))], (8255 ^ _775828) ^ [_908438, _908440, _908442, _908444, _908446] : [class_Orderings_Oord(_908438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908440, _908438)), _908442), _908444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908438), hAPP(_908442, _908446)), hAPP(_908444, _908446))))], (27635 ^ _775828) ^ [_1267151, _1267153, _1267155, _1267157, _1267159] : [-(hBOOL(hAPP(hAPP(c_member(_1267151), _1267153), c_SetInterval_Oord_OatLeastAtMost(_1267151, _1267155, _1267157, _1267159)))), hBOOL(hAPP(hAPP(_1267155, _1267157), _1267153)), hBOOL(hAPP(hAPP(_1267155, _1267153), _1267159))], (47069 ^ _775828) ^ [_1713263, _1713265, _1713267, _1713269] : [-(_1713263 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1713265), hAPP(hAPP(c_List_Olist_OCons(_1713265), _1713267), _1713269)), _1713263) = hAPP(hAPP(c_List_Onth(_1713265), _1713269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1713263), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24344 ^ _775828) ^ [_1203005, _1203007] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1203005), _1203007)), _1203007) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1203005), _1203007))], (10348 ^ _775828) ^ [_944014] : [class_Rings_Oring__1(_944014), -(hAPP(c_Int_Oring__1__class_Oof__int(_944014), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_944014))], (44479 ^ _775828) ^ [_1649604, _1649606, _1649608, _1649610, _1649612] : [-(_1649604 = c_Orderings_Obot__class_Obot(tc_fun(_1649606, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1649608, tc_HOL_Obool)), _1649610), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649606, tc_fun(_1649608, tc_HOL_Obool)), _1649604), _1649612)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649606, tc_fun(_1649608, tc_HOL_Obool)), _1649604), hAPP(hAPP(c_COMBB(tc_fun(_1649608, tc_HOL_Obool), tc_fun(_1649608, tc_HOL_Obool), _1649606), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1649608, tc_HOL_Obool)), _1649610)), _1649612)))], (8369 ^ _775828) ^ [_910245, _910247, _910249] : [class_Orderings_Oorder(_910245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910245), _910247), _910249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910245), _910249), _910247)), -(_910249 = _910247)], (19642 ^ _775828) ^ [_1113322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113322), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1113322)), c_Int_OPls)))], (20806 ^ _775828) ^ [_1133848, _1133850] : [class_Int_Onumber__ring(_1133848), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1133848), hAPP(c_Int_Onumber__class_Onumber__of(_1133848), 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)))), _1133850)) = c_Groups_Oone__class_Oone(_1133848))], (14423 ^ _775828) ^ [_1017383, _1017385, _1017387, _1017389] : [c_Com_Ocom_OWhile(_1017383, _1017385) = c_Com_Ocom_OSemi(_1017387, _1017389)], (26952 ^ _775828) ^ [_1251901, _1251903, _1251905] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251901), _1251903)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251901), _1251905)))))], (27531 ^ _775828) ^ [_1265052, _1265054] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265054), _1265052)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1265052), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265054))))], (47223 ^ _775828) ^ [_1717798, _1717800, _1717802, _1717804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1717798), _1717800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717802, tc_HOL_Obool)), hAPP(c_List_Oset(_1717802), hAPP(hAPP(c_List_Otake(_1717802), _1717798), _1717804))), hAPP(c_List_Oset(_1717802), hAPP(hAPP(c_List_Otake(_1717802), _1717800), _1717804)))))], (31625 ^ _775828) ^ [_1358164, _1358166, _1358168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358164, _1358164), tc_HOL_Obool)), _1358166), _1358168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358164, _1358164), tc_HOL_Obool)), _1358168), c_Transitive__Closure_Ortrancl(_1358164, _1358166))), -(c_Transitive__Closure_Ortrancl(_1358164, _1358168) = c_Transitive__Closure_Ortrancl(_1358164, _1358166))], (45413 ^ _775828) ^ [_1670326, _1670328, _1670330, _1670332] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1670326)), hAPP(c_Set_Oimage(_1670328, tc_Option_Ooption(_1670326), _1670330), c_Orderings_Otop__class_Otop(tc_fun(_1670328, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1670326)), hAPP(c_Set_Oimage(_1670328, tc_Option_Ooption(_1670326), c_Map_Omap__add(_1670328, _1670326, _1670330, c_Map_Omap__of(_1670328, _1670326, _1670332))), c_Orderings_Otop__class_Otop(tc_fun(_1670328, tc_HOL_Obool))))))], (43794 ^ _775828) ^ [_1632339, _1632341, _1632343] : [class_Orderings_Olinorder(_1632339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632339), _1632341)), -(c_Big__Operators_Olattice_OSup__fin(_1632339, c_Orderings_Oord__class_Omax(_1632339), hAPP(hAPP(c_Set_Oinsert(_1632339), _1632343), _1632341)) = hAPP(hAPP(c_Finite__Set_Ofold(_1632339, _1632339, c_Orderings_Oord__class_Omax(_1632339)), _1632343), _1632341))], (24768 ^ _775828) ^ [_1211460, _1211462, _1211464] : [-(hBOOL(hAPP(hAPP(c_member(_1211460), _1211462), c_Wellfounded_Oacc(_1211460, _1211464)))), 24772 ^ _775828 : [(24775 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1211460), 24771 ^ [_1211460, _1211462, _1211464]), c_Wellfounded_Oacc(_1211460, _1211464)))], (24773 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1211460, _1211460)), hAPP(hAPP(c_Product__Type_OPair(_1211460, _1211460), 24771 ^ [_1211460, _1211462, _1211464]), _1211462)), _1211464)))]]], (18445 ^ _775828) ^ [_1093152, _1093154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093152), 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)), _1093154)), -(c_Divides_OnegDivAlg(_1093152, _1093154) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1093152), _1093154)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1093152, _1093154)))], (4026 ^ _775828) ^ [_837250, _837252, _837254, _837256] : [-(c_Hilbert__Choice_OEps(_837256, _837252) = c_Hilbert__Choice_OEps(_837254, _837250)), _837256 = _837254, _837252 = _837250], (10312 ^ _775828) ^ [_943236, _943238, _943240] : [class_Rings_Ocomm__semiring__1(_943236), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943236), _943238), _943240)), _943240) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943236), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943236), _943238), c_Groups_Oone__class_Oone(_943236))), _943240))], (3008 ^ _775828) ^ [_821033, _821035] : [_821035 = _821033, -(c_Int_Oint__ge__less__than2(_821035) = c_Int_Oint__ge__less__than2(_821033))], (40929 ^ _775828) ^ [_1563628, _1563630, _1563632, _1563634] : [-(hBOOL(hAPP(hAPP(c_member(_1563628), _1563630), _1563632))), -(hAPP(c_Set_Ovimage(_1563634, _1563628, hAPP(c_COMBK(_1563628, _1563634), _1563630)), _1563632) = c_Orderings_Obot__class_Obot(tc_fun(_1563634, tc_HOL_Obool)))], (20226 ^ _775828) ^ [_1123364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1123364)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123364), c_Int_OMin)))], (44826 ^ _775828) ^ [_1657607, _1657609] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1657607, tc_HOL_Obool), tc_HOL_Obool)), _1657609), hAPP(c_Set_OPow(_1657607), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657607, tc_HOL_Obool), _1657609)))))], (20812 ^ _775828) ^ [_1133959, _1133961] : [class_Int_Onumber__ring(_1133959), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1133959), hAPP(c_Int_Onumber__class_Onumber__of(_1133959), 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)))), _1133961))) = hAPP(c_Int_Onumber__class_Onumber__of(_1133959), c_Int_OMin))], (30968 ^ _775828) ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1342694), _1342696)), 30974 ^ _775828 : [(30977 ^ _775828) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1342698, _1342700, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1342698)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1342698), hAPP(_1342708, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710])), hAPP(_1342704, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710])), hAPP(_1342710, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1342698), tc_HOL_Obool))))], (30975 ^ _775828) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1342698, _1342700, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1342698)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1342698), hAPP(_1342702, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710])), hAPP(_1342704, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710])), hAPP(_1342706, 30973 ^ [_1342694, _1342696, _1342698, _1342700, _1342702, _1342704, _1342706, _1342708, _1342710]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1342698), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1342698, _1342700, hAPP(c_Set_Oimage(_1342694, tc_Hoare__Mirabelle_Otriple(_1342698), hAPP(hAPP(c_COMBS(_1342694, tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698)), hAPP(hAPP(c_COMBS(_1342694, tc_Com_Ocom, tc_fun(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698))), hAPP(hAPP(c_COMBB(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698))), _1342694), c_Hoare__Mirabelle_Otriple_Otriple(_1342698)), _1342702)), _1342704)), _1342706)), _1342696)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1342698, _1342700, hAPP(c_Set_Oimage(_1342694, tc_Hoare__Mirabelle_Otriple(_1342698), hAPP(hAPP(c_COMBS(_1342694, tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698)), hAPP(hAPP(c_COMBS(_1342694, tc_Com_Ocom, tc_fun(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698))), hAPP(hAPP(c_COMBB(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1342698, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1342698))), _1342694), c_Hoare__Mirabelle_Otriple_Otriple(_1342698)), _1342708)), _1342704)), _1342710)), _1342696)))], (38383 ^ _775828) ^ [_1504945, _1504947, _1504949, _1504951] : [c_Map_Odom(_1504945, _1504947, _1504949) = hAPP(hAPP(c_Set_Oinsert(_1504945), _1504951), c_Orderings_Obot__class_Obot(tc_fun(_1504945, tc_HOL_Obool))), -(_1504949 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1504945, tc_Option_Ooption(_1504947)), hAPP(c_COMBK(tc_Option_Ooption(_1504947), _1504945), c_Option_Ooption_ONone(_1504947))), _1504951), hAPP(c_Option_Ooption_OSome(_1504947), 38386 ^ [_1504945, _1504947, _1504949, _1504951])))], (26119 ^ _775828) ^ [_1236931, _1236933, _1236935, _1236937] : [class_Divides_Osemiring__div(_1236931), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), _1236933), _1236935)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), _1236933), _1236937)), 26130 ^ _775828 : [(26137 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), _1236935), _1236937)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236931), _1236935), _1236933)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236931), _1236937), _1236933))))], (26131 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236931), _1236935), _1236933)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236931), _1236937), _1236933))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236931), _1236935), _1236937)))]]], (16274 ^ _775828) ^ [_1052246, _1052248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052248)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1052246)), hAPP(c_Int_Onat, _1052248)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1052246), _1052248)))], (15270 ^ _775828) ^ [_1032202, _1032204, _1032206] : [class_Groups_Ogroup__add(_1032202), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032202), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032202), _1032204), _1032206)), _1032206) = _1032204)], (5857 ^ _775828) ^ [_869108] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _869108), _869108)))], (1530 ^ _775828) ^ [_797571, _797573] : [-(class_Rings_Ono__zero__divisors(_797571)), _797573 = _797571, class_Rings_Ono__zero__divisors(_797573)], (36517 ^ _775828) ^ [_1461867] : [-(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)), _1461867)) = hAPP(c_Int_Onat, _1461867))], (40842 ^ _775828) ^ [_1561502, _1561504, _1561506] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561502, _1561502)), _1561504), c_Transitive__Closure_Ortrancl(_1561502, _1561506))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561502, _1561502)), _1561504), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561502, _1561502), tc_HOL_Obool), 40845 ^ [_1561502, _1561504, _1561506]), _1561506))))], (10420 ^ _775828) ^ [_945388, _945390, _945392, _945394] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_945388), 10423 ^ _775828 : [(10430 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945388), _945392), _945394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945388), _945390), _945392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945388), _945390), _945394))))], (10424 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945388), _945390), _945392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945388), _945390), _945394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945388), _945392), _945394)))]]], (5701 ^ _775828) ^ [_866646, _866648, _866650] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _866646)), _866648), _866650)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _866646))), _866648), _866650)))], (33036 ^ _775828) ^ [_1387207, _1387209, _1387211, _1387213] : [class_Groups_Ocomm__monoid__mult(_1387207), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1387209), _1387211))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387209, _1387207), _1387213), _1387211) = c_Groups_Oone__class_Oone(_1387207))], (51498 ^ _775828) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (29789 ^ _775828) ^ [_1317131, _1317133, _1317135, _1317137] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317131, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1317131), _1317133), _1317135)), _1317137))), hBOOL(hAPP(hAPP(c_member(_1317131), _1317133), _1317137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317131, tc_HOL_Obool)), _1317135), _1317137))], (42238 ^ _775828) ^ [_1596004, _1596006] : [c_Relation_Orefl__on(_1596004, c_Orderings_Otop__class_Otop(tc_fun(_1596004, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1596004, _1596004)), hAPP(c_Product__Type_Oprod_Oprod__case(_1596004, _1596004, tc_HOL_Obool), _1596006))), -(c_Predicate_Oreflp(_1596004, _1596006))], (30255 ^ _775828) ^ [_1327226, _1327228, _1327230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1327226, _1327226), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1327226, _1327226, _1327226), _1327228), _1327230)), _1327228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1327226, _1327228)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1327226, _1327230)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1327226, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1327226, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1327226, tc_HOL_Obool), tc_fun(_1327226, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1327226, _1327228))))], (50678 ^ _775828) ^ [_1796083, _1796085, _1796087, _1796089, _1796091] : [hBOOL(hAPP(hAPP(c_member(_1796083), _1796085), hAPP(c_List_Oset(_1796083), _1796087))), -(hBOOL(hAPP(_1796089, _1796085))), -(c_List_OtakeWhile(_1796083, _1796089, hAPP(hAPP(c_List_Oappend(_1796083), _1796087), _1796091)) = c_List_OtakeWhile(_1796083, _1796089, _1796087))], (17279 ^ _775828) ^ [_1071429, _1071431, _1071433] : [class_Int_Onumber__ring(_1071429), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071429), hAPP(c_Int_Onumber__class_Onumber__of(_1071429), _1071431)), hAPP(c_Int_Onumber__class_Onumber__of(_1071429), _1071433)) = hAPP(c_Int_Onumber__class_Onumber__of(_1071429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071431), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071433))))], (46570 ^ _775828) ^ [_1700103, _1700105, _1700107, _1700109, _1700111, _1700113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1700103, _1700103)), hAPP(hAPP(c_Product__Type_OPair(_1700103, _1700103), _1700105), _1700107)), _1700109)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700103), tc_List_Olist(_1700103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700103), tc_List_Olist(_1700103)), _1700111), _1700113)), c_List_Olistrel(_1700103, _1700109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700103), tc_List_Olist(_1700103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700103), tc_List_Olist(_1700103)), hAPP(hAPP(c_List_Olist_OCons(_1700103), _1700105), _1700111)), hAPP(hAPP(c_List_Olist_OCons(_1700103), _1700107), _1700113))), c_List_Olistrel(_1700103, _1700109))))], (28717 ^ _775828) ^ [_1292004, _1292006, _1292008, _1292010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292004, tc_HOL_Obool)), _1292006), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292004, tc_HOL_Obool)), _1292008), _1292010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292004, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292004, tc_HOL_Obool)), _1292006), _1292008)), _1292010)))], (44393 ^ _775828) ^ [_1646907, _1646909, _1646911, _1646913, _1646915, _1646917] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646907, tc_fun(_1646909, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646911, tc_fun(_1646907, tc_HOL_Obool)), _1646913), _1646915)), _1646917) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646911, tc_fun(_1646909, tc_HOL_Obool)), _1646913), hAPP(hAPP(c_COMBC(_1646911, tc_fun(_1646907, tc_fun(_1646909, tc_HOL_Obool)), tc_fun(_1646909, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1646907, tc_HOL_Obool), tc_fun(tc_fun(_1646907, tc_fun(_1646909, tc_HOL_Obool)), tc_fun(_1646909, tc_HOL_Obool)), _1646911), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646907, tc_fun(_1646909, tc_HOL_Obool))), _1646915)), _1646917)))], (896 ^ _775828) ^ [_789506, _789508, _789510, _789512, _789514, _789516, _789518, _789520] : [-(c_Fun_Oinj__on(_789518, _789514, _789510, _789506)), c_Fun_Oinj__on(_789520, _789516, _789512, _789508), _789520 = _789518, _789516 = _789514, _789512 = _789510, _789508 = _789506], (19002 ^ _775828) ^ [_1102932, _1102934, _1102936, _1102938] : [_1102932 = _1102934, 19005 ^ _775828 : [(19008 ^ _775828) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1102936, _1102938), _1102932) = hAPP(c_Product__Type_Osnd(_1102936, _1102938), _1102934))], (19006 ^ _775828) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1102936, _1102938), _1102932) = hAPP(c_Product__Type_Ofst(_1102936, _1102938), _1102934))]]], (2498 ^ _775828) ^ [_812608, _812610, _812612, _812614, _812616, _812618, _812620, _812622] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_812622, _812618, _812614, _812610) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_812620, _812616, _812612, _812608)), _812622 = _812620, _812618 = _812616, _812614 = _812612, _812610 = _812608], (41922 ^ _775828) ^ [_1588159, _1588161, _1588163, _1588165] : [-(c_Fun_Oinj__on(_1588159, tc_prod(_1588161, _1588159), 41920 ^ [_1588159, _1588161, _1588163, _1588165], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588161, tc_fun(_1588159, tc_HOL_Obool)), _1588163), _1588165)))], (1590 ^ _775828) ^ [_798321, _798323] : [-(class_Nat_Osemiring__char__0(_798321)), _798323 = _798321, class_Nat_Osemiring__char__0(_798323)], (40778 ^ _775828) ^ [_1559911, _1559913, _1559915, _1559917, _1559919] : [hBOOL(hAPP(_1559917, hAPP(_1559915, _1559919))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1559911, _1559913, _1559915), _1559917), _1559919)))], (12355 ^ _775828) ^ [_979628, _979630, _979632] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979630), _979632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979628), _979632)))], (49883 ^ _775828) ^ [_1778032, _1778034, _1778036] : [class_Orderings_Olinorder(_1778032), c_List_Olinorder__class_Osorted(_1778032, _1778034), -(c_List_Olinorder__class_Osorted(_1778032, c_List_Oremove1(_1778032, _1778036, _1778034)))], (24266 ^ _775828) ^ [_1201366, _1201368, _1201370] : [class_Groups_Olinordered__ab__group__add(_1201366), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1201366), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201366), _1201368), _1201370)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201366), hAPP(c_Groups_Ouminus__class_Ouminus(_1201366), _1201368)), hAPP(c_Groups_Ouminus__class_Ouminus(_1201366), _1201370)))], (27220 ^ _775828) ^ [_1257459, _1257461, _1257463] : [hBOOL(hAPP(hAPP(c_member(_1257459), _1257461), hAPP(c_Set_OCollect(_1257459), _1257463))), -(hBOOL(hAPP(_1257463, _1257461)))], (7839 ^ _775828) ^ [_901058, _901060] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _901058), _901060) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _901058 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901060 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17499 ^ _775828) ^ [_1075434] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075434) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075434)))], (48231 ^ _775828) ^ [_1741137, _1741139, _1741141, _1741143] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741137), tc_List_Olist(_1741137))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741137), tc_List_Olist(_1741137)), _1741139), _1741141)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1741137), tc_List_Olist(_1741137)), c_List_Olistrel1(_1741137, _1741143)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741137), tc_List_Olist(_1741137))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741137), tc_List_Olist(_1741137)), _1741139), _1741141)), c_List_Olistrel1(_1741137, hAPP(c_Relation_Oconverse(_1741137, _1741137), _1741143)))))], (6860 ^ _775828) ^ [_884427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _884427)), 6864 ^ _775828 : [(6867 ^ _775828) ^ [] : [-(_884427 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 6863 ^ [_884427]))], (6865 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6863 ^ [_884427])))]]], (46359 ^ _775828) ^ [_1693674, _1693676] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1693674), _1693676)), -(c_Nitpick_Ocard_H(_1693674, _1693676) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693674)), c_Hilbert__Choice_OEps(tc_List_Olist(_1693674), hAPP(hAPP(c_COMBS(tc_List_Olist(_1693674), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1693674)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693674), tc_fun(_1693674, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1693674, tc_HOL_Obool), tc_fun(tc_fun(_1693674, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1693674)), c_fequal), c_List_Oset(_1693674))), _1693676))), c_List_Odistinct(_1693674)))))], (29457 ^ _775828) ^ [_1310186, _1310188, _1310190, _1310192, _1310194] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1310186, _1310188, _1310190), _1310192), _1310194)), -(hBOOL(hAPP(hAPP(_1310190, _1310194), _1310192)))], (50035 ^ _775828) ^ [_1780690] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1780690) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1780690)))], (20022 ^ _775828) ^ [_1119792, _1119794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119792), _1119794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1119792)), c_Int_OBit0(_1119794))))], (16090 ^ _775828) ^ [_1048361, _1048363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048361), _1048363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048363), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9539 ^ _775828) ^ [_929154, _929156] : [class_Groups_Oordered__ab__group__add(_929154), 9542 ^ _775828 : [(9549 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), c_Groups_Ozero__class_Ozero(_929154)), _929156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), hAPP(c_Groups_Ouminus__class_Ouminus(_929154), _929156)), c_Groups_Ozero__class_Ozero(_929154))))], (9543 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), hAPP(c_Groups_Ouminus__class_Ouminus(_929154), _929156)), c_Groups_Ozero__class_Ozero(_929154))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), c_Groups_Ozero__class_Ozero(_929154)), _929156)))]]], (4746 ^ _775828) ^ [_848334, _848336, _848338, _848340] : [-(c_List_Oupt(_848340, _848336) = c_List_Oupt(_848338, _848334)), _848340 = _848338, _848336 = _848334], (16821 ^ _775828) ^ [_1062256, _1062258, _1062260] : [class_Groups_Oordered__ab__group__add__abs(_1062256), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062256), hAPP(c_Groups_Oabs__class_Oabs(_1062256), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062256), _1062258), _1062260))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062256), hAPP(c_Groups_Oabs__class_Oabs(_1062256), _1062258)), hAPP(c_Groups_Oabs__class_Oabs(_1062256), _1062260)))))], (14834 ^ _775828) ^ [_1024150, _1024152, _1024154, _1024156] : [class_Divides_Osemiring__div(_1024150), -(_1024152 = c_Groups_Ozero__class_Ozero(_1024150)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024150), _1024154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024150), _1024156), _1024152))), _1024152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024150), _1024156), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024150), _1024154), _1024152)))], (40656 ^ _775828) ^ [_1557375, _1557377, _1557379, _1557381, _1557383] : [c_Typedef_Otype__definition(_1557375, _1557377, _1557379, _1557381, _1557383), -(hAPP(c_Set_Oimage(_1557377, _1557375, _1557381), _1557383) = c_Orderings_Otop__class_Otop(tc_fun(_1557375, tc_HOL_Obool)))], (13408 ^ _775828) ^ [_998348, _998350, _998352] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_998348, _998350, _998352))), -(hBOOL(hAPP(c_Com_OWT, _998352)))], (46596 ^ _775828) ^ [_1700942, _1700944, _1700946, _1700948, _1700950, _1700952] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700942), tc_List_Olist(_1700942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700942), tc_List_Olist(_1700942)), hAPP(hAPP(c_List_Olist_OCons(_1700942), _1700944), _1700946)), hAPP(hAPP(c_List_Olist_OCons(_1700942), _1700948), _1700950))), c_List_Olex(_1700942, _1700952)))), 46597 ^ _775828 : [(46604 ^ _775828) ^ [] : [_1700944 = _1700948, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700942), tc_List_Olist(_1700942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700942), tc_List_Olist(_1700942)), _1700946), _1700950)), c_List_Olex(_1700942, _1700952)))], (46598 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1700942, _1700942)), hAPP(hAPP(c_Product__Type_OPair(_1700942, _1700942), _1700944), _1700948)), _1700952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700942)), _1700946) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700942)), _1700950)]]], (40333 ^ _775828) ^ [_1549187, _1549189, _1549191, _1549193] : [c_Fun_Oinj__on(_1549187, _1549189, _1549191, c_Orderings_Otop__class_Otop(tc_fun(_1549187, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1549187, _1549189, c_Orderings_Otop__class_Otop(tc_fun(_1549187, tc_HOL_Obool)), _1549191), hAPP(_1549191, _1549193)) = _1549193)], (1750 ^ _775828) ^ [_800321, _800323] : [-(class_Groups_Oone(_800321)), _800323 = _800321, class_Groups_Oone(_800323)], (42010 ^ _775828) ^ [_1590601, _1590603, _1590605, _1590607] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590601), _1590603)), 42016 ^ _775828 : [(42019 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590605), hAPP(_1590607, 42015 ^ [_1590601, _1590603, _1590605, _1590607])))], (42017 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590601), 42015 ^ [_1590601, _1590603, _1590605, _1590607]), _1590603)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1590601, _1590605)), hAPP(hAPP(c_Product__Type_OSigma(_1590601, _1590605), _1590603), _1590607))))], (38954 ^ _775828) ^ [_1517394, _1517396, _1517398, _1517400] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517394), hAPP(c_Set_Oimage(_1517396, _1517394, _1517398), _1517400))), c_Fun_Oinj__on(_1517396, _1517394, _1517398, _1517400), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517396), _1517400)))], (34671 ^ _775828) ^ [_1422731, _1422733, _1422735] : [class_Lattices_Olattice(_1422731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422731), _1422733)), -(_1422733 = c_Orderings_Obot__class_Obot(tc_fun(_1422731, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422731), _1422735)), -(_1422735 = c_Orderings_Obot__class_Obot(tc_fun(_1422731, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422731, tc_HOL_Obool)), _1422733), _1422735) = c_Orderings_Obot__class_Obot(tc_fun(_1422731, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1422731, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422731, tc_HOL_Obool)), _1422733), _1422735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1422731), c_Big__Operators_Olattice__class_OSup__fin(_1422731, _1422733)), c_Big__Operators_Olattice__class_OSup__fin(_1422731, _1422735)))], (27352 ^ _775828) ^ [_1260797, _1260799, _1260801] : [-(hAPP(c_Set_Oimage(tc_prod(_1260797, _1260799), _1260799, c_Product__Type_Osnd(_1260797, _1260799)), _1260801) = hAPP(c_Relation_ORange(_1260797, _1260799), _1260801))], (13829 ^ _775828) ^ [_1006189, _1006191, _1006193] : [hBOOL(hAPP(_1006189, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006191, _1006193))), 13832 ^ _775828 : [(13857 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006193), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13860 ^ _775828 : [(13861 ^ _775828) ^ [_1006811, _1006813] : [-(hBOOL(hAPP(_1006189, _1006811))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006193), _1006811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006811), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1006191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006193), _1006813)), _1006811)]]], (13839 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006193)), 13842 ^ _775828 : [(13843 ^ _775828) ^ [_1006519, _1006521] : [-(hBOOL(hAPP(_1006189, _1006519))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006519), _1006193)), _1006191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006193), _1006521)), _1006519)]]], (13833 ^ _775828) ^ [] : [_1006193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1006189, _1006191)))]]], (39580 ^ _775828) ^ [_1531832, _1531834, _1531836, _1531838] : [c_Orderings_Obot__class_Obot(tc_fun(_1531832, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531834, tc_fun(_1531832, tc_HOL_Obool)), _1531836), _1531838), 39583 ^ _775828 : [(39584 ^ _775828) ^ [_1531948] : [hBOOL(hAPP(hAPP(c_member(_1531834), _1531948), _1531836)), -(hAPP(_1531838, _1531948) = c_Orderings_Obot__class_Obot(tc_fun(_1531832, tc_HOL_Obool)))]]], (6935 ^ _775828) ^ [_885678, _885680, _885682] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885678), _885680)), _885682) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885680), _885682)))], (47795 ^ _775828) ^ [_1730293, _1730295, _1730297, _1730299, _1730301] : [-(hAPP(hAPP(c_List_Oappend(_1730293), _1730295), _1730297) = hAPP(hAPP(c_List_Olist_OCons(_1730293), _1730299), _1730301)), 47796 ^ _775828 : [(47803 ^ _775828) ^ [_1730476] : [_1730295 = hAPP(hAPP(c_List_Olist_OCons(_1730293), _1730299), _1730476), hAPP(hAPP(c_List_Oappend(_1730293), _1730476), _1730297) = _1730301], (47797 ^ _775828) ^ [] : [_1730295 = c_List_Olist_ONil(_1730293), _1730297 = hAPP(hAPP(c_List_Olist_OCons(_1730293), _1730299), _1730301)]]], (51200 ^ _775828) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (3332 ^ _775828) ^ [_826251, _826253, _826255, _826257, _826259, _826261] : [-(c_Relation_Orel__comp(_826261, _826257, _826253) = c_Relation_Orel__comp(_826259, _826255, _826251)), _826261 = _826259, _826257 = _826255, _826253 = _826251], (38344 ^ _775828) ^ [_1504080, _1504082] : [class_Orderings_Olinorder(_1504080), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1504080, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1504080), _1504082), c_Orderings_Obot__class_Obot(tc_fun(_1504080, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1504080), _1504082)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1504080), _1504082))], (28978 ^ _775828) ^ [_1300050, _1300052] : [c_Wellfounded_Owf(_1300050, _1300052), -(c_Wellfounded_Owf(_1300050, c_Transitive__Closure_Otrancl(_1300050, _1300052)))], (30467 ^ _775828) ^ [_1332627, _1332629, _1332631] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332627), _1332629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332627, tc_HOL_Obool)), _1332631), _1332629)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332627), _1332631)))], (15382 ^ _775828) ^ [_1034297, _1034299] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034297), _1034299)), _1034297) = _1034299)], (51220 ^ _775828) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (9637 ^ _775828) ^ [_930814] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _930814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _930814), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19086 ^ _775828) ^ [_1104531, _1104533, _1104535] : [class_Int_Onumber__ring(_1104531), 19089 ^ _775828 : [(19096 ^ _775828) ^ [] : [c_Int_Oiszero(_1104531, hAPP(c_Int_Onumber__class_Onumber__of(_1104531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1104533), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1104535)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1104531), _1104533) = hAPP(c_Int_Onumber__class_Onumber__of(_1104531), _1104535))], (19090 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1104531), _1104533) = hAPP(c_Int_Onumber__class_Onumber__of(_1104531), _1104535), -(c_Int_Oiszero(_1104531, hAPP(c_Int_Onumber__class_Onumber__of(_1104531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1104533), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1104535)))))]]], (8457 ^ _775828) ^ [_911578] : [hBOOL(hAPP(_911578, 8458 ^ [_911578])), 8461 ^ _775828 : [(8462 ^ _775828) ^ [_911672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911672)), -(hBOOL(hAPP(_911578, hAPP(c_Int_Onat, _911672))))]]], (29273 ^ _775828) ^ [_1306668, _1306670, _1306672, _1306674, _1306676] : [hBOOL(hAPP(hAPP(c_member(_1306668), _1306670), _1306672)), -(hAPP(c_Set_Oimage(_1306668, _1306674, hAPP(c_COMBK(_1306674, _1306668), _1306676)), _1306672) = hAPP(hAPP(c_Set_Oinsert(_1306674), _1306676), c_Orderings_Obot__class_Obot(tc_fun(_1306674, tc_HOL_Obool))))], (36565 ^ _775828) ^ [_1462963] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1462963))))], (48950 ^ _775828) ^ [_1758358, _1758360, _1758362] : [c_Equiv__Relations_Oequiv(_1758358, _1758360, _1758362), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1758358), c_List_Olists(_1758358, _1758360), c_List_Olistrel(_1758358, _1758362)))], (27573 ^ _775828) ^ [_1265899, _1265901, _1265903, _1265905, _1265907, _1265909] : [hBOOL(hAPP(hAPP(c_member(_1265899), _1265901), c_SetInterval_Oord_OgreaterThanAtMost(_1265899, _1265903, _1265905, _1265907, _1265909))), 27576 ^ _775828 : [(27579 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1265903, _1265901), _1265909)))], (27577 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1265905, _1265907), _1265901)))]]], (50638 ^ _775828) ^ [_1795444, _1795446, _1795448] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795444)), c_List_OtakeWhile(_1795444, _1795446, _1795448))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795444)), _1795448))))], (34287 ^ _775828) ^ [_1414343, _1414345, _1414347] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414343, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414343, tc_HOL_Obool)), _1414345), _1414347)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414343, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414343, tc_HOL_Obool)), _1414345)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414343, tc_HOL_Obool)), _1414347)))], (19590 ^ _775828) ^ [_1112529] : [_1112529 = c_Int_OMin, -(c_Int_OBit1(_1112529) = c_Int_OMin)], (3760 ^ _775828) ^ [_832953, _832955, _832957, _832959] : [-(c_Relation_ODomain(_832959, _832955) = c_Relation_ODomain(_832957, _832953)), _832959 = _832957, _832955 = _832953], (49415 ^ _775828) ^ [_1768129, _1768131, _1768133, _1768135, _1768137, _1768139] : [class_Orderings_Olinorder(_1768129), -(hBOOL(hAPP(_1768131, _1768133))), -(hAPP(c_List_Ofilter(_1768135, _1768131), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1768135, _1768129, _1768137), _1768133), _1768139)) = hAPP(c_List_Ofilter(_1768135, _1768131), _1768139))], (34365 ^ _775828) ^ [_1416074, _1416076, _1416078, _1416080, _1416082] : [class_Orderings_Olinorder(_1416074), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416074, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1416074, _1416076, _1416078)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1416074, _1416080, _1416082)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1416074, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416074), _1416076), _1416080), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416074), _1416078), _1416082)))], (13322 ^ _775828) ^ [_996513, _996515, _996517] : [class_Divides_Osemiring__div(_996513), -(c_Divides_Odiv__class_Omod(_996513, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996513), _996515), _996517), _996517) = c_Divides_Odiv__class_Omod(_996513, _996515, _996517))], (44840 ^ _775828) ^ [_1657959, _1657961, _1657963] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657959, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1657959, tc_HOL_Obool)), _1657961), _1657963)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657959, tc_HOL_Obool)), _1657961), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657959, tc_HOL_Obool), _1657963)))], (31727 ^ _775828) ^ [_1360696, _1360698, _1360700, _1360702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1360696, _1360696)), hAPP(hAPP(c_Product__Type_OPair(_1360696, _1360696), _1360698), _1360700)), c_Transitive__Closure_Ortrancl(_1360696, _1360702))), -(_1360698 = _1360700), 31734 ^ _775828 : [(31737 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360696, _1360696)), hAPP(hAPP(c_Product__Type_OPair(_1360696, _1360696), _1360698), _1360700)), c_Transitive__Closure_Otrancl(_1360696, _1360702))))], (31735 ^ _775828) ^ [] : [_1360698 = _1360700]]], (33093 ^ _775828) ^ [_1388263, _1388265, _1388267, _1388269, _1388271] : [class_Fields_Ofield__inverse__zero(_1388263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388265), _1388267)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388265, _1388263), hAPP(hAPP(c_COMBS(_1388265, _1388263, _1388263), hAPP(hAPP(c_COMBB(_1388263, tc_fun(_1388263, _1388263), _1388265), c_Rings_Oinverse__class_Odivide(_1388263)), _1388269)), _1388271)), _1388267) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388263), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388265, _1388263), _1388269), _1388267)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388265, _1388263), _1388271), _1388267)))], (44503 ^ _775828) ^ [_1650108, _1650110, _1650112, _1650114, _1650116] : [-(_1650108 = c_Orderings_Obot__class_Obot(tc_fun(_1650110, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650110, tc_fun(_1650112, tc_HOL_Obool)), _1650108), hAPP(hAPP(c_COMBB(tc_fun(_1650112, tc_HOL_Obool), tc_fun(_1650112, tc_HOL_Obool), _1650110), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650112, tc_HOL_Obool)), _1650114)), _1650116)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650112, tc_HOL_Obool)), _1650114), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1650110, tc_fun(_1650112, tc_HOL_Obool)), _1650108), _1650116)))], (39882 ^ _775828) ^ [_1539725] : [-(hAPP(c_Int_Onat, _1539725) = 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, _1539725)), 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)))))))], (7763 ^ _775828) ^ [_899784, _899786] : [class_Groups_Olinordered__ab__group__add(_899784), 7766 ^ _775828 : [(7773 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899784), c_Groups_Ozero__class_Ozero(_899784)), _899786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899784), hAPP(c_Groups_Ouminus__class_Ouminus(_899784), _899786)), _899786)))], (7767 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899784), hAPP(c_Groups_Ouminus__class_Ouminus(_899784), _899786)), _899786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899784), c_Groups_Ozero__class_Ozero(_899784)), _899786)))]]], (37230 ^ _775828) ^ [_1477729, _1477731, _1477733, _1477735] : [class_Rings_Osemiring__1(_1477729), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477731, _1477729), hAPP(c_COMBK(_1477729, _1477731), _1477733)), _1477735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1477729), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1477729), hAPP(c_Finite__Set_Ocard(_1477731), _1477735))), _1477733))], (15200 ^ _775828) ^ [_1031066, _1031068, _1031070] : [class_Groups_Ogroup__add(_1031066), 15203 ^ _775828 : [(15210 ^ _775828) ^ [] : [_1031068 = _1031070, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031066), _1031068), _1031070) = c_Groups_Ozero__class_Ozero(_1031066))], (15204 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031066), _1031068), _1031070) = c_Groups_Ozero__class_Ozero(_1031066), -(_1031068 = _1031070)]]], (14828 ^ _775828) ^ [_1023969, _1023971, _1023973] : [-(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), _1023969), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023971), _1023969))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023971, _1023969))), _1023973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023971), _1023973))], (39744 ^ _775828) ^ [_1536647, _1536649, _1536651, _1536653, _1536655] : [-(_1536647 = c_Orderings_Obot__class_Obot(tc_fun(_1536649, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536649, tc_fun(_1536651, tc_HOL_Obool)), _1536647), hAPP(hAPP(c_COMBC(_1536649, tc_fun(_1536651, tc_HOL_Obool), tc_fun(_1536651, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536651, tc_HOL_Obool), tc_fun(tc_fun(_1536651, tc_HOL_Obool), tc_fun(_1536651, tc_HOL_Obool)), _1536649), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536651, tc_HOL_Obool))), _1536653)), _1536655)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536651, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536649, tc_fun(_1536651, tc_HOL_Obool)), _1536647), _1536653)), _1536655))], (946 ^ _775828) ^ [_790253, _790255, _790257, _790259] : [-(c_List_Olinorder__class_Osorted(_790257, _790253)), c_List_Olinorder__class_Osorted(_790259, _790255), _790259 = _790257, _790255 = _790253], (46183 ^ _775828) ^ [_1688973, _1688975, _1688977, _1688979, _1688981] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688973)), _1688975) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688977)), _1688979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688973)), _1688981) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688977)), _1688979), hBOOL(hAPP(c_List_Odistinct(_1688977), _1688979)), c_Map_Omap__of(_1688977, _1688973, hAPP(hAPP(c_List_Ozip(_1688977, _1688973), _1688979), _1688975)) = c_Map_Omap__of(_1688977, _1688973, hAPP(hAPP(c_List_Ozip(_1688977, _1688973), _1688979), _1688981)), -(_1688975 = _1688981)], (16184 ^ _775828) ^ [_1050685, _1050687] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050685, _1050687) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050685, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050687)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11664 ^ _775828) ^ [_967445, _967447] : [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), _967445), _967447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967447)))], (17253 ^ _775828) ^ [_1070919, _1070921, _1070923, _1070925] : [class_Int_Onumber__ring(_1070919), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070919), hAPP(c_Int_Onumber__class_Onumber__of(_1070919), _1070921)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070919), hAPP(c_Int_Onumber__class_Onumber__of(_1070919), _1070923)), _1070925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070919), hAPP(c_Int_Onumber__class_Onumber__of(_1070919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070921), _1070923))), _1070925))], (49006 ^ _775828) ^ [_1759605, _1759607, _1759609] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1759605)), _1759607), c_List_Olists(_1759605, _1759609))), 49009 ^ _775828 : [(49010 ^ _775828) ^ [_1759713] : [hBOOL(hAPP(hAPP(c_member(_1759605), _1759713), hAPP(c_List_Oset(_1759605), _1759607))), -(hBOOL(hAPP(hAPP(c_member(_1759605), _1759713), _1759609)))]]], (35233 ^ _775828) ^ [_1436413, _1436415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436413), _1436415)), -(hAPP(c_Finite__Set_Ocard(_1436413), _1436415) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1436413, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1436413), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436415))], (7479 ^ _775828) ^ [_895199, _895201, _895203] : [class_Groups_Ogroup__add(_895199), 7482 ^ _775828 : [(7489 ^ _775828) ^ [] : [_895203 = hAPP(c_Groups_Ouminus__class_Ouminus(_895199), _895201), -(_895201 = hAPP(c_Groups_Ouminus__class_Ouminus(_895199), _895203))], (7483 ^ _775828) ^ [] : [_895201 = hAPP(c_Groups_Ouminus__class_Ouminus(_895199), _895203), -(_895203 = hAPP(c_Groups_Ouminus__class_Ouminus(_895199), _895201))]]], (15476 ^ _775828) ^ [_1036151, _1036153, _1036155] : [-(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, _1036151, _1036153)), _1036155), _1036153) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036151), _1036155), _1036153))], (14413 ^ _775828) ^ [_1017094, _1017096, _1017098, _1017100] : [c_Com_Ocom_OAss(_1017094, _1017096) = c_Com_Ocom_OWhile(_1017098, _1017100)], (12137 ^ _775828) ^ [_975803, _975805] : [class_Lattices_Oab__semigroup__idem__mult(_975803), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975803), _975805), _975805) = _975805)], (10148 ^ _775828) ^ [_940144, _940146, _940148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940144), _940146)), _940148)), 10151 ^ _775828 : [(10154 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940146), _940148)))], (10152 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940144), _940148)))]]], (9725 ^ _775828) ^ [_932367, _932369, _932371, _932373] : [class_Rings_Olinordered__semiring__strict(_932367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932367), _932369), _932371)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932367), _932369), _932373))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932367), c_Groups_Ozero__class_Ozero(_932367)), _932369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932367), _932371), _932373)))], (38562 ^ _775828) ^ [_1509101, _1509103, _1509105, _1509107, _1509109] : [c_Equiv__Relations_Oequiv(_1509101, _1509103, _1509105), hBOOL(hAPP(hAPP(c_member(_1509101), _1509107), _1509103)), hBOOL(hAPP(hAPP(c_member(_1509101), _1509109), _1509103)), 38573 ^ _775828 : [(38580 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509101, _1509101)), hAPP(hAPP(c_Product__Type_OPair(_1509101, _1509101), _1509107), _1509109)), _1509105)), -(hAPP(c_Relation_OImage(_1509101, _1509101, _1509105), hAPP(hAPP(c_Set_Oinsert(_1509101), _1509107), c_Orderings_Obot__class_Obot(tc_fun(_1509101, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509101, _1509101, _1509105), hAPP(hAPP(c_Set_Oinsert(_1509101), _1509109), c_Orderings_Obot__class_Obot(tc_fun(_1509101, tc_HOL_Obool)))))], (38574 ^ _775828) ^ [] : [hAPP(c_Relation_OImage(_1509101, _1509101, _1509105), hAPP(hAPP(c_Set_Oinsert(_1509101), _1509107), c_Orderings_Obot__class_Obot(tc_fun(_1509101, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509101, _1509101, _1509105), hAPP(hAPP(c_Set_Oinsert(_1509101), _1509109), c_Orderings_Obot__class_Obot(tc_fun(_1509101, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509101, _1509101)), hAPP(hAPP(c_Product__Type_OPair(_1509101, _1509101), _1509107), _1509109)), _1509105)))]]], (33687 ^ _775828) ^ [_1401357, _1401359, _1401361, _1401363] : [hBOOL(hAPP(hAPP(c_member(_1401357), _1401359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401357, tc_HOL_Obool)), _1401361), _1401363))), -(hBOOL(hAPP(hAPP(c_member(_1401357), _1401359), _1401361)))], (46462 ^ _775828) ^ [_1697907, _1697909, _1697911, _1697913, _1697915] : [hAPP(hAPP(c_List_Olist_OCons(_1697907), _1697909), _1697911) = hAPP(hAPP(c_List_Olist_OCons(_1697907), _1697913), _1697915), 46465 ^ _775828 : [(46468 ^ _775828) ^ [] : [-(_1697911 = _1697915)], (46466 ^ _775828) ^ [] : [-(_1697909 = _1697913)]]], (12715 ^ _775828) ^ [_985774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985774)), -(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)), _985774))))], (18645 ^ _775828) ^ [_1096198, _1096200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096198), _1096200)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1096198), _1096200) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18223 ^ _775828) ^ [_1088663, _1088665] : [class_Int_Onumber__ring(_1088663), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088663), c_Int_Osucc(_1088665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088663), c_Groups_Oone__class_Oone(_1088663)), hAPP(c_Int_Onumber__class_Onumber__of(_1088663), _1088665)))], (33479 ^ _775828) ^ [_1396925, _1396927, _1396929] : [class_Orderings_Olinorder(_1396925), hAPP(_1396927, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396925), 33484 ^ [_1396925, _1396927, _1396929]), 33485 ^ [_1396925, _1396927, _1396929])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396925), hAPP(_1396927, 33484 ^ [_1396925, _1396927, _1396929])), hAPP(_1396927, 33485 ^ [_1396925, _1396927, _1396929])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396925), _1396929)), -(_1396929 = c_Orderings_Obot__class_Obot(tc_fun(_1396925, tc_HOL_Obool))), -(hAPP(_1396927, c_Big__Operators_Olinorder__class_OMin(_1396925, _1396929)) = c_Big__Operators_Olinorder__class_OMin(_1396925, hAPP(c_Set_Oimage(_1396925, _1396925, _1396927), _1396929)))], (23710 ^ _775828) ^ [_1191045, _1191047, _1191049, _1191051] : [class_Orderings_Olinorder(_1191045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191045), _1191047), _1191049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191045), _1191047), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191045), _1191051), _1191049))))], (35783 ^ _775828) ^ [_1447821, _1447823, _1447825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447821)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1447823), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1447825)), 35793 ^ _775828 : [(35799 ^ _775828) ^ [] : [-(_1447823 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35795 ^ [_1447821, _1447823, _1447825]), 35792 ^ [_1447821, _1447823, _1447825]))], (35797 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35795 ^ [_1447821, _1447823, _1447825]), _1447825)))], (35794 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35792 ^ [_1447821, _1447823, _1447825]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1447821))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1447823), _1447821) = _1447823)], (1630 ^ _775828) ^ [_798821, _798823] : [-(class_Groups_Omonoid__mult(_798821)), _798823 = _798821, class_Groups_Omonoid__mult(_798823)], (15636 ^ _775828) ^ [_1039259, _1039261, _1039263] : [class_Groups_Ogroup__add(_1039259), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039259), _1039261), _1039263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), _1039261), hAPP(c_Groups_Ouminus__class_Ouminus(_1039259), _1039263)))], (38073 ^ _775828) ^ [_1497829, _1497831, _1497833, _1497835, _1497837] : [hBOOL(hAPP(hAPP(c_member(_1497829), _1497831), hAPP(c_Relation_OImage(_1497833, _1497829, _1497835), _1497837))), 38077 ^ _775828 : [(38080 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497833, _1497829)), hAPP(hAPP(c_Product__Type_OPair(_1497833, _1497829), 38076 ^ [_1497829, _1497831, _1497833, _1497835, _1497837]), _1497831)), _1497835)))], (38078 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497833), 38076 ^ [_1497829, _1497831, _1497833, _1497835, _1497837]), _1497837)))]]], (8839 ^ _775828) ^ [_917329, _917331, _917333] : [class_Orderings_Oorder(_917329), 8842 ^ _775828 : [(8843 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917329), _917331), _917333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917329), _917331), _917333))), -(_917331 = _917333)], (8853 ^ _775828) ^ [] : [8854 ^ _775828 : [(8857 ^ _775828) ^ [] : [_917331 = _917333], (8855 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917329), _917331), _917333))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917329), _917331), _917333)))]]], (44024 ^ _775828) ^ [_1636688, _1636690, _1636692, _1636694, _1636696, _1636698] : [c_Finite__Set_Ofun__left__comm(_1636688, _1636690, _1636692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636688), _1636694)), -(hBOOL(hAPP(hAPP(c_member(_1636688), _1636696), _1636694))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1636688, _1636690, _1636692), _1636698), hAPP(hAPP(c_Set_Oinsert(_1636688), _1636696), _1636694)) = hAPP(hAPP(c_Finite__Set_Ofold(_1636688, _1636690, _1636692), hAPP(hAPP(_1636692, _1636696), _1636698)), _1636694))], (3960 ^ _775828) ^ [_836145, _836147, _836149, _836151, _836153, _836155, _836157, _836159, _836161, _836163, _836165, _836167] : [-(c_Product__Type_Omap__pair(_836167, _836163, _836159, _836155, _836151, _836147) = c_Product__Type_Omap__pair(_836165, _836161, _836157, _836153, _836149, _836145)), _836167 = _836165, _836163 = _836161, _836159 = _836157, _836155 = _836153, _836151 = _836149, _836147 = _836145], (5565 ^ _775828) ^ [_864010, _864012] : [_864010 = _864012, -(hAPP(c_Nat_OSuc, _864010) = hAPP(c_Nat_OSuc, _864012))], (35633 ^ _775828) ^ [_1445019, _1445021, _1445023, _1445025, _1445027] : [class_Orderings_Oorder(_1445019), 35636 ^ _775828 : [(35657 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1445019, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1445019, _1445021, _1445023)), c_SetInterval_Oord__class_OatLeastAtMost(_1445019, _1445025, _1445027)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445025), _1445027)), 35660 ^ _775828 : [(35663 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445025), _1445021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445023), _1445027)), 35670 ^ _775828 : [(35673 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445019), _1445023), _1445027))], (35671 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445019), _1445025), _1445021))]]], (35661 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445021), _1445023)))]]], (35637 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1445019, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1445019, _1445021, _1445023)), c_SetInterval_Oord__class_OatLeastAtMost(_1445019, _1445025, _1445027))), 35640 ^ _775828 : [(35641 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445021), _1445023)), 35644 ^ _775828 : [(35649 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445019), _1445025), _1445021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445019), _1445023), _1445027)))], (35647 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445023), _1445027)))], (35645 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445025), _1445021)))]]], (35655 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445019), _1445025), _1445027)))]]]]], (45708 ^ _775828) ^ [_1677628, _1677630, _1677632, _1677634] : [-(hAPP(hAPP(c_Option_Omap(_1677628, _1677630), _1677632), hAPP(c_Option_Ooption_OSome(_1677628), _1677634)) = hAPP(c_Option_Ooption_OSome(_1677630), hAPP(_1677632, _1677634)))], (41314 ^ _775828) ^ [_1573615, _1573617, _1573619, _1573621, _1573623, _1573625] : [class_Groups_Ocomm__monoid__add(_1573615), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1573617, _1573615), hAPP(hAPP(c_COMBC(_1573617, tc_fun(_1573619, tc_HOL_Obool), _1573615), hAPP(hAPP(c_COMBB(tc_fun(_1573619, _1573615), tc_fun(tc_fun(_1573619, tc_HOL_Obool), _1573615), _1573617), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1573619, _1573615)), _1573621)), _1573623)), _1573625) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1573617, _1573619), _1573615), hAPP(c_Product__Type_Oprod_Oprod__case(_1573617, _1573619, _1573615), _1573621)), hAPP(hAPP(c_Product__Type_OSigma(_1573617, _1573619), _1573625), hAPP(c_COMBK(tc_fun(_1573619, tc_HOL_Obool), _1573617), _1573623))))], (42085 ^ _775828) ^ [_1592476, _1592478] : [-(c_Product__Type_Omap__pair(_1592476, _1592476, _1592478, _1592478, c_Fun_Oid(_1592476), c_Fun_Oid(_1592478)) = c_Fun_Oid(tc_prod(_1592476, _1592478)))], (4854 ^ _775828) ^ [_850016, _850018] : [_850018 = _850016, -(c_List_Otranspose__rel(_850018) = c_List_Otranspose__rel(_850016))], (47343 ^ _775828) ^ [_1720252, _1720254, _1720256, _1720258] : [class_Orderings_Olinorder(_1720252), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720254, _1720252, _1720256), _1720258), c_List_Olist_ONil(_1720254)) = hAPP(hAPP(c_List_Olist_OCons(_1720254), _1720258), c_List_Olist_ONil(_1720254)))], (17429 ^ _775828) ^ [_1074331, _1074333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1074331), _1074333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074333))))], (40790 ^ _775828) ^ [_1560173, _1560175, _1560177, _1560179, _1560181] : [-(hAPP(c_Set_Ovimage(_1560173, _1560175, _1560177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1560175, tc_HOL_Obool)), _1560179), _1560181)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1560173, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1560173, _1560175, _1560177), _1560179)), hAPP(c_Set_Ovimage(_1560173, _1560175, _1560177), _1560181)))], (29591 ^ _775828) ^ [_1312928, _1312930, _1312932] : [hAPP(c_Relation_ODomain(_1312928, _1312930), _1312932) = c_Orderings_Obot__class_Obot(tc_fun(_1312928, tc_HOL_Obool)), -(_1312932 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1312928, _1312930), tc_HOL_Obool)))], (50419 ^ _775828) ^ [_1789259, _1789261, _1789263, _1789265, _1789267] : [-(c_List_Ofoldr(_1789259, _1789261, _1789263, _1789265, _1789267) = hAPP(c_List_Ofoldl(_1789261, _1789259, hAPP(c_COMBC(_1789259, _1789261, _1789261), _1789263), _1789267), hAPP(c_List_Orev(_1789259), _1789265)))], (20470 ^ _775828) ^ [_1127574] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127574), 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), _1127574), _1127574))], (51524 ^ _775828) ^ [_1808445, _1808447] : [hBOOL(hAPP(hAPP(c_fequal, _1808445), _1808447)), -(_1808445 = _1808447)], (36791 ^ _775828) ^ [_1466920, _1466922] : [class_Orderings_Oorder(_1466920), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1466920, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1466920), _1466922), c_Orderings_Obot__class_Obot(tc_fun(_1466920, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1466920), _1466922)) = hAPP(hAPP(c_Set_Oinsert(_1466920), _1466922), c_Orderings_Obot__class_Obot(tc_fun(_1466920, tc_HOL_Obool))))], (24598 ^ _775828) ^ [_1208051, _1208053, _1208055, _1208057] : [hBOOL(hAPP(hAPP(c_member(_1208051), _1208053), c_Wellfounded_Oacc(_1208051, _1208055))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1208051, _1208051)), hAPP(hAPP(c_Product__Type_OPair(_1208051, _1208051), _1208057), _1208053)), _1208055)), -(hBOOL(hAPP(hAPP(c_member(_1208051), _1208057), c_Wellfounded_Oacc(_1208051, _1208055))))], (36371 ^ _775828) ^ [_1458782, _1458784, _1458786, _1458788, _1458790] : [class_Orderings_Olinorder(_1458782), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458782, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458782, _1458784), _1458786)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458782, _1458788), _1458790)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458782, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1458782), _1458784), _1458788)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1458782), _1458786), _1458790)))], (3602 ^ _775828) ^ [_830572, _830574, _830576, _830578, _830580, _830582, _830584, _830586] : [-(c_New__Random__Sequence_Oneg__bind(_830586, _830582, _830578, _830574) = c_New__Random__Sequence_Oneg__bind(_830584, _830580, _830576, _830572)), _830586 = _830584, _830582 = _830580, _830578 = _830576, _830574 = _830572], (25625 ^ _775828) ^ [_1228866, _1228868, _1228870, _1228872] : [class_Rings_Ocomm__ring__1(_1228866), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228866), _1228868), _1228870)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228866), _1228868), _1228872)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228866), _1228868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228866), _1228870), _1228872))))], (47433 ^ _775828) ^ [_1722031, _1722033] : [hAPP(c_List_Oset(_1722031), _1722033) = c_Orderings_Obot__class_Obot(tc_fun(_1722031, tc_HOL_Obool)), -(_1722033 = c_List_Olist_ONil(_1722031))], (37849 ^ _775828) ^ [_1493059, _1493061, _1493063, _1493065, _1493067] : [class_Groups_Ocomm__monoid__add(_1493059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493061), _1493063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493061, tc_HOL_Obool)), _1493065), _1493063)), 37863 ^ _775828 : [(37866 ^ _775828) ^ [] : [hAPP(_1493067, 37862 ^ [_1493059, _1493061, _1493063, _1493065, _1493067]) = c_Groups_Ozero__class_Ozero(_1493059)], (37864 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493061), 37862 ^ [_1493059, _1493061, _1493063, _1493065, _1493067]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493061, tc_HOL_Obool)), _1493063), _1493065))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493061, _1493059), _1493067), _1493065) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493061, _1493059), _1493067), _1493063))], (32933 ^ _775828) ^ [_1385344, _1385346, _1385348, _1385350] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1385344), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385346, tc_Int_Oint), _1385348), _1385350)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385346, _1385344), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1385344, _1385346), c_Int_Oring__1__class_Oof__int(_1385344)), _1385348)), _1385350)), class_Groups_Ocomm__monoid__mult(_1385344), class_Rings_Oring__1(_1385344)], (4178 ^ _775828) ^ [_839662, _839664, _839666, _839668, _839670, _839672] : [-(c_Map_Odom(_839672, _839668, _839664) = c_Map_Odom(_839670, _839666, _839662)), _839672 = _839670, _839668 = _839666, _839664 = _839662], (10696 ^ _775828) ^ [_950619] : [class_Rings_Ozero__neq__one(_950619), c_Groups_Oone__class_Oone(_950619) = c_Groups_Ozero__class_Ozero(_950619)], (15684 ^ _775828) ^ [_1040177, _1040179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040179), _1040177)), _1040179)))], (43990 ^ _775828) ^ [_1636066, _1636068, _1636070, _1636072, _1636074, _1636076] : [c_Finite__Set_Ofun__left__comm(_1636066, _1636068, _1636070), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1636066, _1636068, _1636070, _1636072, _1636074), _1636076)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1636066, _1636068, _1636070), _1636072), _1636074) = _1636076)], (1906 ^ _775828) ^ [_803418, _803420, _803422, _803424] : [-(c_SMT_Oz3mod(_803424, _803420) = c_SMT_Oz3mod(_803422, _803418)), _803424 = _803422, _803420 = _803418], (15380 ^ _775828) ^ [_1034260, _1034262] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034260), _1034262)), _1034262) = _1034260)], (47335 ^ _775828) ^ [_1720003, _1720005, _1720007, _1720009, _1720011, _1720013, _1720015] : [-(hAPP(hAPP(c_List_Ozip(_1720003, _1720005), hAPP(hAPP(c_List_Olist__update(_1720003, _1720007), _1720009), _1720011)), hAPP(hAPP(c_List_Olist__update(_1720005, _1720013), _1720009), _1720015)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1720003, _1720005), hAPP(hAPP(c_List_Ozip(_1720003, _1720005), _1720007), _1720013)), _1720009), hAPP(hAPP(c_Product__Type_OPair(_1720003, _1720005), _1720011), _1720015)))], (6101 ^ _775828) ^ [_872729, _872731] : [6102 ^ _775828 : [(6105 ^ _775828) ^ [] : [_872729 = _872731], (6103 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872729), _872731))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872729), hAPP(c_Nat_OSuc, _872731))))], (25465 ^ _775828) ^ [_1225004, _1225006] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1225004), _1225006) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1225004)), hAPP(c_Code__Numeral_Onat__of, _1225006))))], (20318 ^ _775828) ^ [_1124920, _1124922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124920), _1124922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1124920)), c_Int_OBit1(_1124922))))], (2278 ^ _775828) ^ [_809150, _809152, _809154, _809156] : [-(c_HOL_OLet(_809156, _809152) = c_HOL_OLet(_809154, _809150)), _809156 = _809154, _809152 = _809150], (21236 ^ _775828) ^ [_1143769, _1143771, _1143773, _1143775] : 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[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _901862), _901866)))], (7889 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901864)))]]], (33561 ^ _775828) ^ [_1398633, _1398635, _1398637] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1398633, _1398633), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1398633, _1398633), _1398635)), c_Transitive__Closure_Ortrancl(_1398633, _1398635)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1398633, _1398633), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1398633, _1398633)), hAPP(hAPP(c_Product__Type_OPair(_1398633, _1398633), _1398637), _1398637)), c_Transitive__Closure_Otrancl(_1398633, _1398635)))], (40690 ^ _775828) ^ [] : [-(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))))], (26295 ^ 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_1386380), _1386006)), hAPP(_1386008, _1386380) = c_Groups_Ozero__class_Ozero(_1386002)]]], (32977 ^ _775828) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386004, _1386002), _1386008), _1386006) = c_Groups_Ozero__class_Ozero(_1386002), 32981 ^ _775828 : [(32984 ^ _775828) ^ [] : [-(hAPP(_1386008, 32980 ^ [_1386002, _1386004, _1386006, _1386008]) = c_Groups_Ozero__class_Ozero(_1386002))], (32982 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386004), 32980 ^ [_1386002, _1386004, _1386006, _1386008]), _1386006)))]]]]], (35351 ^ _775828) ^ [_1439149, _1439151] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1439149, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1439149, tc_HOL_Obool))), hAPP(c_Set_OPow(_1439149), _1439151))))], (6963 ^ _775828) ^ [_886179, _886181, _886183] : [class_Rings_Ono__zero__divisors(_886179), -(_886181 = c_Groups_Ozero__class_Ozero(_886179)), -(_886183 = c_Groups_Ozero__class_Ozero(_886179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886179), _886181), _886183) = c_Groups_Ozero__class_Ozero(_886179)], (36713 ^ _775828) ^ [_1465580, _1465582, _1465584, _1465586] : [c_Finite__Set_Ofolding__one__idem(_1465580, _1465582, _1465584), -(hAPP(hAPP(_1465582, _1465586), _1465586) = _1465586)], (11114 ^ _775828) ^ [_957845, _957847, _957849, _957851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957845, tc_HOL_Obool)), _957847), _957849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957845, tc_HOL_Obool)), _957849), _957851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957845, tc_HOL_Obool)), _957847), _957851)))], (4844 ^ _775828) ^ [_849867, _849869, _849871, _849873] : [-(c_Wellfounded_Oaccp(_849873, _849869) = c_Wellfounded_Oaccp(_849871, _849867)), _849873 = _849871, _849869 = _849867], (30420 ^ _775828) ^ [_1331754] : [30422 ^ _775828 : [(30425 ^ _775828) ^ [_1331864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30421 ^ [_1331754, _1331864]), _1331864))], (30423 ^ _775828) ^ [_1331830] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30421 ^ [_1331754, _1331830]), _1331754)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331754)))], (9985 ^ _775828) ^ [_937161, _937163, _937165] : [-(c_Option_Ooption_Ooption__size(_937161, _937163, hAPP(c_Option_Ooption_OSome(_937161), _937165)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_937163, _937165)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6606 ^ _775828) ^ [_880853, _880855, _880857] : [class_Orderings_Olinorder(_880853), -(_880855 = _880857), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880853), _880855), _880857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880853), _880857), _880855)))], (29189 ^ _775828) ^ [_1304925, _1304927, _1304929] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304925, tc_HOL_Obool)), _1304927), _1304929) = c_Orderings_Obot__class_Obot(tc_fun(_1304925, tc_HOL_Obool)), 29192 ^ _775828 : [(29195 ^ _775828) ^ [] : [-(_1304929 = c_Orderings_Obot__class_Obot(tc_fun(_1304925, tc_HOL_Obool)))], (29193 ^ _775828) ^ [] : [-(_1304927 = c_Orderings_Obot__class_Obot(tc_fun(_1304925, tc_HOL_Obool)))]]], (37058 ^ _775828) ^ [_1473551, _1473553, _1473555] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473551), _1473553)), 37061 ^ _775828 : [(37081 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473551, tc_Nat_Onat), _1473555), _1473553) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 37082 ^ _775828 : [(37083 ^ _775828) ^ [_1474032] : [hBOOL(hAPP(hAPP(c_member(_1473551), _1474032), _1473553)), hAPP(_1473555, _1474032) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37091 ^ _775828 : [(37096 ^ _775828) ^ [] : [hAPP(_1473555, 37090 ^ [_1473551, _1473553, _1473555, _1474032]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37094 ^ _775828) ^ [] : [_1474032 = 37090 ^ [_1473551, _1473553, _1473555, _1474032]], (37092 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473551), 37090 ^ [_1473551, _1473553, _1473555, _1474032]), _1473553)))]]]]], (37062 ^ _775828) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473551, tc_Nat_Onat), _1473555), _1473553) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37066 ^ _775828 : [(37071 ^ _775828) ^ [_1473871] : [hBOOL(hAPP(hAPP(c_member(_1473551), _1473871), _1473553)), -(37065 ^ [_1473551, _1473553, _1473555] = _1473871), -(hAPP(_1473555, _1473871) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37069 ^ _775828) ^ [] : [-(hAPP(_1473555, 37065 ^ [_1473551, _1473553, _1473555]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37067 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473551), 37065 ^ [_1473551, _1473553, _1473555]), _1473553)))]]]]], (24827 ^ _775828) ^ [_1212731, _1212733, _1212735] : [-(c_Product__Type_Ointernal__split(_1212731, _1212733, _1212735) = c_Product__Type_Oprod_Oprod__case(_1212731, _1212733, _1212735))], (30093 ^ _775828) ^ [_1324288, _1324290] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1324288), _1324290)), -(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)))), _1324290, _1324288) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (43962 ^ _775828) ^ [_1635492, _1635494, _1635496, _1635498, _1635500, _1635502] : [c_Finite__Set_Ofun__left__comm(_1635492, _1635494, _1635496), -(hAPP(hAPP(_1635496, _1635498), hAPP(hAPP(_1635496, _1635500), _1635502)) = hAPP(hAPP(_1635496, _1635500), hAPP(hAPP(_1635496, _1635498), _1635502)))], (7013 ^ _775828) ^ [_886927, _886929, _886931, _886933] : [class_Rings_Olinordered__ring__strict(_886927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886927), _886929), _886931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886927), _886933), c_Groups_Ozero__class_Ozero(_886927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886927), _886933), _886931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886927), _886933), _886929))))], (4398 ^ _775828) ^ [_842988, _842990, _842992, _842994] : [-(c_List_Olistrel(_842994, _842990) = c_List_Olistrel(_842992, _842988)), _842994 = _842992, _842990 = _842988], (40756 ^ _775828) ^ [_1559395, _1559397, _1559399, _1559401] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559395, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1559397, _1559395, _1559399), hAPP(c_Set_Ovimage(_1559397, _1559395, _1559399), _1559401))), _1559401)))], (14974 ^ _775828) ^ [_1026910, _1026912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026912)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1026910, _1026912)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1026910), hAPP(c_Int_Onat, _1026912)))], (45991 ^ _775828) ^ [_1683863, _1683865, _1683867] : [class_Orderings_Olinorder(_1683863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1683863), _1683865)), -(c_List_Olinorder__class_Osorted__list__of__set(_1683863, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1683863, tc_HOL_Obool)), _1683865), hAPP(hAPP(c_Set_Oinsert(_1683863), _1683867), c_Orderings_Obot__class_Obot(tc_fun(_1683863, tc_HOL_Obool))))) = c_List_Oremove1(_1683863, _1683867, c_List_Olinorder__class_Osorted__list__of__set(_1683863, _1683865)))], (28269 ^ _775828) ^ [_1282789, _1282791, _1282793, _1282795] : [class_Lattices_Olattice(_1282789), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282789), _1282791), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282789), _1282793), _1282795)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282789), _1282793), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282789), _1282791), _1282795)))], (15668 ^ _775828) ^ [_1039810, _1039812, _1039814] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039810), _1039812)), _1039814) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039810), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039812), _1039814))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039810), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1039812, _1039814))), _1039814)))], (27206 ^ _775828) ^ [_1257215, _1257217, _1257219] : [hBOOL(hAPP(_1257215, _1257217)), -(hBOOL(hAPP(hAPP(c_member(_1257219), _1257217), hAPP(c_Set_OCollect(_1257219), _1257215))))], (17707 ^ _775828) ^ [_1078960, _1078962, _1078964] : [class_Groups_Omonoid__mult(_1078960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078960), hAPP(hAPP(c_Power_Opower__class_Opower(_1078960), _1078962), _1078964)), _1078962) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078960), _1078962), hAPP(hAPP(c_Power_Opower__class_Opower(_1078960), _1078962), _1078964)))], (33376 ^ _775828) ^ [_1394447, _1394449, _1394451, _1394453] : [-(hAPP(c_Map_Orestrict__map(_1394447, _1394449, _1394451, c_Orderings_Obot__class_Obot(tc_fun(_1394447, tc_HOL_Obool))), _1394453) = c_Option_Ooption_ONone(_1394449))], (13148 ^ _775828) ^ [_993276, _993278, _993280] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_993276, _993278, _993280))), 13151 ^ _775828 : [(13154 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _993280)))], (13152 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _993278)))]]], (10076 ^ _775828) ^ [_938862, _938864, _938866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938864), _938866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938862), _938864)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938862), _938866))))], (14528 ^ _775828) ^ [_1019033, _1019035, _1019037] : [-(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), _1019033), _1019035)), _1019037), _1019035) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019037, _1019035))], (40199 ^ _775828) ^ [_1546412, _1546414, _1546416, _1546418] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1546412, _1546414, _1546416), _1546418)), _1546416 = c_Orderings_Obot__class_Obot(tc_fun(_1546412, tc_HOL_Obool))], (24905 ^ _775828) ^ [_1214418, _1214420] : [_1214418 = _1214420, -(c_Random_Oinc__shift(_1214418, _1214420) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (44928 ^ _775828) ^ [_1659890, _1659892, _1659894] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1659890, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659890, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1659890, tc_HOL_Obool), _1659892)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1659890, tc_HOL_Obool), _1659894))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1659890, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1659890, tc_HOL_Obool), tc_HOL_Obool)), _1659892), _1659894)))))], (24280 ^ _775828) ^ [_1201690, _1201692] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1201690)), hAPP(c_Nat_OSuc, _1201692)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1201690), _1201692)))], (22612 ^ _775828) ^ [_1169266, _1169268, _1169270] : [class_Fields_Olinordered__field(_1169266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169266), _1169268), c_Groups_Ozero__class_Ozero(_1169266))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169266), c_Groups_Ozero__class_Ozero(_1169266)), _1169270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169266), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169266), _1169268), _1169270)), c_Groups_Ozero__class_Ozero(_1169266))))], (5859 ^ _775828) ^ [_869136, _869138, _869140] : [5860 ^ _775828 : [(5863 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_869140, _869138), _869136))], (5861 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869136), _869138)))]], 5866 ^ _775828 : [(5869 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_869140, _869138), _869136))], (5867 ^ _775828) ^ [] : [-(_869136 = _869138)]], 5872 ^ _775828 : [(5875 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_869140, _869138), _869136))], (5873 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869138), _869136)))]], -(hBOOL(hAPP(hAPP(_869140, _869138), _869136)))], (28994 ^ _775828) ^ [_1300348, _1300350] : [-(hAPP(c_Relation_ODomain(_1300348, _1300348), c_Transitive__Closure_Otrancl(_1300348, _1300350)) = hAPP(c_Relation_ODomain(_1300348, _1300348), _1300350))], (51458 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (18215 ^ _775828) ^ [_1088517] : [-(c_Int_Osucc(_1088517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088517), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32783 ^ _775828) ^ [_1382011, _1382013, _1382015, _1382017] : [-(c_Sum__Type_OPlus(_1382011, _1382013, _1382015, _1382017) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1382011, _1382013), tc_HOL_Obool))), _1382015 = c_Orderings_Obot__class_Obot(tc_fun(_1382011, tc_HOL_Obool)), _1382017 = c_Orderings_Obot__class_Obot(tc_fun(_1382013, tc_HOL_Obool))], (33791 ^ _775828) ^ [_1403572, _1403574, _1403576, _1403578] : [class_Lattices_Olattice(_1403572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403572), _1403574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403572), _1403576), _1403578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403572), _1403576), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403572), _1403574), _1403578)))], (4118 ^ _775828) ^ [_838690, _838692, _838694, _838696, _838698, _838700, _838702, _838704] : [-(c_Lazy__Sequence_Oanamorph(_838704, _838700, _838696, _838692) = c_Lazy__Sequence_Oanamorph(_838702, _838698, _838694, _838690)), _838704 = _838702, _838700 = _838698, _838696 = _838694, _838692 = _838690], (1120 ^ _775828) ^ [_792446, _792448] : [-(class_Divides_Oring__div(_792446)), _792448 = _792446, class_Divides_Oring__div(_792448)], (51368 ^ _775828) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (21129 ^ _775828) ^ [_1141561, _1141563, _1141565] : [21131 ^ _775828 : [(21134 ^ _775828) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1141561, _1141563), 21130 ^ [_1141561, _1141563, _1141565]))], (21132 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1141563, 21130 ^ [_1141561, _1141563, _1141565]), _1141565)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1141561, _1141563), _1141565)))], (35371 ^ _775828) ^ [_1439597, _1439599] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1439597, tc_HOL_Obool)), _1439599), hAPP(c_Set_OPow(_1439597), _1439599))))], (12538 ^ _775828) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25060 ^ _775828) ^ [_1218000, _1218002] : [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)), _1218000)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218002))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1218000), _1218002)))], (41336 ^ _775828) ^ [_1574576, _1574578, _1574580] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1574576, _1574578), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1574576, _1574578), c_Orderings_Otop__class_Otop(tc_fun(_1574576, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1574578, tc_HOL_Obool), _1574576), _1574580))) = hAPP(hAPP(c_Product__Type_OSigma(_1574576, _1574578), c_Orderings_Otop__class_Otop(tc_fun(_1574576, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1574578, tc_HOL_Obool), _1574576), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1574578, tc_HOL_Obool)), _1574580))))], (4014 ^ _775828) ^ [_837080, _837082] : [_837082 = _837080, -(c_Groups_Oabs__class_Oabs(_837082) = c_Groups_Oabs__class_Oabs(_837080))], (28307 ^ _775828) ^ [_1283677, _1283679, _1283681] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283677, tc_HOL_Obool)), _1283679), _1283681) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283677, tc_HOL_Obool)), _1283681), _1283679))], (44178 ^ _775828) ^ [_1640603, _1640605, _1640607, _1640609, _1640611, _1640613] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640605, _1640607)), hAPP(hAPP(c_Product__Type_OPair(_1640605, _1640607), _1640611), _1640613)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640603, tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1640603, tc_HOL_Obool))), _1640609))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640603, tc_fun(_1640605, tc_fun(_1640607, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1640603, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_fun(_1640605, tc_fun(_1640607, tc_HOL_Obool)), _1640603), hAPP(c_COMBC(_1640605, tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_fun(_1640607, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640607, tc_fun(tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_fun(_1640607, tc_HOL_Obool)), _1640605), c_COMBC(_1640607, tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640607, tc_prod(_1640605, _1640607)), tc_fun(_1640607, tc_fun(tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_HOL_Obool)), _1640605), hAPP(c_COMBB(tc_prod(_1640605, _1640607), tc_fun(tc_fun(tc_prod(_1640605, _1640607), tc_HOL_Obool), tc_HOL_Obool), _1640607), c_member(tc_prod(_1640605, _1640607)))), c_Product__Type_OPair(_1640605, _1640607))))), _1640609)), _1640611), _1640613)))], (27188 ^ _775828) ^ [_1256392, _1256394, _1256396] : [27190 ^ _775828 : [(27191 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1256392), 27189 ^ [_1256392, _1256394, _1256396]), _1256394)))], (27196 ^ _775828) ^ [] : [27189 ^ [_1256392, _1256394, _1256396] = 27192 ^ [_1256392, _1256394, _1256396]], (27200 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1256392, _1256392)), hAPP(hAPP(c_Product__Type_OPair(_1256392, _1256392), 27192 ^ [_1256392, _1256394, _1256396]), 27189 ^ [_1256392, _1256394, _1256396])), _1256396))], (27198 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1256392, _1256392)), hAPP(hAPP(c_Product__Type_OPair(_1256392, _1256392), 27189 ^ [_1256392, _1256394, _1256396]), 27192 ^ [_1256392, _1256394, _1256396])), _1256396))], (27194 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1256392), 27192 ^ [_1256392, _1256394, _1256396]), _1256394)))]], -(c_Relation_Ototal__on(_1256392, _1256394, _1256396))], (38214 ^ _775828) ^ [_1501425, _1501427, _1501429, _1501431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501425), _1501431)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501429), _1501427))), -(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), _1501425), _1501427)), 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), _1501429), _1501431)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (9307 ^ _775828) ^ [_924972, _924974, _924976, _924978] : [class_Rings_Oordered__ring(_924972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), _924974), _924976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), _924978), c_Groups_Ozero__class_Ozero(_924972))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924972), _924976), _924978)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924972), _924974), _924978))))], (22862 ^ _775828) ^ [_1173589, _1173591, _1173593, _1173595, _1173597] : [class_Fields_Olinordered__field(_1173589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173589), c_Groups_Ozero__class_Ozero(_1173589)), _1173591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173589), _1173591), _1173593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173589), c_Groups_Ozero__class_Ozero(_1173589)), _1173595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173589), _1173595), _1173597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173589), _1173591), _1173597)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173589), _1173593), _1173595))))], (32557 ^ _775828) ^ [_1377576, _1377578, _1377580] : [class_Lattices_Olattice(_1377576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377576), _1377578)), -(_1377580 = c_Orderings_Obot__class_Obot(tc_fun(_1377576, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377576, tc_HOL_Obool)), _1377580), _1377578)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1377576), c_Big__Operators_Olattice__class_OSup__fin(_1377576, _1377580)), c_Big__Operators_Olattice__class_OSup__fin(_1377576, _1377578)) = c_Big__Operators_Olattice__class_OSup__fin(_1377576, _1377578))], (20294 ^ _775828) ^ [_1124436, _1124438] : [class_Int_Onumber__ring(_1124436), -(hAPP(c_Int_Onumber__class_Onumber__of(_1124436), c_Int_OBit0(_1124438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124436), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124436), c_Groups_Ozero__class_Ozero(_1124436)), hAPP(c_Int_Onumber__class_Onumber__of(_1124436), _1124438))), hAPP(c_Int_Onumber__class_Onumber__of(_1124436), _1124438)))], (21592 ^ _775828) ^ [_1149662, _1149664] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149662), _1149664), hAPP(c_Int_Onumber__class_Onumber__of(_1149662), c_Int_OBit1(c_Int_OPls))) = _1149664), class_Fields_Ofield(_1149662), class_Int_Onumber__ring(_1149662)], (41960 ^ _775828) ^ [_1589253, _1589255, _1589257, _1589259, _1589261, _1589263] : [class_Groups_Ocomm__monoid__mult(_1589253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589255), _1589257)), 41970 ^ _775828 : [(41973 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589259), hAPP(_1589261, 41969 ^ [_1589253, _1589255, _1589257, _1589259, _1589261, _1589263])))], (41971 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589255), 41969 ^ [_1589253, _1589255, _1589257, _1589259, _1589261, _1589263]), _1589257)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1589253, _1589255, c_Groups_Otimes__class_Otimes(_1589253)), hAPP(hAPP(c_COMBS(_1589255, tc_fun(_1589259, tc_HOL_Obool), _1589253), hAPP(hAPP(c_COMBC(_1589255, _1589253, tc_fun(tc_fun(_1589259, tc_HOL_Obool), _1589253)), hAPP(hAPP(c_COMBB(tc_fun(_1589259, _1589253), tc_fun(_1589253, tc_fun(tc_fun(_1589259, tc_HOL_Obool), _1589253)), _1589255), c_Finite__Set_Ofold__image(_1589253, _1589259, c_Groups_Otimes__class_Otimes(_1589253))), _1589263)), c_Groups_Oone__class_Oone(_1589253))), _1589261)), c_Groups_Oone__class_Oone(_1589253)), _1589257) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1589253, tc_prod(_1589255, _1589259), c_Groups_Otimes__class_Otimes(_1589253)), hAPP(c_Product__Type_Oprod_Oprod__case(_1589255, _1589259, _1589253), _1589263)), c_Groups_Oone__class_Oone(_1589253)), hAPP(hAPP(c_Product__Type_OSigma(_1589255, _1589259), _1589257), _1589261)))], (13128 ^ _775828) ^ [_992924, _992926, _992928, _992930, _992932, _992934] : [c_Natural_Oevaln(_992924, _992926, _992928, _992930), c_Natural_Oevaln(_992932, _992930, _992928, _992934), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_992924, _992932), _992926, _992928, _992934))], (43096 ^ _775828) ^ [_1616196, _1616198, _1616200, _1616202, _1616204, _1616206] : [c_Finite__Set_Ofolding(_1616196, _1616198, _1616200, _1616202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616196), _1616204)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616196), _1616206)), -(hAPP(c_Fun_Ocomp(_1616198, _1616198, _1616198, hAPP(_1616202, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616196, tc_HOL_Obool)), _1616204), _1616206))), hAPP(_1616202, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1616196, tc_HOL_Obool)), _1616204), _1616206))) = hAPP(c_Fun_Ocomp(_1616198, _1616198, _1616198, hAPP(_1616202, _1616204)), hAPP(_1616202, _1616206)))], (50949 ^ _775828) ^ [_1801515, _1801517, _1801519, _1801521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1801515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801517)), c_List_OdropWhile(_1801517, _1801519, _1801521)))), -(hAPP(hAPP(c_List_Onth(_1801517), c_List_OdropWhile(_1801517, _1801519, _1801521)), _1801515) = hAPP(hAPP(c_List_Onth(_1801517), _1801521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1801515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801517)), c_List_OtakeWhile(_1801517, _1801519, _1801521)))))], (50108 ^ _775828) ^ [_1782128] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1782128) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1782128))))], (12457 ^ _775828) ^ [_981329, _981331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981331)), -(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), _981329), _981331))))], (28299 ^ _775828) ^ [_1283504, _1283506, _1283508, _1283510, _1283512] : [class_Lattices_Olattice(_1283504), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283506, _1283504)), _1283508), _1283510), _1283512) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283504), hAPP(_1283508, _1283512)), hAPP(_1283510, _1283512)))], (8979 ^ _775828) ^ [_919422, _919424, _919426] : [class_Groups_Oordered__ab__group__add(_919422), 8982 ^ _775828 : [(8989 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919422), _919426), _919424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919422), hAPP(c_Groups_Ouminus__class_Ouminus(_919422), _919424)), hAPP(c_Groups_Ouminus__class_Ouminus(_919422), _919426))))], (8983 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919422), hAPP(c_Groups_Ouminus__class_Ouminus(_919422), _919424)), hAPP(c_Groups_Ouminus__class_Ouminus(_919422), _919426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919422), _919426), _919424)))]]], (5256 ^ _775828) ^ [_856189, _856191] : [_856191 = _856189, -(c_Power_Opower__class_Opower(_856191) = c_Power_Opower__class_Opower(_856189))], (6346 ^ _775828) ^ [_876737, _876739] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_876737, _876739))))], (41102 ^ _775828) ^ [_1567985, _1567987, _1567989, _1567991] : [-(c_Wellfounded_Omax__extp(_1567985, _1567987, _1567989, _1567991)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567985), _1567989)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567985), _1567991)), -(_1567991 = c_Orderings_Obot__class_Obot(tc_fun(_1567985, tc_HOL_Obool))), 41116 ^ _775828 : [(41119 ^ _775828) ^ [_1568330] : [hBOOL(hAPP(hAPP(c_member(_1567985), _1568330), _1567991)), hBOOL(hAPP(hAPP(_1567987, 41115 ^ [_1567985, _1567987, _1567989, _1567991]), _1568330))], (41117 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567985), 41115 ^ [_1567985, _1567987, _1567989, _1567991]), _1567989)))]]], (28071 ^ _775828) ^ [_1278711, _1278713] : [c_Wellfounded_Owf(_1278711, _1278713), -(c_Wellfounded_OwfP(_1278711, hAPP(hAPP(c_COMBC(_1278711, tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_fun(_1278711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278711, tc_fun(tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_fun(_1278711, tc_HOL_Obool)), _1278711), c_COMBC(_1278711, tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278711, tc_prod(_1278711, _1278711)), tc_fun(_1278711, tc_fun(tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_HOL_Obool)), _1278711), hAPP(c_COMBB(tc_prod(_1278711, _1278711), tc_fun(tc_fun(tc_prod(_1278711, _1278711), tc_HOL_Obool), tc_HOL_Obool), _1278711), c_member(tc_prod(_1278711, _1278711)))), c_Product__Type_OPair(_1278711, _1278711)))), _1278713)))], (10546 ^ _775828) ^ [_947490, _947492, _947494, _947496] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947490), _947492), _947494)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947490), _947496), _947494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947490), _947492), _947496)))], (48285 ^ _775828) ^ [_1742828, _1742830, _1742832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1742828, _1742828), tc_HOL_Obool)), _1742830), _1742832)), c_Relation_Orefl__on(_1742828, c_Orderings_Otop__class_Otop(tc_fun(_1742828, tc_HOL_Obool)), _1742832), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1742828), tc_List_Olist(_1742828)), tc_HOL_Obool)), c_List_Olistrel1(_1742828, _1742830)), c_List_Olistrel(_1742828, _1742832))))], (28801 ^ _775828) ^ [_1294021, _1294023] : [hBOOL(hAPP(_1294021, c_Hilbert__Choice_OEps(_1294023, _1294021))), -(hBOOL(hAPP(_1294021, 28804 ^ [_1294021, _1294023])))], (25385 ^ _775828) ^ [_1223610, _1223612] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1223610), _1223612) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1223610)), hAPP(c_Code__Numeral_Onat__of, _1223612))))], (13662 ^ _775828) ^ [_1003125, _1003127, _1003129, _1003131, _1003133] : [c_Com_Ocom_OCond(_1003125, _1003127, _1003129) = c_Com_Ocom_OAss(_1003131, _1003133)], (29327 ^ _775828) ^ [_1307673, _1307675, _1307677] : [_1307673 = c_Orderings_Obot__class_Obot(tc_fun(_1307675, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1307675), _1307677), _1307673))], (39215 ^ _775828) ^ [_1523053, _1523055, _1523057] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1523053), _1523055), _1523057) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523053, tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool)), _1523055), hAPP(hAPP(c_COMBC(_1523053, tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523053, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool)), _1523053), c_Set_Oinsert(tc_fun(_1523053, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523053, tc_HOL_Obool), tc_fun(_1523053, tc_HOL_Obool), _1523053), c_Relation_OImage(_1523053, _1523053, _1523057)), hAPP(hAPP(c_COMBC(_1523053, tc_fun(_1523053, tc_HOL_Obool), tc_fun(_1523053, tc_HOL_Obool)), c_Set_Oinsert(_1523053)), c_Orderings_Obot__class_Obot(tc_fun(_1523053, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1523053, tc_HOL_Obool), tc_HOL_Obool)))))], (48928 ^ _775828) ^ [_1757766, _1757768] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1757766), hAPP(c_List_Oset(tc_Nat_Onat), _1757768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757766), 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)), _1757768))))], (8213 ^ _775828) ^ [_907848, _907850, _907852] : [class_Orderings_Olinorder(_907848), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907848), _907850), _907852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907848), _907852), _907850)))], (20292 ^ _775828) ^ [_1124407] : [-(c_Int_Osucc(c_Int_OBit0(_1124407)) = c_Int_OBit1(_1124407))], (18325 ^ _775828) ^ [_1091015, _1091017, _1091019, _1091021, _1091023, _1091025] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091015, _1091017), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091019), _1091021))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091015, _1091017), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091023), _1091025))), -(_1091017 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1091019 = _1091023)], (40161 ^ _775828) ^ [_1545746, _1545748] : [class_Lattices_Obounded__lattice__top(_1545746), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1545746), c_Orderings_Otop__class_Otop(_1545746)), _1545748) = c_Orderings_Otop__class_Otop(_1545746))], (18635 ^ _775828) ^ [_1096045, _1096047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096047)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1096045, _1096047), c_Divides_OposDivAlg(_1096045, _1096047))))], (48116 ^ _775828) ^ [_1737669, _1737671, _1737673, _1737675, _1737677, _1737679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737669), tc_List_Olist(_1737669))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737669), tc_List_Olist(_1737669)), hAPP(hAPP(c_List_Oappend(_1737669), _1737671), hAPP(hAPP(c_List_Olist_OCons(_1737669), _1737673), c_List_Olist_ONil(_1737669)))), hAPP(hAPP(c_List_Oappend(_1737669), _1737675), hAPP(hAPP(c_List_Olist_OCons(_1737669), _1737677), c_List_Olist_ONil(_1737669))))), c_List_Olistrel1(_1737669, _1737679))), 48121 ^ _775828 : [(48124 ^ _775828) ^ [] : [-(_1737673 = _1737677)], (48122 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737669), tc_List_Olist(_1737669))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737669), tc_List_Olist(_1737669)), _1737671), _1737675)), c_List_Olistrel1(_1737669, _1737679))))]], 48125 ^ _775828 : [(48128 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1737669, _1737669)), hAPP(hAPP(c_Product__Type_OPair(_1737669, _1737669), _1737673), _1737677)), _1737679)))], (48126 ^ _775828) ^ [] : [-(_1737671 = _1737675)]]], (34117 ^ _775828) ^ [_1410417, _1410419, _1410421, _1410423] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410417, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1410417), _1410419), _1410421)), hAPP(hAPP(c_Set_Oinsert(_1410417), _1410419), _1410423)) = hAPP(hAPP(c_Set_Oinsert(_1410417), _1410419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410417, tc_HOL_Obool)), _1410421), _1410423)))], (34199 ^ _775828) ^ [_1412131, _1412133, _1412135] : [class_Lattices_Oboolean__algebra(_1412131), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1412131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412131), _1412133), _1412135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1412131), hAPP(c_Groups_Ouminus__class_Ouminus(_1412131), _1412133)), hAPP(c_Groups_Ouminus__class_Ouminus(_1412131), _1412135)))], (37290 ^ _775828) ^ [_1479047, _1479049, _1479051, _1479053, _1479055] : [class_Groups_Oab__group__add(_1479047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479049), _1479051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479049, tc_HOL_Obool)), _1479053), _1479051)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479049, _1479047), _1479055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479049, tc_HOL_Obool)), _1479051), _1479053)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1479047), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479049, _1479047), _1479055), _1479051)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479049, _1479047), _1479055), _1479053)))], (35227 ^ _775828) ^ [_1436174, _1436176, _1436178, _1436180] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436174), _1436176)), -(hAPP(c_Set_Oimage(_1436174, _1436178, _1436180), _1436176) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1436178, tc_HOL_Obool), _1436174, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436178, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1436174, tc_fun(_1436178, tc_HOL_Obool), tc_fun(_1436178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1436178, tc_fun(tc_fun(_1436178, tc_HOL_Obool), tc_fun(_1436178, tc_HOL_Obool)), _1436174), c_Set_Oinsert(_1436178)), _1436180)), c_Orderings_Obot__class_Obot(tc_fun(_1436178, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1436178, tc_HOL_Obool))), _1436176))], (4954 ^ _775828) ^ [_851624, _851626, _851628, _851630, _851632, _851634] : [-(c_Map_Omap__of(_851634, _851630, _851626) = c_Map_Omap__of(_851632, _851628, _851624)), _851634 = _851632, _851630 = _851628, _851626 = _851624], (51228 ^ _775828) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (43648 ^ _775828) ^ [_1629498, _1629500, _1629502, _1629504, _1629506, _1629508] : [c_Finite__Set_Ofun__left__comm__idem(_1629498, _1629500, _1629502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629498), _1629504)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1629498, _1629500, _1629502), _1629506), hAPP(hAPP(c_Set_Oinsert(_1629498), _1629508), _1629504)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629498, _1629500, _1629502), hAPP(hAPP(_1629502, _1629508), _1629506)), _1629504))], (15650 ^ _775828) ^ [_1039526, _1039528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039526), _1039528)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039526), _1039528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18237 ^ _775828) ^ [_1088996, _1088998, _1089000, _1089002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1089002, _1088998)), hAPP(_1089002, _1089000))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1088996, _1088996)), hAPP(hAPP(c_Product__Type_OPair(_1088996, _1088996), _1088998), _1089000)), hAPP(c_Wellfounded_Omeasure(_1088996), _1089002))))], (1480 ^ _775828) ^ [_796946, _796948] : [-(class_Rings_Olinordered__semidom(_796946)), _796948 = _796946, class_Rings_Olinordered__semidom(_796948)], (45071 ^ _775828) ^ [_1663190, _1663192, _1663194, _1663196] : [-(_1663190 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1663192, tc_HOL_Obool), tc_HOL_Obool))), 45077 ^ _775828 : [(45080 ^ _775828) ^ [] : [c_Fun_Oinj__on(_1663192, _1663194, _1663196, 45076 ^ [_1663190, _1663192, _1663194, _1663196])], (45078 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1663192, tc_HOL_Obool)), 45076 ^ [_1663190, _1663192, _1663194, _1663196]), _1663190)))]], -(c_Fun_Oinj__on(_1663192, _1663194, _1663196, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663192, tc_HOL_Obool), _1663190)))], (42892 ^ _775828) ^ [_1611376, _1611378, _1611380, _1611382, _1611384, _1611386, _1611388] : [class_Groups_Oab__semigroup__mult(_1611376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611378), _1611380)), c_Fun_Oinj__on(_1611378, _1611382, _1611384, _1611380), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1611376, _1611382, c_Groups_Otimes__class_Otimes(_1611376)), _1611386), _1611388), hAPP(c_Set_Oimage(_1611378, _1611382, _1611384), _1611380)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1611376, _1611378, c_Groups_Otimes__class_Otimes(_1611376)), hAPP(c_Fun_Ocomp(_1611382, _1611376, _1611378, _1611386), _1611384)), _1611388), _1611380))], (10934 ^ _775828) ^ [_954807, _954809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954807), _954809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954807)), hAPP(c_Nat_OSuc, _954809))))], (48209 ^ _775828) ^ [_1740439, _1740441, _1740443, _1740445, _1740447, _1740449] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740439), tc_List_Olist(_1740439))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740439), tc_List_Olist(_1740439)), hAPP(hAPP(c_List_Oappend(_1740439), _1740441), _1740447)), hAPP(hAPP(c_List_Oappend(_1740439), _1740443), _1740449))), c_List_Olistrel1(_1740439, _1740445)))), 48210 ^ _775828 : [(48217 ^ _775828) ^ [] : [_1740441 = _1740443, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740439), tc_List_Olist(_1740439))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740439), tc_List_Olist(_1740439)), _1740447), _1740449)), c_List_Olistrel1(_1740439, _1740445)))], (48211 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740439), tc_List_Olist(_1740439))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740439), tc_List_Olist(_1740439)), _1740441), _1740443)), c_List_Olistrel1(_1740439, _1740445))), _1740447 = _1740449]]], (14411 ^ _775828) ^ [_1017041, _1017043, _1017045, _1017047] : [c_Com_Ocom_OWhile(_1017041, _1017043) = c_Com_Ocom_OAss(_1017045, _1017047)], (4988 ^ _775828) ^ [_852143, _852145, _852147, _852149] : [-(c_List_Obutlast(_852149, _852145) = c_List_Obutlast(_852147, _852143)), _852149 = _852147, _852145 = _852143], (4690 ^ _775828) ^ [_847488, _847490, _847492, _847494, _847496, _847498] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_847498, _847494, _847490) = c_SetInterval_Oord__class_OgreaterThanLessThan(_847496, _847492, _847488)), _847498 = _847496, _847494 = _847492, _847490 = _847488], (28960 ^ _775828) ^ [_1299621, _1299623, _1299625, _1299627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1299621, _1299621)), hAPP(hAPP(c_Product__Type_OPair(_1299621, _1299621), _1299623), _1299625)), _1299627)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1299621, _1299621)), hAPP(hAPP(c_Product__Type_OPair(_1299621, _1299621), _1299623), _1299625)), c_Transitive__Closure_Otrancl(_1299621, _1299627))))], (20880 ^ _775828) ^ [_1135259, _1135261] : [-(c_Divides_OnegDivAlg(_1135259, _1135261) = hAPP(c_Divides_Oadjust(_1135261), c_Divides_OnegDivAlg(_1135259, 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)))), _1135261)))), -(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), _1135259), _1135261)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135261), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26828 ^ _775828) ^ [_1249819, _1249821, _1249823] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1249821), _1249823))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249819), _1249823)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249819), _1249821)))], (7447 ^ _775828) ^ [_894717, _894719, _894721] : [class_Groups_Ogroup__add(_894717), 7450 ^ _775828 : [(7457 ^ _775828) ^ [] : [_894719 = _894721, -(hAPP(c_Groups_Ouminus__class_Ouminus(_894717), _894719) = hAPP(c_Groups_Ouminus__class_Ouminus(_894717), _894721))], (7451 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_894717), _894719) = hAPP(c_Groups_Ouminus__class_Ouminus(_894717), _894721), -(_894719 = _894721)]]], (24917 ^ _775828) ^ [_1214542, _1214544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1214542)), -(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(_1214542), _1214544))), _1214542)))], (8125 ^ _775828) ^ [_906443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _906443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _906443)))], (39694 ^ _775828) ^ [_1535450, _1535452, _1535454, _1535456, _1535458] : [-(_1535450 = c_Orderings_Obot__class_Obot(tc_fun(_1535452, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535452, tc_fun(_1535454, tc_HOL_Obool)), _1535450), hAPP(hAPP(c_COMBB(tc_fun(_1535454, tc_HOL_Obool), tc_fun(_1535454, tc_HOL_Obool), _1535452), hAPP(c_Set_Oinsert(_1535454), _1535456)), _1535458)) = hAPP(hAPP(c_Set_Oinsert(_1535454), _1535456), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535452, tc_fun(_1535454, tc_HOL_Obool)), _1535450), _1535458)))], (44485 ^ _775828) ^ [_1649712, _1649714, _1649716, _1649718, _1649720] : [class_Complete__Lattice_Ocomplete__lattice(_1649712), hBOOL(hAPP(hAPP(c_member(_1649714), _1649716), _1649718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1649712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649714, _1649712), _1649718), _1649720)), hAPP(_1649720, _1649716))))], (37962 ^ _775828) ^ [_1495583, _1495585, _1495587, _1495589, _1495591] : [class_Groups_Ocomm__monoid__add(_1495583), class_Groups_Ocomm__monoid__mult(_1495583), _1495585 = _1495587, c_Nat__Transfer_Onat__set(_1495587), 37980 ^ _775828 : [(37983 ^ _775828) ^ [] : [hAPP(_1495589, 37979 ^ [_1495583, _1495585, _1495587, _1495589, _1495591]) = hAPP(_1495591, 37979 ^ [_1495583, _1495585, _1495587, _1495589, _1495591])], (37981 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37979 ^ [_1495583, _1495585, _1495587, _1495589, _1495591])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1495583), _1495589), _1495585) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1495583), _1495591), _1495587))], (27212 ^ _775828) ^ [_1257322, _1257324] : [-(hAPP(c_Set_OCollect(_1257322), _1257324) = _1257324)], (30281 ^ _775828) ^ [_1328234, _1328236] : [c_Wellfounded_Owf(_1328234, _1328236), -(c_Wellfounded_Owf(tc_fun(_1328234, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1328234, _1328236)))], (7131 ^ _775828) ^ [_889163, _889165, _889167] : [class_Rings_Olinordered__semiring__strict(_889163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889163), c_Groups_Ozero__class_Ozero(_889163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_889163), _889165), _889167))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889163), c_Groups_Ozero__class_Ozero(_889163)), _889167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889163), c_Groups_Ozero__class_Ozero(_889163)), _889165)))], (39136 ^ _775828) ^ [_1521158, _1521160, _1521162, _1521164, _1521166] : [-(c_Fun_Oinj__on(_1521158, _1521160, _1521162, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521158, tc_HOL_Obool)), _1521164), _1521166))), c_Fun_Oinj__on(_1521158, _1521160, _1521162, _1521164), c_Fun_Oinj__on(_1521158, _1521160, _1521162, _1521166), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521160, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521158, _1521160, _1521162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521158, tc_HOL_Obool)), _1521164), _1521166))), hAPP(c_Set_Oimage(_1521158, _1521160, _1521162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521158, tc_HOL_Obool)), _1521166), _1521164))) = c_Orderings_Obot__class_Obot(tc_fun(_1521160, tc_HOL_Obool))], (25763 ^ _775828) ^ [_1231196, _1231198] : [-(_1231196 = _1231198), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231196), _1231198)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231198), _1231196))], (10208 ^ _775828) ^ [_941170, _941172, _941174, _941176] : [class_Groups_Ocancel__semigroup__add(_941170), 10211 ^ _775828 : [(10218 ^ _775828) ^ [] : [_941174 = _941176, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941170), _941172), _941174) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941170), _941172), _941176))], (10212 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941170), _941172), _941174) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941170), _941172), _941176), -(_941174 = _941176)]]], (19754 ^ _775828) ^ [_1115176, _1115178] : [class_Int_Onumber__ring(_1115176), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115176), _1115178), hAPP(c_Int_Onumber__class_Onumber__of(_1115176), c_Int_OBit1(c_Int_OPls))) = _1115178)], (39251 ^ _775828) ^ [_1523836, _1523838, _1523840, _1523842] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523836), _1523838)), 39254 ^ _775828 : [(39255 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523840), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523836, tc_fun(_1523840, tc_HOL_Obool)), _1523838), _1523842))), 39258 ^ _775828 : [(39259 ^ _775828) ^ [_1524020] : [hBOOL(hAPP(hAPP(c_member(_1523836), _1524020), _1523838)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523840), hAPP(_1523842, _1524020))))]]], (39265 ^ _775828) ^ [] : [39267 ^ _775828 : [(39270 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523840), hAPP(_1523842, 39266 ^ [_1523836, _1523838, _1523840, _1523842])))], (39268 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523836), 39266 ^ [_1523836, _1523838, _1523840, _1523842]), _1523838)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523840), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523836, tc_fun(_1523840, tc_HOL_Obool)), _1523838), _1523842))))]]], (50812 ^ _775828) ^ [_1798617, _1798619] : [-(c_List_Oremdups(_1798617, c_List_Oremdups(_1798617, _1798619)) = c_List_Oremdups(_1798617, _1798619))], (51372 ^ _775828) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (18589 ^ _775828) ^ [_1095334] : [class_Int_Onumber__ring(_1095334), -(hAPP(c_Int_Oring__1__class_Oof__int(_1095334), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095334), c_Int_OMin))], (39284 ^ _775828) ^ [_1524504, _1524506, _1524508, _1524510, _1524512] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1524504, _1524506, _1524508, _1524510, c_Orderings_Obot__class_Obot(tc_fun(_1524504, tc_HOL_Obool))), _1524512)), -(_1524512 = _1524510)], (25373 ^ _775828) ^ [_1223430, _1223432] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1223430)), hAPP(c_Code__Numeral_Oof__nat, _1223432)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223430), _1223432)))], (16108 ^ _775828) ^ [_1048770, _1048772, _1048774, _1048776, _1048778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048770), _1048772)), 16111 ^ _775828 : [(16118 ^ _775828) ^ [] : [_1048776 = 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), _1048772), _1048770)), _1048774)), _1048778), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048770), _1048774)), _1048776) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048772), _1048774)), _1048778))], (16112 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048770), _1048774)), _1048776) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048772), _1048774)), _1048778), -(_1048776 = 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), _1048772), _1048770)), _1048774)), _1048778))]]], (17105 ^ _775828) ^ [_1068059, _1068061] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068059), _1068061)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068059) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27909 ^ _775828) ^ [_1274866, _1274868, _1274870, _1274872, _1274874, _1274876, _1274878] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1274866, _1274868, _1274870, _1274872, _1274874), _1274876), _1274878)), 27913 ^ _775828 : [(27916 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1274874, 27912 ^ [_1274866, _1274868, _1274870, _1274872, _1274874, _1274876, _1274878]), _1274878)))], (27914 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1274872, _1274876), 27912 ^ [_1274866, _1274868, _1274870, _1274872, _1274874, _1274876, _1274878])))]]], (23488 ^ _775828) ^ [_1186315, _1186317] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186315), hAPP(c_Nat_OSuc, _1186317)) = 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), _1186315), _1186317)))], (24661 ^ _775828) ^ [_1209205] : [-(c_Nitpick_Ozero__frac(_1209205) = c_Nitpick_OAbs__Frac(_1209205, 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))))], (51468 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (34193 ^ _775828) ^ [_1411992, _1411994, _1411996] : [class_Lattices_Oboolean__algebra(_1411992), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1411992), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411992), _1411994), _1411996)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411992), hAPP(c_Groups_Ouminus__class_Ouminus(_1411992), _1411994)), hAPP(c_Groups_Ouminus__class_Ouminus(_1411992), _1411996)))], (14898 ^ _775828) ^ [_1025400, _1025402, _1025404, _1025406] : [class_Divides_Osemiring__div(_1025400), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025400), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025400), _1025402), _1025404)), _1025404)), c_Divides_Odiv__class_Omod(_1025400, _1025402, _1025404))), _1025406) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025400), _1025402), _1025406))], (13578 ^ _775828) ^ [_1001410, _1001412, _1001414, _1001416] : [hAPP(c_Com_Ocom_OBODY, _1001410) = c_Com_Ocom_OCond(_1001412, _1001414, _1001416)], (42444 ^ _775828) ^ [_1600240, _1600242, _1600244] : [c_Relation_Osingle__valued(_1600240, _1600242, _1600244), 42447 ^ _775828 : [(42448 ^ _775828) ^ [_1600361, _1600363] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600240, _1600242)), hAPP(hAPP(c_Product__Type_OPair(_1600240, _1600242), _1600363), _1600361)), _1600244)), 42451 ^ _775828 : [(42452 ^ _775828) ^ [_1600487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600240, _1600242)), hAPP(hAPP(c_Product__Type_OPair(_1600240, _1600242), _1600363), _1600487)), _1600244)), -(_1600361 = _1600487)]]]]], (43890 ^ _775828) ^ [_1634100, _1634102, _1634104] : [class_Orderings_Olinorder(_1634100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634100), _1634102)), -(hBOOL(hAPP(hAPP(c_member(_1634100), _1634104), _1634102))), -(c_Big__Operators_Olinorder__class_OMax(_1634100, hAPP(hAPP(c_Set_Oinsert(_1634100), _1634104), _1634102)) = hAPP(hAPP(c_Finite__Set_Ofold(_1634100, _1634100, c_Orderings_Oord__class_Omax(_1634100)), _1634104), _1634102))], (1450 ^ _775828) ^ [_796571, _796573] : [-(class_Rings_Oordered__comm__semiring(_796571)), _796573 = _796571, class_Rings_Oordered__comm__semiring(_796573)], (45347 ^ _775828) ^ [_1669036, _1669038, _1669040] : [-(c_Map_Omap__add(_1669036, _1669038, hAPP(c_COMBK(tc_Option_Ooption(_1669038), _1669036), c_Option_Ooption_ONone(_1669038)), _1669040) = _1669040)], (24657 ^ _775828) ^ [_1209110, _1209112] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1209110), _1209112) = 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), _1209110)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1209112)))))], (33999 ^ _775828) ^ [_1408283, _1408285, _1408287, _1408289] : [class_Lattices_Osemilattice__inf(_1408283), 34002 ^ _775828 : [(34011 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408283), _1408287), _1408289)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), _1408287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), _1408289))], (34003 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408283), _1408287), _1408289))), 34006 ^ _775828 : [(34009 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), _1408289)))], (34007 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408283), _1408285), _1408287)))]]]]], (24348 ^ _775828) ^ [_1203096, _1203098] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1203096), hAPP(c_Nat_OSuc, _1203098)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1203098), 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)), _1203098)), _1203096))], (30263 ^ _775828) ^ [_1327627, _1327629, _1327631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327627, tc_HOL_Obool)), _1327629), hAPP(hAPP(c_Set_Oinsert(_1327627), _1327631), c_Orderings_Obot__class_Obot(tc_fun(_1327627, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1327627, _1327631, _1327629) = _1327631)], (11438 ^ _775828) ^ [_963793, _963795] : [class_Groups_Olinordered__ab__group__add(_963793), 11441 ^ _775828 : [(11448 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963793), c_Groups_Ozero__class_Ozero(_963793)), _963795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963793), c_Groups_Ozero__class_Ozero(_963793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963793), _963795), _963795))))], (11442 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963793), c_Groups_Ozero__class_Ozero(_963793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963793), _963795), _963795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963793), c_Groups_Ozero__class_Ozero(_963793)), _963795)))]]], (45929 ^ _775828) ^ [_1682750, _1682752] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1682750, _1682752))))], (24650 ^ _775828) ^ [_1208943, _1208945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1208943, _1208943)), hAPP(hAPP(c_Product__Type_OPair(_1208943, _1208943), 24651 ^ [_1208943, _1208945]), 24651 ^ [_1208943, _1208945])), _1208945)), -(c_Nitpick_Orefl_H(_1208943, _1208945))], (44055 ^ _775828) ^ [_1637324, _1637326, _1637328, _1637330] : [class_Complete__Lattice_Ocomplete__lattice(_1637324), hBOOL(hAPP(c_Finite__Set_Ofinite(_1637326), _1637328)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637326, _1637324), _1637328), _1637330) = hAPP(hAPP(c_Finite__Set_Ofold(_1637326, _1637324, hAPP(hAPP(c_COMBB(_1637324, tc_fun(_1637324, _1637324), _1637326), c_Lattices_Osemilattice__inf__class_Oinf(_1637324)), _1637330)), c_Orderings_Otop__class_Otop(_1637324)), _1637328))], (38416 ^ _775828) ^ [_1505644, _1505646, _1505648, _1505650, _1505652] : [hAPP(_1505644, _1505646) = hAPP(c_Option_Ooption_OSome(_1505648), _1505650), -(hAPP(hAPP(c_Set_Oinsert(_1505652), _1505646), c_Map_Odom(_1505652, _1505648, _1505644)) = c_Map_Odom(_1505652, _1505648, _1505644))], (30499 ^ _775828) ^ [_1333157, _1333159] : [class_Finite__Set_Ofinite(_1333157), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333157), _1333159)))], (35465 ^ _775828) ^ [_1442122, _1442124] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1442122, _1442124))))], (32005 ^ _775828) ^ [_1367903, _1367905] : [class_Groups_Olinordered__ab__group__add(_1367903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367903), _1367905)), -(_1367905 = c_Orderings_Obot__class_Obot(tc_fun(_1367903, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367903), c_Big__Operators_Olinorder__class_OMin(_1367903, _1367905)) = c_Big__Operators_Olinorder__class_OMax(_1367903, hAPP(c_Set_Oimage(_1367903, _1367903, c_Groups_Ouminus__class_Ouminus(_1367903)), _1367905)))], (9005 ^ _775828) ^ [] : [-(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))))], (50822 ^ _775828) ^ [_1798833, _1798835, _1798837] : [-(hBOOL(hAPP(hAPP(c_member(_1798833), _1798835), hAPP(c_List_Oset(_1798833), _1798837)))), -(c_List_Oremdups(_1798833, hAPP(hAPP(c_List_Olist_OCons(_1798833), _1798835), _1798837)) = hAPP(hAPP(c_List_Olist_OCons(_1798833), _1798835), c_List_Oremdups(_1798833, _1798837)))], (27252 ^ _775828) ^ [_1258280, _1258282, _1258284] : [-(hAPP(c_Relation_Oconverse(_1258280, _1258282), _1258284) = hAPP(c_Set_OCollect(tc_prod(_1258282, _1258280)), hAPP(c_Product__Type_Oprod_Oprod__case(_1258282, _1258280, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1258282, tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_fun(_1258280, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1258280, tc_fun(tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_fun(_1258280, tc_HOL_Obool)), _1258282), c_COMBC(_1258280, tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1258280, tc_prod(_1258280, _1258282)), tc_fun(_1258280, tc_fun(tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_HOL_Obool)), _1258282), hAPP(c_COMBB(tc_prod(_1258280, _1258282), tc_fun(tc_fun(tc_prod(_1258280, _1258282), tc_HOL_Obool), tc_HOL_Obool), _1258280), c_member(tc_prod(_1258280, _1258282)))), hAPP(c_COMBC(_1258280, _1258282, tc_prod(_1258280, _1258282)), c_Product__Type_OPair(_1258280, _1258282))))), _1258284))))], (23992 ^ _775828) ^ [_1195937, _1195939, _1195941, _1195943] : [class_Orderings_Olinorder(_1195937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195937), _1195939), _1195941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195937), _1195939), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195937), _1195943), _1195941))))], (51392 ^ _775828) ^ [_1806982, _1806984] : [-(class_Finite__Set_Ofinite(tc_sum(_1806982, _1806984))), class_Finite__Set_Ofinite(_1806982), class_Finite__Set_Ofinite(_1806984)], (51386 ^ _775828) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (50607 ^ _775828) ^ [_1794727, _1794729, _1794731, _1794733, _1794735] : [-(hAPP(hAPP(c_List_Ozip(_1794727, _1794729), _1794731), c_List_OtakeWhile(_1794729, _1794733, _1794735)) = c_List_OtakeWhile(tc_prod(_1794727, _1794729), hAPP(c_Fun_Ocomp(_1794729, tc_HOL_Obool, tc_prod(_1794727, _1794729), _1794733), c_Product__Type_Osnd(_1794727, _1794729)), hAPP(hAPP(c_List_Ozip(_1794727, _1794729), _1794731), _1794735)))], (30001 ^ _775828) ^ [_1322694, _1322696, _1322698] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1322694, _1322696) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1322698), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 30004 ^ _775828 : [(30007 ^ _775828) ^ [] : [-(_1322696 = _1322698)], (30005 ^ _775828) ^ [] : [-(_1322694 = _1322696)]]], (43810 ^ _775828) ^ [_1632797, _1632799, _1632801, _1632803, _1632805] : [c_Finite__Set_Ofolding__one(_1632797, _1632799, _1632801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632797), _1632803)), -(hBOOL(hAPP(hAPP(c_member(_1632797), _1632805), _1632803))), -(hAPP(_1632801, hAPP(hAPP(c_Set_Oinsert(_1632797), _1632805), _1632803)) = hAPP(hAPP(c_Finite__Set_Ofold(_1632797, _1632797, _1632799), _1632805), _1632803))], (16589 ^ _775828) ^ [_1058009, _1058011, _1058013] : [class_Groups_Oordered__ab__group__add__abs(_1058009), -(hAPP(c_Groups_Oabs__class_Oabs(_1058009), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058009), _1058011), _1058013)) = hAPP(c_Groups_Oabs__class_Oabs(_1058009), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058009), _1058013), _1058011)))], (13384 ^ _775828) ^ [_997860, _997862, _997864, _997866] : [class_Divides_Oring__div(_997860), c_Divides_Odiv__class_Omod(_997860, _997862, _997864) = c_Divides_Odiv__class_Omod(_997860, _997866, _997864), -(c_Divides_Odiv__class_Omod(_997860, hAPP(c_Groups_Ouminus__class_Ouminus(_997860), _997862), _997864) = c_Divides_Odiv__class_Omod(_997860, hAPP(c_Groups_Ouminus__class_Ouminus(_997860), _997866), _997864))], (24855 ^ _775828) ^ [_1213494, _1213496, _1213498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1213494), _1213496)), -(c_Random_Ominus__shift(_1213498, _1213494, _1213496) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1213498), _1213494)), _1213496))], (12691 ^ _775828) ^ [_985363] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _985363)) = 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), _985363)))], (20560 ^ _775828) ^ [_1129131, _1129133] : [class_Rings_Olinordered__idom(_1129131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129131), hAPP(hAPP(c_Power_Opower__class_Opower(_1129131), _1129133), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1129131)))], (14576 ^ _775828) ^ [_1019827, _1019829, _1019831, _1019833] : [class_Divides_Osemiring__div(_1019827), 14579 ^ _775828 : [(14586 ^ _775828) ^ [] : [-(_1019829 = c_Groups_Ozero__class_Ozero(_1019827)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019827), _1019829), _1019831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019827), _1019829), _1019833)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019827), _1019831), _1019833))], (14580 ^ _775828) ^ [] : [_1019829 = c_Groups_Ozero__class_Ozero(_1019827), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019827), _1019829), _1019831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019827), _1019829), _1019833)) = c_Groups_Ozero__class_Ozero(_1019827))]]], (34115 ^ _775828) ^ [_1410335, _1410337, _1410339, _1410341] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410335, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1410337, _1410335), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1410337, _1410335), tc_HOL_Obool)), _1410339), _1410341))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410335, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1410337, _1410335), _1410339)), hAPP(c_Relation_ORange(_1410337, _1410335), _1410341)))))], (36333 ^ _775828) ^ [_1457949, _1457951, _1457953, _1457955] : [class_Orderings_Oorder(_1457949), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457949, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457949, _1457951), _1457953)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457949, _1457953), _1457955)) = c_Orderings_Obot__class_Obot(tc_fun(_1457949, tc_HOL_Obool)))], (23730 ^ _775828) ^ [_1191385, _1191387, _1191389] : [class_Orderings_Olinorder(_1191385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191385), _1191387), _1191389)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191385), _1191389), _1191387) = _1191389)], (16312 ^ _775828) ^ [_1053010, _1053012, _1053014, _1053016, _1053018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053010), _1053012)), 16315 ^ _775828 : [(16322 ^ _775828) ^ [] : [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), _1053012), _1053010)), _1053014)), _1053016)), _1053018)), -(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), _1053012), _1053014)), _1053016)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053010), _1053014)), _1053018))))], (16316 ^ _775828) ^ [] : [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), _1053012), _1053014)), _1053016)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053010), _1053014)), _1053018))), -(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), _1053012), _1053010)), _1053014)), _1053016)), _1053018)))]]], (49349 ^ _775828) ^ [_1766651, _1766653, _1766655, _1766657] : [-(hAPP(hAPP(c_List_Oappend(_1766651), _1766653), hAPP(hAPP(c_List_Olist_OCons(_1766651), _1766655), c_List_Olist_ONil(_1766651))) = _1766657), -(_1766657 = c_List_Olist_ONil(_1766651)), c_List_Obutlast(_1766651, _1766657) = _1766653, c_List_Olast(_1766651, _1766657) = _1766655], (47077 ^ _775828) ^ [_1713476, _1713478, _1713480, _1713482] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1713478), hAPP(hAPP(c_List_Olist_OCons(_1713478), _1713480), _1713482)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713476)) = _1713480)], (20336 ^ _775828) ^ [_1125265, _1125267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1125265)), c_Int_OBit0(_1125267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125265), _1125267)))], (34471 ^ _775828) ^ [_1418344, _1418346, _1418348, _1418350, _1418352] : [class_Groups_Ocomm__monoid__mult(_1418344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418346), _1418348)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418346), _1418350)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418344), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418346, _1418344), _1418352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418346, tc_HOL_Obool)), _1418348), _1418350))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418346, _1418344), _1418352), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418346, tc_HOL_Obool)), _1418348), _1418350))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418344), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418346, _1418344), _1418352), _1418348)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418346, _1418344), _1418352), _1418350)))], (47146 ^ _775828) ^ [_1715558, _1715560] : [-(c_Random_Oselect(_1715558, _1715560) = 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(_1715558, 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(_1715558)), _1715560)))), hAPP(hAPP(c_COMBB(_1715558, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1715558, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1715558, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1715558, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1715558), _1715560)), c_Code__Numeral_Onat__of))))], (3260 ^ _775828) ^ [_825155, _825157, _825159, _825161, _825163, _825165, _825167, _825169] : [-(c_Sum__Type_OPlus(_825169, _825165, _825161, _825157) = c_Sum__Type_OPlus(_825167, _825163, _825159, _825155)), _825169 = _825167, _825165 = _825163, _825161 = _825159, _825157 = _825155], (39466 ^ _775828) ^ [_1529354, _1529356, _1529358] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1529354, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1529356)), _1529358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529354, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1529354, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1529356)), _1529358)), hAPP(_1529358, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24170 ^ _775828) ^ [_1199086, _1199088, _1199090] : [class_Orderings_Olinorder(_1199086), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199086), _1199088), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199086), _1199088), _1199090)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199086), _1199088), _1199090))], (27964 ^ _775828) ^ [_1275945, _1275947, _1275949] : [c_Wellfounded_Owf(_1275945, _1275947), hBOOL(hAPP(hAPP(c_member(tc_prod(_1275945, _1275945)), hAPP(hAPP(c_Product__Type_OPair(_1275945, _1275945), _1275949), _1275949)), _1275947))], (3316 ^ _775828) ^ [_826017, _826019] : [_826019 = _826017, -(c_Int_Oring__1__class_Oof__int(_826019) = c_Int_Oring__1__class_Oof__int(_826017))], (51324 ^ _775828) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (8168 ^ _775828) ^ [_907120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907120), _907120)))], (10940 ^ _775828) ^ [_954933, _954935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954933), hAPP(c_Nat_OSuc, _954935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954933), _954935))), -(_954933 = hAPP(c_Nat_OSuc, _954935))], (32459 ^ _775828) ^ [_1375632, _1375634] : [class_Orderings_Olinorder(_1375632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375632), _1375634)), -(_1375634 = c_Orderings_Obot__class_Obot(tc_fun(_1375632, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1375632), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375632), 32472 ^ [_1375632, _1375634]), 32473 ^ [_1375632, _1375634])), hAPP(hAPP(c_Set_Oinsert(_1375632), 32472 ^ [_1375632, _1375634]), hAPP(hAPP(c_Set_Oinsert(_1375632), 32473 ^ [_1375632, _1375634]), c_Orderings_Obot__class_Obot(tc_fun(_1375632, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1375632), c_Big__Operators_Olinorder__class_OMax(_1375632, _1375634)), _1375634)))], (32025 ^ _775828) ^ [_1368210, _1368212] : [class_Orderings_Olinorder(_1368210), -(c_Big__Operators_Olinorder__class_OMin(_1368210, hAPP(hAPP(c_Set_Oinsert(_1368210), _1368212), c_Orderings_Obot__class_Obot(tc_fun(_1368210, tc_HOL_Obool)))) = _1368212)], (16953 ^ _775828) ^ [_1064807, _1064809, _1064811, _1064813] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064807), hAPP(c_Int_Onumber__class_Onumber__of(_1064807), _1064809)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064807), _1064811), _1064813)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064807), hAPP(c_Int_Onumber__class_Onumber__of(_1064807), _1064809)), _1064811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064807), hAPP(c_Int_Onumber__class_Onumber__of(_1064807), _1064809)), _1064813))), class_Int_Onumber(_1064807), class_Rings_Osemiring(_1064807)], (5559 ^ _775828) ^ [_863925, _863927] : [hAPP(c_Nat_OSuc, _863925) = hAPP(c_Nat_OSuc, _863927), -(_863925 = _863927)], (43588 ^ _775828) ^ [_1628141, _1628143, _1628145, _1628147] : [-(hAPP(c_Finite__Set_Ofold__image(_1628141, _1628143, _1628145), _1628147) = c_Finite__Set_Ofold(_1628143, _1628141, hAPP(hAPP(c_COMBB(_1628141, tc_fun(_1628141, _1628141), _1628143), _1628145), _1628147)))], (25429 ^ _775828) ^ [_1224333, _1224335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1224333), _1224335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224333)), hAPP(c_Code__Numeral_Onat__of, _1224335))))], (3290 ^ _775828) ^ [_825626, _825628] : [_825628 = _825626, -(c_Int_OBit1(_825628) = c_Int_OBit1(_825626))], (21070 ^ _775828) ^ [_1138809, _1138811, _1138813, _1138815] : [_1138813 = _1138815, -(hAPP(hAPP(c_COMBC(_1138809, tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_fun(_1138811, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138811, tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_fun(_1138811, tc_HOL_Obool)), _1138809), c_COMBC(_1138811, tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138811, tc_prod(_1138809, _1138811)), tc_fun(_1138811, tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), _1138809), hAPP(c_COMBB(tc_prod(_1138809, _1138811), tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool), _1138811), c_member(tc_prod(_1138809, _1138811)))), c_Product__Type_OPair(_1138809, _1138811)))), _1138813) = hAPP(hAPP(c_COMBC(_1138809, tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_fun(_1138811, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138811, tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_fun(_1138811, tc_HOL_Obool)), _1138809), c_COMBC(_1138811, tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138811, tc_prod(_1138809, _1138811)), tc_fun(_1138811, tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool)), _1138809), hAPP(c_COMBB(tc_prod(_1138809, _1138811), tc_fun(tc_fun(tc_prod(_1138809, _1138811), tc_HOL_Obool), tc_HOL_Obool), _1138811), c_member(tc_prod(_1138809, _1138811)))), c_Product__Type_OPair(_1138809, _1138811)))), _1138815))], (44870 ^ _775828) ^ [_1658576] : [class_Complete__Lattice_Ocomplete__lattice(_1658576), -(c_Complete__Lattice_OSup__class_OSup(_1658576, c_Orderings_Obot__class_Obot(tc_fun(_1658576, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1658576))], (18309 ^ _775828) ^ [_1090860] : [-(_1090860 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1090860), 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)))))], (15896 ^ _775828) ^ [_1044182, _1044184] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044182), hAPP(c_Nat_OSuc, _1044184)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044182), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1044184))], (16799 ^ _775828) ^ [_1061937, _1061939] : [class_Groups_Oordered__ab__group__add__abs(_1061937), 16802 ^ _775828 : [(16809 ^ _775828) ^ [] : [-(_1061939 = c_Groups_Ozero__class_Ozero(_1061937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061937), c_Groups_Ozero__class_Ozero(_1061937)), hAPP(c_Groups_Oabs__class_Oabs(_1061937), _1061939))))], (16803 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061937), c_Groups_Ozero__class_Ozero(_1061937)), hAPP(c_Groups_Oabs__class_Oabs(_1061937), _1061939))), _1061939 = c_Groups_Ozero__class_Ozero(_1061937)]]], (37950 ^ _775828) ^ [_1495303, _1495305] : [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)), _1495303), _1495305)), 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)), _1495303), 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)), _1495305), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (27118 ^ _775828) ^ [_1254891, _1254893] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1254891), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254893)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254891)), _1254893)))], (614 ^ _775828) ^ [_785131, _785133, _785135, _785137, _785139, _785141] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_785139, _785135, _785131)), c_Hoare__Mirabelle_Ohoare__derivs(_785141, _785137, _785133), _785141 = _785139, _785137 = _785135, _785133 = _785131], (50225 ^ _775828) ^ [_1784912] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1784912)), c_List_Otranspose__rel(_1784912)), c_List_Olist_ONil(tc_List_Olist(_1784912)))), -(c_List_Otranspose(_1784912, c_List_Olist_ONil(tc_List_Olist(_1784912))) = c_List_Olist_ONil(tc_List_Olist(_1784912)))], (31225 ^ _775828) ^ [_1349812, _1349814] : [class_Orderings_Olinorder(_1349812), -(c_Big__Operators_Olattice_OInf__fin(_1349812, c_Orderings_Oord__class_Omin(_1349812), hAPP(hAPP(c_Set_Oinsert(_1349812), _1349814), c_Orderings_Obot__class_Obot(tc_fun(_1349812, tc_HOL_Obool)))) = _1349814)], (23472 ^ _775828) ^ [_1185970, _1185972, _1185974, _1185976, _1185978] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185970, _1185972, _1185974), _1185976), _1185978) = hAPP(hAPP(_1185976, hAPP(c_Product__Type_Ofst(_1185970, _1185972), _1185978)), hAPP(c_Product__Type_Osnd(_1185970, _1185972), _1185978)))], (10970 ^ _775828) ^ [_955369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955369)), _955369))], (25537 ^ _775828) ^ [_1227364] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227364), _1227364)))], (46440 ^ _775828) ^ [_1697371, _1697373, _1697375, _1697377] : [hBOOL(hAPP(hAPP(c_member(_1697371), _1697373), hAPP(c_List_Oset(_1697371), hAPP(hAPP(c_List_Olist_OCons(_1697371), _1697375), _1697377)))), -(_1697373 = _1697375), -(hBOOL(hAPP(hAPP(c_member(_1697371), _1697373), hAPP(c_List_Oset(_1697371), _1697377))))], (40173 ^ _775828) ^ [_1545944, _1545946] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545944, tc_HOL_Obool)), _1545946), c_Orderings_Otop__class_Otop(tc_fun(_1545944, tc_HOL_Obool)))))], (1550 ^ _775828) ^ [_797821, _797823] : [-(class_Rings_Ocomm__semiring__1(_797821)), _797823 = _797821, class_Rings_Ocomm__semiring__1(_797823)], (42369 ^ _775828) ^ [_1598638] : [class_Orderings_Olinorder(_1598638), -(c_Finite__Set_Ofun__left__comm__idem(_1598638, _1598638, c_Orderings_Oord__class_Omax(_1598638)))], (48703 ^ _775828) ^ [_1752715, _1752717, _1752719] : [-(hAPP(c_List_Orotate(_1752715, _1752717), _1752719) = hAPP(c_List_Orotate(_1752715, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1752717, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752715)), _1752719))), _1752719))], (33567 ^ _775828) ^ [_1398819, _1398821, _1398823, _1398825] : [hBOOL(hAPP(_1398819, _1398821)), hBOOL(hAPP(_1398823, _1398821)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398825, tc_HOL_Obool)), _1398819), _1398823), _1398821)))], (19020 ^ _775828) ^ [_1103270, _1103272, _1103274, _1103276, _1103278, _1103280] : [-(c_Product__Type_Oprod_Oprod__rec(_1103270, _1103272, _1103274, _1103276, hAPP(hAPP(c_Product__Type_OPair(_1103270, _1103272), _1103278), _1103280)) = hAPP(hAPP(_1103276, _1103278), _1103280))], (13176 ^ _775828) ^ [_993747, _993749, _993751, _993753, _993755] : [c_Com_Ocom_OSemi(_993747, _993749) = c_Com_Ocom_OCond(_993751, _993753, _993755)], (39578 ^ _775828) ^ [_1531753, _1531755, _1531757] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531753, tc_fun(_1531755, tc_HOL_Obool)), _1531757), hAPP(c_COMBK(tc_fun(_1531755, tc_HOL_Obool), _1531753), c_Orderings_Obot__class_Obot(tc_fun(_1531755, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1531755, tc_HOL_Obool)))], (18045 ^ _775828) ^ [_1085148, _1085150, _1085152] : [class_Rings_Olinordered__idom(_1085148), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085148), c_Groups_Ozero__class_Ozero(_1085148)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085148), hAPP(c_Groups_Oabs__class_Oabs(_1085148), _1085150)), _1085152))))], (18315 ^ _775828) ^ [_1090899, _1090901, _1090903] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1090899, _1090899), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1090901), _1090903))), -(_1090899 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1090903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9607 ^ _775828) ^ [_930301] : [9609 ^ _775828 : [(9612 ^ _775828) ^ [] : [hBOOL(hAPP(_930301, 9608 ^ [_930301]))], (9610 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9608 ^ [_930301])))]], 9613 ^ _775828 : [(9614 ^ _775828) ^ [_930428] : [-(hBOOL(hAPP(_930301, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930428))))]]], (12377 ^ _775828) ^ [_980013, _980015, _980017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _980013), _980015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980013), _980017)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980015), _980017))))], (29171 ^ _775828) ^ [_1304494, _1304496, _1304498, _1304500] : [29172 ^ _775828 : [(29175 ^ _775828) ^ [] : [_1304496 = _1304500], (29173 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304494), _1304496), _1304498))]], -(hBOOL(hAPP(hAPP(c_member(_1304494), _1304496), hAPP(hAPP(c_Set_Oinsert(_1304494), _1304500), _1304498))))], (23394 ^ _775828) ^ [_1184063, _1184065, _1184067] : [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), _1184063), _1184065))), -(hBOOL(hAPP(hAPP(_1184067, _1184063), _1184065))), 23401 ^ _775828 : [(23404 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1184067, 23399 ^ [_1184063, _1184065, _1184067]), 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)))), 23400 ^ [_1184063, _1184065, _1184067])))), -(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), 23399 ^ [_1184063, _1184065, _1184067]), 23400 ^ [_1184063, _1184065, _1184067])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23400 ^ [_1184063, _1184065, _1184067]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23414 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1184067, 23399 ^ [_1184063, _1184065, _1184067]), 23400 ^ [_1184063, _1184065, _1184067]))], (23402 ^ _775828) ^ [] : [-(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), 23399 ^ [_1184063, _1184065, _1184067]), 23400 ^ [_1184063, _1184065, _1184067]))))]]], (47811 ^ _775828) ^ [_1730640, _1730642, _1730644, _1730646, _1730648, _1730650] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730640)), _1730642) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730644)), _1730646), -(c_Map_Omap__upds(_1730640, _1730644, _1730648, hAPP(hAPP(c_List_Oappend(_1730640), _1730642), _1730650), _1730646) = c_Map_Omap__upds(_1730640, _1730644, _1730648, _1730642, _1730646))], (12479 ^ _775828) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9391 ^ _775828) ^ [_926558, _926560, _926562] : [class_Rings_Oordered__cancel__semiring(_926558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926558), c_Groups_Ozero__class_Ozero(_926558)), _926560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926558), _926562), c_Groups_Ozero__class_Ozero(_926558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926558), _926562), _926560)), c_Groups_Ozero__class_Ozero(_926558))))], (10708 ^ _775828) ^ [_950783, _950785] : [class_Rings_Ocomm__semiring__1(_950783), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950783), c_Groups_Oone__class_Oone(_950783)), _950785) = _950785)], (25259 ^ _775828) ^ [_1221339, _1221341, _1221343, _1221345, _1221347, _1221349, _1221351] : [hBOOL(hAPP(hAPP(_1221339, hAPP(c_Product__Type_Osnd(_1221341, _1221343), _1221345)), hAPP(c_Product__Type_Ofst(_1221341, _1221343), _1221345))), 25266 ^ _775828 : [(25269 ^ _775828) ^ [] : [hBOOL(hAPP(_1221347, hAPP(hAPP(_1221349, 25264 ^ [_1221339, _1221341, _1221343, _1221345, _1221347, _1221349, _1221351]), 25265 ^ [_1221339, _1221341, _1221343, _1221345, _1221347, _1221349, _1221351])))], (25267 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1221339, 25265 ^ [_1221339, _1221341, _1221343, _1221345, _1221347, _1221349, _1221351]), 25264 ^ [_1221339, _1221341, _1221343, _1221345, _1221347, _1221349, _1221351])))]], -(hBOOL(hAPP(_1221347, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1221341, _1221343, _1221351), _1221349), _1221345))))], (5220 ^ _775828) ^ [_855649, _855651, _855653, _855655, _855657, _855659] : [-(c_Set_Oimage(_855659, _855655, _855651) = c_Set_Oimage(_855657, _855653, _855649)), _855659 = _855657, _855655 = _855653, _855651 = _855649], (20824 ^ _775828) ^ [_1134189] : [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), _1134189))), 20827 ^ _775828 : [(20834 ^ _775828) ^ [] : [-(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), _1134189))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134189)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134189)), 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), _1134189)))))], (20828 ^ _775828) ^ [] : [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), _1134189)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134189)) = 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), _1134189))))]]], (47721 ^ _775828) ^ [_1728482, _1728484, _1728486, _1728488, _1728490] : [-(c_Map_Odom(_1728482, _1728484, c_Map_Omap__upds(_1728482, _1728484, _1728486, _1728488, _1728490)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1728482, tc_HOL_Obool)), hAPP(c_List_Oset(_1728482), hAPP(hAPP(c_List_Otake(_1728482), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728484)), _1728490)), _1728488))), c_Map_Odom(_1728482, _1728484, _1728486)))], (51522 ^ _775828) ^ [_1808390, _1808392, _1808394, _1808396, _1808398, _1808400] : [-(hAPP(hAPP(hAPP(c_COMBS(_1808390, _1808392, _1808394), _1808396), _1808398), _1808400) = hAPP(hAPP(_1808396, _1808400), hAPP(_1808398, _1808400)))], (31101 ^ _775828) ^ [_1346091, _1346093] : [c_Nitpick_Owf_H(_1346091, _1346093), 31104 ^ _775828 : [(31107 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1346091, _1346091)), _1346093))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (31105 ^ _775828) ^ [] : [-(c_Wellfounded_Oacyclic(_1346091, _1346093))]]], (47541 ^ _775828) ^ [_1724173, _1724175, _1724177] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1724173)), -(c_List_Osublist(_1724175, hAPP(hAPP(c_List_Olist_OCons(_1724175), _1724177), c_List_Olist_ONil(_1724175)), _1724173) = hAPP(hAPP(c_List_Olist_OCons(_1724175), _1724177), c_List_Olist_ONil(_1724175)))], (18815 ^ _775828) ^ [_1099304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1099304)), 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), _1099304)) = 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), _1099304))))))], (14493 ^ _775828) ^ [_1018512, _1018514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018512), 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)), _1018514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018512), _1018514)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47972 ^ _775828) ^ [_1734513, _1734515, _1734517] : [hAPP(hAPP(c_List_Oappend(_1734513), _1734515), _1734517) = _1734515, -(_1734517 = c_List_Olist_ONil(_1734513))], (33356 ^ _775828) ^ [_1394130, _1394132, _1394134, _1394136, _1394138] : [-(hBOOL(hAPP(hAPP(c_member(_1394130), _1394132), _1394134))), -(hAPP(c_Map_Orestrict__map(_1394130, _1394136, _1394138, _1394134), _1394132) = c_Option_Ooption_ONone(_1394136))], (44467 ^ _775828) ^ [_1649326, _1649328, _1649330, _1649332, _1649334] : [-(_1649326 = c_Orderings_Obot__class_Obot(tc_fun(_1649328, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649328, tc_fun(_1649330, tc_HOL_Obool)), _1649326), hAPP(hAPP(c_COMBC(_1649328, tc_fun(_1649330, tc_HOL_Obool), tc_fun(_1649330, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649330, tc_HOL_Obool), tc_fun(tc_fun(_1649330, tc_HOL_Obool), tc_fun(_1649330, tc_HOL_Obool)), _1649328), c_Groups_Ominus__class_Ominus(tc_fun(_1649330, tc_HOL_Obool))), _1649332)), _1649334)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1649330, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649328, tc_fun(_1649330, tc_HOL_Obool)), _1649326), _1649332)), _1649334))], (42850 ^ _775828) ^ [_1610463, _1610465, _1610467, _1610469, _1610471] : [class_Groups_Ocomm__monoid__add(_1610463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610465), _1610467)), c_Fun_Oinj__on(_1610465, _1610465, _1610469, _1610467), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1610465, _1610463), _1610471), hAPP(c_Set_Oimage(_1610465, _1610465, _1610469), _1610467)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1610465, _1610463), hAPP(c_Fun_Ocomp(_1610465, _1610463, _1610465, _1610471), _1610469)), _1610467))], (48130 ^ _775828) ^ [_1738079, _1738081, _1738083, _1738085, _1738087, _1738089] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1738079), tc_List_Olist(_1738079))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1738079), tc_List_Olist(_1738079)), hAPP(hAPP(c_List_Oappend(_1738079), _1738081), hAPP(hAPP(c_List_Olist_OCons(_1738079), _1738083), c_List_Olist_ONil(_1738079)))), hAPP(hAPP(c_List_Oappend(_1738079), _1738085), hAPP(hAPP(c_List_Olist_OCons(_1738079), _1738087), c_List_Olist_ONil(_1738079))))), c_List_Olistrel1(_1738079, _1738089)))), 48131 ^ _775828 : [(48138 ^ _775828) ^ [] : [_1738081 = _1738085, hBOOL(hAPP(hAPP(c_member(tc_prod(_1738079, _1738079)), hAPP(hAPP(c_Product__Type_OPair(_1738079, _1738079), _1738083), _1738087)), _1738089))], (48132 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1738079), tc_List_Olist(_1738079))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1738079), tc_List_Olist(_1738079)), _1738081), _1738085)), c_List_Olistrel1(_1738079, _1738089))), _1738083 = _1738087]]], (17337 ^ _775828) ^ [_1072580, _1072582, _1072584, _1072586] : [class_Rings_Olinordered__semidom(_1072580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072580), c_Groups_Oone__class_Oone(_1072580)), _1072582)), 17344 ^ _775828 : [(17351 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072584), _1072586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072580), hAPP(hAPP(c_Power_Opower__class_Opower(_1072580), _1072582), _1072584)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072580), _1072582), _1072586))))], (17345 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072580), hAPP(hAPP(c_Power_Opower__class_Opower(_1072580), _1072582), _1072584)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072580), _1072582), _1072586))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072584), _1072586)))]]], (16711 ^ _775828) ^ [_1060476, _1060478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060476), _1060478)), -(c_Divides_Odivmod__nat(_1060476, _1060478) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060476))], (30667 ^ _775828) ^ [_1336221, _1336223, _1336225, _1336227] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336221), hAPP(c_Set_OCollect(_1336221), _1336223))), 30670 ^ 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[] : [-(hBOOL(hAPP(_1336223, 30682 ^ [_1336221, _1336223, _1336225, _1336227])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1336225), hAPP(c_Set_OCollect(_1336225), hAPP(hAPP(c_COMBB(tc_fun(_1336221, tc_HOL_Obool), tc_HOL_Obool, _1336225), c_HOL_OEx(_1336221)), hAPP(hAPP(c_COMBB(tc_fun(_1336221, tc_HOL_Obool), tc_fun(_1336221, tc_HOL_Obool), _1336225), hAPP(c_COMBS(_1336221, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1336221), c_fconj), _1336223))), _1336227))))))]]], (49396 ^ _775828) ^ [_1767737, _1767739, _1767741] : [hAPP(c_List_Ofilter(_1767737, _1767739), _1767741) = _1767741, 49399 ^ _775828 : [(49400 ^ _775828) ^ [_1767828] : [hBOOL(hAPP(hAPP(c_member(_1767737), _1767828), hAPP(c_List_Oset(_1767737), _1767741))), -(hBOOL(hAPP(_1767739, _1767828)))]]], (16202 ^ _775828) ^ [_1050939, _1050941] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050939, _1050941) = 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), _1050939), _1050941) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050941), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050939, _1050941)))], (51460 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (42549 ^ _775828) ^ [_1603202, _1603204, _1603206] : [hBOOL(hAPP(hAPP(c_member(_1603204), _1603202), c_Orderings_Obot__class_Obot(tc_fun(_1603204, tc_HOL_Obool)))), -(hBOOL(hAPP(_1603206, _1603202)))], (35399 ^ _775828) ^ [_1440417, _1440419] : [-(hAPP(c_Set_OPow(_1440417), _1440419) = hAPP(c_Set_OCollect(tc_fun(_1440417, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1440417, tc_HOL_Obool), tc_fun(_1440417, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1440417, tc_HOL_Obool))), _1440419)))], (17087 ^ _775828) ^ [_1067620, _1067622, _1067624, _1067626] : [class_Int_Onumber__ring(_1067620), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067620), hAPP(c_Int_Onumber__class_Onumber__of(_1067620), _1067622)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067620), hAPP(c_Int_Onumber__class_Onumber__of(_1067620), _1067624)), _1067626)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067620), hAPP(c_Int_Onumber__class_Onumber__of(_1067620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067622), _1067624))), _1067626))], (10650 ^ _775828) ^ [_949537, _949539, _949541, _949543] : [class_Rings_Ocomm__semiring__1(_949537), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949537), _949539), _949541)), _949543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949537), _949539), _949543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949537), _949541), _949543)))], (46718 ^ _775828) ^ [_1704906, _1704908] : [class_Groups_Oordered__ab__group__add__abs(_1704906), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1704906), hAPP(c_Groups_Oabs__class_Oabs(_1704906), hAPP(c_List_Omonoid__add__class_Olistsum(_1704906), _1704908))), hAPP(c_List_Omonoid__add__class_Olistsum(_1704906), hAPP(hAPP(c_List_Omap(_1704906, _1704906), c_Groups_Oabs__class_Oabs(_1704906)), _1704908)))))], (35341 ^ _775828) ^ [_1438913, _1438915, _1438917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438913, tc_HOL_Obool)), _1438915), _1438917)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1438913, tc_HOL_Obool)), _1438915), hAPP(c_Set_OPow(_1438913), _1438917))))], (26862 ^ _775828) ^ [_1250432, _1250434, _1250436] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250432), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1250434, _1250436))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250432), _1250436)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250432), _1250434)))], (45694 ^ _775828) ^ [_1677355, _1677357, _1677359] : [-(hAPP(hAPP(c_Option_Omap(_1677355, _1677357), _1677359), c_Option_Ooption_ONone(_1677355)) = c_Option_Ooption_ONone(_1677357))], (34529 ^ _775828) ^ [_1419770, _1419772, _1419774, _1419776, _1419778] : [c_Finite__Set_Ofolding__one(_1419770, _1419772, _1419774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419770), _1419776)), -(_1419776 = c_Orderings_Obot__class_Obot(tc_fun(_1419770, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419770), _1419778)), -(_1419778 = c_Orderings_Obot__class_Obot(tc_fun(_1419770, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419770, tc_HOL_Obool)), _1419776), _1419778) = c_Orderings_Obot__class_Obot(tc_fun(_1419770, tc_HOL_Obool)), -(hAPP(_1419774, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419770, tc_HOL_Obool)), _1419776), _1419778)) = hAPP(hAPP(_1419772, hAPP(_1419774, _1419776)), hAPP(_1419774, _1419778)))], (13340 ^ _775828) ^ [_996892, _996894, _996896, _996898] : [class_Divides_Osemiring__div(_996892), -(c_Divides_Odiv__class_Omod(_996892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996892), _996894), _996896), _996898) = c_Divides_Odiv__class_Omod(_996892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996892), c_Divides_Odiv__class_Omod(_996892, _996894, _996898)), c_Divides_Odiv__class_Omod(_996892, _996896, _996898)), _996898))], (50431 ^ _775828) ^ [_1789594, _1789596, _1789598] : [-(hAPP(c_List_Orev(_1789594), hAPP(c_List_Ofilter(_1789594, _1789596), _1789598)) = hAPP(c_List_Ofilter(_1789594, _1789596), hAPP(c_List_Orev(_1789594), _1789598)))], (27543 ^ _775828) ^ [_1265275, _1265277] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265275), _1265277)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1265275), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265277))))], (28313 ^ _775828) ^ [_1283859, _1283861, _1283863, _1283865] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283859, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283859, tc_HOL_Obool)), _1283861), _1283863)), _1283865) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283859, tc_HOL_Obool)), _1283861), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283859, tc_HOL_Obool)), _1283863), _1283865)))], (26153 ^ _775828) ^ [_1237585] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1237585), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1237585 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12113 ^ _775828) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17957 ^ _775828) ^ [_1083569, _1083571, _1083573] : [class_Rings_Olinordered__semidom(_1083569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083569), c_Groups_Oone__class_Oone(_1083569)), _1083571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083569), hAPP(hAPP(c_Power_Opower__class_Opower(_1083569), _1083571), _1083573)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083569), _1083571), hAPP(hAPP(c_Power_Opower__class_Opower(_1083569), _1083571), _1083573)))))], (100 ^ _775828) ^ [_777202, _777204, _777206, _777208] : [-(c_Nitpick_Orefl_H(_777206, _777202)), c_Nitpick_Orefl_H(_777208, _777204), _777208 = _777206, _777204 = _777202], (38820 ^ _775828) ^ [_1514838, _1514840, _1514842, _1514844] : [c_Fun_Oinj__on(_1514838, _1514840, _1514842, _1514844), 38823 ^ _775828 : [(38824 ^ _775828) ^ [_1514946] : [hBOOL(hAPP(hAPP(c_member(_1514838), _1514946), _1514844)), 38827 ^ _775828 : [(38828 ^ _775828) ^ [_1515048] : [hBOOL(hAPP(hAPP(c_member(_1514838), _1515048), _1514844)), hAPP(_1514842, _1514946) = hAPP(_1514842, _1515048), -(_1514946 = _1515048)]]]]], (50730 ^ _775828) ^ [_1797215, _1797217] : [-(hBOOL(hAPP(c_List_Odistinct(_1797215), c_List_Oremdups(_1797215, _1797217))))], (13550 ^ _775828) ^ [_1000963, _1000965, _1000967] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1000963, _1000965, _1000967))), 13553 ^ _775828 : [(13556 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1000967)))], (13554 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1000965)))]]], (33069 ^ _775828) ^ [_1387751, _1387753, _1387755] : [class_Groups_Ocomm__monoid__add(_1387751), class_Groups_Ocomm__monoid__mult(_1387751), c_Nat__Transfer_Onat__set(_1387753), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1387751), _1387755), _1387753) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1387751), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1387751, tc_Nat_Onat), _1387755), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1387753)))], (18831 ^ _775828) ^ [_1099600, _1099602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099600)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099602)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1099600, _1099602) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1099600, _1099602)))], (42565 ^ _775828) ^ [_1603706, _1603708, _1603710, _1603712] : [42567 ^ _775828 : [(42570 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1603706, _1603706, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1603706, tc_fun(_1603706, _1603708), tc_fun(_1603706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603708, tc_HOL_Obool), tc_fun(tc_fun(_1603706, _1603708), tc_fun(_1603706, tc_HOL_Obool)), _1603706), c_COMBB(_1603708, tc_HOL_Obool, _1603706)), hAPP(hAPP(c_COMBB(_1603708, tc_fun(_1603708, tc_HOL_Obool), _1603706), c_fequal), _1603712))), _1603712)), 42566 ^ [_1603706, _1603708, _1603710, _1603712]))], (42568 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603706, _1603706)), 42566 ^ [_1603706, _1603708, _1603710, _1603712]), _1603710)))]], -(c_Equiv__Relations_Ocongruent(_1603706, _1603708, _1603710, _1603712))], (31599 ^ _775828) ^ [_1357545, _1357547, _1357549, _1357551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1357545, _1357545)), hAPP(hAPP(c_Product__Type_OPair(_1357545, _1357545), _1357547), _1357549)), c_Transitive__Closure_Otrancl(_1357545, _1357551))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1357545, _1357545)), hAPP(hAPP(c_Product__Type_OPair(_1357545, _1357545), _1357547), _1357549)), c_Transitive__Closure_Ortrancl(_1357545, _1357551))))], (39599 ^ _775828) ^ [_1532315, _1532317, _1532319, _1532321, _1532323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532315, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532317, tc_fun(_1532315, tc_HOL_Obool)), _1532319), _1532321)), _1532323)), 39602 ^ _775828 : [(39603 ^ _775828) ^ [_1532448] : [hBOOL(hAPP(hAPP(c_member(_1532317), _1532448), _1532319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532315, tc_HOL_Obool)), hAPP(_1532321, _1532448)), _1532323)))]]], (4474 ^ _775828) ^ [_844124, _844126] : [_844126 = _844124, -(c_Orderings_Obot__class_Obot(_844126) = c_Orderings_Obot__class_Obot(_844124))], (28421 ^ _775828) ^ [_1286220, _1286222, _1286224, _1286226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286220, tc_HOL_Obool)), _1286222), _1286224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286220, tc_HOL_Obool)), _1286226), _1286224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286220, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286220, tc_HOL_Obool)), _1286222), _1286226)), _1286224)))], (27769 ^ _775828) ^ [_1270408, _1270410, _1270412] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1270408, _1270410, _1270410), _1270412), c_Relation_OId(_1270410)) = _1270412)], (28199 ^ _775828) ^ [_1281496] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1281496) = c_Orderings_Oord__class_Omax(_1281496)), class_Lattices_Osemilattice__sup(_1281496), class_Orderings_Olinorder(_1281496)], (51602 ^ _775828) ^ [_1809397, _1809399] : [hBOOL(_1809397), -(hBOOL(hAPP(hAPP(c_fimplies, _1809399), _1809397)))], (29283 ^ _775828) ^ [_1306918, _1306920, _1306922] : [hAPP(c_Relation_ORange(_1306918, _1306920), _1306922) = c_Orderings_Obot__class_Obot(tc_fun(_1306920, tc_HOL_Obool)), -(_1306922 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1306918, _1306920), tc_HOL_Obool)))], (35705 ^ _775828) ^ [_1446309, _1446311, _1446313, _1446315] : [class_Orderings_Oorder(_1446309), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446309, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1446309, _1446311, _1446313)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446309, _1446313, _1446315)) = c_Orderings_Obot__class_Obot(tc_fun(_1446309, tc_HOL_Obool)))], (27412 ^ _775828) ^ [_1262595, _1262597, _1262599, _1262601, _1262603] : [hBOOL(hAPP(hAPP(_1262595, _1262597), _1262599)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1262601, _1262603, _1262595), _1262599)))], (10788 ^ _775828) ^ [_952239, _952241, _952243, _952245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952239, tc_HOL_Obool)), _952241), _952243)), hBOOL(hAPP(hAPP(c_member(_952239), _952245), _952241)), -(hBOOL(hAPP(hAPP(c_member(_952239), _952245), _952243)))], (10826 ^ _775828) ^ [_952837, _952839] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _952837)), _952839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952837), hAPP(c_Nat_OSuc, _952839)))], (28737 ^ _775828) ^ [_1292596, _1292598, _1292600] : [c_Wellfounded_Owf(_1292596, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292596, _1292596), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292596, _1292596), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1292596, _1292596, _1292596), _1292598), _1292598)), hAPP(hAPP(c_Relation_Orel__comp(_1292596, _1292596, _1292596), _1292600), _1292598))), _1292600)), -(c_Wellfounded_Owf(_1292596, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292596, _1292596), tc_HOL_Obool)), _1292598), _1292600)))], (46628 ^ _775828) ^ [_1702445, _1702447, _1702449, _1702451, _1702453] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702445), tc_List_Olist(_1702445))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702445), tc_List_Olist(_1702445)), hAPP(hAPP(c_List_Olist_OCons(_1702445), _1702447), _1702449)), _1702451)), c_List_Olistrel(_1702445, _1702453))), 46633 ^ _775828 : [(46638 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702445), tc_List_Olist(_1702445))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702445), tc_List_Olist(_1702445)), _1702449), 46632 ^ [_1702445, _1702447, _1702449, _1702451, _1702453])), c_List_Olistrel(_1702445, _1702453))))], (46636 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1702445, _1702445)), hAPP(hAPP(c_Product__Type_OPair(_1702445, _1702445), _1702447), 46631 ^ [_1702445, _1702447, _1702449, _1702451, _1702453])), _1702453)))], (46634 ^ _775828) ^ [] : [-(_1702451 = hAPP(hAPP(c_List_Olist_OCons(_1702445), 46631 ^ [_1702445, _1702447, _1702449, _1702451, _1702453]), 46632 ^ [_1702445, _1702447, _1702449, _1702451, _1702453]))]]], (23960 ^ _775828) ^ [_1195409, _1195411, _1195413, _1195415] : [class_Orderings_Olinorder(_1195409), 23963 ^ _775828 : [(23964 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195411), _1195413)), _1195415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), _1195411), _1195415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), _1195413), _1195415)))], (23974 ^ _775828) ^ [] : [23975 ^ _775828 : [(23978 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), _1195413), _1195415))], (23976 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), _1195411), _1195415))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195409), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195411), _1195413)), _1195415)))]]], (36383 ^ _775828) ^ [_1459100, _1459102, _1459104, _1459106] : [class_Orderings_Oorder(_1459100), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459100, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1459100, _1459102, _1459104)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459100, _1459104), _1459106)) = c_Orderings_Obot__class_Obot(tc_fun(_1459100, tc_HOL_Obool)))], (44902 ^ _775828) ^ [_1659226] : [class_Complete__Lattice_Ocomplete__lattice(_1659226), -(c_Complete__Lattice_OInf__class_OInf(_1659226, c_Orderings_Obot__class_Obot(tc_fun(_1659226, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1659226))], (33577 ^ _775828) ^ [_1398990, _1398992, _1398994, _1398996] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398990, tc_HOL_Obool)), _1398992), _1398994), _1398996)), 33580 ^ _775828 : [(33583 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1398994, _1398996)))], (33581 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1398992, _1398996)))]]], (7779 ^ _775828) ^ [_900052, _900054] : [class_Groups_Oordered__ab__group__add(_900052), 7782 ^ _775828 : [(7789 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900052), c_Groups_Ozero__class_Ozero(_900052)), _900054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900052), hAPP(c_Groups_Ouminus__class_Ouminus(_900052), _900054)), c_Groups_Ozero__class_Ozero(_900052))))], (7783 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900052), hAPP(c_Groups_Ouminus__class_Ouminus(_900052), _900054)), c_Groups_Ozero__class_Ozero(_900052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900052), c_Groups_Ozero__class_Ozero(_900052)), _900054)))]]], (13414 ^ _775828) ^ [_998439, _998441, _998443] : [hBOOL(hAPP(c_Com_OWT, _998443)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_998439, _998441, _998443))))], (22386 ^ _775828) ^ [_1165093, _1165095, _1165097, _1165099, _1165101, _1165103] : [hBOOL(hAPP(hAPP(_1165093, _1165095), _1165097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1165099, tc_fun(_1165101, tc_HOL_Obool))), _1165093), _1165103)), -(hBOOL(hAPP(hAPP(_1165103, _1165095), _1165097)))], (32819 ^ _775828) ^ [_1382912, _1382914, _1382916, _1382918, _1382920, _1382922] : [-(hBOOL(hAPP(hAPP(c_member(_1382912), _1382914), _1382916))), -(hAPP(c_Set_Oimage(_1382912, _1382918, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1382912, _1382918), _1382920), _1382914), _1382922)), _1382916) = hAPP(c_Set_Oimage(_1382912, _1382918, _1382920), _1382916))], (36515 ^ _775828) ^ [_1461817, _1461819] : [-(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)), _1461817)), 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), _1461819), _1461817))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1461817), _1461819))], (27483 ^ _775828) ^ [_1264072, _1264074, _1264076, _1264078] : [hBOOL(hAPP(hAPP(_1264076, _1264074), _1264078)), -(hBOOL(hAPP(hAPP(c_member(_1264072), _1264074), c_SetInterval_Oord_OlessThan(_1264072, _1264076, _1264078))))], (17831 ^ _775828) ^ [_1081165, _1081167, _1081169] : [class_Rings_Olinordered__semidom(_1081165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081165), c_Groups_Oone__class_Oone(_1081165)), _1081167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081165), c_Groups_Oone__class_Oone(_1081165)), hAPP(hAPP(c_Power_Opower__class_Opower(_1081165), _1081167), _1081169))))], (39450 ^ _775828) ^ [_1528582, _1528584, _1528586, _1528588] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1528582, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1528584)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1528582, tc_HOL_Obool), tc_Nat_Onat), _1528586), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1528588))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1528582, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1528588, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528584), _1528588))), _1528586))], (30321 ^ _775828) ^ [_1329656, _1329658, _1329660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329656), _1329658)), 30324 ^ _775828 : [(30331 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329656), _1329660), _1329658))), -(hAPP(c_Finite__Set_Ocard(_1329656), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329656, tc_HOL_Obool)), _1329658), hAPP(hAPP(c_Set_Oinsert(_1329656), _1329660), c_Orderings_Obot__class_Obot(tc_fun(_1329656, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1329656), _1329658))], (30325 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329656), _1329660), _1329658)), -(hAPP(c_Finite__Set_Ocard(_1329656), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329656, tc_HOL_Obool)), _1329658), hAPP(hAPP(c_Set_Oinsert(_1329656), _1329660), c_Orderings_Obot__class_Obot(tc_fun(_1329656, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329656), _1329658)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (39325 ^ _775828) ^ [_1525495, _1525497, _1525499, _1525501, _1525503, _1525505] : [c_Fun_Oinj__on(_1525495, _1525497, _1525499, _1525501), hAPP(_1525499, _1525503) = _1525505, hBOOL(hAPP(hAPP(c_member(_1525495), _1525503), _1525501)), -(hAPP(c_Fun_Othe__inv__into(_1525495, _1525497, _1525501, _1525499), _1525505) = _1525503)], (31985 ^ _775828) ^ [_1367610, _1367612] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1367610, _1367612))))], (45395 ^ _775828) ^ [_1669933, _1669935, _1669937, _1669939] : [c_Fun_Oinj__on(_1669933, tc_Option_Ooption(_1669935), c_Map_Omap__add(_1669933, _1669935, _1669937, _1669939), c_Map_Odom(_1669933, _1669935, _1669939)), -(c_Fun_Oinj__on(_1669933, tc_Option_Ooption(_1669935), _1669939, c_Map_Odom(_1669933, _1669935, _1669939)))], (20438 ^ _775828) ^ [] : [-(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))))], (14886 ^ _775828) ^ [_1025100, _1025102, _1025104] : [class_Divides_Osemiring__div(_1025100), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025100), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025100), _1025102), _1025104)), _1025104)), c_Divides_Odiv__class_Omod(_1025100, _1025102, _1025104)) = _1025102)], (34389 ^ _775828) ^ [_1416779, _1416781, _1416783, _1416785, _1416787, _1416789, _1416791, _1416793] : [c_Finite__Set_Ofolding__image__simple(_1416779, _1416781, _1416783, _1416785, _1416787, _1416789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416781), _1416791)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416781), _1416793)), -(hAPP(hAPP(_1416783, hAPP(_1416789, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416781, tc_HOL_Obool)), _1416791), _1416793))), hAPP(_1416789, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416781, tc_HOL_Obool)), _1416791), _1416793))) = hAPP(hAPP(_1416783, hAPP(_1416789, _1416791)), hAPP(_1416789, _1416793)))], (11556 ^ _775828) ^ [_965808] : [class_Rings_Olinordered__semidom(_965808), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965808), c_Groups_Ozero__class_Ozero(_965808)), c_Groups_Oone__class_Oone(_965808))))], (9249 ^ _775828) ^ [_923857, _923859, _923861, _923863, _923865] : [class_Rings_Oordered__semiring(_923857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923857), _923859), _923861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923857), _923863), _923865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923857), c_Groups_Ozero__class_Ozero(_923857)), _923861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923857), c_Groups_Ozero__class_Ozero(_923857)), _923863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923857), _923859), _923863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923857), _923861), _923865))))], (24426 ^ _775828) ^ [_1204703, _1204705, _1204707] : [class_Fields_Olinordered__field__inverse__zero(_1204703), 24432 ^ _775828 : [(24437 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204703), 24431 ^ [_1204703, _1204705, _1204707]), _1204705)), _1204707))], (24435 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204703), 24431 ^ [_1204703, _1204705, _1204707]), c_Groups_Oone__class_Oone(_1204703))))], (24433 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204703), c_Groups_Ozero__class_Ozero(_1204703)), 24431 ^ [_1204703, _1204705, _1204707])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204703), _1204705), _1204707)))], (23468 ^ _775828) ^ [_1185810, _1185812, _1185814, _1185816, _1185818] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185810, _1185812, _1185814), _1185816), _1185818) = hAPP(hAPP(_1185816, hAPP(c_Product__Type_Ofst(_1185810, _1185812), _1185818)), hAPP(c_Product__Type_Osnd(_1185810, _1185812), _1185818)))], (7667 ^ _775828) ^ [_898237, _898239, _898241] : [class_Rings_Oring(_898237), -(hAPP(c_Groups_Ouminus__class_Ouminus(_898237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898237), _898239), _898241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898237), _898239), hAPP(c_Groups_Ouminus__class_Ouminus(_898237), _898241)))], (13404 ^ _775828) ^ [_998246, _998248] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _998246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _998248)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _998246, _998248)))], (1690 ^ _775828) ^ [_799571, _799573] : [-(class_Rings_Osemiring(_799571)), _799573 = _799571, class_Rings_Osemiring(_799573)], (44196 ^ _775828) ^ [_1641578, _1641580, _1641582, _1641584] : [c_Orderings_Otop__class_Otop(tc_fun(_1641578, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641580, tc_fun(_1641578, tc_HOL_Obool)), _1641582), _1641584), 44199 ^ _775828 : [(44200 ^ _775828) ^ [_1641694] : [hBOOL(hAPP(hAPP(c_member(_1641580), _1641694), _1641582)), -(hAPP(_1641584, _1641694) = c_Orderings_Otop__class_Otop(tc_fun(_1641578, tc_HOL_Obool)))]]], (51530 ^ _775828) ^ [_1808534, _1808536] : [_1808534 = _1808536, -(hBOOL(hAPP(hAPP(c_fequal, _1808534), _1808536)))], (42162 ^ _775828) ^ [_1594514, _1594516, _1594518] : [c_Relation_Orefl__on(_1594514, _1594516, _1594518), -(c_Relation_Orefl__on(_1594514, _1594516, hAPP(c_Relation_Oconverse(_1594514, _1594514), _1594518)))], (12231 ^ _775828) ^ [_977405, _977407, _977409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977405), _977407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977405), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977409), _977407))))], (42204 ^ _775828) ^ [_1595298, _1595300, _1595302, _1595304, _1595306] : [c_Relation_Orefl__on(_1595298, _1595300, _1595302), hBOOL(hAPP(hAPP(c_member(tc_prod(_1595298, _1595298)), hAPP(hAPP(c_Product__Type_OPair(_1595298, _1595298), _1595304), _1595306)), _1595302)), -(hBOOL(hAPP(hAPP(c_member(_1595298), _1595304), _1595300)))], (42555 ^ _775828) ^ [_1603330, _1603332, _1603334, _1603336] : [c_Equiv__Relations_Ocongruent(_1603330, _1603332, _1603334, _1603336), 42558 ^ _775828 : [(42559 ^ _775828) ^ [_1603475] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603330, _1603330)), _1603475), _1603334)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1603330, _1603330, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1603330, tc_fun(_1603330, _1603332), tc_fun(_1603330, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603332, tc_HOL_Obool), tc_fun(tc_fun(_1603330, _1603332), tc_fun(_1603330, tc_HOL_Obool)), _1603330), c_COMBB(_1603332, tc_HOL_Obool, _1603330)), hAPP(hAPP(c_COMBB(_1603332, tc_fun(_1603332, tc_HOL_Obool), _1603330), c_fequal), _1603336))), _1603336)), _1603475)))]]], (12546 ^ _775828) ^ [_982758, _982760, _982762] : [class_Rings_Oring__1(_982758), hBOOL(hAPP(hAPP(c_member(_982758), _982760), c_Int_Oring__1__class_OInts(_982758))), hBOOL(hAPP(hAPP(c_member(_982758), _982762), c_Int_Oring__1__class_OInts(_982758))), -(hBOOL(hAPP(hAPP(c_member(_982758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982758), _982760), _982762)), c_Int_Oring__1__class_OInts(_982758))))], (24925 ^ _775828) ^ [_1214667, _1214669, _1214671] : [class_Fields_Olinordered__field(_1214667), 24931 ^ _775828 : [(24934 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214667), _1214669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214667), _1214671), 24930 ^ [_1214667, _1214669, _1214671])))], (24932 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214667), c_Groups_Ozero__class_Ozero(_1214667)), 24930 ^ [_1214667, _1214669, _1214671])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214667), _1214669), _1214671)))], (36761 ^ _775828) ^ [_1466381, _1466383, _1466385] : [class_Orderings_Olinorder(_1466381), 36764 ^ _775828 : [(36771 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1466381), _1466383), _1466385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1466381, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466381), _1466383)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466381), _1466385))))], (36765 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1466381, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466381), _1466383)), hAPP(c_SetInterval_Oord__class_OlessThan(_1466381), _1466385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1466381), _1466383), _1466385)))]]], (7343 ^ _775828) ^ [_892861, _892863, _892865] : [class_Rings_Olinordered__idom(_892861), 7346 ^ _775828 : [(7353 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _892863), _892865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892861), hAPP(c_Int_Oring__1__class_Oof__int(_892861), _892863)), hAPP(c_Int_Oring__1__class_Oof__int(_892861), _892865))))], (7347 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892861), hAPP(c_Int_Oring__1__class_Oof__int(_892861), _892863)), hAPP(c_Int_Oring__1__class_Oof__int(_892861), _892865))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _892863), _892865)))]]], (2454 ^ _775828) ^ [_811924, _811926, _811928, _811930, _811932, _811934, _811936, _811938] : [-(c_Random__Sequence_ORandom(_811938, _811934, _811930, _811926) = c_Random__Sequence_ORandom(_811936, _811932, _811928, _811924)), _811938 = _811936, _811934 = _811932, _811930 = _811928, _811926 = _811924], (19994 ^ _775828) ^ [_1119292, _1119294] : [class_Rings_Osemiring__1(_1119292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119294)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119292), 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)))), _1119294))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119292), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119292), hAPP(c_Int_Onat, _1119294))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119292), hAPP(c_Int_Onat, _1119294))))], (9695 ^ _775828) ^ [_931797] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931797))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14419 ^ _775828) ^ [_1017268, _1017270, _1017272, _1017274, _1017276] : [c_Com_Ocom_OLocal(_1017268, _1017270, _1017272) = c_Com_Ocom_OWhile(_1017274, _1017276)], (25499 ^ _775828) ^ [_1225696, _1225698, _1225700, _1225702] : [-(c_New__Random__Sequence_Opos__empty(_1225696, _1225698, _1225700, _1225702) = c_New__DSequence_Opos__empty(_1225696))], (20800 ^ _775828) ^ [_1133717, _1133719] : [class_Rings_Oring__1(_1133717), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1133717), hAPP(c_Groups_Ouminus__class_Ouminus(_1133717), c_Groups_Oone__class_Oone(_1133717))), 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)))), _1133719))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1133717), c_Groups_Oone__class_Oone(_1133717)))], (39646 ^ _775828) ^ [_1534126, _1534128, _1534130, _1534132, _1534134] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534126, tc_fun(_1534128, tc_HOL_Obool)), _1534130), hAPP(hAPP(c_COMBC(_1534126, tc_fun(_1534128, tc_HOL_Obool), tc_fun(_1534128, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534128, tc_HOL_Obool), tc_fun(tc_fun(_1534128, tc_HOL_Obool), tc_fun(_1534128, tc_HOL_Obool)), _1534126), c_Groups_Ominus__class_Ominus(tc_fun(_1534128, tc_HOL_Obool))), _1534132)), _1534134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1534128, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534126, tc_fun(_1534128, tc_HOL_Obool)), _1534130), _1534132)), _1534134))], (7893 ^ _775828) ^ [_902011, _902013, _902015] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902011), _902013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902015), _902013)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902011), _902015))], (3728 ^ _775828) ^ [_832477, _832479] : [_832479 = _832477, -(c_SetInterval_Oord__class_OgreaterThan(_832479) = c_SetInterval_Oord__class_OgreaterThan(_832477))], (27214 ^ _775828) ^ [_1257352, _1257354, _1257356] : [hBOOL(hAPP(hAPP(c_member(_1257352), _1257354), hAPP(c_Set_OCollect(_1257352), _1257356))), -(hBOOL(hAPP(_1257356, _1257354)))], (9293 ^ _775828) ^ [_924703, _924705, _924707, _924709] : [class_Rings_Oordered__ring(_924703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924703), _924705), _924707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924703), _924709), c_Groups_Ozero__class_Ozero(_924703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924703), _924709), _924707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924703), _924709), _924705))))], (42712 ^ _775828) ^ [_1607287, _1607289, _1607291, _1607293, _1607295, _1607297] : [c_Fun_Oinj__on(_1607287, _1607289, _1607291, _1607293), 42715 ^ _775828 : [(42722 ^ _775828) ^ [] : [c_Fun_Oinj__on(_1607287, _1607295, hAPP(c_Fun_Ocomp(_1607289, _1607295, _1607287, _1607297), _1607291), _1607293), -(c_Fun_Oinj__on(_1607289, _1607295, _1607297, hAPP(c_Set_Oimage(_1607287, _1607289, _1607291), _1607293)))], (42716 ^ _775828) ^ [] : [c_Fun_Oinj__on(_1607289, _1607295, _1607297, hAPP(c_Set_Oimage(_1607287, _1607289, _1607291), _1607293)), -(c_Fun_Oinj__on(_1607287, _1607295, hAPP(c_Fun_Ocomp(_1607289, _1607295, _1607287, _1607297), _1607291), _1607293))]]], (6834 ^ _775828) ^ [_884113, _884115] : [-(_884113 = hAPP(c_Option_Ooption_OSome(_884115), 6835 ^ [_884113, _884115])), -(_884113 = c_Option_Ooption_ONone(_884115))], (41498 ^ _775828) ^ [_1578866, _1578868, _1578870] : [-(hAPP(c_Finite__Set_Ofold1(_1578866, _1578868), _1578870) = c_HOL_OThe(_1578866, c_Finite__Set_Ofold1Set(_1578866, _1578868, _1578870)))], (47451 ^ _775828) ^ [_1722337, _1722339] : [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(_1722337)), _1722339))), _1722339 = c_List_Olist_ONil(_1722337)], (51280 ^ _775828) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (51128 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (47213 ^ _775828) ^ [_1717496, _1717498, _1717500, _1717502, _1717504] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1717496, _1717498)), _1717500), hAPP(hAPP(c_List_Ozip(_1717496, _1717498), _1717502), _1717504)) = hAPP(hAPP(c_List_Ozip(_1717496, _1717498), hAPP(hAPP(c_List_Otake(_1717496), _1717500), _1717502)), hAPP(hAPP(c_List_Otake(_1717498), _1717500), _1717504)))], (33767 ^ _775828) ^ [_1403054, _1403056, _1403058] : [class_Lattices_Osemilattice__inf(_1403054), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403054), _1403056), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403054), _1403056), _1403058)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403054), _1403056), _1403058))], (16779 ^ _775828) ^ [_1061627, _1061629] : [class_Groups_Oordered__ab__group__add__abs(_1061627), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061627), c_Groups_Ozero__class_Ozero(_1061627)), _1061629)), -(hAPP(c_Groups_Oabs__class_Oabs(_1061627), _1061629) = _1061629)], (47341 ^ _775828) ^ [_1720221, _1720223] : [-(c_List_Osublist(_1720221, _1720223, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1720221))], (42762 ^ _775828) ^ [_1608365, _1608367, _1608369, _1608371, _1608373, _1608375] : [-(hAPP(hAPP(c_Fun_Ocomp(_1608365, _1608367, _1608369, _1608371), _1608373), _1608375) = hAPP(_1608371, hAPP(_1608373, _1608375)))], (19150 ^ _775828) ^ [_1105421] : [class_Rings_Osemiring__1(_1105421), c_Int_Oiszero(_1105421, c_Groups_Oone__class_Oone(_1105421))], (23588 ^ _775828) ^ [_1188569, _1188571, _1188573, _1188575, _1188577] : [-(hAPP(c_Product__Type_Osnd(_1188569, _1188571), hAPP(c_Product__Type_Oapsnd(_1188573, _1188571, _1188569, _1188575), _1188577)) = hAPP(_1188575, hAPP(c_Product__Type_Osnd(_1188569, _1188573), _1188577)))], (33334 ^ _775828) ^ [_1393604, _1393606, _1393608, _1393610, _1393612] : [hBOOL(hAPP(hAPP(c_member(_1393604), _1393606), _1393608)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1393604, tc_Option_Ooption(_1393610)), c_Map_Orestrict__map(_1393604, _1393610, _1393612, _1393608)), _1393606), c_Option_Ooption_ONone(_1393610)) = c_Map_Orestrict__map(_1393604, _1393610, _1393612, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393604, tc_HOL_Obool)), _1393608), hAPP(hAPP(c_Set_Oinsert(_1393604), _1393606), c_Orderings_Obot__class_Obot(tc_fun(_1393604, tc_HOL_Obool))))))], (28311 ^ _775828) ^ [_1283786, _1283788, _1283790, _1283792] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283786, tc_HOL_Obool)), _1283788), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283786, tc_HOL_Obool)), _1283790), _1283792)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283786, tc_HOL_Obool)), _1283790), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283786, tc_HOL_Obool)), _1283788), _1283792)))], (15232 ^ _775828) ^ [_1031548, _1031550] : [class_Groups_Ogroup__add(_1031548), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031548), _1031550), _1031550) = c_Groups_Ozero__class_Ozero(_1031548))], (45038 ^ _775828) ^ [_1662288, _1662290] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662288, tc_HOL_Obool), _1662290) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1662288, tc_HOL_Obool), tc_fun(_1662288, tc_HOL_Obool)), _1662290), c_COMBI(tc_fun(_1662288, tc_HOL_Obool))))], (47229 ^ _775828) ^ [_1717961, _1717963, _1717965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1717963))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1717963), _1717961), _1717965)) = 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), _1717963)), _1717965)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1717963), _1717961)))], (8577 ^ _775828) ^ [_913440] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913440))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _913440)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43320 ^ _775828) ^ [_1622002, _1622004, _1622006, _1622008, _1622010] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622002, _1622002)), hAPP(hAPP(c_Product__Type_OPair(_1622002, _1622002), _1622004), _1622006)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1622002, _1622002), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1622008)), _1622010))), 43324 ^ _775828 : [(43327 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622002, _1622002)), hAPP(hAPP(c_Product__Type_OPair(_1622002, _1622002), 43323 ^ [_1622002, _1622004, _1622006, _1622008, _1622010]), _1622006)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1622002, _1622002), tc_HOL_Obool), _1622008), _1622010))))], (43325 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622002, _1622002)), hAPP(hAPP(c_Product__Type_OPair(_1622002, _1622002), _1622004), 43323 ^ [_1622002, _1622004, _1622006, _1622008, _1622010])), _1622010)))]]], (45684 ^ _775828) ^ [_1677049] : [-(hAPP(c_Option_Omap(_1677049, _1677049), c_COMBI(_1677049)) = c_Fun_Oid(tc_Option_Ooption(_1677049)))], (44351 ^ _775828) ^ [_1645815, _1645817, _1645819, _1645821, _1645823] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645815, tc_fun(_1645817, tc_HOL_Obool)), _1645819), hAPP(hAPP(c_COMBS(_1645815, tc_fun(_1645817, tc_HOL_Obool), tc_fun(_1645817, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645817, tc_HOL_Obool), tc_fun(tc_fun(_1645817, tc_HOL_Obool), tc_fun(_1645817, tc_HOL_Obool)), _1645815), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645817, tc_HOL_Obool))), _1645821)), _1645823)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645817, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645815, tc_fun(_1645817, tc_HOL_Obool)), _1645819), _1645821)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645815, tc_fun(_1645817, tc_HOL_Obool)), _1645819), _1645823)))], (46556 ^ _775828) ^ [_1699825, _1699827, _1699829, _1699831, _1699833, _1699835] : [_1699825 = _1699827, -(hAPP(c_Map_Omap__of(_1699829, _1699831, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1699829, _1699831)), hAPP(hAPP(c_Product__Type_OPair(_1699829, _1699831), _1699825), _1699833)), _1699835)), _1699827) = hAPP(c_Option_Ooption_OSome(_1699831), _1699833))], (28209 ^ _775828) ^ [_1281625, _1281627, _1281629, _1281631, _1281633] : [class_Lattices_Olattice(_1281625), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281627, _1281625)), _1281629), _1281631), _1281633) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281625), hAPP(_1281629, _1281633)), hAPP(_1281631, _1281633)))], (25459 ^ _775828) ^ [_1224878] : [-(c_Code__Numeral_OSuc__code__numeral(_1224878) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1224878))))], (3302 ^ _775828) ^ [_825796, _825798, _825800, _825802, _825804, _825806] : [-(c_Finite__Set_Ofold1Set(_825806, _825802, _825798) = c_Finite__Set_Ofold1Set(_825804, _825800, _825796)), _825806 = _825804, _825802 = _825800, _825798 = _825796], (8631 ^ _775828) ^ [_914298] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914298)) = _914298)], (43472 ^ _775828) ^ [_1625823, _1625825, _1625827] : [class_Orderings_Olinorder(_1625823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625823), _1625825)), 43482 ^ _775828 : [(43485 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625823), 43481 ^ [_1625823, _1625825, _1625827]), _1625827))], (43483 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625823), 43481 ^ [_1625823, _1625825, _1625827]), _1625825)))]], hBOOL(hAPP(hAPP(c_member(_1625823), _1625827), _1625825)), -(c_Big__Operators_Olinorder__class_OMax(_1625823, _1625825) = _1625827)], (28884 ^ _775828) ^ [_1297091, _1297093, _1297095, _1297097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1297091, _1297091)), hAPP(hAPP(c_Product__Type_OPair(_1297091, _1297091), _1297095), _1297097)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool)), _1297093), c_Relation_OId(_1297091)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297091, tc_fun(_1297091, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1297091, tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_fun(_1297091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297091, tc_fun(tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_fun(_1297091, tc_HOL_Obool)), _1297091), c_COMBC(_1297091, tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297091, tc_prod(_1297091, _1297091)), tc_fun(_1297091, tc_fun(tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_HOL_Obool)), _1297091), hAPP(c_COMBB(tc_prod(_1297091, _1297091), tc_fun(tc_fun(tc_prod(_1297091, _1297091), tc_HOL_Obool), tc_HOL_Obool), _1297091), c_member(tc_prod(_1297091, _1297091)))), c_Product__Type_OPair(_1297091, _1297091)))), _1297093)), c_fequal), _1297095), _1297097)))], (11686 ^ _775828) ^ [_967789, _967791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967789), _967791)), -(_967791 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967789), 11689 ^ [_967789, _967791])))], (32825 ^ _775828) ^ [_1382991, _1382993, _1382995, _1382997] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1382991, _1382993), _1382995), _1382997), hAPP(_1382995, _1382997)) = _1382995)], (34277 ^ _775828) ^ [_1414004, _1414006, _1414008, _1414010] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414004, tc_HOL_Obool)), _1414006), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414004, tc_HOL_Obool)), _1414008), _1414010)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414004, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414004, tc_HOL_Obool)), _1414006), _1414008)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414004, tc_HOL_Obool)), _1414006), _1414010)))], (40574 ^ _775828) ^ [_1555486, _1555488] : [-(hBOOL(hAPP(hAPP(c_member(_1555486), _1555488), c_Orderings_Otop__class_Otop(tc_fun(_1555486, tc_HOL_Obool)))))], (51096 ^ _775828) ^ [_1804218, _1804220] : [class_Orderings_Oord(_1804218), -(class_Orderings_Oord(tc_fun(_1804220, _1804218)))], (7417 ^ _775828) ^ [_894187, _894189, _894191, _894193, _894195] : [-(c_Option_Ooption_Ooption__rec(_894187, _894189, _894191, _894193, hAPP(c_Option_Ooption_OSome(_894189), _894195)) = hAPP(_894193, _894195))], (34741 ^ _775828) ^ [_1424033, _1424035, _1424037] : [class_Orderings_Olinorder(_1424033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424033), _1424035)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424033), _1424037)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424033, tc_HOL_Obool)), _1424035), _1424037) = c_Orderings_Obot__class_Obot(tc_fun(_1424033, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424033), c_Big__Operators_Olinorder__class_OMin(_1424033, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424033, tc_HOL_Obool)), _1424035), _1424037))), c_Big__Operators_Olinorder__class_OMin(_1424033, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424033, tc_HOL_Obool)), _1424035), _1424037))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424033), c_Big__Operators_Olinorder__class_OMin(_1424033, _1424035)), c_Big__Operators_Olinorder__class_OMin(_1424033, _1424037)))], (49801 ^ _775828) ^ [_1776802, _1776804, _1776806] : [class_Orderings_Olinorder(_1776802), c_List_Olinorder__class_Osorted(_1776802, _1776804), -(c_List_Olinorder__class_Osorted(_1776802, hAPP(hAPP(c_List_Odrop(_1776802), _1776806), _1776804)))], (30067 ^ _775828) ^ [_1323816, _1323818] : [30068 ^ _775828 : [(30071 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323818), _1323816))], (30069 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323816), _1323818)))]], -(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)))), _1323816, _1323818) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30111 ^ _775828) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7415 ^ _775828) ^ [_894140, _894142, _894144, _894146, _894148] : [-(hAPP(c_Option_Ooption_Ooption__case(_894140, _894142, _894144, _894146), hAPP(c_Option_Ooption_OSome(_894142), _894148)) = hAPP(_894146, _894148))], (5788 ^ _775828) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33773 ^ _775828) ^ [_1403179, _1403181, _1403183] : [class_Lattices_Olattice(_1403179), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403179), _1403181), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403179), _1403181), _1403183)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403179), _1403181), _1403183))], (11040 ^ _775828) ^ [_956507] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956507), _956507))))], (29529 ^ _775828) ^ [_1311542, _1311544, _1311546] : [-(hAPP(hAPP(c_Set_Oinsert(_1311542), _1311544), hAPP(hAPP(c_Set_Oinsert(_1311542), _1311544), _1311546)) = hAPP(hAPP(c_Set_Oinsert(_1311542), _1311544), _1311546))], (10106 ^ _775828) ^ [_939419, _939421, _939423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939419), _939421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939421), _939423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939419), _939423)))], (48543 ^ _775828) ^ [_1749469, _1749471, _1749473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749471)), _1749473))), -(hAPP(hAPP(c_List_Olist_OCons(_1749471), hAPP(hAPP(c_List_Onth(_1749471), _1749473), _1749469)), hAPP(hAPP(c_List_Odrop(_1749471), hAPP(c_Nat_OSuc, _1749469)), _1749473)) = hAPP(hAPP(c_List_Odrop(_1749471), _1749469), _1749473))], (25281 ^ _775828) ^ [_1221812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1221812)), _1221812 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50417 ^ _775828) ^ [_1789224, _1789226] : [-(hAPP(c_List_Orev(_1789224), hAPP(c_List_Orev(_1789224), _1789226)) = _1789226)], (20300 ^ _775828) ^ [_1124596, _1124598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1124596)), c_Int_OBit1(_1124598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124596), _1124598)))], (14179 ^ _775828) ^ [_1012827, _1012829, _1012831, _1012833, _1012835] : [hBOOL(hAPP(_1012827, _1012829)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1012831), _1012829), _1012833)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1012827, _1012831)), _1012833), _1012835)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1012827, _1012831)), _1012829), _1012835)))], (50353 ^ _775828) ^ [_1787868, _1787870, _1787872] : [-(hAPP(c_List_Orev(_1787868), hAPP(hAPP(c_List_Olist_OCons(_1787868), _1787870), _1787872)) = hAPP(hAPP(c_List_Oappend(_1787868), hAPP(c_List_Orev(_1787868), _1787872)), hAPP(hAPP(c_List_Olist_OCons(_1787868), _1787870), c_List_Olist_ONil(_1787868))))], (9915 ^ _775828) ^ [_935996] : [_935996 = 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), _935996)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30587 ^ _775828) ^ [_1334843, _1334845, _1334847] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334843), hAPP(c_Set_OCollect(_1334843), hAPP(hAPP(c_COMBS(_1334843, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1334843), c_fdisj), _1334845)), _1334847))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334843), hAPP(c_Set_OCollect(_1334843), _1334845))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334843), hAPP(c_Set_OCollect(_1334843), _1334847)))], (25691 ^ _775828) ^ [_1229985, _1229987, _1229989, _1229991] : [class_Divides_Osemiring__div(_1229985), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229985), _1229987), _1229989)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229985), _1229987), _1229991)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229985), _1229987), c_Divides_Odiv__class_Omod(_1229985, _1229989, _1229991))))], (33957 ^ _775828) ^ [_1407551, _1407553, _1407555] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407551, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407551, tc_HOL_Obool)), _1407553), _1407555)), _1407553)))], (50862 ^ _775828) ^ [_1799842, _1799844, _1799846] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799842)), c_List_OdropWhile(_1799842, _1799844, _1799846))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799842)), _1799846))))], (27887 ^ _775828) ^ [_1274485, _1274487] : [c_Wellfounded_Owf(_1274485, _1274487), -(c_Wellfounded_Owf(_1274485, hAPP(hAPP(c_Relation_Orel__comp(_1274485, _1274485, _1274485), _1274487), _1274487)))], (51352 ^ _775828) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (14427 ^ _775828) ^ [_1017483, _1017485] : [c_Com_Ocom_OWhile(_1017483, _1017485) = c_Com_Ocom_OSKIP], (46285 ^ _775828) ^ [_1691927, _1691929, _1691931] : [-(_1691927 = _1691929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691931)), _1691927) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691931)), _1691929), 46291 ^ _775828 : [(46294 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1691931, _1691931, tc_HOL_Obool), c_fequal), 46290 ^ [_1691927, _1691929, _1691931]))], (46292 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1691931, _1691931)), 46290 ^ [_1691927, _1691929, _1691931]), hAPP(c_List_Oset(tc_prod(_1691931, _1691931)), hAPP(hAPP(c_List_Ozip(_1691931, _1691931), _1691927), _1691929)))))]]], (50277 ^ _775828) ^ [_1786135, _1786137] : [c_List_Olist_ONil(_1786135) = c_List_Oconcat(_1786135, _1786137), 50280 ^ _775828 : [(50281 ^ _775828) ^ [_1786226] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1786135)), _1786226), hAPP(c_List_Oset(tc_List_Olist(_1786135)), _1786137))), -(_1786226 = c_List_Olist_ONil(_1786135))]]], (49365 ^ _775828) ^ [_1767070, _1767072, _1767074, _1767076, _1767078] : [c_List_Opartition(_1767070, _1767072, _1767074) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767070), tc_List_Olist(_1767070)), _1767076), _1767078), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1767070, tc_HOL_Obool)), hAPP(c_List_Oset(_1767070), _1767076)), hAPP(c_List_Oset(_1767070), _1767078)) = hAPP(c_List_Oset(_1767070), _1767074))], (39012 ^ _775828) ^ [_1518448, _1518450, _1518452, _1518454, _1518456, _1518458] : [c_Fun_Oinj__on(_1518448, _1518450, _1518452, _1518454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518448, tc_HOL_Obool)), _1518456), _1518454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518448, tc_HOL_Obool)), _1518458), _1518454)), -(hAPP(c_Set_Oimage(_1518448, _1518450, _1518452), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518448, tc_HOL_Obool)), _1518456), _1518458)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518450, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1518448, _1518450, _1518452), _1518456)), hAPP(c_Set_Oimage(_1518448, _1518450, _1518452), _1518458)))], (27244 ^ _775828) ^ [_1257997, _1257999] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1257997, tc_HOL_Obool)), _1257999) = hAPP(c_Set_OCollect(_1257997), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1257997), c_fNot), hAPP(hAPP(c_COMBC(_1257997, tc_fun(_1257997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257997)), _1257999))))], (16352 ^ _775828) ^ [_1053706, _1053708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1053706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053708)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1053708), _1053706)), _1053708) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1053708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053706), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (21802 ^ _775828) ^ [_1153855, _1153857, _1153859, _1153861] : [class_Fields_Olinordered__field__inverse__zero(_1153855), class_Int_Onumber(_1153855), 21809 ^ _775828 : [(21810 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153855), _1153859), _1153861))), 21813 ^ _775828 : [(21820 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), c_Groups_Ozero__class_Ozero(_1153855)), _1153861))), 21823 ^ _775828 : [(21830 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153861), c_Groups_Ozero__class_Ozero(_1153855)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), c_Groups_Ozero__class_Ozero(_1153855))))], (21824 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153861), c_Groups_Ozero__class_Ozero(_1153855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), _1153861))))]]], (21814 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), c_Groups_Ozero__class_Ozero(_1153855)), _1153861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), _1153861)), _1153859)))]]], (21836 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153855), _1153859), _1153861)))), 21839 ^ _775828 : [(21842 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), _1153861)), _1153859))], (21840 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), c_Groups_Ozero__class_Ozero(_1153855)), _1153861)))]], 21843 ^ _775828 : [(21846 ^ _775828) ^ [] : [21847 ^ _775828 : [(21850 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), _1153861)))], (21848 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153861), c_Groups_Ozero__class_Ozero(_1153855))))]], 21851 ^ _775828 : [(21854 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), hAPP(c_Int_Onumber__class_Onumber__of(_1153855), _1153857)), c_Groups_Ozero__class_Ozero(_1153855)))], (21852 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), _1153861), c_Groups_Ozero__class_Ozero(_1153855)))]]], (21844 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153855), c_Groups_Ozero__class_Ozero(_1153855)), _1153861))]]]]], (46612 ^ _775828) ^ [_1701398, _1701400, _1701402, _1701404] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1701398), tc_List_Olist(_1701398), c_List_Olistrel(_1701398, _1701400)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1701398)), hAPP(hAPP(c_List_Olist_OCons(_1701398), _1701402), _1701404)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1701398), tc_HOL_Obool)))) = c_List_Oset__Cons(_1701398, hAPP(c_Relation_OImage(_1701398, _1701398, _1701400), hAPP(hAPP(c_Set_Oinsert(_1701398), _1701402), c_Orderings_Obot__class_Obot(tc_fun(_1701398, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1701398), tc_List_Olist(_1701398), c_List_Olistrel(_1701398, _1701400)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1701398)), _1701404), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1701398), tc_HOL_Obool))))))], (11192 ^ _775828) ^ [_959340, _959342, _959344, _959346, _959348, _959350] : [class_Rings_Olinordered__semiring__1__strict(_959340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959340), _959342), _959344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959340), _959346), _959344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959340), c_Groups_Ozero__class_Ozero(_959340)), _959348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959340), c_Groups_Ozero__class_Ozero(_959340)), _959350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959340), _959348), _959350) = c_Groups_Oone__class_Oone(_959340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959340), _959348), _959342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959340), _959350), _959346))), _959344)))], (7295 ^ _775828) ^ [_892141, _892143, _892145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _892141), _892143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _892145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _892145), _892141)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _892145), _892143))))], (46075 ^ _775828) ^ [_1686332, _1686334, _1686336, _1686338, _1686340, _1686342, _1686344, _1686346] : [-(hAPP(hAPP(c_List_Ozip(_1686332, _1686334), hAPP(hAPP(c_List_Omap(_1686336, _1686332), _1686338), _1686340)), hAPP(hAPP(c_List_Omap(_1686342, _1686334), _1686344), _1686346)) = hAPP(hAPP(c_List_Omap(tc_prod(_1686336, _1686342), tc_prod(_1686332, _1686334)), hAPP(c_Product__Type_Oprod_Oprod__case(_1686336, _1686342, tc_prod(_1686332, _1686334)), hAPP(hAPP(c_COMBC(_1686336, tc_fun(_1686342, _1686334), tc_fun(_1686342, tc_prod(_1686332, _1686334))), hAPP(hAPP(c_COMBB(tc_fun(_1686334, tc_prod(_1686332, _1686334)), tc_fun(tc_fun(_1686342, _1686334), tc_fun(_1686342, tc_prod(_1686332, _1686334))), _1686336), c_COMBB(_1686334, tc_prod(_1686332, _1686334), _1686342)), hAPP(hAPP(c_COMBB(_1686332, tc_fun(_1686334, tc_prod(_1686332, _1686334)), _1686336), c_Product__Type_OPair(_1686332, _1686334)), _1686338))), _1686344))), hAPP(hAPP(c_List_Ozip(_1686336, _1686342), _1686340), _1686346)))], (24777 ^ _775828) ^ [_1211687, _1211689, _1211691, _1211693, _1211695, _1211697, _1211699] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1211687, _1211689, _1211691, _1211693), _1211695), _1211697), _1211699) = hAPP(hAPP(_1211697, hAPP(c_Product__Type_Ofst(_1211689, _1211691), hAPP(_1211695, _1211699))), hAPP(c_Product__Type_Osnd(_1211689, _1211691), hAPP(_1211695, _1211699))))], (48255 ^ _775828) ^ [_1742030, _1742032, _1742034, _1742036, _1742038, _1742040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742030), tc_List_Olist(_1742030))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742030), tc_List_Olist(_1742030)), hAPP(hAPP(c_List_Olist_OCons(_1742030), _1742032), _1742034)), hAPP(hAPP(c_List_Olist_OCons(_1742030), _1742036), _1742038))), c_List_Olistrel1(_1742030, _1742040))), 48260 ^ _775828 : [(48263 ^ _775828) ^ [] : [-(_1742034 = _1742038)], (48261 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1742030, _1742030)), hAPP(hAPP(c_Product__Type_OPair(_1742030, _1742030), _1742032), _1742036)), _1742040)))]], 48264 ^ _775828 : [(48267 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742030), tc_List_Olist(_1742030))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742030), tc_List_Olist(_1742030)), _1742034), _1742038)), c_List_Olistrel1(_1742030, _1742040))))], (48265 ^ _775828) ^ [] : [-(_1742032 = _1742036)]]], (51370 ^ _775828) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (18155 ^ _775828) ^ [_1087419, _1087421, _1087423, _1087425, _1087427, _1087429, _1087431] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1087419, _1087421), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1087423), _1087425))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1087427, _1087421), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1087429), _1087431))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1087421)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1087419), _1087427), _1087421), 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), _1087423), _1087429)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1087425), _1087431)), _1087421))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1087425), _1087431), _1087421)))))], (24372 ^ _775828) ^ [_1203614, _1203616] : [c_Code__Numeral_OSuc__code__numeral(_1203614) = c_Code__Numeral_OSuc__code__numeral(_1203616), -(_1203614 = _1203616)], (41018 ^ _775828) ^ [_1566118, _1566120] : [-(c_Transitive__Closure_Ortrancl(_1566118, _1566120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1566118, _1566118), 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(_1566118, _1566118), tc_HOL_Obool), tc_fun(tc_prod(_1566118, _1566118), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1566118, _1566118), tc_HOL_Obool)), _1566120)))], (40207 ^ _775828) ^ [_1546569, _1546571, _1546573, _1546575] : [-(hBOOL(hAPP(hAPP(c_member(_1546569), hAPP(_1546571, _1546573)), hAPP(c_Set_Oimage(_1546575, _1546569, _1546571), c_Orderings_Otop__class_Otop(tc_fun(_1546575, tc_HOL_Obool))))))], (43251 ^ _775828) ^ [_1619830, _1619832, _1619834, _1619836, _1619838] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1619830), _1619832), _1619834), _1619836), _1619838) = c_New__DSequence_Opos__single(_1619830, _1619832))], (18229 ^ _775828) ^ [_1088782, _1088784] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088782, _1088784), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1088782), _1088784)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1088782, _1088784)))))], (15766 ^ _775828) ^ [_1041654, _1041656, _1041658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041654), _1041656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041654), _1041658)), 15773 ^ _775828 : [(15780 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041656), _1041658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041656), _1041654)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041658), _1041654))))], (15774 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041656), _1041654)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041658), _1041654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041656), _1041658)))]]], (43302 ^ _775828) ^ [_1621378, _1621380, _1621382, _1621384, _1621386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621378, _1621378)), hAPP(hAPP(c_Product__Type_OPair(_1621378, _1621378), _1621380), _1621382)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621378, _1621378), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1621384)), _1621386))), 43306 ^ _775828 : [(43309 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621378, _1621378)), hAPP(hAPP(c_Product__Type_OPair(_1621378, _1621378), 43305 ^ [_1621378, _1621380, _1621382, _1621384, _1621386]), _1621382)), _1621386)))], (43307 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621378, _1621378)), hAPP(hAPP(c_Product__Type_OPair(_1621378, _1621378), _1621380), 43305 ^ [_1621378, _1621380, _1621382, _1621384, _1621386])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621378, _1621378), tc_HOL_Obool), _1621384), _1621386))))]]], (14235 ^ _775828) ^ [_1013706, _1013708, _1013710] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013706), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013708, _1013710)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013706), _1013708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013706), _1013710)))], (16346 ^ _775828) ^ [_1053644, _1053646] : [-(_1053644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053644), _1053646) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053644), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1053646)))], (33721 ^ _775828) ^ [_1402279] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1402279) = c_Orderings_Oord__class_Omin(_1402279)), class_Lattices_Osemilattice__inf(_1402279), class_Orderings_Olinorder(_1402279)], (31237 ^ _775828) ^ [_1350038, _1350040, _1350042] : [class_Orderings_Olinorder(_1350038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350038), _1350040)), -(_1350040 = c_Orderings_Obot__class_Obot(tc_fun(_1350038, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1350038, c_Orderings_Oord__class_Omin(_1350038), hAPP(hAPP(c_Set_Oinsert(_1350038), _1350042), _1350040)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1350038), _1350042), c_Big__Operators_Olattice_OInf__fin(_1350038, c_Orderings_Oord__class_Omin(_1350038), _1350040)))], (3408 ^ _775828) ^ [_827449, _827451, _827453, _827455, _827457, _827459, _827461, _827463] : [-(c_Product__Type_Oapsnd(_827463, _827459, _827455, _827451) = c_Product__Type_Oapsnd(_827461, _827457, _827453, _827449)), _827463 = _827461, _827459 = _827457, _827455 = _827453, _827451 = _827449], (18383 ^ _775828) ^ [_1091791, _1091793] : [-(_1091791 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091793, _1091791), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1091793), _1091791)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1091793, _1091791)))))], (47261 ^ _775828) ^ [_1718581, _1718583, _1718585, _1718587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718581)), _1718583)), _1718585)), -(hAPP(hAPP(c_List_Olist__update(_1718581, _1718583), _1718585), _1718587) = _1718583)], (40391 ^ _775828) ^ [_1550282, _1550284, _1550286, _1550288, _1550290] : [c_Fun_Oinj__on(_1550282, _1550284, _1550286, c_Orderings_Otop__class_Otop(tc_fun(_1550282, tc_HOL_Obool))), 40394 ^ _775828 : [(40401 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550282), _1550288), _1550290)), -(hBOOL(hAPP(hAPP(c_member(_1550284), hAPP(_1550286, _1550288)), hAPP(c_Set_Oimage(_1550282, _1550284, _1550286), _1550290))))], (40395 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550284), hAPP(_1550286, _1550288)), hAPP(c_Set_Oimage(_1550282, _1550284, _1550286), _1550290))), -(hBOOL(hAPP(hAPP(c_member(_1550282), _1550288), _1550290)))]]], (5809 ^ _775828) ^ [_868421, _868423] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_868421, _868423)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43311 ^ _775828) ^ [_1621690, _1621692, _1621694, _1621696, _1621698] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621690, _1621690)), hAPP(hAPP(c_Product__Type_OPair(_1621690, _1621690), _1621692), _1621694)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621690, _1621690), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1621696)), _1621698))), 43315 ^ _775828 : [(43318 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621690, _1621690)), hAPP(hAPP(c_Product__Type_OPair(_1621690, _1621690), 43314 ^ [_1621690, _1621692, _1621694, _1621696, _1621698]), _1621694)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621690, _1621690), tc_HOL_Obool), _1621696), _1621698))))], (43316 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621690, _1621690)), hAPP(hAPP(c_Product__Type_OPair(_1621690, _1621690), _1621692), 43314 ^ [_1621690, _1621692, _1621694, _1621696, _1621698])), _1621698)))]]], (48737 ^ _775828) ^ [_1753406, _1753408] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753406)), hAPP(c_List_Otl(_1753406), _1753408)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753406)), _1753408)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (27749 ^ _775828) ^ [_1269850, _1269852, _1269854, _1269856, _1269858] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1269850, _1269852)), hAPP(hAPP(c_Product__Type_OPair(_1269850, _1269852), _1269854), _1269856)), _1269858)), -(hBOOL(hAPP(hAPP(c_member(_1269850), _1269854), hAPP(c_Relation_ODomain(_1269850, _1269852), _1269858))))], (23296 ^ _775828) ^ [_1181760, _1181762, _1181764, _1181766] : [class_Fields_Olinordered__field(_1181760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181760), _1181762), _1181764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181760), c_Groups_Ozero__class_Ozero(_1181760)), _1181766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181760), c_Groups_Ozero__class_Ozero(_1181760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181760), _1181764), _1181762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181760), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181760), _1181766), _1181764)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181760), _1181766), _1181762))))], (24242 ^ _775828) ^ [_1200762, _1200764, _1200766, _1200768] : [class_Orderings_Olinorder(_1200762), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200762), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200762), _1200764), _1200766)), _1200768) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200762), _1200764), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200762), _1200766), _1200768)))], (16517 ^ _775828) ^ [_1056753, _1056755] : [class_Int_Onumber__ring(_1056753), 16520 ^ _775828 : [(16527 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1056755)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056753), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056755)) = hAPP(c_Int_Onumber__class_Onumber__of(_1056753), _1056755))], (16521 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1056755))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056753), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056755)) = c_Groups_Ozero__class_Ozero(_1056753))]]], (40537 ^ _775828) ^ [_1553628, _1553630, _1553632, _1553634, _1553636, _1553638] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553628, tc_fun(_1553630, tc_fun(_1553632, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1553628, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_fun(_1553630, tc_fun(_1553632, tc_HOL_Obool)), _1553628), hAPP(c_COMBC(_1553630, tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_fun(_1553632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553632, tc_fun(tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_fun(_1553632, tc_HOL_Obool)), _1553630), c_COMBC(_1553632, tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553632, tc_prod(_1553630, _1553632)), tc_fun(_1553632, tc_fun(tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_HOL_Obool)), _1553630), hAPP(c_COMBB(tc_prod(_1553630, _1553632), tc_fun(tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool), tc_HOL_Obool), _1553632), c_member(tc_prod(_1553630, _1553632)))), c_Product__Type_OPair(_1553630, _1553632))))), _1553634)), _1553636), _1553638)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553630, _1553632)), hAPP(hAPP(c_Product__Type_OPair(_1553630, _1553632), _1553636), _1553638)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553628, tc_fun(tc_prod(_1553630, _1553632), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1553628, tc_HOL_Obool))), _1553634))))], (46087 ^ _775828) ^ [_1686742, _1686744, _1686746, _1686748, _1686750, _1686752, _1686754, _1686756] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686742)), _1686744) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686746)), _1686748), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686742)), _1686750) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686746)), _1686748), -(hBOOL(hAPP(hAPP(c_member(_1686746), _1686752), hAPP(c_List_Oset(_1686746), _1686748)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1686746, tc_Option_Ooption(_1686742)), c_Map_Omap__of(_1686746, _1686742, hAPP(hAPP(c_List_Ozip(_1686746, _1686742), _1686748), _1686744))), _1686752), hAPP(c_Option_Ooption_OSome(_1686742), _1686754)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1686746, tc_Option_Ooption(_1686742)), c_Map_Omap__of(_1686746, _1686742, hAPP(hAPP(c_List_Ozip(_1686746, _1686742), _1686748), _1686750))), _1686752), hAPP(c_Option_Ooption_OSome(_1686742), _1686756)), -(c_Map_Omap__of(_1686746, _1686742, hAPP(hAPP(c_List_Ozip(_1686746, _1686742), _1686748), _1686744)) = c_Map_Omap__of(_1686746, _1686742, hAPP(hAPP(c_List_Ozip(_1686746, _1686742), _1686748), _1686750)))], (7547 ^ _775828) ^ [_896224, _896226] : [class_Groups_Ogroup__add(_896224), 7550 ^ _775828 : [(7557 ^ _775828) ^ [] : [_896226 = c_Groups_Ozero__class_Ozero(_896224), -(hAPP(c_Groups_Ouminus__class_Ouminus(_896224), _896226) = c_Groups_Ozero__class_Ozero(_896224))], (7551 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_896224), _896226) = c_Groups_Ozero__class_Ozero(_896224), -(_896226 = c_Groups_Ozero__class_Ozero(_896224))]]], (6109 ^ _775828) ^ [_872881, _872883] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872881), _872883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872883), hAPP(c_Nat_OSuc, _872881))))], (17629 ^ _775828) ^ [_1077623, _1077625, _1077627] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077623))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077625)), _1077627)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077625)), _1077627))], (13304 ^ _775828) ^ [_996134, _996136, _996138, _996140] : [class_Divides_Osemiring__div(_996134), -(c_Divides_Odiv__class_Omod(_996134, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996134), _996136), _996138), _996140) = c_Divides_Odiv__class_Omod(_996134, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996134), c_Divides_Odiv__class_Omod(_996134, _996136, _996140)), _996138), _996140))], (49451 ^ _775828) ^ [_1768825, _1768827, _1768829, _1768831] : [-(hBOOL(hAPP(_1768825, _1768827))), -(hAPP(c_List_Ofilter(_1768829, _1768825), hAPP(hAPP(c_List_Olist_OCons(_1768829), _1768827), _1768831)) = hAPP(c_List_Ofilter(_1768829, _1768825), _1768831))], (32543 ^ _775828) ^ [_1377368, _1377370, _1377372] : [class_Lattices_Olattice(_1377368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377368), _1377370)), -(_1377370 = c_Orderings_Obot__class_Obot(tc_fun(_1377368, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1377368, hAPP(hAPP(c_Set_Oinsert(_1377368), _1377372), _1377370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1377368), _1377372), c_Big__Operators_Olattice__class_OSup__fin(_1377368, _1377370)))], (9507 ^ _775828) ^ [_928612, _928614] : [class_Groups_Oordered__ab__group__add(_928612), 9510 ^ _775828 : [(9517 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928612), _928614), c_Groups_Ozero__class_Ozero(_928612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928612), c_Groups_Ozero__class_Ozero(_928612)), hAPP(c_Groups_Ouminus__class_Ouminus(_928612), _928614))))], (9511 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928612), c_Groups_Ozero__class_Ozero(_928612)), hAPP(c_Groups_Ouminus__class_Ouminus(_928612), _928614))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928612), _928614), c_Groups_Ozero__class_Ozero(_928612))))]]], (27525 ^ _775828) ^ [_1264951, _1264953] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1264951), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1264953))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1264953), _1264951)))], (13170 ^ _775828) ^ [_993625, _993627, _993629] : [class_Divides_Osemiring__div(_993625), -(c_Divides_Odiv__class_Omod(_993625, c_Divides_Odiv__class_Omod(_993625, _993627, _993629), _993629) = c_Divides_Odiv__class_Omod(_993625, _993627, _993629))], (8537 ^ _775828) ^ [_912789, _912791, _912793] : [class_Rings_Olinordered__idom(_912789), 8540 ^ _775828 : [(8547 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _912791), _912793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912789), hAPP(c_Int_Oring__1__class_Oof__int(_912789), _912791)), hAPP(c_Int_Oring__1__class_Oof__int(_912789), _912793))))], (8541 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912789), hAPP(c_Int_Oring__1__class_Oof__int(_912789), _912791)), hAPP(c_Int_Oring__1__class_Oof__int(_912789), _912793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _912791), _912793)))]]], (2340 ^ _775828) ^ [_810111, _810113, _810115, _810117] : [-(c_Nitpick_Oinverse__frac(_810117, _810113) = c_Nitpick_Oinverse__frac(_810115, _810111)), _810117 = _810115, _810113 = _810111], (9753 ^ _775828) ^ [_932905, _932907, _932909, _932911] : [class_Rings_Olinordered__semiring__strict(_932905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932905), _932907), _932909)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932905), _932911), _932909))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932905), c_Groups_Ozero__class_Ozero(_932905)), _932909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932905), _932907), _932911)))], (35373 ^ _775828) ^ [_1439637, _1439639, _1439641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439637, tc_HOL_Obool)), _1439639), _1439641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1439637, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1439637), _1439639)), hAPP(c_Set_OPow(_1439637), _1439641))))], (24881 ^ _775828) ^ [_1213978, _1213980, _1213982] : [c_Nitpick_Oless__eq__frac(_1213978, _1213980, _1213982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1213978), c_Nitpick_Oplus__frac(_1213978, _1213980, c_Nitpick_Ouminus__frac(_1213978, _1213982)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32845 ^ _775828) ^ [_1383338, _1383340, _1383342, _1383344, _1383346, _1383348] : [-(_1383338 = _1383340), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383342, _1383344), _1383346), _1383340), _1383348), _1383338) = hAPP(_1383346, _1383338))], (44595 ^ _775828) ^ [_1652081, _1652083, _1652085, _1652087, _1652089] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652081, tc_fun(_1652083, tc_HOL_Obool)), _1652085), _1652087), _1652089)), 44598 ^ _775828 : [(44599 ^ _775828) ^ [_1652190] : [hBOOL(hAPP(hAPP(c_member(_1652081), _1652190), _1652085)), -(hBOOL(hAPP(hAPP(_1652087, _1652190), _1652089)))]]], (49638 ^ _775828) ^ [_1773812, _1773814, _1773816] : [class_Orderings_Olinorder(_1773812), 49641 ^ _775828 : [(49660 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1773812, hAPP(hAPP(c_List_Oappend(_1773812), _1773814), _1773816))), c_List_Olinorder__class_Osorted(_1773812, _1773814), c_List_Olinorder__class_Osorted(_1773812, _1773816), 49670 ^ _775828 : [(49676 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1773812), 49669 ^ [_1773812, _1773814, _1773816]), 49672 ^ [_1773812, _1773814, _1773816]))], (49674 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773812), 49672 ^ [_1773812, _1773814, _1773816]), hAPP(c_List_Oset(_1773812), _1773816))))], (49671 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773812), 49669 ^ [_1773812, _1773814, _1773816]), hAPP(c_List_Oset(_1773812), _1773814))))]]], (49642 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1773812, hAPP(hAPP(c_List_Oappend(_1773812), _1773814), _1773816)), 49645 ^ _775828 : [(49650 ^ _775828) ^ [_1774048] : [hBOOL(hAPP(hAPP(c_member(_1773812), _1774048), hAPP(c_List_Oset(_1773812), _1773814))), 49653 ^ _775828 : [(49654 ^ _775828) ^ [_1774158] : [hBOOL(hAPP(hAPP(c_member(_1773812), _1774158), hAPP(c_List_Oset(_1773812), _1773816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1773812), _1774048), _1774158)))]]], (49648 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1773812, _1773816))], (49646 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1773812, _1773814))]]]]], (47421 ^ _775828) ^ [_1721816, _1721818] : [c_Orderings_Obot__class_Obot(tc_fun(_1721816, tc_HOL_Obool)) = hAPP(c_List_Oset(_1721816), _1721818), -(_1721818 = c_List_Olist_ONil(_1721816))], (28245 ^ _775828) ^ [_1282271, _1282273, _1282275] : [class_Lattices_Osemilattice__sup(_1282271), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282271), _1282273), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282271), _1282273), _1282275)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282271), _1282273), _1282275))], (38092 ^ _775828) ^ [_1498311, _1498313, _1498315] : [c_Wellfounded_Owf(_1498311, _1498313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498311, tc_HOL_Obool)), _1498315), hAPP(c_Relation_OImage(_1498311, _1498311, _1498313), _1498315))), -(_1498315 = c_Orderings_Obot__class_Obot(tc_fun(_1498311, tc_HOL_Obool)))], (49295 ^ _775828) ^ [_1765519] : [-(c_List_Obutlast(_1765519, c_List_Olist_ONil(_1765519)) = c_List_Olist_ONil(_1765519))], (12149 ^ _775828) ^ [_975985, _975987, _975989] : [class_Lattices_Oab__semigroup__idem__mult(_975985), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975985), _975987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975985), _975987), _975989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975985), _975987), _975989))], (13672 ^ _775828) ^ [_1003404, _1003406, _1003408] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1003404, _1003406, _1003408)], (17451 ^ _775828) ^ [_1074682, _1074684] : [17452 ^ _775828 : [(17455 ^ _775828) ^ [] : [_1074682 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17453 ^ _775828) ^ [] : [_1074684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1074682), _1074684) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20350 ^ _775828) ^ [_1125532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1125532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1125532)))], (26325 ^ _775828) ^ [_1240541, _1240543, _1240545] : [class_Divides_Osemiring__div(_1240541), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240541), _1240543), _1240545)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240541), _1240543), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240541), _1240545), _1240543)) = _1240545)], (44519 ^ _775828) ^ [_1650442, _1650444, _1650446, _1650448, _1650450] : [class_Complete__Lattice_Ocomplete__lattice(_1650442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650444), _1650446)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1650442), _1650448), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650444, _1650442), _1650446), _1650450)) = hAPP(hAPP(c_Finite__Set_Ofold(_1650444, _1650442, hAPP(hAPP(c_COMBB(_1650442, tc_fun(_1650442, _1650442), _1650444), c_Lattices_Osemilattice__inf__class_Oinf(_1650442)), _1650450)), _1650448), _1650446))], (48970 ^ _775828) ^ [_1758750, _1758752, _1758754, _1758756] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758750)), hAPP(hAPP(c_List_Oappend(_1758750), _1758752), _1758754)), c_List_Olists(_1758750, _1758756))), 48973 ^ _775828 : [(48976 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758750)), _1758754), c_List_Olists(_1758750, _1758756))))], (48974 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758750)), _1758752), c_List_Olists(_1758750, _1758756))))]]], (15460 ^ _775828) ^ [_1035757, _1035759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035757), _1035759)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035759, _1035757) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035759), _1035757), _1035757))], (48906 ^ _775828) ^ [_1757061, _1757063, _1757065, _1757067, _1757069] : [hBOOL(hAPP(hAPP(c_member(_1757061), _1757063), hAPP(c_List_Oset(_1757061), _1757065))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757067), hAPP(_1757069, _1757063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757067), c_List_Olist_Olist__size(_1757061, _1757069, _1757065))))], (28659 ^ _775828) ^ [_1290640, _1290642, _1290644, _1290646] : [28660 ^ _775828 : [(28663 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1290640), _1290642), _1290646))], (28661 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1290640), _1290642), _1290644))]], -(hBOOL(hAPP(hAPP(c_member(_1290640), _1290642), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290640, tc_HOL_Obool)), _1290644), _1290646))))], (16577 ^ _775828) ^ [_1057743, _1057745] : [class_Rings_Olinordered__idom(_1057743), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057743), hAPP(c_Groups_Oabs__class_Oabs(_1057743), _1057745)), hAPP(c_Groups_Oabs__class_Oabs(_1057743), _1057745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057743), _1057745), _1057745))], (50088 ^ _775828) ^ [_1781744, _1781746, _1781748, _1781750, _1781752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1781744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1781746), _1781748))), -(hAPP(hAPP(c_List_Onth(_1781750), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1781750), _1781752), c_List_Oupt(_1781748, _1781746))), _1781744) = hAPP(_1781752, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1781748), _1781744)))], (16196 ^ _775828) ^ [_1050846, _1050848] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050846, _1050848) = 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), _1050846), _1050848) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26844 ^ _775828) ^ [_1250108, _1250110] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1250108)), _1250110)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250108), _1250110)))], (2258 ^ _775828) ^ [_808852, _808854, _808856, _808858] : [-(c_Nitpick_Onorm__frac(_808858, _808854) = c_Nitpick_Onorm__frac(_808856, _808852)), _808858 = _808856, _808854 = _808852], (8931 ^ _775828) ^ [_918647, _918649, _918651] : [class_Orderings_Olinorder(_918647), 8934 ^ _775828 : [(8941 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918647), _918651), _918649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918647), _918649), _918651))], (8935 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918647), _918649), _918651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918647), _918651), _918649)))]]], (4230 ^ _775828) ^ [_840482, _840484, _840486, _840488] : [-(c_Nat_Ocompow(_840488, _840484) = c_Nat_Ocompow(_840486, _840482)), _840488 = _840486, _840484 = _840482], (46383 ^ _775828) ^ [_1694706, _1694708, _1694710, _1694712] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694706), tc_List_Olist(_1694706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694706), tc_List_Olist(_1694706)), _1694708), _1694710)), c_List_Olistrel(_1694706, _1694712)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694706)), _1694708) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694706)), _1694710), 46389 ^ _775828 : [(46392 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1694706, _1694706, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1694706, tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_fun(_1694706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1694706, tc_fun(tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_fun(_1694706, tc_HOL_Obool)), _1694706), c_COMBC(_1694706, tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1694706, tc_prod(_1694706, _1694706)), tc_fun(_1694706, tc_fun(tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_HOL_Obool)), _1694706), hAPP(c_COMBB(tc_prod(_1694706, _1694706), tc_fun(tc_fun(tc_prod(_1694706, _1694706), tc_HOL_Obool), tc_HOL_Obool), _1694706), c_member(tc_prod(_1694706, _1694706)))), c_Product__Type_OPair(_1694706, _1694706)))), _1694712)), 46388 ^ [_1694706, _1694708, _1694710, _1694712]))], (46390 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1694706, _1694706)), 46388 ^ [_1694706, _1694708, _1694710, _1694712]), hAPP(c_List_Oset(tc_prod(_1694706, _1694706)), hAPP(hAPP(c_List_Ozip(_1694706, _1694706), _1694708), _1694710)))))]]], (47148 ^ _775828) ^ [_1715667, _1715669, _1715671, _1715673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715667), tc_List_Olist(_1715667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715667), tc_List_Olist(_1715667)), _1715669), _1715671)), c_List_Olexord(_1715667, _1715673))), 47153 ^ _775828 : [(47156 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1715667), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715667)), _1715669)), _1715671) = _1715669)], (47154 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715667)), _1715669)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715667)), _1715671))))]], 47158 ^ _775828 : [(47163 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1715667, _1715667)), hAPP(hAPP(c_Product__Type_OPair(_1715667, _1715667), hAPP(hAPP(c_List_Onth(_1715667), _1715669), 47157 ^ [_1715667, _1715669, _1715671, _1715673])), hAPP(hAPP(c_List_Onth(_1715667), _1715671), 47157 ^ [_1715667, _1715669, _1715671, _1715673]))), _1715673)))], (47161 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1715667), 47157 ^ [_1715667, _1715669, _1715671, _1715673]), _1715669) = hAPP(hAPP(c_List_Otake(_1715667), 47157 ^ [_1715667, _1715669, _1715671, _1715673]), _1715671))], (47159 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47157 ^ [_1715667, _1715669, _1715671, _1715673]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715667)), _1715669)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715667)), _1715671)))))]]], (29279 ^ _775828) ^ [_1306817] : [-(c_Relation_OId__on(_1306817, c_Orderings_Obot__class_Obot(tc_fun(_1306817, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1306817, _1306817), tc_HOL_Obool)))], (44332 ^ _775828) ^ [_1645294, _1645296, _1645298, _1645300, _1645302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1645294, tc_HOL_Obool)), _1645296), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645298, tc_fun(_1645294, tc_HOL_Obool)), _1645300), _1645302))), 44335 ^ _775828 : [(44336 ^ _775828) ^ [_1645427] : [hBOOL(hAPP(hAPP(c_member(_1645298), _1645427), _1645300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1645294, tc_HOL_Obool)), _1645296), hAPP(_1645302, _1645427))))]]], (20484 ^ _775828) ^ [_1127808, _1127810] : [class_Rings_Olinordered__idom(_1127808), -(hAPP(c_Groups_Oabs__class_Oabs(_1127808), hAPP(hAPP(c_Power_Opower__class_Opower(_1127808), _1127810), 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(_1127808), _1127810), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (28561 ^ _775828) ^ [_1288779, _1288781, _1288783, _1288785] : [class_Lattices_Osemilattice__sup(_1288779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288779), _1288781), _1288783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288779), _1288785), _1288783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288779), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288779), _1288781), _1288785)), _1288783)))], (21270 ^ _775828) ^ [_1144327, _1144329, _1144331, _1144333] : [class_Rings_Odivision__ring(_1144327), -(_1144329 = c_Groups_Ozero__class_Ozero(_1144327)), 21277 ^ _775828 : [(21284 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144327), _1144331), _1144329) = _1144333, -(_1144331 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144327), _1144333), _1144329))], (21278 ^ _775828) ^ [] : [_1144331 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144327), _1144333), _1144329), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144327), _1144331), _1144329) = _1144333)]]], (51174 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (36954 ^ _775828) ^ [_1470961, _1470963, _1470965, _1470967, _1470969] : [class_Rings_Osemiring__0(_1470961), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470961), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470963, _1470961), _1470965), _1470967)), _1470969) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470963, _1470961), hAPP(hAPP(c_COMBC(_1470963, _1470961, _1470961), hAPP(hAPP(c_COMBB(_1470961, tc_fun(_1470961, _1470961), _1470963), c_Groups_Otimes__class_Otimes(_1470961)), _1470965)), _1470969)), _1470967))], (31051 ^ _775828) ^ [_1344926, _1344928, _1344930, _1344932, _1344934] : [c_Finite__Set_Ofolding__one(_1344926, _1344928, _1344930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344926), _1344932)), -(hBOOL(hAPP(hAPP(c_member(_1344926), _1344934), _1344932))), -(_1344932 = c_Orderings_Obot__class_Obot(tc_fun(_1344926, tc_HOL_Obool))), -(hAPP(_1344930, hAPP(hAPP(c_Set_Oinsert(_1344926), _1344934), _1344932)) = hAPP(hAPP(_1344928, _1344934), hAPP(_1344930, _1344932)))], (20092 ^ _775828) ^ [_1120975, _1120977] : [c_Int_OBit1(_1120975) = c_Int_OBit0(_1120977)], (49921 ^ _775828) ^ [_1778648, _1778650] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778648), _1778650))), -(c_List_Oupt(_1778648, _1778650) = c_List_Olist_ONil(tc_Nat_Onat))], (5557 ^ _775828) ^ [_863884] : [hAPP(c_Nat_OSuc, _863884) = _863884], (40511 ^ _775828) ^ [_1552920, _1552922, _1552924, _1552926, _1552928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1552920)), hAPP(c_Set_Oimage(_1552922, tc_Option_Ooption(_1552920), _1552924), c_Orderings_Otop__class_Otop(tc_fun(_1552922, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1552920)), hAPP(c_Set_Oimage(_1552922, tc_Option_Ooption(_1552920), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1552922, tc_Option_Ooption(_1552920)), _1552924), _1552926), hAPP(c_Option_Ooption_OSome(_1552920), _1552928))), c_Orderings_Otop__class_Otop(tc_fun(_1552922, tc_HOL_Obool))))))], (44828 ^ _775828) ^ [_1657656] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657656, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1657656, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1657656, tc_HOL_Obool)))], (15238 ^ _775828) ^ [_1031643, _1031645] : [class_Groups_Ogroup__add(_1031643), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031643), _1031645), c_Groups_Ozero__class_Ozero(_1031643)) = _1031645)], (1640 ^ _775828) ^ [_798946, _798948] : [-(class_Groups_Omonoid__add(_798946)), _798948 = _798946, class_Groups_Omonoid__add(_798948)], (29643 ^ _775828) ^ [_1313870, _1313872, _1313874] : [hBOOL(hAPP(_1313870, _1313872)), -(hAPP(c_Set_OCollect(_1313874), hAPP(hAPP(c_COMBS(_1313874, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1313874), c_fconj), hAPP(c_fequal, _1313872))), _1313870)) = hAPP(hAPP(c_Set_Oinsert(_1313874), _1313872), c_Orderings_Obot__class_Obot(tc_fun(_1313874, tc_HOL_Obool))))], (24230 ^ _775828) ^ [_1200476, _1200478, _1200480, _1200482] : [class_Orderings_Olinorder(_1200476), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200476), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200476), _1200478), _1200480)), _1200482) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200476), _1200478), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200476), _1200480), _1200482)))], (2926 ^ _775828) ^ [_819758, _819760, _819762, _819764, _819766, _819768] : [-(c_SetInterval_Oord_OlessThan(_819768, _819764, _819760) = c_SetInterval_Oord_OlessThan(_819766, _819762, _819758)), _819768 = _819766, _819764 = _819762, _819760 = _819758], (42918 ^ _775828) ^ [] : [-(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))], (6724 ^ _775828) ^ [] : [-(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))], (38404 ^ _775828) ^ [_1505465, _1505467, _1505469, _1505471] : [-(hAPP(_1505471, _1505467) = c_Option_Ooption_ONone(_1505469)), -(hBOOL(hAPP(hAPP(c_member(_1505465), _1505467), c_Map_Odom(_1505465, _1505469, _1505471))))], (46147 ^ _775828) ^ [_1688173, _1688175, _1688177, _1688179, _1688181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1688173), tc_List_Olist(_1688173))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1688173), tc_List_Olist(_1688173)), _1688175), _1688177)), hAPP(c_List_Olexn(_1688173, _1688179), _1688181))), 46150 ^ _775828 : [(46153 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688173)), _1688177) = _1688181)], (46151 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688173)), _1688175) = _1688181)]]], (49441 ^ _775828) ^ [_1768552, _1768554, _1768556] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1768552), tc_List_Olist(_1768552)), c_List_Opartition(_1768552, _1768554, _1768556)) = hAPP(c_List_Ofilter(_1768552, _1768554), _1768556))], (19636 ^ _775828) ^ [_1113227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1113227)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113227), c_Int_OPls)))], (29299 ^ _775828) ^ [_1307276, _1307278] : [-(hBOOL(hAPP(hAPP(c_member(_1307276), 29300 ^ [_1307276, _1307278]), _1307278))), -(_1307278 = c_Orderings_Obot__class_Obot(tc_fun(_1307276, tc_HOL_Obool)))], (4528 ^ _775828) ^ [_844965, _844967, _844969, _844971] : [-(c_Random_Oselect__weight(_844971, _844967) = c_Random_Oselect__weight(_844969, _844965)), _844971 = _844969, _844967 = _844965], (24853 ^ _775828) ^ [_1213436, _1213438] : [-(c_Nitpick_Oinverse__frac(_1213436, _1213438) = hAPP(hAPP(c_Nitpick_Ofrac(_1213436), hAPP(c_Nitpick_Odenom(_1213436), _1213438)), hAPP(c_Nitpick_Onum(_1213436), _1213438)))], (5456 ^ _775828) ^ [_861857, _861859] : [hAPP(_861857, 5457 ^ [_861857, _861859]) = hAPP(_861859, 5457 ^ [_861857, _861859]), -(_861857 = _861859)], (38696 ^ _775828) ^ [_1512147, _1512149, _1512151] : [_1512149 = c_Orderings_Obot__class_Obot(tc_fun(_1512147, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512147), _1512149), _1512151) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1512147, tc_HOL_Obool), tc_HOL_Obool)))], (13004 ^ _775828) ^ [_990728, _990730] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_990728, _990730)) = 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(_990728)), c_Com_Ocom_Ocom__size(_990730))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37100 ^ _775828) ^ [_1474385, _1474387, _1474389] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474385), _1474387)), 37103 ^ _775828 : [(37123 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474385, tc_Nat_Onat), _1474389), _1474387) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 37124 ^ _775828 : [(37125 ^ _775828) ^ [_1474866] : [hBOOL(hAPP(hAPP(c_member(_1474385), _1474866), _1474387)), hAPP(_1474389, _1474866) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37133 ^ _775828 : [(37138 ^ _775828) ^ [] : [hAPP(_1474389, 37132 ^ [_1474385, _1474387, _1474389, _1474866]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37136 ^ _775828) ^ [] : [_1474866 = 37132 ^ [_1474385, _1474387, _1474389, _1474866]], (37134 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474385), 37132 ^ [_1474385, _1474387, _1474389, _1474866]), _1474387)))]]]]], (37104 ^ _775828) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474385, tc_Nat_Onat), _1474389), _1474387) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37108 ^ _775828 : [(37113 ^ _775828) ^ [_1474705] : [hBOOL(hAPP(hAPP(c_member(_1474385), _1474705), _1474387)), -(37107 ^ [_1474385, _1474387, _1474389] = _1474705), -(hAPP(_1474389, _1474705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37111 ^ _775828) ^ [] : [-(hAPP(_1474389, 37107 ^ [_1474385, _1474387, _1474389]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37109 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474385), 37107 ^ [_1474385, _1474387, _1474389]), _1474387)))]]]]], (33743 ^ _775828) ^ [_1402636, _1402638] : [class_Lattices_Osemilattice__inf(_1402636), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402636), _1402638), _1402638) = _1402638)], (10252 ^ _775828) ^ [_941912, _941914, _941916] : [_941912 = _941916, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941912), _941914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941916), _941914))], (29771 ^ _775828) ^ [_1316630, _1316632, _1316634] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1316630, _1316632, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316630)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316630), _1316634), c_Com_Ocom_OSKIP), _1316634)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316630), tc_HOL_Obool)))))], (7359 ^ _775828) ^ [_893138, _893140, _893142] : [class_Rings_Osemiring__1(_893138), hBOOL(hAPP(hAPP(c_member(_893138), _893140), c_Nat_Osemiring__1__class_ONats(_893138))), hBOOL(hAPP(hAPP(c_member(_893138), _893142), c_Nat_Osemiring__1__class_ONats(_893138))), -(hBOOL(hAPP(hAPP(c_member(_893138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_893138), _893140), _893142)), c_Nat_Osemiring__1__class_ONats(_893138))))], (37526 ^ _775828) ^ [_1485046, _1485048, _1485050, _1485052, _1485054] : [class_Groups_Ocomm__monoid__add(_1485046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485048), _1485050)), hBOOL(hAPP(hAPP(c_member(_1485048), _1485052), _1485050)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485048, _1485046), _1485054), _1485050) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1485046), hAPP(_1485054, _1485052)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485048, _1485046), _1485054), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485048, tc_HOL_Obool)), _1485050), hAPP(hAPP(c_Set_Oinsert(_1485048), _1485052), c_Orderings_Obot__class_Obot(tc_fun(_1485048, tc_HOL_Obool)))))))], (20744 ^ _775828) ^ [_1132603, _1132605] : [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), _1132603))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1132605))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1132603))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132605)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132603)))], (716 ^ _775828) ^ [_786744, _786746, _786748, _786750, _786752, _786754] : [-(c_Finite__Set_Ofolding__one__idem(_786752, _786748, _786744)), c_Finite__Set_Ofolding__one__idem(_786754, _786750, _786746), _786754 = _786752, _786750 = _786748, _786746 = _786744], (5136 ^ _775828) ^ [_854399, _854401, _854403, _854405, _854407, _854409] : [-(c_List_OdropWhile(_854409, _854405, _854401) = c_List_OdropWhile(_854407, _854403, _854399)), _854409 = _854407, _854405 = _854403, _854401 = _854399], (35605 ^ _775828) ^ [_1444423, _1444425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1444423)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1444423, _1444425)))], (43774 ^ _775828) ^ [_1631963, _1631965, _1631967] : [class_Orderings_Olinorder(_1631963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631963), _1631965)), -(c_Big__Operators_Olinorder__class_OMax(_1631963, hAPP(hAPP(c_Set_Oinsert(_1631963), _1631967), _1631965)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631963, _1631963, c_Orderings_Oord__class_Omax(_1631963)), _1631967), _1631965))], (11130 ^ _775828) ^ [_958179, _958181, _958183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958179, tc_HOL_Obool)), _958181), _958183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958179, tc_HOL_Obool)), _958181), _958183))), -(_958181 = _958183)], (30800 ^ _775828) ^ [_1339142, _1339144, _1339146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339142), _1339144)), -(hBOOL(hAPP(hAPP(c_member(_1339142), _1339146), _1339144))), -(hAPP(c_Finite__Set_Ocard(_1339142), hAPP(hAPP(c_Set_Oinsert(_1339142), _1339146), _1339144)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1339142), _1339144)))], (42314 ^ _775828) ^ [_1597544, _1597546, _1597548, _1597550, _1597552, _1597554, _1597556, _1597558] : [c_Finite__Set_Ofolding__image__simple(_1597544, _1597546, _1597548, _1597550, _1597552, _1597554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597546), _1597556)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597546), _1597558)), 42328 ^ _775828 : [(42331 ^ _775828) ^ [] : [hAPP(_1597552, 42327 ^ [_1597544, _1597546, _1597548, _1597550, _1597552, _1597554, _1597556, _1597558]) = _1597550], (42329 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597546), 42327 ^ [_1597544, _1597546, _1597548, _1597550, _1597552, _1597554, _1597556, _1597558]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1597546, tc_HOL_Obool)), _1597556), _1597558))))]], -(hAPP(_1597554, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597546, tc_HOL_Obool)), _1597556), _1597558)) = hAPP(hAPP(_1597548, hAPP(_1597554, _1597556)), hAPP(_1597554, _1597558)))], (40800 ^ _775828) ^ [_1560472, _1560474, _1560476] : [-(hAPP(c_Set_Ovimage(_1560472, _1560474, _1560476), c_Orderings_Obot__class_Obot(tc_fun(_1560474, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1560472, tc_HOL_Obool)))], (34187 ^ _775828) ^ [_1411873, _1411875, _1411877] : [class_Lattices_Oboolean__algebra(_1411873), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1411873), _1411875), _1411877) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411873), _1411875), hAPP(c_Groups_Ouminus__class_Ouminus(_1411873), _1411877)))], (5118 ^ _775828) ^ [_854144, _854146] : [_854146 = _854144, -(c_List_Ohd(_854146) = c_List_Ohd(_854144))], (20004 ^ _775828) ^ [_1119508, _1119510] : [c_Int_OBit0(_1119508) = c_Int_OBit0(_1119510), -(_1119508 = _1119510)], (38678 ^ _775828) ^ [_1511772, _1511774, _1511776] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1511772, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511772), _1511774), _1511776), -(_1511774 = c_Orderings_Obot__class_Obot(tc_fun(_1511772, tc_HOL_Obool)))], (16651 ^ _775828) ^ [_1059295, _1059297, _1059299, _1059301] : [class_Rings_Ocomm__semiring__1(_1059295), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1059295), hAPP(hAPP(c_Power_Opower__class_Opower(_1059295), _1059297), _1059299)), _1059301) = hAPP(hAPP(c_Power_Opower__class_Opower(_1059295), _1059297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059299), _1059301)))], (14157 ^ _775828) ^ [_1012513, _1012515] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1012513, _1012515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1012515)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4968 ^ _775828) ^ [_851845, _851847, _851849, _851851] : [-(c_List_Ozip(_851851, _851847) = c_List_Ozip(_851849, _851845)), _851851 = _851849, _851847 = _851845], (13628 ^ _775828) ^ [_1002540, _1002542, _1002544] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1002540, _1002542, _1002544)], (33158 ^ _775828) ^ [_1389556, _1389558, _1389560, _1389562, _1389564] : [class_Groups_Ocomm__monoid__mult(_1389556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389558), _1389560)), 33165 ^ _775828 : [(33172 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389558), _1389562), _1389560))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389558, _1389556), hAPP(hAPP(c_COMBC(_1389558, _1389556, _1389556), hAPP(hAPP(c_COMBS(_1389558, _1389556, tc_fun(_1389556, _1389556)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1389556, tc_fun(_1389556, _1389556)), _1389558), c_If(_1389556)), hAPP(hAPP(c_COMBC(_1389558, _1389558, tc_HOL_Obool), c_fequal), _1389562))), _1389564)), c_Groups_Oone__class_Oone(_1389556))), _1389560) = c_Groups_Oone__class_Oone(_1389556))], (33166 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1389558), _1389562), _1389560)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389558, _1389556), hAPP(hAPP(c_COMBC(_1389558, _1389556, _1389556), hAPP(hAPP(c_COMBS(_1389558, _1389556, tc_fun(_1389556, _1389556)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1389556, tc_fun(_1389556, _1389556)), _1389558), c_If(_1389556)), hAPP(hAPP(c_COMBC(_1389558, _1389558, tc_HOL_Obool), c_fequal), _1389562))), _1389564)), c_Groups_Oone__class_Oone(_1389556))), _1389560) = hAPP(_1389564, _1389562))]]], (25331 ^ _775828) ^ [_1222623, _1222625, _1222627, _1222629, _1222631] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1222623, _1222625, tc_HOL_Obool, _1222627), _1222629), _1222631)), -(hBOOL(hAPP(_1222627, hAPP(hAPP(c_Product__Type_OPair(_1222623, _1222625), _1222629), _1222631))))], (40025 ^ _775828) ^ [] : [-(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)))], (30359 ^ _775828) ^ [_1330516, _1330518, _1330520] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330516), _1330518)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330516), hAPP(hAPP(c_Set_Oinsert(_1330516), _1330520), _1330518))))], (50800 ^ _775828) ^ [_1798385, _1798387] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798385)), c_List_Oremdups(_1798385, _1798387)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798385)), _1798387), -(c_List_Oremdups(_1798385, _1798387) = _1798387)], (4860 ^ _775828) ^ [_850101, _850103, _850105, _850107, _850109, _850111, _850113, _850115] : [-(c_List_Olist_Olist__case(_850115, _850111, _850107, _850103) = c_List_Olist_Olist__case(_850113, _850109, _850105, _850101)), _850115 = _850113, _850111 = _850109, _850107 = _850105, _850103 = _850101], (7661 ^ _775828) ^ [_898108, _898110, _898112] : [class_Rings_Oring(_898108), -(hAPP(c_Groups_Ouminus__class_Ouminus(_898108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898108), _898110), _898112)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898108), hAPP(c_Groups_Ouminus__class_Ouminus(_898108), _898110)), _898112))], (13012 ^ _775828) ^ [_990924, _990926, _990928] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_990924, _990926, _990928)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_990928)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50929 ^ _775828) ^ [_1801070, _1801072, _1801074, _1801076, _1801078] : [c_List_OdropWhile(_1801070, _1801072, _1801074) = hAPP(hAPP(c_List_Olist_OCons(_1801070), _1801076), _1801078), 50932 ^ _775828 : [(50935 ^ _775828) ^ [] : [hBOOL(hAPP(_1801072, _1801076))], (50933 ^ _775828) ^ [] : [-(_1801074 = hAPP(hAPP(c_List_Oappend(_1801070), c_List_OtakeWhile(_1801070, _1801072, _1801074)), hAPP(hAPP(c_List_Olist_OCons(_1801070), _1801076), _1801078)))]]], (20222 ^ _775828) ^ [_1123266, _1123268] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1123266)), c_Int_OBit1(_1123268)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123266), _1123268)))], (14503 ^ _775828) ^ [_1018673] : [-(_1018673 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018673), _1018673) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (45438 ^ _775828) ^ [_1671156, _1671158, _1671160] : [-(c_Smallcheck_Oorelse(_1671156, _1671158, _1671160) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1671156), _1671156, _1671160, c_Option_Ooption_OSome(_1671156)), _1671158))], (44403 ^ _775828) ^ [_1647370, _1647372, _1647374, _1647376, _1647378, _1647380] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647370, tc_fun(_1647372, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1647374, _1647370, _1647376), _1647378)), _1647380) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647374, tc_fun(_1647372, tc_HOL_Obool)), _1647378), hAPP(hAPP(c_COMBB(_1647370, tc_fun(_1647372, tc_HOL_Obool), _1647374), _1647380), _1647376)))], (19198 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (5971 ^ _775828) ^ [_870837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870837), _870837))], (29711 ^ _775828) ^ [_1315479, _1315481] : [hBOOL(hAPP(hAPP(c_member(_1315479), _1315481), c_Orderings_Obot__class_Obot(tc_fun(_1315479, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1315479, tc_HOL_Obool)), _1315481)))], (27010 ^ _775828) ^ [_1253067, _1253069, _1253071] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253067), _1253071))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1253067, _1253069) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1253071, _1253069))], (31473 ^ _775828) ^ [_1354344, _1354346, _1354348] : [class_Orderings_Olinorder(_1354344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354344), _1354346)), hBOOL(hAPP(hAPP(c_member(_1354344), _1354348), _1354346)), 31484 ^ _775828 : [(31491 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354344, tc_HOL_Obool)), _1354346), hAPP(hAPP(c_Set_Oinsert(_1354344), _1354348), c_Orderings_Obot__class_Obot(tc_fun(_1354344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354344, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1354344, c_Orderings_Oord__class_Omax(_1354344), _1354346) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354344), _1354348), c_Big__Operators_Olattice_OSup__fin(_1354344, c_Orderings_Oord__class_Omax(_1354344), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354344, tc_HOL_Obool)), _1354346), hAPP(hAPP(c_Set_Oinsert(_1354344), _1354348), c_Orderings_Obot__class_Obot(tc_fun(_1354344, tc_HOL_Obool)))))))], (31485 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354344, tc_HOL_Obool)), _1354346), hAPP(hAPP(c_Set_Oinsert(_1354344), _1354348), c_Orderings_Obot__class_Obot(tc_fun(_1354344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354344, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1354344, c_Orderings_Oord__class_Omax(_1354344), _1354346) = _1354348)]]], (27835 ^ _775828) ^ [_1273008, _1273010, _1273012, _1273014, _1273016, _1273018, _1273020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1273008, _1273012)), hAPP(hAPP(c_Product__Type_OPair(_1273008, _1273012), _1273018), _1273020)), hAPP(hAPP(c_Relation_Orel__comp(_1273008, _1273010, _1273012), _1273014), _1273016))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1273008, _1273010, _1273012, hAPP(hAPP(c_COMBC(_1273008, tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_fun(_1273010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273010, tc_fun(tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_fun(_1273010, tc_HOL_Obool)), _1273008), c_COMBC(_1273010, tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273010, tc_prod(_1273008, _1273010)), tc_fun(_1273010, tc_fun(tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_HOL_Obool)), _1273008), hAPP(c_COMBB(tc_prod(_1273008, _1273010), tc_fun(tc_fun(tc_prod(_1273008, _1273010), tc_HOL_Obool), tc_HOL_Obool), _1273010), c_member(tc_prod(_1273008, _1273010)))), c_Product__Type_OPair(_1273008, _1273010)))), _1273014), hAPP(hAPP(c_COMBC(_1273010, tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_fun(_1273012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273012, tc_fun(tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_fun(_1273012, tc_HOL_Obool)), _1273010), c_COMBC(_1273012, tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273012, tc_prod(_1273010, _1273012)), tc_fun(_1273012, tc_fun(tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_HOL_Obool)), _1273010), hAPP(c_COMBB(tc_prod(_1273010, _1273012), tc_fun(tc_fun(tc_prod(_1273010, _1273012), tc_HOL_Obool), tc_HOL_Obool), _1273012), c_member(tc_prod(_1273010, _1273012)))), c_Product__Type_OPair(_1273010, _1273012)))), _1273016)), _1273018), _1273020)))], (49622 ^ _775828) ^ [_1773583, _1773585] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1773583, _1773585)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1773585), _1773583))], (14874 ^ _775828) ^ [_1024834, _1024836, _1024838] : [class_Divides_Osemiring__div(_1024834), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024834), c_Divides_Odiv__class_Omod(_1024834, _1024836, _1024838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024834), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024834), _1024836), _1024838)), _1024838)) = _1024836)], (36990 ^ _775828) ^ [_1472065, _1472067, _1472069, _1472071] : [class_Groups_Ocomm__monoid__add(_1472065), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1472067), _1472069))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472067, _1472065), _1472071), _1472069) = c_Groups_Ozero__class_Ozero(_1472065))], (31069 ^ _775828) ^ [_1345171, _1345173, _1345175, _1345177, _1345179, _1345181, _1345183, _1345185] : [c_Finite__Set_Ofolding__image__simple(_1345171, _1345173, _1345175, _1345177, _1345179, _1345181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345173), _1345183)), -(hAPP(_1345181, hAPP(hAPP(c_Set_Oinsert(_1345173), _1345185), _1345183)) = hAPP(hAPP(_1345175, hAPP(_1345179, _1345185)), hAPP(_1345181, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345173, tc_HOL_Obool)), _1345183), hAPP(hAPP(c_Set_Oinsert(_1345173), _1345185), c_Orderings_Obot__class_Obot(tc_fun(_1345173, tc_HOL_Obool)))))))], (5723 ^ _775828) ^ [_867046, _867048] : [class_Groups_Ozero(_867046), 5726 ^ _775828 : [(5733 ^ _775828) ^ [] : [_867048 = c_Groups_Ozero__class_Ozero(_867046), -(c_Groups_Ozero__class_Ozero(_867046) = _867048)], (5727 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_867046) = _867048, -(_867048 = c_Groups_Ozero__class_Ozero(_867046))]]], (23184 ^ _775828) ^ [_1179633, _1179635, _1179637, _1179639] : [class_Fields_Ofield__inverse__zero(_1179633), -(_1179635 = c_Groups_Ozero__class_Ozero(_1179633)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179633), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179633), _1179637), _1179635)), _1179639) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179633), _1179637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179633), _1179639), _1179635))), _1179635))], (1760 ^ _775828) ^ [_800446, _800448] : [-(class_Rings_Odvd(_800446)), _800448 = _800446, class_Rings_Odvd(_800448)], (29267 ^ _775828) ^ [_1306595, _1306597, _1306599, _1306601] : [-(_1306595 = c_Orderings_Obot__class_Obot(tc_fun(_1306597, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1306597, _1306599, hAPP(c_COMBK(_1306599, _1306597), _1306601)), _1306595) = hAPP(hAPP(c_Set_Oinsert(_1306599), _1306601), c_Orderings_Obot__class_Obot(tc_fun(_1306599, tc_HOL_Obool))))], (23538 ^ _775828) ^ [_1187432, _1187434] : [_1187432 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1187432, _1187434) = _1187434)], (50858 ^ _775828) ^ [_1799734, _1799736, _1799738, _1799740, _1799742] : [-(c_List_OdropWhile(_1799734, _1799736, hAPP(hAPP(c_List_Omap(_1799738, _1799734), _1799740), _1799742)) = hAPP(hAPP(c_List_Omap(_1799738, _1799734), _1799740), c_List_OdropWhile(_1799738, hAPP(c_Fun_Ocomp(_1799734, tc_HOL_Obool, _1799738, _1799736), _1799740), _1799742)))], (45953 ^ _775828) ^ [_1683191, _1683193, _1683195] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1683191, tc_HOL_Obool)), hAPP(c_List_Oset(_1683191), c_List_Oremove1(_1683191, _1683193, _1683195))), hAPP(c_List_Oset(_1683191), _1683195))))], (30635 ^ _775828) ^ [_1335812, _1335814] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335812), _1335814))), -(hAPP(c_Finite__Set_Ocard(_1335812), _1335814) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48647 ^ _775828) ^ [_1751592, _1751594, _1751596] : [-(_1751592 = c_List_Olist_ONil(_1751594)), -(hAPP(c_List_Ohd(_1751594), hAPP(c_List_Orotate(_1751594, _1751596), _1751592)) = hAPP(hAPP(c_List_Onth(_1751594), _1751592), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1751596, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751594)), _1751592))))], (51330 ^ _775828) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (8285 ^ _775828) ^ [_908923, _908925, _908927, _908929] : [class_Orderings_Oord(_908923), _908925 = _908927, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908923), _908927), _908929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908923), _908925), _908929)))], (29127 ^ _775828) ^ [_1303552, _1303554] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303552, _1303552)), hAPP(hAPP(c_Product__Type_OPair(_1303552, _1303552), 29128 ^ [_1303552, _1303554]), 29128 ^ [_1303552, _1303554])), c_Transitive__Closure_Otrancl(_1303552, _1303554)))), -(c_Wellfounded_Oacyclic(_1303552, _1303554))], (48699 ^ _775828) ^ [_1752611, _1752613, _1752615, _1752617] : [-(hAPP(hAPP(c_List_Omap(_1752611, _1752613), _1752615), hAPP(c_List_Otl(_1752611), _1752617)) = hAPP(c_List_Otl(_1752613), hAPP(hAPP(c_List_Omap(_1752611, _1752613), _1752615), _1752617)))], (12017 ^ _775828) ^ [_973823, _973825] : [-(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), _973823), _973825)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _973823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _973825))], (7005 ^ _775828) ^ [_886796, _886798] : [class_Rings_Omult__zero(_886796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886796), c_Groups_Ozero__class_Ozero(_886796)), _886798) = c_Groups_Ozero__class_Ozero(_886796))], (29082 ^ _775828) ^ [_1302242, _1302244] : [-(c_Transitive__Closure_Otrancl(_1302242, _1302244) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1302242, _1302242), tc_HOL_Obool)), _1302244), hAPP(hAPP(c_Relation_Orel__comp(_1302242, _1302242, _1302242), c_Transitive__Closure_Otrancl(_1302242, _1302244)), _1302244)))], (38462 ^ _775828) ^ [_1506929, _1506931, _1506933, _1506935, _1506937, _1506939] : [c_Equiv__Relations_Oequiv(_1506929, _1506931, _1506933), hBOOL(hAPP(hAPP(c_member(_1506929), _1506935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506929, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1506929, _1506929, _1506933), hAPP(hAPP(c_Set_Oinsert(_1506929), _1506937), c_Orderings_Obot__class_Obot(tc_fun(_1506929, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1506929, _1506929, _1506933), hAPP(hAPP(c_Set_Oinsert(_1506929), _1506939), c_Orderings_Obot__class_Obot(tc_fun(_1506929, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506929, _1506929)), hAPP(hAPP(c_Product__Type_OPair(_1506929, _1506929), _1506937), _1506939)), _1506933)))], (24663 ^ _775828) ^ [_1209233, _1209235] : [-(c_Nitpick_Onat__lcm(_1209233, _1209235) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1209233), _1209235)), c_Nitpick_Onat__gcd(_1209233, _1209235)))], (27796 ^ _775828) ^ [_1271030, _1271032, _1271034, _1271036] : [27797 ^ _775828 : [(27798 ^ _775828) ^ [_1271105] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1271030, _1271034)), hAPP(hAPP(c_Product__Type_OPair(_1271030, _1271034), _1271032), _1271105)), _1271036))]], -(hBOOL(hAPP(hAPP(c_member(_1271030), _1271032), hAPP(c_Relation_ODomain(_1271030, _1271034), _1271036))))], (36447 ^ _775828) ^ [_1460380, _1460382, _1460384, _1460386] : [class_Orderings_Olinorder(_1460380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460380), _1460382), _1460384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460380), _1460384), _1460386)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460380, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1460380, _1460382, _1460384)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1460380, _1460384, _1460386)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460380, _1460382), _1460386))], (49600 ^ _775828) ^ [_1773118, _1773120, _1773122] : [class_Orderings_Olinorder(_1773118), -(c_List_Olinorder__class_Osorted(_1773118, hAPP(c_List_Ofilter(_1773118, hAPP(hAPP(c_COMBC(_1773118, _1773118, tc_HOL_Obool), c_fequal), hAPP(_1773120, _1773122))), _1773122)))], (13292 ^ _775828) ^ [_995856, _995858, _995860, _995862] : [class_Divides_Osemiring__div(_995856), -(c_Divides_Odiv__class_Omod(_995856, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995856), _995858), c_Divides_Odiv__class_Omod(_995856, _995860, _995862)), _995862) = c_Divides_Odiv__class_Omod(_995856, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995856), _995858), _995860), _995862))], (14360 ^ _775828) ^ [_1016031, _1016033, _1016035] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1016031, _1016033)), _1016035), _1016035)), hBOOL(hAPP(_1016031, _1016035)), 14368 ^ _775828 : [(14371 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1016031, _1016033)), 14367 ^ [_1016031, _1016033, _1016035]), _1016035)))], (14369 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1016033), _1016035), 14367 ^ [_1016031, _1016033, _1016035])))]]], (20104 ^ _775828) ^ [_1121204] : [c_Int_OMin = c_Int_OBit0(_1121204)], (48677 ^ _775828) ^ [_1752182, _1752184, _1752186] : [hBOOL(hAPP(c_List_Odistinct(_1752182), hAPP(c_List_Orotate(_1752182, _1752184), _1752186))), -(hBOOL(hAPP(c_List_Odistinct(_1752182), _1752186)))], (450 ^ _775828) ^ [_782511, _782513, _782515, _782517, _782519, _782521, _782523, _782525, _782527, _782529] : [-(c_Typedef_Otype__definition(_782527, _782523, _782519, _782515, _782511)), c_Typedef_Otype__definition(_782529, _782525, _782521, _782517, _782513), _782529 = _782527, _782525 = _782523, _782521 = _782519, _782517 = _782515, _782513 = _782511], (32931 ^ _775828) ^ [_1385286, _1385288, _1385290] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, tc_Nat_Onat), _1385288), _1385290)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1385286), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1385288)), _1385290))], (38508 ^ _775828) ^ [_1507934, _1507936, _1507938, _1507940, _1507942, _1507944] : [hBOOL(hAPP(hAPP(c_member(_1507934), _1507936), _1507938)), -(hAPP(c_Fun_Ooverride__on(_1507934, _1507940, _1507942, _1507944, _1507938), _1507936) = hAPP(_1507944, _1507936))], (1922 ^ _775828) ^ [_803652, _803654, _803656, _803658, _803660, _803662] : [-(c_Com_Ocom_OCall(_803662, _803658, _803654) = c_Com_Ocom_OCall(_803660, _803656, _803652)), _803662 = _803660, _803658 = _803656, _803654 = _803652], (39299 ^ _775828) ^ [_1524825, _1524827, _1524829, _1524831, _1524833] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524825, tc_fun(_1524827, tc_HOL_Obool)), _1524829), _1524831), _1524833))), 39300 ^ _775828 : [(39301 ^ _775828) ^ [_1524897] : [hBOOL(hAPP(hAPP(c_member(_1524825), _1524897), _1524829)), hBOOL(hAPP(hAPP(_1524831, _1524897), _1524833))]]], (23470 ^ _775828) ^ [_1185869, _1185871, _1185873, _1185875, _1185877, _1185879] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1185869, _1185871), _1185871, _1185873), hAPP(hAPP(c_COMBB(_1185875, tc_fun(_1185871, _1185873), tc_prod(_1185869, _1185871)), _1185877), hAPP(hAPP(c_COMBB(_1185869, _1185875, tc_prod(_1185869, _1185871)), _1185879), c_Product__Type_Ofst(_1185869, _1185871)))), c_Product__Type_Osnd(_1185869, _1185871)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1185869, _1185871, _1185873), hAPP(hAPP(c_COMBB(_1185875, tc_fun(_1185871, _1185873), _1185869), _1185877), _1185879)))], (33364 ^ _775828) ^ [_1394273, _1394275, _1394277, _1394279, _1394281] : [hBOOL(hAPP(hAPP(c_member(_1394273), _1394275), _1394277)), -(hAPP(c_Map_Orestrict__map(_1394273, _1394279, _1394281, _1394277), _1394275) = hAPP(_1394281, _1394275))], (46141 ^ _775828) ^ [_1687998, _1688000, _1688002, _1688004] : [class_Orderings_Olinorder(_1687998), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687998, _1687998, c_COMBI(_1687998)), _1688000), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687998, _1687998, c_COMBI(_1687998)), _1688002), _1688004)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687998, _1687998, c_COMBI(_1687998)), _1688002), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687998, _1687998, c_COMBI(_1687998)), _1688000), _1688004)))], (30113 ^ _775828) ^ [_1324601, _1324603] : [hAPP(hAPP(c_Relation_Orel__comp(_1324601, _1324601, _1324601), _1324603), _1324603) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324601, _1324601), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1324601, _1324603))], (6187 ^ _775828) ^ [_874161, _874163] : [class_Rings_Olinordered__semidom(_874161), 6190 ^ _775828 : [(6197 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _874163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874161), c_Groups_Ozero__class_Ozero(_874161)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_874161), _874163))))], (6191 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874161), c_Groups_Ozero__class_Ozero(_874161)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_874161), _874163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _874163)))]]], (48048 ^ _775828) ^ [_1735827, _1735829, _1735831, _1735833, _1735835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735827), tc_List_Olist(_1735827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735827), tc_List_Olist(_1735827)), _1735829), _1735831)), c_List_Olexord(_1735827, _1735833))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735827), tc_List_Olist(_1735827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735827), tc_List_Olist(_1735827)), hAPP(hAPP(c_List_Oappend(_1735827), _1735835), _1735829)), hAPP(hAPP(c_List_Oappend(_1735827), _1735835), _1735831))), c_List_Olexord(_1735827, _1735833))))], (47205 ^ _775828) ^ [_1717326, _1717328, _1717330] : [hBOOL(hAPP(c_List_Odistinct(_1717326), _1717328)), -(hBOOL(hAPP(c_List_Odistinct(_1717326), hAPP(hAPP(c_List_Otake(_1717326), _1717330), _1717328))))], (14225 ^ _775828) ^ [_1013534, _1013536] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1013534), _1013536) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013534, _1013536)), _1013536))], (19736 ^ _775828) ^ [_1114840] : [-(c_Int_Opred(_1114840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114840), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (45558 ^ _775828) ^ [_1673987, _1673989, _1673991, _1673993, _1673995, _1673997] : [-(hAPP(hAPP(c_List_Omap(_1673987, _1673989), _1673991), hAPP(hAPP(c_List_Omap(_1673993, _1673987), _1673995), _1673997)) = hAPP(hAPP(c_List_Omap(_1673993, _1673989), hAPP(c_Fun_Ocomp(_1673987, _1673989, _1673993, _1673991), _1673995)), _1673997))], (17093 ^ _775828) ^ [_1067789, _1067791, _1067793] : [class_Int_Onumber__ring(_1067789), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067789), hAPP(c_Int_Onumber__class_Onumber__of(_1067789), _1067791)), hAPP(c_Int_Onumber__class_Onumber__of(_1067789), _1067793)) = hAPP(c_Int_Onumber__class_Onumber__of(_1067789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067791), _1067793)))], (33400 ^ _775828) ^ [_1395066, _1395068, _1395070, _1395072, _1395074, _1395076] : [hBOOL(hAPP(hAPP(c_member(_1395066), _1395068), _1395070)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1395066, tc_Option_Ooption(_1395072)), c_Map_Orestrict__map(_1395066, _1395072, _1395074, _1395070)), _1395068), _1395076) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1395066, tc_Option_Ooption(_1395072)), c_Map_Orestrict__map(_1395066, _1395072, _1395074, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395066, tc_HOL_Obool)), _1395070), hAPP(hAPP(c_Set_Oinsert(_1395066), _1395068), c_Orderings_Obot__class_Obot(tc_fun(_1395066, tc_HOL_Obool)))))), _1395068), _1395076))], (5531 ^ _775828) ^ [_863419, _863421] : [hAPP(c_Com_Ocom_OBODY, _863419) = hAPP(c_Com_Ocom_OBODY, _863421), -(_863419 = _863421)], (36081 ^ _775828) ^ [_1453445, _1453447, _1453449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453445)), 36084 ^ _775828 : [(36085 ^ _775828) ^ [_1453579] : [36087 ^ _775828 : [(36093 ^ _775828) ^ [] : [-(_1453579 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36089 ^ [_1453445, _1453447, _1453449, _1453579]), 36086 ^ [_1453445, _1453447, _1453449, _1453579]))], (36091 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36089 ^ [_1453445, _1453447, _1453449, _1453579]), _1453447)))], (36088 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36086 ^ [_1453445, _1453447, _1453449, _1453579]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1453445))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453449), _1453579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453449), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1453579), _1453445))))]]], (15316 ^ _775828) ^ [_1033209, _1033211, _1033213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033209), _1033211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1033209), _1033213)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1033211), _1033213))))], (24948 ^ _775828) ^ [_1215185, _1215187, _1215189, _1215191, _1215193, _1215195] : [_1215185 = hAPP(_1215187, _1215189), hBOOL(hAPP(hAPP(c_member(_1215191), _1215189), _1215193)), -(hBOOL(hAPP(hAPP(c_member(_1215195), _1215185), hAPP(c_Set_Oimage(_1215191, _1215195, _1215187), _1215193))))], (27804 ^ _775828) ^ [_1271272, _1271274] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1271272)), -(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)), _1271272))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1271274))))) = 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)), _1271272))), 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, _1271274))))))], (33809 ^ _775828) ^ [_1404001, _1404003, _1404005, _1404007] : [class_Lattices_Olattice(_1404001), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404001), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404001), _1404003), _1404005)), _1404007) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404001), _1404003), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404001), _1404005), _1404007)))], (13682 ^ _775828) ^ [_1003667, _1003669, _1003671, _1003673, _1003675] : [c_Com_Ocom_OCall(_1003667, _1003669, _1003671) = c_Com_Ocom_OSemi(_1003673, _1003675)], (6640 ^ _775828) ^ [_881247, _881249, _881251] : [class_Orderings_Olinorder(_881247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881247), _881249), _881251))), -(_881249 = _881251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881247), _881251), _881249)))], (5893 ^ _775828) ^ [_869691, _869693] : [-(_869691 = _869693), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869691), _869693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869693), _869691)))], (37620 ^ _775828) ^ [_1487332, _1487334, _1487336] : [37622 ^ _775828 : [(37625 ^ _775828) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1487336, 37621 ^ [_1487332, _1487334, _1487336]))], (37623 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487332), 37621 ^ [_1487332, _1487334, _1487336]), _1487334)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487332, tc_Int_Oint), _1487336), _1487334) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487332, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1487332), c_Int_Onat), _1487336)), _1487334)))], (19910 ^ _775828) ^ [_1117518, _1117520] : [class_Int_Onumber__ring(_1117518), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117518), hAPP(c_Int_Onumber__class_Onumber__of(_1117518), _1117520)), c_Groups_Oone__class_Oone(_1117518)) = hAPP(c_Int_Onumber__class_Onumber__of(_1117518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117520), c_Int_OBit1(c_Int_OPls))))], (8245 ^ _775828) ^ [_908293, _908295, _908297] : [class_Orderings_Opreorder(_908293), _908295 = _908297, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908293), _908295), _908297)))], (42692 ^ _775828) ^ [_1606787, _1606789, _1606791, _1606793, _1606795, _1606797, _1606799, _1606801, _1606803, _1606805] : [-(c_Product__Type_Omap__pair(_1606787, _1606789, _1606791, _1606793, hAPP(c_Fun_Ocomp(_1606795, _1606789, _1606787, _1606797), _1606799), hAPP(c_Fun_Ocomp(_1606801, _1606793, _1606791, _1606803), _1606805)) = hAPP(c_Fun_Ocomp(tc_prod(_1606795, _1606801), tc_prod(_1606789, _1606793), tc_prod(_1606787, _1606791), c_Product__Type_Omap__pair(_1606795, _1606789, _1606801, _1606793, _1606797, _1606803)), c_Product__Type_Omap__pair(_1606787, _1606795, _1606791, _1606801, _1606799, _1606805)))], (39648 ^ _775828) ^ [_1534235, _1534237, _1534239, _1534241, _1534243] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1534235, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534237, tc_fun(_1534235, tc_HOL_Obool)), _1534239), _1534241)), _1534243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534237, tc_fun(_1534235, tc_HOL_Obool)), _1534239), hAPP(hAPP(c_COMBC(_1534237, tc_fun(_1534235, tc_HOL_Obool), tc_fun(_1534235, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534235, tc_HOL_Obool), tc_fun(tc_fun(_1534235, tc_HOL_Obool), tc_fun(_1534235, tc_HOL_Obool)), _1534237), c_Groups_Ominus__class_Ominus(tc_fun(_1534235, tc_HOL_Obool))), _1534241)), _1534243)))], (29096 ^ _775828) ^ [_1302683, _1302685] : [c_Wellfounded_Owf(_1302683, hAPP(c_Relation_Oconverse(_1302683, _1302683), _1302685)), -(c_Wellfounded_Owf(_1302683, hAPP(c_Relation_Oconverse(_1302683, _1302683), c_Transitive__Closure_Otrancl(_1302683, _1302685))))], (6949 ^ _775828) ^ [_886007, _886009, _886011] : [class_Rings_Ono__zero__divisors(_886007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886007), _886009), _886011) = c_Groups_Ozero__class_Ozero(_886007), -(_886009 = c_Groups_Ozero__class_Ozero(_886007)), -(_886011 = c_Groups_Ozero__class_Ozero(_886007))], (46398 ^ _775828) ^ [_1695504, _1695506, _1695508, _1695510] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695504), tc_List_Olist(_1695504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695504), tc_List_Olist(_1695504)), _1695506), _1695508)), c_List_Olistrel(_1695504, _1695510))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695504)), _1695506) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695504)), _1695508))], (16441 ^ _775828) ^ [_1055482, _1055484, _1055486, _1055488] : [hBOOL(hAPP(hAPP(c_member(_1055482), _1055484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055482, tc_HOL_Obool)), _1055486), _1055488))), 16444 ^ _775828 : [(16447 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1055482), _1055484), _1055488))], (16445 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1055482), _1055484), _1055486)))]]], (48377 ^ _775828) ^ [_1745504, _1745506] : [_1745506 = c_List_Olist_ONil(_1745504), -(hAPP(c_List_Orotate1(_1745504), _1745506) = c_List_Olist_ONil(_1745504))], (18783 ^ _775828) ^ [_1098724, _1098726, _1098728] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098724), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098726)), _1098728)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1098724, _1098726), hAPP(c_Divides_OnegateSnd, _1098728))))], (19258 ^ _775828) ^ [] : [-(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))))], (19822 ^ _775828) ^ [] : [-(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))))))], (27781 ^ _775828) ^ [_1270671, _1270673, _1270675] : [-(hAPP(c_Relation_ORange(_1270671, _1270673), hAPP(c_Relation_Oconverse(_1270673, _1270671), _1270675)) = hAPP(c_Relation_ODomain(_1270673, _1270671), _1270675))], (25971 ^ _775828) ^ [_1234509, _1234511] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234509), _1234511)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234511), _1234509))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234511), _1234509)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234509), _1234511)))], (38029 ^ _775828) ^ [_1496972, _1496974, _1496976] : [-(hAPP(c_Relation_OImage(_1496972, _1496972, c_Relation_OId__on(_1496972, _1496974)), _1496976) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496972, tc_HOL_Obool)), _1496974), _1496976))], (42832 ^ _775828) ^ [_1610114, _1610116, _1610118, _1610120, _1610122, _1610124, _1610126, _1610128] : [class_Groups_Ocomm__monoid__mult(_1610114), c_Fun_Oinj__on(_1610116, _1610118, _1610120, _1610122), _1610124 = hAPP(c_Set_Oimage(_1610116, _1610118, _1610120), _1610122), _1610126 = hAPP(c_Fun_Ocomp(_1610118, _1610114, _1610116, _1610128), _1610120), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1610118, _1610114), _1610128), _1610124) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1610116, _1610114), _1610126), _1610122))], (14880 ^ _775828) ^ [_1024967, _1024969, _1024971] : [class_Divides_Osemiring__div(_1024967), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024967), _1024969), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024967), _1024971), _1024969))), c_Divides_Odiv__class_Omod(_1024967, _1024971, _1024969)) = _1024971)], (26910 ^ _775828) ^ [_1251196, _1251198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251196), _1251198)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251198), _1251196))], (10810 ^ _775828) ^ [_952605, _952607] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952605), _952607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _952607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11889 ^ _775828) ^ [_971471, _971473, _971475] : [class_Groups_Oordered__comm__monoid__add(_971471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971471), _971473), c_Groups_Ozero__class_Ozero(_971471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971471), _971475), c_Groups_Ozero__class_Ozero(_971471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971471), _971473), _971475)), c_Groups_Ozero__class_Ozero(_971471))))], (26061 ^ _775828) ^ [_1235979, _1235981] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235979), _1235981)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235981), _1235979))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235981), _1235979)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235979), _1235981)))], (40473 ^ _775828) ^ [_1551955, _1551957, _1551959, _1551961, _1551963] : [c_Fun_Oinj__on(_1551955, _1551957, _1551959, c_Orderings_Otop__class_Otop(tc_fun(_1551955, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1551955, _1551957, _1551959), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551955, tc_HOL_Obool)), _1551961), _1551963)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551957, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551955, _1551957, _1551959), _1551961)), hAPP(c_Set_Oimage(_1551955, _1551957, _1551959), _1551963)))], (13759 ^ _775828) ^ [_1005023, _1005025] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005023, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005025)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005023, _1005025) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (12389 ^ _775828) ^ [_980311, _980313] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980311), _980313) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12392 ^ _775828 : [(12395 ^ _775828) ^ [] : [-(_980313 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12393 ^ _775828) ^ [] : [-(_980311 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33304 ^ _775828) ^ [_1392882, _1392884, _1392886, _1392888, _1392890] : [class_Fields_Ofield(_1392882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392884), _1392886)), -(hAPP(_1392888, _1392890) = c_Groups_Ozero__class_Ozero(_1392882)), 33315 ^ _775828 : [(33322 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392884), _1392890), _1392886))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392884, _1392882), _1392888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392884, tc_HOL_Obool)), _1392886), hAPP(hAPP(c_Set_Oinsert(_1392884), _1392890), c_Orderings_Obot__class_Obot(tc_fun(_1392884, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392884, _1392882), _1392888), _1392886))], (33316 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1392884), _1392890), _1392886)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392884, _1392882), _1392888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392884, tc_HOL_Obool)), _1392886), hAPP(hAPP(c_Set_Oinsert(_1392884), _1392890), c_Orderings_Obot__class_Obot(tc_fun(_1392884, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392882), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392884, _1392882), _1392888), _1392886)), hAPP(_1392888, _1392890)))]]], (1700 ^ _775828) ^ [_799696, _799698] : [-(class_Orderings_Oord(_799696)), _799698 = _799696, class_Orderings_Oord(_799698)], (49230 ^ _775828) ^ [_1764253, _1764255, _1764257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764253), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764255)), _1764257))), -(c_List_Obutlast(_1764255, hAPP(hAPP(c_List_Otake(_1764255), _1764253), _1764257)) = hAPP(hAPP(c_List_Otake(_1764255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1764253), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1764257))], (15342 ^ _775828) ^ [_1033656, _1033658] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1033656)), hAPP(c_Nat_OSuc, _1033658)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033656), _1033658))], (15700 ^ _775828) ^ [_1040450, _1040452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040452), _1040450)), -(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), _1040450), _1040452))))], (17505 ^ _775828) ^ [_1075552, _1075554] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1075552), _1075554)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075552)), _1075554))], (18085 ^ _775828) ^ [_1085982, _1085984, _1085986, _1085988] : [class_Rings_Olinordered__semidom(_1085982), hAPP(hAPP(c_Power_Opower__class_Opower(_1085982), _1085984), _1085986) = hAPP(hAPP(c_Power_Opower__class_Opower(_1085982), _1085988), _1085986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085982), c_Groups_Ozero__class_Ozero(_1085982)), _1085984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085982), c_Groups_Ozero__class_Ozero(_1085982)), _1085988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1085986)), -(_1085984 = _1085988)], (13094 ^ _775828) ^ [_992298, _992300, _992302, _992304, _992306] : [-(hBOOL(hAPP(_992298, _992300))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_992302), _992300), _992304)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_992298, _992306, _992302)), _992300), _992304)))], (48673 ^ _775828) ^ [_1752065, _1752067, _1752069] : [-(hAPP(hAPP(c_List_Otake(_1752065), _1752067), hAPP(c_List_Otl(_1752065), _1752069)) = hAPP(c_List_Otl(_1752065), hAPP(hAPP(c_List_Otake(_1752065), hAPP(c_Nat_OSuc, _1752067)), _1752069)))], (10043 ^ _775828) ^ [_938306, _938308] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938306, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938306, tc_HOL_Obool)), _938308)) = _938308)], (45702 ^ _775828) ^ [_1677519, _1677521, _1677523, _1677525] : [_1677525 = c_Option_Ooption_ONone(_1677519), -(hAPP(hAPP(c_Option_Omap(_1677519, _1677521), _1677523), _1677525) = c_Option_Ooption_ONone(_1677521))], (25833 ^ _775828) ^ [_1232342, _1232344] : [_1232342 = _1232344, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232342), _1232344)))], (12693 ^ _775828) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51316 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (35855 ^ _775828) ^ [_1449170, _1449172, _1449174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449170)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1449172), _1449174)), 35862 ^ _775828 : [(35863 ^ _775828) ^ [_1449360] : [35865 ^ _775828 : [(35871 ^ _775828) ^ [] : [-(_1449360 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35867 ^ [_1449170, _1449172, _1449174, _1449360]), 35864 ^ [_1449170, _1449172, _1449174, _1449360]))], (35869 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35867 ^ [_1449170, _1449172, _1449174, _1449360]), _1449174)))], (35866 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35864 ^ [_1449170, _1449172, _1449174, _1449360]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449170))))]], -(_1449360 = _1449172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449360), _1449170) = _1449172]]], (18988 ^ _775828) ^ [_1102641, _1102643, _1102645, _1102647, _1102649] : [hAPP(c_Product__Type_Ofst(_1102641, _1102643), hAPP(hAPP(c_Product__Type_OPair(_1102641, _1102643), _1102645), _1102647)) = _1102649, -(_1102645 = _1102649)], (50086 ^ _775828) ^ [_1781706, _1781708] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1781706, _1781708) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1781706), _1781708)))], (49439 ^ _775828) ^ [_1768485, _1768487, _1768489, _1768491] : [-(hAPP(c_List_Ofilter(_1768485, _1768487), hAPP(c_List_Ofilter(_1768485, _1768489), _1768491)) = hAPP(c_List_Ofilter(_1768485, hAPP(hAPP(c_COMBS(_1768485, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768485), c_fconj), _1768489)), _1768487)), _1768491))], (32869 ^ _775828) ^ [_1383684, _1383686, _1383688, _1383690, _1383692] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383684, _1383686), _1383688), _1383690), _1383692), _1383690) = _1383692)], (24749 ^ _775828) ^ [_1210898, _1210900, _1210902, _1210904, _1210906, _1210908] : [24752 ^ _775828 : [(24755 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1210904), _1210906), hAPP(hAPP(_1210908, 24750 ^ [_1210898, _1210900, _1210902, _1210904, _1210906, _1210908]), 24751 ^ [_1210898, _1210900, _1210902, _1210904, _1210906, _1210908])))], (24753 ^ _775828) ^ [] : [-(_1210898 = hAPP(hAPP(c_Product__Type_OPair(_1210900, _1210902), 24750 ^ [_1210898, _1210900, _1210902, _1210904, _1210906, _1210908]), 24751 ^ [_1210898, _1210900, _1210902, _1210904, _1210906, _1210908]))]], -(hBOOL(hAPP(hAPP(c_member(_1210904), _1210906), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1210900, _1210902, tc_fun(_1210904, tc_HOL_Obool)), _1210908), _1210898))))], (49865 ^ _775828) ^ [_1777755, _1777757, _1777759] : [class_Orderings_Olinorder(_1777755), 49868 ^ _775828 : [(49875 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1777755, _1777759), -(c_List_Olinorder__class_Osorted(_1777755, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1777755, _1777755, c_COMBI(_1777755)), _1777757), _1777759)))], (49869 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1777755, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1777755, _1777755, c_COMBI(_1777755)), _1777757), _1777759)), -(c_List_Olinorder__class_Osorted(_1777755, _1777759))]]], (21088 ^ _775828) ^ [_1140611, _1140613, _1140615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140611, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1140611, tc_fun(_1140611, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140611)), _1140613)), hAPP(hAPP(c_COMBC(_1140611, tc_fun(_1140611, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140611)), _1140615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140611, tc_HOL_Obool)), _1140613), _1140615)))], (11148 ^ _775828) ^ [_958484, _958486, _958488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958484, tc_HOL_Obool)), _958486), _958488)), 11151 ^ _775828 : [(11154 ^ _775828) ^ [] : [_958486 = _958488], (11152 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958484, tc_HOL_Obool)), _958486), _958488)))]]], (41897 ^ _775828) ^ [_1587696, _1587698] : [-(hAPP(hAPP(c_Nat_Ocompow(_1587696, _1587696), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1587698) = c_Fun_Oid(_1587696))], (29553 ^ _775828) ^ [_1312043, _1312045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312043, tc_HOL_Obool)), _1312045), c_Orderings_Obot__class_Obot(tc_fun(_1312043, tc_HOL_Obool)))), -(_1312045 = c_Orderings_Obot__class_Obot(tc_fun(_1312043, tc_HOL_Obool)))], (23234 ^ _775828) ^ [_1180523, _1180525, _1180527, _1180529, _1180531] : [class_Fields_Ofield(_1180523), -(_1180525 = c_Groups_Ozero__class_Ozero(_1180523)), -(_1180527 = c_Groups_Ozero__class_Ozero(_1180523)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180523), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180523), _1180529), _1180525)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180523), _1180531), _1180527)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180523), _1180529), _1180527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180523), _1180531), _1180525))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180523), _1180525), _1180527)))], (29245 ^ _775828) ^ [_1306132, _1306134, _1306136, _1306138] : [c_Hoare__Mirabelle_Ohoare__derivs(_1306132, _1306134, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1306132)), _1306136), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1306132), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1306132, _1306134, _1306138), -(c_Hoare__Mirabelle_Ohoare__derivs(_1306132, _1306134, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1306132)), _1306136), _1306138)))], (25705 ^ _775828) ^ [_1230226, _1230228, _1230230, _1230232] : [class_Divides_Osemiring__div(_1230226), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230226), _1230228), _1230230)), -(c_Divides_Odiv__class_Omod(_1230226, c_Divides_Odiv__class_Omod(_1230226, _1230232, _1230230), _1230228) = c_Divides_Odiv__class_Omod(_1230226, _1230232, _1230228))], (7849 ^ _775828) ^ [_901216, _901218] : [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), _901216), _901218))), 7852 ^ _775828 : [(7855 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901218)))], (7853 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901216)))]]], (40957 ^ _775828) ^ [_1564412, _1564414, _1564416, _1564418, _1564420] : [c_Fun_Oinj__on(_1564412, _1564414, _1564416, c_Orderings_Otop__class_Otop(tc_fun(_1564412, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564414, tc_HOL_Obool)), _1564418), hAPP(c_Set_Oimage(_1564412, _1564414, _1564416), _1564420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564412, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1564412, _1564414, _1564416), _1564418)), _1564420)))], (21914 ^ _775828) ^ [_1156047, _1156049] : [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), _1156047))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156049), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156047))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156049), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156047))), 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), _1156049))), c_COMBI(tc_Int_Oint))))], (31497 ^ _775828) ^ [_1354868, _1354870, _1354872] : [class_Orderings_Olinorder(_1354868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354868), _1354870)), -(_1354870 = c_Orderings_Obot__class_Obot(tc_fun(_1354868, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354868), _1354872), c_Big__Operators_Olattice_OInf__fin(_1354868, c_Orderings_Oord__class_Omin(_1354868), _1354870)) = c_Big__Operators_Olattice_OInf__fin(_1354868, c_Orderings_Oord__class_Omin(_1354868), hAPP(c_Set_OCollect(_1354868), hAPP(hAPP(c_COMBB(tc_fun(_1354868, tc_HOL_Obool), tc_HOL_Obool, _1354868), c_HOL_OEx(_1354868)), hAPP(hAPP(c_COMBC(_1354868, tc_fun(_1354868, tc_HOL_Obool), tc_fun(_1354868, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354868, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1354868, tc_HOL_Obool), tc_fun(_1354868, tc_HOL_Obool)), _1354868), c_COMBS(_1354868, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354868, tc_HOL_Obool), tc_fun(_1354868, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1354868), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1354868), c_fconj)), hAPP(hAPP(c_COMBC(_1354868, tc_fun(_1354868, _1354868), tc_fun(_1354868, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354868, tc_HOL_Obool), tc_fun(tc_fun(_1354868, _1354868), tc_fun(_1354868, tc_HOL_Obool)), _1354868), c_COMBB(_1354868, tc_HOL_Obool, _1354868)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1354868), _1354872))))), hAPP(hAPP(c_COMBC(_1354868, tc_fun(_1354868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354868)), _1354870))))))], (51510 ^ _775828) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (48787 ^ _775828) ^ [_1754574, _1754576, _1754578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1754574), _1754576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1754574), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1754576), _1754578))))], (22712 ^ _775828) ^ [_1171087, _1171089, _1171091, _1171093] : [class_Fields_Ofield__inverse__zero(_1171087), 22715 ^ _775828 : [(22716 ^ _775828) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171087), _1171089), _1171091) = _1171093, 22719 ^ _775828 : [(22726 ^ _775828) ^ [] : [_1171091 = c_Groups_Ozero__class_Ozero(_1171087), -(_1171093 = c_Groups_Ozero__class_Ozero(_1171087))], (22720 ^ _775828) ^ [] : [-(_1171091 = c_Groups_Ozero__class_Ozero(_1171087)), -(_1171089 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171087), _1171093), _1171091))]]], (22732 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171087), _1171089), _1171091) = _1171093), 22735 ^ _775828 : [(22738 ^ _775828) ^ [] : [_1171089 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171087), _1171093), _1171091)], (22736 ^ _775828) ^ [] : [_1171091 = c_Groups_Ozero__class_Ozero(_1171087)]], 22739 ^ _775828 : [(22742 ^ _775828) ^ [] : [_1171093 = c_Groups_Ozero__class_Ozero(_1171087)], (22740 ^ _775828) ^ [] : [-(_1171091 = c_Groups_Ozero__class_Ozero(_1171087))]]]]], (48978 ^ _775828) ^ [_1758941, _1758943, _1758945, _1758947] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758941)), hAPP(hAPP(c_List_Oappend(_1758941), _1758943), _1758945)), c_List_Olists(_1758941, _1758947)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758941)), _1758943), c_List_Olists(_1758941, _1758947))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758941)), _1758945), c_List_Olists(_1758941, _1758947)))], (40915 ^ _775828) ^ [_1563287, _1563289, _1563291, _1563293] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563287, _1563287)), hAPP(hAPP(c_Product__Type_OPair(_1563287, _1563287), _1563289), _1563291)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1563287, _1563287), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1563293))), -(_1563289 = _1563291)], (17987 ^ _775828) ^ [_1084054, _1084056, _1084058] : [class_Rings_Olinordered__semidom(_1084054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084054), c_Groups_Oone__class_Oone(_1084054)), _1084056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084054), c_Groups_Oone__class_Oone(_1084054)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084054), _1084056), hAPP(c_Nat_OSuc, _1084058)))))], (42702 ^ _775828) ^ [_1607100, _1607102, _1607104, _1607106, _1607108, _1607110] : [c_Fun_Oinj__on(_1607100, _1607102, _1607104, _1607106), c_Fun_Oinj__on(_1607102, _1607108, _1607110, hAPP(c_Set_Oimage(_1607100, _1607102, _1607104), _1607106)), -(c_Fun_Oinj__on(_1607100, _1607108, hAPP(c_Fun_Ocomp(_1607102, _1607108, _1607100, _1607110), _1607104), _1607106))], (38198 ^ _775828) ^ [_1500932, _1500934] : [-(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), _1500932), _1500934)), 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), _1500934), _1500932)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (26197 ^ _775828) ^ [_1238325, _1238327, _1238329, _1238331, _1238333] : [class_Rings_Ocomm__semiring__1(_1238325), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238325), _1238327), _1238329)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238325), _1238331), _1238333)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238325), _1238327), _1238331)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238325), _1238329), _1238333))))], (17291 ^ _775828) ^ [_1071745, _1071747, _1071749, _1071751] : [class_Rings_Olinordered__semidom(_1071745), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071745), _1071747), _1071749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071745), c_Groups_Ozero__class_Ozero(_1071745)), _1071747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1071751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071745), hAPP(hAPP(c_Power_Opower__class_Opower(_1071745), _1071747), _1071751)), hAPP(hAPP(c_Power_Opower__class_Opower(_1071745), _1071749), _1071751))))], (32919 ^ _775828) ^ [_1385025, _1385027, _1385029] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385025, tc_Nat_Onat), _1385027), _1385029) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385025, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1385025), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1385027)), _1385029)))], (14748 ^ _775828) ^ [_1022527, _1022529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022527), 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)), _1022529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022527), _1022529)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45389 ^ _775828) ^ [_1669785, _1669787, _1669789, _1669791, _1669793] : [hBOOL(hAPP(hAPP(c_member(_1669785), _1669787), c_Map_Odom(_1669785, _1669789, _1669791))), -(hAPP(c_Map_Omap__add(_1669785, _1669789, _1669793, _1669791), _1669787) = hAPP(_1669791, _1669787))], (4036 ^ _775828) ^ [_837399, _837401, _837403, _837405, _837407, _837409, _837411, _837413] : [-(c_Nitpick_Osetsum_H(_837413, _837409, _837405, _837401) = c_Nitpick_Osetsum_H(_837411, _837407, _837403, _837399)), _837413 = _837411, _837409 = _837407, _837405 = _837403, _837401 = _837399], (49425 ^ _775828) ^ [_1768275, _1768277, _1768279] : [hBOOL(hAPP(c_List_Odistinct(_1768275), _1768277)), -(hBOOL(hAPP(c_List_Odistinct(_1768275), hAPP(c_List_Ofilter(_1768275, _1768279), _1768277))))], (1400 ^ _775828) ^ [_795946, _795948] : [-(class_Rings_Olinordered__semiring__strict(_795946)), _795948 = _795946, class_Rings_Olinordered__semiring__strict(_795948)], (6410 ^ _775828) ^ [_877819, _877821, _877823] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _877819))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_877821, _877819, _877823))))], (28649 ^ _775828) ^ [_1290486, _1290488, _1290490, _1290492] : [hBOOL(hAPP(hAPP(c_member(_1290486), _1290488), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290486, tc_HOL_Obool)), _1290490), _1290492))), -(hBOOL(hAPP(hAPP(c_member(_1290486), _1290488), _1290490))), -(hBOOL(hAPP(hAPP(c_member(_1290486), _1290488), _1290492)))], (29815 ^ _775828) ^ [_1317647, _1317649, _1317651, _1317653, _1317655] : [hBOOL(hAPP(hAPP(c_member(_1317647), _1317649), _1317651)), -(hAPP(hAPP(c_Set_Oinsert(_1317653), hAPP(_1317655, _1317649)), hAPP(c_Set_Oimage(_1317647, _1317653, _1317655), _1317651)) = hAPP(c_Set_Oimage(_1317647, _1317653, _1317655), _1317651))], (26930 ^ _775828) ^ [_1251487, _1251489, _1251491] : [-(_1251487 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26933 ^ _775828 : [(26940 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251487), _1251489)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251487), _1251491))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251489), _1251491)))], (26934 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251489), _1251491)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251487), _1251489)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251487), _1251491))))]]], (13670 ^ _775828) ^ [_1003348, _1003350, _1003352, _1003354, _1003356, _1003358] : [c_Com_Ocom_OCond(_1003348, _1003350, _1003352) = c_Com_Ocom_OCall(_1003354, _1003356, _1003358)], (48028 ^ _775828) ^ [_1735500, _1735502, _1735504] : [c_List_Olist_ONil(_1735500) = hAPP(hAPP(c_List_Oappend(_1735500), _1735502), _1735504), 48031 ^ _775828 : [(48034 ^ _775828) ^ [] : [-(_1735504 = c_List_Olist_ONil(_1735500))], (48032 ^ _775828) ^ [] : [-(_1735502 = c_List_Olist_ONil(_1735500))]]], (43658 ^ _775828) ^ [_1629721, _1629723, _1629725, _1629727, _1629729] : [class_Complete__Lattice_Ocomplete__lattice(_1629721), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629723), _1629725)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1629721), _1629727), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1629723, _1629721), _1629725), _1629729)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629723, _1629721, hAPP(hAPP(c_COMBB(_1629721, tc_fun(_1629721, _1629721), _1629723), c_Lattices_Osemilattice__sup__class_Osup(_1629721)), _1629729)), _1629727), _1629725))], (10330 ^ _775828) ^ [_943657, _943659, _943661] : [class_Rings_Osemiring__1(_943657), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_943657), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943659), _943661)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943657), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_943657), _943659)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_943657), _943661)))], (27954 ^ _775828) ^ [_1275731, _1275733, _1275735, _1275737] : [c_Wellfounded_Owf(_1275731, _1275733), hBOOL(hAPP(hAPP(c_member(tc_prod(_1275731, _1275731)), hAPP(hAPP(c_Product__Type_OPair(_1275731, _1275731), _1275735), _1275737)), _1275733)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1275731, _1275731)), hAPP(hAPP(c_Product__Type_OPair(_1275731, _1275731), _1275737), _1275735)), _1275733))], (45649 ^ _775828) ^ [_1676088, _1676090, _1676092, _1676094] : [hAPP(c_List_Oset(_1676088), _1676090) = c_Map_Odom(_1676088, _1676092, _1676094), -(c_Map_Omap__of(_1676088, _1676092, hAPP(hAPP(c_List_Omap(_1676088, tc_prod(_1676088, _1676092)), hAPP(hAPP(c_COMBS(_1676088, _1676092, tc_prod(_1676088, _1676092)), c_Product__Type_OPair(_1676088, _1676092)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1676092), _1676092, _1676088), c_Option_Othe(_1676092)), _1676094))), _1676090)) = _1676094)], (19348 ^ _775828) ^ [_1108460, _1108462] : [class_Int_Onumber__ring(_1108460), class_Rings_Olinordered__idom(_1108460), 19355 ^ _775828 : [(19362 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108462), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108460), hAPP(c_Int_Onumber__class_Onumber__of(_1108460), _1108462)), c_Groups_Ozero__class_Ozero(_1108460))))], (19356 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108460), hAPP(c_Int_Onumber__class_Onumber__of(_1108460), _1108462)), c_Groups_Ozero__class_Ozero(_1108460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108462), c_Int_OPls)))]]], (30930 ^ _775828) ^ [_1341795, _1341797, _1341799, _1341801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341795), _1341797)), hBOOL(hAPP(hAPP(c_member(_1341795), _1341799), _1341797)), -(hBOOL(hAPP(hAPP(c_member(_1341795), _1341799), _1341801))), -(hAPP(c_Finite__Set_Ocard(_1341795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341795, tc_HOL_Obool)), _1341797), hAPP(hAPP(c_Set_Oinsert(_1341795), _1341799), _1341801))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1341795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341795, tc_HOL_Obool)), _1341797), _1341801))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47407 ^ _775828) ^ [_1721569] : [-(hBOOL(hAPP(c_List_Odistinct(_1721569), c_List_Olist_ONil(_1721569))))], (13734 ^ _775828) ^ [_1004588, _1004590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1004588), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1004588), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004590, _1004588))))], (13240 ^ _775828) ^ [_994950, _994952, _994954, _994956, _994958, _994960] : [-(c_Com_Ocom_OLocal(_994950, _994952, _994954) = c_Com_Ocom_OLocal(_994956, _994958, _994960)), _994950 = _994956, _994952 = _994958, _994954 = _994960], (39824 ^ _775828) ^ [_1538482] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1538482)) = _1538482)], (46931 ^ _775828) ^ [_1709964, _1709966, _1709968] : [46933 ^ _775828 : [(46936 ^ _775828) ^ [] : [hBOOL(hAPP(_1709968, 46932 ^ [_1709964, _1709966, _1709968]))], (46934 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709964), 46932 ^ [_1709964, _1709966, _1709968]), hAPP(c_List_Oset(_1709964), _1709966))))]], 46937 ^ _775828 : [(46938 ^ _775828) ^ [_1710148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710148), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709964)), _1709966))), -(hBOOL(hAPP(_1709968, hAPP(hAPP(c_List_Onth(_1709964), _1709966), _1710148))))]]], (25457 ^ _775828) ^ [_1224841, _1224843] : [-(c_Code__Numeral_Onat__of__aux(_1224841, _1224843) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224841)), _1224843))], (9349 ^ _775828) ^ [_925779, _925781, _925783, _925785] : [class_Rings_Oordered__semiring(_925779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925779), _925781), _925783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925779), c_Groups_Ozero__class_Ozero(_925779)), _925785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925779), _925781), _925785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925779), _925783), _925785))))], (24212 ^ _775828) ^ [_1200015, _1200017, _1200019, _1200021] : [class_Orderings_Olinorder(_1200015), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200015), _1200017), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200015), _1200019), _1200021)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200015), _1200019), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200015), _1200017), _1200021)))], (48659 ^ _775828) ^ [_1751819] : [-(hAPP(c_List_Otl(_1751819), c_List_Olist_ONil(_1751819)) = c_List_Olist_ONil(_1751819))], (42614 ^ _775828) ^ [_1604884, _1604886, _1604888] : [c_Wellfounded_OwfP(_1604884, hAPP(_1604886, 42615 ^ [_1604884, _1604886, _1604888])), 42622 ^ _775828 : [(42625 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1604884, tc_HOL_Obool)), c_Predicate_ODomainP(_1604884, _1604884, hAPP(_1604886, 42620 ^ [_1604884, _1604886, _1604888]))), c_Predicate_ORangeP(_1604884, _1604884, hAPP(_1604886, 42621 ^ [_1604884, _1604886, _1604888]))) = c_Orderings_Obot__class_Obot(tc_fun(_1604884, tc_HOL_Obool))], (42623 ^ _775828) ^ [] : [hAPP(_1604886, 42620 ^ [_1604884, _1604886, _1604888]) = hAPP(_1604886, 42621 ^ [_1604884, _1604886, _1604888])]], -(c_Wellfounded_OwfP(_1604884, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1604888, tc_fun(_1604884, tc_fun(_1604884, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1604888, tc_HOL_Obool))), _1604886)))], (19512 ^ _775828) ^ [_1111137, _1111139] : [class_Int_Onumber__ring(_1111137), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1111137), hAPP(c_Int_Onumber__class_Onumber__of(_1111137), _1111139)), c_Groups_Oone__class_Oone(_1111137)) = hAPP(c_Int_Onumber__class_Onumber__of(_1111137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111139), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (22692 ^ _775828) ^ [_1170763, _1170765, _1170767, _1170769] : [class_Fields_Ofield__inverse__zero(_1170763), -(_1170765 = c_Groups_Ozero__class_Ozero(_1170763)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170763), _1170765), _1170767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170763), _1170765), _1170769)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170763), _1170767), _1170769))], (42694 ^ _775828) ^ [_1606882, _1606884, _1606886, _1606888, _1606890, _1606892, _1606894, _1606896, _1606898, _1606900] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1606882, _1606884), tc_prod(_1606886, _1606888), tc_prod(_1606890, _1606892), c_Product__Type_Omap__pair(_1606882, _1606886, _1606884, _1606888, _1606894, _1606896)), c_Product__Type_Omap__pair(_1606890, _1606882, _1606892, _1606884, _1606898, _1606900)) = c_Product__Type_Omap__pair(_1606890, _1606886, _1606892, _1606888, hAPP(c_Fun_Ocomp(_1606882, _1606886, _1606890, _1606894), _1606898), hAPP(c_Fun_Ocomp(_1606884, _1606888, _1606892, _1606896), _1606900)))], (14243 ^ _775828) ^ [_1013898, _1013900] : [class_Divides_Osemiring__div(_1013898), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1013898), _1013900), c_Groups_Ozero__class_Ozero(_1013898)) = c_Groups_Ozero__class_Ozero(_1013898))], (49327 ^ _775828) ^ [_1766304, _1766306, _1766308, _1766310] : [-(_1766304 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766306)), _1766308)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1766306, hAPP(hAPP(c_List_Olist__update(_1766306, _1766308), _1766304), _1766310)) = hAPP(hAPP(c_List_Olist__update(_1766306, c_List_Obutlast(_1766306, _1766308)), _1766304), _1766310))], (39274 ^ _775828) ^ [_1524311, _1524313, _1524315, _1524317, _1524319, _1524321] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1524311, _1524313, _1524315, _1524317, _1524319), _1524321)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524311), _1524319)))], (14526 ^ _775828) ^ [_1018998, _1019000] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018998, _1019000)), _1019000) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17323 ^ _775828) ^ [_1072315, _1072317, _1072319, _1072321] : [class_Rings_Olinordered__semidom(_1072315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072315), c_Groups_Oone__class_Oone(_1072315)), _1072317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072315), hAPP(hAPP(c_Power_Opower__class_Opower(_1072315), _1072317), _1072319)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072315), _1072317), _1072321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072319), _1072321)))], (33875 ^ _775828) ^ [_1405386, _1405388, _1405390] : [class_Lattices_Olattice(_1405386), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405386), _1405388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405386), _1405388), _1405390)) = _1405388)], (19796 ^ _775828) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (31693 ^ _775828) ^ [_1359905, _1359907, _1359909, _1359911] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1359905, _1359905)), hAPP(hAPP(c_Product__Type_OPair(_1359905, _1359905), _1359907), _1359909)), c_Transitive__Closure_Ortrancl(_1359905, _1359911))), -(_1359907 = _1359909), 31700 ^ _775828 : [(31703 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1359905, _1359905)), hAPP(hAPP(c_Product__Type_OPair(_1359905, _1359905), _1359907), _1359909)), c_Transitive__Closure_Otrancl(_1359905, _1359911))))], (31701 ^ _775828) ^ [] : [_1359907 = _1359909]]], (45040 ^ _775828) ^ [_1662339, _1662341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1662339, tc_HOL_Obool)), _1662341)), 45046 ^ _775828 : [(45049 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1662339), 45045 ^ [_1662339, _1662341]))], (45047 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1662339, tc_HOL_Obool)), 45045 ^ [_1662339, _1662341]), _1662341)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1662339), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662339, tc_HOL_Obool), _1662341))))], (20270 ^ _775828) ^ [_1124083, _1124085] : [class_Int_Onumber__ring(_1124083), class_Int_Oring__char__0(_1124083), 20277 ^ _775828 : [(20284 ^ _775828) ^ [] : [c_Int_Oiszero(_1124083, hAPP(c_Int_Onumber__class_Onumber__of(_1124083), _1124085)), -(c_Int_Oiszero(_1124083, hAPP(c_Int_Onumber__class_Onumber__of(_1124083), c_Int_OBit0(_1124085))))], (20278 ^ _775828) ^ [] : [c_Int_Oiszero(_1124083, hAPP(c_Int_Onumber__class_Onumber__of(_1124083), c_Int_OBit0(_1124085))), -(c_Int_Oiszero(_1124083, hAPP(c_Int_Onumber__class_Onumber__of(_1124083), _1124085)))]]], (18373 ^ _775828) ^ [_1091665, _1091667, _1091669, _1091671] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091665, _1091667), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091669), _1091671))), -(_1091667 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1091665), _1091667) = _1091669)], (4104 ^ _775828) ^ [_838469, _838471, _838473, _838475, _838477, _838479] : [-(c_Relation_OImage(_838479, _838475, _838471) = c_Relation_OImage(_838477, _838473, _838469)), _838479 = _838477, _838475 = _838473, _838471 = _838469], (5268 ^ _775828) ^ [_856359, _856361, _856363, _856365, _856367, _856369] : [-(c_Enum_On__lists(_856369, _856365, _856361) = c_Enum_On__lists(_856367, _856363, _856359)), _856369 = _856367, _856365 = _856363, _856361 = _856359], (35347 ^ _775828) ^ [_1439042] : [-(hAPP(c_Set_OPow(_1439042), c_Orderings_Obot__class_Obot(tc_fun(_1439042, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1439042, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1439042, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1439042, tc_HOL_Obool), tc_HOL_Obool))))], (46568 ^ _775828) ^ [_1700048, _1700050, _1700052] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700048)), hAPP(hAPP(c_List_Olist_OCons(_1700048), _1700050), _1700052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700048)), _1700052)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41020 ^ _775828) ^ [_1566189] : [-(c_Nat_Ofunpow(_1566189) = c_Nat_Ocompow(_1566189, _1566189))], (5719 ^ _775828) ^ [_866989] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _866989)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46674 ^ _775828) ^ [_1703560, _1703562, _1703564] : [-(c_Random_Oselect__weight(_1703560, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1703560)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1703560), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1703562)), _1703564)) = c_Random_Oselect__weight(_1703560, _1703564))], (19970 ^ _775828) ^ [_1118750, _1118752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118750), 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)))), _1118752)), 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)))), _1118750)) = 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), _1118752), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1118750))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40059 ^ _775828) ^ [] : [-(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))], (27767 ^ _775828) ^ [_1270339, _1270341, _1270343, _1270345, _1270347] : [-(hAPP(c_Relation_Oconverse(_1270339, _1270341), hAPP(hAPP(c_Relation_Orel__comp(_1270339, _1270343, _1270341), _1270345), _1270347)) = hAPP(hAPP(c_Relation_Orel__comp(_1270341, _1270343, _1270339), hAPP(c_Relation_Oconverse(_1270343, _1270341), _1270347)), hAPP(c_Relation_Oconverse(_1270339, _1270343), _1270345)))], (2156 ^ _775828) ^ [_807317, _807319] : [_807319 = _807317, -(c_Int_Opred(_807319) = c_Int_Opred(_807317))], (27034 ^ _775828) ^ [_1253507, _1253509] : [class_Orderings_Oorder(_1253507), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1253507, 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)))), _1253509), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1253507, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1253509))], (40836 ^ _775828) ^ [_1561333, _1561335, _1561337, _1561339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561333, _1561333)), _1561335), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561333, _1561333), tc_HOL_Obool), _1561337), _1561339))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561333, _1561333)), _1561335), c_Transitive__Closure_Ortrancl(_1561333, _1561339))))], (38011 ^ _775828) ^ [_1496523, _1496525, _1496527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496523, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496523, _1496523, _1496525), _1496527)), _1496527)), -(hAPP(c_Relation_OImage(_1496523, _1496523, c_Transitive__Closure_Ortrancl(_1496523, _1496525)), _1496527) = _1496527)], (29397 ^ _775828) ^ [_1308971, _1308973, _1308975] : [hBOOL(hAPP(hAPP(c_member(_1308971), _1308973), hAPP(hAPP(c_Set_Oinsert(_1308971), _1308975), c_Orderings_Obot__class_Obot(tc_fun(_1308971, tc_HOL_Obool))))), -(_1308973 = _1308975)], (23608 ^ _775828) ^ [_1189067, _1189069] : [23609 ^ _775828 : [(23612 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189069), _1189067))], (23610 ^ _775828) ^ [] : [_1189067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1189069, _1189067) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189069))], (50124 ^ _775828) ^ [_1782404, _1782406, _1782408, _1782410] : [class_Orderings_Olinorder(_1782404), c_List_Olinorder__class_Osorted(_1782404, _1782406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1782408), _1782410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782410), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782404)), _1782406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1782404), hAPP(hAPP(c_List_Onth(_1782404), _1782406), _1782408)), hAPP(hAPP(c_List_Onth(_1782404), _1782406), _1782410))))], (17081 ^ _775828) ^ [_1067523, _1067525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1067523)), -(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), _1067523), _1067525))))], (33919 ^ _775828) ^ [_1406576, _1406578, _1406580, _1406582] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406576, tc_HOL_Obool)), _1406578), _1406580)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406576, tc_HOL_Obool)), _1406580), _1406582))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406576, tc_HOL_Obool)), _1406582), _1406578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406576, tc_HOL_Obool)), _1406578), _1406580)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406576, tc_HOL_Obool)), _1406580), _1406582))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406576, tc_HOL_Obool)), _1406582), _1406578)))], (49588 ^ _775828) ^ [_1772946] : [class_Orderings_Olinorder(_1772946), -(c_List_Olinorder__class_Osorted(_1772946, c_List_Olist_ONil(_1772946)))], (3476 ^ _775828) ^ [_828527, _828529, _828531, _828533] : [-(c_Com_Ocom_OWhile(_828533, _828529) = c_Com_Ocom_OWhile(_828531, _828527)), _828533 = _828531, _828529 = _828527], (48551 ^ _775828) ^ [_1749675, _1749677, _1749679, _1749681] : [-(hAPP(c_List_Orotate1(_1749677), hAPP(hAPP(c_List_Olist_OCons(_1749677), _1749679), _1749681)) = hAPP(hAPP(c_List_Oappend(_1749677), _1749681), hAPP(hAPP(c_List_Olist_OCons(_1749677), _1749679), c_List_Olist_ONil(_1749677))))], (34583 ^ _775828) ^ [_1420935, _1420937, _1420939] : [class_Lattices_Olattice(_1420935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420935), _1420937)), -(hBOOL(hAPP(hAPP(c_member(_1420935), _1420939), _1420937))), -(_1420937 = c_Orderings_Obot__class_Obot(tc_fun(_1420935, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1420935, hAPP(hAPP(c_Set_Oinsert(_1420935), _1420939), _1420937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420935), _1420939), c_Big__Operators_Olattice__class_OInf__fin(_1420935, _1420937)))], (25387 ^ _775828) ^ [_1223674, _1223676, _1223678, _1223680, _1223682] : [_1223674 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1223676, _1223678, _1223680, _1223682), _1223674) = c_Lazy__Sequence_Oempty(_1223678))], (15900 ^ _775828) ^ [_1044260, _1044262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044260), _1044262)), -(c_Nat__Transfer_Otsub(_1044262, _1044260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044262), _1044260))], (51320 ^ _775828) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (5967 ^ _775828) ^ [_870750, _870752, _870754, _870756, _870758] : [c_Com_Ocom_OAss(_870750, _870752) = c_Com_Ocom_OCall(_870754, _870756, _870758)], (16465 ^ _775828) ^ [_1055946, _1055948] : [class_Int_Onumber__ring(_1055946), -(hAPP(c_Int_Oring__1__class_Oof__int(_1055946), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055948)) = hAPP(c_Int_Onumber__class_Onumber__of(_1055946), _1055948))], (15982 ^ _775828) ^ [_1046345, _1046347, _1046349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046345)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046345), _1046347)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046345), _1046349)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046347), _1046349))], (47221 ^ _775828) ^ [_1717733, _1717735, _1717737, _1717739, _1717741] : [-(hAPP(hAPP(c_List_Otake(_1717733), _1717735), hAPP(hAPP(c_List_Omap(_1717737, _1717733), _1717739), _1717741)) = hAPP(hAPP(c_List_Omap(_1717737, _1717733), _1717739), hAPP(hAPP(c_List_Otake(_1717737), _1717735), _1717741)))], (49387 ^ _775828) ^ [_1767602, _1767604, _1767606] : [49389 ^ _775828 : [(49392 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1767604, 49388 ^ [_1767602, _1767604, _1767606])))], (49390 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767602), 49388 ^ [_1767602, _1767604, _1767606]), hAPP(c_List_Oset(_1767602), _1767606))))]], -(hAPP(c_List_Ofilter(_1767602, _1767604), _1767606) = c_List_Olist_ONil(_1767602))], (42375 ^ _775828) ^ [_1598717] : [class_Orderings_Olinorder(_1598717), -(c_Finite__Set_Ofun__left__comm__idem(_1598717, _1598717, c_Orderings_Oord__class_Omin(_1598717)))], (4252 ^ _775828) ^ [_840801, _840803, _840805, _840807] : [-(c_Finite__Set_Ofold1(_840807, _840803) = c_Finite__Set_Ofold1(_840805, _840801)), _840807 = _840805, _840803 = _840801], (36155 ^ _775828) ^ [_1454800, _1454802, _1454804, _1454806, _1454808] : [class_Orderings_Olinorder(_1454800), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454800, _1454802), _1454804) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454800, _1454806), _1454808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454800), _1454802), _1454804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454800), _1454806), _1454808)), -(_1454802 = _1454806)], (48926 ^ _775828) ^ [_1757459, _1757461, _1757463, _1757465, _1757467] : [-(c_Map_Omap__upds(_1757459, _1757461, _1757463, _1757465, _1757467) = hAPP(c_List_Ofoldl(tc_fun(_1757459, tc_Option_Ooption(_1757461)), tc_prod(_1757459, _1757461), hAPP(hAPP(c_COMBB(tc_fun(_1757459, tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461)))), tc_fun(tc_prod(_1757459, _1757461), tc_fun(_1757459, tc_Option_Ooption(_1757461))), tc_fun(_1757459, tc_Option_Ooption(_1757461))), c_Product__Type_Oprod_Oprod__case(_1757459, _1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461)))), hAPP(hAPP(c_COMBC(tc_fun(_1757459, tc_Option_Ooption(_1757461)), tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757459, tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461))))), hAPP(hAPP(c_COMBB(tc_fun(_1757459, tc_fun(tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461))))), tc_fun(tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757459, tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461))))), tc_fun(_1757459, tc_Option_Ooption(_1757461))), c_COMBC(_1757459, tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461))))), hAPP(hAPP(c_COMBB(tc_fun(_1757459, tc_fun(tc_Option_Ooption(_1757461), tc_fun(_1757459, tc_Option_Ooption(_1757461)))), tc_fun(_1757459, tc_fun(tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461))))), tc_fun(_1757459, tc_Option_Ooption(_1757461))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1757461), tc_fun(_1757459, tc_Option_Ooption(_1757461))), tc_fun(tc_fun(_1757461, tc_Option_Ooption(_1757461)), tc_fun(_1757461, tc_fun(_1757459, tc_Option_Ooption(_1757461)))), _1757459), c_COMBB(tc_Option_Ooption(_1757461), tc_fun(_1757459, tc_Option_Ooption(_1757461)), _1757461))), c_Fun_Ofun__upd(_1757459, tc_Option_Ooption(_1757461))))), c_Option_Ooption_OSome(_1757461))), _1757463), hAPP(hAPP(c_List_Ozip(_1757459, _1757461), _1757465), _1757467)))], (26643 ^ _775828) ^ [_1246800, _1246802, _1246804, _1246806] : [class_Divides_Osemiring__div(_1246800), -(_1246802 = c_Groups_Ozero__class_Ozero(_1246800)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246800), _1246802), _1246804)), 26654 ^ _775828 : [(26661 ^ _775828) ^ [] : [_1246804 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246800), _1246806), _1246802), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246800), _1246804), _1246802) = _1246806)], (26655 ^ _775828) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246800), _1246804), _1246802) = _1246806, -(_1246804 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246800), _1246806), _1246802))]]], (8477 ^ _775828) ^ [_911941] : [8478 ^ _775828 : [(8479 ^ _775828) ^ [_911998] : [hBOOL(hAPP(_911941, _911998))]], 8481 ^ _775828 : [(8484 ^ _775828) ^ [] : [-(hBOOL(hAPP(_911941, hAPP(c_Int_Onat, 8480 ^ [_911941]))))], (8482 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8480 ^ [_911941])))]]], (48431 ^ _775828) ^ [_1746736, _1746738, _1746740, _1746742, _1746744] : [hAPP(hAPP(c_List_Odrop(_1746736), _1746738), _1746740) = hAPP(hAPP(c_List_Olist_OCons(_1746736), _1746742), _1746744), -(hAPP(hAPP(c_List_Onth(_1746736), _1746740), _1746738) = _1746742)], (48078 ^ _775828) ^ [_1736593, _1736595, _1736597, _1736599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736593), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736595)), _1736597))), -(hAPP(hAPP(c_List_Onth(_1736595), hAPP(hAPP(c_List_Oappend(_1736595), _1736597), _1736599)), _1736593) = hAPP(hAPP(c_List_Onth(_1736595), _1736597), _1736593))], (36984 ^ _775828) ^ [_1471882, _1471884, _1471886, _1471888, _1471890] : [class_Fields_Ofield(_1471882), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1471882), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471884, _1471882), _1471886), _1471888)), _1471890) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471884, _1471882), hAPP(hAPP(c_COMBC(_1471884, _1471882, _1471882), hAPP(hAPP(c_COMBB(_1471882, tc_fun(_1471882, _1471882), _1471884), c_Rings_Oinverse__class_Odivide(_1471882)), _1471886)), _1471890)), _1471888))], (3860 ^ _775828) ^ [_834537, _834539, _834541, _834543, _834545, _834547] : [-(c_Smallcheck_Osmall_H(_834547, _834543, _834539) = c_Smallcheck_Osmall_H(_834545, _834541, _834537)), _834547 = _834545, _834543 = _834541, _834539 = _834537], (39527 ^ _775828) ^ [_1530670, _1530672, _1530674, _1530676, _1530678] : [-(hBOOL(hAPP(hAPP(c_member(_1530670), _1530672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530674, tc_fun(_1530670, tc_HOL_Obool)), _1530676), _1530678)))), 39528 ^ _775828 : [(39529 ^ _775828) ^ [_1530752] : [hBOOL(hAPP(hAPP(c_member(_1530674), _1530752), _1530676)), hBOOL(hAPP(hAPP(c_member(_1530670), _1530672), hAPP(_1530678, _1530752)))]]], (582 ^ _775828) ^ [_784669, _784671, _784673, _784675] : [-(c_Wellfounded_OwfP(_784673, _784669)), c_Wellfounded_OwfP(_784675, _784671), _784675 = _784673, _784671 = _784669], (29257 ^ _775828) ^ [_1306362, _1306364] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1306362, _1306364, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1306362), tc_HOL_Obool))))], (1870 ^ _775828) ^ [_802878, _802880, _802882, _802884, _802886, _802888] : [-(c_Option_Ooption_Ooption__size(_802888, _802884, _802880) = c_Option_Ooption_Ooption__size(_802886, _802882, _802878)), _802888 = _802886, _802884 = _802882, _802880 = _802878], (33641 ^ _775828) ^ [_1400270, _1400272] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400270, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1400270, tc_HOL_Obool))), _1400272) = c_Orderings_Obot__class_Obot(tc_fun(_1400270, tc_HOL_Obool)))], (29703 ^ _775828) ^ [_1315268, _1315270, _1315272] : [-(hAPP(hAPP(c_Set_Oinsert(_1315268), _1315270), hAPP(c_Set_OCollect(_1315268), _1315272)) = hAPP(c_Set_OCollect(_1315268), hAPP(hAPP(c_COMBS(_1315268, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1315268), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1315268), c_fNot), hAPP(hAPP(c_COMBC(_1315268, _1315268, tc_HOL_Obool), c_fequal), _1315270)))), _1315272)))], (1834 ^ _775828) ^ [_802268, _802270, _802272, _802274, _802276, _802278] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_802278, _802274, _802270) = c_Hoare__Mirabelle_Otriple_Otriple__size(_802276, _802272, _802268)), _802278 = _802276, _802274 = _802272, _802270 = _802268], (26095 ^ _775828) ^ [_1236552, _1236554] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236552), _1236554)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236554), _1236552))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236554), _1236552)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236552), _1236554)))], (37236 ^ _775828) ^ [_1477874, _1477876, _1477878] : [class_Groups_Ocomm__monoid__add(_1477874), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477874), _1477876), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1477878))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1477874), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477874), _1477876), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1477878))), hAPP(_1477876, _1477878)))], (39620 ^ _775828) ^ [_1532913, _1532915, _1532917, _1532919, _1532921, _1532923] : [-(hAPP(c_Set_Oimage(_1532913, _1532915, _1532917), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532919, tc_fun(_1532913, tc_HOL_Obool)), _1532921), _1532923)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532919, tc_fun(_1532915, tc_HOL_Obool)), _1532921), hAPP(hAPP(c_COMBB(tc_fun(_1532913, tc_HOL_Obool), tc_fun(_1532915, tc_HOL_Obool), _1532919), c_Set_Oimage(_1532913, _1532915, _1532917)), _1532923)))], (44693 ^ _775828) ^ [_1654972, _1654974, _1654976] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1654972, tc_HOL_Obool)), _1654974), _1654976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654972, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654972, tc_HOL_Obool), _1654976)), _1654974)))], (20496 ^ _775828) ^ [] : [-(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))))], (41496 ^ _775828) ^ [_1578797, _1578799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578797, _1578797), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1578797, _1578799)), hAPP(hAPP(c_Product__Type_OSigma(_1578797, _1578797), hAPP(c_Relation_OField(_1578797), _1578799)), hAPP(c_COMBK(tc_fun(_1578797, tc_HOL_Obool), _1578797), hAPP(c_Relation_OField(_1578797), _1578799))))))], (9335 ^ _775828) ^ [_925510, _925512, _925514, _925516] : [class_Rings_Oordered__semiring(_925510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925510), _925512), _925514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925510), c_Groups_Ozero__class_Ozero(_925510)), _925516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925510), _925516), _925512)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925510), _925516), _925514))))], (6494 ^ _775828) ^ [_879118, _879120, _879122, _879124] : [class_Orderings_Oord(_879118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879118), _879120), _879122)), _879122 = _879124, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879118), _879120), _879124)))], (6350 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (36725 ^ _775828) ^ [_1465751] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1465751)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1465751), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1465751)))], (30295 ^ _775828) ^ [_1328430, _1328432, _1328434, _1328436, _1328438, _1328440] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool)), _1328432), _1328434)), c_Wellfounded_Omax__ext(_1328430, _1328436))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool)), _1328438), _1328440)), c_Wellfounded_Omax__ext(_1328430, _1328436))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1328430, tc_HOL_Obool), tc_fun(_1328430, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328430, tc_HOL_Obool)), _1328432), _1328438)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328430, tc_HOL_Obool)), _1328434), _1328440))), c_Wellfounded_Omax__ext(_1328430, _1328436))))], (114 ^ _775828) ^ [_777395, _777397] : [-(class_Rings_Oinverse(_777395)), _777397 = _777395, class_Rings_Oinverse(_777397)], (49915 ^ _775828) ^ [_1778537, _1778539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778537), _1778539)), -(c_List_Oupt(_1778537, _1778539) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1778537), c_List_Oupt(hAPP(c_Nat_OSuc, _1778537), _1778539)))], (36293 ^ _775828) ^ [_1457184, _1457186, _1457188, _1457190, _1457192] : [class_Orderings_Olinorder(_1457184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457184, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457184, _1457186), _1457188)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457184, _1457190), _1457192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457184), _1457188), _1457186))), 36304 ^ _775828 : [(36307 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457184), _1457188), _1457192)))], (36305 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457184), _1457190), _1457186)))]]], (49552 ^ _775828) ^ [_1771765, _1771767, _1771769, _1771771] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1771765, tc_Nat_Onat), _1771765), c_Product__Type_Ofst(_1771765, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1771765, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1771765, tc_Nat_Onat)), _1771767), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1771765, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1771765, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1771765, tc_Nat_Onat), _1771769), _1771771))) = hAPP(hAPP(c_List_Omap(tc_prod(_1771765, tc_Nat_Onat), _1771765), c_Product__Type_Ofst(_1771765, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1771765, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1771765, tc_Nat_Onat)), _1771767), c_Product__Type_Osnd(_1771765, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1771765, tc_Nat_Onat), _1771769), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1771771)))))], (37370 ^ _775828) ^ [_1480731, _1480733, _1480735, _1480737, _1480739] : [class_Groups_Ocomm__monoid__add(_1480731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480733), _1480735)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480733, _1480731), _1480737), hAPP(c_Set_OCollect(_1480733), hAPP(hAPP(c_COMBS(_1480733, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1480733), c_fconj), hAPP(hAPP(c_COMBC(_1480733, tc_fun(_1480733, tc_HOL_Obool), tc_HOL_Obool), c_member(_1480733)), _1480735))), hAPP(hAPP(c_COMBC(_1480733, tc_fun(_1480733, tc_HOL_Obool), tc_HOL_Obool), c_member(_1480733)), _1480739)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480733, _1480731), hAPP(hAPP(c_COMBC(_1480733, _1480731, _1480731), hAPP(hAPP(c_COMBS(_1480733, _1480731, tc_fun(_1480731, _1480731)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1480731, tc_fun(_1480731, _1480731)), _1480733), c_If(_1480731)), hAPP(hAPP(c_COMBC(_1480733, tc_fun(_1480733, tc_HOL_Obool), tc_HOL_Obool), c_member(_1480733)), _1480739))), _1480737)), c_Groups_Ozero__class_Ozero(_1480731))), _1480735))], (48653 ^ _775828) ^ [_1751662, _1751664, _1751666] : [-(hAPP(hAPP(c_List_Odrop(_1751662), hAPP(c_Nat_OSuc, _1751664)), _1751666) = hAPP(hAPP(c_List_Odrop(_1751662), _1751664), hAPP(c_List_Otl(_1751662), _1751666)))], (44842 ^ _775828) ^ [_1658020, _1658022, _1658024, _1658026] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1658020, tc_HOL_Obool), hAPP(c_Set_Oimage(_1658022, tc_fun(_1658020, tc_HOL_Obool), _1658024), _1658026)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658022, tc_fun(_1658020, tc_HOL_Obool)), _1658026), _1658024))], (11701 ^ _775828) ^ [_968068, _968070] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968068)), _968070) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968068), _968070)))], (37442 ^ _775828) ^ [_1482912, _1482914, _1482916, _1482918] : [hBOOL(hAPP(hAPP(c_member(_1482912), _1482914), _1482916)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482912, tc_Nat_Onat), _1482918), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482912, tc_HOL_Obool)), _1482916), hAPP(hAPP(c_Set_Oinsert(_1482912), _1482914), c_Orderings_Obot__class_Obot(tc_fun(_1482912, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482912, tc_Nat_Onat), _1482918), _1482916)), hAPP(_1482918, _1482914)))], (41218 ^ _775828) ^ [_1571156, _1571158, _1571160, _1571162, _1571164, _1571166] : [-(hAPP(c_Set_Oimage(_1571156, tc_prod(_1571158, _1571160), hAPP(hAPP(c_COMBS(_1571156, _1571160, tc_prod(_1571158, _1571160)), hAPP(hAPP(c_COMBB(_1571158, tc_fun(_1571160, tc_prod(_1571158, _1571160)), _1571156), c_Product__Type_OPair(_1571158, _1571160)), _1571162)), _1571164)), _1571166) = hAPP(hAPP(c_Product__Type_OSigma(_1571158, _1571160), hAPP(c_Set_Oimage(_1571156, _1571158, _1571162), _1571166)), hAPP(hAPP(c_COMBB(tc_fun(_1571156, tc_HOL_Obool), tc_fun(_1571160, tc_HOL_Obool), _1571158), c_Set_Oimage(_1571156, _1571160, _1571164)), hAPP(hAPP(c_COMBC(_1571158, tc_fun(_1571156, tc_HOL_Obool), tc_fun(_1571156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571156, tc_HOL_Obool), tc_fun(tc_fun(_1571156, tc_HOL_Obool), tc_fun(_1571156, tc_HOL_Obool)), _1571158), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1571156, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1571158, tc_HOL_Obool), tc_fun(_1571156, tc_HOL_Obool), _1571158), c_Set_Ovimage(_1571156, _1571158, _1571162)), hAPP(hAPP(c_COMBC(_1571158, tc_fun(_1571158, tc_HOL_Obool), tc_fun(_1571158, tc_HOL_Obool)), c_Set_Oinsert(_1571158)), c_Orderings_Obot__class_Obot(tc_fun(_1571158, tc_HOL_Obool)))))), _1571166))))], (42141 ^ _775828) ^ [_1594027, _1594029, _1594031] : [-(c_Relation_Orefl__on(_1594027, _1594029, _1594031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1594027, _1594027), tc_HOL_Obool)), _1594031), hAPP(hAPP(c_Product__Type_OSigma(_1594027, _1594027), _1594029), hAPP(c_COMBK(tc_fun(_1594027, tc_HOL_Obool), _1594027), _1594029)))), 42147 ^ _775828 : [(42150 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594027, _1594027)), hAPP(hAPP(c_Product__Type_OPair(_1594027, _1594027), 42146 ^ [_1594027, _1594029, _1594031]), 42146 ^ [_1594027, _1594029, _1594031])), _1594031))], (42148 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1594027), 42146 ^ [_1594027, _1594029, _1594031]), _1594029)))]]], (23418 ^ _775828) ^ [_1184558, _1184560, _1184562] : [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), _1184558), _1184560))), -(hBOOL(hAPP(hAPP(_1184562, _1184558), _1184560))), 23425 ^ _775828 : [(23428 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1184562, 23423 ^ [_1184558, _1184560, _1184562]), 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)))), 23424 ^ [_1184558, _1184560, _1184562])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23423 ^ [_1184558, _1184560, _1184562]), 23424 ^ [_1184558, _1184560, _1184562]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23424 ^ [_1184558, _1184560, _1184562]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23438 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1184562, 23423 ^ [_1184558, _1184560, _1184562]), 23424 ^ [_1184558, _1184560, _1184562]))], (23426 ^ _775828) ^ [] : [-(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), 23423 ^ [_1184558, _1184560, _1184562]), 23424 ^ [_1184558, _1184560, _1184562]))))]]], (17501 ^ _775828) ^ [_1075466, _1075468] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075466)), _1075468) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1075466), _1075468)))], (10508 ^ _775828) ^ [_946864, _946866] : [class_Groups_Olinordered__ab__group__add(_946864), 10511 ^ _775828 : [(10518 ^ _775828) ^ [] : [_946866 = c_Groups_Ozero__class_Ozero(_946864), -(c_Groups_Ozero__class_Ozero(_946864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946864), _946866), _946866))], (10512 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_946864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946864), _946866), _946866), -(_946866 = c_Groups_Ozero__class_Ozero(_946864))]]], (17581 ^ _775828) ^ [_1076825, _1076827] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076825) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076827), 17584 ^ _775828 : [(17591 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076825)))), 17594 ^ _775828 : [(17601 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076827)))), -(_1076825 = _1076827)], (17595 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076827))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076825) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17585 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076827)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10013 ^ _775828) ^ [_937599, _937601, _937603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937599, tc_HOL_Obool)), _937601), _937603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937599, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937599, tc_HOL_Obool)), _937603)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937599, tc_HOL_Obool)), _937601))))], (25010 ^ _775828) ^ [_1216598, _1216600, _1216602, _1216604, _1216606] : [-(hBOOL(hAPP(hAPP(c_member(_1216598), _1216600), hAPP(c_Set_Oimage(_1216602, _1216598, _1216604), _1216606)))), 25011 ^ _775828 : [(25012 ^ _775828) ^ [_1216668] : [hBOOL(hAPP(hAPP(c_member(_1216602), _1216668), _1216606)), _1216600 = hAPP(_1216604, _1216668)]]], (28776 ^ _775828) ^ [_1293607, _1293609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293607, _1293607)), _1293609), c_Relation_OId(_1293607))), -(_1293609 = hAPP(hAPP(c_Product__Type_OPair(_1293607, _1293607), 28779 ^ [_1293607, _1293609]), 28779 ^ [_1293607, _1293609]))], (50377 ^ _775828) ^ [_1788486, _1788488] : [hBOOL(hAPP(c_List_Odistinct(_1788486), _1788488)), -(hBOOL(hAPP(c_List_Odistinct(_1788486), hAPP(c_List_Orev(_1788486), _1788488))))], (12536 ^ _775828) ^ [] : [-(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))], (6828 ^ _775828) ^ [_883981, _883983] : [-(hAPP(c_Option_Othe(_883981), hAPP(c_Option_Ooption_OSome(_883981), _883983)) = _883983)], (40945 ^ _775828) ^ [_1564008, _1564010, _1564012, _1564014, _1564016, _1564018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564008, _1564008)), hAPP(hAPP(c_Product__Type_OPair(_1564008, _1564008), _1564010), _1564012)), _1564014)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564008, _1564008)), hAPP(hAPP(c_Product__Type_OPair(_1564008, _1564008), _1564012), _1564016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1564008, _1564008), tc_HOL_Obool), _1564018), _1564014))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564008, _1564008)), hAPP(hAPP(c_Product__Type_OPair(_1564008, _1564008), _1564010), _1564016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1564008, _1564008), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1564018)), _1564014))))], (51254 ^ _775828) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (33419 ^ _775828) ^ [_1395692, _1395694, _1395696] : [class_Orderings_Olinorder(_1395692), hAPP(_1395694, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1395692), 33424 ^ [_1395692, _1395694, _1395696]), 33425 ^ [_1395692, _1395694, _1395696])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1395692), hAPP(_1395694, 33424 ^ [_1395692, _1395694, _1395696])), hAPP(_1395694, 33425 ^ [_1395692, _1395694, _1395696])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395692), _1395696)), -(_1395696 = c_Orderings_Obot__class_Obot(tc_fun(_1395692, tc_HOL_Obool))), -(hAPP(_1395694, c_Big__Operators_Olattice_OSup__fin(_1395692, c_Orderings_Oord__class_Omax(_1395692), _1395696)) = c_Big__Operators_Olattice_OSup__fin(_1395692, c_Orderings_Oord__class_Omax(_1395692), hAPP(c_Set_Oimage(_1395692, _1395692, _1395694), _1395696)))], (5945 ^ _775828) ^ [_870437, _870439] : [-(_870437 = _870439), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870437), _870439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870439), _870437)))], (41484 ^ _775828) ^ [_1578562, _1578564, _1578566, _1578568] : [_1578562 = c_Orderings_Obot__class_Obot(tc_fun(_1578564, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1578564, _1578566), _1578566, c_Product__Type_Osnd(_1578564, _1578566)), hAPP(hAPP(c_Product__Type_OSigma(_1578564, _1578566), _1578562), hAPP(c_COMBK(tc_fun(_1578566, tc_HOL_Obool), _1578564), _1578568))) = c_Orderings_Obot__class_Obot(tc_fun(_1578566, tc_HOL_Obool)))], (38894 ^ _775828) ^ [_1516325, _1516327, _1516329, _1516331, _1516333, _1516335] : [c_Fun_Oinj__on(_1516325, _1516327, _1516329, _1516331), -(_1516333 = _1516335), hBOOL(hAPP(hAPP(c_member(_1516325), _1516333), _1516331)), hBOOL(hAPP(hAPP(c_member(_1516325), _1516335), _1516331)), hAPP(_1516329, _1516333) = hAPP(_1516329, _1516335)], (1130 ^ _775828) ^ [_792571, _792573] : [-(class_Rings_Ocomm__ring(_792571)), _792573 = _792571, class_Rings_Ocomm__ring(_792573)], (41320 ^ _775828) ^ [_1573860, _1573862, _1573864, _1573866, _1573868] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1573860, _1573862), _1573864), hAPP(hAPP(c_COMBS(_1573860, tc_fun(_1573862, tc_HOL_Obool), tc_fun(_1573862, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573862, tc_HOL_Obool), tc_fun(tc_fun(_1573862, tc_HOL_Obool), tc_fun(_1573862, tc_HOL_Obool)), _1573860), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1573862, tc_HOL_Obool))), _1573866)), _1573868)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573860, _1573862), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1573860, _1573862), _1573864), _1573866)), hAPP(hAPP(c_Product__Type_OSigma(_1573860, _1573862), _1573864), _1573868)))], (14409 ^ _775828) ^ [_1016985, _1016987, _1016989, _1016991, _1016993] : [c_Com_Ocom_OWhile(_1016985, _1016987) = c_Com_Ocom_OCond(_1016989, _1016991, _1016993)], (23446 ^ _775828) ^ [_1185223, _1185225, _1185227, _1185229, _1185231, _1185233] : [_1185223 = _1185225, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185227, _1185229, _1185231), _1185233), _1185223) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185227, _1185229, _1185231), _1185233), _1185225))], (41368 ^ _775828) ^ [_1575531, _1575533, _1575535, _1575537, _1575539] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575531, _1575533), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1575531, tc_HOL_Obool)), _1575535), _1575537)), _1575539) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575531, _1575533), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575531, _1575533), _1575535), _1575539)), hAPP(hAPP(c_Product__Type_OSigma(_1575531, _1575533), _1575537), _1575539)))], (5985 ^ _775828) ^ [_871026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _871026)), _871026 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28257 ^ _775828) ^ [_1282521, _1282523, _1282525] : [class_Lattices_Osemilattice__sup(_1282521), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282521), _1282523), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282521), _1282523), _1282525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282521), _1282523), _1282525))], (7961 ^ _775828) ^ [_903298, _903300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _903298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _903300)), -(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), _903300), _903298))))], (16601 ^ _775828) ^ [_1058229, _1058231] : [class_Groups_Oordered__ab__group__add__abs(_1058229), -(hAPP(c_Groups_Oabs__class_Oabs(_1058229), hAPP(c_Groups_Ouminus__class_Ouminus(_1058229), _1058231)) = hAPP(c_Groups_Oabs__class_Oabs(_1058229), _1058231))], (2574 ^ _775828) ^ [_813838, _813840, _813842, _813844, _813846, _813848, _813850, _813852, _813854, _813856] : [-(c_Nitpick_Opair__box_Opair__box__rec(_813856, _813852, _813848, _813844, _813840) = c_Nitpick_Opair__box_Opair__box__rec(_813854, _813850, _813846, _813842, _813838)), _813856 = _813854, _813852 = _813850, _813848 = _813846, _813844 = _813842, _813840 = _813838], (10 ^ _775828) ^ [_775951, _775953, _775955] : [-(_775955 = _775951), _775955 = _775953, _775953 = _775951], (47978 ^ _775828) ^ [_1734608, _1734610, _1734612] : [_1734612 = c_List_Olist_ONil(_1734608), -(hAPP(hAPP(c_List_Oappend(_1734608), _1734610), _1734612) = _1734610)], (15706 ^ _775828) ^ [_1040555, _1040557] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040555), _1040557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1040555)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1040557)))], (4328 ^ _775828) ^ [_841929, _841931, _841933, _841935, _841937, _841939] : [-(c_Big__Operators_Olattice_OInf__fin(_841939, _841935, _841931) = c_Big__Operators_Olattice_OInf__fin(_841937, _841933, _841929)), _841939 = _841937, _841935 = _841933, _841931 = _841929], (31049 ^ _775828) ^ [_1344898] : [-(c_Wellfounded_Owf(tc_fun(_1344898, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1344898)))], (14227 ^ _775828) ^ [_1013577, _1013579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013577), _1013579)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013577, _1013579) = _1013577)], (5475 ^ _775828) ^ [_862345, _862347, _862349, _862351, _862353, _862355, _862357] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862345), _862347), _862349), _862351) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862345), _862353), _862355), _862357), 5478 ^ _775828 : [(5483 ^ _775828) ^ [] : [-(_862351 = _862357)], (5481 ^ _775828) ^ [] : [-(_862349 = _862355)], (5479 ^ _775828) ^ [] : [-(_862347 = _862353)]]], (24958 ^ _775828) ^ [_1215402, _1215404, _1215406, _1215408, _1215410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215402, tc_HOL_Obool)), _1215404), hAPP(c_Set_Oimage(_1215406, _1215402, _1215408), _1215410))), 24962 ^ _775828 : [(24965 ^ _775828) ^ [] : [-(_1215404 = hAPP(c_Set_Oimage(_1215406, _1215402, _1215408), 24961 ^ [_1215402, _1215404, _1215406, _1215408, _1215410]))], (24963 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215406, tc_HOL_Obool)), 24961 ^ [_1215402, _1215404, _1215406, _1215408, _1215410]), _1215410)))]]], (47547 ^ _775828) ^ [_1724298, _1724300, _1724302] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1724298))), -(c_List_Osublist(_1724300, hAPP(hAPP(c_List_Olist_OCons(_1724300), _1724302), c_List_Olist_ONil(_1724300)), _1724298) = c_List_Olist_ONil(_1724300))], (41180 ^ _775828) ^ [_1569987, _1569989, _1569991, _1569993, _1569995] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1569987, _1569989, hAPP(hAPP(c_Set_Oinsert(_1569987), _1569991), _1569993)), _1569995)), 41185 ^ _775828 : [(41190 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1569987), 41183 ^ [_1569987, _1569989, _1569991, _1569993, _1569995]), 41184 ^ [_1569987, _1569989, _1569991, _1569993, _1569995]))], (41188 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1569987, _1569987, _1569989, 41183 ^ [_1569987, _1569989, _1569991, _1569993, _1569995], 41184 ^ [_1569987, _1569989, _1569991, _1569993, _1569995]), _1569995)))], (41186 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1569987), _1569991), _1569993) = hAPP(hAPP(c_Set_Oinsert(_1569987), 41183 ^ [_1569987, _1569989, _1569991, _1569993, _1569995]), 41184 ^ [_1569987, _1569989, _1569991, _1569993, _1569995]))]]], (45927 ^ _775828) ^ [_1682715, _1682717] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1682715, _1682717)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1682715, _1682717))], (19518 ^ _775828) ^ [_1111264] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1111264)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1111264))))], (42675 ^ _775828) ^ [_1606399, _1606401, _1606403, _1606405] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1606399, tc_Nat_Onat), _1606401), _1606403) = hAPP(c_Nat_OSuc, _1606405), 42679 ^ _775828 : [(42682 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1606401, 42678 ^ [_1606399, _1606401, _1606403, _1606405]))))], (42680 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606399), 42678 ^ [_1606399, _1606401, _1606403, _1606405]), _1606403)))]]], (15388 ^ _775828) ^ [_1034436, _1034438, _1034440] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034436), _1034438)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034440), _1034438)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034436), _1034440))], (15514 ^ _775828) ^ [_1036807, _1036809, _1036811] : [hBOOL(hAPP(_1036807, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036809), _1036811)))), 15517 ^ _775828 : [(15524 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036809), _1036811)), -(hBOOL(hAPP(_1036807, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15518 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036811), _1036809)), -(hBOOL(hAPP(_1036807, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1036809)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1036811)))))]]], (30477 ^ _775828) ^ [_1332796, _1332798, _1332800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332796), _1332798)), 30480 ^ _775828 : [(30487 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332796), _1332800)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332796, tc_HOL_Obool)), _1332800), _1332798))))], (30481 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332796, tc_HOL_Obool)), _1332800), _1332798))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332796), _1332800)))]]], (38624 ^ _775828) ^ [_1510530, _1510532, _1510534, _1510536, _1510538] : [c_Equiv__Relations_Oequiv(_1510530, _1510532, _1510534), hBOOL(hAPP(hAPP(c_member(_1510530), _1510536), _1510532)), hBOOL(hAPP(hAPP(c_member(_1510530), _1510538), _1510532)), 38635 ^ _775828 : [(38642 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510530, _1510530)), hAPP(hAPP(c_Product__Type_OPair(_1510530, _1510530), _1510536), _1510538)), _1510534)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510530), hAPP(hAPP(c_Set_Oinsert(_1510530), _1510536), c_Orderings_Obot__class_Obot(tc_fun(_1510530, tc_HOL_Obool)))), _1510534) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510530), hAPP(hAPP(c_Set_Oinsert(_1510530), _1510538), c_Orderings_Obot__class_Obot(tc_fun(_1510530, tc_HOL_Obool)))), _1510534))], (38636 ^ _775828) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510530), hAPP(hAPP(c_Set_Oinsert(_1510530), _1510536), c_Orderings_Obot__class_Obot(tc_fun(_1510530, tc_HOL_Obool)))), _1510534) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510530), hAPP(hAPP(c_Set_Oinsert(_1510530), _1510538), c_Orderings_Obot__class_Obot(tc_fun(_1510530, tc_HOL_Obool)))), _1510534), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510530, _1510530)), hAPP(hAPP(c_Product__Type_OPair(_1510530, _1510530), _1510536), _1510538)), _1510534)))]]], (10142 ^ _775828) ^ [_940033, _940035, _940037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940033), _940035)), _940037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940033), _940037)))], (40519 ^ _775828) ^ [_1553217] : [-(c_Fun_Oinj__on(_1553217, tc_fun(_1553217, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1553217, tc_fun(_1553217, tc_HOL_Obool), tc_fun(_1553217, tc_HOL_Obool)), c_Set_Oinsert(_1553217)), c_Orderings_Obot__class_Obot(tc_fun(_1553217, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1553217, tc_HOL_Obool))))], (28114 ^ _775828) ^ [] : [-(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))))], (26974 ^ _775828) ^ [_1252378, _1252380] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252378)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252380))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252378), _1252380)))], (17669 ^ _775828) ^ [_1078344, _1078346] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078344)))), 17672 ^ _775828 : [(17679 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078346)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078346)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078346))))], (17673 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078346))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078346)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078344))]]], (32669 ^ _775828) ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618] : [c_Nitpick_Ofold__graph_H(_1379606, _1379608, _1379610, _1379612, _1379614, hAPP(hAPP(_1379610, _1379616), _1379618)), 32674 ^ _775828 : [(32677 ^ _775828) ^ [] : [-(hAPP(hAPP(_1379610, _1379616), _1379618) = _1379612)], (32675 ^ _775828) ^ [] : [-(_1379614 = c_Orderings_Obot__class_Obot(tc_fun(_1379606, tc_HOL_Obool)))]], 32680 ^ _775828 : [(32685 ^ _775828) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1379606, _1379608, _1379610, _1379612, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379606, tc_HOL_Obool)), _1379614), hAPP(hAPP(c_Set_Oinsert(_1379606), 32678 ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618]), c_Orderings_Obot__class_Obot(tc_fun(_1379606, tc_HOL_Obool)))), 32679 ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618]))], (32683 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379606), 32678 ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618]), _1379614)))], (32681 ^ _775828) ^ [] : [-(hAPP(hAPP(_1379610, _1379616), _1379618) = hAPP(hAPP(_1379610, 32678 ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618]), 32679 ^ [_1379606, _1379608, _1379610, _1379612, _1379614, _1379616, _1379618]))]]], (24515 ^ _775828) ^ [_1206624, _1206626] : [c_Nat__Transfer_Ois__nat(_1206624), c_Nat__Transfer_Ois__nat(_1206626), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206624), _1206626)))], (4510 ^ _775828) ^ [_844664, _844666, _844668, _844670, _844672, _844674, _844676, _844678] : [-(c_Option_Ooption_Ooption__case(_844678, _844674, _844670, _844666) = c_Option_Ooption_Ooption__case(_844676, _844672, _844668, _844664)), _844678 = _844676, _844674 = _844672, _844670 = _844668, _844666 = _844664], (38236 ^ _775828) ^ [_1502088] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1502088)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1502088)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1502088)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (7515 ^ _775828) ^ [_895766, _895768] : [class_Groups_Ogroup__add(_895766), 7518 ^ _775828 : [(7525 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_895766) = _895768, -(c_Groups_Ozero__class_Ozero(_895766) = hAPP(c_Groups_Ouminus__class_Ouminus(_895766), _895768))], (7519 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_895766) = hAPP(c_Groups_Ouminus__class_Ouminus(_895766), _895768), -(c_Groups_Ozero__class_Ozero(_895766) = _895768)]]], (19186 ^ _775828) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (18629 ^ _775828) ^ [_1096001, _1096003] : [-(_1096001 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1096003, _1096001), c_Divides_Odivmod__int(_1096003, _1096001))))], (21654 ^ _775828) ^ [_1150870, _1150872] : [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(_1150872))), 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), _1150870)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150870)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150872))))], (24843 ^ _775828) ^ [_1213243, _1213245, _1213247] : [-(c_Nitpick_Oof__frac(_1213245, _1213243, _1213247) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213243), hAPP(c_Int_Oring__1__class_Oof__int(_1213243), hAPP(c_Nitpick_Onum(_1213245), _1213247))), hAPP(c_Int_Oring__1__class_Oof__int(_1213243), hAPP(c_Nitpick_Odenom(_1213245), _1213247)))), class_Rings_Oinverse(_1213243), class_Rings_Oring__1(_1213243)], (46263 ^ _775828) ^ [_1690631, _1690633] : [-(c_List_Olenlex(_1690631, _1690633) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690631), tc_List_Olist(_1690631), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1690631), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), tc_List_Olist(_1690631)), c_COMBS(tc_List_Olist(_1690631), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1690631)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1690631)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690631), tc_fun(tc_List_Olist(_1690631), tc_Nat_Onat), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1690631), tc_Nat_Onat), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), tc_List_Olist(_1690631)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1690631))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1690631)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1690631))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1690631)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1690631), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), tc_List_Olist(_1690631)), c_COMBS(tc_List_Olist(_1690631), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1690631)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1690631)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690631), tc_fun(tc_List_Olist(_1690631), tc_Nat_Onat), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1690631), tc_Nat_Onat), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), tc_List_Olist(_1690631)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1690631))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1690631)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1690631))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1690631)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690631), tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690631), tc_HOL_Obool)), tc_List_Olist(_1690631)), c_COMBC(tc_List_Olist(_1690631), tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690631), tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631))), tc_fun(tc_List_Olist(_1690631), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1690631)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1690631)), c_member(tc_prod(tc_List_Olist(_1690631), tc_List_Olist(_1690631))))), c_Product__Type_OPair(tc_List_Olist(_1690631), tc_List_Olist(_1690631))))), c_List_Olex(_1690631, _1690633)))))))], (14407 ^ _775828) ^ [_1016926, _1016928, _1016930, _1016932, _1016934] : [c_Com_Ocom_OCond(_1016926, _1016928, _1016930) = c_Com_Ocom_OWhile(_1016932, _1016934)], (30337 ^ _775828) ^ [_1330020, _1330022, _1330024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330020), _1330022)), hBOOL(hAPP(hAPP(c_member(_1330020), _1330024), _1330022)), -(hAPP(c_Finite__Set_Ocard(_1330020), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330020, tc_HOL_Obool)), _1330022), hAPP(hAPP(c_Set_Oinsert(_1330020), _1330024), c_Orderings_Obot__class_Obot(tc_fun(_1330020, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330020), _1330022)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8154 ^ _775828) ^ [_906936, _906938] : [class_Orderings_Opreorder(_906936), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906936), _906938), _906938)))], (27555 ^ _775828) ^ [_1265512, _1265514, _1265516, _1265518] : [hBOOL(hAPP(hAPP(_1265516, _1265514), _1265518)), -(hBOOL(hAPP(hAPP(c_member(_1265512), _1265514), c_SetInterval_Oord_OatMost(_1265512, _1265516, _1265518))))], (22654 ^ _775828) ^ [_1170045, _1170047, _1170049, _1170051] : [class_Fields_Olinordered__field(_1170045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170045), _1170047), _1170049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170045), _1170051), c_Groups_Ozero__class_Ozero(_1170045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170045), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170045), _1170049), _1170051)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170045), _1170047), _1170051))))], (272 ^ _775828) ^ [_779772, _779774, _779776, _779778] : [-(c_Nitpick_Owf_H(_779776, _779772)), c_Nitpick_Owf_H(_779778, _779774), _779778 = _779776, _779774 = _779772], (39409 ^ _775828) ^ [_1527259, _1527261, _1527263, _1527265] : [-(hAPP(c_Set_Oimage(_1527259, _1527261, _1527263), _1527265) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527259, tc_fun(_1527261, tc_HOL_Obool)), _1527265), hAPP(hAPP(c_COMBC(_1527259, tc_fun(_1527261, tc_HOL_Obool), tc_fun(_1527261, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1527261, tc_fun(tc_fun(_1527261, tc_HOL_Obool), tc_fun(_1527261, tc_HOL_Obool)), _1527259), c_Set_Oinsert(_1527261)), _1527263)), c_Orderings_Obot__class_Obot(tc_fun(_1527261, tc_HOL_Obool)))))], (10894 ^ _775828) ^ [_954189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954189), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_954189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9151 ^ _775828) ^ [_922154, _922156] : [class_Rings_Olinordered__idom(_922154), 9154 ^ _775828 : [(9161 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922156), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922154), hAPP(c_Int_Oring__1__class_Oof__int(_922154), _922156)), c_Groups_Ozero__class_Ozero(_922154))))], (9155 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922154), hAPP(c_Int_Oring__1__class_Oof__int(_922154), _922156)), c_Groups_Ozero__class_Ozero(_922154))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922156), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5523 ^ _775828) ^ [_863247, _863249, _863251, _863253] : [-(c_Hoare__Mirabelle_Otriple__valid(_863247, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_863247), _863249), hAPP(c_Com_Ocom_OBODY, _863251)), _863253)))], (47966 ^ _775828) ^ [_1734394, _1734396, _1734398] : [_1734396 = c_List_Olist_ONil(_1734394), -(hAPP(hAPP(c_List_Oappend(_1734394), _1734396), _1734398) = _1734398)], (142 ^ _775828) ^ [_777789, _777791, _777793, _777795, _777797, _777799] : [-(c_Nitpick_Oless__eq__frac(_777797, _777793, _777789)), c_Nitpick_Oless__eq__frac(_777799, _777795, _777791), _777799 = _777797, _777795 = _777793, _777791 = _777789], (24679 ^ _775828) ^ [_1209438, _1209440] : [-(c_Nitpick_Onumber__of__frac(_1209438, _1209440) = c_Nitpick_OAbs__Frac(_1209438, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1209440), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19168 ^ _775828) ^ [_1105673, _1105675] : [class_Int_Onumber__ring(_1105673), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105673), _1105675), hAPP(c_Int_Onumber__class_Onumber__of(_1105673), c_Int_OPls)) = _1105675)], (3940 ^ _775828) ^ [_835847, _835849, _835851, _835853] : [-(c_Relation_Oinv__image(_835853, _835849) = c_Relation_Oinv__image(_835851, _835847)), _835853 = _835851, _835849 = _835847], (10892 ^ _775828) ^ [_954152] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954152)))], (19814 ^ _775828) ^ [] : [-(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)))], (11156 ^ _775828) ^ [_958633, _958635, _958637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958633, tc_HOL_Obool)), _958635), _958637))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958633, tc_HOL_Obool)), _958635), _958637)), -(_958635 = _958637)], (34951 ^ _775828) ^ [_1428816, _1428818, _1428820] : [class_Lattices_Odistrib__lattice(_1428816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428816), _1428818)), -(_1428818 = c_Orderings_Obot__class_Obot(tc_fun(_1428816, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428816), _1428820), c_Big__Operators_Olattice__class_OSup__fin(_1428816, _1428818)) = c_Big__Operators_Olattice__class_OSup__fin(_1428816, hAPP(c_Set_OCollect(_1428816), hAPP(hAPP(c_COMBB(tc_fun(_1428816, tc_HOL_Obool), tc_HOL_Obool, _1428816), c_HOL_OEx(_1428816)), hAPP(hAPP(c_COMBC(_1428816, tc_fun(_1428816, tc_HOL_Obool), tc_fun(_1428816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428816, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1428816, tc_HOL_Obool), tc_fun(_1428816, tc_HOL_Obool)), _1428816), c_COMBS(_1428816, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428816, tc_HOL_Obool), tc_fun(_1428816, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1428816), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1428816), c_fconj)), hAPP(hAPP(c_COMBC(_1428816, tc_fun(_1428816, _1428816), tc_fun(_1428816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428816, tc_HOL_Obool), tc_fun(tc_fun(_1428816, _1428816), tc_fun(_1428816, tc_HOL_Obool)), _1428816), c_COMBB(_1428816, tc_HOL_Obool, _1428816)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428816), _1428820))))), hAPP(hAPP(c_COMBC(_1428816, tc_fun(_1428816, tc_HOL_Obool), tc_HOL_Obool), c_member(_1428816)), _1428818))))))], (19934 ^ _775828) ^ [_1118018, _1118020] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118018))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118020)) = 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)))), _1118018), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118020)))], (8607 ^ _775828) ^ [_913870, _913872, _913874] : [hBOOL(hAPP(hAPP(c_member(_913870), _913872), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_913870, tc_HOL_Obool)), _913874))), hBOOL(hAPP(hAPP(c_member(_913870), _913872), _913874))], (39682 ^ _775828) ^ [_1535096, _1535098, _1535100, _1535102, _1535104] : [hBOOL(hAPP(hAPP(c_member(_1535096), _1535098), _1535100)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535102, tc_HOL_Obool)), hAPP(_1535104, _1535098)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535096, tc_fun(_1535102, tc_HOL_Obool)), _1535100), _1535104)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535096, tc_fun(_1535102, tc_HOL_Obool)), _1535100), _1535104))], (42073 ^ _775828) ^ [_1592188, _1592190, _1592192] : [-(hAPP(c_Product__Type_Omap__pair(_1592188, _1592188, _1592190, _1592190, c_COMBI(_1592188), c_COMBI(_1592190)), _1592192) = _1592192)], (16827 ^ _775828) ^ [_1062409, _1062411, _1062413, _1062415, _1062417] : [class_Rings_Olinordered__idom(_1062409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062409), hAPP(c_Groups_Oabs__class_Oabs(_1062409), _1062411)), _1062413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062409), hAPP(c_Groups_Oabs__class_Oabs(_1062409), _1062415)), _1062417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062409), hAPP(c_Groups_Oabs__class_Oabs(_1062409), _1062411)), hAPP(c_Groups_Oabs__class_Oabs(_1062409), _1062415))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062409), _1062413), _1062417))))], (7989 ^ _775828) ^ [_903846, _903848, _903850, _903852] : [class_Rings_Ocomm__semiring__1(_903846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903846), _903848), _903850)), _903852) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903846), _903848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903846), _903850), _903852)))], (1610 ^ _775828) ^ [_798571, _798573] : [-(class_Orderings_Opreorder(_798571)), _798573 = _798571, class_Orderings_Opreorder(_798573)], (42784 ^ _775828) ^ [_1608929, _1608931, _1608933, _1608935, _1608937, _1608939, _1608941] : [-(hAPP(c_Fun_Ocomp(_1608929, _1608931, _1608933, _1608935), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1608933, _1608929), _1608937), _1608939), _1608941)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1608933, _1608931), hAPP(c_Fun_Ocomp(_1608929, _1608931, _1608933, _1608935), _1608937)), _1608939), hAPP(_1608935, _1608941)))], (35318 ^ _775828) ^ [_1438071, _1438073, _1438075, _1438077, _1438079] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1438071, _1438071)), hAPP(hAPP(c_Product__Type_OPair(_1438071, _1438071), hAPP(_1438073, hAPP(c_Nat_OSuc, 35319 ^ [_1438071, _1438073, _1438075, _1438077, _1438079]))), hAPP(_1438073, 35319 ^ [_1438071, _1438073, _1438075, _1438077, _1438079]))), c_Transitive__Closure_Ortrancl(_1438071, _1438075))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438071, _1438071)), hAPP(hAPP(c_Product__Type_OPair(_1438071, _1438071), hAPP(_1438073, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1438077), _1438079))), hAPP(_1438073, _1438077))), c_Transitive__Closure_Ortrancl(_1438071, _1438075))))], (8139 ^ _775828) ^ [_906653, _906655] : [-(c_Option_Ooption_Ooption__size(_906653, _906655, c_Option_Ooption_ONone(_906653)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42938 ^ _775828) ^ [_1612691, _1612693, _1612695, _1612697, _1612699] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1612691, _1612693, _1612695), _1612697), _1612699)), 42941 ^ _775828 : [(42944 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1612695, _1612699)))], (42942 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1612693, _1612697), _1612699)))]]], (6811 ^ _775828) ^ [_883731, _883733] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _883731) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _883733), -(hBOOL(hAPP(c_Com_OWT, _883733)))], (12481 ^ _775828) ^ [_981732, _981734] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981732)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981734)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981732), _981734)))], (35559 ^ _775828) ^ [_1443638, _1443640, _1443642] : [class_Orderings_Oorder(_1443638), _1443640 = _1443642, -(c_SetInterval_Oord__class_OatLeastAtMost(_1443638, _1443640, _1443642) = hAPP(hAPP(c_Set_Oinsert(_1443638), _1443640), c_Orderings_Obot__class_Obot(tc_fun(_1443638, tc_HOL_Obool))))], (14205 ^ _775828) ^ [_1013242, _1013244, _1013246, _1013248] : [c_Com_Ocom_OWhile(_1013242, _1013244) = c_Com_Ocom_OWhile(_1013246, _1013248), 14208 ^ _775828 : [(14211 ^ _775828) ^ [] : [-(_1013244 = _1013248)], (14209 ^ _775828) ^ [] : [-(_1013242 = _1013246)]]], (29963 ^ _775828) ^ [_1321862] : [-(c_Wellfounded_Owf(_1321862, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1321862, _1321862), tc_HOL_Obool))))], (27054 ^ _775828) ^ [_1253810, _1253812] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253810)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253812))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253812), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253810)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (560 ^ _775828) ^ [_784316, _784318, _784320, _784322, _784324, _784326, _784328, _784330] : [-(c_Equiv__Relations_Ocongruent(_784328, _784324, _784320, _784316)), c_Equiv__Relations_Ocongruent(_784330, _784326, _784322, _784318), _784330 = _784328, _784326 = _784324, _784322 = _784320, _784318 = _784316], (36217 ^ _775828) ^ [_1455949, _1455951] : [36225 ^ _775828 : [(36228 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1455951, 36224 ^ [_1455949, _1455951])))], (36226 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36224 ^ [_1455949, _1455951]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1455949))))]], 36218 ^ _775828 : [(36219 ^ _775828) ^ [_1456017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1456017), _1455949)), hBOOL(hAPP(_1455951, _1456017))]]], (48577 ^ _775828) ^ [_1750288, _1750290, _1750292, _1750294, _1750296] : [-(hAPP(hAPP(c_List_Ozip(_1750288, _1750290), hAPP(hAPP(c_List_Oappend(_1750288), _1750292), _1750294)), _1750296) = hAPP(hAPP(c_List_Oappend(tc_prod(_1750288, _1750290)), hAPP(hAPP(c_List_Ozip(_1750288, _1750290), _1750292), hAPP(hAPP(c_List_Otake(_1750290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750288)), _1750292)), _1750296))), hAPP(hAPP(c_List_Ozip(_1750288, _1750290), _1750294), hAPP(hAPP(c_List_Odrop(_1750290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750288)), _1750292)), _1750296))))], (5571 ^ _775828) ^ [_864101, _864103] : [hAPP(c_Nat_OSuc, _864101) = hAPP(c_Nat_OSuc, _864103), -(_864101 = _864103)], (16290 ^ _775828) ^ [_1052522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052522)), -(_1052522 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052522), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (18065 ^ _775828) ^ [_1085534, _1085536, _1085538] : [class_Rings_Oring__1(_1085534), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1085534), hAPP(c_Groups_Ouminus__class_Ouminus(_1085534), _1085536)), _1085538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085534), hAPP(hAPP(c_Power_Opower__class_Opower(_1085534), hAPP(c_Groups_Ouminus__class_Ouminus(_1085534), c_Groups_Oone__class_Oone(_1085534))), _1085538)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085534), _1085536), _1085538)))], (47375 ^ _775828) ^ [_1720970, _1720972, _1720974, _1720976] : [-(c_List_Ofoldr(_1720970, _1720972, _1720974, c_List_Olist_ONil(_1720970), _1720976) = _1720976)], (38818 ^ _775828) ^ [_1514788, _1514790] : [-(c_Fun_Oinj__on(_1514788, _1514788, c_COMBI(_1514788), _1514790))], (28044 ^ _775828) ^ [_1277767, _1277769, _1277771, _1277773] : [28046 ^ _775828 : [(28049 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1277769, hAPP(_1277771, 28045 ^ [_1277767, _1277769, _1277771, _1277773]))), hAPP(_1277769, 28045 ^ [_1277767, _1277769, _1277771, _1277773])))], (28047 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1277767, 28045 ^ [_1277767, _1277769, _1277771, _1277773])))]], -(c_Wellfounded_Owf(_1277773, hAPP(c_Set_OCollect(tc_prod(_1277773, _1277773)), hAPP(c_Product__Type_Oprod_Oprod__case(_1277773, _1277773, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1277773, tc_HOL_Obool), tc_fun(_1277773, tc_HOL_Obool), _1277773), hAPP(c_COMBS(_1277773, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1277773), c_fconj), _1277767))), hAPP(hAPP(c_COMBC(_1277773, tc_fun(_1277773, _1277773), tc_fun(_1277773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1277773, tc_HOL_Obool), tc_fun(tc_fun(_1277773, _1277773), tc_fun(_1277773, tc_HOL_Obool)), _1277773), c_COMBB(_1277773, tc_HOL_Obool, _1277773)), c_fequal)), _1277771))))))], (21378 ^ _775828) ^ [_1146116, _1146118] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1146116)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1146118)), hAPP(c_Int_Onat, _1146116)) = hAPP(c_Int_Onat, _1146118))], (34181 ^ _775828) ^ [_1411768, _1411770] : [class_Lattices_Oboolean__algebra(_1411768), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411768), hAPP(c_Groups_Ouminus__class_Ouminus(_1411768), _1411770)), _1411770) = c_Orderings_Obot__class_Obot(_1411768))], (44443 ^ _775828) ^ [_1648683, _1648685, _1648687, _1648689, _1648691] : [-(_1648683 = c_Orderings_Obot__class_Obot(tc_fun(_1648685, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648685, tc_fun(_1648687, tc_HOL_Obool)), _1648683), hAPP(hAPP(c_COMBB(tc_fun(_1648687, tc_HOL_Obool), tc_fun(_1648687, tc_HOL_Obool), _1648685), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648687, tc_HOL_Obool)), _1648689)), _1648691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648687, tc_HOL_Obool)), _1648689), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648685, tc_fun(_1648687, tc_HOL_Obool)), _1648683), _1648691)))], (10288 ^ _775828) ^ [_942698, _942700, _942702, _942704] : [class_Rings_Ocomm__semiring__1(_942698), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942698), _942700), _942702)), _942704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942698), _942700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942698), _942702), _942704)))], (41266 ^ _775828) ^ [_1572454, _1572456, _1572458, _1572460] : [-(hAPP(c_Set_Oimage(tc_prod(_1572454, _1572456), tc_prod(_1572456, _1572454), hAPP(c_Product__Type_Oprod_Oprod__case(_1572454, _1572456, tc_prod(_1572456, _1572454)), hAPP(c_COMBC(_1572456, _1572454, tc_prod(_1572456, _1572454)), c_Product__Type_OPair(_1572456, _1572454)))), hAPP(hAPP(c_Product__Type_OSigma(_1572454, _1572456), _1572458), hAPP(c_COMBK(tc_fun(_1572456, tc_HOL_Obool), _1572454), _1572460))) = hAPP(hAPP(c_Product__Type_OSigma(_1572456, _1572454), _1572460), hAPP(c_COMBK(tc_fun(_1572454, tc_HOL_Obool), _1572456), _1572458)))], (18821 ^ _775828) ^ [_1099439, _1099441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099441)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1099439), _1099441) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1099439, _1099441)))], (28281 ^ _775828) ^ [_1283075, _1283077, _1283079, _1283081] : [class_Lattices_Osemilattice__sup(_1283075), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283075), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283075), _1283077), _1283079)), _1283081) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283075), _1283077), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283075), _1283079), _1283081)))], (28455 ^ _775828) ^ [_1286939, _1286941, _1286943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286939, tc_HOL_Obool)), _1286941), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286939, tc_HOL_Obool)), _1286943), _1286941))))], (16847 ^ _775828) ^ [_1062883, _1062885, _1062887] : [class_Groups_Oordered__ab__group__add__abs(_1062883), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062883), hAPP(c_Groups_Oabs__class_Oabs(_1062883), _1062885)), hAPP(c_Groups_Oabs__class_Oabs(_1062883), _1062887))), hAPP(c_Groups_Oabs__class_Oabs(_1062883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062883), _1062885), _1062887)))))], (42471 ^ _775828) ^ [_1600984, _1600986, _1600988, _1600990, _1600992] : [c_Relation_Osingle__valued(_1600984, _1600984, _1600986), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600984, _1600984)), hAPP(hAPP(c_Product__Type_OPair(_1600984, _1600984), _1600988), _1600990)), c_Transitive__Closure_Ortrancl(_1600984, _1600986))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600984, _1600984)), hAPP(hAPP(c_Product__Type_OPair(_1600984, _1600984), _1600988), _1600992)), c_Transitive__Closure_Ortrancl(_1600984, _1600986))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600984, _1600984)), hAPP(hAPP(c_Product__Type_OPair(_1600984, _1600984), _1600990), _1600992)), c_Transitive__Closure_Ortrancl(_1600984, _1600986)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600984, _1600984)), hAPP(hAPP(c_Product__Type_OPair(_1600984, _1600984), _1600992), _1600990)), c_Transitive__Closure_Ortrancl(_1600984, _1600986))))], (48956 ^ _775828) ^ [_1758457, _1758459, _1758461] : [c_Relation_Orefl__on(_1758457, _1758459, _1758461), -(c_Relation_Orefl__on(tc_List_Olist(_1758457), c_List_Olists(_1758457, _1758459), c_List_Olistrel(_1758457, _1758461)))], (33386 ^ _775828) ^ [_1394707, _1394709] : [-(c_Map_Oran(_1394707, _1394709, hAPP(c_COMBK(tc_Option_Ooption(_1394709), _1394707), c_Option_Ooption_ONone(_1394709))) = c_Orderings_Obot__class_Obot(tc_fun(_1394709, tc_HOL_Obool)))], (18619 ^ _775828) ^ [_1095846, _1095848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095846), 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)), _1095848)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1095846, _1095848), c_Divides_OnegDivAlg(_1095846, _1095848))))], (15756 ^ _775828) ^ [_1041467, _1041469, _1041471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041467), _1041469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041471), _1041467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041467), _1041471)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041469), _1041471))))], (47199 ^ _775828) ^ [_1717207, _1717209, _1717211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717207)), _1717209)), _1717211)), -(hAPP(hAPP(c_List_Otake(_1717207), _1717211), _1717209) = _1717209)], (30511 ^ _775828) ^ [_1333337] : [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)), _1333337))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1333337)))], (6137 ^ _775828) ^ [_873373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _873373)), -(_873373 = hAPP(c_Nat_OSuc, 6140 ^ [_873373]))], (8141 ^ _775828) ^ [_906684, _906686, _906688, _906690] : [8143 ^ _775828 : [(8146 ^ _775828) ^ [] : [hBOOL(hAPP(_906688, 8142 ^ [_906684, _906686, _906688, _906690]))], (8144 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906684), 8142 ^ [_906684, _906686, _906688, _906690]), c_Option_Oset(_906684, _906686))))]], _906686 = hAPP(c_Option_Ooption_OSome(_906684), _906690), -(hBOOL(hAPP(_906688, _906690)))], (31749 ^ _775828) ^ [_1361225, _1361227, _1361229, _1361231, _1361233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1361225, _1361225)), hAPP(hAPP(c_Product__Type_OPair(_1361225, _1361225), _1361227), _1361229)), c_Transitive__Closure_Otrancl(_1361225, _1361231))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1361225, _1361225)), hAPP(hAPP(c_Product__Type_OPair(_1361225, _1361225), _1361229), _1361233)), c_Transitive__Closure_Ortrancl(_1361225, _1361231))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361225, _1361225)), hAPP(hAPP(c_Product__Type_OPair(_1361225, _1361225), _1361227), _1361233)), c_Transitive__Closure_Otrancl(_1361225, _1361231))))], (7829 ^ _775828) ^ [_900893, _900895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _900893)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _900895))))], (35842 ^ _775828) ^ [_1448914, _1448916] : [35844 ^ _775828 : [(35847 ^ _775828) ^ [] : [hBOOL(hAPP(_1448916, 35843 ^ [_1448914, _1448916]))], (35845 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35843 ^ [_1448914, _1448916]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448914))))]], 35848 ^ _775828 : [(35849 ^ _775828) ^ [_1449069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1449069), _1448914)), -(hBOOL(hAPP(_1448916, _1449069)))]]], (37775 ^ _775828) ^ [_1491098, _1491100, _1491102, _1491104, _1491106, _1491108] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491098), _1491100)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491102), _1491104)), 37785 ^ _775828 : [(37788 ^ _775828) ^ [] : [hAPP(c_Finite__Set_Ocard(_1491098), hAPP(c_Set_OCollect(_1491098), hAPP(hAPP(c_COMBS(_1491098, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491098), c_fconj), hAPP(hAPP(c_COMBC(_1491098, tc_fun(_1491098, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491098)), _1491100))), hAPP(hAPP(c_COMBC(_1491098, _1491102, tc_HOL_Obool), _1491106), 37784 ^ [_1491098, _1491100, _1491102, _1491104, _1491106, _1491108])))) = hAPP(_1491108, 37784 ^ [_1491098, _1491100, _1491102, _1491104, _1491106, _1491108])], (37786 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491102), 37784 ^ [_1491098, _1491100, _1491102, _1491104, _1491106, _1491108]), _1491104)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491098, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1491102, tc_HOL_Obool), tc_Nat_Onat, _1491098), c_Finite__Set_Ocard(_1491102)), hAPP(hAPP(c_COMBB(tc_fun(_1491102, tc_HOL_Obool), tc_fun(_1491102, tc_HOL_Obool), _1491098), c_Set_OCollect(_1491102)), hAPP(hAPP(c_COMBB(tc_fun(_1491102, tc_HOL_Obool), tc_fun(_1491102, tc_HOL_Obool), _1491098), hAPP(c_COMBS(_1491102, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491102), c_fconj), hAPP(hAPP(c_COMBC(_1491102, tc_fun(_1491102, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491102)), _1491104)))), _1491106)))), _1491100) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491102, tc_Nat_Onat), _1491108), _1491104))], (37691 ^ _775828) ^ [_1489174, _1489176, _1489178, _1489180, _1489182] : [class_Groups_Oordered__ab__semigroup__add(_1489174), class_Rings_Osemiring__1(_1489174), 37701 ^ _775828 : [(37704 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1489174), hAPP(_1489180, 37700 ^ [_1489174, _1489176, _1489178, _1489180, _1489182])), _1489182))], (37702 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489176), 37700 ^ [_1489174, _1489176, _1489178, _1489180, _1489182]), _1489178)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1489174), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489176, _1489174), _1489180), _1489178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1489174), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1489174), hAPP(c_Finite__Set_Ocard(_1489176), _1489178))), _1489182))))], (40857 ^ _775828) ^ [_1561897, _1561899, _1561901] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561897, _1561897), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1561899)), _1561901) = hAPP(hAPP(c_Relation_Orel__comp(_1561897, _1561897, _1561897), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561897, _1561897), tc_HOL_Obool), _1561899), _1561901)), _1561901))], (30597 ^ _775828) ^ [_1335072] : [c_Nat__Transfer_Onat__set(_1335072), 30600 ^ _775828 : [(30607 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1335072))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1335072)))], (30601 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1335072)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1335072))))]]], (29048 ^ _775828) ^ [_1301642, _1301644, _1301646, _1301648] : [c_Hoare__Mirabelle_Ohoare__derivs(_1301642, _1301644, _1301646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1301642), tc_HOL_Obool)), _1301644), _1301648)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1301642, _1301648, _1301646))], (7055 ^ _775828) ^ [_887734, _887736, _887738, _887740] : [class_Rings_Olinordered__semiring__strict(_887734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887734), _887736), _887738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887734), c_Groups_Ozero__class_Ozero(_887734)), _887740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_887734), _887740), _887736)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_887734), _887740), _887738))))], (37604 ^ _775828) ^ [_1486894, _1486896, _1486898, _1486900] : [class_Groups_Oab__group__add(_1486894), 37607 ^ _775828 : [(37614 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1486896), _1486898))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486894), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1486894, _1486894), hAPP(hAPP(c_COMBB(_1486894, tc_fun(_1486894, _1486894), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1486894)), _1486900)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1486894, tc_Nat_Onat), _1486900), 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, _1486896, _1486898)) = c_Groups_Ozero__class_Ozero(_1486894))], (37608 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1486896), _1486898)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486894), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1486894, _1486894), hAPP(hAPP(c_COMBB(_1486894, tc_fun(_1486894, _1486894), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1486894)), _1486900)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1486894, tc_Nat_Onat), _1486900), 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, _1486896, _1486898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1486894), hAPP(_1486900, _1486896)), hAPP(_1486900, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1486898), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (43592 ^ _775828) ^ [_1628244, _1628246, _1628248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1628244), _1628246)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1628244, tc_HOL_Obool)), _1628246), _1628248) = hAPP(hAPP(c_Finite__Set_Ofold(_1628244, tc_fun(_1628244, tc_HOL_Obool), c_Set_Oinsert(_1628244)), _1628248), _1628246))], (24513 ^ _775828) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47359 ^ _775828) ^ [_1720698] : [class_Orderings_Olinorder(_1720698), -(c_List_Olinorder__class_Osorted__list__of__set(_1720698, c_Orderings_Obot__class_Obot(tc_fun(_1720698, tc_HOL_Obool))) = c_List_Olist_ONil(_1720698))], (50142 ^ _775828) ^ [_1782731, _1782733] : [class_Orderings_Olinorder(_1782731), 50145 ^ _775828 : [(50146 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1782731, _1782733), 50149 ^ _775828 : [(50150 ^ _775828) ^ [_1782902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782902), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782731)), _1782733))), 50153 ^ _775828 : [(50154 ^ _775828) ^ [_1783019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1783019), _1782902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1782731), hAPP(hAPP(c_List_Onth(_1782731), _1782733), _1783019)), hAPP(hAPP(c_List_Onth(_1782731), _1782733), _1782902))))]]]]], (50160 ^ _775828) ^ [] : [50162 ^ _775828 : [(50168 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1782731), hAPP(hAPP(c_List_Onth(_1782731), _1782733), 50164 ^ [_1782731, _1782733])), hAPP(hAPP(c_List_Onth(_1782731), _1782733), 50161 ^ [_1782731, _1782733])))], (50166 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50164 ^ [_1782731, _1782733]), 50161 ^ [_1782731, _1782733])))], (50163 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50161 ^ [_1782731, _1782733]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782731)), _1782733))))]], -(c_List_Olinorder__class_Osorted(_1782731, _1782733))]]], (41891 ^ _775828) ^ [_1587604, _1587606] : [-(c_Product__Type_Oapfst(_1587604, _1587604, _1587606, c_Fun_Oid(_1587604)) = c_Fun_Oid(tc_prod(_1587604, _1587606)))], (5903 ^ _775828) ^ [_869771, _869773, _869775, _869777, _869779, _869781] : [c_Com_Ocom_OCall(_869771, _869773, _869775) = c_Com_Ocom_OCall(_869777, _869779, _869781), 5906 ^ _775828 : [(5911 ^ _775828) ^ [] : [-(_869775 = _869781)], (5909 ^ _775828) ^ [] : [-(_869773 = _869779)], (5907 ^ _775828) ^ [] : [-(_869771 = _869777)]]], (25809 ^ _775828) ^ [_1231954, _1231956] : [25816 ^ _775828 : [(25819 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231956), _1231954))], (25817 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231954), _1231956)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231954), _1231956)), -(_1231954 = _1231956)], (43784 ^ _775828) ^ [_1632148, _1632150, _1632152] : [class_Orderings_Olinorder(_1632148), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632148), _1632150)), -(c_Big__Operators_Olattice_OInf__fin(_1632148, c_Orderings_Oord__class_Omin(_1632148), hAPP(hAPP(c_Set_Oinsert(_1632148), _1632152), _1632150)) = hAPP(hAPP(c_Finite__Set_Ofold(_1632148, _1632148, c_Orderings_Oord__class_Omin(_1632148)), _1632152), _1632150))], (29893 ^ _775828) ^ [_1319421, _1319423] : [_1319423 = c_Orderings_Obot__class_Obot(tc_fun(_1319421, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319421, tc_HOL_Obool)), _1319423), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1319421, tc_HOL_Obool)), _1319423))))], (44285 ^ _775828) ^ [_1643725, _1643727, _1643729, _1643731, _1643733, _1643735] : [class_Complete__Lattice_Ocomplete__lattice(_1643725), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643727, _1643725), _1643729), hAPP(hAPP(c_COMBB(tc_fun(_1643731, _1643725), _1643725, _1643727), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643731, _1643725), _1643733)), _1643735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643731, _1643725), _1643733), hAPP(hAPP(c_COMBB(tc_fun(_1643727, _1643725), _1643725, _1643731), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643727, _1643725), _1643729)), hAPP(c_COMBC(_1643727, _1643731, _1643725), _1643735))))], (35531 ^ _775828) ^ [_1443135, _1443137, _1443139, _1443141, _1443143] : [class_Orderings_Oorder(_1443135), 35534 ^ _775828 : [(35547 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443135, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1443135, _1443137, _1443139)), c_SetInterval_Oord__class_OatLeastAtMost(_1443135, _1443141, _1443143)))), 35548 ^ _775828 : [(35551 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443141), _1443137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443139), _1443143))], (35549 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443137), _1443139)))]]], (35535 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443135, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1443135, _1443137, _1443139)), c_SetInterval_Oord__class_OatLeastAtMost(_1443135, _1443141, _1443143))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443137), _1443139)), 35542 ^ _775828 : [(35545 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443139), _1443143)))], (35543 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443135), _1443141), _1443137)))]]]]], (33222 ^ _775828) ^ [_1391053, _1391055, _1391057, _1391059, _1391061] : [class_Groups_Ocomm__monoid__mult(_1391053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391055), _1391057)), -(hBOOL(hAPP(hAPP(c_member(_1391055), _1391059), _1391057))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391055, _1391053), _1391061), hAPP(hAPP(c_Set_Oinsert(_1391055), _1391059), _1391057)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391053), hAPP(_1391061, _1391059)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391055, _1391053), _1391061), _1391057)))], (32949 ^ _775828) ^ [_1385662, _1385664, _1385666, _1385668] : [class_Fields_Olinordered__field(_1385662), -(hAPP(c_Groups_Oabs__class_Oabs(_1385662), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385664, _1385662), _1385666), _1385668)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385664, _1385662), hAPP(hAPP(c_COMBB(_1385662, _1385662, _1385664), c_Groups_Oabs__class_Oabs(_1385662)), _1385666)), _1385668))], (43164 ^ _775828) ^ [_1617957, _1617959, _1617961, _1617963, _1617965, _1617967] : [c_Finite__Set_Ofolding__idem(_1617957, _1617959, _1617961, _1617963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617957), _1617965)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617957), _1617967)), -(hAPP(_1617963, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1617957, tc_HOL_Obool)), _1617965), _1617967)) = hAPP(c_Fun_Ocomp(_1617959, _1617959, _1617959, hAPP(_1617963, _1617965)), hAPP(_1617963, _1617967)))], (1260 ^ _775828) ^ [_794196, _794198] : [-(class_Lattices_Osemilattice__sup(_794196)), _794198 = _794196, class_Lattices_Osemilattice__sup(_794198)], (9683 ^ _775828) ^ [_931581, _931583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931581), hAPP(c_Int_Onat, _931583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931581)), _931583)))], (20058 ^ _775828) ^ [_1120461, _1120463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120461), _1120463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120461)), c_Int_OBit0(_1120463))))], (29603 ^ _775828) ^ [_1313160, _1313162, _1313164, _1313166, _1313168] : [-(hAPP(c_Relation_ODomain(_1313160, _1313162), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1313160, _1313162)), hAPP(hAPP(c_Product__Type_OPair(_1313160, _1313162), _1313164), _1313166)), _1313168)) = hAPP(hAPP(c_Set_Oinsert(_1313160), _1313164), hAPP(c_Relation_ODomain(_1313160, _1313162), _1313168)))], (17497 ^ _775828) ^ [_1075402] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075402)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075402))], (43576 ^ _775828) ^ [_1627908, _1627910, _1627912, _1627914, _1627916, _1627918] : [c_Finite__Set_Ofolding(_1627908, _1627910, _1627912, _1627914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627908), _1627916)), -(hAPP(hAPP(_1627914, _1627916), _1627918) = hAPP(hAPP(c_Finite__Set_Ofold(_1627908, _1627910, _1627912), _1627918), _1627916))], (47879 ^ _775828) ^ [_1732498, _1732500, _1732502, _1732504, _1732506] : [hAPP(hAPP(c_List_Oappend(_1732498), _1732500), _1732502) = hAPP(hAPP(c_List_Oappend(_1732498), _1732504), _1732506), 47885 ^ _775828 : [(47888 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1732498), 47882 ^ [_1732498, _1732500, _1732502, _1732504, _1732506]), _1732502) = _1732506)], (47886 ^ _775828) ^ [] : [-(_1732500 = hAPP(hAPP(c_List_Oappend(_1732498), _1732504), 47882 ^ [_1732498, _1732500, _1732502, _1732504, _1732506]))]], 47889 ^ _775828 : [(47892 ^ _775828) ^ [] : [-(_1732502 = hAPP(hAPP(c_List_Oappend(_1732498), 47882 ^ [_1732498, _1732500, _1732502, _1732504, _1732506]), _1732506))], (47890 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1732498), _1732500), 47882 ^ [_1732498, _1732500, _1732502, _1732504, _1732506]) = _1732504)]]], (36721 ^ _775828) ^ [_1465704] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1465704) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1465704))], (45432 ^ _775828) ^ [_1670801, _1670803, _1670805] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1670801), c_Map_Odom(_1670801, _1670803, c_Map_Omap__of(_1670801, _1670803, _1670805)))))], (29773 ^ _775828) ^ [_1316686, _1316688] : [-(c_Relation_Ototal__on(_1316686, c_Orderings_Obot__class_Obot(tc_fun(_1316686, tc_HOL_Obool)), _1316688))], (41887 ^ _775828) ^ [_1587544, _1587546] : [-(hAPP(c_Fun_Oid(_1587544), _1587546) = _1587546)], (27581 ^ _775828) ^ [_1266052, _1266054, _1266056, _1266058, _1266060, _1266062] : [-(hBOOL(hAPP(hAPP(c_member(_1266052), _1266054), c_SetInterval_Oord_OgreaterThanAtMost(_1266052, _1266056, _1266058, _1266060, _1266062)))), hBOOL(hAPP(hAPP(_1266058, _1266060), _1266054)), hBOOL(hAPP(hAPP(_1266056, _1266054), _1266062))], (27549 ^ _775828) ^ [_1265403, _1265405, _1265407, _1265409] : [hBOOL(hAPP(hAPP(c_member(_1265403), _1265405), c_SetInterval_Oord_OatMost(_1265403, _1265407, _1265409))), -(hBOOL(hAPP(hAPP(_1265407, _1265405), _1265409)))], (30269 ^ _775828) ^ [_1327754, _1327756, _1327758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327754, tc_HOL_Obool)), _1327756), hAPP(hAPP(c_Set_Oinsert(_1327754), _1327758), c_Orderings_Obot__class_Obot(tc_fun(_1327754, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1327754, _1327758, _1327756) = c_HOL_OThe(_1327754, hAPP(hAPP(c_COMBC(_1327754, tc_fun(_1327754, tc_HOL_Obool), tc_HOL_Obool), c_member(_1327754)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327754, tc_HOL_Obool)), _1327756), hAPP(hAPP(c_Set_Oinsert(_1327754), _1327758), c_Orderings_Obot__class_Obot(tc_fun(_1327754, tc_HOL_Obool)))))))], (10870 ^ _775828) ^ [_953683, _953685, _953687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953683), _953685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953685), _953687))))], (24366 ^ _775828) ^ [_1203408] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1203408)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1203408)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5955 ^ _775828) ^ [_870486, _870488] : [5956 ^ _775828 : [(5959 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870488), _870486))], (5957 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870486), _870488))]], _870486 = _870488], (6334 ^ _775828) ^ [_876522, _876524, _876526, _876528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_876522, tc_HOL_Obool)), _876524), _876526)), hBOOL(hAPP(hAPP(c_member(_876522), _876528), _876524)), -(hBOOL(hAPP(hAPP(c_member(_876522), _876528), _876526)))], (50049 ^ _775828) ^ [_1781008, _1781010, _1781012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1781008), _1781010)), _1781012)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1781008, _1781012)), _1781010) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1781008), _1781010))], (50605 ^ _775828) ^ [_1794699] : [-(c_List_Oreturn__list(_1794699) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1794699))], (46925 ^ _775828) ^ [_1709792, _1709794, _1709796, _1709798] : [-(hAPP(hAPP(c_List_Onth(_1709792), hAPP(hAPP(c_List_Olist_OCons(_1709792), _1709794), _1709796)), _1709798) = c_Nat_Onat_Onat__case(_1709792, _1709794, hAPP(c_List_Onth(_1709792), _1709796), _1709798))], (11618 ^ _775828) ^ [_966779, _966781] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966779), _966781)), 11619 ^ _775828 : [(11626 ^ _775828) ^ [] : [_966779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _966781 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11620 ^ _775828) ^ [] : [_966779 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (20472 ^ _775828) ^ [_1127609] : [-(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)))), _1127609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127609), _1127609))], (21674 ^ _775828) ^ [_1151314, _1151316, _1151318] : [class_Int_Onumber__ring(_1151314), 21677 ^ _775828 : [(21684 ^ _775828) ^ [] : [-(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), _1151316)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1151314), _1151318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1151316))) = c_Groups_Oone__class_Oone(_1151314))], (21678 ^ _775828) ^ [] : [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), _1151316))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1151314), _1151318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1151316))) = hAPP(hAPP(c_HOL_OLet(_1151314, _1151314), hAPP(hAPP(c_Power_Opower__class_Opower(_1151314), _1151318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151316))), hAPP(hAPP(c_COMBS(_1151314, _1151314, _1151314), hAPP(hAPP(c_COMBB(_1151314, tc_fun(_1151314, _1151314), _1151314), c_Groups_Otimes__class_Otimes(_1151314)), hAPP(c_Groups_Otimes__class_Otimes(_1151314), _1151318))), c_COMBI(_1151314))))]]], (35816 ^ _775828) ^ [_1448405, _1448407] : [35824 ^ _775828 : [(35827 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1448407, 35823 ^ [_1448405, _1448407])))], (35825 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35823 ^ [_1448405, _1448407]), _1448405)))]], 35817 ^ _775828 : [(35818 ^ _775828) ^ [_1448474] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1448474), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448405))), hBOOL(hAPP(_1448407, _1448474))]]], (48934 ^ _775828) ^ [_1757875, _1757877, _1757879] : [-(c_List_Olist_Olist__size(_1757875, _1757877, _1757879) = 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(_1757875, tc_Nat_Onat), _1757877), _1757879))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757875)), _1757879)))], (23896 ^ _775828) ^ [_1194256, _1194258, _1194260] : [class_Orderings_Olinorder(_1194256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194256), _1194258), _1194260)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194256), _1194260), _1194258) = _1194258)], (46171 ^ _775828) ^ [_1688735, _1688737] : [hAPP(c_Finite__Set_Ocard(_1688735), hAPP(c_List_Oset(_1688735), _1688737)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688735)), _1688737), -(hBOOL(hAPP(c_List_Odistinct(_1688735), _1688737)))], (29489 ^ _775828) ^ [_1310734, _1310736, _1310738, _1310740] : [29490 ^ _775828 : [(29493 ^ _775828) ^ [] : [hBOOL(hAPP(_1310738, _1310740))], (29491 ^ _775828) ^ [] : [_1310736 = _1310740]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1310734), _1310736), _1310738), _1310740)))], (27300 ^ _775828) ^ [_1259576, _1259578, _1259580, _1259582] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1259576, _1259578)), _1259580), hAPP(c_Relation_Oconverse(_1259578, _1259576), _1259582))), 27305 ^ _775828 : [(27308 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1259578, _1259576)), hAPP(hAPP(c_Product__Type_OPair(_1259578, _1259576), 27303 ^ [_1259576, _1259578, _1259580, _1259582]), 27304 ^ [_1259576, _1259578, _1259580, _1259582])), _1259582)))], (27306 ^ _775828) ^ [] : [-(_1259580 = hAPP(hAPP(c_Product__Type_OPair(_1259576, _1259578), 27304 ^ [_1259576, _1259578, _1259580, _1259582]), 27303 ^ [_1259576, _1259578, _1259580, _1259582]))]]], (2222 ^ _775828) ^ [_808320, _808322, _808324, _808326] : [-(c_Nitpick_Onat__lcm(_808326, _808322) = c_Nitpick_Onat__lcm(_808324, _808320)), _808326 = _808324, _808322 = _808320], (24807 ^ _775828) ^ [_1212395, _1212397] : [24808 ^ _775828 : [(24811 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1212397), _1212395))], (24809 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1212395), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1212395, _1212397) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (50461 ^ _775828) ^ [_1790391, _1790393, _1790395] : [c_List_Oconcat(_1790391, _1790393) = c_List_Oconcat(_1790391, _1790395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1790391))), _1790393) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1790391))), _1790395), 50471 ^ _775828 : [(50474 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1790391), tc_List_Olist(_1790391), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1790391), tc_fun(tc_List_Olist(_1790391), tc_Nat_Onat), tc_fun(tc_List_Olist(_1790391), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1790391), tc_Nat_Onat), tc_fun(tc_List_Olist(_1790391), tc_HOL_Obool)), tc_List_Olist(_1790391)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1790391))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1790391)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1790391))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1790391)))), 50470 ^ [_1790391, _1790393, _1790395]))], (50472 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1790391), tc_List_Olist(_1790391))), 50470 ^ [_1790391, _1790393, _1790395]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1790391), tc_List_Olist(_1790391))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1790391), tc_List_Olist(_1790391)), _1790393), _1790395)))))]], -(_1790393 = _1790395)], (49025 ^ _775828) ^ [_1760052, _1760054] : [-(c_List_Olists(_1760052, _1760054) = hAPP(c_Set_OCollect(tc_List_Olist(_1760052)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1760052), tc_fun(_1760052, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1760052, tc_HOL_Obool), tc_fun(tc_fun(_1760052, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1760052)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1760052, tc_HOL_Obool))), c_List_Oset(_1760052))), _1760054)))], (17489 ^ _775828) ^ [_1075276] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075276) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1075276))], (34697 ^ _775828) ^ [_1423208, _1423210, _1423212] : [class_Lattices_Olattice(_1423208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423208), _1423210)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423208), _1423212)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423208, tc_HOL_Obool)), _1423210), _1423212) = c_Orderings_Obot__class_Obot(tc_fun(_1423208, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1423208), c_Big__Operators_Olattice__class_OSup__fin(_1423208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423208, tc_HOL_Obool)), _1423210), _1423212))), c_Big__Operators_Olattice__class_OSup__fin(_1423208, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423208, tc_HOL_Obool)), _1423210), _1423212))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1423208), c_Big__Operators_Olattice__class_OSup__fin(_1423208, _1423210)), c_Big__Operators_Olattice__class_OSup__fin(_1423208, _1423212)))], (1916 ^ _775828) ^ [_803567, _803569] : [_803569 = _803567, -(c_Com_Ocom_Ocom__size(_803569) = c_Com_Ocom_Ocom__size(_803567))], (51562 ^ _775828) ^ [_1808915, _1808917] : [hBOOL(hAPP(hAPP(c_fconj, _1808915), _1808917)), -(hBOOL(_1808915))], (19456 ^ _775828) ^ [_1110213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110213), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110213)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3278 ^ _775828) ^ [_825456, _825458] : [_825458 = _825456, -(c_SetInterval_Oord__class_OatLeast(_825458) = c_SetInterval_Oord__class_OatLeast(_825456))], (23458 ^ _775828) ^ [_1185570, _1185572, _1185574, _1185576] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1185570, _1185572, _1185574), hAPP(hAPP(c_COMBB(tc_fun(_1185572, tc_prod(_1185570, _1185572)), tc_fun(_1185572, _1185574), _1185570), hAPP(c_COMBB(tc_prod(_1185570, _1185572), _1185574, _1185572), _1185576)), c_Product__Type_OPair(_1185570, _1185572))) = _1185576)], (36247 ^ _775828) ^ [_1456481, _1456483] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1456481), _1456483)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1456483), _1456481))], (25609 ^ _775828) ^ [_1228598, _1228600, _1228602] : [class_Rings_Olinordered__idom(_1228598), 25612 ^ _775828 : [(25619 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228598), _1228600), _1228602)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228598), _1228600), hAPP(c_Groups_Oabs__class_Oabs(_1228598), _1228602))))], (25613 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228598), _1228600), hAPP(c_Groups_Oabs__class_Oabs(_1228598), _1228602))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228598), _1228600), _1228602)))]]], (50447 ^ _775828) ^ [_1789783, _1789785, _1789787] : [-(hAPP(c_List_Orev(_1789783), hAPP(hAPP(c_List_Otake(_1789783), _1789785), _1789787)) = hAPP(hAPP(c_List_Odrop(_1789783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789783)), _1789787)), _1789785)), hAPP(c_List_Orev(_1789783), _1789787)))], (25341 ^ _775828) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42798 ^ _775828) ^ [_1609311, _1609313, _1609315] : [-(hAPP(hAPP(c_Nat_Ocompow(_1609311, _1609311), hAPP(c_Nat_OSuc, _1609313)), _1609315) = hAPP(c_Fun_Ocomp(_1609311, _1609311, _1609311, _1609315), hAPP(hAPP(c_Nat_Ocompow(_1609311, _1609311), _1609313), _1609315)))], (20180 ^ _775828) ^ [_1122529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1122529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1122529)))], (1380 ^ _775828) ^ [_795696, _795698] : [-(class_Rings_Olinordered__comm__semiring__strict(_795696)), _795698 = _795696, class_Rings_Olinordered__comm__semiring__strict(_795698)], (43253 ^ _775828) ^ [_1619878, _1619880, _1619882, _1619884] : [-(c_New__Random__Sequence_Oneg__map(_1619878, _1619880, _1619882, _1619884) = c_New__Random__Sequence_Oneg__bind(_1619878, _1619880, _1619884, hAPP(c_Fun_Ocomp(_1619880, 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(_1619880)))))), _1619878, c_New__Random__Sequence_Oneg__single(_1619880)), _1619882)))], (25539 ^ _775828) ^ [_1227392, _1227394] : [class_Rings_Ocomm__semiring__1(_1227392), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227392), _1227394), c_Groups_Ozero__class_Ozero(_1227392))))], (47235 ^ _775828) ^ [_1718118, _1718120] : [-(_1718118 = c_List_Olist_ONil(_1718120)), -(c_Random_Oselect__weight(_1718120, hAPP(hAPP(c_List_Omap(_1718120, tc_prod(tc_Code__Numeral_Ocode__numeral, _1718120)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1718120), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1718118)) = c_Random_Oselect(_1718120, _1718118))], (20126 ^ _775828) ^ [_1121566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1121566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1121566))))], (12359 ^ _775828) ^ [_979716, _979718] : [class_Rings_Olinordered__idom(_979716), -(c_Groups_Osgn__class_Osgn(_979716, c_Groups_Osgn__class_Osgn(_979716, _979718)) = c_Groups_Osgn__class_Osgn(_979716, _979718))], (28765 ^ _775828) ^ [_1293272, _1293274, _1293276] : [-(c_Hilbert__Choice_OEps(tc_prod(_1293272, _1293274), hAPP(c_Product__Type_Oprod_Oprod__case(_1293272, _1293274, tc_HOL_Obool), _1293276)) = c_Hilbert__Choice_OEps(tc_prod(_1293272, _1293274), hAPP(hAPP(c_COMBS(tc_prod(_1293272, _1293274), _1293274, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1293272, tc_fun(_1293274, tc_HOL_Obool), tc_prod(_1293272, _1293274)), _1293276), c_Product__Type_Ofst(_1293272, _1293274))), c_Product__Type_Osnd(_1293272, _1293274))))], (8613 ^ _775828) ^ [_913988, _913990, _913992] : [-(hBOOL(hAPP(hAPP(c_member(_913988), _913990), _913992))), -(hBOOL(hAPP(hAPP(c_member(_913988), _913990), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_913988, tc_HOL_Obool)), _913992))))], (6091 ^ _775828) ^ [_872617, _872619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872617), hAPP(c_Nat_OSuc, _872619))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872617), _872619))), -(_872617 = _872619)], (24254 ^ _775828) ^ [_1201048, _1201050, _1201052, _1201054] : [class_Orderings_Olinorder(_1201048), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201048), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201048), _1201050), _1201052)), _1201054) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201048), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201048), _1201050), _1201054)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201048), _1201052), _1201054)))], (46353 ^ _775828) ^ [_1693362, _1693364, _1693366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1693362), _1693364)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1693362)), hAPP(c_Set_OCollect(tc_List_Olist(_1693362)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1693362), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1693362)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693362), tc_fun(_1693362, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1693362, tc_HOL_Obool), tc_fun(tc_fun(_1693362, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1693362)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1693362, tc_HOL_Obool))), c_List_Oset(_1693362))), _1693364))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693362), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693362)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1693362)))), _1693366))))))], (27773 ^ _775828) ^ [_1270486, _1270488] : [-(hAPP(c_Relation_ODomain(_1270486, _1270486), c_Relation_OId__on(_1270486, _1270488)) = _1270488)], (50892 ^ _775828) ^ [_1800324, _1800326] : [-(c_List_OdropWhile(_1800324, _1800326, c_List_Olist_ONil(_1800324)) = c_List_Olist_ONil(_1800324))], (49463 ^ _775828) ^ [_1769085, _1769087, _1769089] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1769085), tc_List_Olist(_1769085)), c_List_Opartition(_1769085, _1769087, _1769089)) = hAPP(c_List_Ofilter(_1769085, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1769085, c_fNot), _1769087)), _1769089))], (28134 ^ _775828) ^ [_1280041, _1280043] : [c_Wellfounded_OwfP(_1280041, _1280043), -(c_Wellfounded_Oacyclic(_1280041, hAPP(c_Set_OCollect(tc_prod(_1280041, _1280041)), hAPP(c_Product__Type_Oprod_Oprod__case(_1280041, _1280041, tc_HOL_Obool), _1280043))))], (45610 ^ _775828) ^ [_1675158] : [-(hAPP(c_List_Omap(_1675158, _1675158), c_Fun_Oid(_1675158)) = c_Fun_Oid(tc_List_Olist(_1675158)))], (30307 ^ _775828) ^ [] : [-(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)))))], (27240 ^ _775828) ^ [_1257841, _1257843] : [-(hAPP(c_Set_OCollect(_1257841), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1257841), c_fNot), _1257843)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1257841, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1257841), _1257843)))], (6698 ^ _775828) ^ [_882046, _882048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882046)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882046), _882048)))], (48461 ^ _775828) ^ [_1747415, _1747417, _1747419] : [-(hAPP(hAPP(c_List_Oappend(_1747415), hAPP(hAPP(c_List_Otake(_1747415), _1747417), _1747419)), hAPP(hAPP(c_List_Odrop(_1747415), _1747417), _1747419)) = _1747419)], (9973 ^ _775828) ^ [_936985] : [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, _936985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _936985)))], (27987 ^ _775828) ^ [_1276363, _1276365, _1276367] : [c_Wellfounded_Owf(_1276363, _1276365), -(hBOOL(hAPP(hAPP(c_member(_1276363), _1276367), c_Wellfounded_Oacc(_1276363, _1276365))))], (37350 ^ _775828) ^ [_1480273, _1480275, _1480277, _1480279] : [class_Groups_Ocomm__monoid__add(_1480273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1480275), _1480277)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480273), _1480279), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1480275), _1480277)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1480273), hAPP(_1480279, _1480275)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480273), _1480279), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1480275)), _1480277))))], (25307 ^ _775828) ^ [_1222232, _1222234] : [hAPP(c_Code__Numeral_Oof__nat, _1222232) = hAPP(c_Code__Numeral_Oof__nat, _1222234), -(_1222232 = _1222234)], (39634 ^ _775828) ^ [_1533573, _1533575, _1533577, _1533579, _1533581] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533573, tc_HOL_Obool)), _1533575), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533577, tc_fun(_1533573, tc_HOL_Obool)), _1533579), _1533581)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533577, tc_fun(_1533573, tc_HOL_Obool)), _1533579), hAPP(hAPP(c_COMBB(tc_fun(_1533573, tc_HOL_Obool), tc_fun(_1533573, tc_HOL_Obool), _1533577), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533573, tc_HOL_Obool)), _1533575)), _1533581)))], (14323 ^ _775828) ^ [_1015325, _1015327, _1015329, _1015331] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1015325, _1015327)), _1015329), _1015331)), 14328 ^ _775828 : [(14331 ^ _775828) ^ [] : [hBOOL(hAPP(_1015325, _1015329))], (14329 ^ _775828) ^ [] : [-(_1015331 = _1015329)]], 14332 ^ _775828 : [(14338 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1015325, _1015327)), 14334 ^ [_1015325, _1015327, _1015329, _1015331]), _1015331)))], (14336 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1015327), _1015329), 14334 ^ [_1015325, _1015327, _1015329, _1015331])))], (14333 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1015325, _1015329)))]]], (32103 ^ _775828) ^ [_1369448, _1369450, _1369452] : [class_Orderings_Olinorder(_1369448), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369448), _1369450)), hBOOL(hAPP(hAPP(c_member(_1369448), _1369452), _1369450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369448), c_Big__Operators_Olinorder__class_OMin(_1369448, _1369450)), _1369452)))], (50172 ^ _775828) ^ [_1783455, _1783457, _1783459, _1783461, _1783463] : [class_Orderings_Olinorder(_1783455), c_Fun_Oinj__on(_1783457, _1783455, _1783459, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1783457, tc_HOL_Obool)), hAPP(c_List_Oset(_1783457), _1783461)), hAPP(c_List_Oset(_1783457), _1783463))), c_List_Olinorder__class_Osorted(_1783455, hAPP(hAPP(c_List_Omap(_1783457, _1783455), _1783459), _1783461)), hBOOL(hAPP(c_List_Odistinct(_1783455), hAPP(hAPP(c_List_Omap(_1783457, _1783455), _1783459), _1783461))), c_List_Olinorder__class_Osorted(_1783455, hAPP(hAPP(c_List_Omap(_1783457, _1783455), _1783459), _1783463)), hBOOL(hAPP(c_List_Odistinct(_1783455), hAPP(hAPP(c_List_Omap(_1783457, _1783455), _1783459), _1783463))), hAPP(c_List_Oset(_1783457), _1783461) = hAPP(c_List_Oset(_1783457), _1783463), -(_1783461 = _1783463)], (35711 ^ _775828) ^ [_1446445, _1446447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446445), _1446447)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1446447, _1446445) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (18297 ^ _775828) ^ [_1090489, _1090491, _1090493, _1090495, _1090497, _1090499, _1090501, _1090503] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1090489, _1090491), tc_prod(_1090489, _1090491))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1090489, _1090491), tc_prod(_1090489, _1090491)), hAPP(hAPP(c_Product__Type_OPair(_1090489, _1090491), _1090493), _1090495)), hAPP(hAPP(c_Product__Type_OPair(_1090489, _1090491), _1090497), _1090499))), c_Wellfounded_Olex__prod(_1090489, _1090491, _1090501, _1090503)))), 18298 ^ _775828 : [(18301 ^ _775828) ^ [] : [_1090493 = _1090497, hBOOL(hAPP(hAPP(c_member(tc_prod(_1090491, _1090491)), hAPP(hAPP(c_Product__Type_OPair(_1090491, _1090491), _1090495), _1090499)), _1090503))], (18299 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1090489, _1090489)), hAPP(hAPP(c_Product__Type_OPair(_1090489, _1090489), _1090493), _1090497)), _1090501))]]], (44307 ^ _775828) ^ [_1644686, _1644688, _1644690, _1644692, _1644694] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644686, tc_fun(_1644688, tc_HOL_Obool)), _1644690), hAPP(hAPP(c_COMBB(tc_fun(_1644688, tc_HOL_Obool), tc_fun(_1644688, tc_HOL_Obool), _1644686), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644688, tc_HOL_Obool)), _1644692)), _1644694)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644688, tc_HOL_Obool)), _1644692), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644686, tc_fun(_1644688, tc_HOL_Obool)), _1644690), _1644694)))], (34657 ^ _775828) ^ [_1422432, _1422434, _1422436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422432), _1422434)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422432), _1422436)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422432, tc_HOL_Obool)), _1422434), _1422436) = c_Orderings_Obot__class_Obot(tc_fun(_1422432, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1422432), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422432, tc_HOL_Obool)), _1422434), _1422436)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1422432), _1422434)), hAPP(c_Finite__Set_Ocard(_1422432), _1422436)))], (18877 ^ _775828) ^ [_1100552, _1100554] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1100552, _1100554) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1100552, _1100554)))], (33362 ^ _775828) ^ [_1394189, _1394191, _1394193, _1394195, _1394197] : [-(c_Map_Orestrict__map(_1394189, _1394191, _1394193, hAPP(hAPP(c_Set_Oinsert(_1394189), _1394195), _1394197)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394189, tc_Option_Ooption(_1394191)), c_Map_Orestrict__map(_1394189, _1394191, _1394193, _1394197)), _1394195), hAPP(_1394193, _1394195)))], (10912 ^ _775828) ^ [_954460, _954462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954460), hAPP(c_Nat_OSuc, _954462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954460), _954462))), -(_954460 = hAPP(c_Nat_OSuc, _954462))], (25066 ^ _775828) ^ [_1218111] : [-(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)), _1218111)) = _1218111)], (30275 ^ _775828) ^ [_1327863, _1327865, _1327867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1327863, _1327863), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1327863, _1327863, _1327863), _1327865), _1327867)), _1327865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1327863, _1327865)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1327863, _1327867)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1327863, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1327863, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1327863, tc_HOL_Obool), tc_fun(_1327863, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1327863, _1327865))))], (9825 ^ _775828) ^ [_934289, _934291, _934293, _934295, _934297] : [class_Rings_Olinordered__semiring__strict(_934289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934289), _934291), _934293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934289), _934295), _934297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934289), c_Groups_Ozero__class_Ozero(_934289)), _934291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934289), c_Groups_Ozero__class_Ozero(_934289)), _934295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934289), _934291), _934295)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934289), _934293), _934297))))], (47267 ^ _775828) ^ [_1718704, _1718706] : [-(hAPP(hAPP(c_List_Otake(_1718704), _1718706), c_List_Olist_ONil(_1718704)) = c_List_Olist_ONil(_1718704))], (37891 ^ _775828) ^ [_1493961, _1493963, _1493965, _1493967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1493961), _1493963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493961, tc_HOL_Obool)), _1493963), _1493965)), hBOOL(hAPP(_1493967, c_Orderings_Obot__class_Obot(tc_fun(_1493961, tc_HOL_Obool)))), 37906 ^ _775828 : [(37907 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493961), 37905 ^ [_1493961, _1493963, _1493965, _1493967])))], (37911 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1493961), 37904 ^ [_1493961, _1493963, _1493965, _1493967]), 37905 ^ [_1493961, _1493963, _1493965, _1493967]))], (37915 ^ _775828) ^ [] : [hBOOL(hAPP(_1493967, hAPP(hAPP(c_Set_Oinsert(_1493961), 37904 ^ [_1493961, _1493963, _1493965, _1493967]), 37905 ^ [_1493961, _1493963, _1493965, _1493967])))], (37913 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1493967, 37905 ^ [_1493961, _1493963, _1493965, _1493967])))], (37909 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493961), 37904 ^ [_1493961, _1493963, _1493965, _1493967]), _1493965)))]], -(hBOOL(hAPP(_1493967, _1493963)))], (36869 ^ _775828) ^ [_1468458, _1468460, _1468462] : [-(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), _1468458)), 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))), _1468460))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468462))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1468462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1468458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1468458), 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), _1468462), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1468460)))))], (50955 ^ _775828) ^ [_1801702, _1801704, _1801706, _1801708, _1801710] : [class_Groups_Omonoid__add(_1801702), 50961 ^ _775828 : [(50966 ^ _775828) ^ [] : [hAPP(_1801710, 50960 ^ [_1801702, _1801704, _1801706, _1801708, _1801710]) = c_Groups_Ozero__class_Ozero(_1801702)], (50964 ^ _775828) ^ [] : [hBOOL(hAPP(_1801708, 50960 ^ [_1801702, _1801704, _1801706, _1801708, _1801710]))], (50962 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801704), 50960 ^ [_1801702, _1801704, _1801706, _1801708, _1801710]), hAPP(c_List_Oset(_1801704), _1801706))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1801702), hAPP(hAPP(c_List_Omap(_1801704, _1801702), _1801710), hAPP(c_List_Ofilter(_1801704, _1801708), _1801706))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1801702), hAPP(hAPP(c_List_Omap(_1801704, _1801702), _1801710), _1801706)))], (47287 ^ _775828) ^ [_1719014, _1719016] : [-(hAPP(hAPP(c_List_Otake(_1719014), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1719016) = c_List_Olist_ONil(_1719014))], (39840 ^ _775828) ^ [_1538762, _1538764, _1538766, _1538768, _1538770, _1538772, _1538774, _1538776, _1538778, _1538780] : [c_Equiv__Relations_Ocongruent2(_1538762, _1538764, _1538766, _1538768, _1538770, _1538772), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538762, _1538762)), hAPP(hAPP(c_Product__Type_OPair(_1538762, _1538762), _1538774), _1538776)), _1538768)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538764, _1538764)), hAPP(hAPP(c_Product__Type_OPair(_1538764, _1538764), _1538778), _1538780)), _1538770)), -(hAPP(hAPP(_1538772, _1538774), _1538778) = hAPP(hAPP(_1538772, _1538776), _1538780))], (28667 ^ _775828) ^ [_1290825, _1290827, _1290829, _1290831] : [-(hAPP(c_Relation_ORange(_1290825, _1290827), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1290825, _1290827), tc_HOL_Obool)), _1290829), _1290831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290827, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1290825, _1290827), _1290829)), hAPP(c_Relation_ORange(_1290825, _1290827), _1290831)))], (19988 ^ _775828) ^ [_1119165, _1119167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119165)), -(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)))), _1119167)), 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)))), _1119165)) = 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, _1119167, _1119165))))], (24833 ^ _775828) ^ [_1212939, _1212941, _1212943, _1212945, _1212947] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212939, _1212941, _1212939, _1212943), hAPP(c_Product__Type_OPair(_1212941, _1212939), _1212945)), _1212947) = hAPP(_1212947, _1212945))], (14832 ^ _775828) ^ [_1024103, _1024105] : [-(_1024103 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024105), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024103), _1024105))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024103, _1024105)))], (23464 ^ _775828) ^ [_1185738, _1185740, _1185742] : [-(c_Nat_Onat_Onat__case(_1185738, _1185740, _1185742, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1185740)], (10768 ^ _775828) ^ [_951869, _951871, _951873, _951875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951869, tc_HOL_Obool)), _951871), _951873)), hBOOL(hAPP(hAPP(c_member(_951869), _951875), _951871)), -(hBOOL(hAPP(hAPP(c_member(_951869), _951875), _951873)))], (41899 ^ _775828) ^ [_1587732, _1587734] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1587732, _1587734, tc_prod(_1587732, _1587734)), c_Product__Type_OPair(_1587732, _1587734)) = c_Fun_Oid(tc_prod(_1587732, _1587734)))], (48565 ^ _775828) ^ [_1749968, _1749970, _1749972, _1749974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1749968), _1749970)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749972)), _1749974))), -(hAPP(hAPP(c_List_Otake(_1749972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1749968), _1749970)), _1749974) = hAPP(hAPP(c_List_Oappend(_1749972), hAPP(hAPP(c_List_Otake(_1749972), _1749968), _1749974)), hAPP(hAPP(c_List_Otake(_1749972), _1749970), hAPP(hAPP(c_List_Odrop(_1749972), _1749968), _1749974))))], (51390 ^ _775828) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (13310 ^ _775828) ^ [_996269, _996271, _996273, _996275] : [class_Divides_Osemiring__div(_996269), -(c_Divides_Odiv__class_Omod(_996269, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996269), _996271), _996273), _996275) = c_Divides_Odiv__class_Omod(_996269, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996269), _996271), c_Divides_Odiv__class_Omod(_996269, _996273, _996275)), _996275))], (45710 ^ _775828) ^ [_1677703, _1677705, _1677707, _1677709, _1677711] : [hAPP(hAPP(c_Option_Omap(_1677703, _1677705), _1677707), _1677709) = hAPP(c_Option_Ooption_OSome(_1677705), _1677711), 45714 ^ _775828 : [(45717 ^ _775828) ^ [] : [-(hAPP(_1677707, 45713 ^ [_1677703, _1677705, _1677707, _1677709, _1677711]) = _1677711)], (45715 ^ _775828) ^ [] : [-(_1677709 = hAPP(c_Option_Ooption_OSome(_1677703), 45713 ^ [_1677703, _1677705, _1677707, _1677709, _1677711]))]]], (23070 ^ _775828) ^ [_1177459, _1177461, _1177463, _1177465] : [class_Fields_Olinordered__field(_1177459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177459), c_Groups_Ozero__class_Ozero(_1177459)), _1177461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177459), _1177463), _1177461)), _1177465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177459), _1177463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177459), _1177465), _1177461))))], (6011 ^ _775828) ^ [_871374, _871376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _871374)), _871376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871374), _871376)))], (31651 ^ _775828) ^ [_1358789, _1358791, _1358793, _1358795, _1358797] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1358789, _1358789)), hAPP(hAPP(c_Product__Type_OPair(_1358789, _1358789), _1358791), _1358793)), c_Transitive__Closure_Ortrancl(_1358789, _1358795))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1358789, _1358789)), hAPP(hAPP(c_Product__Type_OPair(_1358789, _1358789), _1358793), _1358797)), _1358795)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1358789, _1358789)), hAPP(hAPP(c_Product__Type_OPair(_1358789, _1358789), _1358791), _1358797)), c_Transitive__Closure_Ortrancl(_1358789, _1358795))))], (29090 ^ _775828) ^ [_1302490, _1302492, _1302494, _1302496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302490, _1302490)), hAPP(hAPP(c_Product__Type_OPair(_1302490, _1302490), _1302492), _1302494)), c_Transitive__Closure_Otrancl(_1302490, hAPP(c_Relation_Oconverse(_1302490, _1302490), _1302496)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302490, _1302490)), hAPP(hAPP(c_Product__Type_OPair(_1302490, _1302490), _1302492), _1302494)), hAPP(c_Relation_Oconverse(_1302490, _1302490), c_Transitive__Closure_Otrancl(_1302490, _1302496)))))], (51274 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (22818 ^ _775828) ^ [_1172743, _1172745, _1172747, _1172749, _1172751] : [class_Fields_Olinordered__field(_1172743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172743), c_Groups_Ozero__class_Ozero(_1172743)), _1172745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172743), _1172745), _1172747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172743), c_Groups_Ozero__class_Ozero(_1172743)), _1172749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172743), _1172749), _1172751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172743), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172743), _1172745), _1172751)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172743), _1172747), _1172749))))], (31909 ^ _775828) ^ [_1365768, _1365770] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1365768, _1365770))))], (26753 ^ _775828) ^ [_1248647, _1248649] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1248647, _1248647)), hAPP(hAPP(c_Product__Type_OPair(_1248647, _1248647), 26754 ^ [_1248647, _1248649]), 26754 ^ [_1248647, _1248649])), _1248649))), -(c_Relation_Oirrefl(_1248647, _1248649))], (33949 ^ _775828) ^ [_1407382, _1407384, _1407386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407382, tc_HOL_Obool)), _1407384), _1407386)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407382, tc_HOL_Obool)), _1407384), _1407386) = _1407384)], (29969 ^ _775828) ^ [] : [-(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))))], (5678 ^ _775828) ^ [_866161, _866163, _866165, _866167] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_866161)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866161), _866163), _866165), _866167)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37870 ^ _775828) ^ [_1493510, _1493512, _1493514, _1493516, _1493518] : [class_Groups_Ocomm__monoid__add(_1493510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493512), _1493514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493512, tc_HOL_Obool)), _1493516), _1493514)), 37884 ^ _775828 : [(37887 ^ _775828) ^ [] : [hAPP(_1493518, 37883 ^ [_1493510, _1493512, _1493514, _1493516, _1493518]) = c_Groups_Ozero__class_Ozero(_1493510)], (37885 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493512), 37883 ^ [_1493510, _1493512, _1493514, _1493516, _1493518]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493512, tc_HOL_Obool)), _1493514), _1493516))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493512, _1493510), _1493518), _1493514) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493512, _1493510), _1493518), _1493516))], (44405 ^ _775828) ^ [_1647447, _1647449, _1647451, _1647453, _1647455, _1647457] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647447, tc_fun(_1647449, tc_HOL_Obool)), _1647451), hAPP(hAPP(c_COMBB(_1647453, tc_fun(_1647449, tc_HOL_Obool), _1647447), _1647455), _1647457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647453, tc_fun(_1647449, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1647447, _1647453, _1647457), _1647451)), _1647455))], (44387 ^ _775828) ^ [_1646607, _1646609, _1646611, _1646613, _1646615] : [-(hAPP(c_Relation_Oconverse(_1646607, _1646609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646611, tc_fun(tc_prod(_1646607, _1646609), tc_HOL_Obool)), _1646613), _1646615)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646611, tc_fun(tc_prod(_1646609, _1646607), tc_HOL_Obool)), _1646613), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1646607, _1646609), tc_HOL_Obool), tc_fun(tc_prod(_1646609, _1646607), tc_HOL_Obool), _1646611), c_Relation_Oconverse(_1646607, _1646609)), _1646615)))], (44641 ^ _775828) ^ [_1653362, _1653364] : [class_Complete__Lattice_Ocomplete__lattice(_1653362), -(c_Complete__Lattice_OSup__class_OSup(_1653362, _1653364) = c_Complete__Lattice_OInf__class_OInf(_1653362, hAPP(c_Set_OCollect(_1653362), hAPP(hAPP(c_COMBB(tc_fun(_1653362, tc_HOL_Obool), tc_HOL_Obool, _1653362), c_HOL_OAll(_1653362)), hAPP(hAPP(c_COMBB(tc_fun(_1653362, tc_HOL_Obool), tc_fun(_1653362, tc_HOL_Obool), _1653362), hAPP(c_COMBS(_1653362, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1653362), c_fimplies), hAPP(hAPP(c_COMBC(_1653362, tc_fun(_1653362, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653362)), _1653364)))), hAPP(c_COMBC(_1653362, _1653362, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1653362)))))))], (44411 ^ _775828) ^ [_1647686, _1647688, _1647690, _1647692, _1647694, _1647696] : [-(hAPP(c_Set_Ovimage(_1647686, _1647688, _1647690), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647692, tc_fun(_1647688, tc_HOL_Obool)), _1647694), _1647696)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647692, tc_fun(_1647686, tc_HOL_Obool)), _1647694), hAPP(hAPP(c_COMBB(tc_fun(_1647688, tc_HOL_Obool), tc_fun(_1647686, tc_HOL_Obool), _1647692), c_Set_Ovimage(_1647686, _1647688, _1647690)), _1647696)))], (46267 ^ _775828) ^ [_1691295, _1691297, _1691299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1691295), _1691297)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1691295)), hAPP(c_Set_OCollect(tc_List_Olist(_1691295)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1691295), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1691295)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691295), tc_fun(_1691295, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1691295, tc_HOL_Obool), tc_fun(tc_fun(_1691295, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1691295)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1691295, tc_HOL_Obool))), c_List_Oset(_1691295))), _1691297))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691295), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1691295)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1691295)))), _1691299))))))], (24134 ^ _775828) ^ [_1198432, _1198434, _1198436] : [class_Orderings_Olinorder(_1198432), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198432), _1198434), _1198436) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198432), _1198436), _1198434))], (20192 ^ _775828) ^ [_1122716, _1122718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1122716)), c_Int_OBit0(_1122718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122716), _1122718)))], (5979 ^ _775828) ^ [_870994] : [-(_870994 = 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)), _870994)))], (27519 ^ _775828) ^ [_1264819, _1264821, _1264823] : [c_Relation_Ototal__on(_1264819, _1264821, _1264823), -(c_Relation_Ototal__on(_1264819, _1264821, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1264819, _1264819), tc_HOL_Obool)), _1264823), c_Relation_OId(_1264819))))], (38932 ^ _775828) ^ [_1516982, _1516984, _1516986, _1516988, _1516990] : [c_Fun_Oinj__on(_1516982, _1516984, _1516986, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1516982, tc_HOL_Obool)), _1516988), _1516990)), 38935 ^ _775828 : [(38942 ^ _775828) ^ [] : [_1516988 = _1516990, -(hAPP(c_Set_Oimage(_1516982, _1516984, _1516986), _1516988) = hAPP(c_Set_Oimage(_1516982, _1516984, _1516986), _1516990))], (38936 ^ _775828) ^ [] : [hAPP(c_Set_Oimage(_1516982, _1516984, _1516986), _1516988) = hAPP(c_Set_Oimage(_1516982, _1516984, _1516986), _1516990), -(_1516988 = _1516990)]]], (7403 ^ _775828) ^ [_893924, _893926, _893928] : [hBOOL(hAPP(hAPP(c_member(_893924), _893926), c_Option_Oset(_893924, _893928))), -(_893928 = hAPP(c_Option_Ooption_OSome(_893924), _893926))], (20034 ^ _775828) ^ [_1120015, _1120017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120015), _1120017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1120015)), c_Int_OBit0(_1120017))))], (28625 ^ _775828) ^ [_1289950, _1289952, _1289954, _1289956] : [class_Lattices_Osemilattice__sup(_1289950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289950), _1289952), _1289954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289950), _1289952), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289950), _1289956), _1289954))))], (31705 ^ _775828) ^ [_1360163, _1360165, _1360167, _1360169] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360163, _1360163)), hAPP(hAPP(c_Product__Type_OPair(_1360163, _1360163), _1360165), _1360167)), c_Transitive__Closure_Ortrancl(_1360163, _1360169)))), 31706 ^ _775828 : [(31709 ^ _775828) ^ [] : [-(_1360165 = _1360167), hBOOL(hAPP(hAPP(c_member(tc_prod(_1360163, _1360163)), hAPP(hAPP(c_Product__Type_OPair(_1360163, _1360163), _1360165), _1360167)), c_Transitive__Closure_Otrancl(_1360163, _1360169)))], (31707 ^ _775828) ^ [] : [_1360165 = _1360167]]], (45482 ^ _775828) ^ [_1672029, _1672031, _1672033, _1672035] : [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)), _1672029), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1672031), _1672033)))), -(hBOOL(hAPP(hAPP(hAPP(_1672035, _1672029), _1672031), _1672033))), 45490 ^ _775828 : [(45493 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 45488 ^ [_1672029, _1672031, _1672033, _1672035]), 45489 ^ [_1672029, _1672031, _1672033, _1672035]))), hAPP(45487 ^ [_1672029, _1672031, _1672033, _1672035], 45489 ^ [_1672029, _1672031, _1672033, _1672035]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1672035, 45487 ^ [_1672029, _1672031, _1672033, _1672035]), 45488 ^ [_1672029, _1672031, _1672033, _1672035]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45489 ^ [_1672029, _1672031, _1672033, _1672035]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45503 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1672035, 45487 ^ [_1672029, _1672031, _1672033, _1672035]), 45488 ^ [_1672029, _1672031, _1672033, _1672035]), 45489 ^ [_1672029, _1672031, _1672033, _1672035]))], (45491 ^ _775828) ^ [] : [-(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)), 45487 ^ [_1672029, _1672031, _1672033, _1672035]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 45488 ^ [_1672029, _1672031, _1672033, _1672035]), 45489 ^ [_1672029, _1672031, _1672033, _1672035])))))]]], (37842 ^ _775828) ^ [_1492826, _1492828, _1492830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1492826, 37843 ^ [_1492826, _1492828, _1492830])), hAPP(_1492828, 37843 ^ [_1492826, _1492828, _1492830]))), -(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), _1492828), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1492830))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1492826), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1492830))) = 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)), _1492828)), _1492826)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1492830)))], (5234 ^ _775828) ^ [_855870, _855872] : [_855872 = _855870, -(c_Set_OPow(_855872) = c_Set_OPow(_855870))], (25168 ^ _775828) ^ [_1219991, _1219993] : [c_Nat__Transfer_Ois__nat(_1219991), c_Nat__Transfer_Onat__set(_1219993), 25175 ^ _775828 : [(25182 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1219991)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219993))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1219991), _1219993)))], (25176 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1219991), _1219993)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1219991)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1219993))))]]], (39072 ^ _775828) ^ [_1519715, _1519717, _1519719, _1519721, _1519723, _1519725] : [c_Fun_Oinj__on(_1519715, _1519717, _1519719, _1519721), -(hBOOL(hAPP(hAPP(c_member(_1519717), _1519723), hAPP(c_Set_Oimage(_1519715, _1519717, _1519719), _1519721)))), -(c_Fun_Oinj__on(_1519715, _1519717, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1519715, _1519717), _1519719), _1519725), _1519723), _1519721))], (23476 ^ _775828) ^ [_1186103, _1186105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1186103)), _1186105)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186103), _1186105)))], (12111 ^ _775828) ^ [] : [-(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))], (26882 ^ _775828) ^ [_1250774, _1250776] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250774), _1250776)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250776), _1250774)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1250774) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1250776))], (51490 ^ _775828) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (25325 ^ _775828) ^ [_1222498, _1222500, _1222502, _1222504, _1222506] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1222498, _1222500, tc_HOL_Obool, _1222502), _1222504), _1222506)), -(hBOOL(hAPP(_1222502, hAPP(hAPP(c_Product__Type_OPair(_1222498, _1222500), _1222504), _1222506))))], (27495 ^ _775828) ^ [_1264317, _1264319, _1264321, _1264323] : [hBOOL(hAPP(hAPP(_1264321, _1264323), _1264319)), -(hBOOL(hAPP(hAPP(c_member(_1264317), _1264319), c_SetInterval_Oord_OgreaterThan(_1264317, _1264321, _1264323))))], (19128 ^ _775828) ^ [_1105133, _1105135] : [class_Rings_Osemiring__1(_1105133), 19131 ^ _775828 : [(19138 ^ _775828) ^ [] : [_1105135 = c_Groups_Ozero__class_Ozero(_1105133), -(c_Int_Oiszero(_1105133, _1105135))], (19132 ^ _775828) ^ [] : [c_Int_Oiszero(_1105133, _1105135), -(_1105135 = c_Groups_Ozero__class_Ozero(_1105133))]]], (50595 ^ _775828) ^ [_1794423, _1794425] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1794423), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1794423))), _1794425))), -(c_List_Otranspose(_1794423, c_List_Otranspose(_1794423, _1794425)) = c_List_OtakeWhile(tc_List_Olist(_1794423), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1794423)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1794423), tc_List_Olist(_1794423), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1794423))), _1794425))], (6318 ^ _775828) ^ [_876281, _876283, _876285] : [class_Nat_Osemiring__char__0(_876281), 6321 ^ _775828 : [(6328 ^ _775828) ^ [] : [_876283 = _876285, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876281), _876283) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876281), _876285))], (6322 ^ _775828) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876281), _876283) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876281), _876285), -(_876283 = _876285)]]], (2074 ^ _775828) ^ [_806096, _806098, _806100, _806102] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_806102, _806098) = c_Code__Numeral_Odiv__mod__code__numeral(_806100, _806096)), _806102 = _806100, _806098 = _806096], (48014 ^ _775828) ^ [_1735251, _1735253, _1735255] : [_1735251 = hAPP(hAPP(c_List_Oappend(_1735253), _1735251), _1735255), -(_1735255 = c_List_Olist_ONil(_1735253))], (50788 ^ _775828) ^ [_1798190, _1798192] : [c_List_Oremdups(_1798190, _1798192) = _1798192, -(hBOOL(hAPP(c_List_Odistinct(_1798190), _1798192)))], (42796 ^ _775828) ^ [_1609248, _1609250, _1609252, _1609254] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1609248, _1609250), tc_fun(_1609248, _1609250)), _1609252), c_Fun_Ocomp(_1609250, _1609250, _1609248, _1609254)) = c_Fun_Ocomp(_1609250, _1609250, _1609248, hAPP(hAPP(c_Nat_Ocompow(_1609250, _1609250), _1609252), _1609254)))], (28689 ^ _775828) ^ [_1291472, _1291474, _1291476] : [c_Wellfounded_Oacyclic(_1291472, _1291474), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1291472, _1291472), tc_HOL_Obool)), _1291476), _1291474)), -(c_Wellfounded_Oacyclic(_1291472, _1291476))], (24441 ^ _775828) ^ [_1205052, _1205054] : [class_Orderings_Olinorder(_1205052), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205052), _1205054), _1205054) = _1205054)], (42962 ^ _775828) ^ [_1613230, _1613232, _1613234, _1613236, _1613238, _1613240] : [c_Finite__Set_Ofolding(_1613230, _1613232, _1613234, _1613236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613230), _1613238)), hBOOL(hAPP(hAPP(c_member(_1613230), _1613240), _1613238)), -(hAPP(_1613236, _1613238) = hAPP(c_Fun_Ocomp(_1613232, _1613232, _1613232, hAPP(_1613236, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1613230, tc_HOL_Obool)), _1613238), hAPP(hAPP(c_Set_Oinsert(_1613230), _1613240), c_Orderings_Obot__class_Obot(tc_fun(_1613230, tc_HOL_Obool)))))), hAPP(_1613234, _1613240)))], (22408 ^ _775828) ^ [_1165590, _1165592, _1165594] : [class_Fields_Ofield__inverse__zero(_1165590), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1165590), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165590), _1165592), _1165594)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165590), _1165592), hAPP(c_Groups_Ouminus__class_Ouminus(_1165590), _1165594)))], (51160 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51186 ^ _775828) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (34639 ^ _775828) ^ [_1422037, _1422039, _1422041, _1422043, _1422045] : [class_Groups_Ocomm__monoid__mult(_1422037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422039), _1422041)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422039), _1422043)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422039, tc_HOL_Obool)), _1422041), _1422043) = c_Orderings_Obot__class_Obot(tc_fun(_1422039, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422039, _1422037), _1422045), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422039, tc_HOL_Obool)), _1422041), _1422043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422037), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422039, _1422037), _1422045), _1422041)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422039, _1422037), _1422045), _1422043)))], (20306 ^ _775828) ^ [_1124697, _1124699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124697), _1124699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1124697)), c_Int_OBit1(_1124699))))], (44868 ^ _775828) ^ [_1658506, _1658508, _1658510] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658506, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1658506, tc_HOL_Obool), tc_HOL_Obool)), _1658508), _1658510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658506, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658506, tc_HOL_Obool), _1658508)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658506, tc_HOL_Obool), _1658510)))], (21582 ^ _775828) ^ [_1149511, _1149513] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149511), _1149513), hAPP(c_Int_Onumber__class_Onumber__of(_1149511), c_Int_OBit1(c_Int_OPls))) = _1149513), class_Fields_Ofield(_1149511), class_Int_Onumber__ring(_1149511)], (47517 ^ _775828) ^ [_1723635, _1723637, _1723639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723635), tc_List_Olist(_1723635))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723635), tc_List_Olist(_1723635)), _1723637), c_List_Olist_ONil(_1723635))), c_List_Olexord(_1723635, _1723639)))], (48725 ^ _775828) ^ [_1753178, _1753180, _1753182] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1753178, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753180)), _1753182)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1753180, _1753178), _1753182) = _1753182)], (20072 ^ _775828) ^ [_1120673] : [c_Int_OPls = _1120673, -(c_Int_OPls = c_Int_OBit0(_1120673))], (25469 ^ _775828) ^ [_1225161, _1225163] : [-(hAPP(c_New__DSequence_Opos__empty(_1225161), _1225163) = c_Lazy__Sequence_Oempty(_1225161))], (43162 ^ _775828) ^ [_1617886, _1617888, _1617890, _1617892] : [-(c_Random__Sequence_Omap(_1617886, _1617888, _1617890, _1617892) = c_Random__Sequence_Obind(_1617886, _1617888, _1617892, hAPP(c_Fun_Ocomp(_1617888, 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(_1617888)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1617886, c_Random__Sequence_Osingle(_1617888)), _1617890)))], (26355 ^ _775828) ^ [_1241108, _1241110, _1241112, _1241114] : [class_Divides_Osemiring__div(_1241108), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241108), _1241110), _1241112)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241108), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241108), _1241112), _1241110)), _1241114) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241108), _1241112), _1241114)), _1241110))], (47165 ^ _775828) ^ [_1716207, _1716209, _1716211, _1716213] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716207), tc_List_Olist(_1716207))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716207), tc_List_Olist(_1716207)), _1716209), _1716211)), c_List_Olexord(_1716207, _1716213)))), 47166 ^ _775828 : [(47173 ^ _775828) ^ [_1716514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1716514), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716207)), _1716209)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716207)), _1716211)))), hAPP(hAPP(c_List_Otake(_1716207), _1716514), _1716209) = hAPP(hAPP(c_List_Otake(_1716207), _1716514), _1716211), hBOOL(hAPP(hAPP(c_member(tc_prod(_1716207, _1716207)), hAPP(hAPP(c_Product__Type_OPair(_1716207, _1716207), hAPP(hAPP(c_List_Onth(_1716207), _1716209), _1716514)), hAPP(hAPP(c_List_Onth(_1716207), _1716211), _1716514))), _1716213))], (47167 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716207)), _1716209)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716207)), _1716211))), hAPP(hAPP(c_List_Otake(_1716207), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716207)), _1716209)), _1716211) = _1716209]]], (2110 ^ _775828) ^ [_806628, _806630, _806632, _806634] : [-(c_Groups_Osgn__class_Osgn(_806634, _806630) = c_Groups_Osgn__class_Osgn(_806632, _806628)), _806634 = _806632, _806630 = _806628], (32575 ^ _775828) ^ [_1377890, _1377892, _1377894] : [class_Lattices_Olattice(_1377890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377890), _1377892)), -(_1377892 = c_Orderings_Obot__class_Obot(tc_fun(_1377890, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377890), _1377894)), -(_1377894 = c_Orderings_Obot__class_Obot(tc_fun(_1377890, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1377890, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377890, tc_HOL_Obool)), _1377892), _1377894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1377890), c_Big__Operators_Olattice__class_OSup__fin(_1377890, _1377892)), c_Big__Operators_Olattice__class_OSup__fin(_1377890, _1377894)))], (40359 ^ _775828) ^ [_1549623, _1549625, _1549627, _1549629] : [c_Fun_Oinj__on(_1549623, _1549625, _1549627, c_Orderings_Otop__class_Otop(tc_fun(_1549623, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1549623, tc_fun(_1549629, _1549625), hAPP(hAPP(c_COMBB(_1549625, tc_fun(_1549629, _1549625), _1549623), c_COMBK(_1549625, _1549629)), _1549627), c_Orderings_Otop__class_Otop(tc_fun(_1549623, tc_HOL_Obool))))], (40535 ^ _775828) ^ [] : [-(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))))], (18865 ^ _775828) ^ [_1100330, _1100332, _1100334, _1100336] : [hAPP(c_Product__Type_Ofst(_1100330, _1100332), _1100334) = hAPP(c_Product__Type_Ofst(_1100330, _1100332), _1100336), hAPP(c_Product__Type_Osnd(_1100330, _1100332), _1100334) = hAPP(c_Product__Type_Osnd(_1100330, _1100332), _1100336), -(_1100334 = _1100336)], (40572 ^ _775828) ^ [] : [-(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))], (30447 ^ _775828) ^ [_1332277, _1332279, _1332281] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332277), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332277, tc_HOL_Obool)), _1332279), _1332281)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332277), _1332279)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332277), _1332281))], (42928 ^ _775828) ^ [_1612314, _1612316, _1612318, _1612320, _1612322, _1612324, _1612326] : [c_Hoare__Mirabelle_Ohoare__derivs(_1612314, _1612316, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1612314)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1612314), c_Hoare__Mirabelle_Opeek__and(_1612314, _1612318, _1612320)), _1612322), _1612324)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1612314), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1612314, _1612316, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1612314)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1612314), c_Hoare__Mirabelle_Opeek__and(_1612314, _1612318, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1612320))), _1612326), _1612324)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1612314), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1612314, _1612316, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1612314)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1612314), _1612318), c_Com_Ocom_OCond(_1612320, _1612322, _1612326)), _1612324)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1612314), tc_HOL_Obool)))))], (5262 ^ _775828) ^ [_856274, _856276] : [_856276 = _856274, -(c_List_Oset(_856276) = c_List_Oset(_856274))], (47289 ^ _775828) ^ [_1719049, _1719051, _1719053, _1719055] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719049)), hAPP(hAPP(c_List_Olist__update(_1719049, _1719051), _1719053), _1719055)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719049)), _1719051))], (51290 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (56 ^ _775828) ^ [_776634, _776636, _776638, _776640] : [-(c_Int_Oiszero(_776638, _776634)), c_Int_Oiszero(_776640, _776636), _776640 = _776638, _776636 = _776634], (31717 ^ _775828) ^ [_1360429, _1360431, _1360433, _1360435, _1360437] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1360429, _1360429)), hAPP(hAPP(c_Product__Type_OPair(_1360429, _1360429), _1360431), _1360433)), _1360435)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1360429, _1360429)), hAPP(hAPP(c_Product__Type_OPair(_1360429, _1360429), _1360433), _1360437)), c_Transitive__Closure_Ortrancl(_1360429, _1360435))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360429, _1360429)), hAPP(hAPP(c_Product__Type_OPair(_1360429, _1360429), _1360431), _1360437)), c_Transitive__Closure_Otrancl(_1360429, _1360435))))], (11787 ^ _775828) ^ [] : [-(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))))], (7733 ^ _775828) ^ [_899227, _899229] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _899227)), _899229) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _899227), _899229)))], (16362 ^ _775828) ^ [_1053891, _1053893, _1053895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053891)), 16368 ^ _775828 : [(16371 ^ _775828) ^ [] : [hBOOL(hAPP(_1053893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16367 ^ [_1053891, _1053893, _1053895]), _1053891)))], (16369 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1053893, 16367 ^ [_1053891, _1053893, _1053895])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053895)), 16376 ^ _775828 : [(16377 ^ _775828) ^ [_1054180] : [hBOOL(hAPP(_1053893, _1054180)), -(hBOOL(hAPP(_1053893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1054180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053895), _1053891)))))]]], (45359 ^ _775828) ^ [_1669304, _1669306, _1669308, _1669310, _1669312] : [-(hAPP(c_Map_Omap__add(_1669304, _1669306, _1669308, _1669310), _1669312) = c_Option_Ooption_ONone(_1669306)), hAPP(_1669310, _1669312) = c_Option_Ooption_ONone(_1669306), hAPP(_1669308, _1669312) = c_Option_Ooption_ONone(_1669306)], (8355 ^ _775828) ^ [_910012, _910014, _910016, _910018] : [class_Orderings_Opreorder(_910012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910012), _910014), _910016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910012), _910016), _910018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910012), _910014), _910018)))], (38424 ^ _775828) ^ [_1505846, _1505848, _1505850] : [c_Map_Odom(_1505846, _1505848, _1505850) = c_Orderings_Obot__class_Obot(tc_fun(_1505846, tc_HOL_Obool)), -(_1505850 = hAPP(c_COMBK(tc_Option_Ooption(_1505848), _1505846), c_Option_Ooption_ONone(_1505848)))], (35267 ^ _775828) ^ [_1436997, _1436999, _1437001, _1437003, _1437005] : [class_Groups_Ocomm__monoid__mult(_1436997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436999), _1437001)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436999), _1437003)), 35281 ^ _775828 : [(35284 ^ _775828) ^ [] : [hAPP(_1437005, 35280 ^ [_1436997, _1436999, _1437001, _1437003, _1437005]) = c_Groups_Oone__class_Oone(_1436997)], (35282 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1436999), 35280 ^ [_1436997, _1436999, _1437001, _1437003, _1437005]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436999, tc_HOL_Obool)), _1437001), _1437003))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436997, _1436999, c_Groups_Otimes__class_Otimes(_1436997)), _1437005), c_Groups_Oone__class_Oone(_1436997)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436999, tc_HOL_Obool)), _1437001), _1437003)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436997), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436997, _1436999, c_Groups_Otimes__class_Otimes(_1436997)), _1437005), c_Groups_Oone__class_Oone(_1436997)), _1437001)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436997, _1436999, c_Groups_Otimes__class_Otimes(_1436997)), _1437005), c_Groups_Oone__class_Oone(_1436997)), _1437003)))], (6596 ^ _775828) ^ [_880707, _880709, _880711] : [class_Orderings_Oorder(_880707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880707), _880709), _880711)), _880709 = _880711], (26715 ^ _775828) ^ [_1248022, _1248024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248022)), 26718 ^ _775828 : [(26725 ^ _775828) ^ [] : [_1248024 = 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), _1248024), _1248022)), _1248022)))], (26719 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248024), _1248022)), _1248022)), -(_1248024 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (51156 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (18996 ^ _775828) ^ [_1102798, _1102800, _1102802, _1102804, _1102806] : [hAPP(c_Product__Type_Osnd(_1102798, _1102800), hAPP(hAPP(c_Product__Type_OPair(_1102798, _1102800), _1102802), _1102804)) = _1102806, -(_1102804 = _1102806)], (21602 ^ _775828) ^ [_1149813, _1149815] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149813), _1149815), hAPP(c_Int_Onumber__class_Onumber__of(_1149813), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1149813), _1149815)), class_Fields_Ofield__inverse__zero(_1149813), class_Int_Onumber__ring(_1149813)], (8069 ^ _775828) ^ [_905472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _905472), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_905472 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8072 ^ [_905472]))))], (2874 ^ _775828) ^ [_818922, _818924, _818926, _818928, _818930, _818932, _818934, _818936] : [-(c_New__DSequence_Oneg__bind(_818936, _818932, _818928, _818924) = c_New__DSequence_Oneg__bind(_818934, _818930, _818926, _818922)), _818936 = _818934, _818932 = _818930, _818928 = _818926, _818924 = _818922], (22482 ^ _775828) ^ [_1166986, _1166988, _1166990] : [class_Fields_Olinordered__field__inverse__zero(_1166986), 22485 ^ _775828 : [(22500 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166986), _1166988), _1166990)))), 22501 ^ _775828 : [(22508 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), _1166988), c_Groups_Ozero__class_Ozero(_1166986))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), _1166990), c_Groups_Ozero__class_Ozero(_1166986)))], (22502 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), _1166988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), _1166990))]]], (22486 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166986), _1166988), _1166990))), 22491 ^ _775828 : [(22494 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), _1166990)))], (22492 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), c_Groups_Ozero__class_Ozero(_1166986)), _1166988)))]], 22495 ^ _775828 : [(22498 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), _1166990), c_Groups_Ozero__class_Ozero(_1166986))))], (22496 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166986), _1166988), c_Groups_Ozero__class_Ozero(_1166986))))]]]]], (35829 ^ _775828) ^ [_1448660, _1448662] : [35831 ^ _775828 : [(35834 ^ _775828) ^ [] : [hBOOL(hAPP(_1448662, 35830 ^ [_1448660, _1448662]))], (35832 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35830 ^ [_1448660, _1448662]), _1448660)))]], 35835 ^ _775828 : [(35836 ^ _775828) ^ [_1448811] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1448811), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448660))), -(hBOOL(hAPP(_1448662, _1448811)))]]], (21396 ^ _775828) ^ [_1146412, _1146414, _1146416, _1146418] : [class_Fields_Ofield__inverse__zero(_1146412), class_Int_Onumber(_1146412), 21403 ^ _775828 : [(21404 ^ _775828) ^ [] : [_1146414 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146412), _1146416), hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418)), 21407 ^ _775828 : [(21414 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418) = c_Groups_Ozero__class_Ozero(_1146412), -(_1146414 = c_Groups_Ozero__class_Ozero(_1146412))], (21408 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418) = c_Groups_Ozero__class_Ozero(_1146412)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146412), _1146414), hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418)) = _1146416)]]], (21420 ^ _775828) ^ [] : [-(_1146414 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146412), _1146416), hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418))), 21423 ^ _775828 : [(21426 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146412), _1146414), hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418)) = _1146416], (21424 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418) = c_Groups_Ozero__class_Ozero(_1146412)]], 21427 ^ _775828 : [(21430 ^ _775828) ^ [] : [_1146414 = c_Groups_Ozero__class_Ozero(_1146412)], (21428 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1146412), _1146418) = c_Groups_Ozero__class_Ozero(_1146412))]]]]], (17751 ^ _775828) ^ [_1079887] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079887))), -(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), _1079887)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5835 ^ _775828) ^ [_868771, _868773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _868771), _868773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _868771)), hAPP(c_Nat_OSuc, _868773))))], (40031 ^ _775828) ^ [_1543431, _1543433, _1543435, _1543437, _1543439] : [c_Fun_Oinj__on(_1543431, _1543433, _1543435, c_Orderings_Otop__class_Otop(tc_fun(_1543431, tc_HOL_Obool))), hAPP(_1543435, _1543437) = hAPP(_1543435, _1543439), -(_1543437 = _1543439)], (3088 ^ _775828) ^ [_822327, _822329, _822331, _822333] : [-(c_Option_Oset(_822333, _822329) = c_Option_Oset(_822331, _822327)), _822333 = _822331, _822329 = _822327], (29947 ^ _775828) ^ [_1321479, _1321481] : [-(c_Set_Othe__elem(_1321479, _1321481) = c_HOL_OThe(_1321479, hAPP(hAPP(c_COMBB(tc_fun(_1321479, tc_HOL_Obool), tc_HOL_Obool, _1321479), hAPP(c_fequal, _1321481)), hAPP(hAPP(c_COMBC(_1321479, tc_fun(_1321479, tc_HOL_Obool), tc_fun(_1321479, tc_HOL_Obool)), c_Set_Oinsert(_1321479)), c_Orderings_Obot__class_Obot(tc_fun(_1321479, tc_HOL_Obool))))))], (31597 ^ _775828) ^ [_1357496, _1357498, _1357500] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1357496, _1357496)), hAPP(hAPP(c_Product__Type_OPair(_1357496, _1357496), _1357498), _1357498)), c_Transitive__Closure_Ortrancl(_1357496, _1357500))))], (6566 ^ _775828) ^ [_880241, _880243, _880245] : [class_Orderings_Oorder(_880241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880241), _880243), _880245)), _880243 = _880245], (18655 ^ _775828) ^ [_1096374, _1096376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096374)), 18658 ^ _775828 : [(18665 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096376))), 18668 ^ _775828 : [(18675 ^ _775828) ^ [] : [-(_1096374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1096374, _1096376) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096374), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096376))))], (18669 ^ _775828) ^ [] : [_1096374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1096374, _1096376) = 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)))]]], (18659 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096376)), -(c_Divides_Odivmod__int(_1096374, _1096376) = c_Divides_OposDivAlg(_1096374, _1096376))]]], (22190 ^ _775828) ^ [_1161496, _1161498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161496), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161498)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161496)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161498))], (14546 ^ _775828) ^ [_1019409, _1019411, _1019413, _1019415] : [class_Divides_Osemiring__div(_1019409), -(_1019411 = c_Groups_Ozero__class_Ozero(_1019409)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019409), _1019413), _1019411)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019409), _1019415), _1019411)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019409), _1019413), _1019415))], (30309 ^ _775828) ^ [_1328880, _1328882, _1328884, _1328886] : [c_Wellfounded_Omax__extp(_1328880, hAPP(hAPP(c_COMBC(_1328880, tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_fun(_1328880, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1328880, tc_fun(tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_fun(_1328880, tc_HOL_Obool)), _1328880), c_COMBC(_1328880, tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1328880, tc_prod(_1328880, _1328880)), tc_fun(_1328880, tc_fun(tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_HOL_Obool)), _1328880), hAPP(c_COMBB(tc_prod(_1328880, _1328880), tc_fun(tc_fun(tc_prod(_1328880, _1328880), tc_HOL_Obool), tc_HOL_Obool), _1328880), c_member(tc_prod(_1328880, _1328880)))), c_Product__Type_OPair(_1328880, _1328880)))), _1328882), _1328884, _1328886), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1328880, tc_HOL_Obool), tc_fun(_1328880, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1328880, tc_HOL_Obool), tc_fun(_1328880, tc_HOL_Obool)), _1328884), _1328886)), c_Wellfounded_Omax__ext(_1328880, _1328882))))], (10464 ^ _775828) ^ [_946192, _946194, _946196] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_946192), 10467 ^ _775828 : [(10474 ^ _775828) ^ [] : [_946196 = c_Groups_Ozero__class_Ozero(_946192), -(_946194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946192), _946194), _946196))], (10468 ^ _775828) ^ [] : [_946194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946192), _946194), _946196), -(_946196 = c_Groups_Ozero__class_Ozero(_946192))]]], (51446 ^ _775828) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (14996 ^ _775828) ^ [_1027237, _1027239] : [-(_1027237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14999 ^ _775828 : [(15006 ^ _775828) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1027239, _1027237) = 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), _1027239)), _1027237) = 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), _1027239), _1027237))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15000 ^ _775828) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1027239, _1027237) = 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), _1027239)), _1027237) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027239), _1027237)))]]], (6121 ^ _775828) ^ [_873047, _873049, _873051] : [c_Com_Ocom_OAss(_873047, _873049) = hAPP(c_Com_Ocom_OBODY, _873051)], (40806 ^ _775828) ^ [_1560644, _1560646, _1560648, _1560650] : [hAPP(c_Set_Oimage(_1560644, _1560646, _1560648), c_Orderings_Otop__class_Otop(tc_fun(_1560644, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560646, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1560644, _1560646, _1560648), hAPP(c_Set_Ovimage(_1560644, _1560646, _1560648), _1560650)) = _1560650)], (18681 ^ _775828) ^ [_1096744, _1096746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096744))), 18684 ^ _775828 : [(18691 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096746))), -(c_Divides_Odivmod__int(_1096744, _1096746) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096744), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096746))))], (18685 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096746)), -(c_Divides_Odivmod__int(_1096744, _1096746) = c_Divides_OnegDivAlg(_1096744, _1096746))]]], (25024 ^ _775828) ^ [_1216934, _1216936, _1216938, _1216940, _1216942, _1216944] : [-(c_Nitpick_Opair__box_Opair__box__size(_1216934, _1216936, _1216938, _1216940, c_Nitpick_Opair__box_OPairBox(_1216934, _1216936, _1216942, _1216944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1216938, _1216942)), hAPP(_1216940, _1216944))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51120 ^ _775828) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (7563 ^ _775828) ^ [_896456, _896458] : [class_Groups_Olinordered__ab__group__add(_896456), 7566 ^ _775828 : [(7573 ^ _775828) ^ [] : [_896458 = c_Groups_Ozero__class_Ozero(_896456), -(hAPP(c_Groups_Ouminus__class_Ouminus(_896456), _896458) = _896458)], (7567 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_896456), _896458) = _896458, -(_896458 = c_Groups_Ozero__class_Ozero(_896456))]]], (26946 ^ _775828) ^ [_1251782, _1251784, _1251786] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251782), _1251786)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251782), _1251784)))], (47559 ^ _775828) ^ [_1724482, _1724484, _1724486, _1724488] : [-(_1724482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1724484), _1724482), hAPP(hAPP(c_List_Olist_OCons(_1724484), _1724486), _1724488)) = hAPP(hAPP(c_List_Olist_OCons(_1724484), _1724486), hAPP(hAPP(c_List_Otake(_1724484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1724482), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1724488)))], (33236 ^ _775828) ^ [_1391333, _1391335, _1391337, _1391339, _1391341, _1391343, _1391345] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1391333, tc_Option_Ooption(_1391335)), _1391337), _1391339), hAPP(c_Option_Ooption_OSome(_1391335), _1391341)), _1391343) = hAPP(c_Option_Ooption_OSome(_1391335), _1391345), 33241 ^ _775828 : [(33244 ^ _775828) ^ [] : [-(_1391341 = _1391345)], (33242 ^ _775828) ^ [] : [-(_1391343 = _1391339)]], 33245 ^ _775828 : [(33248 ^ _775828) ^ [] : [-(hAPP(_1391337, _1391343) = hAPP(c_Option_Ooption_OSome(_1391335), _1391345))], (33246 ^ _775828) ^ [] : [_1391343 = _1391339]]], (12397 ^ _775828) ^ [_980422, _980424] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980422), _980424) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _980422 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _980424 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (9229 ^ _775828) ^ [_923481, _923483, _923485] : [class_Rings_Oordered__ring(_923481), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923481), c_Groups_Ozero__class_Ozero(_923481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923481), _923483), _923485)))), 9234 ^ _775828 : [(9241 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923481), _923483), c_Groups_Ozero__class_Ozero(_923481))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923481), _923485), c_Groups_Ozero__class_Ozero(_923481)))], (9235 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923481), c_Groups_Ozero__class_Ozero(_923481)), _923483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923481), c_Groups_Ozero__class_Ozero(_923481)), _923485))]]], (8675 ^ _775828) ^ [_915026, _915028, _915030, _915032] : [class_Orderings_Opreorder(_915026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915026), _915028), _915030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915026), _915030), _915032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915026), _915028), _915032)))], (18771 ^ _775828) ^ [_1098494, _1098496] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1098494), _1098496)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1098494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098496)))], (26814 ^ _775828) ^ [_1249575, _1249577] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1249575)), _1249577))), 26817 ^ _775828 : [(26820 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249575), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249577)))], (26818 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249575)))]], 26821 ^ _775828 : [(26824 ^ _775828) ^ [] : [_1249577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26822 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249575))]]], (1680 ^ _775828) ^ [_799446, _799448] : [-(class_Orderings_Oorder(_799446)), _799448 = _799446, class_Orderings_Oorder(_799448)], (12630 ^ _775828) ^ [_984208, _984210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984208), _984210)), -(_984210 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984208), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 12633 ^ [_984208, _984210]))))], (36251 ^ _775828) ^ [_1456567, _1456569, _1456571] : [class_Orderings_Oorder(_1456567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456567), _1456569), _1456571)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456567, _1456571), _1456569) = c_Orderings_Obot__class_Obot(tc_fun(_1456567, tc_HOL_Obool)))], (30623 ^ _775828) ^ [_1335504, _1335506, _1335508, _1335510] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335504), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335504, tc_HOL_Obool)), _1335506), hAPP(hAPP(c_Set_Oinsert(_1335504), _1335508), _1335510)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335504), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335504, tc_HOL_Obool)), _1335506), _1335510))))], (43720 ^ _775828) ^ [_1630946, _1630948, _1630950, _1630952] : [class_Orderings_Olinorder(_1630946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630946), _1630948)), hBOOL(hAPP(hAPP(c_member(_1630946), _1630950), _1630948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630946), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1630946), _1630950), _1630952)), hAPP(hAPP(c_Finite__Set_Ofold(_1630946, _1630946, c_Orderings_Oord__class_Omax(_1630946)), _1630952), _1630948))))], (16038 ^ _775828) ^ [_1047353, _1047355, _1047357] : [-(hBOOL(hAPP(_1047353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047355), _1047357)))), 16041 ^ _775828 : [(16044 ^ _775828) ^ [] : [hBOOL(hAPP(_1047353, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16042 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047355), _1047357)))]], 16046 ^ _775828 : [(16049 ^ _775828) ^ [] : [hBOOL(hAPP(_1047353, 16045 ^ [_1047353, _1047355, _1047357]))], (16047 ^ _775828) ^ [] : [-(_1047355 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047357), 16045 ^ [_1047353, _1047355, _1047357]))]]], (48715 ^ _775828) ^ [_1752910, _1752912, _1752914] : [-(hAPP(c_List_Orotate(_1752910, hAPP(c_Nat_OSuc, _1752912)), _1752914) = hAPP(c_List_Orotate1(_1752910), hAPP(c_List_Orotate(_1752910, _1752912), _1752914)))], (3818 ^ _775828) ^ [_833874, _833876, _833878, _833880, _833882, _833884] : [-(c_Smallcheck_Oorelse(_833884, _833880, _833876) = c_Smallcheck_Oorelse(_833882, _833878, _833874)), _833884 = _833882, _833880 = _833878, _833876 = _833874], (12767 ^ _775828) ^ [_986576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986576)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _986576)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _986576)))], (14958 ^ _775828) ^ [_1026632, _1026634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1026632)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026632), _1026634)), _1026632) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15726 ^ _775828) ^ [_1040932, _1040934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040932), _1040934)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040932), _1040934) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8829 ^ _775828) ^ [_917209, _917211, _917213] : [class_Orderings_Olinorder(_917209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917209), _917211), _917213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917209), _917213), _917211)))], (36461 ^ _775828) ^ [_1460649, _1460651, _1460653] : [c_Wellfounded_Owf(_1460649, _1460651), -(c_Wellfounded_Owf(tc_List_Olist(_1460649), hAPP(c_List_Olexn(_1460649, _1460651), _1460653)))], (28683 ^ _775828) ^ [_1291395, _1291397] : [c_Wellfounded_Owf(_1291395, _1291397), -(c_Wellfounded_Oacyclic(_1291395, _1291397))], (45369 ^ _775828) ^ [_1669487, _1669489, _1669491, _1669493, _1669495, _1669497] : [hAPP(_1669487, _1669489) = hAPP(c_Option_Ooption_OSome(_1669491), _1669493), -(hAPP(c_Map_Omap__add(_1669495, _1669491, _1669497, _1669487), _1669489) = hAPP(c_Option_Ooption_OSome(_1669491), _1669493))], (44250 ^ _775828) ^ [_1642863, _1642865, _1642867, _1642869, _1642871] : [-(hAPP(hAPP(c_Set_Oinsert(_1642863), _1642865), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642867, tc_fun(_1642863, tc_HOL_Obool)), _1642869), _1642871)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642867, tc_fun(_1642863, tc_HOL_Obool)), _1642869), hAPP(hAPP(c_COMBB(tc_fun(_1642863, tc_HOL_Obool), tc_fun(_1642863, tc_HOL_Obool), _1642867), hAPP(c_Set_Oinsert(_1642863), _1642865)), _1642871)))], (51378 ^ _775828) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (27739 ^ _775828) ^ [_1269563, _1269565, _1269567, _1269569, _1269571, _1269573, _1269575, _1269577] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1269563, _1269565)), hAPP(hAPP(c_Product__Type_OPair(_1269563, _1269565), _1269567), _1269569)), _1269571)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1269565, _1269573)), hAPP(hAPP(c_Product__Type_OPair(_1269565, _1269573), _1269569), _1269575)), _1269577)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1269563, _1269573)), hAPP(hAPP(c_Product__Type_OPair(_1269563, _1269573), _1269567), _1269575)), hAPP(hAPP(c_Relation_Orel__comp(_1269563, _1269565, _1269573), _1269571), _1269577))))], (596 ^ _775828) ^ [_784862, _784864, _784866, _784868, _784870, _784872] : [-(c_Hoare__Mirabelle_Ohoare__valids(_784870, _784866, _784862)), c_Hoare__Mirabelle_Ohoare__valids(_784872, _784868, _784864), _784872 = _784870, _784868 = _784866, _784864 = _784862], (3046 ^ _775828) ^ [_821640, _821642, _821644, _821646] : [-(c_Com_Ocom_OSemi(_821646, _821642) = c_Com_Ocom_OSemi(_821644, _821640)), _821646 = _821644, _821642 = _821640], (20502 ^ _775828) ^ [_1128141, _1128143] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128141)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128143))) = 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), _1128141), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128143))))], (17309 ^ _775828) ^ [_1072074, _1072076, _1072078] : [class_Rings_Olinordered__semidom(_1072074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072074), c_Groups_Oone__class_Oone(_1072074)), _1072076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072074), c_Groups_Oone__class_Oone(_1072074)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072074), _1072076), _1072078))))], (2954 ^ _775828) ^ [_820200, _820202, _820204, _820206, _820208, _820210] : [-(c_SetInterval_Oord_OatMost(_820210, _820206, _820202) = c_SetInterval_Oord_OatMost(_820208, _820204, _820200)), _820210 = _820208, _820206 = _820204, _820202 = _820200], (10720 ^ _775828) ^ [_950973, _950975] : [class_Groups_Ocomm__monoid__mult(_950973), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950973), _950975), c_Groups_Oone__class_Oone(_950973)) = _950975)], (51234 ^ _775828) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (27076 ^ _775828) ^ [_1254204, _1254206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254206)), 27083 ^ _775828 : [(27090 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254204), _1254206)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1254204)), hAPP(c_Int_Onat, _1254206))))], (27084 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1254204)), hAPP(c_Int_Onat, _1254206))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254204), _1254206)))]]], (7977 ^ _775828) ^ [_903560, _903562, _903564, _903566] : [class_Rings_Ocomm__semiring__1(_903560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903560), _903562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903560), _903564), _903566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903560), _903564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903560), _903562), _903566)))], (21920 ^ _775828) ^ [_1156204, _1156206] : [-(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), _1156204)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156206), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156204))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10246 ^ _775828) ^ [_941813, _941815, _941817] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941813), _941815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941817), _941815), -(_941813 = _941817)], (23948 ^ _775828) ^ [_1195186, _1195188, _1195190, _1195192] : [class_Orderings_Olinorder(_1195186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195186), _1195188), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195186), _1195190), _1195192))), 23955 ^ _775828 : [(23958 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195186), _1195188), _1195192)))], (23956 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195186), _1195188), _1195190)))]]], (42335 ^ _775828) ^ [_1598045] : [-(c_Finite__Set_Ofun__left__comm__idem(_1598045, tc_fun(_1598045, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1598045, tc_HOL_Obool), tc_fun(tc_fun(_1598045, tc_HOL_Obool), tc_fun(_1598045, tc_HOL_Obool)), _1598045), hAPP(c_COMBC(tc_fun(_1598045, tc_HOL_Obool), tc_fun(_1598045, tc_HOL_Obool), tc_fun(_1598045, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1598045, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1598045, tc_fun(_1598045, tc_HOL_Obool), tc_fun(_1598045, tc_HOL_Obool)), c_Set_Oinsert(_1598045)), c_Orderings_Obot__class_Obot(tc_fun(_1598045, tc_HOL_Obool))))))], (28193 ^ _775828) ^ [_1281277, _1281279, _1281281] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281277, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281277, tc_HOL_Obool)), _1281279), _1281281)), _1281281) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281277, tc_HOL_Obool)), _1281279), _1281281))], (47063 ^ _775828) ^ [_1713156, _1713158, _1713160, _1713162] : [_1713156 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1713158), hAPP(hAPP(c_List_Olist_OCons(_1713158), _1713160), _1713162)), _1713156) = _1713160)], (2404 ^ _775828) ^ [_811085, _811087, _811089, _811091, _811093, _811095, _811097, _811099] : [-(c_Random_Oiterate(_811099, _811095, _811091, _811087) = c_Random_Oiterate(_811097, _811093, _811089, _811085)), _811099 = _811097, _811095 = _811093, _811091 = _811089, _811087 = _811085], (40000 ^ _775828) ^ [_1542903, _1542905, _1542907, _1542909, _1542911] : [hBOOL(hAPP(hAPP(c_member(_1542903), _1542905), c_Map_Oran(_1542907, _1542903, c_Map_Orestrict__map(_1542907, _1542903, _1542909, _1542911)))), 40004 ^ _775828 : [(40007 ^ _775828) ^ [] : [-(hAPP(_1542909, 40003 ^ [_1542903, _1542905, _1542907, _1542909, _1542911]) = hAPP(c_Option_Ooption_OSome(_1542903), _1542905))], (40005 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542907), 40003 ^ [_1542903, _1542905, _1542907, _1542909, _1542911]), _1542911)))]]], (44689 ^ _775828) ^ [_1654869, _1654871, _1654873] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654869, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1654869, tc_HOL_Obool)), _1654871), _1654873)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654869, tc_HOL_Obool)), _1654871), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654869, tc_HOL_Obool), _1654873)))], (23934 ^ _775828) ^ [_1194915, _1194917, _1194919, _1194921, _1194923] : [class_Orderings_Olinorder(_1194915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194915), _1194917), _1194919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194915), _1194921), _1194923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194915), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194915), _1194917), _1194921)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194915), _1194919), _1194923))))], (31169 ^ _775828) ^ [_1348622, _1348624, _1348626] : [class_Orderings_Olinorder(_1348622), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348622), _1348624)), -(_1348624 = c_Orderings_Obot__class_Obot(tc_fun(_1348622, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348622), _1348626), c_Big__Operators_Olattice_OSup__fin(_1348622, c_Orderings_Oord__class_Omax(_1348622), _1348624)) = c_Big__Operators_Olattice_OSup__fin(_1348622, c_Orderings_Oord__class_Omax(_1348622), hAPP(c_Set_OCollect(_1348622), hAPP(hAPP(c_COMBB(tc_fun(_1348622, tc_HOL_Obool), tc_HOL_Obool, _1348622), c_HOL_OEx(_1348622)), hAPP(hAPP(c_COMBC(_1348622, tc_fun(_1348622, tc_HOL_Obool), tc_fun(_1348622, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348622, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1348622, tc_HOL_Obool), tc_fun(_1348622, tc_HOL_Obool)), _1348622), c_COMBS(_1348622, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348622, tc_HOL_Obool), tc_fun(_1348622, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1348622), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1348622), c_fconj)), hAPP(hAPP(c_COMBC(_1348622, tc_fun(_1348622, _1348622), tc_fun(_1348622, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348622, tc_HOL_Obool), tc_fun(tc_fun(_1348622, _1348622), tc_fun(_1348622, tc_HOL_Obool)), _1348622), c_COMBB(_1348622, tc_HOL_Obool, _1348622)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1348622), _1348626))))), hAPP(hAPP(c_COMBC(_1348622, tc_fun(_1348622, tc_HOL_Obool), tc_HOL_Obool), c_member(_1348622)), _1348624))))))], (47609 ^ _775828) ^ [_1725445, _1725447] : [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), _1725445), _1725447))), 47612 ^ _775828 : [(47619 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1725445), _1725447))), -(c_List_Oupto(_1725445, _1725447) = c_List_Olist_ONil(tc_Int_Oint))], (47613 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1725445), _1725447)), -(c_List_Oupto(_1725445, _1725447) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1725445), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1725445), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1725447)))]]], (26263 ^ _775828) ^ [_1239477, _1239479, _1239481, _1239483] : [class_Rings_Oidom(_1239477), 26266 ^ _775828 : [(26267 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239477), _1239479), _1239481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239477), _1239483), _1239481))), -(_1239481 = c_Groups_Ozero__class_Ozero(_1239477)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239477), _1239479), _1239483)))], (26277 ^ _775828) ^ [] : [26278 ^ _775828 : [(26281 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239477), _1239479), _1239483))], (26279 ^ _775828) ^ [] : [_1239481 = c_Groups_Ozero__class_Ozero(_1239477)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239477), _1239479), _1239481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239477), _1239483), _1239481))))]]], (41926 ^ _775828) ^ [_1588299, _1588301, _1588303, _1588305, _1588307, _1588309] : [class_Groups_Ocomm__monoid__mult(_1588299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588301), _1588303)), 41936 ^ _775828 : [(41939 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1588305), hAPP(_1588307, 41935 ^ [_1588299, _1588301, _1588303, _1588305, _1588307, _1588309])))], (41937 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588301), 41935 ^ [_1588299, _1588301, _1588303, _1588305, _1588307, _1588309]), _1588303)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588301, _1588299), hAPP(hAPP(c_COMBS(_1588301, tc_fun(_1588305, tc_HOL_Obool), _1588299), hAPP(hAPP(c_COMBB(tc_fun(_1588305, _1588299), tc_fun(tc_fun(_1588305, tc_HOL_Obool), _1588299), _1588301), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588305, _1588299)), _1588309)), _1588307)), _1588303) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1588301, _1588305), _1588299), hAPP(c_Product__Type_Oprod_Oprod__case(_1588301, _1588305, _1588299), _1588309)), hAPP(hAPP(c_Product__Type_OSigma(_1588301, _1588305), _1588303), _1588307)))], (48367 ^ _775828) ^ [_1745279, _1745281, _1745283, _1745285] : [-(hAPP(hAPP(c_List_Odrop(_1745279), _1745281), hAPP(hAPP(c_List_Oappend(_1745279), _1745283), _1745285)) = hAPP(hAPP(c_List_Oappend(_1745279), hAPP(hAPP(c_List_Odrop(_1745279), _1745281), _1745283)), hAPP(hAPP(c_List_Odrop(_1745279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1745281), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745279)), _1745283))), _1745285)))], (28808 ^ _775828) ^ [_1294120, _1294122] : [28809 ^ _775828 : [(28810 ^ _775828) ^ [_1294166] : [hBOOL(hAPP(_1294120, _1294166))]], -(hBOOL(hAPP(_1294120, c_Hilbert__Choice_OEps(_1294122, _1294120))))], (25785 ^ _775828) ^ [_1231552, _1231554] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231552), _1231554))), 25786 ^ _775828 : [(25787 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231552), _1231554)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231554), _1231552)))], (25793 ^ _775828) ^ [] : [_1231552 = _1231554]]], (11604 ^ _775828) ^ [_966595, _966597] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966595), _966597), 11609 ^ _775828 : [(11612 ^ _775828) ^ [] : [-(_966597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11610 ^ _775828) ^ [] : [-(_966595 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11613 ^ _775828 : [(11616 ^ _775828) ^ [] : [-(_966597 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11614 ^ _775828) ^ [] : [-(_966595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42794 ^ _775828) ^ [_1609178, _1609180, _1609182, _1609184] : [-(hAPP(hAPP(c_Nat_Ocompow(_1609178, _1609178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1609180), _1609182)), _1609184) = hAPP(c_Fun_Ocomp(_1609178, _1609178, _1609178, hAPP(hAPP(c_Nat_Ocompow(_1609178, _1609178), _1609180), _1609184)), hAPP(hAPP(c_Nat_Ocompow(_1609178, _1609178), _1609182), _1609184)))], (20220 ^ _775828) ^ [_1123233] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1123233)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1123233)))], (1030 ^ _775828) ^ [_791321, _791323] : [-(class_Rings_Olinordered__semiring__1(_791321)), _791323 = _791321, class_Rings_Olinordered__semiring__1(_791323)], (32031 ^ _775828) ^ [_1368317, _1368319, _1368321] : [class_Orderings_Oorder(_1368317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368317), _1368319), _1368321)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1368317, _1368321, _1368319) = c_Orderings_Obot__class_Obot(tc_fun(_1368317, tc_HOL_Obool)))], (6751 ^ _775828) ^ [_882928, _882930, _882932] : [class_Rings_Olinordered__idom(_882928), -(_882930 = _882932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882928), _882930), _882932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882928), _882932), _882930)))], (46201 ^ _775828) ^ [_1689346, _1689348, _1689350, _1689352] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689346)), _1689348) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689350)), _1689352), -(hAPP(hAPP(c_List_Omap(tc_prod(_1689346, _1689350), _1689346), c_Product__Type_Ofst(_1689346, _1689350)), hAPP(hAPP(c_List_Ozip(_1689346, _1689350), _1689348), _1689352)) = _1689348)], (38326 ^ _775828) ^ [_1503707, _1503709] : [class_Groups_Oordered__ab__group__add(_1503707), -(hAPP(c_Set_Oimage(_1503707, _1503707, c_Groups_Ouminus__class_Ouminus(_1503707)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503707), _1503709)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1503707), hAPP(c_Groups_Ouminus__class_Ouminus(_1503707), _1503709)))], (35723 ^ _775828) ^ [_1446597, _1446599] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1446597, _1446599)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446599), _1446597)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48581 ^ _775828) ^ [_1750502, _1750504, _1750506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750502), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750504)), _1750506))), -(_1750506 = hAPP(hAPP(c_List_Oappend(_1750504), hAPP(hAPP(c_List_Otake(_1750504), _1750502), _1750506)), hAPP(hAPP(c_List_Olist_OCons(_1750504), hAPP(hAPP(c_List_Onth(_1750504), _1750506), _1750502)), hAPP(hAPP(c_List_Odrop(_1750504), hAPP(c_Nat_OSuc, _1750502)), _1750506))))], (41332 ^ _775828) ^ [_1574413, _1574415, _1574417, _1574419] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1574413, _1574415)), hAPP(hAPP(c_Product__Type_OSigma(_1574413, _1574415), _1574417), hAPP(c_COMBK(tc_fun(_1574415, tc_HOL_Obool), _1574413), _1574419))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1574413), _1574417)), hAPP(c_Finite__Set_Ocard(_1574415), _1574419)))], (20312 ^ _775828) ^ [_1124819, _1124821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1124819)), c_Int_OBit1(_1124821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124819), _1124821)))], (47439 ^ _775828) ^ [_1722128, _1722130] : [_1722130 = c_List_Olist_ONil(_1722128), -(hAPP(c_List_Oset(_1722128), _1722130) = c_Orderings_Obot__class_Obot(tc_fun(_1722128, tc_HOL_Obool)))], (29187 ^ _775828) ^ [_1304840, _1304842, _1304844, _1304846] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304840, tc_HOL_Obool)), _1304842), hAPP(hAPP(c_Set_Oinsert(_1304840), _1304844), _1304846)) = hAPP(hAPP(c_Set_Oinsert(_1304840), _1304844), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304840, tc_HOL_Obool)), _1304842), _1304846)))], (13440 ^ _775828) ^ [_998890, _998892, _998894, _998896, _998898, _998900] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_998890, _998892, _998894), _998896, _998898, _998900)), 13441 ^ _775828 : [(13448 ^ _775828) ^ [] : [-(hBOOL(hAPP(_998890, _998896))), c_Natural_Oevaln(_998894, _998896, _998898, _998900)], (13442 ^ _775828) ^ [] : [hBOOL(hAPP(_998890, _998896)), c_Natural_Oevaln(_998892, _998896, _998898, _998900)]]], (29747 ^ _775828) ^ [_1316055, _1316057] : [class_Lattices_Obounded__lattice__bot(_1316055), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316055), _1316057), c_Orderings_Obot__class_Obot(_1316055)) = _1316057)], (24644 ^ _775828) ^ [_1208823, _1208825] : [c_Nitpick_Orefl_H(_1208823, _1208825), 24647 ^ _775828 : [(24648 ^ _775828) ^ [_1208901] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1208823, _1208823)), hAPP(hAPP(c_Product__Type_OPair(_1208823, _1208823), _1208901), _1208901)), _1208825)))]]], (49837 ^ _775828) ^ [_1777335, _1777337] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1777335), _1777337) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1777335, _1777337)))], (15028 ^ _775828) ^ [_1027784, _1027786, _1027788] : [class_Divides_Osemiring__div(_1027784), -(_1027786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027784), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1027784), _1027786), _1027788)), _1027788)), c_Divides_Odiv__class_Omod(_1027784, _1027786, _1027788)))], (7913 ^ _775828) ^ [_902375, _902377, _902379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902375), _902377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902379), _902375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902379), _902377))))], (26177 ^ _775828) ^ [_1237967, _1237969, _1237971, _1237973] : [class_Rings_Ocomm__semiring__1(_1237967), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237967), _1237969), _1237971)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237967), _1237969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237967), _1237971), _1237973))))], (42754 ^ _775828) ^ [_1608102, _1608104, _1608106, _1608108, _1608110, _1608112] : [-(hAPP(c_Set_Ovimage(_1608102, _1608104, hAPP(c_Fun_Ocomp(_1608106, _1608104, _1608102, _1608108), _1608110)), _1608112) = hAPP(c_Set_Ovimage(_1608102, _1608106, _1608110), hAPP(c_Set_Ovimage(_1608106, _1608104, _1608108), _1608112)))], (24400 ^ _775828) ^ [_1204229, _1204231, _1204233, _1204235, _1204237] : [-(hAPP(c_Product__Type_Osnd(_1204229, _1204231), hAPP(c_Product__Type_Oapfst(_1204233, _1204229, _1204231, _1204235), _1204237)) = hAPP(c_Product__Type_Osnd(_1204233, _1204231), _1204237))], (37708 ^ _775828) ^ [_1489564, _1489566, _1489568, _1489570, _1489572] : [class_Groups_Ocomm__monoid__add(_1489564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489566), _1489568)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489566), _1489570)), 37722 ^ _775828 : [(37725 ^ _775828) ^ [] : [hAPP(_1489572, 37721 ^ [_1489564, _1489566, _1489568, _1489570, _1489572]) = c_Groups_Ozero__class_Ozero(_1489564)], (37723 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489566), 37721 ^ [_1489564, _1489566, _1489568, _1489570, _1489572]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489566, tc_HOL_Obool)), _1489568), _1489570))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489566, _1489564), _1489572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489566, tc_HOL_Obool)), _1489568), _1489570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1489564), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489566, _1489564), _1489572), _1489568)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489566, _1489564), _1489572), _1489570)))], (41354 ^ _775828) ^ [_1575021, _1575023, _1575025] : [c_Equiv__Relations_Oequiv(_1575021, _1575023, _1575025), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575021, _1575021), tc_HOL_Obool)), _1575025), hAPP(hAPP(c_Product__Type_OSigma(_1575021, _1575021), _1575023), hAPP(c_COMBK(tc_fun(_1575021, tc_HOL_Obool), _1575021), _1575023)))))], (28878 ^ _775828) ^ [_1296670, _1296672, _1296674, _1296676] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296670, tc_fun(_1296670, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1296670, tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_fun(_1296670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296670, tc_fun(tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_fun(_1296670, tc_HOL_Obool)), _1296670), c_COMBC(_1296670, tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296670, tc_prod(_1296670, _1296670)), tc_fun(_1296670, tc_fun(tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_HOL_Obool)), _1296670), hAPP(c_COMBB(tc_prod(_1296670, _1296670), tc_fun(tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool), tc_HOL_Obool), _1296670), c_member(tc_prod(_1296670, _1296670)))), c_Product__Type_OPair(_1296670, _1296670)))), _1296672)), c_fequal), _1296674), _1296676)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1296670, _1296670)), hAPP(hAPP(c_Product__Type_OPair(_1296670, _1296670), _1296674), _1296676)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1296670, _1296670), tc_HOL_Obool)), _1296672), c_Relation_OId(_1296670)))))], (25273 ^ _775828) ^ [_1221736, _1221738] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1221736), _1221738) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1221736, 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)))), _1221738))))], (10116 ^ _775828) ^ [_939582, _939584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939582), _939584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939584), _939582)), -(_939582 = _939584)], (2136 ^ _775828) ^ [_807011, _807013] : [_807013 = _807011, -(c_Natural_Oevalc(_807013) = c_Natural_Oevalc(_807011))], (18879 ^ _775828) ^ [_1100605, _1100607, _1100609] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1100605, _1100607), _1100609)), 18882 ^ _775828 : [(18891 ^ _775828) ^ [] : [-(_1100607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 18894 ^ _775828 : [(18903 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100607))), 18906 ^ _775828 : [(18909 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1100609)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18907 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100607), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1100609))))]]], (18895 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100607)), 18898 ^ _775828 : [(18901 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1100609)), _1100607)))], (18899 ^ _775828) ^ [] : [-(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), _1100609))))]]]]], (18885 ^ _775828) ^ [] : [_1100607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1100609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18883 ^ _775828) ^ [] : [-(_1100605 = 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), _1100609)), _1100607)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1100609)))]]], (42489 ^ _775828) ^ [_1601392, _1601394, _1601396] : [c_Relation_Orefl__on(_1601392, _1601394, _1601396), 42492 ^ _775828 : [(42499 ^ _775828) ^ [_1601876] : [hBOOL(hAPP(hAPP(c_member(_1601392), _1601876), _1601394)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601392, _1601392)), hAPP(hAPP(c_Product__Type_OPair(_1601392, _1601392), _1601876), _1601876)), _1601396)))], (42493 ^ _775828) ^ [_1601603] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601392, _1601392)), _1601603), _1601396)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1601392, _1601392, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1601392, tc_fun(_1601392, tc_HOL_Obool), tc_fun(_1601392, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1601392, tc_HOL_Obool), tc_fun(_1601392, tc_HOL_Obool)), _1601392), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1601392)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601392), c_fconj), hAPP(hAPP(c_COMBC(_1601392, tc_fun(_1601392, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601392)), _1601394)))), hAPP(hAPP(c_COMBC(_1601392, tc_fun(_1601392, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601392)), _1601394))), _1601603)))]]], (50385 ^ _775828) ^ [_1788647, _1788649] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788647)), hAPP(c_List_Orev(_1788647), _1788649)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788647)), _1788649))], (19110 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (27246 ^ _775828) ^ [_1258060, _1258062, _1258064, _1258066] : [-(c_Nitpick_Oprod(_1258060, _1258062, _1258064, _1258066) = hAPP(c_Set_OCollect(tc_prod(_1258060, _1258062)), hAPP(c_Product__Type_Oprod_Oprod__case(_1258060, _1258062, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1258060, tc_fun(_1258062, tc_HOL_Obool), tc_fun(_1258062, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1258062, tc_HOL_Obool), tc_fun(_1258062, tc_HOL_Obool)), _1258060), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1258062)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1258060), c_fconj), hAPP(hAPP(c_COMBC(_1258060, tc_fun(_1258060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1258060)), _1258064)))), hAPP(hAPP(c_COMBC(_1258062, tc_fun(_1258062, tc_HOL_Obool), tc_HOL_Obool), c_member(_1258062)), _1258066)))))], (24370 ^ _775828) ^ [_1203521, _1203523, _1203525, _1203527, _1203529, _1203531, _1203533] : [-(hAPP(c_Product__Type_Oapfst(_1203521, _1203523, _1203525, _1203527), hAPP(c_Product__Type_Oapsnd(_1203529, _1203525, _1203521, _1203531), _1203533)) = hAPP(hAPP(c_Product__Type_OPair(_1203523, _1203525), hAPP(_1203527, hAPP(c_Product__Type_Ofst(_1203521, _1203529), _1203533))), hAPP(_1203531, hAPP(c_Product__Type_Osnd(_1203521, _1203529), _1203533))))], (9027 ^ _775828) ^ [_920231] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920231)))], (9616 ^ _775828) ^ [_930458] : [hBOOL(hAPP(_930458, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9617 ^ [_930458]))), 9620 ^ _775828 : [(9621 ^ _775828) ^ [_930558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930558)), -(hBOOL(hAPP(_930458, _930558)))]]], (35473 ^ _775828) ^ [_1442294, _1442296] : [c_Nat__Transfer_Ois__nat(_1442294), c_Nat__Transfer_Ois__nat(_1442296), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1442294, _1442296) = 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, _1442294), hAPP(c_Int_Onat, _1442296))))], (5969 ^ _775828) ^ [_870800, _870802] : [c_Com_Ocom_OAss(_870800, _870802) = c_Com_Ocom_OSKIP], (34353 ^ _775828) ^ [_1415766, _1415768, _1415770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415766, tc_HOL_Obool)), _1415768), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1415766, tc_HOL_Obool)), _1415770))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415766, tc_HOL_Obool)), _1415768), _1415770) = c_Orderings_Obot__class_Obot(tc_fun(_1415766, tc_HOL_Obool)))], (10802 ^ _775828) ^ [_952494, _952496] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952494), _952496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 10805 ^ _775828 : [(10808 ^ _775828) ^ [] : [-(_952496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10806 ^ _775828) ^ [] : [-(_952494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27361 ^ _775828) ^ [_1261021, _1261023, _1261025, _1261027] : [27362 ^ _775828 : [(27363 ^ _775828) ^ [_1261096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1261025, _1261021)), hAPP(hAPP(c_Product__Type_OPair(_1261025, _1261021), _1261096), _1261023)), _1261027))]], -(hBOOL(hAPP(hAPP(c_member(_1261021), _1261023), hAPP(c_Relation_ORange(_1261025, _1261021), _1261027))))], (40708 ^ _775828) ^ [_1558271, _1558273, _1558275, _1558277, _1558279, _1558281, _1558283] : [c_Typedef_Otype__definition(_1558271, _1558273, _1558275, _1558277, _1558279), hBOOL(hAPP(hAPP(c_member(_1558273), _1558281), _1558279)), hBOOL(hAPP(hAPP(c_member(_1558273), _1558283), _1558279)), 40719 ^ _775828 : [(40726 ^ _775828) ^ [] : [_1558281 = _1558283, -(hAPP(_1558277, _1558281) = hAPP(_1558277, _1558283))], (40720 ^ _775828) ^ [] : [hAPP(_1558277, _1558281) = hAPP(_1558277, _1558283), -(_1558281 = _1558283)]]], (40983 ^ _775828) ^ [_1565147, _1565149, _1565151, _1565153, _1565155, _1565157] : [-(hBOOL(hAPP(hAPP(c_member(_1565147), _1565149), _1565151))), 40986 ^ _775828 : [(40993 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565147), _1565153), _1565151))), -(hAPP(c_Set_Ovimage(_1565155, _1565147, hAPP(hAPP(c_COMBC(_1565155, _1565147, _1565147), hAPP(hAPP(c_COMBC(_1565155, _1565147, tc_fun(_1565147, _1565147)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565147, tc_fun(_1565147, _1565147)), _1565155), c_If(_1565147)), hAPP(hAPP(c_COMBC(_1565155, tc_fun(_1565155, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565155)), _1565157))), _1565149)), _1565153)), _1565151) = c_Orderings_Obot__class_Obot(tc_fun(_1565155, tc_HOL_Obool)))], (40987 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1565147), _1565153), _1565151)), -(hAPP(c_Set_Ovimage(_1565155, _1565147, hAPP(hAPP(c_COMBC(_1565155, _1565147, _1565147), hAPP(hAPP(c_COMBC(_1565155, _1565147, tc_fun(_1565147, _1565147)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565147, tc_fun(_1565147, _1565147)), _1565155), c_If(_1565147)), hAPP(hAPP(c_COMBC(_1565155, tc_fun(_1565155, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565155)), _1565157))), _1565149)), _1565153)), _1565151) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1565155, tc_HOL_Obool)), _1565157))]]], (36427 ^ _775828) ^ [_1459954, _1459956, _1459958] : [class_Orderings_Olinorder(_1459954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459954), _1459956), _1459958)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459954, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459954, _1459956), _1459958)), hAPP(hAPP(c_Set_Oinsert(_1459954), _1459958), c_Orderings_Obot__class_Obot(tc_fun(_1459954, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1459954, _1459956, _1459958))], (4878 ^ _775828) ^ [_850402, _850404, _850406, _850408] : [-(c_List_Otranspose(_850408, _850404) = c_List_Otranspose(_850406, _850402)), _850408 = _850406, _850404 = _850402], (17663 ^ _775828) ^ [_1078242, _1078244] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078242))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078242), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078244)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16905 ^ _775828) ^ [_1063993, _1063995] : [class_Groups_Oordered__ab__group__add__abs(_1063993), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063993), hAPP(c_Groups_Ouminus__class_Ouminus(_1063993), _1063995)), hAPP(c_Groups_Oabs__class_Oabs(_1063993), _1063995))))], (20342 ^ _775828) ^ [_1125366, _1125368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125366), _1125368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1125366)), c_Int_OBit0(_1125368))))], (51580 ^ _775828) ^ [_1809176, _1809178] : [hBOOL(_1809176), -(hBOOL(hAPP(hAPP(c_fdisj, _1809178), _1809176)))], (33803 ^ _775828) ^ [_1403858, _1403860, _1403862, _1403864] : [class_Lattices_Osemilattice__inf(_1403858), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403858), _1403860), _1403862)), _1403864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403858), _1403860), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403858), _1403862), _1403864)))], (50732 ^ _775828) ^ [_1797247, _1797249] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797247)), c_List_Oremdups(_1797247, _1797249))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797247)), _1797249))))], (38316 ^ _775828) ^ [_1503512, _1503514, _1503516] : [class_Orderings_Olinorder(_1503512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503512), _1503514), _1503516)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503512, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1503512, _1503514, _1503516)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503512), _1503516)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503512), _1503514))], (51188 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (24697 ^ _775828) ^ [_1209693, _1209695, _1209697] : [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), _1209693), _1209695))), -(hBOOL(hAPP(hAPP(_1209697, _1209693), _1209695))), 24704 ^ _775828 : [(24707 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24703 ^ [_1209693, _1209695, _1209697]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1209697, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24702 ^ [_1209693, _1209695, _1209697])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24703 ^ [_1209693, _1209695, _1209697]))))], (24713 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1209697, 24702 ^ [_1209693, _1209695, _1209697]), 24703 ^ [_1209693, _1209695, _1209697]))], (24705 ^ _775828) ^ [] : [-(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), 24702 ^ [_1209693, _1209695, _1209697]), 24703 ^ [_1209693, _1209695, _1209697]))))]]], (38108 ^ _775828) ^ [_1498703, _1498705, _1498707, _1498709, _1498711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498705, tc_HOL_Obool)), _1498709), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498705, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1498703, _1498705, hAPP(c_Relation_Oconverse(_1498705, _1498703), _1498707)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498703, tc_HOL_Obool)), _1498711))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498703, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1498705, _1498703, _1498707), _1498709)), _1498711)))], (51248 ^ _775828) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (29977 ^ _775828) ^ [_1322149, _1322151, _1322153, _1322155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1322149, _1322151)), hAPP(hAPP(c_Product__Type_OPair(_1322149, _1322151), _1322153), _1322155)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322149, _1322151), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1322149, tc_fun(_1322151, tc_HOL_Obool))), _1322153), _1322155)))], (40529 ^ _775828) ^ [_1553408, _1553410, _1553412, _1553414] : [c_Fun_Oinj__on(_1553408, _1553410, _1553412, c_Orderings_Otop__class_Otop(tc_fun(_1553408, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1553410, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1553408, _1553410, _1553412), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1553408, tc_HOL_Obool)), _1553414))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1553410, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1553408, _1553410, _1553412), _1553414)))))], (29951 ^ _775828) ^ [_1321582, _1321584] : [-(c_Set_Othe__elem(_1321582, hAPP(hAPP(c_Set_Oinsert(_1321582), _1321584), c_Orderings_Obot__class_Obot(tc_fun(_1321582, tc_HOL_Obool)))) = _1321584)], (30393 ^ _775828) ^ [_1331254] : [-(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)), _1331254)))))], (32145 ^ _775828) ^ [_1370035, _1370037, _1370039] : [class_Orderings_Olinorder(_1370035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370035), _1370037)), hBOOL(hAPP(hAPP(c_member(_1370035), _1370039), _1370037)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1370035), _1370039), c_Big__Operators_Olinorder__class_OMin(_1370035, _1370037)) = c_Big__Operators_Olinorder__class_OMin(_1370035, _1370037))], (15820 ^ _775828) ^ [_1042677, _1042679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042677), _1042679)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042679), _1042677)), _1042677) = _1042679)], (45564 ^ _775828) ^ [_1674194, _1674196, _1674198, _1674200, _1674202] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1674194), tc_List_Olist(_1674196), tc_List_Olist(_1674198), hAPP(c_List_Omap(_1674194, _1674196), _1674200)), hAPP(c_List_Omap(_1674198, _1674194), _1674202)) = hAPP(c_List_Omap(_1674198, _1674196), hAPP(c_Fun_Ocomp(_1674194, _1674196, _1674198, _1674200), _1674202)))], (1250 ^ _775828) ^ [_794071, _794073] : [-(class_Lattices_Obounded__lattice__bot(_794071)), _794073 = _794071, class_Lattices_Obounded__lattice__bot(_794073)], (30549 ^ _775828) ^ [_1334052, _1334054, _1334056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334054, _1334052)), _1334056)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334052, _1334054)), hAPP(c_Relation_Oconverse(_1334054, _1334052), _1334056))))], (37677 ^ _775828) ^ [_1488929, _1488931, _1488933] : [class_Groups_Ocomm__monoid__add(_1488929), class_Groups_Ocomm__monoid__mult(_1488929), c_Nat__Transfer_Onat__set(_1488931), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1488929), _1488933), _1488931) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1488929), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1488929, tc_Nat_Onat), _1488933), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1488931)))], (44529 ^ _775828) ^ [_1650673, _1650675] : [class_Complete__Lattice_Ocomplete__lattice(_1650673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650673), _1650675)), -(c_Complete__Lattice_OInf__class_OInf(_1650673, _1650675) = hAPP(hAPP(c_Finite__Set_Ofold(_1650673, _1650673, c_Lattices_Osemilattice__inf__class_Oinf(_1650673)), c_Orderings_Otop__class_Otop(_1650673)), _1650675))], (51166 ^ _775828) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (49189 ^ _775828) ^ [_1763354, _1763356, _1763358] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763354)), _1763356), c_List_Olists(_1763354, _1763358))), -(_1763356 = c_List_Olist_ONil(_1763354)), 49198 ^ _775828 : [(49203 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763354)), 49197 ^ [_1763354, _1763356, _1763358]), c_List_Olists(_1763354, _1763358))))], (49201 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763354), 49196 ^ [_1763354, _1763356, _1763358]), _1763358)))], (49199 ^ _775828) ^ [] : [-(_1763356 = hAPP(hAPP(c_List_Olist_OCons(_1763354), 49196 ^ [_1763354, _1763356, _1763358]), 49197 ^ [_1763354, _1763356, _1763358]))]]], (31989 ^ _775828) ^ [_1367672, _1367674] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1367672, _1367674))))], (14830 ^ _775828) ^ [_1024030, _1024032, _1024034] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024030), _1024032)), _1024034) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024030), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024032), _1024034))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024030), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024032, _1024034))), _1024034)))], (17539 ^ _775828) ^ [_1076118, _1076120] : [_1076118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076120), _1076118) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (42337 ^ _775828) ^ [_1598138] : [-(c_Finite__Set_Ofun__left__comm__idem(_1598138, tc_fun(_1598138, tc_HOL_Obool), c_Set_Oinsert(_1598138)))], (48421 ^ _775828) ^ [_1746473, _1746475, _1746477, _1746479, _1746481] : [-(hAPP(hAPP(c_List_Odrop(_1746473), _1746475), hAPP(hAPP(c_List_Omap(_1746477, _1746473), _1746479), _1746481)) = hAPP(hAPP(c_List_Omap(_1746477, _1746473), _1746479), hAPP(hAPP(c_List_Odrop(_1746477), _1746475), _1746481)))], (50700 ^ _775828) ^ [_1796562, _1796564, _1796566, _1796568, _1796570] : [-(c_Map_Omap__upds(_1796562, _1796564, _1796566, _1796568, _1796570) = c_Map_Omap__add(_1796562, _1796564, _1796566, c_Map_Omap__of(_1796562, _1796564, hAPP(c_List_Orev(tc_prod(_1796562, _1796564)), hAPP(hAPP(c_List_Ozip(_1796562, _1796564), _1796568), _1796570)))))], (31351 ^ _775828) ^ [_1351979, _1351981, _1351983] : [class_Orderings_Olinorder(_1351979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351979), _1351981)), -(_1351981 = c_Orderings_Obot__class_Obot(tc_fun(_1351979, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351979), _1351983)), -(_1351983 = c_Orderings_Obot__class_Obot(tc_fun(_1351979, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1351979, c_Orderings_Oord__class_Omax(_1351979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351979, tc_HOL_Obool)), _1351981), _1351983)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351979), c_Big__Operators_Olattice_OSup__fin(_1351979, c_Orderings_Oord__class_Omax(_1351979), _1351981)), c_Big__Operators_Olattice_OSup__fin(_1351979, c_Orderings_Oord__class_Omax(_1351979), _1351983)))], (26856 ^ _775828) ^ [_1250327, _1250329] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250327), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1250329))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250327), _1250329)))], (33849 ^ _775828) ^ [_1404937, _1404939] : [class_Lattices_Olattice(_1404937), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404937), _1404939), _1404939) = _1404939)], (30009 ^ _775828) ^ [_1322817, _1322819, _1322821] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1322817, _1322819) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1322821), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1322817 = _1322819, _1322819 = _1322821], (39280 ^ _775828) ^ [_1524420, _1524422, _1524424, _1524426] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1524420, _1524422, _1524424, _1524426, c_Orderings_Obot__class_Obot(tc_fun(_1524420, tc_HOL_Obool))), _1524426)))], (19618 ^ _775828) ^ [_1112930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112930), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1112930)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40576 ^ _775828) ^ [_1555523] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1555523)), c_Int_OInteg)))], (12293 ^ _775828) ^ [_978528, _978530, _978532] : [-(_978528 = _978530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978532, tc_HOL_Obool)), _978528), _978530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978532, tc_HOL_Obool)), _978530), _978528))], (51014 ^ _775828) ^ [_1803141, _1803143] : [class_Lattices_Obounded__lattice(_1803141), -(class_Lattices_Obounded__lattice(tc_fun(_1803143, _1803141)))], (38870 ^ _775828) ^ [_1515924, _1515926, _1515928, _1515930, _1515932, _1515934] : [c_Fun_Oinj__on(_1515924, _1515926, _1515928, _1515930), hBOOL(hAPP(hAPP(c_member(_1515924), _1515932), _1515930)), hBOOL(hAPP(hAPP(c_member(_1515924), _1515934), _1515930)), 38881 ^ _775828 : [(38888 ^ _775828) ^ [] : [_1515932 = _1515934, -(hAPP(_1515928, _1515932) = hAPP(_1515928, _1515934))], (38882 ^ _775828) ^ [] : [hAPP(_1515928, _1515932) = hAPP(_1515928, _1515934), -(_1515932 = _1515934)]]], (28998 ^ _775828) ^ [_1300431, _1300433, _1300435, _1300437, _1300439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1300431, _1300431)), hAPP(hAPP(c_Product__Type_OPair(_1300431, _1300431), _1300433), _1300435)), _1300437)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1300431, _1300431)), hAPP(hAPP(c_Product__Type_OPair(_1300431, _1300431), _1300435), _1300439)), _1300437)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1300431, _1300431)), hAPP(hAPP(c_Product__Type_OPair(_1300431, _1300431), _1300433), _1300439)), c_Transitive__Closure_Otrancl(_1300431, _1300437))))], (32611 ^ _775828) ^ [_1378425, _1378427, _1378429] : [class_Lattices_Olattice(_1378425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378425), _1378427)), -(hBOOL(hAPP(hAPP(c_member(_1378425), _1378429), _1378427))), -(_1378427 = c_Orderings_Obot__class_Obot(tc_fun(_1378425, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1378425, hAPP(hAPP(c_Set_Oinsert(_1378425), _1378429), _1378427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1378425), _1378429), c_Big__Operators_Olattice__class_OSup__fin(_1378425, _1378427)))], (24402 ^ _775828) ^ [_1204280, _1204282, _1204284, _1204286, _1204288, _1204290, _1204292] : [-(hAPP(c_Product__Type_Oapsnd(_1204280, _1204282, _1204284, _1204286), hAPP(c_Product__Type_Oapfst(_1204288, _1204284, _1204280, _1204290), _1204292)) = hAPP(c_Product__Type_Oapfst(_1204288, _1204284, _1204282, _1204290), hAPP(c_Product__Type_Oapsnd(_1204280, _1204282, _1204288, _1204286), _1204292)))], (49273 ^ _775828) ^ [_1765172, _1765174, _1765176] : [-(_1765172 = c_List_Olist_ONil(_1765174)), -(c_List_Obutlast(_1765174, hAPP(hAPP(c_List_Olist_OCons(_1765174), _1765176), _1765172)) = hAPP(hAPP(c_List_Olist_OCons(_1765174), _1765176), c_List_Obutlast(_1765174, _1765172)))], (11454 ^ _775828) ^ [_964076, _964078, _964080, _964082, _964084, _964086] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_964076), -(_964078 = c_Groups_Ozero__class_Ozero(_964076)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964076), _964080), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964076), _964078), _964084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964076), _964082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964076), _964078), _964086)), _964080 = _964082, -(_964084 = _964086)], (49564 ^ _775828) ^ [_1772277, _1772279] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1772277))), c_List_Otranspose(_1772277, _1772279)) = c_List_Ofoldr(tc_List_Olist(_1772277), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1772277)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1772277))), _1772279, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10182 ^ _775828) ^ [_940738, _940740, _940742, _940744] : [class_Groups_Ocancel__semigroup__add(_940738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940738), _940740), _940742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940738), _940740), _940744), -(_940742 = _940744)], (12037 ^ _775828) ^ [_974173, _974175, _974177] : [12038 ^ _775828 : [(12041 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974175), _974177))], (12039 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _974173)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974173), _974175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974173), _974177))))], (37340 ^ _775828) ^ [_1480084, _1480086, _1480088] : [class_Groups_Ocomm__monoid__add(_1480084), hAPP(_1480086, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1480084), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480084), _1480086), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1480088)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480084), _1480086), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1480088)))], (10828 ^ _775828) ^ [_952880, _952882] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _952880)), _952882) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952880), _952882)))], (13196 ^ _775828) ^ [_994228, _994230, _994232, _994234] : [-(c_Com_Ocom_OSemi(_994228, _994230) = c_Com_Ocom_OSemi(_994232, _994234)), _994228 = _994232, _994230 = _994234], (2142 ^ _775828) ^ [_807096, _807098, _807100, _807102, _807104, _807106] : [-(c_Nat_Onat_Onat__rec(_807106, _807102, _807098) = c_Nat_Onat_Onat__rec(_807104, _807100, _807096)), _807106 = _807104, _807102 = _807100, _807098 = _807096], (8013 ^ _775828) ^ [_904486, _904488, _904490, _904492, _904494] : [class_Rings_Ocomm__semiring__1(_904486), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), _904488), _904490)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), _904492), _904494)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), _904488), _904492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904486), _904490), _904494)))], (50245 ^ _775828) ^ [_1785542, _1785544, _1785546] : [-(hAPP(c_List_Ofilter(_1785542, _1785544), c_List_Oconcat(_1785542, _1785546)) = c_List_Oconcat(_1785542, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785542), tc_List_Olist(_1785542)), c_List_Ofilter(_1785542, _1785544)), _1785546)))], (48181 ^ _775828) ^ [_1739453, _1739455, _1739457, _1739459, _1739461] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739453), tc_List_Olist(_1739453))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739453), tc_List_Olist(_1739453)), _1739455), _1739457)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739453), c_List_Olistrel1(_1739453, _1739459)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739453), tc_List_Olist(_1739453))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739453), tc_List_Olist(_1739453)), hAPP(hAPP(c_List_Olist_OCons(_1739453), _1739461), _1739455)), hAPP(hAPP(c_List_Olist_OCons(_1739453), _1739461), _1739457))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739453), c_List_Olistrel1(_1739453, _1739459)))))], (26501 ^ _775828) ^ [_1243876, _1243878, _1243880] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243878), _1243880))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243876), _1243878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243880), _1243878)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243876), _1243880)))], (17159 ^ _775828) ^ [_1069074, _1069076, _1069078] : [class_Rings_Oordered__ring__abs(_1069074), -(hAPP(c_Groups_Oabs__class_Oabs(_1069074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069074), _1069076), _1069078)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069074), hAPP(c_Groups_Oabs__class_Oabs(_1069074), _1069076)), hAPP(c_Groups_Oabs__class_Oabs(_1069074), _1069078))), 17166 ^ _775828 : [(17169 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069074), _1069076), c_Groups_Ozero__class_Ozero(_1069074)))], (17167 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069074), c_Groups_Ozero__class_Ozero(_1069074)), _1069076))]], 17170 ^ _775828 : [(17173 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069074), _1069078), c_Groups_Ozero__class_Ozero(_1069074)))], (17171 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069074), c_Groups_Ozero__class_Ozero(_1069074)), _1069078))]]], (24610 ^ _775828) ^ [_1208284, _1208286, _1208288] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1208284, _1208286, _1208288, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1208286)], (25126 ^ _775828) ^ [_1219335, _1219337, _1219339, _1219341, _1219343, _1219345] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1219335, _1219337, _1219339, _1219341, c_Nitpick_Opair__box_OPairBox(_1219335, _1219337, _1219343, _1219345)) = hAPP(hAPP(_1219341, _1219343), _1219345))], (24056 ^ _775828) ^ [_1197024, _1197026, _1197028, _1197030] : [class_Orderings_Olinorder(_1197024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197024), _1197026), _1197028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197024), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197024), _1197030), _1197026)), _1197028)))], (24739 ^ _775828) ^ [_1210629, _1210631, _1210633, _1210635, _1210637, _1210639] : [hBOOL(hAPP(hAPP(c_member(_1210629), _1210631), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1210633, _1210635, tc_fun(_1210629, tc_HOL_Obool)), _1210637), _1210639))), 24744 ^ _775828 : [(24747 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210629), _1210631), hAPP(hAPP(_1210637, 24742 ^ [_1210629, _1210631, _1210633, _1210635, _1210637, _1210639]), 24743 ^ [_1210629, _1210631, _1210633, _1210635, _1210637, _1210639]))))], (24745 ^ _775828) ^ [] : [-(_1210639 = hAPP(hAPP(c_Product__Type_OPair(_1210633, _1210635), 24742 ^ [_1210629, _1210631, _1210633, _1210635, _1210637, _1210639]), 24743 ^ [_1210629, _1210631, _1210633, _1210635, _1210637, _1210639]))]]], (40377 ^ _775828) ^ [_1549952, _1549954] : [class_Lattices_Oboolean__algebra(_1549952), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1549952), _1549954), hAPP(c_Groups_Ouminus__class_Ouminus(_1549952), _1549954)) = c_Orderings_Otop__class_Otop(_1549952))], (8553 ^ _775828) ^ [_913066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _913066), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _913066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11422 ^ _775828) ^ [_963510, _963512] : [class_Groups_Olinordered__ab__group__add(_963510), 11425 ^ _775828 : [(11432 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963510), _963512), c_Groups_Ozero__class_Ozero(_963510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963510), _963512), _963512)), c_Groups_Ozero__class_Ozero(_963510))))], (11426 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963510), _963512), _963512)), c_Groups_Ozero__class_Ozero(_963510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963510), _963512), c_Groups_Ozero__class_Ozero(_963510))))]]], (50253 ^ _775828) ^ [_1785729, _1785731] : [c_List_Olist_ONil(_1785729) = hAPP(c_List_Orev(_1785729), _1785731), -(_1785731 = c_List_Olist_ONil(_1785729))], (1798 ^ _775828) ^ [_801666, _801668, _801670, _801672, _801674, _801676, _801678, _801680] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_801680, _801676, _801672, _801668) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_801678, _801674, _801670, _801666)), _801680 = _801678, _801676 = _801674, _801672 = _801670, _801668 = _801666], (23258 ^ _775828) ^ [_1180985, _1180987, _1180989] : [class_Fields_Olinordered__field(_1180985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180985), _1180987), _1180989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180985), _1180987), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180985), _1180987), _1180989)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180985), c_Groups_Oone__class_Oone(_1180985)), c_Groups_Oone__class_Oone(_1180985))))))], (27286 ^ _775828) ^ [_1259206, _1259208, _1259210, _1259212, _1259214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1259206, _1259208)), hAPP(hAPP(c_Product__Type_OPair(_1259206, _1259208), _1259210), _1259212)), _1259214)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1259208, _1259206)), hAPP(hAPP(c_Product__Type_OPair(_1259208, _1259206), _1259212), _1259210)), hAPP(c_Relation_Oconverse(_1259206, _1259208), _1259214))))], (13706 ^ _775828) ^ [_1004122, _1004124, _1004126, _1004128] : [class_Divides_Osemiring__div(_1004122), -(c_Divides_Odiv__class_Omod(_1004122, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004122), _1004124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004122), _1004126), _1004128)), _1004126) = c_Divides_Odiv__class_Omod(_1004122, _1004124, _1004126))], (48295 ^ _775828) ^ [_1743045, _1743047, _1743049, _1743051, _1743053, _1743055, _1743057, _1743059] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1743045, _1743045)), hAPP(hAPP(c_Product__Type_OPair(_1743045, _1743045), _1743047), _1743049)), _1743051)), _1743053 = hAPP(hAPP(c_List_Oappend(_1743045), _1743055), hAPP(hAPP(c_List_Olist_OCons(_1743045), _1743047), _1743057)), _1743059 = hAPP(hAPP(c_List_Oappend(_1743045), _1743055), hAPP(hAPP(c_List_Olist_OCons(_1743045), _1743049), _1743057)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743045), tc_List_Olist(_1743045))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743045), tc_List_Olist(_1743045)), _1743053), _1743059)), c_List_Olistrel1(_1743045, _1743051))))], (45822 ^ _775828) ^ [_1680088, _1680090, _1680092, _1680094] : [-(c_Map_Omap__of(_1680088, _1680090, hAPP(hAPP(c_List_Omap(_1680088, tc_prod(_1680088, _1680090)), hAPP(hAPP(c_COMBS(_1680088, _1680090, tc_prod(_1680088, _1680090)), c_Product__Type_OPair(_1680088, _1680090)), _1680092)), _1680094)) = c_Map_Orestrict__map(_1680088, _1680090, hAPP(c_Fun_Ocomp(_1680090, tc_Option_Ooption(_1680090), _1680088, c_Option_Ooption_OSome(_1680090)), _1680092), hAPP(c_List_Oset(_1680088), _1680094)))], (15180 ^ _775828) ^ [_1030711, _1030713, _1030715, _1030717, _1030719] : [class_Groups_Oordered__ab__group__add(_1030711), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030711), _1030713), _1030715) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030711), _1030717), _1030719), 15187 ^ _775828 : [(15194 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030711), _1030717), _1030719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030711), _1030713), _1030715)))], (15188 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030711), _1030713), _1030715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030711), _1030717), _1030719)))]]], (46163 ^ _775828) ^ [_1688579, _1688581, _1688583] : [class_Orderings_Olinorder(_1688579), -(c_List_Oremove1(_1688579, _1688581, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1688579, _1688579, c_COMBI(_1688579)), _1688581), _1688583)) = _1688583)], (40209 ^ _775828) ^ [_1546620, _1546622, _1546624, _1546626, _1546628] : [_1546620 = hAPP(_1546622, _1546624), -(hBOOL(hAPP(hAPP(c_member(_1546626), _1546620), hAPP(c_Set_Oimage(_1546628, _1546626, _1546622), c_Orderings_Otop__class_Otop(tc_fun(_1546628, tc_HOL_Obool))))))], (11504 ^ _775828) ^ [_964950, _964952] : [class_Groups_Oab__group__add(_964950), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964950), hAPP(c_Groups_Ouminus__class_Ouminus(_964950), _964952)), _964952) = c_Groups_Ozero__class_Ozero(_964950))], (17393 ^ _775828) ^ [_1073633, _1073635, _1073637] : [class_Rings_Olinordered__semidom(_1073633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073633), c_Groups_Ozero__class_Ozero(_1073633)), _1073635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073633), _1073635), c_Groups_Oone__class_Oone(_1073633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073633), hAPP(hAPP(c_Power_Opower__class_Opower(_1073633), _1073635), hAPP(c_Nat_OSuc, _1073637))), c_Groups_Oone__class_Oone(_1073633))))], (40319 ^ _775828) ^ [_1548764, _1548766, _1548768, _1548770] : [hBOOL(hAPP(hAPP(c_member(_1548766), _1548770), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548764, tc_fun(_1548766, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1548764, tc_HOL_Obool))), _1548768))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548764, tc_fun(_1548766, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1548764, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1548766, tc_HOL_Obool), tc_fun(_1548766, tc_HOL_Obool), _1548764), hAPP(c_COMBC(_1548766, tc_fun(_1548766, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548766))), _1548768)), _1548770)))], (12115 ^ _775828) ^ [_975502, _975504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975502)), 12118 ^ _775828 : [(12127 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _975502), _975504) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _975502 = c_Groups_Oone__class_Oone(tc_Int_Oint), _975504 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (12119 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _975502), _975504) = c_Groups_Oone__class_Oone(tc_Int_Oint), 12122 ^ _775828 : [(12125 ^ _775828) ^ [] : [-(_975504 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (12123 ^ _775828) ^ [] : [-(_975502 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (50202 ^ _775828) ^ [_1784038, _1784040, _1784042, _1784044] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1784038, tc_Nat_Onat), _1784038), c_Product__Type_Ofst(_1784038, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1784038, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1784038, 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(_1784038, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1784038, tc_Nat_Onat))), _1784040)), hAPP(hAPP(c_List_Ozip(_1784038, tc_Nat_Onat), _1784042), c_List_Oupt(_1784044, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1784044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784038)), _1784042)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1784038, tc_Nat_Onat), _1784038), c_Product__Type_Ofst(_1784038, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1784038, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1784038, 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(_1784038, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1784038, 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(_1784038, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1784038, tc_Nat_Onat))), _1784044))), _1784040)), hAPP(hAPP(c_List_Ozip(_1784038, tc_Nat_Onat), _1784042), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784038)), _1784042))))))], (5595 ^ _775828) ^ [_864519, _864521, _864523, _864525, _864527] : [c_Hoare__Mirabelle_Otriple__valid(_864519, _864521, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864519), _864523), _864525), _864527)), 5598 ^ _775828 : [(5599 ^ _775828) ^ [_864640, _864642] : [hBOOL(hAPP(hAPP(_864523, _864642), _864640)), 5602 ^ _775828 : [(5603 ^ _775828) ^ [_864730] : [c_Natural_Oevaln(_864525, _864640, _864521, _864730), -(hBOOL(hAPP(hAPP(_864527, _864642), _864730)))]]]]], (49746 ^ _775828) ^ [_1775904, _1775906] : [c_List_Oupt(_1775904, _1775906) = c_List_Olist_ONil(tc_Nat_Onat), -(_1775906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1775906), _1775904)))], (36948 ^ _775828) ^ [_1470622, _1470624, _1470626, _1470628, _1470630, _1470632, _1470634] : [class_Rings_Osemiring__0(_1470622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470622), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470624, _1470622), _1470626), _1470628)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470630, _1470622), _1470632), _1470634)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470624, _1470622), hAPP(hAPP(c_COMBC(_1470624, tc_fun(_1470630, tc_HOL_Obool), _1470622), hAPP(hAPP(c_COMBB(tc_fun(_1470630, _1470622), tc_fun(tc_fun(_1470630, tc_HOL_Obool), _1470622), _1470624), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470630, _1470622)), hAPP(hAPP(c_COMBC(_1470624, tc_fun(_1470630, _1470622), tc_fun(_1470630, _1470622)), hAPP(hAPP(c_COMBB(tc_fun(_1470622, _1470622), tc_fun(tc_fun(_1470630, _1470622), tc_fun(_1470630, _1470622)), _1470624), c_COMBB(_1470622, _1470622, _1470630)), hAPP(hAPP(c_COMBB(_1470622, tc_fun(_1470622, _1470622), _1470624), c_Groups_Otimes__class_Otimes(_1470622)), _1470626))), _1470632))), _1470634)), _1470628))], (32089 ^ _775828) ^ [_1369221, _1369223, _1369225] : [class_Orderings_Olinorder(_1369221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369221), _1369223)), hBOOL(hAPP(hAPP(c_member(_1369221), _1369225), _1369223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369221), _1369225), c_Big__Operators_Olinorder__class_OMax(_1369221, _1369223))))], (28747 ^ _775828) ^ [] : [-(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))))], (42244 ^ _775828) ^ [_1596125, _1596127, _1596129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596125, _1596125), tc_HOL_Obool)), _1596127), hAPP(hAPP(c_Product__Type_OSigma(_1596125, _1596125), _1596129), hAPP(c_COMBK(tc_fun(_1596125, tc_HOL_Obool), _1596125), _1596129)))), 42250 ^ _775828 : [(42253 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596125, _1596125)), hAPP(hAPP(c_Product__Type_OPair(_1596125, _1596125), 42249 ^ [_1596125, _1596127, _1596129]), 42249 ^ [_1596125, _1596127, _1596129])), _1596127))], (42251 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1596125), 42249 ^ [_1596125, _1596127, _1596129]), _1596129)))]], -(c_Relation_Orefl__on(_1596125, _1596129, _1596127))], (12417 ^ _775828) ^ [_980720, _980722] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980720), _980722)), _980720 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _980722 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5485 ^ _775828) ^ [_862522, _862524, _862526, _862528, _862530, _862532, _862534] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862522), _862524), _862526), _862528) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862522), _862530), _862532), _862534)), _862524 = _862530, _862526 = _862532, _862528 = _862534], (44647 ^ _775828) ^ [_1653603, _1653605] : [class_Complete__Lattice_Ocomplete__lattice(_1653603), -(c_Complete__Lattice_OInf__class_OInf(_1653603, _1653605) = c_Complete__Lattice_OSup__class_OSup(_1653603, hAPP(c_Set_OCollect(_1653603), hAPP(hAPP(c_COMBB(tc_fun(_1653603, tc_HOL_Obool), tc_HOL_Obool, _1653603), c_HOL_OAll(_1653603)), hAPP(hAPP(c_COMBB(tc_fun(_1653603, tc_HOL_Obool), tc_fun(_1653603, tc_HOL_Obool), _1653603), hAPP(c_COMBS(_1653603, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1653603), c_fimplies), hAPP(hAPP(c_COMBC(_1653603, tc_fun(_1653603, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653603)), _1653605)))), c_Orderings_Oord__class_Oless__eq(_1653603))))))], (27250 ^ _775828) ^ [_1258234] : [-(c_Int_Oint__ge__less__than(_1258234) = 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), _1258234)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (40830 ^ _775828) ^ [_1561202, _1561204, _1561206, _1561208, _1561210] : [hBOOL(hAPP(hAPP(c_member(_1561202), hAPP(_1561204, _1561206)), _1561208)), -(hBOOL(hAPP(hAPP(c_member(_1561210), _1561206), hAPP(c_Set_Ovimage(_1561210, _1561202, _1561204), _1561208))))], (29759 ^ _775828) ^ [_1316245, _1316247, _1316249, _1316251, _1316253, _1316255, _1316257] : [c_Hoare__Mirabelle_Ohoare__derivs(_1316245, _1316247, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316245)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316245), _1316249), _1316251), _1316253)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316245), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1316245, _1316247, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316245)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316245), _1316253), _1316255), _1316257)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316245), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1316245, _1316247, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316245)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316245), _1316249), c_Com_Ocom_OSemi(_1316251, _1316255)), _1316257)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316245), tc_HOL_Obool)))))], (20250 ^ _775828) ^ [_1123744, _1123746] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123744))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123746))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123744)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123746)))], (19790 ^ _775828) ^ [_1115754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1115754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1115754))))], (46105 ^ _775828) ^ [_1687286, _1687288, _1687290, _1687292] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1687286, _1687288))), hAPP(hAPP(c_List_Ozip(_1687286, _1687288), _1687290), _1687292)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687286)), _1687290)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687288)), _1687292)))], (22216 ^ _775828) ^ [_1161921, _1161923] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1161921, _1161923) = 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), _1161921), _1161923)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1161921, _1161923)))], (13398 ^ _775828) ^ [_998101, _998103, _998105] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998101), _998103), _998105) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998101), c_Divides_Odiv__class_Omod(tc_Int_Oint, _998103, _998105)), _998105))], (38548 ^ _775828) ^ [_1508768, _1508770, _1508772, _1508774, _1508776] : [hAPP(c_Relation_OImage(_1508768, _1508768, _1508770), hAPP(hAPP(c_Set_Oinsert(_1508768), _1508772), c_Orderings_Obot__class_Obot(tc_fun(_1508768, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508768, _1508768, _1508770), hAPP(hAPP(c_Set_Oinsert(_1508768), _1508774), c_Orderings_Obot__class_Obot(tc_fun(_1508768, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1508768, _1508776, _1508770), hBOOL(hAPP(hAPP(c_member(_1508768), _1508774), _1508776)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508768, _1508768)), hAPP(hAPP(c_Product__Type_OPair(_1508768, _1508768), _1508772), _1508774)), _1508770)))], (51476 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (44395 ^ _775828) ^ [_1647026, _1647028, _1647030, _1647032, _1647034] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647026, tc_HOL_Obool)), _1647028), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647030, tc_fun(_1647026, tc_HOL_Obool)), _1647032), _1647034)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1647030, tc_fun(_1647026, tc_HOL_Obool)), _1647032), hAPP(hAPP(c_COMBB(tc_fun(_1647026, tc_HOL_Obool), tc_fun(_1647026, tc_HOL_Obool), _1647030), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647026, tc_HOL_Obool)), _1647028)), _1647034)))], (49981 ^ _775828) ^ [_1779710, _1779712] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779710)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779712)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779710), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1779712)) = c_List_Olist_ONil(tc_Nat_Onat))], (12387 ^ _775828) ^ [_980250, _980252] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980250), _980252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _980250)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _980252)))], (30171 ^ _775828) ^ [_1325760, _1325762] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325760), _1325762))), -(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), _1325760, _1325762))], (42910 ^ _775828) ^ [_1611757, _1611759, _1611761, _1611763, _1611765, _1611767] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1611757, _1611759), _1611757, tc_prod(_1611761, _1611763), c_Product__Type_Ofst(_1611757, _1611759)), c_Product__Type_Omap__pair(_1611761, _1611757, _1611763, _1611759, _1611765, _1611767)) = hAPP(c_Fun_Ocomp(_1611761, _1611757, tc_prod(_1611761, _1611763), _1611765), c_Product__Type_Ofst(_1611761, _1611763)))], (26798 ^ _775828) ^ [_1249363, _1249365] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1249363)), _1249365)), 26801 ^ _775828 : [(26808 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249363))), -(_1249365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26802 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249363)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1249363), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249365))))]]], (37380 ^ _775828) ^ [_1481140, _1481142, _1481144, _1481146, _1481148] : [class_Groups_Ocomm__monoid__add(_1481140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481142), _1481144)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481142, _1481140), _1481146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481142, tc_HOL_Obool)), _1481144), _1481148)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481142, _1481140), hAPP(hAPP(c_COMBC(_1481142, _1481140, _1481140), hAPP(hAPP(c_COMBS(_1481142, _1481140, tc_fun(_1481140, _1481140)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1481140, tc_fun(_1481140, _1481140)), _1481142), c_If(_1481140)), hAPP(hAPP(c_COMBC(_1481142, tc_fun(_1481142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481142)), _1481148))), _1481146)), c_Groups_Ozero__class_Ozero(_1481140))), _1481144))], (34291 ^ _775828) ^ [_1414473, _1414475, _1414477] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414473, tc_HOL_Obool)), _1414475), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414473, tc_HOL_Obool)), _1414477)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414473, tc_HOL_Obool)), _1414475), _1414477))], (51300 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (13156 ^ _775828) ^ [_993405, _993407, _993409] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_993405, _993407, _993409))), -(hBOOL(hAPP(c_Com_OWT, _993409)))], (6129 ^ _775828) ^ [_873236, _873238] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _873236, _873238, _873236))], (11032 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (1950 ^ _775828) ^ [_804094, _804096, _804098, _804100] : [-(c_SMT_Oz3div(_804100, _804096) = c_SMT_Oz3div(_804098, _804094)), _804100 = _804098, _804096 = _804094], (8061 ^ _775828) ^ [_905329, _905331, _905333] : [8062 ^ _775828 : [(8065 ^ _775828) ^ [] : [_905331 = _905333], (8063 ^ _775828) ^ [] : [_905329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _905329), _905331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _905329), _905333))], (1340 ^ _775828) ^ [_795196, _795198] : [-(class_Finite__Set_Ofinite(_795196)), _795198 = _795196, class_Finite__Set_Ofinite(_795198)], (2940 ^ _775828) ^ [_819979, _819981, _819983, _819985, _819987, _819989] : [-(c_SetInterval_Oord_OgreaterThan(_819989, _819985, _819981) = c_SetInterval_Oord_OgreaterThan(_819987, _819983, _819979)), _819989 = _819987, _819985 = _819983, _819981 = _819979], (28984 ^ _775828) ^ [_1300133, _1300135, _1300137, _1300139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1300133, _1300133)), _1300135), c_Transitive__Closure_Otrancl(_1300133, _1300137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1300133, _1300133), tc_HOL_Obool)), _1300137), _1300139)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1300133, _1300133)), _1300135), c_Transitive__Closure_Otrancl(_1300133, _1300139))))], (31029 ^ _775828) ^ [_1344539, _1344541, _1344543, _1344545] : [c_Finite__Set_Ofolding__one(_1344539, _1344541, _1344543), -(hAPP(_1344543, hAPP(hAPP(c_Set_Oinsert(_1344539), _1344545), c_Orderings_Obot__class_Obot(tc_fun(_1344539, tc_HOL_Obool)))) = _1344545)], (12371 ^ _775828) ^ [_979890, _979892, _979894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _979890), _979892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979894), _979890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979894), _979892))))], (29571 ^ _775828) ^ [_1312403, _1312405, _1312407, _1312409] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312403, tc_HOL_Obool)), _1312405), hAPP(hAPP(c_Set_Oinsert(_1312403), _1312407), _1312409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312403, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312403, tc_HOL_Obool)), _1312405), _1312409)), hAPP(hAPP(c_Set_Oinsert(_1312403), _1312407), c_Orderings_Obot__class_Obot(tc_fun(_1312403, tc_HOL_Obool)))))], (436 ^ _775828) ^ [_782318, _782320, _782322, _782324] : [-(c_Equiv__Relations_Oequivp(_782322, _782318)), c_Equiv__Relations_Oequivp(_782324, _782320), _782324 = _782322, _782320 = _782318], (26591 ^ _775828) ^ [_1245843, _1245845, _1245847] : [class_Divides_Osemiring__div(_1245843), class_Int_Onumber(_1245843), 26598 ^ _775828 : [(26605 ^ _775828) ^ [] : [c_Divides_Odiv__class_Omod(_1245843, hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245847), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245845)) = c_Groups_Ozero__class_Ozero(_1245843), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245843), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245845)), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245847))))], (26599 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245843), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245845)), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245847))), -(c_Divides_Odiv__class_Omod(_1245843, hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245847), hAPP(c_Int_Onumber__class_Onumber__of(_1245843), _1245845)) = c_Groups_Ozero__class_Ozero(_1245843))]]], (30251 ^ _775828) ^ [] : [-(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)))], (6917 ^ _775828) ^ [_885400, _885402] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885400), _885402) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _885402), _885400))], (17871 ^ _775828) ^ [_1081842, _1081844, _1081846] : [class_Groups_Omonoid__mult(_1081842), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081842), _1081844), hAPP(c_Nat_OSuc, _1081846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081842), hAPP(hAPP(c_Power_Opower__class_Opower(_1081842), _1081844), _1081846)), _1081844))], (2130 ^ _775828) ^ [_806926, _806928] : [_806928 = _806926, -(c_Hoare__Mirabelle_OMGT(_806928) = c_Hoare__Mirabelle_OMGT(_806926))], (36521 ^ _775828) ^ [_1461942, _1461944] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461942), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1461944) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1461942, _1461944))], (42075 ^ _775828) ^ [_1592229, _1592231, _1592233, _1592235, _1592237, _1592239, _1592241] : [-(hAPP(c_Product__Type_Ofst(_1592229, _1592231), hAPP(c_Product__Type_Omap__pair(_1592233, _1592229, _1592235, _1592231, _1592237, _1592239), _1592241)) = hAPP(_1592237, hAPP(c_Product__Type_Ofst(_1592233, _1592235), _1592241)))], (12679 ^ _775828) ^ [_985143, _985145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985143), _985145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _985143), c_Groups_Oone__class_Oone(tc_Int_Oint))), _985145)))], (24378 ^ _775828) ^ [_1203695, _1203697] : [_1203695 = _1203697, -(c_Code__Numeral_OSuc__code__numeral(_1203695) = c_Code__Numeral_OSuc__code__numeral(_1203697))], (16130 ^ _775828) ^ [_1049332, _1049334, _1049336, _1049338, _1049340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049332), _1049334)), 16133 ^ _775828 : [(16140 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049338), 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), _1049334), _1049332)), _1049336)), _1049340))), -(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), _1049332), _1049336)), _1049338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049334), _1049336)), _1049340))))], (16134 ^ _775828) ^ [] : [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), _1049332), _1049336)), _1049338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049334), _1049336)), _1049340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049338), 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), _1049334), _1049332)), _1049336)), _1049340))))]]], (49756 ^ _775828) ^ [_1776006, _1776008] : [49757 ^ _775828 : [(49760 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1776008), _1776006))], (49758 ^ _775828) ^ [] : [_1776008 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1776006, _1776008) = c_List_Olist_ONil(tc_Nat_Onat))], (38436 ^ _775828) ^ [_1506078, _1506080] : [-(c_Map_Odom(_1506078, _1506080, hAPP(c_COMBK(tc_Option_Ooption(_1506080), _1506078), c_Option_Ooption_ONone(_1506080))) = c_Orderings_Obot__class_Obot(tc_fun(_1506078, tc_HOL_Obool)))], (20040 ^ _775828) ^ [_1120137, _1120139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120137)), c_Int_OBit0(_1120139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120137), _1120139)))], (47691 ^ _775828) ^ [_1727723, _1727725, _1727727, _1727729, _1727731, _1727733] : [-(c_Map_Omap__add(_1727723, _1727725, _1727727, c_Map_Omap__upds(_1727723, _1727725, _1727729, _1727731, _1727733)) = c_Map_Omap__upds(_1727723, _1727725, c_Map_Omap__add(_1727723, _1727725, _1727727, _1727729), _1727731, _1727733))], (41885 ^ _775828) ^ [_1587515, _1587517] : [-(c_Fun_Oinj__on(_1587515, _1587515, c_Fun_Oid(_1587515), _1587517))], (46125 ^ _775828) ^ [_1687673, _1687675, _1687677, _1687679, _1687681] : [class_Orderings_Olinorder(_1687673), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687675)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687675, _1687673, _1687677), _1687679), _1687681)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687675)), _1687681)))], (24887 ^ _775828) ^ [_1214089, _1214091, _1214093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1214089), c_Nitpick_Oplus__frac(_1214089, _1214091, c_Nitpick_Ouminus__frac(_1214089, _1214093)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1214089, _1214091, _1214093))], (29887 ^ _775828) ^ [_1319302, _1319304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319302, tc_HOL_Obool)), _1319304), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1319302, tc_HOL_Obool)), _1319304))), -(_1319304 = c_Orderings_Obot__class_Obot(tc_fun(_1319302, tc_HOL_Obool)))], (48171 ^ _775828) ^ [_1739193, _1739195, _1739197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1739193, _1739193), tc_HOL_Obool)), _1739195), _1739197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1739193), tc_List_Olist(_1739193)), tc_HOL_Obool)), c_List_Olistrel1(_1739193, _1739195)), c_List_Olistrel1(_1739193, _1739197))))], (19824 ^ _775828) ^ [_1116209] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1116209))) = 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)))), _1116209))], (45781 ^ _775828) ^ [_1679328, _1679330, _1679332, _1679334, _1679336] : [hAPP(c_Map_Omap__of(_1679328, _1679330, _1679332), _1679334) = hAPP(c_Option_Ooption_OSome(_1679330), _1679336), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679328, _1679330)), hAPP(hAPP(c_Product__Type_OPair(_1679328, _1679330), _1679334), _1679336)), hAPP(c_List_Oset(tc_prod(_1679328, _1679330)), _1679332))))], (23586 ^ _775828) ^ [_1188518, _1188520, _1188522, _1188524, _1188526] : [-(hAPP(c_Product__Type_Ofst(_1188518, _1188520), hAPP(c_Product__Type_Oapsnd(_1188522, _1188520, _1188518, _1188524), _1188526)) = hAPP(c_Product__Type_Ofst(_1188518, _1188522), _1188526))], (27617 ^ _775828) ^ [_1266791, _1266793, _1266795, _1266797, _1266799] : [-(hBOOL(hAPP(hAPP(c_member(_1266791), _1266793), c_SetInterval_Oord_OgreaterThanLessThan(_1266791, _1266795, _1266797, _1266799)))), hBOOL(hAPP(hAPP(_1266795, _1266797), _1266793)), hBOOL(hAPP(hAPP(_1266795, _1266793), _1266799))], (44258 ^ _775828) ^ [_1643207, _1643209, _1643211, _1643213, _1643215] : [class_Complete__Lattice_Ocomplete__lattice(_1643207), class_Orderings_Olinorder(_1643207), 44265 ^ _775828 : [(44275 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643207), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643209, _1643207), _1643211), _1643213)), _1643215))), 44276 ^ _775828 : [(44277 ^ _775828) ^ [_1643555] : [hBOOL(hAPP(hAPP(c_member(_1643209), _1643555), _1643211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643207), hAPP(_1643213, _1643555)), _1643215))]]], (44266 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643207), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643209, _1643207), _1643211), _1643213)), _1643215)), 44270 ^ _775828 : [(44273 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643207), hAPP(_1643213, 44269 ^ [_1643207, _1643209, _1643211, _1643213, _1643215])), _1643215)))], (44271 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1643209), 44269 ^ [_1643207, _1643209, _1643211, _1643213, _1643215]), _1643211)))]]]]], (32893 ^ _775828) ^ [_1384212, _1384214, _1384216, _1384218, _1384220, _1384222] : [class_Groups_Ocomm__monoid__mult(_1384212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384214), _1384216)), 32900 ^ _775828 : [(32907 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384214), _1384218), _1384216))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384214, _1384212), hAPP(hAPP(c_COMBC(_1384214, _1384212, _1384212), hAPP(hAPP(c_COMBS(_1384214, _1384212, tc_fun(_1384212, _1384212)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1384212, tc_fun(_1384212, _1384212)), _1384214), c_If(_1384212)), hAPP(hAPP(c_COMBC(_1384214, _1384214, tc_HOL_Obool), c_fequal), _1384218))), _1384220)), _1384222)), _1384216) = hAPP(hAPP(c_Power_Opower__class_Opower(_1384212), _1384222), hAPP(c_Finite__Set_Ocard(_1384214), _1384216)))], (32901 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1384214), _1384218), _1384216)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384214, _1384212), hAPP(hAPP(c_COMBC(_1384214, _1384212, _1384212), hAPP(hAPP(c_COMBS(_1384214, _1384212, tc_fun(_1384212, _1384212)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1384212, tc_fun(_1384212, _1384212)), _1384214), c_If(_1384212)), hAPP(hAPP(c_COMBC(_1384214, _1384214, tc_HOL_Obool), c_fequal), _1384218))), _1384220)), _1384222)), _1384216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384212), hAPP(_1384220, _1384218)), hAPP(hAPP(c_Power_Opower__class_Opower(_1384212), _1384222), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1384214), _1384216)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (27609 ^ _775828) ^ [_1266642, _1266644, _1266646, _1266648, _1266650] : [hBOOL(hAPP(hAPP(c_member(_1266642), _1266644), c_SetInterval_Oord_OgreaterThanLessThan(_1266642, _1266646, _1266648, _1266650))), 27612 ^ _775828 : [(27615 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1266646, _1266644), _1266650)))], (27613 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1266646, _1266648), _1266644)))]]], (24388 ^ _775828) ^ [_1203925, _1203927, _1203929, _1203931, _1203933, _1203935] : [hAPP(c_Product__Type_Oapfst(_1203925, _1203927, _1203929, _1203931), _1203933) = hAPP(c_Product__Type_Oapfst(_1203925, _1203927, _1203929, _1203935), _1203933), -(hAPP(_1203931, hAPP(c_Product__Type_Ofst(_1203925, _1203929), _1203933)) = hAPP(_1203935, hAPP(c_Product__Type_Ofst(_1203925, _1203929), _1203933)))], (28293 ^ _775828) ^ [_1283361, _1283363, _1283365, _1283367] : [class_Lattices_Osemilattice__sup(_1283361), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283361), _1283363), _1283365)), _1283367) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283361), _1283363), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283361), _1283365), _1283367)))], (19800 ^ _775828) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (40505 ^ _775828) ^ [_1552799, _1552801, _1552803, _1552805] : [_1552803 = _1552805, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1552799, _1552801, hAPP(hAPP(c_Set_Oinsert(_1552799), _1552803), c_Orderings_Obot__class_Obot(tc_fun(_1552799, tc_HOL_Obool)))), _1552805)))], (31099 ^ _775828) ^ [_1345916] : [-(c_Wellfounded_Ofinite__psubset(_1345916) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1345916, tc_HOL_Obool), tc_fun(_1345916, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1345916, tc_HOL_Obool), tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1345916, tc_HOL_Obool), tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1345916, tc_HOL_Obool)), c_COMBS(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1345916, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1345916, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1345916, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1345916, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1345916)))))], (36777 ^ _775828) ^ [_1466673, _1466675, _1466677, _1466679, _1466681] : [c_Finite__Set_Ofolding__one__idem(_1466673, _1466675, _1466677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466673), _1466679)), hBOOL(hAPP(hAPP(c_member(_1466673), _1466681), _1466679)), -(hAPP(hAPP(_1466675, _1466681), hAPP(_1466677, _1466679)) = hAPP(_1466677, _1466679))], (5589 ^ _775828) ^ [_864399] : [hAPP(c_Nat_OSuc, _864399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34293 ^ _775828) ^ [_1414530, _1414532, _1414534, _1414536] : [class_Orderings_Oorder(_1414530), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414530, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1414530, _1414532, _1414534)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1414530, _1414534, _1414536)) = c_Orderings_Obot__class_Obot(tc_fun(_1414530, tc_HOL_Obool)))], (18799 ^ _775828) ^ [_1099008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1099008)), 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), _1099008)) = 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), _1099008))))))], (37248 ^ _775828) ^ [_1478186, _1478188, _1478190, _1478192, _1478194] : [class_Groups_Ocomm__monoid__add(_1478186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478188), _1478190)), -(hBOOL(hAPP(hAPP(c_member(_1478188), _1478192), _1478190))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478188, _1478186), _1478194), hAPP(hAPP(c_Set_Oinsert(_1478188), _1478192), _1478190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478186), hAPP(_1478194, _1478192)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478188, _1478186), _1478194), _1478190)))], (12155 ^ _775828) ^ [_976110, _976112] : [class_Lattices_Oboolean__algebra(_976110), -(hAPP(c_Groups_Ouminus__class_Ouminus(_976110), hAPP(c_Groups_Ouminus__class_Ouminus(_976110), _976112)) = _976112)], (51464 ^ _775828) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (45690 ^ _775828) ^ [_1677223, _1677225, _1677227, _1677229, _1677231, _1677233] : [-(hAPP(hAPP(c_Option_Omap(_1677223, _1677225), _1677227), hAPP(hAPP(c_Option_Omap(_1677229, _1677223), _1677231), _1677233)) = hAPP(hAPP(c_Option_Omap(_1677229, _1677225), hAPP(c_Fun_Ocomp(_1677223, _1677225, _1677229, _1677227), _1677231)), _1677233))], (18175 ^ _775828) ^ [_1087877] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087877)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087877)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1087877)))], (46660 ^ _775828) ^ [_1703249, _1703251, _1703253, _1703255] : [hBOOL(hAPP(hAPP(c_member(_1703249), _1703251), hAPP(c_List_Oset(_1703249), c_List_Osublist(_1703249, _1703253, _1703255)))), -(hBOOL(hAPP(hAPP(c_member(_1703249), _1703251), hAPP(c_List_Oset(_1703249), _1703253))))], (9209 ^ _775828) ^ [_923105, _923107, _923109] : [class_Rings_Oordered__cancel__semiring(_923105), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923105), _923107), _923109)), c_Groups_Ozero__class_Ozero(_923105)))), 9214 ^ _775828 : [(9221 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923105), _923107), c_Groups_Ozero__class_Ozero(_923105))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923105), c_Groups_Ozero__class_Ozero(_923105)), _923109))], (9215 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923105), c_Groups_Ozero__class_Ozero(_923105)), _923107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923105), _923109), c_Groups_Ozero__class_Ozero(_923105)))]]], (26920 ^ _775828) ^ [_1251350, _1251352, _1251354] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251350), _1251352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251350), _1251354))), -(_1251350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251352), _1251354)))], (16212 ^ _775828) ^ [_1051101, _1051103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051101), _1051103)), -(c_Nat__Transfer_Otsub(_1051103, _1051101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1051103), _1051101))], (20638 ^ _775828) ^ [_1130373, _1130375, _1130377] : [class_Rings_Oring__1(_1130373), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1130373), hAPP(c_Groups_Ouminus__class_Ouminus(_1130373), _1130375)), 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)))), _1130377)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1130373), _1130375), 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)))), _1130377)))], (38648 ^ _775828) ^ [_1511084, _1511086, _1511088] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511084), hAPP(hAPP(c_Set_Oinsert(_1511084), _1511086), c_Orderings_Obot__class_Obot(tc_fun(_1511084, tc_HOL_Obool)))), _1511088) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1511084, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1511084, _1511084, _1511088), hAPP(hAPP(c_Set_Oinsert(_1511084), _1511086), c_Orderings_Obot__class_Obot(tc_fun(_1511084, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1511084, tc_HOL_Obool), tc_HOL_Obool))))], (39557 ^ _775828) ^ [_1531303, _1531305, _1531307, _1531309] : [39559 ^ _775828 : [(39562 ^ _775828) ^ [] : [hAPP(_1531309, 39558 ^ [_1531303, _1531305, _1531307, _1531309]) = c_Orderings_Obot__class_Obot(tc_fun(_1531305, tc_HOL_Obool))], (39560 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531303), 39558 ^ [_1531303, _1531305, _1531307, _1531309]), _1531307)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531303, tc_fun(_1531305, tc_HOL_Obool)), _1531307), _1531309) = c_Orderings_Obot__class_Obot(tc_fun(_1531305, tc_HOL_Obool)))], (45307 ^ _775828) ^ [_1668245, _1668247, _1668249, _1668251] : [-(c_Map_Odom(_1668245, _1668247, c_Map_Omap__add(_1668245, _1668247, _1668249, _1668251)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1668245, tc_HOL_Obool)), c_Map_Odom(_1668245, _1668247, _1668251)), c_Map_Odom(_1668245, _1668247, _1668249)))], (25573 ^ _775828) ^ [_1227990, _1227992, _1227994] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227990), _1227992)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227990), _1227994)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227990), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227992), _1227994))))], (13328 ^ _775828) ^ [_996622, _996624, _996626, _996628] : [class_Divides_Osemiring__div(_996622), -(c_Divides_Odiv__class_Omod(_996622, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996622), _996624), _996626), _996628) = c_Divides_Odiv__class_Omod(_996622, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996622), _996624), c_Divides_Odiv__class_Omod(_996622, _996626, _996628)), _996628))], (8383 ^ _775828) ^ [_910458, _910460, _910462, _910464] : [class_Orderings_Oorder(_910458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910458), _910460), _910462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910458), _910464), _910460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910458), _910464), _910462)))], (5094 ^ _775828) ^ [_853758, _853760] : [_853760 = _853758, -(c_List_Orev(_853760) = c_List_Orev(_853758))], (49142 ^ _775828) ^ [_1762325, _1762327] : [-(_1762325 = c_List_Olist_ONil(_1762327)), -(hBOOL(hAPP(hAPP(c_member(_1762327), c_List_Olast(_1762327, _1762325)), hAPP(c_List_Oset(_1762327), _1762325))))], (39980 ^ _775828) ^ [_1542494, _1542496, _1542498, _1542500, _1542502, _1542504, _1542506] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542494, tc_fun(_1542496, tc_fun(_1542498, tc_HOL_Obool))), _1542500), _1542502), _1542504), _1542506))), 39981 ^ _775828 : [(39982 ^ _775828) ^ [_1542579] : [hBOOL(hAPP(hAPP(c_member(_1542494), _1542579), _1542500)), hBOOL(hAPP(hAPP(hAPP(_1542502, _1542579), _1542504), _1542506))]]], (20016 ^ _775828) ^ [_1119691, _1119693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1119691)), c_Int_OBit0(_1119693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119691), _1119693)))], (40029 ^ _775828) ^ [] : [-(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)))], (34511 ^ _775828) ^ [_1419414, _1419416, _1419418, _1419420, _1419422] : [c_Finite__Set_Ofolding__one(_1419414, _1419416, _1419418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419414), _1419420)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419414), _1419422)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419414, tc_HOL_Obool)), _1419420), _1419422) = c_Orderings_Obot__class_Obot(tc_fun(_1419414, tc_HOL_Obool))), -(hAPP(hAPP(_1419416, hAPP(_1419418, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419414, tc_HOL_Obool)), _1419420), _1419422))), hAPP(_1419418, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419414, tc_HOL_Obool)), _1419420), _1419422))) = hAPP(hAPP(_1419416, hAPP(_1419418, _1419420)), hAPP(_1419418, _1419422)))], (42673 ^ _775828) ^ [_1606285, _1606287, _1606289, _1606291, _1606293, _1606295] : [-(hAPP(c_Set_Ovimage(_1606285, tc_prod(_1606287, _1606289), _1606291), hAPP(hAPP(c_Product__Type_OSigma(_1606287, _1606289), _1606293), hAPP(c_COMBK(tc_fun(_1606289, tc_HOL_Obool), _1606287), _1606295))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606285, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1606285, _1606287, hAPP(c_Fun_Ocomp(tc_prod(_1606287, _1606289), _1606287, _1606285, c_Product__Type_Ofst(_1606287, _1606289)), _1606291)), _1606293)), hAPP(c_Set_Ovimage(_1606285, _1606289, hAPP(c_Fun_Ocomp(tc_prod(_1606287, _1606289), _1606289, _1606285, c_Product__Type_Osnd(_1606287, _1606289)), _1606291)), _1606295)))], (46213 ^ _775828) ^ [_1689660, _1689662, _1689664, _1689666, _1689668] : [class_Orderings_Olinorder(_1689660), 46216 ^ _775828 : [(46225 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1689662), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1689662, _1689660, _1689664), _1689666), _1689668)))), -(hBOOL(hAPP(hAPP(c_member(_1689662), _1689666), hAPP(c_List_Oset(_1689662), _1689668)))), hBOOL(hAPP(c_List_Odistinct(_1689662), _1689668))], (46217 ^ _775828) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1689662), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1689662, _1689660, _1689664), _1689666), _1689668))), 46220 ^ _775828 : [(46223 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1689662), _1689668)))], (46221 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1689662), _1689666), hAPP(c_List_Oset(_1689662), _1689668)))]]]]], (46177 ^ _775828) ^ [_1688854, _1688856] : [hBOOL(hAPP(c_List_Odistinct(_1688854), _1688856)), -(hAPP(c_Finite__Set_Ocard(_1688854), hAPP(c_List_Oset(_1688854), _1688856)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688854)), _1688856))], (33354 ^ _775828) ^ [_1394085, _1394087, _1394089, _1394091] : [-(hAPP(c_Map_Orestrict__map(_1394085, _1394087, hAPP(c_COMBK(tc_Option_Ooption(_1394087), _1394085), c_Option_Ooption_ONone(_1394087)), _1394089), _1394091) = c_Option_Ooption_ONone(_1394087))], (28615 ^ _775828) ^ [_1289771, _1289773, _1289775, _1289777] : [class_Lattices_Osemilattice__sup(_1289771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289771), _1289773), _1289775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289771), _1289773), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289771), _1289775), _1289777))))], (39026 ^ _775828) ^ [_1518783, _1518785, _1518787, _1518789] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518783), _1518785)), hAPP(c_Finite__Set_Ocard(_1518787), hAPP(c_Set_Oimage(_1518783, _1518787, _1518789), _1518785)) = hAPP(c_Finite__Set_Ocard(_1518783), _1518785), -(c_Fun_Oinj__on(_1518783, _1518787, _1518789, _1518785))], (12369 ^ _775828) ^ [_979864] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979864) = _979864)], (12009 ^ _775828) ^ [_973700, _973702] : [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), _973700), _973702))), 12012 ^ _775828 : [(12015 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _973702)))], (12013 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _973700)))]]], (17851 ^ _775828) ^ [_1081503, _1081505, _1081507, _1081509] : [class_Rings_Olinordered__semidom(_1081503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081503), c_Groups_Oone__class_Oone(_1081503)), _1081505)), 17858 ^ _775828 : [(17865 ^ _775828) ^ [] : [_1081507 = _1081509, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081503), _1081505), _1081507) = hAPP(hAPP(c_Power_Opower__class_Opower(_1081503), _1081505), _1081509))], (17859 ^ _775828) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1081503), _1081505), _1081507) = hAPP(hAPP(c_Power_Opower__class_Opower(_1081503), _1081505), _1081509), -(_1081507 = _1081509)]]], (42792 ^ _775828) ^ [_1609128, _1609130, _1609132, _1609134, _1609136, _1609138] : [-(hAPP(hAPP(c_Fun_Ocomp(_1609128, _1609130, _1609132, hAPP(c_COMBK(_1609130, _1609128), _1609134)), _1609136), _1609138) = _1609134)], (33046 ^ _775828) ^ [_1387331, _1387333, _1387335] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1387331), _1387333)), 33049 ^ _775828 : [(33050 ^ _775828) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387331, tc_Nat_Onat), _1387335), _1387333) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 33053 ^ _775828 : [(33054 ^ _775828) ^ [_1387493] : [hBOOL(hAPP(hAPP(c_member(_1387331), _1387493), _1387333)), -(hAPP(_1387335, _1387493) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33060 ^ _775828) ^ [] : [33062 ^ _775828 : [(33065 ^ _775828) ^ [] : [hAPP(_1387335, 33061 ^ [_1387331, _1387333, _1387335]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (33063 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387331), 33061 ^ [_1387331, _1387333, _1387335]), _1387333)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387331, tc_Nat_Onat), _1387335), _1387333) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (42182 ^ _775828) ^ [_1594879] : [-(c_Relation_Orefl__on(_1594879, c_Orderings_Otop__class_Otop(tc_fun(_1594879, tc_HOL_Obool)), c_Relation_OId(_1594879)))], (45036 ^ _775828) ^ [_1662237, _1662239] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1662237, tc_HOL_Obool), _1662239) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1662237, tc_HOL_Obool), tc_fun(_1662237, tc_HOL_Obool)), _1662239), c_COMBI(tc_fun(_1662237, tc_HOL_Obool))))], (23662 ^ _775828) ^ [_1190230, _1190232, _1190234] : [class_Orderings_Olinorder(_1190230), 23665 ^ _775828 : [(23672 ^ _775828) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190230), _1190232), _1190234) = _1190234, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190230), _1190232), _1190234)))], (23666 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190230), _1190232), _1190234)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190230), _1190232), _1190234) = _1190234)]]], (2784 ^ _775828) ^ [_817345, _817347] : [_817347 = _817345, -(c_New__DSequence_Opos__empty(_817347) = c_New__DSequence_Opos__empty(_817345))], (45676 ^ _775828) ^ [_1676838, _1676840, _1676842, _1676844] : [-(hAPP(c_List_Oset(_1676838), hAPP(hAPP(c_List_Omap(_1676840, _1676838), _1676842), _1676844)) = hAPP(c_Set_Oimage(_1676840, _1676838, _1676842), hAPP(c_List_Oset(_1676840), _1676844)))], (28305 ^ _775828) ^ [_1283641, _1283643] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283641, tc_HOL_Obool)), _1283643), _1283643) = _1283643)], (29569 ^ _775828) ^ [_1312357, _1312359] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312357, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1312357, tc_HOL_Obool))), _1312359) = c_Orderings_Obot__class_Obot(tc_fun(_1312357, tc_HOL_Obool)))], (50712 ^ _775828) ^ [_1796821, _1796823, _1796825, _1796827, _1796829] : [class_Orderings_Olinorder(_1796821), c_List_Olinorder__class_Osorted(_1796821, hAPP(c_List_Orev(_1796821), hAPP(hAPP(c_List_Omap(_1796823, _1796821), _1796825), _1796827))), -(hAPP(c_List_Ofilter(_1796823, hAPP(hAPP(c_COMBB(_1796821, tc_HOL_Obool, _1796823), hAPP(c_Orderings_Oord__class_Oless(_1796821), _1796829)), _1796825)), _1796827) = c_List_OtakeWhile(_1796823, hAPP(hAPP(c_COMBB(_1796821, tc_HOL_Obool, _1796823), hAPP(c_Orderings_Oord__class_Oless(_1796821), _1796829)), _1796825), _1796827))], (20264 ^ _775828) ^ [_1124005] : [-(c_Int_Opred(c_Int_OBit1(_1124005)) = c_Int_OBit0(_1124005))], (50057 ^ _775828) ^ [_1781180, _1781182, _1781184] : [class_Orderings_Olinorder(_1781180), 50060 ^ _775828 : [(50073 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781180, hAPP(hAPP(c_List_Olist_OCons(_1781180), _1781182), _1781184))), 50077 ^ _775828 : [(50080 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781180), _1781182), 50076 ^ [_1781180, _1781182, _1781184]))], (50078 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781180), 50076 ^ [_1781180, _1781182, _1781184]), hAPP(c_List_Oset(_1781180), _1781184))))]], c_List_Olinorder__class_Osorted(_1781180, _1781184)], (50061 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1781180, hAPP(hAPP(c_List_Olist_OCons(_1781180), _1781182), _1781184)), 50064 ^ _775828 : [(50065 ^ _775828) ^ [_1781348] : [hBOOL(hAPP(hAPP(c_member(_1781180), _1781348), hAPP(c_List_Oset(_1781180), _1781184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781180), _1781182), _1781348)))], (50071 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781180, _1781184))]]]]], (28637 ^ _775828) ^ [_1290203, _1290205, _1290207, _1290209] : [hBOOL(hAPP(hAPP(c_member(_1290203), _1290205), _1290207)), -(hBOOL(hAPP(hAPP(c_member(_1290203), _1290205), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290203, tc_HOL_Obool)), _1290209), _1290207))))], (44359 ^ _775828) ^ [_1646087, _1646089, _1646091, _1646093, _1646095] : [-(_1646087 = c_Orderings_Obot__class_Obot(tc_fun(_1646089, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646091, tc_HOL_Obool)), _1646093), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646089, tc_fun(_1646091, tc_HOL_Obool)), _1646087), _1646095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646089, tc_fun(_1646091, tc_HOL_Obool)), _1646087), hAPP(hAPP(c_COMBB(tc_fun(_1646091, tc_HOL_Obool), tc_fun(_1646091, tc_HOL_Obool), _1646089), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646091, tc_HOL_Obool)), _1646093)), _1646095)))], (29161 ^ _775828) ^ [_1304354, _1304356, _1304358, _1304360] : [hBOOL(hAPP(hAPP(c_member(_1304354), _1304356), hAPP(hAPP(c_Set_Oinsert(_1304354), _1304358), _1304360))), -(_1304356 = _1304358), -(hBOOL(hAPP(hAPP(c_member(_1304354), _1304356), _1304360)))], (40999 ^ _775828) ^ [_1565670, _1565672, _1565674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565670, _1565670)), _1565672), c_Transitive__Closure_Otrancl(_1565670, _1565674))), 41003 ^ _775828 : [(41006 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565670, _1565670)), _1565672), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1565670, _1565670), tc_HOL_Obool), 41002 ^ [_1565670, _1565672, _1565674]), _1565674))))], (41004 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41002 ^ [_1565670, _1565672, _1565674])))]]], (32073 ^ _775828) ^ [_1368918, _1368920, _1368922, _1368924] : [class_Orderings_Olinorder(_1368918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368918), _1368920), _1368922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368918), _1368922), _1368924)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1368918, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1368918, _1368920, _1368922)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1368918, _1368922, _1368924)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1368918, _1368920, _1368924))], (2892 ^ _775828) ^ [_819223, _819225, _819227, _819229] : [-(c_FunDef_Orp__inv__image(_819229, _819225) = c_FunDef_Orp__inv__image(_819227, _819223)), _819229 = _819227, _819225 = _819223], (39361 ^ _775828) ^ [_1526157, _1526159, _1526161, _1526163, _1526165] : [class_Groups_Oab__semigroup__mult(_1526157), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1526157, _1526157, c_Groups_Otimes__class_Otimes(_1526157), _1526159, _1526161), _1526163)), -(hBOOL(hAPP(hAPP(c_member(_1526157), _1526159), _1526161))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1526157, _1526157, c_Groups_Otimes__class_Otimes(_1526157), _1526165, hAPP(hAPP(c_Set_Oinsert(_1526157), _1526159), _1526161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1526157), _1526165), _1526163))))], (9847 ^ _775828) ^ [_934712, _934714, _934716, _934718, _934720] : [class_Rings_Olinordered__semiring__strict(_934712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934712), _934714), _934716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934712), _934718), _934720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934712), c_Groups_Ozero__class_Ozero(_934712)), _934716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934712), c_Groups_Ozero__class_Ozero(_934712)), _934718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934712), _934714), _934718)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934712), _934716), _934720))))], (5973 ^ _775828) ^ [_870880, _870882, _870884] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_870880, _870882, _870884)], (13490 ^ _775828) ^ [_999819, _999821, _999823, _999825, _999827] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_999819, _999821, _999823)), _999825), _999827)), 13495 ^ _775828 : [(13498 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_999821), _999825), _999827)))], (13496 ^ _775828) ^ [] : [-(hBOOL(hAPP(_999819, _999825)))]], 13499 ^ _775828 : [(13502 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_999823), _999825), _999827)))], (13500 ^ _775828) ^ [] : [hBOOL(hAPP(_999819, _999825))]]], (25909 ^ _775828) ^ [_1233506, _1233508] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233506), _1233508)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233508), _1233506)), -(_1233506 = _1233508)], (19174 ^ _775828) ^ [_1105774, _1105776] : [class_Int_Onumber__ring(_1105774), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105774), hAPP(c_Int_Onumber__class_Onumber__of(_1105774), c_Int_OPls)), _1105776) = _1105776)], (14802 ^ _775828) ^ [_1023466, _1023468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1023468, _1023466)), _1023466)))], (16224 ^ _775828) ^ [_1051264, _1051266, _1051268] : [hBOOL(hAPP(_1051264, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051266), _1051268))), 16227 ^ _775828 : [(16234 ^ _775828) ^ [] : [-(_1051268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16237 ^ _775828 : [(16238 ^ _775828) ^ [_1051516, _1051518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051516), _1051268)), _1051266 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051268), _1051518)), _1051516), -(hBOOL(hAPP(_1051264, _1051518)))]]], (16228 ^ _775828) ^ [] : [_1051268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1051264, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (38767 ^ _775828) ^ [_1513631, _1513633, _1513635, _1513637] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513631), _1513633)), c_Equiv__Relations_Oequiv(_1513631, _1513633, _1513635), 38777 ^ _775828 : [(38780 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1513637), hAPP(c_Finite__Set_Ocard(_1513631), 38776 ^ [_1513631, _1513633, _1513635, _1513637])))], (38778 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1513631, tc_HOL_Obool)), 38776 ^ [_1513631, _1513633, _1513635, _1513637]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513631), _1513633), _1513635))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1513637), hAPP(c_Finite__Set_Ocard(_1513631), _1513633))))], (38922 ^ _775828) ^ [_1516807, _1516809, _1516811, _1516813, _1516815] : [c_Fun_Oinj__on(_1516807, _1516809, _1516811, _1516813), c_Fun_Oinj__on(_1516807, _1516809, _1516811, _1516815), -(c_Fun_Oinj__on(_1516807, _1516809, _1516811, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516807, tc_HOL_Obool)), _1516813), _1516815)))], (19294 ^ _775828) ^ [_1107596, _1107598] : [19295 ^ _775828 : [(19298 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107596), c_Int_OPls))], (19296 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107596), _1107598))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107596)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107598))))], (33328 ^ _775828) ^ [_1393423, _1393425, _1393427, _1393429, _1393431] : [hAPP(_1393423, _1393425) = c_Option_Ooption_ONone(_1393427), -(c_Map_Oran(_1393429, _1393427, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1393429, tc_Option_Ooption(_1393427)), _1393423), _1393425), hAPP(c_Option_Ooption_OSome(_1393427), _1393431))) = hAPP(hAPP(c_Set_Oinsert(_1393427), _1393431), c_Map_Oran(_1393429, _1393427, _1393423)))], (33893 ^ _775828) ^ [_1405763, _1405765, _1405767, _1405769] : [class_Lattices_Odistrib__lattice(_1405763), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405763), _1405765), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405763), _1405767), _1405769)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405763), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405763), _1405765), _1405767)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405763), _1405765), _1405769)))], (21434 ^ _775828) ^ [_1147022, _1147024, _1147026, _1147028] : [class_Fields_Ofield__inverse__zero(_1147022), class_Int_Onumber(_1147022), 21441 ^ _775828 : [(21442 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147022), _1147026), _1147028), 21445 ^ _775828 : [(21452 ^ _775828) ^ [] : [_1147028 = c_Groups_Ozero__class_Ozero(_1147022), -(hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024) = c_Groups_Ozero__class_Ozero(_1147022))], (21446 ^ _775828) ^ [] : [-(_1147028 = c_Groups_Ozero__class_Ozero(_1147022)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147022), hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024)), _1147028) = _1147026)]]], (21458 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147022), _1147026), _1147028)), 21461 ^ _775828 : [(21464 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147022), hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024)), _1147028) = _1147026], (21462 ^ _775828) ^ [] : [_1147028 = c_Groups_Ozero__class_Ozero(_1147022)]], 21465 ^ _775828 : [(21468 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147022), _1147024) = c_Groups_Ozero__class_Ozero(_1147022)], (21466 ^ _775828) ^ [] : [-(_1147028 = c_Groups_Ozero__class_Ozero(_1147022))]]]]], (1110 ^ _775828) ^ [_792321, _792323] : [-(class_Groups_Ogroup__add(_792321)), _792323 = _792321, class_Groups_Ogroup__add(_792323)], (31251 ^ _775828) ^ [_1350258, _1350260, _1350262] : [class_Orderings_Olinorder(_1350258), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350258), _1350260)), -(_1350260 = c_Orderings_Obot__class_Obot(tc_fun(_1350258, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1350258, c_Orderings_Oord__class_Omax(_1350258), hAPP(hAPP(c_Set_Oinsert(_1350258), _1350262), _1350260)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350258), _1350262), c_Big__Operators_Olattice_OSup__fin(_1350258, c_Orderings_Oord__class_Omax(_1350258), _1350260)))], (25120 ^ _775828) ^ [_1219182, _1219184, _1219186, _1219188] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1219182), _1219184), _1219186), _1219188) = 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(_1219182)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1219182), _1219184)))], (6977 ^ _775828) ^ [_886399, _886401, _886403] : [class_Rings_Oring__no__zero__divisors(_886399), 6980 ^ _775828 : [(6981 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886399), _886401), _886403) = c_Groups_Ozero__class_Ozero(_886399), -(_886401 = c_Groups_Ozero__class_Ozero(_886399)), -(_886403 = c_Groups_Ozero__class_Ozero(_886399))], (6991 ^ _775828) ^ [] : [6992 ^ _775828 : [(6995 ^ _775828) ^ [] : [_886403 = c_Groups_Ozero__class_Ozero(_886399)], (6993 ^ _775828) ^ [] : [_886401 = c_Groups_Ozero__class_Ozero(_886399)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886399), _886401), _886403) = c_Groups_Ozero__class_Ozero(_886399))]]], (37262 ^ _775828) ^ [_1478436, _1478438, _1478440, _1478442, _1478444] : [class_Groups_Ocomm__monoid__add(_1478436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478438), _1478440)), -(hBOOL(hAPP(hAPP(c_member(_1478438), _1478442), _1478440))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478438, _1478436), _1478444), hAPP(hAPP(c_Set_Oinsert(_1478438), _1478442), _1478440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478436), hAPP(_1478444, _1478442)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478438, _1478436), _1478444), _1478440)))], (34435 ^ _775828) ^ [_1417634, _1417636, _1417638] : [class_Lattices_Olattice(_1417634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417634), _1417636)), -(_1417636 = c_Orderings_Obot__class_Obot(tc_fun(_1417634, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417634), _1417638)), -(_1417638 = c_Orderings_Obot__class_Obot(tc_fun(_1417634, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1417634, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417634, tc_HOL_Obool)), _1417636), _1417638)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417634), c_Big__Operators_Olattice__class_OInf__fin(_1417634, _1417636)), c_Big__Operators_Olattice__class_OInf__fin(_1417634, _1417638)))], (51306 ^ _775828) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (25919 ^ _775828) ^ [_1233655, _1233657, _1233659] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233655), _1233657)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233657), _1233659)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233655), _1233659)))], (5368 ^ _775828) ^ [_857835, _857837, _857839, _857841, _857843, _857845] : [-(c_COMBB(_857845, _857841, _857837) = c_COMBB(_857843, _857839, _857835)), _857845 = _857843, _857841 = _857839, _857837 = _857835], (11861 ^ _775828) ^ [_970965, _970967, _970969, _970971] : [class_Groups_Oordered__comm__monoid__add(_970965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970965), c_Groups_Ozero__class_Ozero(_970965)), _970967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970965), _970969), _970971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970965), _970969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970965), _970967), _970971))))], (7097 ^ _775828) ^ [_888527, _888529, _888531] : [class_Rings_Olinordered__semiring__strict(_888527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888527), _888529), c_Groups_Ozero__class_Ozero(_888527))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888527), c_Groups_Ozero__class_Ozero(_888527)), _888531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888527), _888529), _888531)), c_Groups_Ozero__class_Ozero(_888527))))], (35037 ^ _775828) ^ [_1430808, _1430810] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1430808), _1430810) = 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)), _1430808)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1430810))))], (51502 ^ _775828) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (23886 ^ _775828) ^ [_1194095, _1194097, _1194099] : [class_Orderings_Olinorder(_1194095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194095), _1194097), _1194099)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194095), _1194097), _1194099) = _1194097)], (32041 ^ _775828) ^ [_1368480, _1368482, _1368484] : [class_Orderings_Oorder(_1368480), 32044 ^ _775828 : [(32051 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368480), _1368482), _1368484))), -(c_Orderings_Obot__class_Obot(tc_fun(_1368480, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1368480, _1368482, _1368484))], (32045 ^ _775828) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1368480, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1368480, _1368482, _1368484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368480), _1368482), _1368484))]]], (46077 ^ _775828) ^ [_1686503, _1686505, _1686507] : [class_Orderings_Olinorder(_1686503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1686503), _1686505)), -(c_List_Olinorder__class_Osorted__list__of__set(_1686503, hAPP(hAPP(c_Set_Oinsert(_1686503), _1686507), _1686505)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1686503, _1686503, c_COMBI(_1686503)), _1686507), c_List_Olinorder__class_Osorted__list__of__set(_1686503, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1686503, tc_HOL_Obool)), _1686505), hAPP(hAPP(c_Set_Oinsert(_1686503), _1686507), c_Orderings_Obot__class_Obot(tc_fun(_1686503, tc_HOL_Obool)))))))], (20906 ^ _775828) ^ [_1135600, _1135602] : [20907 ^ _775828 : [(20910 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135602), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20908 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135600), _1135602))]], -(c_Divides_OposDivAlg(_1135600, _1135602) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135600))], (50357 ^ _775828) ^ [_1787989, _1787991, _1787993, _1787995] : [-(hAPP(c_List_Orev(_1787989), hAPP(hAPP(c_List_Omap(_1787991, _1787989), _1787993), _1787995)) = hAPP(hAPP(c_List_Omap(_1787991, _1787989), _1787993), hAPP(c_List_Orev(_1787991), _1787995)))], (43409 ^ _775828) ^ [_1624289, _1624291, _1624293, _1624295] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1624289, tc_HOL_Obool), tc_fun(_1624289, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1624289, tc_HOL_Obool), tc_fun(_1624289, tc_HOL_Obool)), _1624291), _1624293)), c_Wellfounded_Omax__ext(_1624289, _1624295)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624289), _1624291)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624289), _1624293)), -(_1624293 = c_Orderings_Obot__class_Obot(tc_fun(_1624289, tc_HOL_Obool))), 43423 ^ _775828 : [(43426 ^ _775828) ^ [_1624694] : [hBOOL(hAPP(hAPP(c_member(_1624289), _1624694), _1624293)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1624289, _1624289)), hAPP(hAPP(c_Product__Type_OPair(_1624289, _1624289), 43422 ^ [_1624289, _1624291, _1624293, _1624295]), _1624694)), _1624295))], (43424 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624289), 43422 ^ [_1624289, _1624291, _1624293, _1624295]), _1624291)))]]], (11472 ^ _775828) ^ [_964414, _964416, _964418] : [class_Rings_Olinordered__ring__strict(_964414), 11475 ^ _775828 : [(11484 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964414), _964416), _964416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964414), _964418), _964418)) = c_Groups_Ozero__class_Ozero(_964414)), _964416 = c_Groups_Ozero__class_Ozero(_964414), _964418 = c_Groups_Ozero__class_Ozero(_964414)], (11476 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964414), _964416), _964416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964414), _964418), _964418)) = c_Groups_Ozero__class_Ozero(_964414), 11479 ^ _775828 : [(11482 ^ _775828) ^ [] : [-(_964418 = c_Groups_Ozero__class_Ozero(_964414))], (11480 ^ _775828) ^ [] : [-(_964416 = c_Groups_Ozero__class_Ozero(_964414))]]]]], (37750 ^ _775828) ^ [_1490554, _1490556, _1490558, _1490560, _1490562] : [class_Groups_Ocomm__monoid__add(_1490554), class_Groups_Oordered__ab__semigroup__add(_1490554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490556), _1490558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490556, tc_HOL_Obool)), _1490560), _1490558)), 37768 ^ _775828 : [(37771 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1490554), c_Groups_Ozero__class_Ozero(_1490554)), hAPP(_1490562, 37767 ^ [_1490554, _1490556, _1490558, _1490560, _1490562])))], (37769 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490556), 37767 ^ [_1490554, _1490556, _1490558, _1490560, _1490562]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490556, tc_HOL_Obool)), _1490558), _1490560))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1490554), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490556, _1490554), _1490562), _1490560)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490556, _1490554), _1490562), _1490558))))], (47649 ^ _775828) ^ [_1726748, _1726750, _1726752] : [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), _1726748), _1726750))), -(hBOOL(hAPP(hAPP(_1726752, _1726748), _1726750))), 47656 ^ _775828 : [(47659 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 47654 ^ [_1726748, _1726750, _1726752]), 47655 ^ [_1726748, _1726750, _1726752])), -(hBOOL(hAPP(hAPP(_1726752, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 47654 ^ [_1726748, _1726750, _1726752]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 47655 ^ [_1726748, _1726750, _1726752])))], (47665 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1726752, 47654 ^ [_1726748, _1726750, _1726752]), 47655 ^ [_1726748, _1726750, _1726752]))], (47657 ^ _775828) ^ [] : [-(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), 47654 ^ [_1726748, _1726750, _1726752]), 47655 ^ [_1726748, _1726750, _1726752]))))]]], (36543 ^ _775828) ^ [_1462455, _1462457, _1462459, _1462461] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462455), _1462457)), 36546 ^ _775828 : [(36547 ^ _775828) ^ [_1462613] : [36549 ^ _775828 : [(36555 ^ _775828) ^ [] : [-(_1462613 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36551 ^ [_1462455, _1462457, _1462459, _1462461, _1462613]), 36548 ^ [_1462455, _1462457, _1462459, _1462461, _1462613]))], (36553 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36551 ^ [_1462455, _1462457, _1462459, _1462461, _1462613]), _1462459)))], (36550 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36548 ^ [_1462455, _1462457, _1462459, _1462461, _1462613]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1462457))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462613), _1462461)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1462613), _1462457)), _1462461)))]]], (25497 ^ _775828) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (4578 ^ _775828) ^ [_845734, _845736] : [_845736 = _845734, -(c_Option_Ooption_ONone(_845736) = c_Option_Ooption_ONone(_845734))], (42345 ^ _775828) ^ [_1598288, _1598290, _1598292, _1598294, _1598296] : [c_Finite__Set_Ofun__left__comm__idem(_1598288, _1598290, _1598292), -(c_Finite__Set_Ofun__left__comm__idem(_1598294, _1598290, hAPP(hAPP(c_COMBB(_1598288, tc_fun(_1598290, _1598290), _1598294), _1598292), _1598296)))], (47643 ^ _775828) ^ [_1726434, _1726436, _1726438, _1726440] : [-(hAPP(c_List_Olist_Olist__case(_1726434, _1726436, _1726438, _1726440), c_List_Olist_ONil(_1726436)) = _1726438)], (25092 ^ _775828) ^ [_1218589, _1218591, _1218593, _1218595, _1218597, _1218599] : [c_Nitpick_Opair__box_OPairBox(_1218589, _1218591, _1218593, _1218595) = c_Nitpick_Opair__box_OPairBox(_1218589, _1218591, _1218597, _1218599), 25095 ^ _775828 : [(25098 ^ _775828) ^ [] : [-(_1218595 = _1218599)], (25096 ^ _775828) ^ [] : [-(_1218593 = _1218597)]]], (4318 ^ _775828) ^ [_841780, _841782, _841784, _841786] : [-(c_Big__Operators_Olinorder__class_OMax(_841786, _841782) = c_Big__Operators_Olinorder__class_OMax(_841784, _841780)), _841786 = _841784, _841782 = _841780], (30177 ^ _775828) ^ [_1325808] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1325808) = 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)), _1325808)))], (10172 ^ _775828) ^ [_940571, _940573, _940575, _940577] : [class_Groups_Ocancel__ab__semigroup__add(_940571), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940571), _940573), _940575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940571), _940573), _940577), -(_940575 = _940577)], (25026 ^ _775828) ^ [_1216996, _1216998, _1217000] : [-(c_HOL_OThe(tc_prod(_1216996, _1216998), hAPP(c_Product__Type_Oprod_Oprod__case(_1216996, _1216998, tc_HOL_Obool), _1217000)) = c_HOL_OThe(tc_prod(_1216996, _1216998), hAPP(hAPP(c_COMBS(tc_prod(_1216996, _1216998), _1216998, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1216996, tc_fun(_1216998, tc_HOL_Obool), tc_prod(_1216996, _1216998)), _1217000), c_Product__Type_Ofst(_1216996, _1216998))), c_Product__Type_Osnd(_1216996, _1216998))))], (49130 ^ _775828) ^ [_1762162, _1762164, _1762166] : [_1762162 = c_List_Olist_ONil(_1762164), -(c_List_Olast(_1762164, hAPP(hAPP(c_List_Oappend(_1762164), _1762166), _1762162)) = c_List_Olast(_1762164, _1762166))], (29415 ^ _775828) ^ [_1309309, _1309311, _1309313, _1309315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309309, tc_HOL_Obool)), _1309311), _1309313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309309, tc_HOL_Obool)), _1309311), hAPP(hAPP(c_Set_Oinsert(_1309309), _1309315), _1309313))))], (51496 ^ _775828) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (17713 ^ _775828) ^ [_1079101, _1079103, _1079105, _1079107] : [class_Groups_Ocomm__monoid__mult(_1079101), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079101), _1079103), _1079105)), _1079107) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079101), hAPP(hAPP(c_Power_Opower__class_Opower(_1079101), _1079103), _1079107)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079101), _1079105), _1079107)))], (6937 ^ _775828) ^ [_885729, _885731, _885733, _885735] : [class_Groups_Oab__semigroup__mult(_885729), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885729), _885731), _885733)), _885735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885729), _885731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_885729), _885733), _885735)))], (11036 ^ _775828) ^ [_956379, _956381, _956383] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956379), _956381)), _956383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956379), _956383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956381), _956383)))], (46420 ^ _775828) ^ [_1696184, _1696186, _1696188, _1696190] : [c_List_Olistrelp(_1696184, hAPP(hAPP(c_COMBC(_1696184, tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_fun(_1696184, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1696184, tc_fun(tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_fun(_1696184, tc_HOL_Obool)), _1696184), c_COMBC(_1696184, tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1696184, tc_prod(_1696184, _1696184)), tc_fun(_1696184, tc_fun(tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_HOL_Obool)), _1696184), hAPP(c_COMBB(tc_prod(_1696184, _1696184), tc_fun(tc_fun(tc_prod(_1696184, _1696184), tc_HOL_Obool), tc_HOL_Obool), _1696184), c_member(tc_prod(_1696184, _1696184)))), c_Product__Type_OPair(_1696184, _1696184)))), _1696186), _1696188, _1696190), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696184), tc_List_Olist(_1696184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696184), tc_List_Olist(_1696184)), _1696188), _1696190)), c_List_Olistrel(_1696184, _1696186))))], (6390 ^ _775828) ^ [_877446, _877448, _877450] : [class_Rings_Olinordered__semidom(_877446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877446), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877446), _877448)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877446), _877450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _877448), _877450)))], (5913 ^ _775828) ^ [_869918, _869920, _869922, _869924, _869926, _869928] : [-(c_Com_Ocom_OCall(_869918, _869920, _869922) = c_Com_Ocom_OCall(_869924, _869926, _869928)), _869918 = _869924, _869920 = _869926, _869922 = _869928], (6799 ^ _775828) ^ [_883555, _883557] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883555) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883557), -(_883555 = _883557)], (33797 ^ _775828) ^ [_1403715, _1403717, _1403719, _1403721] : [class_Lattices_Osemilattice__inf(_1403715), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403715), _1403717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403715), _1403719), _1403721)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403715), _1403719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403715), _1403717), _1403721)))], (44673 ^ _775828) ^ [_1654458, _1654460, _1654462, _1654464] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654458, tc_HOL_Obool), tc_fun(_1654460, tc_HOL_Obool)), _1654462), hAPP(hAPP(c_COMBC(tc_fun(_1654458, tc_HOL_Obool), tc_fun(_1654458, tc_fun(_1654460, tc_HOL_Obool)), tc_fun(_1654460, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1654458, tc_fun(_1654460, tc_HOL_Obool))), _1654464)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1654458, tc_fun(_1654460, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654458, tc_HOL_Obool), _1654462)), _1654464))], (42170 ^ _775828) ^ [_1594645] : [-(c_Relation_Orefl__on(_1594645, c_Orderings_Obot__class_Obot(tc_fun(_1594645, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594645, _1594645), tc_HOL_Obool))))], (50553 ^ _775828) ^ [_1793229, _1793231] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1793229), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1793229))), _1793231))), 50556 ^ _775828 : [(50563 ^ _775828) ^ [] : [-(_1793231 = c_List_Olist_ONil(tc_List_Olist(_1793229))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1793229))), c_List_Otranspose(_1793229, _1793231)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793229)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1793229)), _1793231), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50557 ^ _775828) ^ [] : [_1793231 = c_List_Olist_ONil(tc_List_Olist(_1793229)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1793229))), c_List_Otranspose(_1793229, _1793231)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20726 ^ _775828) ^ [_1132157, _1132159, _1132161] : [class_Groups_Omonoid__mult(_1132157), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1132157), _1132159), 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)))), _1132161))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132157), _1132159), hAPP(hAPP(c_Power_Opower__class_Opower(_1132157), hAPP(hAPP(c_Power_Opower__class_Opower(_1132157), _1132159), _1132161)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (47681 ^ _775828) ^ [_1727585, _1727587, _1727589, _1727591] : [-(c_Map_Omap__upds(_1727585, _1727587, _1727589, c_List_Olist_ONil(_1727585), _1727591) = _1727589)], (29183 ^ _775828) ^ [_1304740, _1304742] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304740, tc_HOL_Obool)), _1304742), c_Orderings_Obot__class_Obot(tc_fun(_1304740, tc_HOL_Obool))) = _1304742)], (51130 ^ _775828) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (47044 ^ _775828) ^ [_1712717, _1712719, _1712721] : [hBOOL(hAPP(hAPP(c_member(_1712717), _1712719), hAPP(c_List_Oset(_1712717), _1712721))), 47048 ^ _775828 : [(47051 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1712717), _1712721), 47047 ^ [_1712717, _1712719, _1712721]) = _1712719)], (47049 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47047 ^ [_1712717, _1712719, _1712721]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712717)), _1712721))))]]], (30950 ^ _775828) ^ [_1342270, _1342272, _1342274] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1342270, tc_HOL_Obool), tc_fun(_1342270, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1342270, tc_HOL_Obool), tc_fun(_1342270, tc_HOL_Obool)), _1342272), _1342274)), c_Wellfounded_Ofinite__psubset(_1342270))), 30953 ^ _775828 : [(30956 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1342270), _1342274)))], (30954 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1342270, tc_HOL_Obool)), _1342272), _1342274)))]]], (24977 ^ _775828) ^ [_1215851, _1215853, _1215855, _1215857, _1215859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215851, tc_HOL_Obool)), _1215853), _1215855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215857, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215851, _1215857, _1215859), _1215853)), hAPP(c_Set_Oimage(_1215851, _1215857, _1215859), _1215855))))], (46780 ^ _775828) ^ [_1706366, _1706368, _1706370] : [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, _1706366), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1706366)), _1706368)))), -(hBOOL(hAPP(hAPP(c_member(_1706366), hAPP(c_Product__Type_Ofst(_1706366, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1706366, _1706368), _1706370))), hAPP(c_List_Oset(_1706366), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1706366), _1706366), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1706366)), _1706368)))))], (32241 ^ _775828) ^ [_1371615, _1371617, _1371619] : [class_Orderings_Olinorder(_1371615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371615), _1371617)), -(_1371619 = c_Orderings_Obot__class_Obot(tc_fun(_1371615, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371615, tc_HOL_Obool)), _1371619), _1371617)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371615), c_Big__Operators_Olinorder__class_OMin(_1371615, _1371619)), c_Big__Operators_Olinorder__class_OMin(_1371615, _1371617)) = c_Big__Operators_Olinorder__class_OMin(_1371615, _1371617))], (25471 ^ _775828) ^ [_1225193, _1225195, _1225197, _1225199, _1225201] : [-(hAPP(c_New__DSequence_Opos__bind(_1225193, _1225195, _1225197, _1225199), _1225201) = c_Lazy__Sequence_Obind(_1225193, _1225195, hAPP(_1225197, _1225201), hAPP(hAPP(c_COMBC(_1225193, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1225195)), _1225199), _1225201)))], (35803 ^ _775828) ^ [_1448175, _1448177] : [35811 ^ _775828 : [(35814 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1448177, 35810 ^ [_1448175, _1448177])))], (35812 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35810 ^ [_1448175, _1448177]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448175))))]], 35804 ^ _775828 : [(35805 ^ _775828) ^ [_1448244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1448244), _1448175)), hBOOL(hAPP(_1448177, _1448244))]]], (34163 ^ _775828) ^ [_1411317, _1411319, _1411321, _1411323] : [class_Lattices_Olattice(_1411317), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411317), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411317), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411317), _1411319), _1411321)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411317), _1411319), _1411323))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411317), _1411319), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411317), _1411321), _1411323)))))], (31183 ^ _775828) ^ [_1349120, _1349122] : [class_Orderings_Olinorder(_1349120), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349120), _1349122)), -(_1349122 = c_Orderings_Obot__class_Obot(tc_fun(_1349120, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349120), c_Big__Operators_Olattice_OInf__fin(_1349120, c_Orderings_Oord__class_Omin(_1349120), _1349122)), c_Big__Operators_Olattice_OSup__fin(_1349120, c_Orderings_Oord__class_Omax(_1349120), _1349122))))], (36191 ^ _775828) ^ [_1455429, _1455431] : [36193 ^ _775828 : [(36196 ^ _775828) ^ [] : [hBOOL(hAPP(_1455431, 36192 ^ [_1455429, _1455431]))], (36194 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 36192 ^ [_1455429, _1455431]), _1455429)))]], 36197 ^ _775828 : [(36198 ^ _775828) ^ [_1455579] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1455579), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1455429))), -(hBOOL(hAPP(_1455431, _1455579)))]]], (1200 ^ _775828) ^ [_793446, _793448] : [-(class_Rings_Oidom(_793446)), _793448 = _793446, class_Rings_Oidom(_793448)], (20232 ^ _775828) ^ [_1123459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123459), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1123459)), c_Int_OMin)))], (38758 ^ _775828) ^ [_1513403, _1513405, _1513407, _1513409] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1513403, tc_HOL_Obool)), _1513405), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513403), _1513407), _1513409))), 38762 ^ _775828 : [(38765 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513403), 38761 ^ [_1513403, _1513405, _1513407, _1513409]), _1513407)))], (38763 ^ _775828) ^ [] : [-(_1513405 = hAPP(c_Relation_OImage(_1513403, _1513403, _1513409), hAPP(hAPP(c_Set_Oinsert(_1513403), 38761 ^ [_1513403, _1513405, _1513407, _1513409]), c_Orderings_Obot__class_Obot(tc_fun(_1513403, tc_HOL_Obool)))))]]], (37196 ^ _775828) ^ [_1476498, _1476500, _1476502, _1476504, _1476506] : [class_Groups_Ocomm__monoid__add(_1476498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476500), _1476502)), 37203 ^ _775828 : [(37210 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476500), _1476504), _1476502))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476500, _1476498), hAPP(hAPP(c_COMBC(_1476500, _1476498, _1476498), hAPP(hAPP(c_COMBS(_1476500, _1476498, tc_fun(_1476498, _1476498)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1476498, tc_fun(_1476498, _1476498)), _1476500), c_If(_1476498)), hAPP(hAPP(c_COMBC(_1476500, _1476500, tc_HOL_Obool), c_fequal), _1476504))), _1476506)), c_Groups_Ozero__class_Ozero(_1476498))), _1476502) = c_Groups_Ozero__class_Ozero(_1476498))], (37204 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1476500), _1476504), _1476502)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476500, _1476498), hAPP(hAPP(c_COMBC(_1476500, _1476498, _1476498), hAPP(hAPP(c_COMBS(_1476500, _1476498, tc_fun(_1476498, _1476498)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1476498, tc_fun(_1476498, _1476498)), _1476500), c_If(_1476498)), hAPP(hAPP(c_COMBC(_1476500, _1476500, tc_HOL_Obool), c_fequal), _1476504))), _1476506)), c_Groups_Ozero__class_Ozero(_1476498))), _1476502) = hAPP(_1476506, _1476504))]]], (23866 ^ _775828) ^ [_1193737, _1193739, _1193741, _1193743] : [class_Orderings_Olinorder(_1193737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193737), _1193739), _1193741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193737), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193737), _1193739), _1193743)), _1193741)))], (42916 ^ _775828) ^ [_1611974, _1611976, _1611978, _1611980, _1611982, _1611984, _1611986] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1611974, _1611976, _1611978), hAPP(c_Fun_Ocomp(_1611980, tc_fun(_1611976, _1611978), _1611974, _1611982), _1611984)), _1611986) = hAPP(hAPP(_1611982, hAPP(_1611984, hAPP(c_Product__Type_Ofst(_1611974, _1611976), _1611986))), hAPP(c_Product__Type_Osnd(_1611974, _1611976), _1611986)))], (11290 ^ _775828) ^ [_961101, _961103, _961105] : [class_Groups_Oordered__comm__monoid__add(_961101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961101), c_Groups_Ozero__class_Ozero(_961101)), _961103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961101), c_Groups_Ozero__class_Ozero(_961101)), _961105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961101), c_Groups_Ozero__class_Ozero(_961101)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961101), _961103), _961105))))], (27733 ^ _775828) ^ [_1269433, _1269435] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1269433)), 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)), _1269433))), 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, _1269435))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51538 ^ _775828) ^ [] : [-(hBOOL(c_fTrue))], (29261 ^ _775828) ^ [_1306474, _1306476, _1306478, _1306480] : [_1306474 = c_Orderings_Obot__class_Obot(tc_fun(_1306476, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1306476, _1306478, hAPP(c_COMBK(_1306478, _1306476), _1306480)), _1306474) = c_Orderings_Obot__class_Obot(tc_fun(_1306478, tc_HOL_Obool)))], (18339 ^ _775828) ^ [_1091219, _1091221, _1091223, _1091225, _1091227, _1091229] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091219, _1091221), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091223), _1091225))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091219, _1091221), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091227), _1091229))), -(_1091221 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1091225 = _1091229)], (24940 ^ _775828) ^ [_1214963, _1214965] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1214963), _1214965) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1214963), _1214965))], (15694 ^ _775828) ^ [_1040351, _1040353] : [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), _1040351), _1040353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040353), _1040351)))], (14223 ^ _775828) ^ [_1013508] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013508) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4740 ^ _775828) ^ [_848249, _848251] : [_848251 = _848249, -(c_Lattices_Osemilattice__sup__class_Osup(_848251) = c_Lattices_Osemilattice__sup__class_Osup(_848249))], (50754 ^ _775828) ^ [_1797656, _1797658] : [c_List_Oremdups(_1797656, _1797658) = c_List_Olist_ONil(_1797656), -(_1797658 = c_List_Olist_ONil(_1797656))], (42357 ^ _775828) ^ [_1598480] : [class_Lattices_Osemilattice__inf(_1598480), -(c_Finite__Set_Ofun__left__comm__idem(_1598480, _1598480, c_Lattices_Osemilattice__inf__class_Oinf(_1598480)))], (23740 ^ _775828) ^ [_1191546, _1191548, _1191550, _1191552] : [class_Orderings_Olinorder(_1191546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191546), _1191548), _1191550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191546), _1191552), _1191550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191546), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191546), _1191548), _1191552)), _1191550)))], (50988 ^ _775828) ^ [_1802588, _1802590] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1802588), tc_fun(_1802588, tc_HOL_Obool), c_List_Oset(_1802588)), hAPP(c_List_Oset(tc_List_Olist(_1802588)), c_Enum_Osublists(_1802588, _1802590))) = hAPP(c_Set_OPow(_1802588), hAPP(c_List_Oset(_1802588), _1802590)))], (29391 ^ _775828) ^ [_1308850, _1308852, _1308854] : [_1308852 = _1308854, -(hBOOL(hAPP(hAPP(c_member(_1308850), _1308852), hAPP(hAPP(c_Set_Oinsert(_1308850), _1308854), c_Orderings_Obot__class_Obot(tc_fun(_1308850, tc_HOL_Obool))))))], (39150 ^ _775828) ^ [_1521497, _1521499, _1521501, _1521503] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521497), _1521499)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521501), _1521503)), 39157 ^ _775828 : [(39158 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1521497), _1521499)), hAPP(c_Finite__Set_Ocard(_1521501), _1521503)))), 39159 ^ _775828 : [(39160 ^ _775828) ^ [_1521708] : [c_Fun_Oinj__on(_1521497, _1521501, _1521708, _1521499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521497, _1521501, _1521708), _1521499)), _1521503))]]], (39168 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1521497), _1521499)), hAPP(c_Finite__Set_Ocard(_1521501), _1521503))), 39172 ^ _775828 : [(39175 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521497, _1521501, 39171 ^ [_1521497, _1521499, _1521501, _1521503]), _1521499)), _1521503)))], (39173 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1521497, _1521501, 39171 ^ [_1521497, _1521499, _1521501, _1521503], _1521499))]]]]], (28037 ^ _775828) ^ [_1277666, _1277668] : [28039 ^ _775828 : [(28040 ^ _775828) ^ [_1277691] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1277666, _1277666)), hAPP(hAPP(c_Product__Type_OPair(_1277666, _1277666), hAPP(28038 ^ [_1277666, _1277668], hAPP(c_Nat_OSuc, _1277691))), hAPP(28038 ^ [_1277666, _1277668], _1277691))), _1277668)))]], -(c_Wellfounded_Owf(_1277666, _1277668))], (20174 ^ _775828) ^ [_1122416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122416), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1122416)), c_Int_OPls)))], (4710 ^ _775828) ^ [_847794, _847796, _847798, _847800] : [-(c_List_Olinorder__class_Osorted__list__of__set(_847800, _847796) = c_List_Olinorder__class_Osorted__list__of__set(_847798, _847794)), _847800 = _847798, _847796 = _847794], (8007 ^ _775828) ^ [_904309, _904311, _904313, _904315, _904317] : [class_Rings_Ocomm__semiring__1(_904309), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), _904311), _904313)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), _904315), _904317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), _904315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904309), _904311), _904313)), _904317)))], (25247 ^ _775828) ^ [_1221167, _1221169] : [c_Nat__Transfer_Onat__set(_1221167), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1221169), _1221167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221169)))], (25593 ^ _775828) ^ [_1228330, _1228332, _1228334] : [class_Rings_Olinordered__idom(_1228330), 25596 ^ _775828 : [(25603 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228330), _1228332), _1228334)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228330), hAPP(c_Groups_Oabs__class_Oabs(_1228330), _1228332)), _1228334)))], (25597 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228330), hAPP(c_Groups_Oabs__class_Oabs(_1228330), _1228332)), _1228334)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228330), _1228332), _1228334)))]]], (24288 ^ _775828) ^ [_1201817] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1201817), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1201817)], (38172 ^ _775828) ^ [_1500111] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1500111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1500111)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1500111), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49509 ^ _775828) ^ [_1770642, _1770644, _1770646, _1770648] : [-(c_List_Omap__filter(_1770642, _1770644, _1770646, _1770648) = hAPP(hAPP(c_List_Omap(_1770642, _1770644), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1770644), _1770644, _1770642, c_Option_Othe(_1770644)), _1770646)), hAPP(c_List_Ofilter(_1770642, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1770642), c_fNot), hAPP(hAPP(c_COMBC(_1770642, tc_Option_Ooption(_1770644), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1770644), tc_fun(tc_Option_Ooption(_1770644), tc_HOL_Obool), _1770642), c_fequal), _1770646)), c_Option_Ooption_ONone(_1770644)))), _1770648)))], (50816 ^ _775828) ^ [_1798708, _1798710, _1798712] : [hBOOL(hAPP(hAPP(c_member(_1798708), _1798710), hAPP(c_List_Oset(_1798708), _1798712))), -(c_List_Oremdups(_1798708, hAPP(hAPP(c_List_Olist_OCons(_1798708), _1798710), _1798712)) = c_List_Oremdups(_1798708, _1798712))], (38206 ^ _775828) ^ [_1501159, _1501161] : [-(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), _1501159), _1501161)), 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), _1501159), _1501161))], (36123 ^ _775828) ^ [_1454286, _1454288] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454286), _1454288))))], (31785 ^ _775828) ^ [_1362227, _1362229] : [-(c_Transitive__Closure_Ortrancl(_1362227, _1362229) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1362227, _1362227), tc_HOL_Obool)), c_Relation_OId(_1362227)), hAPP(hAPP(c_Relation_Orel__comp(_1362227, _1362227, _1362227), c_Transitive__Closure_Ortrancl(_1362227, _1362229)), _1362229)))], (20588 ^ _775828) ^ [_1129616, _1129618] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1129616), hAPP(c_Int_Onumber__class_Onumber__of(_1129616), _1129618)), 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(_1129616), hAPP(c_Int_Onumber__class_Onumber__of(_1129616), _1129618)), hAPP(c_Int_Onumber__class_Onumber__of(_1129616), _1129618))), class_Groups_Omonoid__mult(_1129616), class_Int_Onumber(_1129616)], (19870 ^ _775828) ^ [_1116899, _1116901] : [class_Int_Onumber__ring(_1116899), class_Rings_Olinordered__idom(_1116899), 19877 ^ _775828 : [(19884 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116901), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116899), hAPP(c_Int_Onumber__class_Onumber__of(_1116899), _1116901)), c_Groups_Oone__class_Oone(_1116899))))], (19878 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116899), hAPP(c_Int_Onumber__class_Onumber__of(_1116899), _1116901)), c_Groups_Oone__class_Oone(_1116899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116901), c_Int_OBit1(c_Int_OPls))))]]], (18978 ^ _775828) ^ [_1102446, _1102448, _1102450, _1102452, _1102454, _1102456] : [hAPP(hAPP(c_Product__Type_OPair(_1102446, _1102448), _1102450), _1102452) = hAPP(hAPP(c_Product__Type_OPair(_1102446, _1102448), _1102454), _1102456), 18981 ^ _775828 : [(18984 ^ _775828) ^ [] : [-(_1102452 = _1102456)], (18982 ^ _775828) ^ [] : [-(_1102450 = _1102454)]]], (20480 ^ _775828) ^ [] : [-(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)))))], (51462 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (16667 ^ _775828) ^ [_1059655, _1059657, _1059659, _1059661, _1059663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059655, tc_HOL_Obool)), _1059657), _1059659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059655, tc_HOL_Obool)), _1059661), _1059663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059655, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059655, tc_HOL_Obool)), _1059657), _1059663)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059655, tc_HOL_Obool)), _1059659), _1059661))))], (47038 ^ _775828) ^ [_1712556, _1712558, _1712560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712556), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712558)), _1712560))), -(hBOOL(hAPP(hAPP(c_member(_1712558), hAPP(hAPP(c_List_Onth(_1712558), _1712560), _1712556)), hAPP(c_List_Oset(_1712558), _1712560))))], (40027 ^ _775828) ^ [] : [-(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)))], (25215 ^ _775828) ^ [_1220734] : [-(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)), _1220734)))], (49431 ^ _775828) ^ [_1768382, _1768384, _1768386, _1768388] : [-(hAPP(c_List_Ofilter(_1768382, _1768384), c_List_Oremove1(_1768382, _1768386, _1768388)) = c_List_Oremove1(_1768382, _1768386, hAPP(c_List_Ofilter(_1768382, _1768384), _1768388)))], (24324 ^ _775828) ^ [_1202613, _1202615, _1202617] : [class_Int_Onumber(_1202613), class_Orderings_Oord(_1202613), 24331 ^ _775828 : [(24338 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202613), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202615)), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202617)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1202613), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202615)), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202617)) = hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202617))], (24332 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202613), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202615)), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202617))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1202613), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202615)), hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202617)) = hAPP(c_Int_Onumber__class_Onumber__of(_1202613), _1202615))]]], (2838 ^ _775828) ^ [_818320, _818322, _818324, _818326, _818328, _818330, _818332, _818334] : [-(c_New__DSequence_Opos__bind(_818334, _818330, _818326, _818322) = c_New__DSequence_Opos__bind(_818332, _818328, _818324, _818320)), _818334 = _818332, _818330 = _818328, _818326 = _818324, _818322 = _818320], (12831 ^ _775828) ^ [_987536, _987538] : [class_Rings_Olinordered__idom(_987536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987536), _987538), c_Groups_Ozero__class_Ozero(_987536))), -(c_Groups_Osgn__class_Osgn(_987536, _987538) = hAPP(c_Groups_Ouminus__class_Ouminus(_987536), c_Groups_Oone__class_Oone(_987536)))], (38220 ^ _775828) ^ [_1501645, _1501647, _1501649, _1501651] : [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), _1501645), _1501647)), 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), _1501649), _1501651)), 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), _1501645), _1501651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501649), _1501647))))], (49299 ^ _775828) ^ [_1765598, _1765600, _1765602] : [-(hAPP(hAPP(c_List_Odrop(_1765598), _1765600), c_List_Obutlast(_1765598, _1765602)) = c_List_Obutlast(_1765598, hAPP(hAPP(c_List_Odrop(_1765598), _1765600), _1765602)))], (18187 ^ _775828) ^ [_1088022, _1088024, _1088026, _1088028] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088022, _1088024), _1088026)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088022, _1088024), _1088028)), -(_1088026 = _1088028)], (27022 ^ _775828) ^ [_1253285] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253285) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253285), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48587 ^ _775828) ^ [_1750691, _1750693, _1750695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750691), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750693)), _1750695))), -(hAPP(hAPP(c_List_Oappend(_1750693), hAPP(hAPP(c_List_Otake(_1750693), _1750691), _1750695)), hAPP(hAPP(c_List_Olist_OCons(_1750693), hAPP(c_List_Ohd(_1750693), hAPP(hAPP(c_List_Odrop(_1750693), _1750691), _1750695))), c_List_Olist_ONil(_1750693))) = hAPP(hAPP(c_List_Otake(_1750693), hAPP(c_Nat_OSuc, _1750691)), _1750695))], (22402 ^ _775828) ^ [_1165461, _1165463, _1165465] : [class_Fields_Ofield__inverse__zero(_1165461), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165461), hAPP(c_Groups_Ouminus__class_Ouminus(_1165461), _1165463)), hAPP(c_Groups_Ouminus__class_Ouminus(_1165461), _1165465)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165461), _1165463), _1165465))], (3786 ^ _775828) ^ [_833336, _833338, _833340, _833342, _833344, _833346, _833348, _833350, _833352, _833354] : [-(c_Finite__Set_Ofold__graph(_833354, _833350, _833346, _833342, _833338) = c_Finite__Set_Ofold__graph(_833352, _833348, _833344, _833340, _833336)), _833354 = _833352, _833350 = _833348, _833346 = _833344, _833342 = _833340, _833338 = _833336], (25961 ^ _775828) ^ [_1234356, _1234358] : [_1234356 = _1234358, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234356), _1234358)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234358), _1234356)))], (49377 ^ _775828) ^ [_1767397, _1767399, _1767401] : [hAPP(c_List_Ofilter(_1767397, _1767399), _1767401) = c_List_Olist_ONil(_1767397), 49380 ^ _775828 : [(49381 ^ _775828) ^ [_1767494] : [hBOOL(hAPP(hAPP(c_member(_1767397), _1767494), hAPP(c_List_Oset(_1767397), _1767401))), hBOOL(hAPP(_1767399, _1767494))]]], (19506 ^ _775828) ^ [_1111010, _1111012] : [class_Int_Onumber__ring(_1111010), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1111010), c_Groups_Oone__class_Oone(_1111010)), hAPP(c_Int_Onumber__class_Onumber__of(_1111010), _1111012)) = hAPP(c_Int_Onumber__class_Onumber__of(_1111010), 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), _1111012))))], (3450 ^ _775828) ^ [_828136, _828138] : [_828138 = _828136, -(c_Nitpick_Odenom(_828138) = c_Nitpick_Odenom(_828136))], (42728 ^ _775828) ^ [_1607579, _1607581, _1607583, _1607585, _1607587] : [c_Fun_Oinj__on(_1607579, _1607581, _1607583, c_Orderings_Otop__class_Otop(tc_fun(_1607579, tc_HOL_Obool))), c_Fun_Oinj__on(_1607585, _1607579, _1607587, c_Orderings_Otop__class_Otop(tc_fun(_1607585, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1607585, _1607581, hAPP(c_Fun_Ocomp(_1607579, _1607581, _1607585, _1607583), _1607587), c_Orderings_Otop__class_Otop(tc_fun(_1607585, tc_HOL_Obool))))], (44495 ^ _775828) ^ [] : [-(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)))], (48387 ^ _775828) ^ [_1745735, _1745737, _1745739, _1745741] : [hBOOL(hAPP(hAPP(c_member(_1745735), _1745737), hAPP(c_List_Oset(_1745735), hAPP(hAPP(c_List_Odrop(_1745735), _1745739), _1745741)))), -(hBOOL(hAPP(hAPP(c_member(_1745735), _1745737), hAPP(c_List_Oset(_1745735), _1745741))))], (18549 ^ _775828) ^ [_1094807, _1094809] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094807), _1094809) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1094807 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1094807 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (27096 ^ _775828) ^ [_1254518, _1254520] : [-(_1254518 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27099 ^ _775828 : [(27106 ^ _775828) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254520) = 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), _1254518), _1254520)), _1254518)))], (27100 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254518), _1254520)), _1254518)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254520) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (32921 ^ _775828) ^ [_1385083, _1385085, _1385087, _1385089] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385083), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385085, tc_Nat_Onat), _1385087), _1385089)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385085, _1385083), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1385083, _1385085), c_Nat_Osemiring__1__class_Oof__nat(_1385083)), _1385087)), _1385089)), class_Groups_Ocomm__monoid__mult(_1385083), class_Rings_Osemiring__1(_1385083)], (47683 ^ _775828) ^ [_1727622, _1727624, _1727626, _1727628] : [-(c_Map_Omap__upds(_1727622, _1727624, _1727626, _1727628, c_List_Olist_ONil(_1727624)) = _1727626)], (49507 ^ _775828) ^ [_1770562, _1770564, _1770566] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770562)), hAPP(c_List_Ofilter(_1770562, _1770564), _1770566)) = 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(_1770562)), _1770566)))), hAPP(hAPP(c_COMBB(_1770562, tc_HOL_Obool, tc_Nat_Onat), _1770564), hAPP(c_List_Onth(_1770562), _1770566))))))], (28816 ^ _775828) ^ [_1294264, _1294266] : [-(c_Hilbert__Choice_OEps(_1294264, hAPP(c_fequal, _1294266)) = _1294266)], (5088 ^ _775828) ^ [_853673, _853675] : [_853675 = _853673, -(c_List_Otl(_853675) = c_List_Otl(_853673))], (16911 ^ _775828) ^ [_1064102, _1064104, _1064106] : [class_Rings_Olinordered__idom(_1064102), 16914 ^ _775828 : [(16923 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), hAPP(c_Groups_Oabs__class_Oabs(_1064102), _1064104)), _1064106))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), _1064104), _1064106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), hAPP(c_Groups_Ouminus__class_Ouminus(_1064102), _1064104)), _1064106))], (16915 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), hAPP(c_Groups_Oabs__class_Oabs(_1064102), _1064104)), _1064106)), 16918 ^ _775828 : [(16921 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), hAPP(c_Groups_Ouminus__class_Ouminus(_1064102), _1064104)), _1064106)))], (16919 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064102), _1064104), _1064106)))]]]]], (17417 ^ _775828) ^ [_1074100, _1074102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074100), _1074102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074100)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074102))))], (13664 ^ _775828) ^ [_1003178, _1003180, _1003182] : [hAPP(c_Com_Ocom_OBODY, _1003178) = c_Com_Ocom_OSemi(_1003180, _1003182)], (48383 ^ _775828) ^ [_1745601, _1745603, _1745605, _1745607] : [-(hAPP(hAPP(c_List_Odrop(_1745601), _1745603), hAPP(hAPP(c_List_Otake(_1745601), _1745605), _1745607)) = hAPP(hAPP(c_List_Otake(_1745601), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1745605), _1745603)), hAPP(hAPP(c_List_Odrop(_1745601), _1745603), _1745607)))], (35139 ^ _775828) ^ [_1434177, _1434179, _1434181, _1434183, _1434185, _1434187] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434177, tc_fun(_1434179, tc_HOL_Obool))), _1434181), _1434183), _1434185), _1434187)), -(hBOOL(hAPP(hAPP(_1434181, _1434185), _1434187)))], (34051 ^ _775828) ^ [_1409182, _1409184, _1409186] : [class_Lattices_Osemilattice__inf(_1409182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409182), _1409184), _1409186)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409182), _1409186), _1409184) = _1409184)], (40057 ^ _775828) ^ [] : [-(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))))], (12661 ^ _775828) ^ [_984807, _984809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984809), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984807), _984809)))], (6144 ^ _775828) ^ [_873464] : [6145 ^ _775828 : [(6146 ^ _775828) ^ [_873506] : [_873464 = hAPP(c_Nat_OSuc, _873506)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _873464)))], (24491 ^ _775828) ^ [_1206063, _1206065, _1206067] : [hBOOL(hAPP(hAPP(c_member(_1206063), _1206067), c_Wellfounded_Oacc(_1206063, _1206065))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1206063, hAPP(hAPP(c_COMBC(_1206063, tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_fun(_1206063, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1206063, tc_fun(tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_fun(_1206063, tc_HOL_Obool)), _1206063), c_COMBC(_1206063, tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1206063, tc_prod(_1206063, _1206063)), tc_fun(_1206063, tc_fun(tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_HOL_Obool)), _1206063), hAPP(c_COMBB(tc_prod(_1206063, _1206063), tc_fun(tc_fun(tc_prod(_1206063, _1206063), tc_HOL_Obool), tc_HOL_Obool), _1206063), c_member(tc_prod(_1206063, _1206063)))), c_Product__Type_OPair(_1206063, _1206063)))), _1206065)), _1206067)))], (11781 ^ _775828) ^ [_969488, _969490, _969492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969490), _969492)), -(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, _969488)), _969490)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969488)), _969492))))], (51298 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (5450 ^ _775828) ^ [_859068, _859070] : [_859070 = _859068, -(v_Q(_859070) = v_Q(_859068))], (43590 ^ _775828) ^ [_1628194, _1628196, _1628198, _1628200, _1628202] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1628194, _1628196, _1628198), _1628200), _1628202) = c_HOL_OThe(_1628196, c_Finite__Set_Ofold__graph(_1628194, _1628196, _1628198, _1628200, _1628202)))], (680 ^ _775828) ^ [_786198, _786200, _786202, _786204] : [-(c_Wellfounded_Owf(_786202, _786198)), c_Wellfounded_Owf(_786204, _786200), _786204 = _786202, _786200 = _786198], (45262 ^ _775828) ^ [_1667177, _1667179, _1667181, _1667183, _1667185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667177, tc_HOL_Obool)), _1667179), _1667181)), 45268 ^ _775828 : [(45273 ^ _775828) ^ [] : [hBOOL(hAPP(_1667185, 45267 ^ [_1667177, _1667179, _1667181, _1667183, _1667185]))], (45271 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1667183, 45267 ^ [_1667177, _1667179, _1667181, _1667183, _1667185])))], (45269 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667177), 45267 ^ [_1667177, _1667179, _1667181, _1667183, _1667185]), _1667179)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667177, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667177, tc_HOL_Obool)), _1667179), hAPP(c_Set_OCollect(_1667177), _1667183))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667177, tc_HOL_Obool)), _1667181), hAPP(c_Set_OCollect(_1667177), _1667185)))))], (46241 ^ _775828) ^ [_1690183, _1690185, _1690187, _1690189, _1690191] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690183)), _1690185) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690187)), _1690189), 46244 ^ _775828 : [(46253 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1690183, _1690187), _1690185), _1690189) = _1690191), hAPP(hAPP(c_List_Omap(tc_prod(_1690183, _1690187), _1690183), c_Product__Type_Ofst(_1690183, _1690187)), _1690191) = _1690185, hAPP(hAPP(c_List_Omap(tc_prod(_1690183, _1690187), _1690187), c_Product__Type_Osnd(_1690183, _1690187)), _1690191) = _1690189], (46245 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Ozip(_1690183, _1690187), _1690185), _1690189) = _1690191, 46248 ^ _775828 : [(46251 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1690183, _1690187), _1690187), c_Product__Type_Osnd(_1690183, _1690187)), _1690191) = _1690189)], (46249 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1690183, _1690187), _1690183), c_Product__Type_Ofst(_1690183, _1690187)), _1690191) = _1690185)]]]]], (31689 ^ _775828) ^ [_1359790, _1359792] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1359790, _1359790), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1359790, _1359792)), c_Relation_OId(_1359790)) = c_Transitive__Closure_Ortrancl(_1359790, _1359792))], (5796 ^ _775828) ^ [_868212, _868214, _868216] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_868212), _868214), _868216)), -(c_Natural_Oevaln(_868212, _868214, 5799 ^ [_868212, _868214, _868216], _868216))], (25505 ^ _775828) ^ [_1225966, _1225968, _1225970, _1225972, _1225974] : [-(hAPP(c_New__DSequence_Oneg__bind(_1225966, _1225968, _1225970, _1225972), _1225974) = c_Lazy__Sequence_Ohb__bind(_1225966, _1225968, hAPP(_1225970, _1225974), hAPP(hAPP(c_COMBC(_1225966, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1225968))), _1225972), _1225974)))], (26850 ^ _775828) ^ [_1250228, _1250230] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250228), _1250230)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250228), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1250230))))], (51202 ^ _775828) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (30920 ^ _775828) ^ [_1341562, _1341564, _1341566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341562), _1341564)), hBOOL(hAPP(hAPP(c_member(_1341562), _1341566), _1341564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1341562), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341562, tc_HOL_Obool)), _1341564), hAPP(hAPP(c_Set_Oinsert(_1341562), _1341566), c_Orderings_Obot__class_Obot(tc_fun(_1341562, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1341562), _1341564))))], (476 ^ _775828) ^ [_782956, _782958, _782960, _782962, _782964, _782966, _782968, _782970] : [-(c_Wellfounded_Omax__extp(_782968, _782964, _782960, _782956)), c_Wellfounded_Omax__extp(_782970, _782966, _782962, _782958), _782970 = _782968, _782966 = _782964, _782962 = _782960, _782958 = _782956], (20720 ^ _775828) ^ [_1132040, _1132042, _1132044] : [class_Rings_Olinordered__idom(_1132040), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132040), c_Groups_Ozero__class_Ozero(_1132040)), hAPP(hAPP(c_Power_Opower__class_Opower(_1132040), _1132042), 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)))), _1132044)))))], (46929 ^ _775828) ^ [_1709903, _1709905, _1709907] : [-(hAPP(hAPP(c_List_Onth(_1709903), hAPP(hAPP(c_List_Olist_OCons(_1709903), _1709905), _1709907)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1709905)], (20490 ^ _775828) ^ [_1127925, _1127927] : [class_Rings_Olinordered__idom(_1127925), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127925), hAPP(c_Groups_Oabs__class_Oabs(_1127925), _1127927)), 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(_1127925), _1127927), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35393 ^ _775828) ^ [_1440220, _1440222, _1440224, _1440226, _1440228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440220, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1440222, _1440220, _1440224), _1440226)), _1440228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1440220, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1440222, tc_HOL_Obool), tc_fun(_1440220, tc_HOL_Obool), c_Set_Oimage(_1440222, _1440220, _1440224)), hAPP(c_Set_OPow(_1440222), _1440226))), hAPP(c_Set_OPow(_1440220), _1440228))))], (16631 ^ _775828) ^ [_1058882, _1058884, _1058886, _1058888] : [hBOOL(hAPP(hAPP(c_member(_1058882), _1058884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058882, tc_HOL_Obool)), _1058886), _1058888))), 16634 ^ _775828 : [(16637 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1058882), _1058884), _1058888))], (16635 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058882), _1058884), _1058886)))]]], (832 ^ _775828) ^ [_788574, _788576] : [-(class_Lattices_Oab__semigroup__idem__mult(_788574)), _788576 = _788574, class_Lattices_Oab__semigroup__idem__mult(_788576)], (18467 ^ _775828) ^ [_1093561, _1093563] : [_1093561 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1093563, _1093561) = 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), _1093563)))], (6654 ^ _775828) ^ [_881390] : [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), _881390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _881390)))], (46007 ^ _775828) ^ [_1684255, _1684257, _1684259, _1684261, _1684263] : [-(hBOOL(hAPP(hAPP(c_member(_1684255), _1684257), hAPP(c_List_Oset(_1684255), _1684259)))), -(hAPP(c_Map_Omap__of(_1684255, _1684261, hAPP(hAPP(c_List_Ozip(_1684255, _1684261), _1684259), hAPP(hAPP(c_List_Omap(_1684255, _1684261), _1684263), _1684259))), _1684257) = c_Option_Ooption_ONone(_1684261))], (18403 ^ _775828) ^ [_1092158, _1092160, _1092162, _1092164] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1092158, _1092160), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1092162), _1092164))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092158), _1092160), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1092164), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092162)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092162)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1092164), 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), _1092160), _1092164))))))], (42575 ^ _775828) ^ [_1604079] : [-(_1604079 = hAPP(c_Int_OAbs__Integ, 42573 ^ [_1604079]))], (19798 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (38120 ^ _775828) ^ [_1499011, _1499013] : [class_Orderings_Olinorder(_1499011), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499011, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499011), _1499013)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1499011), _1499013))], (30561 ^ _775828) ^ [_1334286, _1334288] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334286, _1334286)), _1334288)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334286), hAPP(c_Relation_OField(_1334286), _1334288))))], (13939 ^ _775828) ^ [_1008290, _1008292, _1008294, _1008296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008292), _1008294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1008294), 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), _1008292), _1008290)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008292), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008296, _1008290))), _1008294))))], (12203 ^ _775828) ^ [_976901] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _976901)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_976901)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39413 ^ _775828) ^ [_1527441, _1527443, _1527445, _1527447, _1527449, _1527451, _1527453] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527441, _1527443, _1527445), _1527447), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527449, tc_fun(tc_prod(_1527443, _1527445), tc_HOL_Obool)), _1527451), _1527453)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527449, tc_fun(tc_prod(_1527441, _1527445), tc_HOL_Obool)), _1527451), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527443, _1527445), tc_HOL_Obool), tc_fun(tc_prod(_1527441, _1527445), tc_HOL_Obool), _1527449), hAPP(c_Relation_Orel__comp(_1527441, _1527443, _1527445), _1527447)), _1527453)))], (44342 ^ _775828) ^ [_1645552, _1645554, _1645556, _1645558, _1645560] : [44344 ^ _775828 : [(44347 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1645552, tc_HOL_Obool)), _1645554), hAPP(_1645560, 44343 ^ [_1645552, _1645554, _1645556, _1645558, _1645560])))], (44345 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1645556), 44343 ^ [_1645552, _1645554, _1645556, _1645558, _1645560]), _1645558)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1645552, tc_HOL_Obool)), _1645554), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645556, tc_fun(_1645552, tc_HOL_Obool)), _1645558), _1645560))))], (14844 ^ _775828) ^ [_1024328, _1024330, _1024332, _1024334] : [class_Divides_Osemiring__div(_1024328), -(_1024330 = c_Groups_Ozero__class_Ozero(_1024328)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024328), _1024332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024328), _1024330), _1024334))), _1024330) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024328), _1024334), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024328), _1024332), _1024330)))], (27970 ^ _775828) ^ [_1276063] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1276063)))], (40267 ^ _775828) ^ [_1547719, _1547721] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547719, tc_HOL_Obool)), _1547721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1547719, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1547719, tc_HOL_Obool))), _1547721))], (17277 ^ _775828) ^ [_1071374, _1071376] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1071374), _1071376))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1071374))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1071376))))], (6175 ^ _775828) ^ [_873939, _873941] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873939), hAPP(c_Nat_OSuc, _873941)))), 6176 ^ _775828 : [(6179 ^ _775828) ^ [_874027] : [_873939 = hAPP(c_Nat_OSuc, _874027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874027), _873941))], (6177 ^ _775828) ^ [] : [_873939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (27972 ^ _775828) ^ [_1276088] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1276088)))], (20090 ^ _775828) ^ [_1120934, _1120936] : [c_Int_OBit0(_1120934) = c_Int_OBit1(_1120936)], (47723 ^ _775828) ^ [_1728558, _1728560, _1728562, _1728564, _1728566, _1728568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728558)), _1728560)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728562)), _1728564))), -(c_Map_Omap__upds(_1728558, _1728562, _1728566, hAPP(hAPP(c_List_Oappend(_1728558), _1728560), hAPP(hAPP(c_List_Olist_OCons(_1728558), _1728568), c_List_Olist_ONil(_1728558))), _1728564) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1728558, tc_Option_Ooption(_1728562)), c_Map_Omap__upds(_1728558, _1728562, _1728566, _1728560, _1728564)), _1728568), hAPP(c_Option_Ooption_OSome(_1728562), hAPP(hAPP(c_List_Onth(_1728562), _1728564), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728558)), _1728560)))))], (3390 ^ _775828) ^ [_827148, _827150, _827152, _827154, _827156, _827158, _827160, _827162] : [-(c_Product__Type_Oapfst(_827162, _827158, _827154, _827150) = c_Product__Type_Oapfst(_827160, _827156, _827152, _827148)), _827162 = _827160, _827158 = _827156, _827154 = _827152, _827150 = _827148], (20452 ^ _775828) ^ [] : [-(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))))))], (34253 ^ _775828) ^ [_1413276, _1413278, _1413280, _1413282, _1413284] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413276, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1413278, _1413276, _1413280), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413278, tc_HOL_Obool)), _1413282), _1413284))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413276, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1413278, _1413276, _1413280), _1413282)), hAPP(c_Set_Oimage(_1413278, _1413276, _1413280), _1413284)))))], (1300 ^ _775828) ^ [_794696, _794698] : [-(class_Lattices_Olattice(_794696)), _794698 = _794696, class_Lattices_Olattice(_794698)], (2168 ^ _775828) ^ [_807487, _807489, _807491, _807493] : [-(c_Orderings_Oord_Omin(_807493, _807489) = c_Orderings_Oord_Omin(_807491, _807487)), _807493 = _807491, _807489 = _807487], (7437 ^ _775828) ^ [_894525] : [-(c_Option_Ois__none(_894525, c_Option_Ooption_ONone(_894525)))], (46802 ^ _775828) ^ [_1706951, _1706953, _1706955, _1706957, _1706959] : [class_Orderings_Olinorder(_1706951), -(hBOOL(hAPP(hAPP(c_member(_1706951), hAPP(_1706953, _1706955)), hAPP(c_Set_Oimage(_1706957, _1706951, _1706953), hAPP(c_List_Oset(_1706957), _1706959))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1706957, _1706951, _1706953, _1706955, _1706959) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706957, _1706951, _1706953), _1706955), _1706959))], (20644 ^ _775828) ^ [_1130504, _1130506, _1130508] : [class_Rings_Olinordered__semidom(_1130504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130504), hAPP(hAPP(c_Power_Opower__class_Opower(_1130504), _1130506), 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(_1130504), _1130508), 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(_1130504), c_Groups_Ozero__class_Ozero(_1130504)), _1130508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130504), _1130506), _1130508)))], (5463 ^ _775828) ^ [_862007, _862009, _862011, _862013, _862015] : [c_Hoare__Mirabelle_Otriple__valid(_862007, _862009, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862007), _862011), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _862013))), _862015)), -(c_Hoare__Mirabelle_Otriple__valid(_862007, hAPP(c_Nat_OSuc, _862009), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_862007), _862011), hAPP(c_Com_Ocom_OBODY, _862013)), _862015)))], (30143 ^ _775828) ^ [_1325336, _1325338] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325338, _1325336) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325336), _1325338)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325338), _1325336)))], (31283 ^ _775828) ^ [_1350810, _1350812, _1350814] : [class_Orderings_Olinorder(_1350810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350810), _1350812)), -(_1350814 = c_Orderings_Obot__class_Obot(tc_fun(_1350810, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350810, tc_HOL_Obool)), _1350814), _1350812)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350810), c_Big__Operators_Olattice_OSup__fin(_1350810, c_Orderings_Oord__class_Omax(_1350810), _1350814)), c_Big__Operators_Olattice_OSup__fin(_1350810, c_Orderings_Oord__class_Omax(_1350810), _1350812)) = c_Big__Operators_Olattice_OSup__fin(_1350810, c_Orderings_Oord__class_Omax(_1350810), _1350812))], (30439 ^ _775828) ^ [_1332130, _1332132, _1332134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332130), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332130, tc_HOL_Obool)), _1332132), _1332134))), 30442 ^ _775828 : [(30445 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332130), _1332134)))], (30443 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332130), _1332132)))]]], (27863 ^ _775828) ^ [_1274083, _1274085, _1274087, _1274089, _1274091] : [hBOOL(hAPP(hAPP(_1274083, _1274085), _1274087)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1274089, _1274091, _1274083), _1274085)))], (44675 ^ _775828) ^ [_1654548, _1654550, _1654552] : [-(hAPP(c_Relation_ORange(_1654548, _1654550), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1654548, _1654550), tc_HOL_Obool), _1654552)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1654548, _1654550), tc_HOL_Obool), tc_fun(_1654550, tc_HOL_Obool)), _1654552), c_Relation_ORange(_1654548, _1654550)))], (36567 ^ _775828) ^ [_1462991, _1462993, _1462995] : [class_Orderings_Olinorder(_1462991), 36570 ^ _775828 : [(36577 ^ _775828) ^ [] : [_1462993 = _1462995, -(hAPP(c_SetInterval_Oord__class_OatMost(_1462991), _1462993) = hAPP(c_SetInterval_Oord__class_OatMost(_1462991), _1462995))], (36571 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1462991), _1462993) = hAPP(c_SetInterval_Oord__class_OatMost(_1462991), _1462995), -(_1462993 = _1462995)]]], (30958 ^ _775828) ^ [_1342465, _1342467, _1342469] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1342465, tc_HOL_Obool), tc_fun(_1342465, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1342465, tc_HOL_Obool), tc_fun(_1342465, tc_HOL_Obool)), _1342467), _1342469)), c_Wellfounded_Ofinite__psubset(_1342465)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1342465, tc_HOL_Obool)), _1342467), _1342469)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342465), _1342469))], (39355 ^ _775828) ^ [_1526034, _1526036, _1526038, _1526040] : [c_Fun_Oinj__on(_1526034, _1526036, _1526038, _1526040), -(hAPP(c_Set_Oimage(_1526036, _1526034, c_Fun_Othe__inv__into(_1526034, _1526036, _1526040, _1526038)), hAPP(c_Set_Oimage(_1526034, _1526036, _1526038), _1526040)) = _1526040)], (27980 ^ _775828) ^ [_1276230, _1276232] : [hBOOL(hAPP(hAPP(c_member(_1276230), 27981 ^ [_1276230, _1276232]), c_Wellfounded_Oacc(_1276230, _1276232))), -(c_Wellfounded_Owf(_1276230, _1276232))], (26731 ^ _775828) ^ [_1248266, _1248268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248266)), 26734 ^ _775828 : [(26741 ^ _775828) ^ [] : [_1248268 = 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), _1248266), _1248268)), _1248266)))], (26735 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248266), _1248268)), _1248266)), -(_1248268 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (43562 ^ _775828) ^ [_1627688, _1627690, _1627692] : [class_Orderings_Olinorder(_1627688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627688), _1627690)), -(hBOOL(hAPP(hAPP(c_member(_1627688), _1627692), _1627690))), -(c_Big__Operators_Olattice_OSup__fin(_1627688, c_Orderings_Oord__class_Omax(_1627688), hAPP(hAPP(c_Set_Oinsert(_1627688), _1627692), _1627690)) = hAPP(hAPP(c_Finite__Set_Ofold(_1627688, _1627688, c_Orderings_Oord__class_Omax(_1627688)), _1627692), _1627690))], (41859 ^ _775828) ^ [_1585963, _1585965, _1585967, _1585969] : [c_Big__Operators_Osemilattice__big(_1585963, _1585965, _1585967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585963), _1585969)), -(hAPP(_1585967, _1585969) = hAPP(c_Finite__Set_Ofold1(_1585963, _1585965), _1585969))], (19162 ^ _775828) ^ [_1105586] : [class_Int_Onumber__ring(_1105586), -(c_Groups_Ozero__class_Ozero(_1105586) = hAPP(c_Int_Onumber__class_Onumber__of(_1105586), c_Int_OPls))], (47409 ^ _775828) ^ [_1721598, _1721600, _1721602, _1721604, _1721606] : [class_Orderings_Olinorder(_1721598), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721600, _1721598, _1721602), _1721604), _1721606) = c_List_Olist_ONil(_1721600)], (12055 ^ _775828) ^ [_974530, _974532, _974534] : [12056 ^ _775828 : [(12059 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974530), _974534))], (12057 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _974532)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974530), _974532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974534), _974532))))], (16657 ^ _775828) ^ [_1059434, _1059436, _1059438, _1059440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059434, tc_HOL_Obool)), _1059436), _1059438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059434, tc_HOL_Obool)), _1059438), _1059440)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059434, tc_HOL_Obool)), _1059438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059434, tc_HOL_Obool)), _1059440), _1059436)) = _1059436)], (35025 ^ _775828) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (32887 ^ _775828) ^ [_1384124, _1384126, _1384128, _1384130, _1384132, _1384134] : [-(hBOOL(hAPP(hAPP(c_member(_1384124), _1384126), _1384128))), -(hAPP(c_Set_Oimage(_1384124, tc_Option_Ooption(_1384130), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1384124, tc_Option_Ooption(_1384130)), _1384132), _1384126), hAPP(c_Option_Ooption_OSome(_1384130), _1384134))), _1384128) = hAPP(c_Set_Oimage(_1384124, tc_Option_Ooption(_1384130), _1384132), _1384128))], (12685 ^ _775828) ^ [_985254, _985256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985254), _985256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _985254), c_Groups_Oone__class_Oone(tc_Int_Oint))), _985256)))], (18435 ^ _775828) ^ [_1092847, _1092849, _1092851, _1092853, _1092855, _1092857, _1092859] : [hBOOL(hAPP(_1092847, _1092849)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1092851, _1092851)), hAPP(hAPP(c_Product__Type_OPair(_1092851, _1092851), _1092853), _1092855)), hAPP(_1092857, _1092849))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1092859, _1092851), tc_prod(_1092859, _1092851))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1092859, _1092851), tc_prod(_1092859, _1092851)), hAPP(hAPP(c_Product__Type_OPair(_1092859, _1092851), _1092849), _1092853)), hAPP(hAPP(c_Product__Type_OPair(_1092859, _1092851), _1092849), _1092855))), c_Recdef_Osame__fst(_1092859, _1092851, _1092847, _1092857))))], (19022 ^ _775828) ^ [_1103324, _1103326, _1103328] : [19024 ^ _775828 : [(19027 ^ _775828) ^ [] : [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(_1103326, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19023 ^ [_1103324, _1103326, _1103328]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1103326, 19023 ^ [_1103324, _1103326, _1103328])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19025 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19023 ^ [_1103324, _1103326, _1103328]), _1103324)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1103326, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1103328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103328), hAPP(_1103326, _1103324))), 19037 ^ _775828 : [(19040 ^ _775828) ^ [] : [-(hAPP(_1103326, 19036 ^ [_1103324, _1103326, _1103328]) = _1103328)], (19038 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19036 ^ [_1103324, _1103326, _1103328]), _1103324)))]]], (38114 ^ _775828) ^ [_1498900, _1498902] : [class_Orderings_Olinorder(_1498900), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498900, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1498900), _1498902)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1498900), _1498902))], (12273 ^ _775828) ^ [_978161, _978163, _978165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978161, tc_HOL_Obool)), _978163), _978165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978161, tc_HOL_Obool)), _978165), _978163)), -(_978163 = _978165)], (17199 ^ _775828) ^ [_1070044, _1070046] : [class_Groups_Oordered__ab__group__add__abs(_1070044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070044), _1070046), c_Groups_Ozero__class_Ozero(_1070044))), -(hAPP(c_Groups_Oabs__class_Oabs(_1070044), _1070046) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070044), _1070046))], (5130 ^ _775828) ^ [_854314, _854316] : [_854316 = _854314, -(c_List_Odrop(_854316) = c_List_Odrop(_854314))], (36509 ^ _775828) ^ [_1461705, _1461707] : [-(hAPP(c_List_Olexn(_1461705, _1461707), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1461705), tc_List_Olist(_1461705)), tc_HOL_Obool)))], (40784 ^ _775828) ^ [_1560024, _1560026] : [-(hAPP(c_Set_Ovimage(_1560024, _1560024, c_COMBI(_1560024)), _1560026) = _1560026)], (35735 ^ _775828) ^ [_1446853, _1446855, _1446857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446853)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446855), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1446857)), 35742 ^ _775828 : [(35743 ^ _775828) ^ [_1447061] : [35745 ^ _775828 : [(35751 ^ _775828) ^ [] : [-(_1447061 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35747 ^ [_1446853, _1446855, _1446857, _1447061]), 35744 ^ [_1446853, _1446855, _1446857, _1447061]))], (35749 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35747 ^ [_1446853, _1446855, _1446857, _1447061]), _1446857)))], (35746 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35744 ^ [_1446853, _1446855, _1446857, _1447061]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1446853))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446855), _1447061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1447061), _1446853))))]]], (50383 ^ _775828) ^ [_1788591, _1788593] : [-(hAPP(c_List_Oset(_1788591), c_List_Oconcat(_1788591, _1788593)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1788591), tc_fun(_1788591, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1788591)), _1788593)), c_List_Oset(_1788591)))], (17525 ^ _775828) ^ [_1075905, _1075907] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075905)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075905)), _1075907) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075905)), _1075907)))], (7419 ^ _775828) ^ [_894232, _894234, _894236, _894238] : [-(hAPP(c_Option_Ooption_Ooption__case(_894232, _894234, _894236, _894238), c_Option_Ooption_ONone(_894234)) = _894236)], (3950 ^ _775828) ^ [_835996, _835998, _836000, _836002] : [-(c_Nitpick_Ocard_H(_836002, _835998) = c_Nitpick_Ocard_H(_836000, _835996)), _836002 = _836000, _835998 = _835996], (32277 ^ _775828) ^ [_1372243, _1372245, _1372247] : [class_Orderings_Olinorder(_1372243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372243), _1372245)), -(_1372245 = c_Orderings_Obot__class_Obot(tc_fun(_1372243, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372243), _1372247)), -(_1372247 = c_Orderings_Obot__class_Obot(tc_fun(_1372243, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1372243, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372243, tc_HOL_Obool)), _1372245), _1372247)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372243), c_Big__Operators_Olinorder__class_OMin(_1372243, _1372245)), c_Big__Operators_Olinorder__class_OMin(_1372243, _1372247)))], (19748 ^ _775828) ^ [_1115075, _1115077] : [class_Int_Onumber__ring(_1115075), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115075), hAPP(c_Int_Onumber__class_Onumber__of(_1115075), c_Int_OBit1(c_Int_OPls))), _1115077) = _1115077)], (47934 ^ _775828) ^ [_1733707, _1733709, _1733711, _1733713, _1733715, _1733717] : [hAPP(hAPP(c_List_Oappend(_1733707), _1733709), _1733711) = _1733713, _1733715 = hAPP(hAPP(c_List_Oappend(_1733707), _1733711), _1733717), -(hAPP(hAPP(c_List_Oappend(_1733707), _1733709), _1733715) = hAPP(hAPP(c_List_Oappend(_1733707), _1733713), _1733717))], (38142 ^ _775828) ^ [_1499452, _1499454, _1499456, _1499458] : [class_Orderings_Olinorder(_1499452), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499452, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499452), _1499454)), c_SetInterval_Oord__class_OatLeastAtMost(_1499452, _1499456, _1499458)) = c_SetInterval_Oord__class_OatLeastAtMost(_1499452, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1499452), _1499454), _1499456), _1499458))], (41604 ^ _775828) ^ [_1581344, _1581346, _1581348] : [class_Lattices_Osemilattice__inf(_1581344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581344), _1581346)), -(_1581346 = c_Orderings_Obot__class_Obot(tc_fun(_1581344, tc_HOL_Obool))), 41615 ^ _775828 : [(41616 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1581344), _1581348), hAPP(c_Finite__Set_Ofold1(_1581344, c_Lattices_Osemilattice__inf__class_Oinf(_1581344)), _1581346))), 41619 ^ _775828 : [(41620 ^ _775828) ^ [_1581637] : [hBOOL(hAPP(hAPP(c_member(_1581344), _1581637), _1581346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1581344), _1581348), _1581637)))]]], (41626 ^ _775828) ^ [] : [41628 ^ _775828 : [(41631 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1581344), _1581348), 41627 ^ [_1581344, _1581346, _1581348]))], (41629 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581344), 41627 ^ [_1581344, _1581346, _1581348]), _1581346)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1581344), _1581348), hAPP(c_Finite__Set_Ofold1(_1581344, c_Lattices_Osemilattice__inf__class_Oinf(_1581344)), _1581346))))]]], (33965 ^ _775828) ^ [_1407706, _1407708, _1407710] : [class_Lattices_Osemilattice__inf(_1407706), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407706), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407706), _1407708), _1407710)), _1407708)))], (15826 ^ _775828) ^ [_1042788, _1042790, _1042792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042788), _1042790)), 15829 ^ _775828 : [(15836 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042792), _1042788)), _1042790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042792), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042790), _1042788))))], (15830 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042792), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042790), _1042788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042792), _1042788)), _1042790)))]]], (19120 ^ _775828) ^ [_1105038] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1105038), c_Int_OPls) = _1105038)], (45375 ^ _775828) ^ [_1669614, _1669616, _1669618, _1669620, _1669622] : [-(c_Map_Omap__add(_1669614, _1669616, _1669618, c_Map_Omap__add(_1669614, _1669616, _1669620, _1669622)) = c_Map_Omap__add(_1669614, _1669616, c_Map_Omap__add(_1669614, _1669616, _1669618, _1669620), _1669622))], (40121 ^ _775828) ^ [_1545114] : [c_Orderings_Otop__class_Otop(tc_fun(_1545114, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1545114, tc_HOL_Obool))], (7579 ^ _775828) ^ [_896682, _896684, _896686] : [class_Groups_Oordered__ab__group__add(_896682), 7582 ^ _775828 : [(7589 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896682), _896686), _896684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896682), hAPP(c_Groups_Ouminus__class_Ouminus(_896682), _896684)), hAPP(c_Groups_Ouminus__class_Ouminus(_896682), _896686))))], (7583 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896682), hAPP(c_Groups_Ouminus__class_Ouminus(_896682), _896684)), hAPP(c_Groups_Ouminus__class_Ouminus(_896682), _896686))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896682), _896686), _896684)))]]], (19308 ^ _775828) ^ [_1107841, _1107843] : [class_Int_Onumber__ring(_1107841), class_Rings_Olinordered__idom(_1107841), 19315 ^ _775828 : [(19322 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107841), c_Groups_Ozero__class_Ozero(_1107841)), hAPP(c_Int_Onumber__class_Onumber__of(_1107841), _1107843))))], (19316 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107841), c_Groups_Ozero__class_Ozero(_1107841)), hAPP(c_Int_Onumber__class_Onumber__of(_1107841), _1107843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107843)))]]], (27938 ^ _775828) ^ [_1275399, _1275401, _1275403] : [c_Wellfounded_Owf(_1275399, _1275401), hBOOL(hAPP(hAPP(c_member(tc_prod(_1275399, _1275399)), hAPP(hAPP(c_Product__Type_OPair(_1275399, _1275399), _1275403), _1275403)), _1275401))], (16963 ^ _775828) ^ [_1065050, _1065052, _1065054, _1065056] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065050), _1065052), _1065054)), hAPP(c_Int_Onumber__class_Onumber__of(_1065050), _1065056)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065050), _1065052), hAPP(c_Int_Onumber__class_Onumber__of(_1065050), _1065056))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065050), _1065054), hAPP(c_Int_Onumber__class_Onumber__of(_1065050), _1065056)))), class_Int_Onumber(_1065050), class_Rings_Osemiring(_1065050)], (38684 ^ _775828) ^ [_1511889, _1511891, _1511893] : [_1511891 = c_Orderings_Obot__class_Obot(tc_fun(_1511889, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1511889, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511889), _1511891), _1511893))], (51214 ^ _775828) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (43261 ^ _775828) ^ [_1620063, _1620065] : [43263 ^ _775828 : [(43266 ^ _775828) ^ [] : [43262 ^ [_1620063, _1620065] = c_Orderings_Obot__class_Obot(tc_fun(_1620063, tc_HOL_Obool))], (43264 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620063, tc_HOL_Obool)), 43262 ^ [_1620063, _1620065]), hAPP(c_Relation_OImage(_1620063, _1620063, _1620065), 43262 ^ [_1620063, _1620065]))))]], -(c_Wellfounded_Owf(_1620063, _1620065))], (48193 ^ _775828) ^ [_1739943, _1739945, _1739947, _1739949] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739943), tc_List_Olist(_1739943))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739943), tc_List_Olist(_1739943)), _1739945), _1739947)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739943), c_List_Olistrel1(_1739943, _1739949)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739943)), _1739945) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739943)), _1739947))], (10037 ^ _775828) ^ [_938193, _938195, _938197] : [_938195 = _938197, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938193, tc_HOL_Obool)), _938195) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938193, tc_HOL_Obool)), _938197))], (5525 ^ _775828) ^ [_863291, _863293, _863295, _863297] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863291)), _863293, _863295, _863297), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _863291), _863293, hAPP(c_Nat_OSuc, _863295), _863297))], (530 ^ _775828) ^ [_783771, _783773, _783775, _783777, _783779, _783781, _783783, _783785, _783787, _783789, _783791, _783793] : [-(c_Finite__Set_Ofolding__image__simple(_783791, _783787, _783783, _783779, _783775, _783771)), c_Finite__Set_Ofolding__image__simple(_783793, _783789, _783785, _783781, _783777, _783773), _783793 = _783791, _783789 = _783787, _783785 = _783783, _783781 = _783779, _783777 = _783775, _783773 = _783771], (42592 ^ _775828) ^ [_1604429, _1604431, _1604433] : [42594 ^ _775828 : [(42597 ^ _775828) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1604429, hAPP(c_Nat_OSuc, _1604433), 42593 ^ [_1604429, _1604431, _1604433])], (42595 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604429)), 42593 ^ [_1604429, _1604431, _1604433]), _1604431)))]], 42598 ^ _775828 : [(42599 ^ _775828) ^ [_1604602] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604429)), _1604602), _1604431)), -(c_Hoare__Mirabelle_Otriple__valid(_1604429, _1604433, _1604602))]]], (38410 ^ _775828) ^ [_1505523, _1505525, _1505527, _1505529, _1505531] : [hAPP(_1505523, _1505525) = hAPP(c_Option_Ooption_OSome(_1505527), _1505529), -(hBOOL(hAPP(hAPP(c_member(_1505531), _1505525), c_Map_Odom(_1505531, _1505527, _1505523))))], (20872 ^ _775828) ^ [_1135100, _1135102] : [20873 ^ _775828 : [(20876 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135102), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20874 ^ _775828) ^ [] : [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), _1135100), _1135102)))]], -(c_Divides_OnegDivAlg(_1135100, _1135102) = 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), _1135100), _1135102)))], (13016 ^ _775828) ^ [_991008, _991010, _991012, _991014] : [_991008 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991010), _991012)), _991014), -(_991010 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _991008, _991010) = _991014), 13023 ^ _775828 : [(13026 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991014), _991010))], (13024 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991010)))]], 13031 ^ _775828 : [(13034 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991010), _991014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991014), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13032 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991010))]]], (10888 ^ _775828) ^ [_954068, _954070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954068), _954070)), _954070))], (22598 ^ _775828) ^ [_1169011, _1169013, _1169015] : [class_Fields_Olinordered__field(_1169011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169011), c_Groups_Ozero__class_Ozero(_1169011)), _1169013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169011), _1169015), c_Groups_Ozero__class_Ozero(_1169011))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169011), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169011), _1169013), _1169015)), c_Groups_Ozero__class_Ozero(_1169011))))], (10386 ^ _775828) ^ [_944727, _944729, _944731, _944733, _944735] : [class_Groups_Oordered__ab__semigroup__add(_944727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944727), _944729), _944731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944727), _944733), _944735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944727), _944729), _944733)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944727), _944731), _944735))))], (17731 ^ _775828) ^ [_1079484, _1079486, _1079488, _1079490] : [class_Groups_Omonoid__mult(_1079484), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079484), _1079486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1079488), _1079490)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079484), hAPP(hAPP(c_Power_Opower__class_Opower(_1079484), _1079486), _1079488)), _1079490))], (40069 ^ _775828) ^ [_1544018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1544018)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1544018), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544018), c_Orderings_Otop__class_Otop(tc_fun(_1544018, tc_HOL_Obool)))))], (49539 ^ _775828) ^ [_1771500, _1771502] : [49541 ^ _775828 : [(49544 ^ _775828) ^ [] : [49540 ^ [_1771500, _1771502] = c_List_Olist_ONil(_1771500)], (49542 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771500)), 49540 ^ [_1771500, _1771502]), hAPP(c_List_Oset(tc_List_Olist(_1771500)), _1771502))))]], -(c_List_Otranspose(_1771500, _1771502) = c_List_Olist_ONil(tc_List_Olist(_1771500)))], (28767 ^ _775828) ^ [_1293353, _1293355] : [-(hAPP(c_Relation_OField(_1293353), _1293355) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293353, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1293353, _1293353), _1293355)), hAPP(c_Relation_ORange(_1293353, _1293353), _1293355)))], (8397 ^ _775828) ^ [_910691, _910693, _910695, _910697, _910699] : [class_Orderings_Oord(_910691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910693, _910691)), _910695), _910697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910691), hAPP(_910695, _910699)), hAPP(_910697, _910699))))], (45941 ^ _775828) ^ [_1682949] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1682949)), -(c_List_Onat__list(_1682949))], (20168 ^ _775828) ^ [_1122321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1122321)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122321), c_Int_OPls)))], (17153 ^ _775828) ^ [_1068971, _1068973] : [class_Int_Onumber__ring(_1068971), -(hBOOL(hAPP(hAPP(c_member(_1068971), hAPP(c_Int_Onumber__class_Onumber__of(_1068971), _1068973)), c_Int_Oring__1__class_OInts(_1068971))))], (4192 ^ _775828) ^ [_839883, _839885, _839887, _839889] : [-(c_Relation_Oconverse(_839889, _839885) = c_Relation_Oconverse(_839887, _839883)), _839889 = _839887, _839885 = _839883], (35699 ^ _775828) ^ [_1446182, _1446184, _1446186, _1446188] : [class_Orderings_Oorder(_1446182), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446182, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446182, _1446184, _1446186)), c_SetInterval_Oord__class_OatLeastAtMost(_1446182, _1446186, _1446188)) = c_Orderings_Obot__class_Obot(tc_fun(_1446182, tc_HOL_Obool)))], (27853 ^ _775828) ^ [_1273888, _1273890, _1273892, _1273894, _1273896, _1273898, _1273900, _1273902] : [hBOOL(hAPP(hAPP(_1273888, _1273890), _1273892)), hBOOL(hAPP(hAPP(_1273894, _1273892), _1273896)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1273898, _1273900, _1273902, _1273888, _1273894), _1273890), _1273896)))], (28030 ^ _775828) ^ [_1277463, _1277465] : [c_Wellfounded_Owf(_1277463, _1277465), 28034 ^ _775828 : [(28035 ^ _775828) ^ [_1277599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1277463, _1277463)), hAPP(hAPP(c_Product__Type_OPair(_1277463, _1277463), hAPP(_1277599, hAPP(c_Nat_OSuc, 28033 ^ [_1277463, _1277465, _1277599]))), hAPP(_1277599, 28033 ^ [_1277463, _1277465, _1277599]))), _1277465))]]], (46676 ^ _775828) ^ [_1703613, _1703615, _1703617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1703613), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1703615), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1703615)), _1703617)))), -(hBOOL(hAPP(hAPP(c_member(_1703615), hAPP(c_Random_Opick(_1703615, _1703617), _1703613)), hAPP(c_List_Oset(_1703615), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1703615), _1703615), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1703615)), _1703617)))))], (41458 ^ _775828) ^ [_1577887, _1577889, _1577891, _1577893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577887, _1577889)), hAPP(hAPP(c_Product__Type_OSigma(_1577887, _1577889), _1577891), hAPP(c_COMBK(tc_fun(_1577889, tc_HOL_Obool), _1577887), _1577893)))), -(_1577893 = c_Orderings_Obot__class_Obot(tc_fun(_1577889, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577887), _1577891)))], (5713 ^ _775828) ^ [_866894] : [class_Rings_Osemiring__1(_866894), -(hBOOL(hAPP(hAPP(c_member(_866894), c_Groups_Ozero__class_Ozero(_866894)), c_Nat_Osemiring__1__class_ONats(_866894))))], (7159 ^ _775828) ^ [_889673, _889675, _889677] : [class_Rings_Olinordered__semiring__strict(_889673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889673), c_Groups_Ozero__class_Ozero(_889673)), _889675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889673), _889677), c_Groups_Ozero__class_Ozero(_889673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_889673), _889677), _889675)), c_Groups_Ozero__class_Ozero(_889673))))], (17883 ^ _775828) ^ [_1082104, _1082106] : [class_Power_Opower(_1082104), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082104), _1082106), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1082104))], (43066 ^ _775828) ^ [_1615654, _1615656, _1615658, _1615660] : [c_Finite__Set_Ofolding(_1615654, _1615656, _1615658, _1615660), -(hAPP(_1615660, c_Orderings_Obot__class_Obot(tc_fun(_1615654, tc_HOL_Obool))) = c_Fun_Oid(_1615656))], (8531 ^ _775828) ^ [_912703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912703)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _912703))], (3846 ^ _775828) ^ [_834316, _834318, _834320, _834322, _834324, _834326] : [-(c_Smallcheck_Ofull__small_H(_834326, _834322, _834318) = c_Smallcheck_Ofull__small_H(_834324, _834320, _834316)), _834326 = _834324, _834322 = _834320, _834318 = _834316], (48741 ^ _775828) ^ [_1753511, _1753513, _1753515] : [-(_1753511 = c_List_Olist_ONil(_1753513)), -(hAPP(hAPP(c_List_Otake(_1753513), hAPP(c_Nat_OSuc, _1753515)), _1753511) = hAPP(hAPP(c_List_Olist_OCons(_1753513), hAPP(c_List_Ohd(_1753513), _1753511)), hAPP(hAPP(c_List_Otake(_1753513), _1753515), hAPP(c_List_Otl(_1753513), _1753511))))], (15130 ^ _775828) ^ [_1029747, _1029749, _1029751, _1029753, _1029755] : [class_Groups_Ominus(_1029747), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029749, _1029747)), _1029751), _1029753), _1029755) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029747), hAPP(_1029751, _1029755)), hAPP(_1029753, _1029755)))], (23920 ^ _775828) ^ [_1194666, _1194668, _1194670, _1194672] : [class_Orderings_Olinorder(_1194666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194666), _1194668), _1194670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194666), _1194668), _1194672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194666), _1194668), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194666), _1194670), _1194672))))], (39116 ^ _775828) ^ [_1520615, _1520617, _1520619, _1520621, _1520623] : [-(c_Fun_Oinj__on(_1520615, _1520617, _1520619, hAPP(hAPP(c_Set_Oinsert(_1520615), _1520621), _1520623))), c_Fun_Oinj__on(_1520615, _1520617, _1520619, _1520623), -(hBOOL(hAPP(hAPP(c_member(_1520617), hAPP(_1520619, _1520621)), hAPP(c_Set_Oimage(_1520615, _1520617, _1520619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520615, tc_HOL_Obool)), _1520623), hAPP(hAPP(c_Set_Oinsert(_1520615), _1520621), c_Orderings_Obot__class_Obot(tc_fun(_1520615, tc_HOL_Obool))))))))], (51124 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (37040 ^ _775828) ^ [_1473014, _1473016, _1473018, _1473020, _1473022] : [class_Groups_Ocomm__monoid__add(_1473014), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473014), _1473016), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473018), _1473020)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473022), _1473020))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473014), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1473014, tc_Nat_Onat), _1473016), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1473020))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1473018), _1473022)))], (17507 ^ _775828) ^ [_1075604, _1075606] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075604))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075604)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075606)) = 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), _1075606)))], (21940 ^ _775828) ^ [_1156542, _1156544] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156542), hAPP(c_Int_Onumber__class_Onumber__of(_1156542), c_Int_OMin)), _1156544) = hAPP(c_Groups_Ouminus__class_Ouminus(_1156542), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156542), c_Groups_Oone__class_Oone(_1156542)), _1156544))), class_Fields_Ofield__inverse__zero(_1156542), class_Int_Onumber__ring(_1156542)], (15792 ^ _775828) ^ [_1042144, _1042146, _1042148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042144), _1042146)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042146), _1042144)), _1042148) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042146), _1042148)), _1042144))], (43286 ^ _775828) ^ [_1620819, _1620821, _1620823, _1620825, _1620827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620819, _1620819)), hAPP(hAPP(c_Product__Type_OPair(_1620819, _1620819), _1620821), _1620823)), c_Transitive__Closure_Ortrancl(_1620819, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620819, _1620819), tc_HOL_Obool)), _1620825), _1620827)))), 43292 ^ _775828 : [(43298 ^ _775828) ^ [] : [43294 ^ [_1620819, _1620821, _1620823, _1620825, _1620827] = 43291 ^ [_1620819, _1620821, _1620823, _1620825, _1620827]], (43296 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620819, _1620819)), hAPP(hAPP(c_Product__Type_OPair(_1620819, _1620819), 43294 ^ [_1620819, _1620821, _1620823, _1620825, _1620827]), 43291 ^ [_1620819, _1620821, _1620823, _1620825, _1620827])), _1620827)))], (43293 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620819, _1620819)), hAPP(hAPP(c_Product__Type_OPair(_1620819, _1620819), 43291 ^ [_1620819, _1620821, _1620823, _1620825, _1620827]), _1620823)), c_Transitive__Closure_Ortrancl(_1620819, _1620825))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620819, _1620819)), hAPP(hAPP(c_Product__Type_OPair(_1620819, _1620819), _1620821), _1620823)), c_Transitive__Closure_Ortrancl(_1620819, _1620825))))], (27727 ^ _775828) ^ [_1269350, _1269352] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1269350))), -(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)), _1269350))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1269352)))) = 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)), _1269350))), 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, _1269352))))))], (20856 ^ _775828) ^ [_1134743, _1134745] : [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), _1134743))), 20859 ^ _775828 : [(20866 ^ _775828) ^ [] : [-(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), _1134745)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134745), 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), _1134743)))))], (20860 ^ _775828) ^ [] : [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), _1134745)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743)) = 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), _1134745)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134743))))]]], (20218 ^ _775828) ^ [_1123190, _1123192] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1123190)), c_Int_OBit0(_1123192)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123190), _1123192)))], (3500 ^ _775828) ^ [_828897, _828899, _828901, _828903, _828905, _828907, _828909, _828911] : [-(c_Random__Sequence_Omap(_828911, _828907, _828903, _828899) = c_Random__Sequence_Omap(_828909, _828905, _828901, _828897)), _828911 = _828909, _828907 = _828905, _828903 = _828901, _828899 = _828897], (15670 ^ _775828) ^ [_1039883, _1039885, _1039887] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1039883, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039885), _1039887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039885), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039883), _1039885), _1039887))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1039883, _1039885)))], (38360 ^ _775828) ^ [_1504418, _1504420, _1504422, _1504424, _1504426] : [hBOOL(hAPP(hAPP(c_member(_1504418), _1504420), hAPP(c_Relation_OImage(_1504422, _1504418, _1504424), _1504426))), 38364 ^ _775828 : [(38367 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504422), 38363 ^ [_1504418, _1504420, _1504422, _1504424, _1504426]), _1504426)))], (38365 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504422, _1504418)), hAPP(hAPP(c_Product__Type_OPair(_1504422, _1504418), 38363 ^ [_1504418, _1504420, _1504422, _1504424, _1504426]), _1504420)), _1504424)))]]], (45813 ^ _775828) ^ [] : [45815 ^ _775828 : [(45818 ^ _775828) ^ [] : [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)), 45814 ^ []))], (45816 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 45814 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (34281 ^ _775828) ^ [_1414172, _1414174] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414172, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414172, tc_HOL_Obool)), _1414174)), _1414174) = c_Orderings_Obot__class_Obot(tc_fun(_1414172, tc_HOL_Obool)))], (37650 ^ _775828) ^ [_1488048, _1488050, _1488052, _1488054, _1488056, _1488058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488048), _1488050)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488052), _1488054)), 37660 ^ _775828 : [(37663 ^ _775828) ^ [] : [hAPP(c_Finite__Set_Ocard(_1488048), hAPP(c_Set_OCollect(_1488048), hAPP(hAPP(c_COMBS(_1488048, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488048), c_fconj), hAPP(hAPP(c_COMBC(_1488048, tc_fun(_1488048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1488048)), _1488050))), hAPP(hAPP(c_COMBC(_1488048, _1488052, tc_HOL_Obool), _1488056), 37659 ^ [_1488048, _1488050, _1488052, _1488054, _1488056, _1488058])))) = _1488058], (37661 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488052), 37659 ^ [_1488048, _1488050, _1488052, _1488054, _1488056, _1488058]), _1488054)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488048, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1488052, tc_HOL_Obool), tc_Nat_Onat, _1488048), c_Finite__Set_Ocard(_1488052)), hAPP(hAPP(c_COMBB(tc_fun(_1488052, tc_HOL_Obool), tc_fun(_1488052, tc_HOL_Obool), _1488048), c_Set_OCollect(_1488052)), hAPP(hAPP(c_COMBB(tc_fun(_1488052, tc_HOL_Obool), tc_fun(_1488052, tc_HOL_Obool), _1488048), hAPP(c_COMBS(_1488052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488052), c_fconj), hAPP(hAPP(c_COMBC(_1488052, tc_fun(_1488052, tc_HOL_Obool), tc_HOL_Obool), c_member(_1488052)), _1488054)))), _1488056)))), _1488050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1488058), hAPP(c_Finite__Set_Ocard(_1488052), _1488054)))], (51382 ^ _775828) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (38448 ^ _775828) ^ [_1506541, _1506543, _1506545, _1506547, _1506549] : [_1506541 = c_Option_Ooption_ONone(_1506543), -(c_Map_Odom(_1506545, _1506543, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1506545, tc_Option_Ooption(_1506543)), _1506547), _1506549), _1506541)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506545, tc_HOL_Obool)), c_Map_Odom(_1506545, _1506543, _1506547)), hAPP(hAPP(c_Set_Oinsert(_1506545), _1506549), c_Orderings_Obot__class_Obot(tc_fun(_1506545, tc_HOL_Obool)))))], (34247 ^ _775828) ^ [_1413197, _1413199, _1413201, _1413203] : [-(hBOOL(hAPP(hAPP(c_member(_1413197), _1413199), _1413201))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413197, tc_HOL_Obool)), _1413201), hAPP(hAPP(c_Set_Oinsert(_1413197), _1413199), _1413203)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413197, tc_HOL_Obool)), _1413201), _1413203))], (2046 ^ _775828) ^ [_805646, _805648, _805650, _805652] : [-(c_Divides_OposDivAlg(_805652, _805648) = c_Divides_OposDivAlg(_805650, _805646)), _805652 = _805650, _805648 = _805646], (51454 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (40877 ^ _775828) ^ [_1562473, _1562475, _1562477, _1562479] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562473), hAPP(c_Set_Ovimage(_1562473, _1562475, _1562477), _1562479))), hAPP(c_Set_Oimage(_1562473, _1562475, _1562477), c_Orderings_Otop__class_Otop(tc_fun(_1562473, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1562475, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1562475), _1562479)))], (24567 ^ _775828) ^ [_1207324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207324)), -(c_Nat__Transfer_Ois__nat(_1207324))], (48807 ^ _775828) ^ [_1754942, _1754944, _1754946] : [class_Groups_Omonoid__add(_1754942), -(hAPP(c_List_Ofoldl(_1754942, _1754942, c_Groups_Oplus__class_Oplus(_1754942), _1754944), _1754946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1754942), _1754944), c_List_Ofoldr(_1754942, _1754942, c_Groups_Oplus__class_Oplus(_1754942), _1754946, c_Groups_Ozero__class_Ozero(_1754942))))], (29259 ^ _775828) ^ [_1306395, _1306397, _1306399, _1306401, _1306403] : [-(hAPP(c_Set_Oimage(_1306395, _1306397, _1306399), hAPP(hAPP(c_Set_Oinsert(_1306395), _1306401), _1306403)) = hAPP(hAPP(c_Set_Oinsert(_1306397), hAPP(_1306399, _1306401)), hAPP(c_Set_Oimage(_1306395, _1306397, _1306399), _1306403)))], (45440 ^ _775828) ^ [_1671199, _1671201] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1671199, _1671201) = c_Smallcheck_Ofull__small_H(_1671199, hAPP(c_Code__Numeral_Oint__of, _1671201), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1671201))))], (24837 ^ _775828) ^ [_1213052, _1213054, _1213056, _1213058, _1213060, _1213062, _1213064] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1213052, _1213054, _1213056, _1213058), _1213060), _1213062), _1213064) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1213054, _1213056, _1213058), _1213062), hAPP(_1213060, _1213064)))], (6133 ^ _775828) ^ [_873300] : [hAPP(c_Com_Ocom_OBODY, _873300) = c_Com_Ocom_OSKIP], (50031 ^ _775828) ^ [_1780603, _1780605] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1780603), hAPP(c_List_Onth(_1780603), _1780605)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780603)), _1780605))) = _1780605)], (33855 ^ _775828) ^ [_1405028, _1405030, _1405032, _1405034] : [class_Lattices_Osemilattice__inf(_1405028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405028), _1405030), _1405032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405028), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405028), _1405030), _1405034)), _1405032)))], (44299 ^ _775828) ^ [_1644288, _1644290, _1644292, _1644294, _1644296] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644288, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644290, tc_fun(_1644288, tc_HOL_Obool)), _1644292), _1644294)), _1644296) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644290, tc_fun(_1644288, tc_HOL_Obool)), _1644292), hAPP(hAPP(c_COMBC(_1644290, tc_fun(_1644288, tc_HOL_Obool), tc_fun(_1644288, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644288, tc_HOL_Obool), tc_fun(tc_fun(_1644288, tc_HOL_Obool), tc_fun(_1644288, tc_HOL_Obool)), _1644290), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644288, tc_HOL_Obool))), _1644294)), _1644296)))], (5192 ^ _775828) ^ [_855245, _855247] : [_855247 = _855245, -(c_Orderings_Oord__class_Oless(_855247) = c_Orderings_Oord__class_Oless(_855245))], (48655 ^ _775828) ^ [_1751713, _1751715, _1751717] : [-(hAPP(hAPP(c_List_Odrop(_1751713), _1751715), hAPP(c_List_Otl(_1751713), _1751717)) = hAPP(c_List_Otl(_1751713), hAPP(hAPP(c_List_Odrop(_1751713), _1751715), _1751717)))], (27431 ^ _775828) ^ [_1262954, _1262956, _1262958] : [-(hAPP(c_Relation_ORange(_1262954, _1262956), hAPP(c_Set_OCollect(tc_prod(_1262954, _1262956)), hAPP(c_Product__Type_Oprod_Oprod__case(_1262954, _1262956, tc_HOL_Obool), _1262958))) = hAPP(c_Set_OCollect(_1262956), hAPP(hAPP(c_COMBB(tc_fun(_1262954, tc_HOL_Obool), tc_HOL_Obool, _1262956), c_HOL_OEx(_1262954)), hAPP(c_COMBC(_1262954, _1262956, tc_HOL_Obool), _1262958))))], (51362 ^ _775828) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (25275 ^ _775828) ^ [_1221780] : [-(_1221780 = 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)), _1221780)))], (21100 ^ _775828) ^ [_1140985, _1140987, _1140989] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1140985, _1140987), _1140989)), 21103 ^ _775828 : [(21104 ^ _775828) ^ [_1141070] : [hBOOL(hAPP(hAPP(_1140987, _1141070), _1140989)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1140985, _1140987), _1141070)))]]], (29547 ^ _775828) ^ [_1311956, _1311958, _1311960] : [-(_1311958 = _1311960), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1311956, _1311956, hAPP(hAPP(c_COMBB(tc_fun(_1311956, tc_HOL_Obool), tc_fun(_1311956, tc_HOL_Obool), _1311956), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1311956), c_fNot)), c_fequal)), _1311958), _1311960)))], (6260 ^ _775828) ^ [_875520, _875522, _875524, _875526] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_875520, _875522), _875524, _875526, hAPP(hAPP(hAPP(c_Natural_Oupdate, _875524), _875520), hAPP(_875522, _875524))))], (33649 ^ _775828) ^ [_1400415, _1400417] : [class_Lattices_Obounded__lattice__bot(_1400415), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1400415), c_Orderings_Obot__class_Obot(_1400415)), _1400417) = c_Orderings_Obot__class_Obot(_1400415))], (32175 ^ _775828) ^ [_1370546, _1370548, _1370550] : [class_Orderings_Olinorder(_1370546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1370546, tc_HOL_Obool)), _1370548), _1370550)), -(_1370548 = c_Orderings_Obot__class_Obot(tc_fun(_1370546, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370546), _1370550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370546), c_Big__Operators_Olinorder__class_OMax(_1370546, _1370548)), c_Big__Operators_Olinorder__class_OMax(_1370546, _1370550))))], (7679 ^ _775828) ^ [_898454, _898456] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898454), _898456) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_898454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_898456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50937 ^ _775828) ^ [_1801251, _1801253, _1801255, _1801257, _1801259] : [-(c_List_OdropWhile(_1801251, _1801253, _1801255) = hAPP(hAPP(c_List_Olist_OCons(_1801251), _1801257), _1801259)), _1801255 = hAPP(hAPP(c_List_Oappend(_1801251), c_List_OtakeWhile(_1801251, _1801253, _1801255)), hAPP(hAPP(c_List_Olist_OCons(_1801251), _1801257), _1801259)), -(hBOOL(hAPP(_1801253, _1801257)))], (14429 ^ _775828) ^ [_1017523, _1017525] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_1017523, _1017525)], (14043 ^ _775828) ^ [_1010330, _1010332, _1010334] : [hBOOL(hAPP(_1010330, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1010332), _1010334))), 14046 ^ _775828 : [(14071 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010334), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14074 ^ _775828 : [(14075 ^ _775828) ^ [_1010994] : [-(hBOOL(hAPP(_1010330, _1010994))), 14076 ^ _775828 : [(14077 ^ _775828) ^ [_1011068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010334), _1011068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1011068), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1010332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010334), _1010994)), _1011068)]]]]], (14053 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010334)), 14056 ^ _775828 : [(14057 ^ _775828) ^ [_1010664] : [-(hBOOL(hAPP(_1010330, _1010664))), 14058 ^ _775828 : [(14059 ^ _775828) ^ [_1010735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010735), _1010334)), _1010332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010334), _1010664)), _1010735)]]]]], (14047 ^ _775828) ^ [] : [_1010334 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1010330, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20738 ^ _775828) ^ [_1132479, _1132481] : [class_Rings_Oring__1(_1132479), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1132479), hAPP(c_Groups_Ouminus__class_Ouminus(_1132479), c_Groups_Oone__class_Oone(_1132479))), 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)))), _1132481)) = c_Groups_Oone__class_Oone(_1132479))], (37142 ^ _775828) ^ [_1475219, _1475221, _1475223, _1475225, _1475227] : [class_Groups_Ocomm__monoid__add(_1475219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1475221), _1475223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1475223), _1475225)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1475219), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475219), _1475227), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475221), _1475223))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475219), _1475227), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475223), _1475225))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475219), _1475227), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1475221), _1475225)))], (29058 ^ _775828) ^ [_1301807, _1301809, _1301811, _1301813] : [c_Hoare__Mirabelle_Ohoare__derivs(_1301807, _1301809, _1301811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1301807), tc_HOL_Obool)), _1301813), _1301811)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1301807, _1301809, _1301813))], (40119 ^ _775828) ^ [_1545047] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1545047), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1545047)), c_Option_Ooption_ONone(_1545047)), hAPP(c_Set_Oimage(_1545047, tc_Option_Ooption(_1545047), c_Option_Ooption_OSome(_1545047)), c_Orderings_Otop__class_Otop(tc_fun(_1545047, tc_HOL_Obool)))))], (33833 ^ _775828) ^ [_1404569, _1404571, _1404573, _1404575] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404569, tc_HOL_Obool)), _1404571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404569, tc_HOL_Obool)), _1404573), _1404575)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404569, tc_HOL_Obool)), _1404573), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404569, tc_HOL_Obool)), _1404571), _1404575)))], (40185 ^ _775828) ^ [_1546169, _1546171] : [-(c_Sum__Type_OPlus(_1546169, _1546171, c_Orderings_Otop__class_Otop(tc_fun(_1546169, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1546171, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1546169, _1546171), tc_HOL_Obool)))], (18805 ^ _775828) ^ [_1099141, _1099143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099141), 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)), _1099143)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1099141, _1099143) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1099141, _1099143)))], (6821 ^ _775828) ^ [_883870] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _883870))), -(hAPP(c_Com_Obody, _883870) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6824 ^ [_883870]))], (29385 ^ _775828) ^ [_1308735, _1308737, _1308739] : [hBOOL(hAPP(hAPP(c_member(_1308735), _1308737), hAPP(hAPP(c_Set_Oinsert(_1308735), _1308739), c_Orderings_Obot__class_Obot(tc_fun(_1308735, tc_HOL_Obool))))), -(_1308737 = _1308739)], (42906 ^ _775828) ^ [_1611687] : [-(c_Nitpick_Onum(_1611687) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1611687, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1611687)))], (20818 ^ _775828) ^ [_1134082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1134082)), -(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), _1134082), 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)))))))], (27152 ^ _775828) ^ [_1255614, _1255616] : [class_Orderings_Oorder(_1255614), 27159 ^ _775828 : [(27162 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255614), hAPP(_1255616, 27157 ^ [_1255614, _1255616])), hAPP(_1255616, 27158 ^ [_1255614, _1255616])))], (27160 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27157 ^ [_1255614, _1255616]), 27158 ^ [_1255614, _1255616])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1255614, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1255616))], (45801 ^ _775828) ^ [_1679795, _1679797, _1679799] : [-(hAPP(c_Option_Omap(_1679795, _1679797), _1679799) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1679797), _1679795, c_Option_Ooption_ONone(_1679797), hAPP(hAPP(c_COMBB(_1679797, tc_Option_Ooption(_1679797), _1679795), c_Option_Ooption_OSome(_1679797)), _1679799)))], (23268 ^ _775828) ^ [_1181200, _1181202, _1181204] : [class_Fields_Olinordered__field__inverse__zero(_1181200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181200), c_Groups_Ozero__class_Ozero(_1181200)), _1181202)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181200), hAPP(c_Groups_Oabs__class_Oabs(_1181200), _1181204)), _1181202) = hAPP(c_Groups_Oabs__class_Oabs(_1181200), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181200), _1181204), _1181202)))], (42764 ^ _775828) ^ [_1608415, _1608417, _1608419, _1608421, _1608423, _1608425, _1608427, _1608429, _1608431] : [hAPP(c_Fun_Ocomp(_1608415, _1608417, _1608419, _1608421), _1608423) = hAPP(c_Fun_Ocomp(_1608425, _1608417, _1608419, _1608427), _1608429), -(hAPP(_1608421, hAPP(_1608423, _1608431)) = hAPP(_1608427, hAPP(_1608429, _1608431)))], (39537 ^ _775828) ^ [_1530919, _1530921, _1530923, _1530925] : [class_Complete__Lattice_Ocomplete__lattice(_1530919), -(_1530921 = c_Orderings_Obot__class_Obot(tc_fun(_1530923, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530923, _1530919), _1530921), hAPP(c_COMBK(_1530919, _1530923), _1530925)) = _1530925)], (34307 ^ _775828) ^ [_1414845, _1414847, _1414849, _1414851] : [-(hBOOL(hAPP(hAPP(c_member(_1414845), _1414847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414845, tc_HOL_Obool)), _1414849), hAPP(c_Set_OCollect(_1414845), _1414851))))), hBOOL(hAPP(hAPP(c_member(_1414845), _1414847), _1414849)), hBOOL(hAPP(_1414851, _1414847))], (48481 ^ _775828) ^ [_1747881, _1747883, _1747885, _1747887] : [-(hAPP(hAPP(c_List_Odrop(_1747881), _1747883), hAPP(hAPP(c_List_Olist_OCons(_1747881), _1747885), _1747887)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1747881), hAPP(hAPP(c_List_Olist_OCons(_1747881), _1747885), _1747887), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1747881), tc_List_Olist(_1747881)), c_List_Odrop(_1747881)), _1747887), _1747883))], (36583 ^ _775828) ^ [_1463232] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1463232) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1463232))], (43668 ^ _775828) ^ [_1629952, _1629954, _1629956, _1629958, _1629960] : [c_Finite__Set_Ofolding__one__idem(_1629952, _1629954, _1629956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629952), _1629958)), -(hAPP(_1629956, hAPP(hAPP(c_Set_Oinsert(_1629952), _1629960), _1629958)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629952, _1629952, _1629954), _1629960), _1629958))], (45947 ^ _775828) ^ [_1683028, _1683030, _1683032] : [hBOOL(hAPP(c_List_Odistinct(_1683028), _1683030)), -(hAPP(c_List_Oset(_1683028), c_List_Oremove1(_1683028, _1683032, _1683030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1683028, tc_HOL_Obool)), hAPP(c_List_Oset(_1683028), _1683030)), hAPP(hAPP(c_Set_Oinsert(_1683028), _1683032), c_Orderings_Obot__class_Obot(tc_fun(_1683028, tc_HOL_Obool)))))], (2380 ^ _775828) ^ [_810715, _810717, _810719, _810721, _810723, _810725] : [-(c_Nitpick_Oplus__frac(_810725, _810721, _810717) = c_Nitpick_Oplus__frac(_810723, _810719, _810715)), _810725 = _810723, _810721 = _810719, _810717 = _810715], (18739 ^ _775828) ^ [_1097902, _1097904] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1097902, _1097904) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1097902, _1097904)))], (41879 ^ _775828) ^ [_1587405, _1587407] : [-(hAPP(c_Set_Oimage(_1587405, _1587405, c_Fun_Oid(_1587405)), _1587407) = _1587407)], (49285 ^ _775828) ^ [_1765368, _1765370] : [-(_1765368 = c_List_Olist_ONil(_1765370)), hBOOL(hAPP(c_List_Odistinct(_1765370), _1765368)), -(hBOOL(hAPP(c_List_Odistinct(_1765370), c_List_Obutlast(_1765370, _1765368))))], (47859 ^ _775828) ^ [_1731852, _1731854, _1731856] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731852)), hAPP(hAPP(c_List_Oappend(_1731852), _1731854), _1731856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731852)), _1731854)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731852)), _1731856)))], (43904 ^ _775828) ^ [_1634314, _1634316, _1634318] : [class_Orderings_Olinorder(_1634314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634314), _1634316)), -(hBOOL(hAPP(hAPP(c_member(_1634314), _1634318), _1634316))), -(c_Big__Operators_Olattice_OInf__fin(_1634314, c_Orderings_Oord__class_Omin(_1634314), hAPP(hAPP(c_Set_Oinsert(_1634314), _1634318), _1634316)) = hAPP(hAPP(c_Finite__Set_Ofold(_1634314, _1634314, c_Orderings_Oord__class_Omin(_1634314)), _1634318), _1634316))], (5851 ^ _775828) ^ [_869021, _869023] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _869021), _869023)), -(_869023 = _869021)], (37480 ^ _775828) ^ [_1483817, _1483819, _1483821, _1483823] : [class_Groups_Ocomm__monoid__add(_1483817), 37483 ^ _775828 : [(37490 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1483819)), _1483821))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483817), _1483823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483821, hAPP(c_Nat_OSuc, _1483819))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483817), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483817), _1483823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483821, _1483819))), hAPP(_1483823, hAPP(c_Nat_OSuc, _1483819))))], (37484 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1483819)), _1483821)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483817), _1483823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483821, hAPP(c_Nat_OSuc, _1483819))) = c_Groups_Ozero__class_Ozero(_1483817))]]], (12643 ^ _775828) ^ [_984465] : [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)), _984465)), _984465)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984465), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51136 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (8170 ^ _775828) ^ [_907144, _907146] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907144), _907146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907146), _907144)))], (50247 ^ _775828) ^ [_1785597, _1785599] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785597)), c_List_Oconcat(_1785597, _1785599)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785597), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1785597))), _1785599)))], (1420 ^ _775828) ^ [_796196, _796198] : [-(class_Groups_Oordered__comm__monoid__add(_796196)), _796198 = _796196, class_Groups_Oordered__comm__monoid__add(_796198)], (50970 ^ _775828) ^ [_1802093, _1802095] : [class_Orderings_Olinorder(_1802093), 50977 ^ _775828 : [(50982 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1802093), hAPP(hAPP(c_List_Onth(_1802093), _1802095), 50975 ^ [_1802093, _1802095])), hAPP(hAPP(c_List_Onth(_1802093), _1802095), 50976 ^ [_1802093, _1802095])))], (50980 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50976 ^ [_1802093, _1802095]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802093)), _1802095))))], (50978 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50975 ^ [_1802093, _1802095]), 50976 ^ [_1802093, _1802095])))]], -(c_List_Olinorder__class_Osorted(_1802093, _1802095))], (10882 ^ _775828) ^ [_953931, _953933, _953935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953933), _953935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953931), _953933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953931), _953935))))], (47241 ^ _775828) ^ [_1718180, _1718182, _1718184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718180), tc_List_Olist(_1718180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718180), tc_List_Olist(_1718180)), _1718182), c_List_Olist_ONil(_1718180))), c_List_Olistrel(_1718180, _1718184))), -(_1718182 = c_List_Olist_ONil(_1718180))], (810 ^ _775828) ^ [_788221, _788223, _788225, _788227, _788229, _788231, _788233, _788235] : [-(c_List_Olistrelp(_788233, _788229, _788225, _788221)), c_List_Olistrelp(_788235, _788231, _788227, _788223), _788235 = _788233, _788231 = _788229, _788227 = _788225, _788223 = _788221], (14964 ^ _775828) ^ [_1026739, _1026741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026739)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026741)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1026739), hAPP(c_Int_Onat, _1026741)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1026739, _1026741)))], (17075 ^ _775828) ^ [_1067388, _1067390, _1067392] : [class_Int_Onumber__ring(_1067388), -(hAPP(c_Int_Onumber__class_Onumber__of(_1067388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067390), _1067392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067388), hAPP(c_Int_Onumber__class_Onumber__of(_1067388), _1067390)), hAPP(c_Int_Onumber__class_Onumber__of(_1067388), _1067392)))], (51432 ^ _775828) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17099 ^ _775828) ^ [_1067924, _1067926, _1067928] : [class_Int_Onumber__ring(_1067924), -(hAPP(c_Int_Onumber__class_Onumber__of(_1067924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067926), _1067928)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067924), hAPP(c_Int_Onumber__class_Onumber__of(_1067924), _1067926)), hAPP(c_Int_Onumber__class_Onumber__of(_1067924), _1067928)))], (46877 ^ _775828) ^ [_1708304, _1708306, _1708308, _1708310, _1708312, _1708314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708304), tc_List_Olist(_1708304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708304), tc_List_Olist(_1708304)), hAPP(hAPP(c_List_Olist_OCons(_1708304), _1708306), _1708308)), hAPP(hAPP(c_List_Olist_OCons(_1708304), _1708310), _1708312))), c_List_Olexord(_1708304, _1708314))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708304, _1708304)), hAPP(hAPP(c_Product__Type_OPair(_1708304, _1708304), _1708306), _1708310)), _1708314))), 46884 ^ _775828 : [(46887 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708304), tc_List_Olist(_1708304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708304), tc_List_Olist(_1708304)), _1708308), _1708312)), c_List_Olexord(_1708304, _1708314))))], (46885 ^ _775828) ^ [] : [-(_1708306 = _1708310)]]], (50766 ^ _775828) ^ [_1797836, _1797838] : [class_Orderings_Olinorder(_1797836), c_List_Olinorder__class_Osorted(_1797836, _1797838), -(c_List_Olinorder__class_Osorted(_1797836, c_List_Oremdups(_1797836, _1797838)))], (27789 ^ _775828) ^ [_1270873, _1270875, _1270877, _1270879] : [hBOOL(hAPP(hAPP(c_member(_1270873), _1270875), hAPP(c_Relation_ODomain(_1270873, _1270877), _1270879))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1270873, _1270877)), hAPP(hAPP(c_Product__Type_OPair(_1270873, _1270877), _1270875), 27792 ^ [_1270873, _1270875, _1270877, _1270879])), _1270879)))], (27350 ^ _775828) ^ [_1260715, _1260717, _1260719, _1260721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260715, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260715, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1260717, _1260715), _1260719)), hAPP(c_Relation_ORange(_1260717, _1260715), _1260721))), hAPP(c_Relation_ORange(_1260717, _1260715), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1260717, _1260715), tc_HOL_Obool)), _1260719), _1260721)))))], (51084 ^ _775828) ^ [_1804060, _1804062] : [class_Orderings_Oorder(_1804060), -(class_Orderings_Oorder(tc_fun(_1804062, _1804060)))], (47780 ^ _775828) ^ [_1730000, _1730002, _1730004, _1730006, _1730008] : [hAPP(hAPP(c_List_Oappend(_1730000), _1730002), _1730004) = hAPP(hAPP(c_List_Olist_OCons(_1730000), _1730006), _1730008), 47785 ^ _775828 : [(47788 ^ _775828) ^ [] : [-(_1730004 = hAPP(hAPP(c_List_Olist_OCons(_1730000), _1730006), _1730008))], (47786 ^ _775828) ^ [] : [-(_1730002 = c_List_Olist_ONil(_1730000))]], 47790 ^ _775828 : [(47793 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1730000), 47789 ^ [_1730000, _1730002, _1730004, _1730006, _1730008]), _1730004) = _1730008)], (47791 ^ _775828) ^ [] : [-(_1730002 = hAPP(hAPP(c_List_Olist_OCons(_1730000), _1730006), 47789 ^ [_1730000, _1730002, _1730004, _1730006, _1730008]))]]], (5991 ^ _775828) ^ [_871117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871117), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (800 ^ _775828) ^ [_788096, _788098] : [-(c_Nat__Transfer_Onat__set(_788096)), _788098 = _788096, c_Nat__Transfer_Onat__set(_788098)], (4572 ^ _775828) ^ [_845649, _845651] : [_845651 = _845649, -(c_Option_Ooption_OSome(_845651) = c_Option_Ooption_OSome(_845649))], (47954 ^ _775828) ^ [_1734182, _1734184, _1734186] : [_1734182 = _1734184, -(_1734182 = hAPP(hAPP(c_List_Oappend(_1734186), c_List_Olist_ONil(_1734186)), _1734184))], (396 ^ _775828) ^ [_781648, _781650] : [-(c_Nat__Transfer_Ois__nat(_781648)), _781650 = _781648, c_Nat__Transfer_Ois__nat(_781650)], (4060 ^ _775828) ^ [_837785, _837787, _837789, _837791, _837793, _837795, _837797, _837799] : [-(c_Product__Type_Oscomp(_837799, _837795, _837791, _837787) = c_Product__Type_Oscomp(_837797, _837793, _837789, _837785)), _837799 = _837797, _837795 = _837793, _837791 = _837789, _837787 = _837785], (4780 ^ _775828) ^ [_848853, _848855, _848857, _848859, _848861, _848863] : [-(c_Product__Type_Oprod_Oprod__case(_848863, _848859, _848855) = c_Product__Type_Oprod_Oprod__case(_848861, _848857, _848853)), _848863 = _848861, _848859 = _848857, _848855 = _848853], (15732 ^ _775828) ^ [_1041051, _1041053, _1041055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041051), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041053), _1041055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041051), _1041055)), _1041053)))], (31871 ^ _775828) ^ [_1364136, _1364138] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1364136, _1364138)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1364138), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1364136), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21346 ^ _775828) ^ [_1145441, _1145443, _1145445] : [class_Rings_Odivision__ring(_1145441), -(_1145443 = c_Groups_Ozero__class_Ozero(_1145441)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1145441), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145441), _1145445), _1145443)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145441), _1145445), hAPP(c_Groups_Ouminus__class_Ouminus(_1145441), _1145443)))], (45604 ^ _775828) ^ [_1675025, _1675027, _1675029] : [c_Fun_Oinj__on(_1675025, _1675027, _1675029, c_Orderings_Otop__class_Otop(tc_fun(_1675025, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1675025), tc_List_Olist(_1675027), hAPP(c_List_Omap(_1675025, _1675027), _1675029), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1675025), tc_HOL_Obool))))], (14914 ^ _775828) ^ [_1025790, _1025792, _1025794] : [hBOOL(hAPP(_1025790, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025792, _1025794))), 14917 ^ _775828 : [(14924 ^ _775828) ^ [] : [-(_1025794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14927 ^ _775828 : [(14928 ^ _775828) ^ [_1026038, _1026040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026038), _1025794)), _1025792 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025794), _1026040)), _1026038), -(hBOOL(hAPP(_1025790, _1026038)))]]], (14918 ^ _775828) ^ [] : [_1025794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1025790, _1025792)))]]], (29439 ^ _775828) ^ [_1309807, _1309809, _1309811, _1309813, _1309815] : [hBOOL(hAPP(hAPP(_1309807, _1309809), _1309811)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1309813, _1309815, _1309807), _1309811), _1309809)))], (49987 ^ _775828) ^ [_1779789, _1779791, _1779793, _1779795] : [c_List_Oupt(_1779789, _1779791) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1779793), _1779795), 49990 ^ _775828 : [(49995 ^ _775828) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1779789), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1779791) = _1779795)], (49993 ^ _775828) ^ [] : [-(_1779789 = _1779793)], (49991 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1779789), _1779791)))]]], (12167 ^ _775828) ^ [_976322, _976324, _976326] : [class_Lattices_Oboolean__algebra(_976322), 12170 ^ _775828 : [(12177 ^ _775828) ^ [] : [_976324 = _976326, -(hAPP(c_Groups_Ouminus__class_Ouminus(_976322), _976324) = hAPP(c_Groups_Ouminus__class_Ouminus(_976322), _976326))], (12171 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_976322), _976324) = hAPP(c_Groups_Ouminus__class_Ouminus(_976322), _976326), -(_976324 = _976326)]]], (13753 ^ _775828) ^ [_1004912, _1004914] : [13754 ^ _775828 : [(13755 ^ _775828) ^ [_1004961] : [_1004912 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1004914), _1004961)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004912, _1004914) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15034 ^ _775828) ^ [_1027935, _1027937, _1027939] : [hBOOL(hAPP(_1027935, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027937), _1027939))), 15039 ^ _775828 : [(15042 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1027935, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15040 ^ _775828) ^ [] : [-(_1027939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15044 ^ _775828 : [(15049 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1027935, 15043 ^ [_1027935, _1027937, _1027939])))], (15047 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027939), hAPP(c_Nat_OSuc, 15043 ^ [_1027935, _1027937, _1027939])))))], (15045 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027939), 15043 ^ [_1027935, _1027937, _1027939])), _1027937)))]]], (39464 ^ _775828) ^ [_1529235, _1529237, _1529239, _1529241, _1529243, _1529245] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529235, tc_fun(_1529237, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529239, tc_fun(_1529235, tc_HOL_Obool)), _1529241), _1529243)), _1529245) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529239, tc_fun(_1529237, tc_HOL_Obool)), _1529241), hAPP(hAPP(c_COMBC(_1529239, tc_fun(_1529235, tc_fun(_1529237, tc_HOL_Obool)), tc_fun(_1529237, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529235, tc_HOL_Obool), tc_fun(tc_fun(_1529235, tc_fun(_1529237, tc_HOL_Obool)), tc_fun(_1529237, tc_HOL_Obool)), _1529239), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529235, tc_fun(_1529237, tc_HOL_Obool))), _1529243)), _1529245)))], (28457 ^ _775828) ^ [_1286987, _1286989, _1286991] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286987, tc_HOL_Obool)), _1286989), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286987, tc_HOL_Obool)), _1286989), _1286991))))], (27928 ^ _775828) ^ [] : [-(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)))))], (20774 ^ _775828) ^ [_1133112, _1133114, _1133116] : [class_Int_Onumber__ring(_1133112), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1133112), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1133112), _1133114), _1133116)), 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(_1133112), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133112), hAPP(hAPP(c_Power_Opower__class_Opower(_1133112), _1133114), 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(_1133112), _1133116), 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(_1133112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133112), hAPP(c_Int_Onumber__class_Onumber__of(_1133112), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1133114)), _1133116)))], (48761 ^ _775828) ^ [_1753887, _1753889, _1753891, _1753893, _1753895, _1753897] : [-(hAPP(c_List_Ofoldl(_1753887, _1753889, _1753891, _1753893), hAPP(hAPP(c_List_Oappend(_1753889), _1753895), _1753897)) = hAPP(c_List_Ofoldl(_1753887, _1753889, _1753891, hAPP(c_List_Ofoldl(_1753887, _1753889, _1753891, _1753893), _1753895)), _1753897))], (13700 ^ _775828) ^ [_1003995, _1003997, _1003999, _1004001] : [class_Divides_Osemiring__div(_1003995), -(c_Divides_Odiv__class_Omod(_1003995, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003995), _1003997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003995), _1003999), _1004001)), _1004001) = c_Divides_Odiv__class_Omod(_1003995, _1003997, _1004001))], (15848 ^ _775828) ^ [_1043214, _1043216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043214), _1043216)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043216), _1043214)) = _1043216)], (5076 ^ _775828) ^ [_853503, _853505] : [_853505 = _853503, -(c_List_Oreturn__list(_853505) = c_List_Oreturn__list(_853503))], (15860 ^ _775828) ^ [_1043466, _1043468, _1043470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043466), _1043468)), _1043470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043470), _1043468))))], (10536 ^ _775828) ^ [_947295, _947297, _947299, _947301] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947295), _947297), _947299)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947295), _947297), _947301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947295), _947299), _947301)))], (20430 ^ _775828) ^ [_1126928] : [class_Rings_Osemiring__1(_1126928), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126928), c_Groups_Ozero__class_Ozero(_1126928)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1126928))], (33755 ^ _775828) ^ [_1402836, _1402838, _1402840] : [class_Lattices_Olattice(_1402836), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402836), _1402838), _1402840) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402836), _1402840), _1402838))], (4020 ^ _775828) ^ [_837165, _837167] : [_837167 = _837165, -(c_Groups_Ouminus__class_Ouminus(_837167) = c_Groups_Ouminus__class_Ouminus(_837165))], (50355 ^ _775828) ^ [_1787931, _1787933] : [-(hAPP(c_List_Orev(_1787931), c_List_Oconcat(_1787931, _1787933)) = c_List_Oconcat(_1787931, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1787931), tc_List_Olist(_1787931)), c_List_Orev(_1787931)), hAPP(c_List_Orev(tc_List_Olist(_1787931)), _1787933))))], (49899 ^ _775828) ^ [_1778264, _1778266, _1778268] : [class_Orderings_Olinorder(_1778264), c_List_Olinorder__class_Osorted(_1778264, _1778266), -(c_List_Olinorder__class_Osorted(_1778264, c_List_Olinorder__class_Oinsort__insert__key(_1778264, _1778264, c_COMBI(_1778264), _1778268, _1778266)))], (47445 ^ _775828) ^ [_1722231] : [class_Groups_Omonoid__add(_1722231), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722231), c_List_Olist_ONil(_1722231)) = c_Groups_Ozero__class_Ozero(_1722231))], (36807 ^ _775828) ^ [_1467278, _1467280, _1467282] : [class_Orderings_Oorder(_1467278), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467278, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1467278), _1467280)), c_SetInterval_Oord__class_OatLeastAtMost(_1467278, _1467280, _1467282)) = c_Orderings_Obot__class_Obot(tc_fun(_1467278, tc_HOL_Obool)))], (35359 ^ _775828) ^ [_1439341, _1439343, _1439345] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1439341, tc_HOL_Obool)), _1439343), hAPP(c_Set_OPow(_1439341), _1439345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439341, tc_HOL_Obool)), _1439343), _1439345)))], (5680 ^ _775828) ^ [_866208, _866210, _866212, _866214] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _866208), _866210, _866212, _866214), 5684 ^ _775828 : [(5687 ^ _775828) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _866208)), _866210, 5683 ^ [_866208, _866210, _866212, _866214], _866214))], (5685 ^ _775828) ^ [] : [-(_866212 = hAPP(c_Nat_OSuc, 5683 ^ [_866208, _866210, _866212, _866214]))]]], (51626 ^ _775828) ^ [_1809728] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1809728), v_Procs)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, v_na, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(_1809728)), hAPP(c_Com_Ocom_OBODY, _1809728)), v_Q(_1809728))))], (21472 ^ _775828) ^ [_1147617, _1147619, _1147621, _1147623] : [class_Fields_Ofield__inverse__zero(_1147617), class_Int_Onumber(_1147617), 21479 ^ _775828 : [(21480 ^ _775828) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147617), _1147619), _1147621) = hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623), 21483 ^ _775828 : [(21490 ^ _775828) ^ [] : [_1147621 = c_Groups_Ozero__class_Ozero(_1147617), -(hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623) = c_Groups_Ozero__class_Ozero(_1147617))], (21484 ^ _775828) ^ [] : [-(_1147621 = c_Groups_Ozero__class_Ozero(_1147617)), -(_1147619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147617), hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623)), _1147621))]]], (21496 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147617), _1147619), _1147621) = hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623)), 21499 ^ _775828 : [(21502 ^ _775828) ^ [] : [_1147619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147617), hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623)), _1147621)], (21500 ^ _775828) ^ [] : [_1147621 = c_Groups_Ozero__class_Ozero(_1147617)]], 21503 ^ _775828 : [(21506 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147617), _1147623) = c_Groups_Ozero__class_Ozero(_1147617)], (21504 ^ _775828) ^ [] : [-(_1147621 = c_Groups_Ozero__class_Ozero(_1147617))]]]]], (9943 ^ _775828) ^ [_936442, _936444] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_936442)), hAPP(c_Option_Ooption_OSome(_936442), _936444)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46770 ^ _775828) ^ [_1706117, _1706119, _1706121, _1706123, _1706125] : [class_Groups_Ocomm__monoid__add(_1706117), hBOOL(hAPP(hAPP(c_member(_1706119), _1706121), hAPP(c_List_Oset(_1706119), _1706123))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1706117), hAPP(hAPP(c_List_Omap(_1706119, _1706117), _1706125), _1706123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706117), hAPP(_1706125, _1706121)), hAPP(c_List_Omonoid__add__class_Olistsum(_1706117), hAPP(hAPP(c_List_Omap(_1706119, _1706117), _1706125), c_List_Oremove1(_1706119, _1706121, _1706123)))))], (51148 ^ _775828) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (29225 ^ _775828) ^ [_1305737, _1305739, _1305741, _1305743] : [c_Orderings_Obot__class_Obot(tc_fun(_1305737, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1305739, _1305737, _1305741), _1305743), -(_1305743 = c_Orderings_Obot__class_Obot(tc_fun(_1305739, tc_HOL_Obool)))], (48749 ^ _775828) ^ [_1753667, _1753669] : [class_Lattices_Oab__semigroup__idem__mult(_1753667), -(_1753669 = c_List_Olist_ONil(_1753667)), -(hAPP(c_Finite__Set_Ofold1(_1753667, c_Groups_Otimes__class_Otimes(_1753667)), hAPP(c_List_Oset(_1753667), _1753669)) 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959869), _959873), c_Groups_Ozero__class_Ozero(_959869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959869), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959869), _959871), _959873)), c_Groups_Ozero__class_Ozero(_959869))))], (4342 ^ _775828) ^ [_842150, _842152] : [_842152 = _842150, -(c_Orderings_Oord__class_Omin(_842152) = c_Orderings_Oord__class_Omin(_842150))], (41268 ^ _775828) ^ [_1572555, _1572557, _1572559] : [-(hAPP(c_Finite__Set_Ofold1(_1572555, _1572557), hAPP(hAPP(c_Set_Oinsert(_1572555), _1572559), c_Orderings_Obot__class_Obot(tc_fun(_1572555, tc_HOL_Obool)))) = _1572559)], (25755 ^ _775828) ^ [_1231077, _1231079] : [_1231077 = _1231079, 25758 ^ _775828 : [(25761 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231079), _1231077)))], (25759 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231077), _1231079)))]]], (40955 ^ _775828) ^ [_1564321, _1564323, _1564325, _1564327] : [-(hAPP(c_Set_Ovimage(_1564321, _1564323, _1564325), _1564327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1564323, tc_fun(_1564321, tc_HOL_Obool)), _1564327), hAPP(hAPP(c_COMBB(tc_fun(_1564323, tc_HOL_Obool), tc_fun(_1564321, tc_HOL_Obool), _1564323), c_Set_Ovimage(_1564321, _1564323, _1564325)), hAPP(hAPP(c_COMBC(_1564323, tc_fun(_1564323, tc_HOL_Obool), tc_fun(_1564323, tc_HOL_Obool)), c_Set_Oinsert(_1564323)), c_Orderings_Obot__class_Obot(tc_fun(_1564323, tc_HOL_Obool))))))], (34829 ^ _775828) ^ [_1425701, _1425703, _1425705] : [class_Orderings_Olinorder(_1425701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425701), _1425703)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425701), _1425705)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425701, tc_HOL_Obool)), _1425703), _1425705) = c_Orderings_Obot__class_Obot(tc_fun(_1425701, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1425701), c_Big__Operators_Olattice_OInf__fin(_1425701, 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c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7834 ^ _775828 : [(7837 ^ _775828) ^ [] : [-(_900949 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7835 ^ _775828) ^ [] : [-(_900947 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (13162 ^ _775828) ^ [_993500, _993502] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_993500, _993502))), 13165 ^ _775828 : [(13168 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _993502)))], (13166 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _993500)))]]], (39854 ^ _775828) ^ [_1539099, _1539101, _1539103, _1539105, _1539107, _1539109] : [c_Equiv__Relations_Ocongruent(_1539099, _1539101, _1539103, _1539105), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539099, _1539099)), hAPP(hAPP(c_Product__Type_OPair(_1539099, _1539099), _1539107), _1539109)), _1539103)), -(hAPP(_1539105, _1539107) = hAPP(_1539105, _1539109))], (48002 ^ _775828) ^ [_1735037, _1735039, _1735041] : [_1735037 = hAPP(hAPP(c_List_Oappend(_1735039), _1735041), _1735037), -(_1735041 = c_List_Olist_ONil(_1735039))], (48243 ^ _775828) ^ [_1741583, _1741585, _1741587, _1741589] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741583), tc_List_Olist(_1741583))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741583), tc_List_Olist(_1741583)), _1741585), _1741587)), c_List_Olistrel1(_1741583, _1741589))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741583), tc_List_Olist(_1741583))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741583), tc_List_Olist(_1741583)), _1741585), _1741587)), c_List_Olistrel(_1741583, c_Transitive__Closure_Ortrancl(_1741583, _1741589)))))], (40792 ^ _775828) ^ [_1560247, _1560249, _1560251, _1560253, _1560255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1560247, tc_HOL_Obool)), _1560249), _1560251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1560253, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1560253, _1560247, _1560255), _1560249)), hAPP(c_Set_Ovimage(_1560253, _1560247, _1560255), _1560251))))], (13605 ^ _775828) ^ [_1002002, _1002004, _1002006, _1002008, _1002010, _1002012] : [c_Com_Ocom_OCall(_1002002, _1002004, _1002006) = c_Com_Ocom_OLocal(_1002008, _1002010, _1002012)], (35061 ^ _775828) ^ [_1432368, _1432370, _1432372, _1432374, _1432376] : [class_Groups_Ocomm__monoid__mult(_1432368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432370), _1432372)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432370), _1432374)), 35075 ^ _775828 : [(35078 ^ _775828) ^ [] : [hAPP(_1432376, 35074 ^ [_1432368, _1432370, _1432372, _1432374, _1432376]) = c_Groups_Oone__class_Oone(_1432368)], (35076 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432370), 35074 ^ [_1432368, _1432370, _1432372, _1432374, _1432376]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432370, tc_HOL_Obool)), _1432372), _1432374))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432370, _1432368), _1432376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432370, tc_HOL_Obool)), _1432372), _1432374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432368), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432370, _1432368), _1432376), _1432372)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432370, _1432368), _1432376), _1432374)))], (16619 ^ _775828) ^ [_1058598, _1058600, _1058602, _1058604] : [hBOOL(hAPP(hAPP(c_member(_1058598), _1058600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058598, tc_HOL_Obool)), _1058602), _1058604))), hBOOL(hAPP(hAPP(c_member(_1058598), _1058600), _1058604))], (19648 ^ _775828) ^ [_1113423] : [-(c_Int_OBit1(_1113423) = 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)), _1113423)), _1113423))], (33585 ^ _775828) ^ [_1399135, _1399137, _1399139, _1399141] : [hBOOL(hAPP(hAPP(c_member(_1399135), _1399137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399135, tc_HOL_Obool)), _1399139), _1399141))), 33588 ^ _775828 : [(33591 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399135), _1399137), _1399141)))], (33589 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399135), _1399137), _1399139)))]]], (48090 ^ _775828) ^ [_1736849, _1736851, _1736853, _1736855, _1736857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736849), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736851)), _1736853))), -(hAPP(hAPP(c_List_Olist__update(_1736851, hAPP(hAPP(c_List_Oappend(_1736851), _1736853), _1736855)), _1736849), _1736857) = hAPP(hAPP(c_List_Oappend(_1736851), hAPP(hAPP(c_List_Olist__update(_1736851, _1736853), _1736849), _1736857)), _1736855))], (31911 ^ _775828) ^ [_1365799, _1365801] : [class_Lattices_Olattice(_1365799), -(c_Big__Operators_Olattice__class_OInf__fin(_1365799, hAPP(hAPP(c_Set_Oinsert(_1365799), _1365801), c_Orderings_Obot__class_Obot(tc_fun(_1365799, tc_HOL_Obool)))) = _1365801)], (51340 ^ _775828) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (35569 ^ _775828) ^ [_1443803, _1443805, _1443807, _1443809] : [class_Orderings_Oorder(_1443803), 35572 ^ _775828 : [(35581 ^ _775828) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1443803, _1443805, _1443807) = hAPP(hAPP(c_Set_Oinsert(_1443803), _1443809), c_Orderings_Obot__class_Obot(tc_fun(_1443803, tc_HOL_Obool)))), _1443805 = _1443807, _1443807 = _1443809], (35573 ^ _775828) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1443803, _1443805, _1443807) = hAPP(hAPP(c_Set_Oinsert(_1443803), _1443809), c_Orderings_Obot__class_Obot(tc_fun(_1443803, tc_HOL_Obool))), 35576 ^ _775828 : [(35579 ^ _775828) ^ [] : [-(_1443807 = _1443809)], (35577 ^ _775828) ^ [] : [-(_1443805 = _1443807)]]]]], (51546 ^ _775828) ^ [_1808741] : [-(hBOOL(_1808741)), -(hBOOL(hAPP(c_fNot, _1808741)))], (42428 ^ _775828) ^ [_1599913] : [-(c_Relation_Osingle__valued(_1599913, _1599913, c_Relation_OId(_1599913)))], (47553 ^ _775828) ^ [_1724371, _1724373, _1724375, _1724377] : [_1724371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1724373), _1724371), hAPP(hAPP(c_List_Olist_OCons(_1724373), _1724375), _1724377)) = c_List_Olist_ONil(_1724373))], (43932 ^ _775828) ^ [_1634863, _1634865, _1634867, _1634869, _1634871, _1634873] : [c_Finite__Set_Ofun__left__comm(_1634863, _1634865, _1634867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634863), _1634869)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1634863, _1634865, _1634867), _1634871), hAPP(hAPP(c_Set_Oinsert(_1634863), _1634873), _1634869)) = hAPP(hAPP(_1634867, _1634873), hAPP(hAPP(c_Finite__Set_Ofold(_1634863, _1634865, _1634867), _1634871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634863, tc_HOL_Obool)), _1634869), hAPP(hAPP(c_Set_Oinsert(_1634863), _1634873), c_Orderings_Obot__class_Obot(tc_fun(_1634863, tc_HOL_Obool)))))))], (40590 ^ _775828) ^ [] : [-(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))], (4004 ^ _775828) ^ [_836931, _836933, _836935, _836937] : [-(c_List_Olexn(_836937, _836933) = c_List_Olexn(_836935, _836931)), _836937 = _836935, _836933 = _836931], (45401 ^ _775828) ^ [_1670052, _1670054, _1670056, _1670058] : [c_Fun_Oinj__on(_1670052, tc_Option_Ooption(_1670054), _1670058, c_Map_Odom(_1670052, _1670054, _1670058)), -(c_Fun_Oinj__on(_1670052, tc_Option_Ooption(_1670054), c_Map_Omap__add(_1670052, _1670054, _1670056, _1670058), c_Map_Odom(_1670052, _1670054, _1670058)))], (5648 ^ _775828) ^ [_865644, _865646, _865648, _865650] : [_865644 = _865646, 5651 ^ _775828 : [(5658 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_865648), _865650), _865646)), -(hBOOL(hAPP(hAPP(c_member(_865648), _865650), _865644)))], (5652 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_865648), _865650), _865644)), -(hBOOL(hAPP(hAPP(c_member(_865648), _865650), _865646)))]]], (21026 ^ _775828) ^ [_1137478, _1137480] : [class_Fields_Olinordered__field__inverse__zero(_1137478), class_Int_Onumber__ring(_1137478), 21033 ^ _775828 : [(21040 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137478), c_Groups_Ozero__class_Ozero(_1137478)), _1137480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137478), c_Groups_Ozero__class_Ozero(_1137478)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137478), _1137480), hAPP(c_Int_Onumber__class_Onumber__of(_1137478), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21034 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137478), c_Groups_Ozero__class_Ozero(_1137478)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137478), _1137480), hAPP(c_Int_Onumber__class_Onumber__of(_1137478), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137478), c_Groups_Ozero__class_Ozero(_1137478)), _1137480)))]]], (35991 ^ _775828) ^ [_1451761, _1451763, _1451765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451761)), 35994 ^ _775828 : [(35995 ^ _775828) ^ [_1451895] : [35997 ^ _775828 : [(36003 ^ _775828) ^ [] : [-(_1451895 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35999 ^ [_1451761, _1451763, _1451765, _1451895]), 35996 ^ [_1451761, _1451763, _1451765, _1451895]))], (36001 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35999 ^ [_1451761, _1451763, _1451765, _1451895]), _1451763)))], (35998 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35996 ^ [_1451761, _1451763, _1451765, _1451895]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451761))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451765), _1451895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451895), _1451761))))]]], (43451 ^ _775828) ^ [_1625327, _1625329, _1625331, _1625333, _1625335, _1625337] : [class_Rings_Ocomm__semiring__1(_1625327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625329), _1625331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625329, tc_HOL_Obool)), _1625333), _1625331)), 43465 ^ _775828 : [(43468 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1625327), hAPP(_1625335, 43464 ^ [_1625327, _1625329, _1625331, _1625333, _1625335, _1625337])), hAPP(_1625337, 43464 ^ [_1625327, _1625329, _1625331, _1625333, _1625335, _1625337])))], (43466 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625329), 43464 ^ [_1625327, _1625329, _1625331, _1625333, _1625335, _1625337]), _1625333)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1625327), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1625329, _1625327), _1625335), _1625333)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1625329, _1625327), _1625337), _1625331))))], (40772 ^ _775828) ^ [_1559804, _1559806, _1559808, _1559810, _1559812] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1559804, _1559806, _1559808), _1559810), _1559812)), -(hBOOL(hAPP(_1559810, hAPP(_1559808, _1559812))))], (14824 ^ _775828) ^ [_1023855, _1023857, _1023859] : [-(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), _1023855), _1023857)), _1023859)), _1023857) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1023859), _1023857))], (24224 ^ _775828) ^ [_1200317, _1200319, _1200321, _1200323] : [class_Orderings_Olinorder(_1200317), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200317), _1200319), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200317), _1200321), _1200323)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200317), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200317), _1200319), _1200321)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200317), _1200319), _1200323)))], (36204 ^ _775828) ^ [_1455680, _1455682] : [36206 ^ _775828 : [(36209 ^ _775828) ^ [] : [hBOOL(hAPP(_1455682, 36205 ^ [_1455680, _1455682]))], (36207 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36205 ^ [_1455680, _1455682]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1455680))))]], 36210 ^ _775828 : [(36211 ^ _775828) ^ [_1455833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1455833), _1455680)), -(hBOOL(hAPP(_1455682, _1455833)))]]], (29618 ^ _775828) ^ [_1313426, _1313428] : [c_Orderings_Obot__class_Obot(tc_fun(_1313426, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1313426), _1313428), 29621 ^ _775828 : [(29622 ^ _775828) ^ [_1313511] : [hBOOL(hAPP(_1313428, _1313511))]]], (11516 ^ _775828) ^ [_965160, _965162, _965164] : [class_Groups_Ogroup__add(_965160), 11519 ^ _775828 : [(11526 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965160), _965162), _965164) = c_Groups_Ozero__class_Ozero(_965160), -(_965162 = hAPP(c_Groups_Ouminus__class_Ouminus(_965160), _965164))], (11520 ^ _775828) ^ [] : [_965162 = hAPP(c_Groups_Ouminus__class_Ouminus(_965160), _965164), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965160), _965162), _965164) = c_Groups_Ozero__class_Ozero(_965160))]]], (23314 ^ _775828) ^ [_1182119, _1182121, _1182123, _1182125] : [class_Fields_Olinordered__field(_1182119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182119), _1182121), c_Groups_Ozero__class_Ozero(_1182119))), 23321 ^ _775828 : [(23328 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182119), _1182125), _1182121)), _1182123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182119), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182119), _1182123), _1182121)), _1182125)))], (23322 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182119), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182119), _1182123), _1182121)), _1182125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182119), _1182125), _1182121)), _1182123)))]]], (36341 ^ _775828) ^ [_1458122, _1458124, _1458126] : [-(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)), _1458122)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458124), _1458126)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458124), _1458122)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458126), _1458122)))], (51506 ^ _775828) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (33459 ^ _775828) ^ [_1396522, _1396524, _1396526] : [class_Orderings_Olinorder(_1396522), hAPP(_1396524, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1396522), 33464 ^ [_1396522, _1396524, _1396526]), 33465 ^ [_1396522, _1396524, _1396526])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1396522), hAPP(_1396524, 33464 ^ [_1396522, _1396524, _1396526])), hAPP(_1396524, 33465 ^ [_1396522, _1396524, _1396526])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396522), _1396526)), -(_1396526 = c_Orderings_Obot__class_Obot(tc_fun(_1396522, tc_HOL_Obool))), -(hAPP(_1396524, c_Big__Operators_Olinorder__class_OMax(_1396522, _1396526)) = c_Big__Operators_Olinorder__class_OMax(_1396522, hAPP(c_Set_Oimage(_1396522, _1396522, _1396524), _1396526)))], (42684 ^ _775828) ^ [_1606581, _1606583, _1606585, _1606587] : [c_Finite__Set_Ofun__left__comm__idem(_1606581, _1606583, _1606585), -(hAPP(c_Fun_Ocomp(_1606583, _1606583, _1606583, hAPP(_1606585, _1606587)), hAPP(_1606585, _1606587)) = hAPP(_1606585, _1606587))], (29567 ^ _775828) ^ [_1312316, _1312318] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312316, tc_HOL_Obool)), _1312318), c_Orderings_Obot__class_Obot(tc_fun(_1312316, tc_HOL_Obool))) = _1312318)], (24985 ^ _775828) ^ [_1216066, _1216068, _1216070, _1216072, _1216074, _1216076] : [hBOOL(hAPP(hAPP(c_member(_1216066), _1216068), _1216070)), _1216072 = hAPP(_1216074, _1216068), -(hBOOL(hAPP(hAPP(c_member(_1216076), _1216072), hAPP(c_Set_Oimage(_1216066, _1216076, _1216074), _1216070))))], (2790 ^ _775828) ^ [_817430, _817432, _817434, _817436, _817438, _817440, _817442, _817444, _817446, _817448, _817450, _817452, _817454, _817456] : [-(c_New__Random__Sequence_Oneg__decr__bind(_817456, _817452, _817448, _817444, _817440, _817436, _817432) = c_New__Random__Sequence_Oneg__decr__bind(_817454, _817450, _817446, _817442, _817438, _817434, _817430)), _817456 = _817454, _817452 = _817450, _817448 = _817446, _817444 = _817442, _817440 = _817438, _817436 = _817434, _817432 = _817430], (38446 ^ _775828) ^ [_1506368, _1506370, _1506372, _1506374, _1506376] : [-(c_Map_Odom(_1506368, _1506370, hAPP(hAPP(c_COMBS(_1506368, tc_Option_Ooption(_1506370), tc_Option_Ooption(_1506370)), hAPP(hAPP(c_COMBS(_1506368, tc_Option_Ooption(_1506370), tc_fun(tc_Option_Ooption(_1506370), tc_Option_Ooption(_1506370))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1506370), tc_fun(tc_Option_Ooption(_1506370), tc_Option_Ooption(_1506370))), _1506368), c_If(tc_Option_Ooption(_1506370))), _1506372)), _1506374)), _1506376)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506368, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506368, tc_HOL_Obool)), c_Map_Odom(_1506368, _1506370, _1506374)), hAPP(c_Set_OCollect(_1506368), _1506372))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506368, tc_HOL_Obool)), c_Map_Odom(_1506368, _1506370, _1506376)), hAPP(c_Set_OCollect(_1506368), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506368), c_fNot), _1506372)))))], (30075 ^ _775828) ^ [_1323979, _1323981] : [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)))), _1323979, _1323981) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323979), _1323981)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323981), _1323979)))], (24002 ^ _775828) ^ [_1196116, _1196118, _1196120, _1196122] : [class_Orderings_Olinorder(_1196116), 24005 ^ _775828 : [(24006 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196116), _1196120), _1196122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), _1196120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), _1196122)))], (24016 ^ _775828) ^ [] : [24017 ^ _775828 : [(24020 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), _1196122))], (24018 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), _1196120))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196118), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196116), _1196120), _1196122))))]]], (928 ^ _775828) ^ [_789984, _789986, _789988, _789990, _789992, _789994] : [-(c_Finite__Set_Ofun__left__comm(_789992, _789988, _789984)), c_Finite__Set_Ofun__left__comm(_789994, _789990, _789986), _789994 = _789992, _789990 = _789988, _789986 = _789984], (26693 ^ _775828) ^ [_1247634, _1247636, _1247638] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247634), _1247636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247634), _1247638))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247634)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247636), _1247638)))], (23036 ^ _775828) ^ [_1176809, _1176811, _1176813, _1176815] : [class_Fields_Olinordered__field(_1176809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176809), c_Groups_Ozero__class_Ozero(_1176809)), _1176811)), 23043 ^ _775828 : [(23050 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176809), _1176813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176809), _1176815), _1176811))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176809), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176809), _1176813), _1176811)), _1176815)))], (23044 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176809), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176809), _1176813), _1176811)), _1176815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176809), _1176813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176809), _1176815), _1176811))))]]], (50860 ^ _775828) ^ [_1799799, _1799801, _1799803] : [-(hAPP(hAPP(c_List_Oappend(_1799799), c_List_OtakeWhile(_1799799, _1799801, _1799803)), c_List_OdropWhile(_1799799, _1799801, _1799803)) = _1799803)], (24983 ^ _775828) ^ [_1216002, _1216004, _1216006, _1216008, _1216010, _1216012] : [-(hAPP(c_Set_Oimage(_1216002, _1216004, _1216006), hAPP(c_Set_Oimage(_1216008, _1216002, _1216010), _1216012)) = hAPP(c_Set_Oimage(_1216008, _1216004, hAPP(hAPP(c_COMBB(_1216002, _1216004, _1216008), _1216006), _1216010)), _1216012))], (45682 ^ _775828) ^ [_1677014] : [-(hAPP(c_Option_Omap(_1677014, _1677014), c_Fun_Oid(_1677014)) = c_Fun_Oid(tc_Option_Ooption(_1677014)))], (12841 ^ _775828) ^ [_987701, _987703, _987705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987701)), _987701 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987701), _987705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _987705), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (47140 ^ _775828) ^ [_1715385, _1715387, _1715389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715385), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715387)), _1715389))), -(hAPP(c_Random_Opick(_1715387, hAPP(hAPP(c_List_Omap(_1715387, tc_prod(tc_Code__Numeral_Ocode__numeral, _1715387)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1715387), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1715389)), hAPP(c_Code__Numeral_Oof__nat, _1715385)) = hAPP(hAPP(c_List_Onth(_1715387), _1715389), _1715385))], (29527 ^ _775828) ^ [_1311481, _1311483, _1311485, _1311487] : [-(hAPP(hAPP(c_Set_Oinsert(_1311481), _1311483), hAPP(hAPP(c_Set_Oinsert(_1311481), _1311485), _1311487)) = hAPP(hAPP(c_Set_Oinsert(_1311481), _1311485), hAPP(hAPP(c_Set_Oinsert(_1311481), _1311483), _1311487)))], (28854 ^ _775828) ^ [_1294933, _1294935, _1294937, _1294939, _1294941, _1294943] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294933, tc_fun(_1294935, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1294933, tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_fun(_1294935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1294935, tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_fun(_1294935, tc_HOL_Obool)), _1294933), c_COMBC(_1294935, tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1294935, tc_prod(_1294933, _1294935)), tc_fun(_1294935, tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), _1294933), hAPP(c_COMBB(tc_prod(_1294933, _1294935), tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool), _1294935), c_member(tc_prod(_1294933, _1294935)))), c_Product__Type_OPair(_1294933, _1294935)))), _1294937)), hAPP(hAPP(c_COMBC(_1294933, tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_fun(_1294935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1294935, tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_fun(_1294935, tc_HOL_Obool)), _1294933), c_COMBC(_1294935, tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1294935, tc_prod(_1294933, _1294935)), tc_fun(_1294935, tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool)), _1294933), hAPP(c_COMBB(tc_prod(_1294933, _1294935), tc_fun(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool), tc_HOL_Obool), _1294935), c_member(tc_prod(_1294933, _1294935)))), c_Product__Type_OPair(_1294933, _1294935)))), _1294939)), _1294941), _1294943)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1294933, _1294935)), hAPP(hAPP(c_Product__Type_OPair(_1294933, _1294935), _1294941), _1294943)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1294933, _1294935), tc_HOL_Obool)), _1294937), _1294939))))], (51336 ^ _775828) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (45434 ^ _775828) ^ [_1670840, _1670842, _1670844] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1670840)), hAPP(c_Set_Oimage(_1670842, tc_Option_Ooption(_1670840), c_Map_Omap__of(_1670842, _1670840, _1670844)), c_Orderings_Otop__class_Otop(tc_fun(_1670842, tc_HOL_Obool))))))], (34235 ^ _775828) ^ [_1412938, _1412940, _1412942, _1412944] : [-(hBOOL(hAPP(hAPP(c_member(_1412938), _1412940), _1412942))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412938, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1412938), _1412940), _1412944)), _1412942) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412938, tc_HOL_Obool)), _1412944), _1412942))], (38912 ^ _775828) ^ [_1516638, _1516640, _1516642, _1516644, _1516646] : [c_Fun_Oinj__on(_1516638, _1516640, _1516642, _1516644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516638, tc_HOL_Obool)), _1516646), _1516644)), -(c_Fun_Oinj__on(_1516638, _1516640, _1516642, _1516646))], (17177 ^ _775828) ^ [_1069469, _1069471, _1069473] : [class_Rings_Olinordered__idom(_1069469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069469), c_Groups_Ozero__class_Ozero(_1069469)), _1069471)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069469), hAPP(c_Groups_Oabs__class_Oabs(_1069469), _1069473)), _1069471) = hAPP(c_Groups_Oabs__class_Oabs(_1069469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069469), _1069473), _1069471)))], (42154 ^ _775828) ^ [_1594376, _1594378] : [-(c_Relation_Orefl__on(_1594376, _1594378, c_Relation_OId__on(_1594376, _1594378)))], (29134 ^ _775828) ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1303624, _1303626)), _1303628), hAPP(hAPP(c_Relation_Orel__comp(_1303624, _1303630, _1303626), _1303632), _1303634))), 29140 ^ _775828 : [(29145 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303630, _1303626)), hAPP(hAPP(c_Product__Type_OPair(_1303630, _1303626), 29138 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634]), 29139 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634])), _1303634)))], (29143 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303624, _1303630)), hAPP(hAPP(c_Product__Type_OPair(_1303624, _1303630), 29137 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634]), 29138 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634])), _1303632)))], (29141 ^ _775828) ^ [] : [-(_1303628 = hAPP(hAPP(c_Product__Type_OPair(_1303624, _1303626), 29137 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634]), 29139 ^ [_1303624, _1303626, _1303628, _1303630, _1303632, _1303634]))]]], (18257 ^ _775828) ^ [_1089455, _1089457, _1089459, _1089461, _1089463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1089455, _1089457)), hAPP(_1089455, _1089459))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1089461, _1089461)), hAPP(hAPP(c_Product__Type_OPair(_1089461, _1089461), _1089457), _1089459)), _1089463)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1089461, _1089461)), hAPP(hAPP(c_Product__Type_OPair(_1089461, _1089461), _1089457), _1089459)), c_Wellfounded_Omlex__prod(_1089461, _1089455, _1089463))))], (16859 ^ _775828) ^ [_1063189, _1063191, _1063193] : [class_Groups_Oordered__ab__group__add__abs(_1063189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063189), hAPP(c_Groups_Oabs__class_Oabs(_1063189), _1063191)), _1063193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063189), hAPP(c_Groups_Ouminus__class_Ouminus(_1063189), _1063191)), _1063193)))], (20498 ^ _775828) ^ [_1128060] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1128060)), 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, _1128060, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44401 ^ _775828) ^ [_1647288, _1647290, _1647292, _1647294] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1647288, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647290, tc_fun(_1647288, tc_HOL_Obool)), _1647292), _1647294)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1647290, tc_fun(_1647288, tc_HOL_Obool)), _1647292), hAPP(hAPP(c_COMBB(tc_fun(_1647288, tc_HOL_Obool), tc_fun(_1647288, tc_HOL_Obool), _1647290), c_Groups_Ouminus__class_Ouminus(tc_fun(_1647288, tc_HOL_Obool))), _1647294)))], (42605 ^ _775828) ^ [_1604709, _1604711] : [42607 ^ _775828 : [(42610 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1604711), 42606 ^ [_1604709, _1604711]))], (42608 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42606 ^ [_1604709, _1604711]), _1604709)))]], -(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)), _1604711), _1604709))], (28108 ^ _775828) ^ [_1279537, _1279539] : [c_Wellfounded_Owf(_1279537, _1279539), -(c_Wellfounded_OwfP(_1279537, c_FunDef_Oin__rel(_1279537, _1279537, _1279539)))], (48026 ^ _775828) ^ [_1735447, _1735449] : [-(hAPP(hAPP(c_List_Oappend(_1735447), _1735449), c_List_Olist_ONil(_1735447)) = _1735449)], (34485 ^ _775828) ^ [_1418705, _1418707, _1418709] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1418705), _1418707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418705), _1418709)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1418705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418705, tc_HOL_Obool)), _1418707), _1418709))), hAPP(c_Finite__Set_Ocard(_1418705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418705, tc_HOL_Obool)), _1418707), _1418709))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1418705), _1418707)), hAPP(c_Finite__Set_Ocard(_1418705), _1418709)))], (4646 ^ _775828) ^ [_846812, _846814, _846816, _846818, _846820, _846822] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_846822, _846818, _846814) = c_SetInterval_Oord__class_OatLeastAtMost(_846820, _846816, _846812)), _846822 = _846820, _846818 = _846816, _846814 = _846812], (40167 ^ _775828) ^ [_1545845, _1545847] : [class_Lattices_Obounded__lattice__top(_1545845), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1545845), _1545847), c_Orderings_Otop__class_Otop(_1545845)) = c_Orderings_Otop__class_Otop(_1545845))], (45692 ^ _775828) ^ [_1677291, _1677293, _1677295, _1677297, _1677299] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1677291), tc_Option_Ooption(_1677293), _1677295, hAPP(c_Option_Omap(_1677291, _1677293), _1677297)), hAPP(c_COMBK(tc_Option_Ooption(_1677291), _1677295), c_Option_Ooption_ONone(_1677291))), _1677299) = c_Option_Ooption_ONone(_1677293))], (47873 ^ _775828) ^ [_1732297, _1732299, _1732301, _1732303, _1732305, _1732307] : [-(c_List_Ofoldr(_1732297, _1732299, _1732301, hAPP(hAPP(c_List_Oappend(_1732297), _1732303), _1732305), _1732307) = c_List_Ofoldr(_1732297, _1732299, _1732301, _1732303, c_List_Ofoldr(_1732297, _1732299, _1732301, _1732305, _1732307)))], (28635 ^ _775828) ^ [_1290129, _1290131, _1290133, _1290135, _1290137] : [-(hAPP(c_Set_Oimage(_1290129, _1290131, _1290133), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290129, tc_HOL_Obool)), _1290135), _1290137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290131, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1290129, _1290131, _1290133), _1290135)), hAPP(c_Set_Oimage(_1290129, _1290131, _1290133), _1290137)))], (18169 ^ _775828) ^ [_1087786] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087786))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087786)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (44135 ^ _775828) ^ [_1639053, _1639055, _1639057, _1639059, _1639061] : [hBOOL(hAPP(hAPP(c_member(_1639053), _1639055), _1639057)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639059, tc_HOL_Obool)), hAPP(_1639061, _1639055)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639053, tc_fun(_1639059, tc_HOL_Obool)), _1639057), _1639061)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639053, tc_fun(_1639059, tc_HOL_Obool)), _1639057), _1639061))], (46169 ^ _775828) ^ [_1688688, _1688690] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1688688), hAPP(c_List_Oset(_1688688), _1688690))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688688)), _1688690))))], (50990 ^ _775828) ^ [_1802647, _1802649, _1802651] : [hBOOL(hAPP(c_List_Odistinct(_1802647), _1802649)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1802647)), c_Enum_On__lists(_1802647, _1802651, _1802649))))], (14089 ^ _775828) ^ [_1011290, _1011292, _1011294] : [-(hBOOL(hAPP(_1011290, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011292), _1011294)))), 14092 ^ _775828 : [(14095 ^ _775828) ^ [] : [hBOOL(hAPP(_1011290, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14093 ^ _775828) ^ [] : [-(_1011294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14098 ^ _775828 : [(14099 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011294)))], (14105 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14101 ^ [_1011290, _1011292, _1011294]), _1011294)))], (14109 ^ _775828) ^ [] : [hBOOL(hAPP(_1011290, 14100 ^ [_1011290, _1011292, _1011294]))], (14107 ^ _775828) ^ [] : [-(_1011292 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011294), 14100 ^ [_1011290, _1011292, _1011294])), 14101 ^ [_1011290, _1011292, _1011294]))], (14103 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14101 ^ [_1011290, _1011292, _1011294])))]], 14110 ^ _775828 : [(14111 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14117 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14113 ^ [_1011290, _1011292, _1011294]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14121 ^ _775828) ^ [] : [hBOOL(hAPP(_1011290, 14112 ^ [_1011290, _1011292, _1011294]))], (14119 ^ _775828) ^ [] : [-(_1011292 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011294), 14112 ^ [_1011290, _1011292, _1011294])), 14113 ^ [_1011290, _1011292, _1011294]))], (14115 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011294), 14113 ^ [_1011290, _1011292, _1011294])))]]], (41490 ^ _775828) ^ [_1578719, _1578721, _1578723, _1578725] : [-(_1578719 = c_Orderings_Obot__class_Obot(tc_fun(_1578721, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1578721, _1578723), _1578723, c_Product__Type_Osnd(_1578721, _1578723)), hAPP(hAPP(c_Product__Type_OSigma(_1578721, _1578723), _1578719), hAPP(c_COMBK(tc_fun(_1578723, tc_HOL_Obool), _1578721), _1578725))) = _1578725)], (43968 ^ _775828) ^ [_1635627] : [class_Groups_Oab__semigroup__mult(_1635627), -(c_Finite__Set_Ofun__left__comm(_1635627, _1635627, c_Groups_Otimes__class_Otimes(_1635627)))], (23124 ^ _775828) ^ [_1178490, _1178492, _1178494, _1178496] : [class_Fields_Olinordered__field(_1178490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178490), _1178492), _1178494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178490), c_Groups_Ozero__class_Ozero(_1178490)), _1178496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178490), c_Groups_Ozero__class_Ozero(_1178490)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178490), _1178494), _1178492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178490), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178490), _1178496), _1178494)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178490), _1178496), _1178492))))], (21022 ^ _775828) ^ [] : [-(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)))], (33881 ^ _775828) ^ [_1405495, _1405497, _1405499] : [class_Lattices_Olattice(_1405495), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1405495), _1405497), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405495), _1405497), _1405499)) = _1405497)], (8313 ^ _775828) ^ [_909361, _909363, _909365, _909367] : [class_Orderings_Oord(_909361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909361), _909363), _909365)), _909365 = _909367, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909361), _909363), _909367)))], (47279 ^ _775828) ^ [_1718871, _1718873, _1718875] : [47280 ^ _775828 : [(47283 ^ _775828) ^ [] : [_1718875 = c_List_Olist_ONil(_1718871)], (47281 ^ _775828) ^ [] : [_1718873 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1718871), _1718873), _1718875) = c_List_Olist_ONil(_1718871))], (44399 ^ _775828) ^ [_1647206, _1647208, _1647210, _1647212] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1647206, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1647208, tc_fun(_1647206, tc_HOL_Obool)), _1647210), _1647212)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647208, tc_fun(_1647206, tc_HOL_Obool)), _1647210), hAPP(hAPP(c_COMBB(tc_fun(_1647206, tc_HOL_Obool), tc_fun(_1647206, tc_HOL_Obool), _1647208), c_Groups_Ouminus__class_Ouminus(tc_fun(_1647206, tc_HOL_Obool))), _1647212)))], (18051 ^ _775828) ^ [_1085269, _1085271, _1085273, _1085275] : [class_Rings_Olinordered__semidom(_1085269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085271), _1085273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085269), c_Groups_Oone__class_Oone(_1085269)), _1085275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085269), hAPP(hAPP(c_Power_Opower__class_Opower(_1085269), _1085275), _1085271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085269), _1085275), _1085273))))], (32753 ^ _775828) ^ [_1381404, _1381406, _1381408, _1381410] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1381404, _1381406)), c_Sum__Type_OPlus(_1381404, _1381406, _1381408, _1381410))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1381404), _1381408)))], (17031 ^ _775828) ^ [_1066503, _1066505] : [class_Rings_Ocomm__semiring__1(_1066503), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1066503), _1066505), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1066503))], (44509 ^ _775828) ^ [_1650216, _1650218, _1650220, _1650222, _1650224, _1650226] : [c_Relation_Osingle__valued(_1650216, _1650218, hAPP(c_Relation_Oconverse(_1650218, _1650216), _1650220)), -(_1650222 = c_Orderings_Obot__class_Obot(tc_fun(_1650224, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1650218, _1650216, _1650220), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650224, tc_fun(_1650218, tc_HOL_Obool)), _1650222), _1650226)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650224, tc_fun(_1650216, tc_HOL_Obool)), _1650222), hAPP(hAPP(c_COMBB(tc_fun(_1650218, tc_HOL_Obool), tc_fun(_1650216, tc_HOL_Obool), _1650224), c_Relation_OImage(_1650218, _1650216, _1650220)), _1650226)))], (6063 ^ _775828) ^ [_872137, _872139] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872137), _872139))), 6066 ^ _775828 : [(6073 ^ _775828) ^ [] : [_872137 = _872139, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872137), hAPP(c_Nat_OSuc, _872139))))], (6067 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872137), hAPP(c_Nat_OSuc, _872139))), -(_872137 = _872139)]]], (47493 ^ _775828) ^ [_1723128, _1723130, _1723132, _1723134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723128), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723130)), _1723132))), 47496 ^ _775828 : [(47503 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Onth(_1723130), _1723132), _1723128) = _1723134, -(hAPP(hAPP(c_List_Olist__update(_1723130, _1723132), _1723128), _1723134) = _1723132)], (47497 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1723130, _1723132), _1723128), _1723134) = _1723132, -(hAPP(hAPP(c_List_Onth(_1723130), _1723132), _1723128) = _1723134)]]], (31551 ^ _775828) ^ [_1356266, _1356268, _1356270, _1356272] : [-(c_Transitive__Closure_Otrancl(_1356266, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1356266, _1356266)), hAPP(hAPP(c_Product__Type_OPair(_1356266, _1356266), _1356268), _1356270)), _1356272)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1356266, _1356266), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1356266, _1356272)), hAPP(c_Set_OCollect(tc_prod(_1356266, _1356266)), hAPP(c_Product__Type_Oprod_Oprod__case(_1356266, _1356266, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1356266, tc_fun(_1356266, tc_HOL_Obool), tc_fun(_1356266, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1356266, tc_HOL_Obool), tc_fun(_1356266, tc_HOL_Obool)), _1356266), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1356266)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1356266), c_fconj), hAPP(hAPP(c_COMBC(_1356266, tc_fun(tc_prod(_1356266, _1356266), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1356266, _1356266), tc_fun(tc_fun(tc_prod(_1356266, _1356266), tc_HOL_Obool), tc_HOL_Obool), _1356266), c_member(tc_prod(_1356266, _1356266))), hAPP(hAPP(c_COMBC(_1356266, _1356266, tc_prod(_1356266, _1356266)), c_Product__Type_OPair(_1356266, _1356266)), _1356268))), c_Transitive__Closure_Ortrancl(_1356266, _1356272))))), hAPP(hAPP(c_COMBC(_1356266, tc_fun(tc_prod(_1356266, _1356266), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1356266, _1356266), tc_fun(tc_fun(tc_prod(_1356266, _1356266), tc_HOL_Obool), tc_HOL_Obool), _1356266), c_member(tc_prod(_1356266, _1356266))), hAPP(c_Product__Type_OPair(_1356266, _1356266), _1356270))), c_Transitive__Closure_Ortrancl(_1356266, _1356272)))))))], (29018 ^ _775828) ^ [_1300959, _1300961, _1300963, _1300965, _1300967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1300959, _1300959)), hAPP(hAPP(c_Product__Type_OPair(_1300959, _1300959), _1300961), _1300963)), c_Transitive__Closure_Otrancl(_1300959, _1300965))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1300959, _1300959)), hAPP(hAPP(c_Product__Type_OPair(_1300959, _1300959), _1300963), _1300967)), _1300965)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1300959, _1300959)), hAPP(hAPP(c_Product__Type_OPair(_1300959, _1300959), _1300961), _1300967)), c_Transitive__Closure_Otrancl(_1300959, _1300965))))], (33499 ^ _775828) ^ [_1397328, _1397330, _1397332] : [class_Lattices_Olattice(_1397328), hAPP(_1397330, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1397328), 33504 ^ [_1397328, _1397330, _1397332]), 33505 ^ [_1397328, _1397330, _1397332])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1397328), hAPP(_1397330, 33504 ^ [_1397328, _1397330, _1397332])), hAPP(_1397330, 33505 ^ [_1397328, _1397330, _1397332])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397328), _1397332)), -(_1397332 = c_Orderings_Obot__class_Obot(tc_fun(_1397328, tc_HOL_Obool))), -(hAPP(_1397330, c_Big__Operators_Olattice__class_OSup__fin(_1397328, _1397332)) = c_Big__Operators_Olattice__class_OSup__fin(_1397328, hAPP(c_Set_Oimage(_1397328, _1397328, _1397330), _1397332)))], (19368 ^ _775828) ^ [_1108774, _1108776] : [class_Int_Onumber__ring(_1108774), class_Rings_Olinordered__idom(_1108774), 19375 ^ _775828 : [(19382 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1108776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108774), c_Groups_Ozero__class_Ozero(_1108774)), hAPP(c_Int_Onumber__class_Onumber__of(_1108774), _1108776))))], (19376 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108774), c_Groups_Ozero__class_Ozero(_1108774)), hAPP(c_Int_Onumber__class_Onumber__of(_1108774), _1108776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1108776)))]]], (48641 ^ _775828) ^ [_1751525, _1751527] : [-(_1751525 = c_List_Olist_ONil(_1751527)), -(hAPP(c_List_Orotate1(_1751527), _1751525) = hAPP(hAPP(c_List_Oappend(_1751527), hAPP(c_List_Otl(_1751527), _1751525)), hAPP(hAPP(c_List_Olist_OCons(_1751527), hAPP(c_List_Ohd(_1751527), _1751525)), c_List_Olist_ONil(_1751527))))], (2908 ^ _775828) ^ [_819457, _819459, _819461, _819463, _819465, _819467, _819469, _819471] : [-(c_Nitpick_Oprod(_819471, _819467, _819463, _819459) = c_Nitpick_Oprod(_819469, _819465, _819461, _819457)), _819471 = _819469, _819467 = _819465, _819463 = _819461, _819459 = _819457], (24282 ^ _775828) ^ [_1201736] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1201736) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28227 ^ _775828) ^ [_1281944, _1281946, _1281948] : [class_Lattices_Osemilattice__sup(_1281944), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281944), _1281946), _1281948) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281944), _1281948), _1281946))], (49909 ^ _775828) ^ [_1778411, _1778413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778411), _1778413)), -(c_List_Oupt(_1778411, _1778413) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1778411), c_List_Oupt(hAPP(c_Nat_OSuc, _1778411), _1778413)))], (33388 ^ _775828) ^ [_1394772, _1394774, _1394776, _1394778, _1394780, _1394782] : [hBOOL(hAPP(hAPP(c_member(_1394772), _1394774), _1394776)), -(c_Map_Orestrict__map(_1394772, _1394778, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394772, tc_Option_Ooption(_1394778)), _1394780), _1394774), _1394782), _1394776) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394772, tc_Option_Ooption(_1394778)), c_Map_Orestrict__map(_1394772, _1394778, _1394780, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394772, tc_HOL_Obool)), _1394776), hAPP(hAPP(c_Set_Oinsert(_1394772), _1394774), c_Orderings_Obot__class_Obot(tc_fun(_1394772, tc_HOL_Obool)))))), _1394774), _1394782))], (45407 ^ _775828) ^ [_1670177, _1670179, _1670181, _1670183] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670177, tc_HOL_Obool)), c_Map_Odom(_1670177, _1670179, _1670181)), c_Map_Odom(_1670177, _1670179, _1670183)) = c_Orderings_Obot__class_Obot(tc_fun(_1670177, tc_HOL_Obool)), -(c_Map_Omap__add(_1670177, _1670179, _1670181, _1670183) = c_Map_Omap__add(_1670177, _1670179, _1670183, _1670181))], (33843 ^ _775828) ^ [_1404826, _1404828, _1404830, _1404832] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404826, tc_HOL_Obool)), _1404828), _1404830), _1404832)), -(hBOOL(hAPP(_1404830, _1404832)))], (27274 ^ _775828) ^ [_1258866, _1258868, _1258870, _1258872, _1258874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1258866, _1258868)), hAPP(hAPP(c_Product__Type_OPair(_1258866, _1258868), _1258870), _1258872)), hAPP(c_Relation_Oconverse(_1258868, _1258866), _1258874))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1258868, _1258866)), hAPP(hAPP(c_Product__Type_OPair(_1258868, _1258866), _1258872), _1258870)), _1258874)))], (24869 ^ _775828) ^ [_1213732, _1213734, _1213736] : [c_Nitpick_Oless__frac(_1213732, _1213734, _1213736), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1213732), c_Nitpick_Oplus__frac(_1213732, _1213734, c_Nitpick_Ouminus__frac(_1213732, _1213736)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12429 ^ _775828) ^ [_980889] : [class_Groups_Osgn__if(_980889), -(c_Groups_Osgn__class_Osgn(_980889, c_Groups_Ozero__class_Ozero(_980889)) = c_Groups_Ozero__class_Ozero(_980889))], (20714 ^ _775828) ^ [_1131825, _1131827, _1131829] : [class_Int_Onumber__ring(_1131825), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1131825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131825), _1131827), _1131829)), 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(_1131825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131825), hAPP(hAPP(c_Power_Opower__class_Opower(_1131825), _1131827), 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(_1131825), _1131829), 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(_1131825), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131825), hAPP(c_Int_Onumber__class_Onumber__of(_1131825), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1131827)), _1131829)))], (46404 ^ _775828) ^ [_1695673, _1695675, _1695677, _1695679, _1695681] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695673), tc_List_Olist(_1695673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695673), tc_List_Olist(_1695673)), _1695675), _1695677)), c_List_Olistrel(_1695673, c_Transitive__Closure_Ortrancl(_1695673, _1695679)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695673), tc_List_Olist(_1695673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695673), tc_List_Olist(_1695673)), _1695677), _1695681)), c_List_Olistrel(_1695673, c_Transitive__Closure_Ortrancl(_1695673, _1695679)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695673), tc_List_Olist(_1695673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695673), tc_List_Olist(_1695673)), _1695675), _1695681)), c_List_Olistrel(_1695673, c_Transitive__Closure_Ortrancl(_1695673, _1695679)))))], (8196 ^ _775828) ^ [_907502, _907504, _907506, _907508] : [class_Orderings_Oord(_907502), 8199 ^ _775828 : [(8206 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907502), hAPP(_907506, 8207 ^ [_907502, _907504, _907506, _907508])), hAPP(_907508, 8207 ^ [_907502, _907504, _907506, _907508]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907504, _907502)), _907506), _907508)))], (8200 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907504, _907502)), _907506), _907508)), 8203 ^ _775828 : [(8204 ^ _775828) ^ [_907659] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907502), hAPP(_907506, _907659)), hAPP(_907508, _907659))))]]]]], (19068 ^ _775828) ^ [_1104327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104327), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104327)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1104327)))], (5664 ^ _775828) ^ [_865923, _865925, _865927] : [hBOOL(hAPP(hAPP(c_member(_865923), _865925), _865927)), -(hBOOL(hAPP(_865927, _865925)))], (31391 ^ _775828) ^ [_1352595, _1352597, _1352599] : [class_Orderings_Olinorder(_1352595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352595), _1352597)), -(hBOOL(hAPP(hAPP(c_member(_1352595), _1352599), _1352597))), -(_1352597 = 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c_Orderings_Obot__class_Obot(tc_fun(_1655121, tc_HOL_Obool)), 44702 ^ _775828 : [(44703 ^ _775828) ^ [_1655256] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1655121, tc_HOL_Obool)), _1655256), _1655123)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655121, tc_HOL_Obool)), _1655256), _1655125) = c_Orderings_Obot__class_Obot(tc_fun(_1655121, tc_HOL_Obool)))]]], (19216 ^ _775828) ^ [_1106344, _1106346] : [class_Int_Onumber__ring(_1106344), 19219 ^ _775828 : [(19226 ^ _775828) ^ [] : [c_Int_Oiszero(_1106344, hAPP(c_Int_Onumber__class_Onumber__of(_1106344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106346), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1106344), _1106346) = c_Groups_Ozero__class_Ozero(_1106344))], (19220 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1106344), _1106346) = c_Groups_Ozero__class_Ozero(_1106344), -(c_Int_Oiszero(_1106344, hAPP(c_Int_Onumber__class_Onumber__of(_1106344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106346), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (15720 ^ _775828) ^ [_1040837, _1040839] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040837), _1040839) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040837), _1040839)))], (47523 ^ _775828) ^ [_1723842, _1723844, _1723846, _1723848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723842), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723844)), _1723846))), -(hBOOL(hAPP(hAPP(c_member(_1723844), _1723848), hAPP(c_List_Oset(_1723844), hAPP(hAPP(c_List_Olist__update(_1723844, _1723846), _1723842), _1723848)))))], (23084 ^ _775828) ^ [_1177728, _1177730, _1177732, _1177734] : [class_Fields_Olinordered__field(_1177728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177728), _1177730), c_Groups_Ozero__class_Ozero(_1177728))), 23091 ^ _775828 : [(23098 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177728), _1177734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177728), _1177732), _1177730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177728), _1177732), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177728), _1177734), _1177730))))], (23092 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177728), _1177732), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177728), _1177734), _1177730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177728), _1177734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177728), _1177732), _1177730))))]]], (6777 ^ _775828) ^ [_883152, _883154, _883156, _883158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_883152, tc_HOL_Obool)), _883154), _883156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_883152, tc_HOL_Obool)), _883156), _883158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_883152, tc_HOL_Obool)), _883154), _883158)))], (46033 ^ _775828) ^ [_1685055, _1685057, _1685059, _1685061] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685055, _1685055)), hAPP(hAPP(c_Product__Type_OPair(_1685055, _1685055), _1685057), _1685059)), hAPP(c_List_Oset(tc_prod(_1685055, _1685055)), hAPP(hAPP(c_List_Ozip(_1685055, _1685055), _1685061), _1685061)))), 46036 ^ _775828 : [(46039 ^ _775828) ^ [] : [-(_1685057 = _1685059)], (46037 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685055), _1685057), hAPP(c_List_Oset(_1685055), _1685061))))]]], (48553 ^ _775828) ^ [_1749752, _1749754, _1749756, _1749758] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1749752) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1749754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1749752)), hAPP(hAPP(c_List_Olist_OCons(_1749754), _1749756), _1749758)) = hAPP(hAPP(c_List_Olist_OCons(_1749754), _1749756), _1749758))], (41276 ^ _775828) ^ [_1572720, _1572722, _1572724, _1572726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572720), _1572722)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572724), _1572726)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572720, _1572724)), hAPP(hAPP(c_Product__Type_OSigma(_1572720, _1572724), _1572722), hAPP(c_COMBK(tc_fun(_1572724, tc_HOL_Obool), _1572720), _1572726)))))], (33540 ^ _775828) ^ [_1398182, _1398184, _1398186, _1398188, _1398190] : [class_Groups_Ocomm__monoid__mult(_1398182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398184), _1398186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398184, tc_HOL_Obool)), _1398188), _1398186)), 33554 ^ _775828 : [(33557 ^ _775828) ^ [] : [hAPP(_1398190, 33553 ^ [_1398182, _1398184, _1398186, _1398188, _1398190]) = c_Groups_Oone__class_Oone(_1398182)], (33555 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398184), 33553 ^ [_1398182, _1398184, _1398186, _1398188, _1398190]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398184, tc_HOL_Obool)), _1398186), _1398188))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398184, _1398182), _1398190), _1398186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398184, _1398182), _1398190), _1398188))], (39249 ^ _775828) ^ [_1523811] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1523811))], (41304 ^ _775828) ^ [_1573364, _1573366, _1573368, _1573370] : [41305 ^ _775828 : [(41308 ^ _775828) ^ [] : [_1573370 = c_Orderings_Obot__class_Obot(tc_fun(_1573366, tc_HOL_Obool))], (41306 ^ _775828) ^ [] : [_1573368 = c_Orderings_Obot__class_Obot(tc_fun(_1573364, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1573364, _1573366), _1573368), hAPP(c_COMBK(tc_fun(_1573366, tc_HOL_Obool), _1573364), _1573370)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1573364, _1573366), tc_HOL_Obool)))], (48936 ^ _775828) ^ [_1757931, _1757933, _1757935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1757931, 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hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503385), _1503389)) = c_Orderings_Obot__class_Obot(tc_fun(_1503385, tc_HOL_Obool)))], (5975 ^ _775828) ^ [_870923, _870925] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_870923, _870925)], (1660 ^ _775828) ^ [_799196, _799198] : [-(class_Rings_Osemiring__0(_799196)), _799198 = _799196, class_Rings_Osemiring__0(_799198)], (4666 ^ _775828) ^ [_847118, _847120, _847122, _847124] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_847124, _847120) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_847122, _847118)), _847124 = _847122, _847120 = _847118], (20608 ^ _775828) ^ [] : [-(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))))], (22270 ^ _775828) ^ [_1162918, _1162920, _1162922, _1162924] : [class_Fields_Olinordered__field__inverse__zero(_1162918), 22273 ^ _775828 : [(22274 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162918), _1162920), _1162922)), _1162924)), 22277 ^ _775828 : [(22284 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162922))), 22287 ^ _775828 : [(22294 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), _1162922), c_Groups_Ozero__class_Ozero(_1162918)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162924)))], (22288 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), _1162922), c_Groups_Ozero__class_Ozero(_1162918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162918), _1162924), _1162922)), _1162920)))]]], (22278 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), _1162920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162918), _1162924), _1162922))))]]], (22300 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162918), _1162920), _1162922)), _1162924))), 22303 ^ _775828 : [(22306 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), _1162920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162918), _1162924), _1162922)))], (22304 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162922)))]], 22307 ^ _775828 : [(22310 ^ _775828) ^ [] : [22311 ^ _775828 : [(22314 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162918), _1162924), _1162922)), _1162920))], (22312 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), _1162922), c_Groups_Ozero__class_Ozero(_1162918))))]], 22315 ^ _775828 : [(22318 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162924))], (22316 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), _1162922), c_Groups_Ozero__class_Ozero(_1162918)))]]], (22308 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162918), c_Groups_Ozero__class_Ozero(_1162918)), _1162922))]]]]], (41022 ^ _775828) ^ [_1566217, _1566219, _1566221, _1566223, _1566225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566217, _1566217)), hAPP(hAPP(c_Product__Type_OPair(_1566217, _1566217), _1566219), _1566221)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566217, _1566217), tc_HOL_Obool), _1566223), _1566225))), 41027 ^ _775828 : [(41030 ^ _775828) ^ [] : [-(_1566219 = _1566221)], (41028 ^ _775828) ^ [] : [-(_1566223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41033 ^ _775828 : [(41038 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566217, _1566217)), hAPP(hAPP(c_Product__Type_OPair(_1566217, _1566217), 41031 ^ [_1566217, _1566219, _1566221, _1566223, _1566225]), _1566221)), _1566225)))], (41036 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566217, _1566217)), hAPP(hAPP(c_Product__Type_OPair(_1566217, _1566217), _1566219), 41031 ^ [_1566217, _1566219, _1566221, _1566223, _1566225])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566217, _1566217), tc_HOL_Obool), 41032 ^ [_1566217, _1566219, _1566221, _1566223, _1566225]), _1566225))))], (41034 ^ _775828) ^ [] : [-(_1566223 = hAPP(c_Nat_OSuc, 41032 ^ [_1566217, _1566219, _1566221, _1566223, _1566225]))]]], (46764 ^ _775828) ^ [_1705958, _1705960, _1705962, _1705964] : [class_Rings_Osemiring__1(_1705958), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705958), hAPP(hAPP(c_List_Omap(_1705960, _1705958), hAPP(c_COMBK(_1705958, _1705960), _1705962)), _1705964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1705958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1705958), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705960)), _1705964))), _1705962))], (44836 ^ _775828) ^ [_1657847] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657847, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1657847, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1657847, tc_HOL_Obool)))], (13875 ^ _775828) ^ [_1007066, _1007068, _1007070] : [-(hBOOL(hAPP(_1007066, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007068, _1007070)))), 13878 ^ _775828 : [(13881 ^ _775828) ^ [] : [hBOOL(hAPP(_1007066, _1007068))], (13879 ^ _775828) ^ [] : [-(_1007070 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13884 ^ _775828 : [(13885 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007070)))], (13891 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13887 ^ [_1007066, _1007068, _1007070]), _1007070)))], (13895 ^ _775828) ^ [] : [hBOOL(hAPP(_1007066, 13887 ^ [_1007066, _1007068, _1007070]))], (13893 ^ _775828) ^ [] : [-(_1007068 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007070), 13886 ^ [_1007066, _1007068, _1007070])), 13887 ^ [_1007066, _1007068, _1007070]))], (13889 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13887 ^ [_1007066, _1007068, _1007070])))]], 13896 ^ _775828 : [(13897 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007070), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13903 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13899 ^ [_1007066, _1007068, _1007070]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13907 ^ _775828) ^ [] : [hBOOL(hAPP(_1007066, 13899 ^ [_1007066, _1007068, _1007070]))], (13905 ^ _775828) ^ [] : [-(_1007068 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007070), 13898 ^ [_1007066, _1007068, _1007070])), 13899 ^ [_1007066, _1007068, _1007070]))], (13901 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007070), 13899 ^ [_1007066, _1007068, _1007070])))]]], (45521 ^ _775828) ^ [_1673146, _1673148, _1673150] : [c_Fun_Oinj__on(_1673146, _1673148, _1673150, c_Orderings_Otop__class_Otop(tc_fun(_1673146, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1673146), tc_List_Olist(_1673148), hAPP(c_List_Omap(_1673146, _1673148), _1673150), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1673146), tc_HOL_Obool))))], (21076 ^ _775828) ^ [_1139385, _1139387, _1139389, _1139391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139385, tc_fun(_1139387, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1139385, tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_fun(_1139387, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139387, tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_fun(_1139387, tc_HOL_Obool)), _1139385), c_COMBC(_1139387, tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139387, tc_prod(_1139385, _1139387)), tc_fun(_1139387, tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), _1139385), hAPP(c_COMBB(tc_prod(_1139385, _1139387), tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool), _1139387), c_member(tc_prod(_1139385, _1139387)))), c_Product__Type_OPair(_1139385, _1139387)))), _1139389)), hAPP(hAPP(c_COMBC(_1139385, tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_fun(_1139387, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139387, tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_fun(_1139387, tc_HOL_Obool)), _1139385), c_COMBC(_1139387, tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139387, tc_prod(_1139385, _1139387)), tc_fun(_1139387, tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool)), _1139385), hAPP(c_COMBB(tc_prod(_1139385, _1139387), tc_fun(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool), tc_HOL_Obool), _1139387), c_member(tc_prod(_1139385, _1139387)))), c_Product__Type_OPair(_1139385, _1139387)))), _1139391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1139385, _1139387), tc_HOL_Obool)), _1139389), _1139391)))], (14808 ^ _775828) ^ [_1023565, _1023567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1023567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023565), _1023567)), _1023565)))], (50579 ^ _775828) ^ [_1793848, _1793850] : [-(c_List_Oconcat(tc_List_Olist(_1793848), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1793848), tc_List_Olist(tc_List_Olist(_1793848))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1793848)), _1793848, c_List_Olist_ONil(tc_List_Olist(_1793848)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1793848), tc_List_Olist(tc_List_Olist(_1793848))), _1793848), hAPP(hAPP(c_COMBC(tc_List_Olist(_1793848), tc_List_Olist(tc_List_Olist(_1793848)), tc_List_Olist(tc_List_Olist(_1793848))), c_List_Olist_OCons(tc_List_Olist(_1793848))), c_List_Olist_ONil(tc_List_Olist(_1793848)))))), _1793850)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1793848), tc_List_Olist(_1793848)), c_List_Otl(_1793848)), hAPP(c_List_Ofilter(tc_List_Olist(_1793848), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1793848)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1793848), tc_List_Olist(_1793848), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1793848)))), _1793850)))], (13426 ^ _775828) ^ [_998658, _998660, _998662, _998664, _998666, _998668] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_998658, _998660, _998662), _998664, _998666, _998668), 13431 ^ _775828 : [(13434 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_998660, _998664, _998666, _998668))], (13432 ^ _775828) ^ [] : [-(hBOOL(hAPP(_998658, _998664)))]], 13435 ^ _775828 : [(13438 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_998662, _998664, _998666, _998668))], (13436 ^ _775828) ^ [] : [hBOOL(hAPP(_998658, _998664))]]], (21206 ^ _775828) ^ [_1143143] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1143143)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143143)), 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))))], (20388 ^ _775828) ^ [_1126207] : [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), _1126207))), 20391 ^ _775828 : [(20394 ^ _775828) ^ [] : [-(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(_1126207)))))], (20392 ^ _775828) ^ [] : [-(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(_1126207)))))]]], (27899 ^ _775828) ^ [_1274677, _1274679, _1274681] : [c_Wellfounded_Owf(_1274677, _1274679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1274677, _1274677), tc_HOL_Obool)), _1274681), _1274679)), -(c_Wellfounded_Owf(_1274677, _1274681))], (24463 ^ _775828) ^ [_1205406, _1205408] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205406), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24466 ^ _775828 : [(24475 ^ _775828) ^ [] : [-(c_Nitpick_Onorm__frac(_1205408, _1205406) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1205408), _1205406)), 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), _1205408))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205406)))), -(_1205408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1205406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24467 ^ _775828) ^ [] : [24468 ^ _775828 : [(24471 ^ _775828) ^ [] : [_1205406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24469 ^ _775828) ^ [] : [_1205408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1205408, _1205406) = 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)))]]], (17375 ^ _775828) ^ [_1073294, _1073296, _1073298, _1073300] : [class_Rings_Olinordered__semidom(_1073294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073296), _1073298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073294), c_Groups_Ozero__class_Ozero(_1073294)), _1073300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073294), _1073300), c_Groups_Oone__class_Oone(_1073294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073294), hAPP(hAPP(c_Power_Opower__class_Opower(_1073294), _1073300), _1073298)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073294), _1073300), _1073296))))], (51500 ^ _775828) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (51448 ^ _775828) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (44291 ^ _775828) ^ [_1643934, _1643936, _1643938, _1643940, _1643942, _1643944] : [class_Complete__Lattice_Ocomplete__lattice(_1643934), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643936, tc_fun(_1643938, _1643934)), _1643940), _1643942), _1643944) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643936, _1643934), _1643940), hAPP(hAPP(c_COMBC(_1643936, _1643938, _1643934), _1643942), _1643944)))], (18737 ^ _775828) ^ [_1097865, _1097867] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1097865), _1097867) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1097865, _1097867)))], (16815 ^ _775828) ^ [_1062152, _1062154] : [class_Groups_Oordered__ab__group__add__abs(_1062152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062152), hAPP(c_Groups_Oabs__class_Oabs(_1062152), _1062154)), c_Groups_Ozero__class_Ozero(_1062152)))], (43678 ^ _775828) ^ [_1630145, _1630147, _1630149, _1630151] : [class_Lattices_Osemilattice__sup(_1630145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630145), _1630147)), hBOOL(hAPP(hAPP(c_member(_1630145), _1630149), _1630147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1630145), _1630149), _1630151)), hAPP(hAPP(c_Finite__Set_Ofold(_1630145, _1630145, c_Lattices_Osemilattice__sup__class_Osup(_1630145)), _1630151), _1630147))))], (6252 ^ _775828) ^ [_875346, _875348, _875350, _875352] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875346, _875348)), _875350), _875352)), -(_875352 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _875350), _875346), hAPP(_875348, _875350)))], (14782 ^ _775828) ^ [_1023098, _1023100, _1023102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023098), _1023100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023098), _1023102)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023100), _1023102))))], (29991 ^ _775828) ^ [_1322488, _1322490, _1322492, _1322494] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1322488, _1322490, _1322492), _1322494), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322490, _1322492), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322488, _1322492), tc_HOL_Obool)))], (28159 ^ _775828) ^ [_1280463, _1280465, _1280467, _1280469] : [28160 ^ _775828 : [(28163 ^ _775828) ^ [] : [hBOOL(hAPP(_1280467, _1280465))], (28161 ^ _775828) ^ [] : [hBOOL(hAPP(_1280463, _1280465))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280469, tc_HOL_Obool)), _1280467), _1280463), _1280465)))], (33971 ^ _775828) ^ [_1407813, _1407815, _1407817] : [class_Lattices_Olattice(_1407813), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407813), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407813), _1407815), _1407817)), _1407817)))], (47625 ^ _775828) ^ [_1725717, _1725719, _1725721, _1725723, _1725725] : [_1725717 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1725719, _1725721, _1725723, _1725717), _1725725) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725721), _1725719), c_List_Olist_ONil(_1725721)), _1725725))], (40570 ^ _775828) ^ [_1555436, _1555438] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1555436, tc_HOL_Obool)), _1555438)))], (5124 ^ _775828) ^ [_854229, _854231] : [_854231 = _854229, -(c_List_Oappend(_854231) = c_List_Oappend(_854229))], (11801 ^ _775828) ^ [_969889, _969891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969889)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969891))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969889), _969891)))], (46063 ^ _775828) ^ [_1685851, _1685853, _1685855, _1685857, _1685859, _1685861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685851, _1685853)), hAPP(hAPP(c_Product__Type_OPair(_1685851, _1685853), _1685855), _1685857)), hAPP(c_List_Oset(tc_prod(_1685851, _1685853)), hAPP(hAPP(c_List_Ozip(_1685851, _1685853), _1685859), _1685861)))), 46066 ^ _775828 : [(46069 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685853), _1685857), hAPP(c_List_Oset(_1685853), _1685861))))], (46067 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685851), _1685855), hAPP(c_List_Oset(_1685851), _1685859))))]]], (19686 ^ _775828) ^ [_1114045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114045)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114045), c_Int_OMin)))], (49406 ^ _775828) ^ [_1767937, _1767939, _1767941] : [49408 ^ _775828 : [(49411 ^ _775828) ^ [] : [hBOOL(hAPP(_1767939, 49407 ^ [_1767937, _1767939, _1767941]))], (49409 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767937), 49407 ^ [_1767937, _1767939, _1767941]), hAPP(c_List_Oset(_1767937), _1767941))))]], -(hAPP(c_List_Ofilter(_1767937, _1767939), _1767941) = _1767941)], (24408 ^ _775828) ^ [_1204415] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1204415)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1204415)], (28942 ^ _775828) ^ [_1299280, _1299282, _1299284, _1299286, _1299288, _1299290] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299280, tc_fun(_1299282, tc_HOL_Obool))), _1299284), _1299286), _1299288), _1299290)), -(hBOOL(hAPP(hAPP(_1299284, _1299288), _1299290))), -(hBOOL(hAPP(hAPP(_1299286, _1299288), _1299290)))], (20956 ^ _775828) ^ [_1136368, _1136370] : [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), _1136368), _1136370))), 20959 ^ _775828 : [(20968 ^ _775828) ^ [] : [-(c_Divides_OnegDivAlg(_1136368, _1136370) = hAPP(c_Divides_Oadjust(_1136370), c_Divides_OnegDivAlg(_1136368, 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)))), _1136370)))), -(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), _1136368), _1136370)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136370), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20960 ^ _775828) ^ [] : [20961 ^ _775828 : [(20964 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136370), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20962 ^ _775828) ^ [] : [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), _1136368), _1136370)))]], -(c_Divides_OnegDivAlg(_1136368, _1136370) = 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), _1136368), _1136370)))]]], (31617 ^ _775828) ^ [_1357977, _1357979] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1357977, _1357977, _1357977), c_Transitive__Closure_Ortrancl(_1357977, _1357979)), c_Transitive__Closure_Ortrancl(_1357977, _1357979)) = c_Transitive__Closure_Ortrancl(_1357977, _1357979))], (4454 ^ _775828) ^ [_843818, _843820, _843822, _843824, _843826, _843828] : [-(c_List_Olist_Olist__size(_843828, _843824, _843820) = c_List_Olist_Olist__size(_843826, _843822, _843818)), _843828 = _843826, _843824 = _843822, _843820 = _843818], (21000 ^ _775828) ^ [_1137057, _1137059] : [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), _1137057), _1137059))), 21003 ^ _775828 : [(21012 ^ _775828) ^ [] : [-(c_Divides_OposDivAlg(_1137057, _1137059) = hAPP(c_Divides_Oadjust(_1137059), c_Divides_OposDivAlg(_1137057, 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)))), _1137059)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137057), _1137059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21004 ^ _775828) ^ [] : [21005 ^ _775828 : [(21008 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137059), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21006 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137057), _1137059))]], -(c_Divides_OposDivAlg(_1137057, _1137059) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137057))]]], (50204 ^ _775828) ^ [_1784243, _1784245, _1784247] : [50205 ^ _775828 : [(50208 ^ _775828) ^ [] : [_1784247 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50206 ^ _775828) ^ [] : [-(_1784243 = c_List_Olist_ONil(tc_List_Olist(_1784245)))]], 50212 ^ _775828 : [(50215 ^ _775828) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784245)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1784245)), _1784243), 50211 ^ [_1784243, _1784245, _1784247])) = _1784247], (50213 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50211 ^ [_1784243, _1784245, _1784247]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1784245))), _1784243))))]], -(c_List_Otranspose(_1784245, _1784243) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1784245)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1784245)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1784245), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1784245)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1784245)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1784245), hAPP(hAPP(c_COMBB(tc_List_Olist(_1784245), tc_fun(tc_Nat_Onat, _1784245), tc_Nat_Onat), c_List_Onth(_1784245)), hAPP(c_List_Onth(tc_List_Olist(_1784245)), _1784243))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1784245))), _1784243)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1784247)))], (17131 ^ _775828) ^ [_1068574, _1068576] : [class_Rings_Olinordered__idom(_1068574), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068574), c_Groups_Osgn__class_Osgn(_1068574, _1068576)), hAPP(c_Groups_Oabs__class_Oabs(_1068574), _1068576)) = _1068576)], (39650 ^ _775828) ^ [_1534344, _1534346, _1534348, _1534350, _1534352] : [class_Complete__Lattice_Ocomplete__lattice(_1534344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1534346, tc_HOL_Obool)), _1534348), _1534350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534346, _1534344), _1534348), _1534352)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534346, _1534344), _1534350), _1534352))))], (31947 ^ _775828) ^ [_1366429, _1366431, _1366433] : [class_Groups_Olinordered__ab__semigroup__add(_1366429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366429), _1366431)), -(_1366431 = c_Orderings_Obot__class_Obot(tc_fun(_1366429, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366429), _1366433), c_Big__Operators_Olinorder__class_OMax(_1366429, _1366431)) = c_Big__Operators_Olinorder__class_OMax(_1366429, hAPP(c_Set_OCollect(_1366429), hAPP(hAPP(c_COMBB(tc_fun(_1366429, tc_HOL_Obool), tc_HOL_Obool, _1366429), c_HOL_OEx(_1366429)), hAPP(hAPP(c_COMBC(_1366429, tc_fun(_1366429, tc_HOL_Obool), tc_fun(_1366429, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366429, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1366429, tc_HOL_Obool), tc_fun(_1366429, tc_HOL_Obool)), _1366429), c_COMBS(_1366429, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366429, tc_HOL_Obool), tc_fun(_1366429, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1366429), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366429), c_fconj)), hAPP(hAPP(c_COMBC(_1366429, tc_fun(_1366429, _1366429), tc_fun(_1366429, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366429, tc_HOL_Obool), tc_fun(tc_fun(_1366429, _1366429), tc_fun(_1366429, tc_HOL_Obool)), _1366429), c_COMBB(_1366429, tc_HOL_Obool, _1366429)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1366429), _1366433))))), hAPP(hAPP(c_COMBC(_1366429, tc_fun(_1366429, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366429)), _1366431))))))], (39397 ^ _775828) ^ [_1526947, _1526949, _1526951, _1526953, _1526955, _1526957] : [hBOOL(hAPP(hAPP(c_member(_1526947), _1526949), _1526951)), hBOOL(hAPP(hAPP(c_member(_1526953), _1526955), hAPP(_1526957, _1526949))), -(hBOOL(hAPP(hAPP(c_member(_1526953), _1526955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526947, tc_fun(_1526953, tc_HOL_Obool)), _1526951), _1526957))))], (38390 ^ _775828) ^ [_1505130, _1505132, _1505134, _1505136] : [38391 ^ _775828 : [(38392 ^ _775828) ^ [_1505219] : [_1505134 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1505130, tc_Option_Ooption(_1505132)), hAPP(c_COMBK(tc_Option_Ooption(_1505132), _1505130), c_Option_Ooption_ONone(_1505132))), _1505136), hAPP(c_Option_Ooption_OSome(_1505132), _1505219))]], -(c_Map_Odom(_1505130, _1505132, _1505134) = hAPP(hAPP(c_Set_Oinsert(_1505130), _1505136), c_Orderings_Obot__class_Obot(tc_fun(_1505130, tc_HOL_Obool))))], (51172 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (16985 ^ _775828) ^ [_1065555, _1065557, _1065559] : [class_Rings_Ocomm__semiring__1(_1065555), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065555), hAPP(hAPP(c_Power_Opower__class_Opower(_1065555), _1065557), _1065559)), _1065557) = hAPP(hAPP(c_Power_Opower__class_Opower(_1065555), _1065557), hAPP(c_Nat_OSuc, _1065559)))], (37464 ^ _775828) ^ [_1483487, _1483489, _1483491, _1483493] : [class_Groups_Ocomm__monoid__add(_1483487), 37467 ^ _775828 : [(37474 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483489), _1483491))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483487), _1483493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483491), hAPP(c_Nat_OSuc, _1483489))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483487), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483487), _1483493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483491), _1483489))), hAPP(_1483493, _1483489)))], (37468 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483489), _1483491)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483487), _1483493), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483491), hAPP(c_Nat_OSuc, _1483489))) = c_Groups_Ozero__class_Ozero(_1483487))]]], (36389 ^ _775828) ^ [_1459231, _1459233, _1459235] : [class_Groups_Oordered__ab__group__add(_1459231), -(hAPP(c_Set_Oimage(_1459231, _1459231, c_Groups_Ouminus__class_Ouminus(_1459231)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459231, _1459233), _1459235)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1459231, hAPP(c_Groups_Ouminus__class_Ouminus(_1459231), _1459235), hAPP(c_Groups_Ouminus__class_Ouminus(_1459231), _1459233)))], (33346 ^ _775828) ^ [_1393872, _1393874, _1393876] : [-(c_Map_Oran(_1393872, _1393874, _1393876) = hAPP(c_Set_OCollect(_1393874), hAPP(hAPP(c_COMBB(tc_fun(_1393872, tc_HOL_Obool), tc_HOL_Obool, _1393874), c_HOL_OEx(_1393872)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1393874), tc_fun(_1393872, tc_HOL_Obool), _1393874), hAPP(c_COMBC(_1393872, tc_Option_Ooption(_1393874), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1393874), tc_fun(tc_Option_Ooption(_1393874), tc_HOL_Obool), _1393872), c_fequal), _1393876))), c_Option_Ooption_OSome(_1393874)))))], (34205 ^ _775828) ^ [_1412270, _1412272, _1412274, _1412276] : [hBOOL(hAPP(hAPP(c_member(_1412270), _1412272), _1412274)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412270, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1412270), _1412272), _1412276)), _1412274) = hAPP(hAPP(c_Set_Oinsert(_1412270), _1412272), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412270, tc_HOL_Obool)), _1412276), _1412274)))], (20144 ^ _775828) ^ [_1121878, _1121880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1121878)), c_Int_OBit1(_1121880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121878), _1121880)))], (10230 ^ _775828) ^ [_941578, _941580] : [class_Groups_Oone(_941578), 10233 ^ _775828 : [(10240 ^ _775828) ^ [] : [_941580 = c_Groups_Oone__class_Oone(_941578), -(c_Groups_Oone__class_Oone(_941578) = _941580)], (10234 ^ _775828) ^ [] : [c_Groups_Oone__class_Oone(_941578) = _941580, -(_941580 = c_Groups_Oone__class_Oone(_941578))]]], (42577 ^ _775828) ^ [_1604107] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42573 ^ [_1604107]), c_Int_OInteg)))], (9989 ^ _775828) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49953 ^ _775828) ^ [_1779138, _1779140, _1779142, _1779144, _1779146] : [class_Orderings_Olinorder(_1779138), c_List_Olinorder__class_Osorted(_1779138, hAPP(hAPP(c_List_Omap(_1779140, _1779138), _1779142), _1779144)), -(c_List_Olinorder__class_Osorted(_1779138, hAPP(hAPP(c_List_Omap(_1779140, _1779138), _1779142), c_List_Oremove1(_1779140, _1779146, _1779144))))], (41286 ^ _775828) ^ [_1572923, _1572925, _1572927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572923, _1572923), tc_HOL_Obool)), _1572925), hAPP(hAPP(c_Product__Type_OSigma(_1572923, _1572923), _1572927), hAPP(c_COMBK(tc_fun(_1572923, tc_HOL_Obool), _1572923), _1572927)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572923, _1572923), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1572923, _1572925)), hAPP(hAPP(c_Product__Type_OSigma(_1572923, _1572923), _1572927), hAPP(c_COMBK(tc_fun(_1572923, tc_HOL_Obool), _1572923), _1572927)))))], (41390 ^ _775828) ^ [_1576266, _1576268, _1576270, _1576272, _1576274, _1576276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576266, _1576268)), hAPP(hAPP(c_Product__Type_OPair(_1576266, _1576268), _1576270), _1576272)), hAPP(hAPP(c_Product__Type_OSigma(_1576266, _1576268), _1576274), _1576276))), -(hBOOL(hAPP(hAPP(c_member(_1576266), _1576270), _1576274)))], (17435 ^ _775828) ^ [_1074442, _1074444] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074442)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074444)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1074442), _1074444)))], (45925 ^ _775828) ^ [_1682680, _1682682] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1682680, _1682682) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1682680, _1682682)))], (35381 ^ _775828) ^ [_1439878, _1439880, _1439882] : [hAPP(c_Set_Oimage(_1439880, tc_fun(_1439880, tc_HOL_Obool), _1439878), _1439882) = hAPP(c_Set_OPow(_1439880), _1439882)], (7503 ^ _775828) ^ [_895564, _895566] : [class_Rings_Oring__1(_895564), -(hAPP(c_Int_Oring__1__class_Oof__int(_895564), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _895566)) = hAPP(c_Groups_Ouminus__class_Ouminus(_895564), hAPP(c_Int_Oring__1__class_Oof__int(_895564), _895566)))], (17459 ^ _775828) ^ [_1074811] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1074811) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15570 ^ _775828) ^ [_1037839, _1037841, _1037843] : [class_Groups_Oordered__ab__group__add(_1037839), 15573 ^ _775828 : [(15580 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037839), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037839), _1037841), _1037843)), c_Groups_Ozero__class_Ozero(_1037839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037839), _1037841), _1037843)))], (15574 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037839), _1037841), _1037843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037839), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037839), _1037841), _1037843)), c_Groups_Ozero__class_Ozero(_1037839))))]]], (32725 ^ _775828) ^ [_1380905, _1380907, _1380909, _1380911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1380905, _1380907)), c_Sum__Type_OPlus(_1380905, _1380907, _1380909, _1380911))), 32728 ^ _775828 : [(32731 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380907), _1380911)))], (32729 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380905), _1380909)))]]], (10996 ^ _775828) ^ [_955759, _955761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955759), _955761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955759), _955761))), -(_955759 = _955761)], (12985 ^ _775828) ^ [_990338, _990340] : [-(hBOOL(hAPP(_990338, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_990338, _990340)), 12993 ^ _775828 : [(12996 ^ _775828) ^ [_990576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990576), 12992 ^ [_990338, _990340])), hBOOL(hAPP(_990338, _990576))], (13002 ^ _775828) ^ [] : [-(hBOOL(hAPP(_990338, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 12992 ^ [_990338, _990340]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (12994 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12992 ^ [_990338, _990340]), _990340)))]]], (23334 ^ _775828) ^ [_1182500, _1182502, _1182504, _1182506] : [class_Fields_Olinordered__field(_1182500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182500), _1182502), c_Groups_Ozero__class_Ozero(_1182500))), 23341 ^ _775828 : [(23348 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182500), _1182506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182500), _1182504), _1182502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182500), _1182504), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182500), _1182506), _1182502))))], (23342 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182500), _1182504), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182500), _1182506), _1182502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182500), _1182506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182500), _1182504), _1182502))))]]], (45775 ^ _775828) ^ [_1679167, _1679169, _1679171, _1679173, _1679175] : [hAPP(c_Map_Omap__of(_1679167, _1679169, _1679171), _1679173) = hAPP(c_Option_Ooption_OSome(_1679169), _1679175), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679167, _1679169)), hAPP(hAPP(c_Product__Type_OPair(_1679167, _1679169), _1679173), _1679175)), hAPP(c_List_Oset(tc_prod(_1679167, _1679169)), _1679171))))], (35679 ^ _775828) ^ [_1445790, _1445792, _1445794, _1445796] : [class_Orderings_Olinorder(_1445790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445790), _1445792), _1445794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445790), _1445794), _1445796)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445790, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1445790, _1445792, _1445794)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1445790, _1445794, _1445796)) = c_SetInterval_Oord__class_OatLeastAtMost(_1445790, _1445792, _1445796))], (19976 ^ _775828) ^ [_1118901, _1118903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118901), 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)))), _1118903))), 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)))), _1118901)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1118903), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1118901))], (46337 ^ _775828) ^ [_1693075, _1693077, _1693079] : [-(hBOOL(hAPP(hAPP(c_member(_1693075), _1693077), hAPP(c_List_Oset(_1693075), _1693079)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693075)), c_List_Oremove1(_1693075, _1693077, _1693079)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693075)), _1693079))], (39177 ^ _775828) ^ [_1522024, _1522026, _1522028, _1522030, _1522032] : [c_Fun_Oinj__on(_1522024, _1522026, _1522028, _1522030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522026, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1522024, _1522026, _1522028), _1522030)), _1522032)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522026), _1522032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1522024), _1522030)), hAPP(c_Finite__Set_Ocard(_1522026), _1522032))))], (25427 ^ _775828) ^ [_1224289] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1224289)) = _1224289)], (51286 ^ _775828) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (80 ^ _775828) ^ [_776952, _776954] : [-(class_Rings_Odivision__ring(_776952)), _776954 = _776952, class_Rings_Odivision__ring(_776954)], (6854 ^ _775828) ^ [_884320, _884322] : [6855 ^ _775828 : [(6856 ^ _775828) ^ [_884368] : [_884320 = hAPP(c_Option_Ooption_OSome(_884322), _884368)]], _884320 = c_Option_Ooption_ONone(_884322)], (25323 ^ _775828) ^ [_1222472] : [-(c_Quickcheck_Obeyond(_1222472, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (25116 ^ _775828) ^ [_1219101, _1219103, _1219105] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1219101, _1219103, _1219105, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1219103)], (8137 ^ _775828) ^ [_906619] : [-(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, _906619))))))], (51480 ^ _775828) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (29325 ^ _775828) ^ [_1307636, _1307638] : [hBOOL(hAPP(hAPP(c_member(_1307636), _1307638), c_Orderings_Obot__class_Obot(tc_fun(_1307636, tc_HOL_Obool))))], (6576 ^ _775828) ^ [_880387, _880389, _880391] : [class_Orderings_Opreorder(_880387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880387), _880389), _880391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880387), _880391), _880389))], (27044 ^ _775828) ^ [_1253642, _1253644] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253642), _1253644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253642), _1253644)))], (8819 ^ _775828) ^ [_917089, _917091, _917093] : [class_Orderings_Olinorder(_917089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917089), _917091), _917093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917089), _917093), _917091)))], (17411 ^ _775828) ^ [_1073995, _1073997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073995)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1073995), _1073997)))], (38802 ^ _775828) ^ [_1514462, _1514464, _1514466, _1514468, _1514470] : [c_Fun_Oinj__on(_1514462, _1514464, _1514466, _1514468), -(c_Fun_Oinj__on(_1514462, _1514464, _1514466, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514462, tc_HOL_Obool)), _1514468), _1514470)))], (49525 ^ _775828) ^ [_1771159, _1771161, _1771163, _1771165] : [-(c_List_Otranspose(_1771159, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1771161), tc_List_Olist(_1771159)), hAPP(c_List_Omap(_1771161, _1771159), _1771163)), _1771165)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1771161), tc_List_Olist(_1771159)), hAPP(c_List_Omap(_1771161, _1771159), _1771163)), c_List_Otranspose(_1771161, _1771165)))], (49499 ^ _775828) ^ [_1769988, _1769990, _1769992] : [hBOOL(hAPP(c_List_Odistinct(_1769988), _1769990)), -(hAPP(c_List_Ofilter(_1769988, hAPP(hAPP(c_COMBC(_1769988, tc_fun(_1769988, tc_HOL_Obool), tc_HOL_Obool), c_member(_1769988)), hAPP(c_List_Oset(_1769988), c_List_Osublist(_1769988, _1769990, _1769992)))), _1769990) = c_List_Osublist(_1769988, _1769990, _1769992))], (35391 ^ _775828) ^ [_1440153, _1440155, _1440157] : [-(hAPP(c_Set_OPow(_1440153), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440153, tc_HOL_Obool)), _1440155), _1440157)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1440153, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1440153), _1440155)), hAPP(c_Set_OPow(_1440153), _1440157)))], (29624 ^ _775828) ^ [_1313534, _1313536] : [-(hBOOL(hAPP(_1313536, 29625 ^ [_1313534, _1313536]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1313534, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1313534), _1313536))], (35389 ^ _775828) ^ [_1440071, _1440073, _1440075] : [-(hAPP(c_Set_OPow(_1440071), hAPP(hAPP(c_Set_Oinsert(_1440071), _1440073), _1440075)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1440071, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1440071), _1440075)), hAPP(c_Set_Oimage(tc_fun(_1440071, tc_HOL_Obool), tc_fun(_1440071, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1440071), _1440073)), hAPP(c_Set_OPow(_1440071), _1440075))))], (6352 ^ _775828) ^ [_876803, _876805] : [class_Rings_Olinordered__semidom(_876803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876803), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876803), _876805)), c_Groups_Ozero__class_Ozero(_876803)))], (50748 ^ _775828) ^ [_1797548, _1797550] : [_1797550 = c_List_Olist_ONil(_1797548), -(c_List_Olist_ONil(_1797548) = c_List_Oremdups(_1797548, _1797550))], (43257 ^ _775828) ^ [_1619979, _1619981, _1619983, _1619985, _1619987] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1619979), _1619981), _1619983), _1619985), _1619987) = c_New__DSequence_Oneg__single(_1619979, _1619981))], (51108 ^ _775828) ^ [_1804376, _1804378] : [class_Groups_Ouminus(_1804376), -(class_Groups_Ouminus(tc_fun(_1804378, _1804376)))], (11917 ^ _775828) ^ [_971981, _971983, _971985] : [class_Rings_Olinordered__ring__strict(_971981), 11920 ^ _775828 : [(11929 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971981), _971983), _971983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971981), _971985), _971985))), c_Groups_Ozero__class_Ozero(_971981)))), _971983 = c_Groups_Ozero__class_Ozero(_971981), _971985 = c_Groups_Ozero__class_Ozero(_971981)], (11921 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971981), _971983), _971983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971981), _971985), _971985))), c_Groups_Ozero__class_Ozero(_971981))), 11924 ^ _775828 : [(11927 ^ _775828) ^ [] : [-(_971985 = c_Groups_Ozero__class_Ozero(_971981))], (11925 ^ _775828) ^ [] : [-(_971983 = c_Groups_Ozero__class_Ozero(_971981))]]]]], (19108 ^ _775828) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27326 ^ _775828) ^ [_1260192, _1260194, _1260196, _1260198] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1260192, _1260192)), hAPP(hAPP(c_Product__Type_OPair(_1260192, _1260192), _1260194), _1260196)), c_Relation_OId__on(_1260192, _1260198))), 27329 ^ _775828 : [(27332 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260192), _1260194), _1260198)))], (27330 ^ _775828) ^ [] : [-(_1260194 = _1260196)]]], (41911 ^ _775828) ^ [_1587968, _1587970, _1587972, _1587974] : [class_Groups_Ocomm__monoid__mult(_1587968), c_Fun_Oinj__on(_1587970, _1587968, _1587972, _1587974), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587970, _1587968), _1587972), _1587974) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587968, _1587968), c_Fun_Oid(_1587968)), hAPP(c_Set_Oimage(_1587970, _1587968, _1587972), _1587974)))], (30629 ^ _775828) ^ [_1335657, _1335659, _1335661, _1335663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335657, tc_HOL_Obool)), _1335659), _1335663))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335657, tc_HOL_Obool)), _1335659), hAPP(hAPP(c_Set_Oinsert(_1335657), _1335661), _1335663)))))], (4618 ^ _775828) ^ [_846338, _846340, _846342, _846344, _846346, _846348, _846350, _846352, _846354, _846356] : [-(c_List_Olinorder__class_Oinsort__insert__key(_846356, _846352, _846348, _846344, _846340) = c_List_Olinorder__class_Oinsort__insert__key(_846354, _846350, _846346, _846342, _846338)), _846356 = _846354, _846352 = _846350, _846348 = _846346, _846344 = _846342, _846340 = _846338], (13674 ^ _775828) ^ [_1003450, _1003452, _1003454] : [c_Com_Ocom_OCond(_1003450, _1003452, _1003454) = c_Com_Ocom_OSKIP], (36645 ^ _775828) ^ [_1464394, _1464396, _1464398] : [class_Orderings_Oorder(_1464394), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464394, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1464394), _1464396)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1464394, _1464396, _1464398)) = c_Orderings_Obot__class_Obot(tc_fun(_1464394, tc_HOL_Obool)))], (310 ^ _775828) ^ [_780283, _780285, _780287, _780289, _780291, _780293, _780295, _780297, _780299, _780301, _780303, _780305] : [-(c_Nitpick_Ofold__graph_H(_780303, _780299, _780295, _780291, _780287, _780283)), c_Nitpick_Ofold__graph_H(_780305, _780301, _780297, _780293, _780289, _780285), _780305 = _780303, _780301 = _780299, _780297 = _780295, _780293 = _780291, _780289 = _780287, _780285 = _780283], (16549 ^ _775828) ^ [_1057261] : [class_Groups_Oordered__ab__group__add__abs(_1057261), -(hAPP(c_Groups_Oabs__class_Oabs(_1057261), c_Groups_Ozero__class_Ozero(_1057261)) = c_Groups_Ozero__class_Ozero(_1057261))], (46982 ^ _775828) ^ [_1711229, _1711231] : [hBOOL(hAPP(c_List_Odistinct(_1711229), _1711231)), 46985 ^ _775828 : [(46986 ^ _775828) ^ [_1711361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711361), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711229)), _1711231))), 46989 ^ _775828 : [(46990 ^ _775828) ^ [_1711488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711488), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711229)), _1711231))), -(_1711361 = _1711488), hAPP(hAPP(c_List_Onth(_1711229), _1711231), _1711361) = hAPP(hAPP(c_List_Onth(_1711229), _1711231), _1711488)]]]]], (20150 ^ _775828) ^ [_1121979, _1121981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121979), _1121981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1121979)), c_Int_OBit1(_1121981))))], (42878 ^ _775828) ^ [_1611013, _1611015, _1611017, _1611019, _1611021, _1611023, _1611025] : [c_Fun_Oinj__on(_1611013, _1611015, _1611017, hAPP(c_Set_Oimage(_1611019, _1611013, _1611021), _1611023)), c_Fun_Oinj__on(_1611019, _1611013, _1611021, _1611023), hBOOL(hAPP(hAPP(c_member(_1611015), _1611025), hAPP(c_Set_Oimage(_1611013, _1611015, _1611017), hAPP(c_Set_Oimage(_1611019, _1611013, _1611021), _1611023)))), -(hAPP(c_Fun_Othe__inv__into(_1611019, _1611015, _1611023, hAPP(c_Fun_Ocomp(_1611013, _1611015, _1611019, _1611017), _1611021)), _1611025) = hAPP(hAPP(c_Fun_Ocomp(_1611013, _1611019, _1611015, c_Fun_Othe__inv__into(_1611019, _1611013, _1611023, _1611021)), c_Fun_Othe__inv__into(_1611013, _1611015, hAPP(c_Set_Oimage(_1611019, _1611013, _1611021), _1611023), _1611017)), _1611025))], (33272 ^ _775828) ^ [_1392065, _1392067, _1392069, _1392071, _1392073, _1392075, _1392077] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1392065, tc_Option_Ooption(_1392067)), _1392069), _1392071), hAPP(c_Option_Ooption_OSome(_1392067), _1392073)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1392065, tc_Option_Ooption(_1392067)), _1392075), _1392071), hAPP(c_Option_Ooption_OSome(_1392067), _1392077)), -(_1392073 = _1392077)], (18535 ^ _775828) ^ [_1094609] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1094609), hAPP(c_Int_Onumber__class_Onumber__of(_1094609), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1094609)), class_Int_Onumber__ring(_1094609), class_Rings_Olinordered__idom(_1094609)], (29403 ^ _775828) ^ [_1309090, _1309092, _1309094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309090, tc_HOL_Obool)), _1309092), hAPP(hAPP(c_Set_Oinsert(_1309090), _1309094), c_Orderings_Obot__class_Obot(tc_fun(_1309090, tc_HOL_Obool))))), -(_1309092 = c_Orderings_Obot__class_Obot(tc_fun(_1309090, tc_HOL_Obool))), -(_1309092 = hAPP(hAPP(c_Set_Oinsert(_1309090), _1309094), c_Orderings_Obot__class_Obot(tc_fun(_1309090, tc_HOL_Obool))))], (45144 ^ _775828) ^ [_1664694, _1664696, _1664698, _1664700] : [class_Orderings_Olinorder(_1664694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1664694), _1664696)), 45154 ^ _775828 : [(45157 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664694), _1664698), 45153 ^ [_1664694, _1664696, _1664698, _1664700]))], (45155 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664694), 45153 ^ [_1664694, _1664696, _1664698, _1664700]), _1664696)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664694), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1664694), _1664698), _1664700)), hAPP(hAPP(c_Finite__Set_Ofold(_1664694, _1664694, c_Orderings_Oord__class_Omin(_1664694)), _1664700), _1664696))))], (3692 ^ _775828) ^ [_831937, _831939] : [_831939 = _831937, -(c_Rings_Odvd__class_Odvd(_831939) = c_Rings_Odvd__class_Odvd(_831937))], (13712 ^ _775828) ^ [_1004249, _1004251] : [class_Divides_Osemiring__div(_1004249), -(c_Divides_Odiv__class_Omod(_1004249, _1004251, c_Groups_Oone__class_Oone(_1004249)) = c_Groups_Ozero__class_Ozero(_1004249))], (17933 ^ _775828) ^ [_1083089, _1083091, _1083093, _1083095] : [class_Rings_Olinordered__semidom(_1083089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083089), hAPP(hAPP(c_Power_Opower__class_Opower(_1083089), _1083091), hAPP(c_Nat_OSuc, _1083093))), hAPP(hAPP(c_Power_Opower__class_Opower(_1083089), _1083095), hAPP(c_Nat_OSuc, _1083093)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083089), c_Groups_Ozero__class_Ozero(_1083089)), _1083095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083089), _1083091), _1083095)))], (12483 ^ _775828) ^ [_981778, _981780] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981778)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981780)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _981778), _981780)))], (8601 ^ _775828) ^ [_913761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913761)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _913761)) = _913761)], (43018 ^ _775828) ^ [_1614582, _1614584, _1614586, _1614588, _1614590, _1614592] : [c_Finite__Set_Ofolding(_1614582, _1614584, _1614586, _1614588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614582), _1614590)), -(hAPP(c_Fun_Ocomp(_1614584, _1614584, _1614584, hAPP(_1614586, _1614592)), hAPP(_1614588, _1614590)) = hAPP(c_Fun_Ocomp(_1614584, _1614584, _1614584, hAPP(_1614588, _1614590)), hAPP(_1614586, _1614592)))], (28866 ^ _775828) ^ [_1296253, _1296255, _1296257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1296253, _1296253), tc_HOL_Obool)), _1296255), _1296257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296253, tc_HOL_Obool)), hAPP(c_Relation_OField(_1296253), _1296255)), hAPP(c_Relation_OField(_1296253), _1296257))))], (19124 ^ _775828) ^ [] : [c_Int_OMin = c_Int_OPls], (39624 ^ _775828) ^ [_1533074, _1533076, _1533078, _1533080, _1533082] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533074, tc_fun(_1533076, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533074, tc_HOL_Obool)), _1533078), _1533080)), _1533082) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533076, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533074, tc_fun(_1533076, tc_HOL_Obool)), _1533078), _1533082)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533074, tc_fun(_1533076, tc_HOL_Obool)), _1533080), _1533082)))], (17651 ^ _775828) ^ [_1078092] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078092))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078092)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50243 ^ _775828) ^ [_1785509, _1785511] : [-(c_Fun_Oinj__on(tc_List_Olist(_1785509), tc_List_Olist(_1785509), c_List_Orev(_1785509), _1785511))], (49162 ^ _775828) ^ [_1762615, _1762617, _1762619, _1762621] : [49165 ^ _775828 : [(49170 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762615, _1762615)), hAPP(hAPP(c_Product__Type_OPair(_1762615, _1762615), 49164 ^ [_1762615, _1762617, _1762619, _1762621]), 49163 ^ [_1762615, _1762617, _1762619, _1762621])), _1762617))], (49168 ^ _775828) ^ [] : [49163 ^ [_1762615, _1762617, _1762619, _1762621] = 49164 ^ [_1762615, _1762617, _1762619, _1762621]], (49166 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762615, _1762615)), hAPP(hAPP(c_Product__Type_OPair(_1762615, _1762615), 49163 ^ [_1762615, _1762617, _1762619, _1762621]), 49164 ^ [_1762615, _1762617, _1762619, _1762621])), _1762617))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762615), tc_List_Olist(_1762615))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762615), tc_List_Olist(_1762615)), _1762619), _1762621)), c_List_Olexord(_1762615, _1762617)))), -(_1762619 = _1762621), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762615), tc_List_Olist(_1762615))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762615), tc_List_Olist(_1762615)), _1762621), _1762619)), c_List_Olexord(_1762615, _1762617))))], (6847 ^ _775828) ^ [_884274, _884276] : [-(_884274 = c_Option_Ooption_ONone(_884276)), -(_884274 = hAPP(c_Option_Ooption_OSome(_884276), 6850 ^ [_884274, _884276]))], (3208 ^ _775828) ^ [_824311, _824313, _824315, _824317, _824319, _824321] : [-(c_Predicate_Oconversep(_824321, _824317, _824313) = c_Predicate_Oconversep(_824319, _824315, _824311)), _824321 = _824319, _824317 = _824315, _824313 = _824311], (33198 ^ _775828) ^ [_1390604, _1390606, _1390608, _1390610] : [class_Groups_Ocomm__monoid__mult(_1390604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390606), _1390608)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390606, _1390604), hAPP(c_COMBK(_1390604, _1390606), _1390610)), _1390608) = hAPP(hAPP(c_Power_Opower__class_Opower(_1390604), _1390610), hAPP(c_Finite__Set_Ocard(_1390606), _1390608)))], (25367 ^ _775828) ^ [_1223319, _1223321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223319), _1223321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1223319)), hAPP(c_Code__Numeral_Oof__nat, _1223321))))], (30555 ^ _775828) ^ [_1334173, _1334175, _1334177] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334173, _1334175)), _1334177)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334173), hAPP(c_Relation_ODomain(_1334173, _1334175), _1334177))))], (26159 ^ _775828) ^ [_1237666] : [_1237666 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1237666), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (39688 ^ _775828) ^ [_1535287, _1535289, _1535291, _1535293, _1535295] : [_1535287 = c_Orderings_Obot__class_Obot(tc_fun(_1535289, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535289, tc_fun(_1535291, tc_HOL_Obool)), _1535287), hAPP(hAPP(c_COMBB(tc_fun(_1535291, tc_HOL_Obool), tc_fun(_1535291, tc_HOL_Obool), _1535289), hAPP(c_Set_Oinsert(_1535291), _1535293)), _1535295)) = c_Orderings_Obot__class_Obot(tc_fun(_1535291, tc_HOL_Obool)))], (46706 ^ _775828) ^ [_1704550, _1704552, _1704554] : [class_Groups_Omonoid__add(_1704550), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704550), hAPP(hAPP(c_List_Omap(_1704552, _1704550), hAPP(c_COMBK(_1704550, _1704552), c_Groups_Ozero__class_Ozero(_1704550))), _1704554)) = c_Groups_Ozero__class_Ozero(_1704550))], (42172 ^ _775828) ^ [_1594682, _1594684, _1594686, _1594688, _1594690] : [c_Relation_Orefl__on(_1594682, _1594684, _1594686), c_Relation_Orefl__on(_1594682, _1594688, _1594690), -(c_Relation_Orefl__on(_1594682, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1594682, tc_HOL_Obool)), _1594684), _1594688), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1594682, _1594682), tc_HOL_Obool)), _1594686), _1594690)))], (6364 ^ _775828) ^ [_876994, _876996, _876998] : [class_Rings_Olinordered__semidom(_876994), 6367 ^ _775828 : [(6374 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876996), _876998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876994), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876994), _876996)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876994), _876998))))], (6368 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876994), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876994), _876996)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876994), _876998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876996), _876998)))]]], (37516 ^ _775828) ^ [_1484663, _1484665, _1484667, _1484669, _1484671, _1484673] : [class_Groups_Ocomm__monoid__add(_1484663), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484665), _1484667)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484665, _1484663), hAPP(hAPP(c_COMBS(_1484665, _1484663, _1484663), hAPP(hAPP(c_COMBS(_1484665, _1484663, tc_fun(_1484663, _1484663)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484663, tc_fun(_1484663, _1484663)), _1484665), c_If(_1484663)), _1484669)), _1484671)), _1484673)), _1484667) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1484663), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484665, _1484663), _1484671), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484665, tc_HOL_Obool)), _1484667), hAPP(c_Set_OCollect(_1484665), _1484669)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484665, _1484663), _1484673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484665, tc_HOL_Obool)), _1484667), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484665, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1484665), _1484669))))))], (41326 ^ _775828) ^ [_1574168, _1574170, _1574172, _1574174, _1574176, _1574178] : [class_Groups_Ocomm__monoid__mult(_1574168), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1574170, _1574168), hAPP(hAPP(c_COMBC(_1574170, tc_fun(_1574172, tc_HOL_Obool), _1574168), hAPP(hAPP(c_COMBB(tc_fun(_1574172, _1574168), tc_fun(tc_fun(_1574172, tc_HOL_Obool), _1574168), _1574170), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1574172, _1574168)), _1574174)), _1574176)), _1574178) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1574170, _1574172), _1574168), hAPP(c_Product__Type_Oprod_Oprod__case(_1574170, _1574172, _1574168), _1574174)), hAPP(hAPP(c_Product__Type_OSigma(_1574170, _1574172), _1574178), hAPP(c_COMBK(tc_fun(_1574172, tc_HOL_Obool), _1574170), _1574176))))], (49445 ^ _775828) ^ [_1768690, _1768692, _1768694, _1768696] : [hBOOL(hAPP(_1768690, _1768692)), -(hAPP(c_List_Ofilter(_1768694, _1768690), hAPP(hAPP(c_List_Olist_OCons(_1768694), _1768692), _1768696)) = hAPP(hAPP(c_List_Olist_OCons(_1768694), _1768692), hAPP(c_List_Ofilter(_1768694, _1768690), _1768696)))], (25357 ^ _775828) ^ [_1223112, _1223114, _1223116, _1223118] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1223112, _1223114, _1223116), c_Product__Type_Ocurry(_1223112, _1223114, _1223116, _1223118)) = _1223118)], (25355 ^ _775828) ^ [_1223071, _1223073, _1223075, _1223077] : [-(c_Product__Type_Ocurry(_1223071, _1223073, _1223075, hAPP(c_Product__Type_Oprod_Oprod__case(_1223071, _1223073, _1223075), _1223077)) = _1223077)], (4150 ^ _775828) ^ [_839212, _839214, _839216, _839218] : [-(c_List_Olistset(_839218, _839214) = c_List_Olistset(_839216, _839212)), _839218 = _839216, _839214 = _839212], (30944 ^ _775828) ^ [_1342075, _1342077, _1342079] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1342075), _1342077)), -(hAPP(c_Finite__Set_Ocard(_1342075), hAPP(hAPP(c_Set_Oinsert(_1342075), _1342079), _1342077)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1342075), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342075, tc_HOL_Obool)), _1342077), hAPP(hAPP(c_Set_Oinsert(_1342075), _1342079), c_Orderings_Obot__class_Obot(tc_fun(_1342075, tc_HOL_Obool)))))))], (4348 ^ _775828) ^ [_842235, _842237, _842239, _842241, _842243, _842245] : [-(c_Big__Operators_Olattice_OSup__fin(_842245, _842241, _842237) = c_Big__Operators_Olattice_OSup__fin(_842243, _842239, _842235)), _842245 = _842243, _842241 = _842239, _842237 = _842235], (29923 ^ _775828) ^ [_1320201, _1320203, _1320205, _1320207, _1320209] : [c_Hoare__Mirabelle_Ohoare__derivs(_1320201, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1320201)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1320201), _1320203), hAPP(c_Com_Ocom_OBODY, _1320205)), _1320207)), _1320209), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1320201)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1320201), _1320203), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1320205))), _1320207)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1320201), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1320201, _1320209, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1320201)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1320201), _1320203), hAPP(c_Com_Ocom_OBODY, _1320205)), _1320207)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1320201), tc_HOL_Obool)))))], (23452 ^ _775828) ^ [_1185348, _1185350, _1185352, _1185354, _1185356, _1185358, _1185360, _1185362] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185348, _1185350, _1185352), _1185354), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185356, _1185358, tc_prod(_1185348, _1185350)), _1185360), _1185362)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185356, _1185358, _1185352), hAPP(hAPP(c_COMBB(tc_fun(_1185358, tc_prod(_1185348, _1185350)), tc_fun(_1185358, _1185352), _1185356), hAPP(c_COMBB(tc_prod(_1185348, _1185350), _1185352, _1185358), hAPP(c_Product__Type_Oprod_Oprod__case(_1185348, _1185350, _1185352), _1185354))), _1185360)), _1185362))], (32649 ^ _775828) ^ [_1379132, _1379134] : [class_Lattices_Olattice(_1379132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379132), _1379134)), -(_1379134 = c_Orderings_Obot__class_Obot(tc_fun(_1379132, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1379132), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1379132), 32662 ^ [_1379132, _1379134]), 32663 ^ [_1379132, _1379134])), hAPP(hAPP(c_Set_Oinsert(_1379132), 32662 ^ [_1379132, _1379134]), hAPP(hAPP(c_Set_Oinsert(_1379132), 32663 ^ [_1379132, _1379134]), c_Orderings_Obot__class_Obot(tc_fun(_1379132, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1379132), c_Big__Operators_Olattice__class_OSup__fin(_1379132, _1379134)), _1379134)))], (37360 ^ _775828) ^ [_1480506, _1480508, _1480510, _1480512] : [class_Groups_Ocomm__monoid__add(_1480506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1480508), _1480510)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480506), _1480512), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1480508, _1480510)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1480506), hAPP(_1480512, _1480508)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480506), _1480512), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1480508), _1480510))))], (19328 ^ _775828) ^ [_1108146, _1108148] : [class_Int_Onumber__ring(_1108146), class_Rings_Olinordered__idom(_1108146), 19335 ^ _775828 : [(19342 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108148), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108146), hAPP(c_Int_Onumber__class_Onumber__of(_1108146), _1108148)), c_Groups_Ozero__class_Ozero(_1108146))))], (19336 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108146), hAPP(c_Int_Onumber__class_Onumber__of(_1108146), _1108148)), c_Groups_Ozero__class_Ozero(_1108146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108148), c_Int_OPls)))]]], (30698 ^ _775828) ^ [_1337287, _1337289] : [hAPP(c_Finite__Set_Ocard(_1337287), _1337289) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1337289 = c_Orderings_Obot__class_Obot(tc_fun(_1337287, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337287), _1337289))], (42996 ^ _775828) ^ [_1613995, _1613997, _1613999, _1614001, _1614003, _1614005] : [c_Finite__Set_Ofolding(_1613995, _1613997, _1613999, _1614001), -(hAPP(c_Fun_Ocomp(_1613997, _1613997, _1613997, hAPP(_1613999, _1614003)), hAPP(_1613999, _1614005)) = hAPP(c_Fun_Ocomp(_1613997, _1613997, _1613997, hAPP(_1613999, _1614005)), hAPP(_1613999, _1614003)))], (51568 ^ _775828) ^ [_1809002, _1809004] : [hBOOL(hAPP(hAPP(c_fconj, _1809002), _1809004)), -(hBOOL(_1809004))], (44764 ^ _775828) ^ [_1656520, _1656522, _1656524] : [class_Complete__Lattice_Ocomplete__lattice(_1656520), class_Orderings_Olinorder(_1656520), 44771 ^ _775828 : [(44781 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656520), _1656522), c_Complete__Lattice_OSup__class_OSup(_1656520, _1656524)))), 44782 ^ _775828 : [(44783 ^ _775828) ^ [_1656826] : [hBOOL(hAPP(hAPP(c_member(_1656520), _1656826), _1656524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656520), _1656522), _1656826))]]], (44772 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656520), _1656522), c_Complete__Lattice_OSup__class_OSup(_1656520, _1656524))), 44776 ^ _775828 : [(44779 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656520), _1656522), 44775 ^ [_1656520, _1656522, _1656524])))], (44777 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656520), 44775 ^ [_1656520, _1656522, _1656524]), _1656524)))]]]]], (33681 ^ _775828) ^ [_1401226, _1401228, _1401230, _1401232] : [hBOOL(hAPP(hAPP(c_member(_1401226), _1401228), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401226, tc_HOL_Obool)), _1401230), _1401232))), -(hBOOL(hAPP(hAPP(c_member(_1401226), _1401228), _1401232)))], (44671 ^ _775828) ^ [_1654368, _1654370, _1654372, _1654374] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1654368, tc_fun(_1654370, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654368, tc_HOL_Obool), _1654372)), _1654374) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654368, tc_HOL_Obool), tc_fun(_1654370, tc_HOL_Obool)), _1654372), hAPP(hAPP(c_COMBC(tc_fun(_1654368, tc_HOL_Obool), tc_fun(_1654368, tc_fun(_1654370, tc_HOL_Obool)), tc_fun(_1654370, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1654368, tc_fun(_1654370, tc_HOL_Obool))), _1654374)))], (29255 ^ _775828) ^ [_1306329, _1306331] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1306329, _1306331, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1306329), tc_HOL_Obool))))], (9711 ^ _775828) ^ [_932098, _932100, _932102, _932104] : [class_Rings_Olinordered__semiring__strict(_932098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932098), _932100), _932102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932098), _932104), _932102))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932098), c_Groups_Ozero__class_Ozero(_932098)), _932102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932100), _932104)))], (48629 ^ _775828) ^ [_1751427, _1751429] : [-(_1751427 = c_List_Olist_ONil(_1751429)), -(hBOOL(hAPP(hAPP(c_member(_1751429), hAPP(c_List_Ohd(_1751429), _1751427)), hAPP(c_List_Oset(_1751429), _1751427))))], (13420 ^ _775828) ^ [_998536, _998538, _998540] : [hBOOL(hAPP(c_Com_OWT, _998536)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_998538, _998540, _998536))))], (40067 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27932 ^ _775828) ^ [_1275312, _1275314, _1275316] : [c_Wellfounded_Owf(_1275312, _1275314), -(c_Wellfounded_Owf(_1275312, c_Wellfounded_Omlex__prod(_1275312, _1275316, _1275314)))], (17947 ^ _775828) ^ [_1083370, _1083372, _1083374] : [class_Rings_Olinordered__semidom(_1083370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083370), c_Groups_Oone__class_Oone(_1083370)), _1083372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083370), c_Groups_Oone__class_Oone(_1083370)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083370), _1083372), hAPP(hAPP(c_Power_Opower__class_Opower(_1083370), _1083372), _1083374)))))], (13666 ^ _775828) ^ [_1003226, _1003228, _1003230] : [c_Com_Ocom_OSemi(_1003226, _1003228) = hAPP(c_Com_Ocom_OBODY, _1003230)], (17503 ^ _775828) ^ [_1075509, _1075511] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075509)), _1075511) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1075509), _1075511)))], (40275 ^ _775828) ^ [_1547882, _1547884] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1547882), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1547884), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 40282 ^ _775828 : [(40289 ^ _775828) ^ [] : [_1547882 = _1547884, -(hAPP(c_Code__Numeral_Oof__nat, _1547882) = hAPP(c_Code__Numeral_Oof__nat, _1547884))], (40283 ^ _775828) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1547882) = hAPP(c_Code__Numeral_Oof__nat, _1547884), -(_1547882 = _1547884)]]], (19650 ^ _775828) ^ [_1113469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1113469)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113469), c_Int_OMin)))], (22078 ^ _775828) ^ [_1159304, _1159306, _1159308, _1159310] : [class_Fields_Olinordered__field__inverse__zero(_1159304), class_Int_Onumber(_1159304), 22085 ^ _775828 : [(22086 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159304), _1159306), _1159308)), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310))), 22089 ^ _775828 : [(22096 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), c_Groups_Ozero__class_Ozero(_1159304)), _1159308))), 22099 ^ _775828 : [(22106 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), _1159308), c_Groups_Ozero__class_Ozero(_1159304)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), c_Groups_Ozero__class_Ozero(_1159304)), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310))))], (22100 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), _1159308), c_Groups_Ozero__class_Ozero(_1159304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159304), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)), _1159308)), _1159306)))]]], (22090 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), c_Groups_Ozero__class_Ozero(_1159304)), _1159308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), _1159306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159304), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)), _1159308))))]]], (22112 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159304), _1159306), _1159308)), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)))), 22115 ^ _775828 : [(22118 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), _1159306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159304), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)), _1159308)))], (22116 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), c_Groups_Ozero__class_Ozero(_1159304)), _1159308)))]], 22119 ^ _775828 : [(22122 ^ _775828) ^ [] : [22123 ^ _775828 : [(22126 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159304), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)), _1159308)), _1159306))], (22124 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), _1159308), c_Groups_Ozero__class_Ozero(_1159304))))]], 22127 ^ _775828 : [(22130 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159304), c_Groups_Ozero__class_Ozero(_1159304)), hAPP(c_Int_Onumber__class_Onumber__of(_1159304), _1159310)))], (22128 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159304), _1159308), c_Groups_Ozero__class_Ozero(_1159304)))]]], (22120 ^ 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948653), _948655), _948657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948653), _948659), _948657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948653), _948655), _948659)))]]], (45187 ^ _775828) ^ [_1665638, _1665640, _1665642, _1665644] : [class_Lattices_Osemilattice__sup(_1665638), hBOOL(hAPP(c_Finite__Set_Ofinite(_1665638), _1665640)), 45197 ^ _775828 : [(45200 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665638), 45196 ^ [_1665638, _1665640, _1665642, _1665644]), _1665642))], (45198 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665638), 45196 ^ [_1665638, _1665640, _1665642, _1665644]), _1665640)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665638), hAPP(hAPP(c_Finite__Set_Ofold(_1665638, _1665638, c_Lattices_Osemilattice__sup__class_Osup(_1665638)), _1665644), _1665640)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1665638), _1665642), _1665644))))], (33887 ^ _775828) ^ [_1405604, 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_977197), _977199)))], (39726 ^ _775828) ^ [_1536181, _1536183, _1536185, _1536187, _1536189] : [_1536181 = c_Orderings_Obot__class_Obot(tc_fun(_1536183, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536185, tc_HOL_Obool)), _1536187), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536183, tc_fun(_1536185, tc_HOL_Obool)), _1536181), _1536189)) = _1536187)], (4212 ^ _775828) ^ [_840181, _840183, _840185, _840187, _840189, _840191, _840193, _840195] : [-(c_Nat_Onat_Onat__case(_840195, _840191, _840187, _840183) = c_Nat_Onat_Onat__case(_840193, _840189, _840185, _840181)), _840195 = _840193, _840191 = _840189, _840187 = _840185, _840183 = _840181], (41881 ^ _775828) ^ [_1587439] : [-(hAPP(c_Set_Oimage(_1587439, _1587439, c_Fun_Oid(_1587439)), c_Orderings_Otop__class_Otop(tc_fun(_1587439, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1587439, tc_HOL_Obool)))], (16459 ^ _775828) ^ [_1055821, _1055823, _1055825] : 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1301972), tc_HOL_Obool)), _1301974), _1301976)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1301972, _1301976, _1301974))], (15136 ^ _775828) ^ [_1029884, _1029886, _1029888] : [class_Rings_Oring__1(_1029884), -(hAPP(c_Int_Oring__1__class_Oof__int(_1029884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1029886), _1029888)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029884), hAPP(c_Int_Oring__1__class_Oof__int(_1029884), _1029886)), hAPP(c_Int_Oring__1__class_Oof__int(_1029884), _1029888)))], (16168 ^ _775828) ^ [_1050285, _1050287, _1050289, _1050291, _1050293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050285), _1050287)), 16171 ^ _775828 : [(16178 ^ _775828) ^ [] : [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), _1050287), _1050285)), _1050289)), _1050291)), _1050293)), -(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), _1050287), _1050289)), _1050291)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050285), _1050289)), _1050293))))], (16172 ^ _775828) ^ [] : [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), _1050287), _1050289)), _1050291)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050285), _1050289)), _1050293))), -(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), _1050287), _1050285)), _1050289)), _1050291)), _1050293)))]]], (51350 ^ _775828) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (40754 ^ _775828) ^ [_1559321, _1559323, _1559325, _1559327, _1559329] : [-(hAPP(c_Set_Ovimage(_1559321, _1559323, _1559325), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1559323, tc_HOL_Obool)), _1559327), _1559329)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1559321, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1559321, _1559323, _1559325), _1559327)), hAPP(c_Set_Ovimage(_1559321, _1559323, _1559325), _1559329)))], (46857 ^ _775828) ^ [_1707926, _1707928, _1707930, _1707932, _1707934] : [class_Orderings_Olinorder(_1707926), hBOOL(hAPP(hAPP(c_member(_1707926), hAPP(_1707928, _1707930)), hAPP(c_Set_Oimage(_1707932, _1707926, _1707928), hAPP(c_List_Oset(_1707932), _1707934)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1707932, _1707926, _1707928, _1707930, _1707934) = _1707934)], (49148 ^ _775828) ^ [_1762378, _1762380, _1762382] : [-(c_List_Olast(_1762378, hAPP(hAPP(c_List_Oappend(_1762378), _1762380), hAPP(hAPP(c_List_Olist_OCons(_1762378), _1762382), c_List_Olist_ONil(_1762378)))) = _1762382)], (752 ^ _775828) ^ [_787282, _787284, _787286, _787288, _787290, _787292] : [-(c_Relation_Osingle__valued(_787290, _787286, _787282)), c_Relation_Osingle__valued(_787292, _787288, _787284), _787292 = _787290, _787288 = _787286, _787284 = _787282], (48205 ^ _775828) ^ [_1740306, _1740308, _1740310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740306), tc_List_Olist(_1740306))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740306), tc_List_Olist(_1740306)), c_List_Olist_ONil(_1740306)), _1740308)), c_List_Olistrel1(_1740306, _1740310)))], (26459 ^ _775828) ^ [_1243170, _1243172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243170), _1243172)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243172), _1243170))], (51150 ^ _775828) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (17657 ^ _775828) ^ [_1078183] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078183)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078183)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078183))], (33663 ^ _775828) ^ [_1400694, _1400696, _1400698] : [c_Wellfounded_Owf(_1400694, _1400696), -(c_Wellfounded_Owf(_1400694, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1400694, _1400694), tc_HOL_Obool)), _1400696), _1400698)))], (19806 ^ _775828) ^ [_1115948] : [class_Int_Onumber__ring(_1115948), c_Int_Oiszero(_1115948, hAPP(c_Int_Onumber__class_Onumber__of(_1115948), c_Int_OBit1(c_Int_OPls)))], (35879 ^ _775828) ^ [_1449620, _1449622, _1449624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449620)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449622), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1449624)), 35889 ^ _775828 : [(35895 ^ _775828) ^ [] : [-(_1449622 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35891 ^ [_1449620, _1449622, _1449624]), 35888 ^ [_1449620, _1449622, _1449624]))], (35893 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35891 ^ [_1449620, _1449622, _1449624]), _1449624)))], (35890 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35888 ^ [_1449620, _1449622, _1449624]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449620))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449622), _1449620) = _1449622)], (51240 ^ _775828) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (13014 ^ _775828) ^ [_990965, _990967, _990969] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_990965, _990967, _990969)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _990969)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46758 ^ _775828) ^ [_1705815, _1705817, _1705819, _1705821] : [class_Groups_Ocomm__monoid__add(_1705815), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705815), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1705815), _1705817), c_List_Oupto(_1705819, _1705821))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1705815), _1705817), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1705819, _1705821))))], (18011 ^ _775828) ^ [_1084508, _1084510, _1084512, _1084514] : [class_Rings_Olinordered__semidom(_1084508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084508), c_Groups_Oone__class_Oone(_1084508)), _1084510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084508), hAPP(hAPP(c_Power_Opower__class_Opower(_1084508), _1084510), _1084512)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084508), _1084510), _1084514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084512), _1084514)))], (16555 ^ _775828) ^ [_1057352, _1057354] : [class_Groups_Oordered__ab__group__add__abs(_1057352), 16558 ^ _775828 : [(16565 ^ _775828) ^ [] : [_1057354 = c_Groups_Ozero__class_Ozero(_1057352), -(hAPP(c_Groups_Oabs__class_Oabs(_1057352), _1057354) = c_Groups_Ozero__class_Ozero(_1057352))], (16559 ^ _775828) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1057352), _1057354) = c_Groups_Ozero__class_Ozero(_1057352), -(_1057354 = c_Groups_Ozero__class_Ozero(_1057352))]]], (28551 ^ _775828) ^ [_1288618, _1288620, _1288622] : [class_Lattices_Osemilattice__sup(_1288618), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288618), _1288620), _1288622)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288618), _1288622), _1288620) = _1288622)], (13640 ^ _775828) ^ [_1002749, _1002751] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_1002749, _1002751)))), hBOOL(hAPP(c_Com_OWT, _1002749)), hBOOL(hAPP(c_Com_OWT, _1002751))], (2248 ^ _775828) ^ [_808703, _808705, _808707, _808709] : [-(c_Nitpick_Onat__gcd(_808709, _808705) = c_Nitpick_Onat__gcd(_808707, _808703)), _808709 = _808707, _808705 = _808703], (14864 ^ _775828) ^ [_1024670, _1024672, _1024674] : [class_Divides_Osemiring__div(_1024670), -(_1024672 = c_Groups_Ozero__class_Ozero(_1024670)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024670), _1024674), _1024672)), _1024672) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024670), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024670), _1024674), _1024672)), c_Groups_Oone__class_Oone(_1024670)))], (36729 ^ _775828) ^ [_1465821, _1465823, _1465825] : [class_Orderings_Oord(_1465821), 36732 ^ _775828 : [(36739 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1465821), _1465823), _1465825)), -(hBOOL(hAPP(hAPP(c_member(_1465821), _1465823), hAPP(c_SetInterval_Oord__class_OlessThan(_1465821), _1465825))))], (36733 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1465821), _1465823), hAPP(c_SetInterval_Oord__class_OlessThan(_1465821), _1465825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1465821), _1465823), _1465825)))]]], (12494 ^ _775828) ^ [_982012, _982014] : [12495 ^ _775828 : [(12496 ^ _775828) ^ [_982065] : [_982014 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _982012), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982065))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _982012), _982014)))], (47764 ^ _775828) ^ [_1729629, _1729631, _1729633, _1729635, _1729637] : [-(hAPP(hAPP(c_List_Olist_OCons(_1729629), _1729631), _1729633) = hAPP(hAPP(c_List_Oappend(_1729629), _1729635), _1729637)), 47765 ^ _775828 : [(47772 ^ _775828) ^ [_1729812] : [hAPP(hAPP(c_List_Olist_OCons(_1729629), _1729631), _1729812) = _1729635, _1729633 = hAPP(hAPP(c_List_Oappend(_1729629), _1729812), _1729637)], (47766 ^ _775828) ^ [] : [_1729635 = c_List_Olist_ONil(_1729629), hAPP(hAPP(c_List_Olist_OCons(_1729629), _1729631), _1729633) = _1729637]]], (7423 ^ _775828) ^ [_894320, _894322] : [c_Option_Ois__none(_894320, hAPP(c_Option_Ooption_OSome(_894320), _894322))], (44922 ^ _775828) ^ [_1659607, _1659609, _1659611, _1659613, _1659615] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659607, tc_fun(_1659609, tc_HOL_Obool)), _1659611), hAPP(hAPP(c_COMBS(_1659607, tc_fun(_1659609, tc_HOL_Obool), tc_fun(_1659609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659609, tc_HOL_Obool), tc_fun(tc_fun(_1659609, tc_HOL_Obool), tc_fun(_1659609, tc_HOL_Obool)), _1659607), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659609, tc_HOL_Obool))), _1659613)), _1659615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659609, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659609, tc_HOL_Obool), hAPP(c_Set_Oimage(_1659607, tc_fun(_1659609, tc_HOL_Obool), _1659613), _1659611))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659609, tc_HOL_Obool), hAPP(c_Set_Oimage(_1659607, tc_fun(_1659609, tc_HOL_Obool), _1659615), _1659611))))], (27418 ^ _775828) ^ [_1262721, _1262723, _1262725, _1262727] : [hBOOL(hAPP(c_Predicate_ORangeP(_1262721, _1262723, _1262725), _1262727)), -(hBOOL(hAPP(hAPP(_1262725, 27421 ^ [_1262721, _1262723, _1262725, _1262727]), _1262727)))], (41468 ^ _775828) ^ [_1578051, _1578053, _1578055, _1578057] : [-(hAPP(c_Set_OCollect(tc_prod(_1578051, _1578053)), hAPP(c_Product__Type_Oprod_Oprod__case(_1578051, _1578053, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1578051, tc_fun(_1578053, tc_HOL_Obool), tc_fun(_1578053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578053, tc_HOL_Obool), tc_fun(_1578053, tc_HOL_Obool)), _1578051), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578053)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578051), c_fconj), _1578055))), _1578057))) = hAPP(hAPP(c_Product__Type_OSigma(_1578051, _1578053), hAPP(c_Set_OCollect(_1578051), _1578055)), hAPP(c_COMBK(tc_fun(_1578053, tc_HOL_Obool), _1578051), hAPP(c_Set_OCollect(_1578053), _1578057))))], (12540 ^ _775828) ^ [_982663] : [class_Rings_Oring__1(_982663), -(hBOOL(hAPP(hAPP(c_member(_982663), c_Groups_Ozero__class_Ozero(_982663)), c_Int_Oring__1__class_OInts(_982663))))], (8019 ^ _775828) ^ [_904663, _904665, _904667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _904663)), 8022 ^ _775828 : [(8029 ^ _775828) ^ [] : [_904665 = _904667, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904663), _904665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904663), _904667))], (8023 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904663), _904665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904663), _904667), -(_904665 = _904667)]]], (11648 ^ _775828) ^ [_967204, _967206] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967204), _967206) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 11649 ^ _775828 : [(11656 ^ _775828) ^ [] : [_967204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _967206 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11650 ^ _775828) ^ [] : [_967204 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19942 ^ _775828) ^ [_1118208, _1118210] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118208)))), _1118210) = 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)))), _1118208)), _1118210))], (47219 ^ _775828) ^ [_1717691, _1717693, _1717695] : [-(c_List_Osublist(_1717691, _1717693, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1717695)) = hAPP(hAPP(c_List_Otake(_1717691), _1717695), _1717693))], (46666 ^ _775828) ^ [_1703385, _1703387, _1703389, _1703391] : [-(hBOOL(hAPP(hAPP(c_member(_1703385), _1703387), hAPP(c_List_Oset(_1703385), _1703389)))), hBOOL(hAPP(hAPP(c_member(_1703385), _1703387), hAPP(c_List_Oset(_1703385), c_List_Osublist(_1703385, _1703389, _1703391))))], (14037 ^ _775828) ^ [_1010157, _1010159, _1010161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010157)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010159, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010161), _1010157)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010161), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1010159), _1010161), _1010157))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010159, _1010161)))], (2968 ^ _775828) ^ [_820421, _820423, _820425, _820427, _820429, _820431] : [-(c_SetInterval_Oord_OatLeast(_820431, _820427, _820423) = c_SetInterval_Oord_OatLeast(_820429, _820425, _820421)), _820431 = _820429, _820427 = _820425, _820423 = _820421], (44605 ^ _775828) ^ [_1652299, _1652301, _1652303, _1652305, _1652307] : [44607 ^ _775828 : [(44610 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1652305, 44606 ^ [_1652299, _1652301, _1652303, _1652305, _1652307]), _1652307))], (44608 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652299), 44606 ^ [_1652299, _1652301, _1652303, _1652305, _1652307]), _1652303)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652299, tc_fun(_1652301, tc_HOL_Obool)), _1652303), _1652305), _1652307)))], (10830 ^ _775828) ^ [_952923, _952925] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952923), hAPP(c_Nat_OSuc, _952925)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952923), _952925)))], (44085 ^ _775828) ^ [_1637937, _1637939, _1637941, _1637943, _1637945, _1637947] : [hBOOL(hAPP(hAPP(c_member(_1637937), _1637939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637941, tc_fun(_1637937, tc_HOL_Obool)), _1637943), _1637945))), hBOOL(hAPP(hAPP(c_member(_1637941), _1637947), _1637943)), -(hBOOL(hAPP(hAPP(c_member(_1637937), _1637939), hAPP(_1637945, _1637947))))], (51494 ^ _775828) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (2370 ^ _775828) ^ [_810566, _810568, _810570, _810572] : [-(c_Nitpick_OAbs__Frac(_810572, _810568) = c_Nitpick_OAbs__Frac(_810570, _810566)), _810572 = _810570, _810568 = _810566], (24681 ^ _775828) ^ [_1209475, _1209477] : [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), _1209475), _1209477))), 24684 ^ _775828 : [(24691 ^ _775828) ^ [] : [-(_1209477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1209475, _1209477) = c_Nitpick_Onat__gcd(_1209477, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209475, _1209477)))], (24685 ^ _775828) ^ [] : [_1209477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1209475, _1209477) = _1209475)]]], (45007 ^ _775828) ^ [_1661455, _1661457, _1661459] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1661455, tc_HOL_Obool)), _1661457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1661455), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661455, tc_HOL_Obool), _1661457))), 45017 ^ _775828 : [(45020 ^ _775828) ^ [] : [hAPP(c_Finite__Set_Ocard(_1661455), 45016 ^ [_1661455, _1661457, _1661459]) = _1661459], (45018 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1661455, tc_HOL_Obool)), 45016 ^ [_1661455, _1661457, _1661459]), _1661457)))]], 45024 ^ _775828 : [(45028 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1661455, tc_HOL_Obool)), 45026 ^ [_1661455, _1661457, _1661459]), _1661457)))], (45030 ^ _775828) ^ [] : [45023 ^ [_1661455, _1661457, _1661459] = 45026 ^ [_1661455, _1661457, _1661459]], (45032 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661455, tc_HOL_Obool)), 45023 ^ [_1661455, _1661457, _1661459]), 45026 ^ [_1661455, _1661457, _1661459]) = c_Orderings_Obot__class_Obot(tc_fun(_1661455, tc_HOL_Obool))], (45025 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1661455, tc_HOL_Obool)), 45023 ^ [_1661455, _1661457, _1661459]), _1661457)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1661459), hAPP(c_Finite__Set_Ocard(tc_fun(_1661455, tc_HOL_Obool)), _1661457)) = hAPP(c_Finite__Set_Ocard(_1661455), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661455, tc_HOL_Obool), _1661457)))], (24665 ^ _775828) ^ [_1209285, _1209287] : [_1209285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1209287, _1209285) = _1209287)], (41725 ^ _775828) ^ [_1583557, _1583559, _1583561] : [class_Lattices_Oab__semigroup__idem__mult(_1583557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583557), _1583559)), -(_1583559 = c_Orderings_Obot__class_Obot(tc_fun(_1583557, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583557), _1583561)), -(_1583561 = c_Orderings_Obot__class_Obot(tc_fun(_1583557, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1583557, c_Groups_Otimes__class_Otimes(_1583557)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1583557, tc_HOL_Obool)), _1583559), _1583561)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1583557), hAPP(c_Finite__Set_Ofold1(_1583557, c_Groups_Otimes__class_Otimes(_1583557)), _1583559)), hAPP(c_Finite__Set_Ofold1(_1583557, c_Groups_Otimes__class_Otimes(_1583557)), _1583561)))], (14566 ^ _775828) ^ [_1019699, _1019701, _1019703] : [class_Divides_Osemiring__div(_1019699), -(_1019701 = c_Groups_Ozero__class_Ozero(_1019699)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019699), _1019703), _1019701)), _1019701) = _1019703)], (19520 ^ _775828) ^ [_1111314, _1111316] : [c_Int_OBit1(_1111314) = c_Int_OBit1(_1111316), -(_1111314 = _1111316)], (10906 ^ _775828) ^ [_954357, _954359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954357)), _954359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954357), _954359)))], (30179 ^ _775828) ^ [_1325840] : [c_Nat__Transfer_Onat__set(_1325840), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1325840) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1325840)))], (24290 ^ _775828) ^ [_1201846, _1201848, _1201850, _1201852] : [class_Groups_Oordered__ab__group__add(_1201846), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201846), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201846), _1201848), _1201850)), _1201852) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201846), _1201848), _1201852)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201846), _1201850), _1201852)))], (5739 ^ _775828) ^ [_867281, _867283, _867285] : [hBOOL(hAPP(hAPP(c_member(_867281), _867283), hAPP(c_fequal, _867285))), -(_867283 = _867285)], (14530 ^ _775828) ^ [_1019080, _1019082, _1019084] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019080), _1019082)), _1019084) = 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), _1019080), _1019084)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019082), _1019084))), 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, _1019080, _1019084)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019082, _1019084))), _1019084)))], (10762 ^ _775828) ^ [_951730, _951732, _951734] : [class_Groups_Oab__group__add(_951730), -(hAPP(c_Groups_Ouminus__class_Ouminus(_951730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951730), _951732), _951734)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951730), hAPP(c_Groups_Ouminus__class_Ouminus(_951730), _951732)), hAPP(c_Groups_Ouminus__class_Ouminus(_951730), _951734)))], (48948 ^ _775828) ^ [_1758319, _1758321] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1758319)), c_List_Olist_ONil(_1758319)), c_List_Olists(_1758319, _1758321))))], (51478 ^ _775828) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (7509 ^ _775828) ^ [_895675] : [class_Groups_Ogroup__add(_895675), -(hAPP(c_Groups_Ouminus__class_Ouminus(_895675), c_Groups_Ozero__class_Ozero(_895675)) = c_Groups_Ozero__class_Ozero(_895675))], (46273 ^ _775828) ^ [_1691616, _1691618, _1691620] : [_1691616 = _1691618, 46276 ^ _775828 : [(46279 ^ _775828) ^ [_1691772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1691620, _1691620)), _1691772), hAPP(c_List_Oset(tc_prod(_1691620, _1691620)), hAPP(hAPP(c_List_Ozip(_1691620, _1691620), _1691616), _1691618)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1691620, _1691620, tc_HOL_Obool), c_fequal), _1691772)))], (46277 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691620)), _1691616) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691620)), _1691618))]]], (15458 ^ _775828) ^ [_1035721, _1035723] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035721), _1035723)), _1035721)))], (40247 ^ _775828) ^ [_1547343, _1547345] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547343), _1547345)), 40250 ^ _775828 : [(40257 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547343), c_Orderings_Otop__class_Otop(tc_fun(_1547343, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547343), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547343, tc_HOL_Obool)), _1547345))))], (40251 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547343), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547343, tc_HOL_Obool)), _1547345))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547343), c_Orderings_Otop__class_Otop(tc_fun(_1547343, tc_HOL_Obool)))))]]], (48621 ^ _775828) ^ [_1751331, _1751333, _1751335] : [-(hAPP(c_List_Ohd(_1751331), hAPP(hAPP(c_List_Olist_OCons(_1751331), _1751333), _1751335)) = _1751333)], (35717 ^ _775828) ^ [_1446534, _1446536] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446534), _1446536))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1446536, _1446534) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1446536), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446536), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1446534)))], (47329 ^ _775828) ^ [_1719894, _1719896, _1719898, _1719900] : [_1719900 = c_List_Olist_ONil(_1719894), -(hAPP(hAPP(c_List_Omap(_1719894, _1719896), _1719898), _1719900) = c_List_Olist_ONil(_1719896))], (29983 ^ _775828) ^ [_1322312, _1322314, _1322316] : [_1322312 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1322314, _1322314), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1322314, _1322314), tc_HOL_Obool)), _1322312), _1322316)))], (48793 ^ _775828) ^ [_1754689, _1754691, _1754693, _1754695] : [-(hAPP(c_List_Ofoldl(_1754689, _1754691, _1754693, _1754695), c_List_Olist_ONil(_1754691)) = _1754695)], (842 ^ _775828) ^ [_788699, _788701, _788703, _788705, _788707, _788709] : [-(c_Finite__Set_Ofun__left__comm__idem(_788707, _788703, _788699)), c_Finite__Set_Ofun__left__comm__idem(_788709, _788705, _788701), _788709 = _788707, _788705 = _788703, _788701 = _788699], (20138 ^ _775828) ^ [_1121762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121762), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1121762)), c_Int_OPls)))], (31511 ^ _775828) ^ [_1355366, _1355368] : [class_Orderings_Olinorder(_1355366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355366), _1355368)), -(_1355368 = c_Orderings_Obot__class_Obot(tc_fun(_1355366, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1355366), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355366), 31524 ^ [_1355366, _1355368]), 31525 ^ [_1355366, _1355368])), hAPP(hAPP(c_Set_Oinsert(_1355366), 31524 ^ [_1355366, _1355368]), hAPP(hAPP(c_Set_Oinsert(_1355366), 31525 ^ [_1355366, _1355368]), c_Orderings_Obot__class_Obot(tc_fun(_1355366, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1355366), c_Big__Operators_Olattice_OSup__fin(_1355366, c_Orderings_Oord__class_Omax(_1355366), _1355368)), _1355368)))], (28354 ^ _775828) ^ [_1284776, _1284778, _1284780, _1284782] : [28356 ^ _775828 : [(28359 ^ _775828) ^ [] : [hBOOL(hAPP(_1284782, 28355 ^ [_1284776, _1284778, _1284780, _1284782]))], (28357 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1284776), 28355 ^ [_1284776, _1284778, _1284780, _1284782]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284776, tc_HOL_Obool)), _1284778), _1284780))))]], 28360 ^ _775828 : [(28367 ^ _775828) ^ [_1285093] : [hBOOL(hAPP(hAPP(c_member(_1284776), _1285093), _1284780)), -(hBOOL(hAPP(_1284782, _1285093)))], (28361 ^ _775828) ^ [_1284996] : [hBOOL(hAPP(hAPP(c_member(_1284776), _1284996), _1284778)), -(hBOOL(hAPP(_1284782, _1284996)))]]], (26892 ^ _775828) ^ [_1250935, _1250937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250937)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250935), _1250937)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250937), _1250935)), -(_1250935 = _1250937)], (5240 ^ _775828) ^ [_855955, _855957] : [_855957 = _855955, -(c_List_Odistinct(_855957) = c_List_Odistinct(_855955))], (39708 ^ _775828) ^ [_1535783, _1535785, _1535787, _1535789, _1535791] : [-(_1535783 = c_Orderings_Obot__class_Obot(tc_fun(_1535785, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1535787), _1535789), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535785, tc_fun(_1535787, tc_HOL_Obool)), _1535783), _1535791)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535785, tc_fun(_1535787, tc_HOL_Obool)), _1535783), hAPP(hAPP(c_COMBB(tc_fun(_1535787, tc_HOL_Obool), tc_fun(_1535787, tc_HOL_Obool), _1535785), hAPP(c_Set_Oinsert(_1535787), _1535789)), _1535791)))], (42129 ^ _775828) ^ [_1593710, _1593712, _1593714] : [c_Relation_Orefl__on(_1593710, _1593712, _1593714), 42132 ^ _775828 : [(42135 ^ _775828) ^ [_1593892] : [hBOOL(hAPP(hAPP(c_member(_1593710), _1593892), _1593712)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593710, _1593710)), hAPP(hAPP(c_Product__Type_OPair(_1593710, _1593710), _1593892), _1593892)), _1593714)))], (42133 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1593710, _1593710), tc_HOL_Obool)), _1593714), hAPP(hAPP(c_Product__Type_OSigma(_1593710, _1593710), _1593712), hAPP(c_COMBK(tc_fun(_1593710, tc_HOL_Obool), _1593710), _1593712)))))]]], (49481 ^ _775828) ^ [_1769558, _1769560, _1769562, _1769564, _1769566] : [c_List_Opartition(_1769558, _1769560, _1769562) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769558), tc_List_Olist(_1769558)), _1769564), _1769566), 49484 ^ _775828 : [(49491 ^ _775828) ^ [_1769820] : [hBOOL(hAPP(hAPP(c_member(_1769558), _1769820), hAPP(c_List_Oset(_1769558), _1769566))), hBOOL(hAPP(_1769560, _1769820))], (49485 ^ _775828) ^ [_1769711] : [hBOOL(hAPP(hAPP(c_member(_1769558), _1769711), hAPP(c_List_Oset(_1769558), _1769564))), -(hBOOL(hAPP(_1769560, _1769711)))]]], (17265 ^ _775828) ^ [_1071185] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071185), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1071185) = _1071185)], (19656 ^ _775828) ^ [_1113564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113564), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1113564)), c_Int_OMin)))], (9271 ^ _775828) ^ [_924280, _924282, _924284, _924286, _924288] : [class_Rings_Oordered__semiring(_924280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924280), _924282), _924284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924280), _924286), _924288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924280), c_Groups_Ozero__class_Ozero(_924280)), _924282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924280), c_Groups_Ozero__class_Ozero(_924280)), _924286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924280), _924282), _924286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924280), _924284), _924288))))], (23466 ^ _775828) ^ [_1185770, _1185772, _1185774, _1185776] : [-(c_Nat_Onat_Onat__case(_1185770, _1185772, _1185774, hAPP(c_Nat_OSuc, _1185776)) = hAPP(_1185774, _1185776))], (45333 ^ _775828) ^ [_1668743, _1668745, _1668747, _1668749, _1668751, _1668753] : [-(hAPP(c_Map_Omap__add(_1668743, _1668745, _1668747, _1668749), _1668751) = hAPP(c_Option_Ooption_OSome(_1668745), _1668753)), 45334 ^ _775828 : [(45337 ^ _775828) ^ [] : [hAPP(_1668749, _1668751) = c_Option_Ooption_ONone(_1668745), hAPP(_1668747, _1668751) = hAPP(c_Option_Ooption_OSome(_1668745), _1668753)], (45335 ^ _775828) ^ [] : [hAPP(_1668749, _1668751) = hAPP(c_Option_Ooption_OSome(_1668745), _1668753)]]], (11494 ^ _775828) ^ [_964789, _964791, _964793] : [class_Groups_Ogroup__add(_964789), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964789), _964791), _964793) = c_Groups_Ozero__class_Ozero(_964789), -(hAPP(c_Groups_Ouminus__class_Ouminus(_964789), _964791) = _964793)], (26009 ^ _775828) ^ [_1235131, _1235133] : [_1235131 = _1235133, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235131), _1235133)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235133), _1235131)))], (18071 ^ _775828) ^ [_1085699, _1085701, _1085703] : [class_Rings_Olinordered__semidom(_1085699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085699), c_Groups_Ozero__class_Ozero(_1085699)), _1085701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085699), _1085701), c_Groups_Oone__class_Oone(_1085699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085699), _1085701), hAPP(hAPP(c_Power_Opower__class_Opower(_1085699), _1085701), _1085703))), hAPP(hAPP(c_Power_Opower__class_Opower(_1085699), _1085701), _1085703))))], (29207 ^ _775828) ^ [_1305265, _1305267, _1305269, _1305271] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305265, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1305265), _1305267), _1305269)), _1305271) = hAPP(hAPP(c_Set_Oinsert(_1305265), _1305267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305265, tc_HOL_Obool)), _1305269), _1305271)))], (20524 ^ _775828) ^ [_1128535, _1128537, _1128539] : [class_Rings_Olinordered__semidom(_1128535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128535), hAPP(hAPP(c_Power_Opower__class_Opower(_1128535), _1128537), 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(_1128535), _1128539), 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(_1128535), c_Groups_Ozero__class_Ozero(_1128535)), _1128539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128535), _1128537), _1128539)))], (296 ^ _775828) ^ [_780090, _780092, _780094, _780096] : [-(c_Wellfounded_Oacyclic(_780094, _780090)), c_Wellfounded_Oacyclic(_780096, _780092), _780096 = _780094, _780092 = _780090], (31023 ^ _775828) ^ [_1344430, _1344432, _1344434, _1344436, _1344438, _1344440] : [c_Finite__Set_Ofolding__image__simple(_1344430, _1344432, _1344434, _1344436, _1344438, _1344440), -(hAPP(_1344440, c_Orderings_Obot__class_Obot(tc_fun(_1344432, tc_HOL_Obool))) = _1344436)], (51322 ^ _775828) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (10272 ^ _775828) ^ [_942290, _942292, _942294] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942292), _942294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942290), _942294)))], (24967 ^ _775828) ^ [_1215606, _1215608, _1215610, _1215612, _1215614] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215606, tc_HOL_Obool)), _1215608), hAPP(c_Set_Oimage(_1215610, _1215606, _1215612), _1215614)))), 24968 ^ _775828 : [(24969 ^ _775828) ^ [_1215686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215610, tc_HOL_Obool)), _1215686), _1215614)), _1215608 = hAPP(c_Set_Oimage(_1215610, _1215606, _1215612), _1215686)]]], (32173 ^ _775828) ^ [_1370505, _1370507] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1370505, _1370507)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1370507), hAPP(c_Nat_OSuc, _1370505)))], (15244 ^ _775828) ^ [_1031738, _1031740, _1031742, _1031744, _1031746] : [class_Groups_Oordered__ab__group__add(_1031738), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031738), _1031740), _1031742) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031738), _1031744), _1031746), 15251 ^ _775828 : [(15258 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031738), _1031744), _1031746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031738), _1031740), _1031742)))], (15252 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031738), _1031740), _1031742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031738), _1031744), _1031746)))]]], (20380 ^ _775828) ^ [_1126023, _1126025] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1126023)), c_Int_OBit1(_1126025)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126023), c_Int_Osucc(_1126025))))], (37034 ^ _775828) ^ [_1472843, _1472845, _1472847, _1472849] : [class_Groups_Ocomm__monoid__add(_1472843), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1472843), _1472845), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1472847)), hAPP(c_Nat_OSuc, _1472849))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1472843), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1472843, tc_Nat_Onat), _1472845), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1472847), _1472849)))], (20374 ^ _775828) ^ [_1125912] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1125912)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1125912)))], (7707 ^ _775828) ^ [_898811, _898813, _898815] : [7708 ^ _775828 : [(7711 ^ _775828) ^ [] : [_898811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7709 ^ _775828) ^ [] : [_898813 = _898815]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898811), _898813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898811), _898815))], (12063 ^ _775828) ^ [_974692, _974694, _974696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _974692)), 12066 ^ _775828 : [(12073 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974694), _974696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974692), _974694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974692), _974696))))], (12067 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974692), _974694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974692), _974696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974694), _974696)))]]], (14461 ^ _775828) ^ [_1017997, _1017999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017997)), 14464 ^ _775828 : [(14471 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017999), 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), _1017999), _1017997)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14465 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017999), _1017997)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017999), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44391 ^ _775828) ^ [_1646788, _1646790, _1646792, _1646794, _1646796, _1646798] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646788, tc_fun(_1646790, tc_HOL_Obool)), _1646792), hAPP(hAPP(c_COMBC(_1646788, tc_fun(_1646794, tc_fun(_1646790, tc_HOL_Obool)), tc_fun(_1646790, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1646794, tc_HOL_Obool), tc_fun(tc_fun(_1646794, tc_fun(_1646790, tc_HOL_Obool)), tc_fun(_1646790, tc_HOL_Obool)), _1646788), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646794, tc_fun(_1646790, tc_HOL_Obool))), _1646796)), _1646798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646794, tc_fun(_1646790, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646788, tc_fun(_1646794, tc_HOL_Obool)), _1646792), _1646796)), _1646798))], (37629 ^ _775828) ^ [_1487562, _1487564, _1487566, _1487568, _1487570] : [class_Groups_Oordered__comm__monoid__add(_1487562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487564), _1487566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487564, tc_HOL_Obool)), _1487568), _1487566)), 37643 ^ _775828 : [(37646 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487562), c_Groups_Ozero__class_Ozero(_1487562)), hAPP(_1487570, 37642 ^ [_1487562, _1487564, _1487566, _1487568, _1487570])))], (37644 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487564), 37642 ^ [_1487562, _1487564, _1487566, _1487568, _1487570]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487564, tc_HOL_Obool)), _1487566), _1487568))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487562), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487564, _1487562), _1487570), _1487568)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487564, _1487562), _1487570), _1487566))))], (30165 ^ _775828) ^ [_1325668, _1325670] : [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), _1325668, _1325670), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325668), _1325670))], (28844 ^ _775828) ^ [_1294739, _1294741] : [c_Nat__Transfer_Onat__set(_1294739), c_Nat__Transfer_Onat__set(_1294741), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1294739), _1294741) = 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), _1294739)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1294741))))], (48179 ^ _775828) ^ [_1739400, _1739402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1739400), tc_List_Olist(_1739400)), tc_HOL_Obool)), c_List_Olistrel(_1739400, _1739402)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739400), c_List_Olistrel1(_1739400, _1739402)))))], (15750 ^ _775828) ^ [_1041344, _1041346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041344), _1041346)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1041346)), _1041344) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041346), _1041344)))], (36377 ^ _775828) ^ [_1458953, _1458955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1458953), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458955), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1458953))))), -(_1458953 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458955), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1458953))))], (6805 ^ _775828) ^ [_883640, _883642] : [_883640 = _883642, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883640) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883642))], (40493 ^ _775828) ^ [_1552566] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1552566), 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, _1552566)) = _1552566)], (44669 ^ _775828) ^ [_1654305, _1654307, _1654309] : [-(hAPP(c_Relation_ODomain(_1654305, _1654307), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1654305, _1654307), tc_HOL_Obool), _1654309)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1654305, _1654307), tc_HOL_Obool), tc_fun(_1654305, tc_HOL_Obool)), _1654309), c_Relation_ODomain(_1654305, _1654307)))], (43204 ^ _775828) ^ [_1618787, _1618789, _1618791, _1618793, _1618795, _1618797] : [c_Finite__Set_Ofolding__idem(_1618787, _1618789, _1618791, _1618793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618787), _1618795)), hBOOL(hAPP(hAPP(c_member(_1618787), _1618797), _1618795)), -(hAPP(c_Fun_Ocomp(_1618789, _1618789, _1618789, hAPP(_1618793, _1618795)), hAPP(_1618791, _1618797)) = hAPP(_1618793, _1618795))], (45678 ^ _775828) ^ [_1676893, _1676895, _1676897, _1676899, _1676901] : [-(c_Map_Odom(_1676893, _1676895, hAPP(hAPP(c_COMBS(_1676893, tc_Option_Ooption(_1676897), tc_Option_Ooption(_1676895)), hAPP(hAPP(c_COMBB(tc_fun(_1676897, _1676895), tc_fun(tc_Option_Ooption(_1676897), tc_Option_Ooption(_1676895)), _1676893), c_Option_Omap(_1676897, _1676895)), _1676899)), _1676901)) = c_Map_Odom(_1676893, _1676897, _1676901))], (16096 ^ _775828) ^ [_1048472, _1048474, _1048476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048472), _1048474)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048474), _1048472))), _1048476) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1048474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048472), _1048476)))], (1720 ^ _775828) ^ [_799946, _799948] : [-(class_Power_Opower(_799946)), _799948 = _799946, class_Power_Opower(_799948)], (11767 ^ _775828) ^ [_969218, _969220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969218)), _969220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969218), _969220)))], (29463 ^ _775828) ^ [_1310293, _1310295, _1310297, _1310299, _1310301] : [hBOOL(hAPP(hAPP(_1310297, _1310301), _1310299)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1310293, _1310295, _1310297), _1310299), _1310301)))], (16383 ^ _775828) ^ [_1054303, _1054305, _1054307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1054307), 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), _1054307), _1054305))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1054303)))))], (15386 ^ _775828) ^ [_1034385, _1034387, _1034389] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034385), _1034387)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034385), _1034389)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034387), _1034389))], (40812 ^ _775828) ^ [_1560811, _1560813, _1560815, _1560817, _1560819] : [hBOOL(hAPP(hAPP(c_member(_1560811), _1560813), hAPP(c_Set_Ovimage(_1560811, _1560815, _1560817), _1560819))), -(hBOOL(hAPP(hAPP(c_member(_1560815), hAPP(_1560817, _1560813)), _1560819)))], (27489 ^ _775828) ^ [_1264208, _1264210, _1264212, _1264214] : [hBOOL(hAPP(hAPP(c_member(_1264208), _1264210), c_SetInterval_Oord_OgreaterThan(_1264208, _1264212, _1264214))), -(hBOOL(hAPP(hAPP(_1264212, _1264214), _1264210)))], (10047 ^ _775828) ^ [_938375, _938377] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938377), _938375))))], (29881 ^ _775828) ^ [_1319132, _1319134, _1319136, _1319138] : [hBOOL(hAPP(hAPP(c_member(_1319132), _1319134), _1319136)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319132, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1319132), _1319134), _1319138)), _1319136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319132, tc_HOL_Obool)), _1319138), _1319136))], (35103 ^ _775828) ^ [_1433358, _1433360, _1433362, _1433364, _1433366] : [class_Groups_Ocomm__monoid__mult(_1433358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433360), _1433362)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433360), _1433364)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433360, tc_HOL_Obool)), _1433362), _1433364) = c_Orderings_Obot__class_Obot(tc_fun(_1433360, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1433358, _1433360, c_Groups_Otimes__class_Otimes(_1433358)), _1433366), c_Groups_Oone__class_Oone(_1433358)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1433360, tc_HOL_Obool)), _1433362), _1433364)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433358), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1433358, _1433360, c_Groups_Otimes__class_Otimes(_1433358)), _1433366), c_Groups_Oone__class_Oone(_1433358)), _1433362)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1433358, _1433360, c_Groups_Otimes__class_Otimes(_1433358)), _1433366), c_Groups_Oone__class_Oone(_1433358)), _1433364)))], (35449 ^ _775828) ^ [_1441826, _1441828, _1441830, _1441832] : [class_Orderings_Olinorder(_1441826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441826), _1441828), _1441830)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441826), _1441830), _1441832)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441826, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1441826, _1441828, _1441830)), c_SetInterval_Oord__class_OatLeastAtMost(_1441826, _1441830, _1441832)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1441826, _1441828, _1441832))], (10950 ^ _775828) ^ [_955051, _955053] : [10951 ^ _775828 : [(10954 ^ _775828) ^ [] : [_955051 = hAPP(c_Nat_OSuc, _955053)], (10952 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955051), _955053))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955051), hAPP(c_Nat_OSuc, _955053))))], (49513 ^ _775828) ^ [_1770841, _1770843, _1770845, _1770847, _1770849, _1770851] : [hAPP(c_Map_Omap__of(_1770841, _1770843, _1770845), _1770847) = hAPP(c_Option_Ooption_OSome(_1770843), _1770849), hBOOL(hAPP(hAPP(_1770851, _1770847), _1770849)), -(hAPP(c_Map_Omap__of(_1770841, _1770843, hAPP(c_List_Ofilter(tc_prod(_1770841, _1770843), hAPP(c_Product__Type_Oprod_Oprod__case(_1770841, _1770843, tc_HOL_Obool), _1770851)), _1770845)), _1770847) = hAPP(c_Option_Ooption_OSome(_1770843), _1770849))], (31113 ^ _775828) ^ [_1346211, _1346213] : [-(c_Nitpick_Owf_H(_1346211, _1346213)), c_Wellfounded_Oacyclic(_1346211, _1346213), 31118 ^ _775828 : [(31121 ^ _775828) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (31119 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1346211, _1346211)), _1346213))]]], (40265 ^ _775828) ^ [_1547670, _1547672] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547670, tc_HOL_Obool)), _1547672), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547670, tc_HOL_Obool)), _1547672)) = c_Orderings_Otop__class_Otop(tc_fun(_1547670, tc_HOL_Obool)))], (12582 ^ _775828) ^ [_983381, _983383] : [class_Rings_Oring__1(_983381), hBOOL(hAPP(hAPP(c_member(_983381), _983383), c_Int_Oring__1__class_OInts(_983381))), -(hBOOL(hAPP(hAPP(c_member(_983381), hAPP(c_Groups_Ouminus__class_Ouminus(_983381), _983383)), c_Int_Oring__1__class_OInts(_983381))))], (13959 ^ _775828) ^ [_1008659, _1008661] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008659))), -(c_SMT_Oz3mod(_1008661, _1008659) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008661, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1008659)))], (35591 ^ _775828) ^ [_1444147, _1444149] : [class_Orderings_Oorder(_1444147), -(c_SetInterval_Oord__class_OatLeastAtMost(_1444147, _1444149, _1444149) = hAPP(hAPP(c_Set_Oinsert(_1444147), _1444149), c_Orderings_Obot__class_Obot(tc_fun(_1444147, tc_HOL_Obool))))], (23492 ^ _775828) ^ [_1186475, _1186477, _1186479, _1186481] : [-(c_Nat_Onat_Onat__case(_1186475, _1186477, _1186479, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1186481)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1186475), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1186481))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1186475, _1186475), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1186475, tc_fun(_1186475, _1186475)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1186475, tc_fun(_1186475, _1186475)), tc_Int_Oint), c_If(_1186475)), c_Nat__Numeral_Oneg)), _1186477)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1186475, tc_Int_Oint), _1186479), c_Int_Onat))))], (28785 ^ _775828) ^ [_1293767, _1293769] : [c_Nat__Transfer_Onat__set(_1293767), c_Nat__Transfer_Onat__set(_1293769), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1293767), _1293769)))], (2326 ^ _775828) ^ [_809890, _809892, _809894, _809896, _809898, _809900] : [-(c_Nitpick_Oof__frac(_809900, _809896, _809892) = c_Nitpick_Oof__frac(_809898, _809894, _809890)), _809900 = _809898, _809896 = _809894, _809892 = _809890], (2614 ^ _775828) ^ [_814528, _814530] : [_814530 = _814528, -(c_Lazy__Sequence_Ohb__not__seq(_814530) = c_Lazy__Sequence_Ohb__not__seq(_814528))], (36727 ^ _775828) ^ [_1465789] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1465789)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1465789))], (15384 ^ _775828) ^ [_1034334, _1034336, _1034338] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034334), _1034336)), _1034338) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034334), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034336), _1034338)))], (5416 ^ _775828) ^ [_858583, _858585] : [_858585 = _858583, -(c_member(_858585) = c_member(_858583))], (3770 ^ _775828) ^ [_833102, _833104, _833106, _833108] : [-(c_Relation_ORange(_833108, _833104) = c_Relation_ORange(_833106, _833102)), _833108 = _833106, _833104 = _833102], (14532 ^ _775828) ^ [_1019163, _1019165] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019163), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019165)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019163, _1019165)))], (51264 ^ _775828) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (29289 ^ _775828) ^ [_1307031, _1307033, _1307035] : [_1307035 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1307031, _1307033), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1307031, _1307033), _1307035) = c_Orderings_Obot__class_Obot(tc_fun(_1307033, tc_HOL_Obool)))], (16406 ^ _775828) ^ [_1054794, _1054796, _1054798] : [16408 ^ _775828 : [(16413 ^ _775828) ^ [] : [hBOOL(hAPP(_1054796, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16407 ^ [_1054794, _1054796, _1054798]), _1054794)))], (16411 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1054796, 16407 ^ [_1054794, _1054796, _1054798])))], (16409 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16407 ^ [_1054794, _1054796, _1054798]), _1054794)))]], hBOOL(hAPP(_1054796, _1054798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1054798), _1054794)), -(hBOOL(hAPP(_1054796, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27258 ^ _775828) ^ [_1258572, _1258574, _1258576] : [c_Relation_Ototal__on(_1258572, _1258574, hAPP(c_Relation_Oconverse(_1258572, _1258572), _1258576)), -(c_Relation_Ototal__on(_1258572, _1258574, _1258576))], (9991 ^ _775828) ^ [_937242, _937244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _937242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _937244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_937242, _937244))))], (51520 ^ _775828) ^ [_1808338, _1808340, _1808342, _1808344, _1808346, _1808348] : [-(hAPP(hAPP(hAPP(c_COMBC(_1808338, _1808340, _1808342), _1808344), _1808346), _1808348) = hAPP(hAPP(_1808344, _1808348), _1808346))], (258 ^ _775828) ^ [_779579, _779581, _779583, _779585] : [-(c_FunDef_Oreduction__pair(_779583, _779579)), c_FunDef_Oreduction__pair(_779585, _779581), _779585 = _779583, _779581 = _779579], (5841 ^ _775828) ^ [_868880] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _868880), hAPP(c_Nat_OSuc, _868880))))], (9947 ^ _775828) ^ [_936511, _936513, _936515] : [class_Lattices_Oboolean__algebra(_936511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936511), _936513), _936515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936511), hAPP(c_Groups_Ouminus__class_Ouminus(_936511), _936515)), hAPP(c_Groups_Ouminus__class_Ouminus(_936511), _936513))))], (20330 ^ _775828) ^ [_1125143, _1125145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125143), _1125145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1125143)), c_Int_OBit0(_1125145))))], (38280 ^ _775828) ^ [_1502839, _1502841, _1502843] : [class_Orderings_Olinorder(_1502839), 38283 ^ _775828 : [(38290 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502839), _1502843), _1502841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502839, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502839), _1502841)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502839), _1502843))))], (38284 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502839, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502839), _1502841)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502839), _1502843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502839), _1502843), _1502841)))]]], (48449 ^ _775828) ^ [_1747127, _1747129, _1747131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747127)), _1747131)), _1747129)), -(hAPP(hAPP(c_List_Odrop(_1747127), _1747129), _1747131) = c_List_Olist_ONil(_1747127))], (10864 ^ _775828) ^ [_953572, _953574, _953576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953572), _953574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953576), _953574))))], (3376 ^ _775828) ^ [_826927, _826929, _826931, _826933, _826935, _826937] : [-(c_Predicate_ORangeP(_826937, _826933, _826929) = c_Predicate_ORangeP(_826935, _826931, _826927)), _826937 = _826935, _826933 = _826931, _826929 = _826927], (24416 ^ _775828) ^ [_1204547] : [class_Orderings_Olinorder(_1204547), -(c_Orderings_Oord_Omax(_1204547, hAPP(c_COMBC(_1204547, _1204547, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1204547))) = c_Orderings_Oord__class_Omin(_1204547))], (16533 ^ _775828) ^ [_1056993, _1056995, _1056997] : [class_Groups_Oordered__ab__group__add__abs(_1056993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056993), hAPP(c_Groups_Oabs__class_Oabs(_1056993), _1056995)), _1056997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056993), _1056995), _1056997)))], (28116 ^ _775828) ^ [_1279640, _1279642, _1279644, _1279646] : [c_FunDef_Oreduction__pair(_1279640, _1279642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool)), _1279644), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool), tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool)), _1279642))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool)), _1279646), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool), tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool)), _1279642))), c_Wellfounded_Owf(_1279640, _1279646), -(c_Wellfounded_Owf(_1279640, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1279640, _1279640), tc_HOL_Obool)), _1279644), _1279646)))], (19126 ^ _775828) ^ [] : [c_Int_OPls = c_Int_OMin], (46522 ^ _775828) ^ [_1699043, _1699045, _1699047, _1699049, _1699051, _1699053] : [class_Orderings_Olinorder(_1699043), 46525 ^ _775828 : [(46532 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699043), hAPP(_1699045, _1699047)), hAPP(_1699045, _1699049)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699051, _1699043, _1699045), _1699047), hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699049), _1699053)) = hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699049), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699051, _1699043, _1699045), _1699047), _1699053)))], (46526 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699043), hAPP(_1699045, _1699047)), hAPP(_1699045, _1699049))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1699051, _1699043, _1699045), _1699047), hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699049), _1699053)) = hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699047), hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699049), _1699053)))]]], (38202 ^ _775828) ^ [_1501014] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1501014) = 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), _1501014), 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))))))], (28437 ^ _775828) ^ [_1286560, _1286562, _1286564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286560, tc_HOL_Obool)), _1286562), _1286564)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286560, tc_HOL_Obool)), _1286562), _1286564) = _1286564)], (24346 ^ _775828) ^ [_1203048, _1203050] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1203048)), _1203050) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1203048), 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), _1203048)), _1203050))], (12207 ^ _775828) ^ [_976975, _976977, _976979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _976975), _976977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _976975), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976979), _976977))))], (19180 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (51210 ^ _775828) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (20780 ^ _775828) ^ [_1133327, _1133329, _1133331] : [class_Rings_Olinordered__idom(_1133327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133327), c_Groups_Ozero__class_Ozero(_1133327)), hAPP(hAPP(c_Power_Opower__class_Opower(_1133327), _1133329), 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)))), _1133331))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133327), c_Groups_Ozero__class_Ozero(_1133327)), _1133329)))], (28471 ^ _775828) ^ [_1287249, _1287251, _1287253] : [class_Lattices_Olattice(_1287249), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287249), _1287251), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287249), _1287253), _1287251))))], (47875 ^ _775828) ^ [_1732356, _1732358, _1732360, _1732362] : [-(c_Map_Omap__of(_1732356, _1732358, hAPP(hAPP(c_List_Oappend(tc_prod(_1732356, _1732358)), _1732360), _1732362)) = c_Map_Omap__add(_1732356, _1732358, c_Map_Omap__of(_1732356, _1732358, _1732362), c_Map_Omap__of(_1732356, _1732358, _1732360)))], (23454 ^ _775828) ^ [_1185454, _1185456, _1185458, _1185460, _1185462, _1185464] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185454, _1185456, _1185458), _1185460), hAPP(hAPP(c_Product__Type_OPair(_1185454, _1185456), _1185462), _1185464)) = hAPP(hAPP(_1185460, _1185462), _1185464))], (7611 ^ _775828) ^ [_897248, _897250, _897252] : [class_Groups_Oordered__ab__group__add(_897248), 7614 ^ _775828 : [(7621 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897248), _897252), hAPP(c_Groups_Ouminus__class_Ouminus(_897248), _897250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897248), _897250), hAPP(c_Groups_Ouminus__class_Ouminus(_897248), _897252))))], (7615 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897248), _897250), hAPP(c_Groups_Ouminus__class_Ouminus(_897248), _897252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897248), _897252), hAPP(c_Groups_Ouminus__class_Ouminus(_897248), _897250))))]]], (2856 ^ _775828) ^ [_818621, _818623, _818625, _818627, _818629, _818631, _818633, _818635] : [-(c_Lazy__Sequence_Ohb__bind(_818635, _818631, _818627, _818623) = c_Lazy__Sequence_Ohb__bind(_818633, _818629, _818625, _818621)), _818635 = _818633, _818631 = _818629, _818627 = _818625, _818623 = _818621], (18181 ^ _775828) ^ [_1087929] : [class_Power_Opower(_1087929), -(c_Power_Opower__class_Opower(_1087929) = c_Power_Opower_Opower(_1087929, c_Groups_Oone__class_Oone(_1087929), c_Groups_Otimes__class_Otimes(_1087929)))], (29211 ^ _775828) ^ [_1305444, _1305446, _1305448, _1305450] : [hAPP(c_Set_Oimage(_1305444, _1305446, _1305448), _1305450) = c_Orderings_Obot__class_Obot(tc_fun(_1305446, tc_HOL_Obool)), -(_1305450 = c_Orderings_Obot__class_Obot(tc_fun(_1305444, tc_HOL_Obool)))], (51348 ^ _775828) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (5358 ^ _775828) ^ [_857686, _857688, _857690, _857692] : [-(c_COMBK(_857692, _857688) = c_COMBK(_857690, _857686)), _857692 = _857690, _857688 = _857686], (29649 ^ _775828) ^ [_1314029, _1314031, _1314033] : [-(hBOOL(hAPP(_1314029, _1314031))), -(hAPP(c_Set_OCollect(_1314033), hAPP(hAPP(c_COMBS(_1314033, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1314033), c_fconj), hAPP(c_fequal, _1314031))), _1314029)) = c_Orderings_Obot__class_Obot(tc_fun(_1314033, tc_HOL_Obool)))], (16717 ^ _775828) ^ [_1060575, _1060577] : [class_Int_Onumber__ring(_1060575), class_Rings_Olinordered__idom(_1060575), 16724 ^ _775828 : [(16731 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060575), hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577)), c_Groups_Ozero__class_Ozero(_1060575)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1060575), hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577)) = hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577))], (16725 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060575), hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577)), c_Groups_Ozero__class_Ozero(_1060575))), -(hAPP(c_Groups_Oabs__class_Oabs(_1060575), hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1060575), hAPP(c_Int_Onumber__class_Onumber__of(_1060575), _1060577)))]]], (47894 ^ _775828) ^ [_1732829, _1732831, _1732833, _1732835, _1732837] : [-(hAPP(hAPP(c_List_Oappend(_1732829), _1732831), _1732833) = hAPP(hAPP(c_List_Oappend(_1732829), _1732835), _1732837)), 47895 ^ _775828 : [(47902 ^ _775828) ^ [_1733053] : [hAPP(hAPP(c_List_Oappend(_1732829), _1732831), _1733053) = _1732835, _1732833 = hAPP(hAPP(c_List_Oappend(_1732829), _1733053), _1732837)], (47896 ^ _775828) ^ [_1732941] : [_1732831 = hAPP(hAPP(c_List_Oappend(_1732829), _1732835), _1732941), hAPP(hAPP(c_List_Oappend(_1732829), _1732941), _1732833) = _1732837]]], (42381 ^ _775828) ^ [_1598796, _1598798, _1598800, _1598802, _1598804] : [c_Relation_Osingle__valued(_1598796, _1598798, hAPP(c_Relation_Oconverse(_1598798, _1598796), _1598800)), -(hAPP(c_Relation_OImage(_1598798, _1598796, _1598800), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598798, tc_HOL_Obool)), _1598802), _1598804)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598796, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598798, _1598796, _1598800), _1598802)), hAPP(c_Relation_OImage(_1598798, _1598796, _1598800), _1598804)))], (47535 ^ _775828) ^ [_1724115, _1724117] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1724115), _1724117))), -(c_List_Oupto(_1724115, _1724117) = c_List_Olist_ONil(tc_Int_Oint))], (34145 ^ _775828) ^ [_1410969, _1410971, _1410973] : [class_Lattices_Olattice(_1410969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410969), _1410971)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410969), _1410973)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410969, tc_HOL_Obool)), _1410971), _1410973) = c_Orderings_Obot__class_Obot(tc_fun(_1410969, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410969), c_Big__Operators_Olattice__class_OInf__fin(_1410969, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410969, tc_HOL_Obool)), _1410971), _1410973))), c_Big__Operators_Olattice__class_OInf__fin(_1410969, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410969, tc_HOL_Obool)), _1410971), _1410973))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410969), c_Big__Operators_Olattice__class_OInf__fin(_1410969, _1410971)), c_Big__Operators_Olattice__class_OInf__fin(_1410969, _1410973)))], (4804 ^ _775828) ^ [_849223, _849225] : [_849225 = _849223, -(c_Groups_Ominus__class_Ominus(_849225) = c_Groups_Ominus__class_Ominus(_849223))], (10452 ^ _775828) ^ [_946002, _946004] : [class_Rings_Ocomm__semiring__1(_946002), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946002), c_Groups_Ozero__class_Ozero(_946002)), _946004) = _946004)], (50876 ^ _775828) ^ [_1800121, _1800123, _1800125, _1800127] : [-(hBOOL(hAPP(_1800121, _1800123))), -(c_List_OdropWhile(_1800125, _1800121, hAPP(hAPP(c_List_Olist_OCons(_1800125), _1800123), _1800127)) = hAPP(hAPP(c_List_Olist_OCons(_1800125), _1800123), _1800127))], (37410 ^ _775828) ^ [_1482141, _1482143, _1482145, _1482147, _1482149] : [class_Groups_Ocomm__monoid__add(_1482141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482143), _1482145)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482143), _1482147)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482143, tc_HOL_Obool)), _1482145), _1482147) = c_Orderings_Obot__class_Obot(tc_fun(_1482143, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482143, _1482141), _1482149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482143, tc_HOL_Obool)), _1482145), _1482147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1482141), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482143, _1482141), _1482149), _1482145)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482143, _1482141), _1482149), _1482147)))], (36277 ^ _775828) ^ [_1456959, _1456961, _1456963] : [class_Orderings_Oorder(_1456959), 36280 ^ _775828 : [(36287 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456959), _1456961), _1456963))), -(c_Orderings_Obot__class_Obot(tc_fun(_1456959, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456959, _1456961), _1456963))], (36281 ^ _775828) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1456959, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456959, _1456961), _1456963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456959), _1456961), _1456963))]]], (40744 ^ _775828) ^ [_1559128, _1559130, _1559132, _1559134, _1559136, _1559138] : [hAPP(_1559128, _1559130) = _1559132, hBOOL(hAPP(hAPP(c_member(_1559134), _1559132), _1559136)), -(hBOOL(hAPP(hAPP(c_member(_1559138), _1559130), hAPP(c_Set_Ovimage(_1559138, _1559134, _1559128), _1559136))))], (25945 ^ _775828) ^ [_1234082, _1234084, _1234086] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234082), _1234084)), 25956 ^ _775828 : [(25959 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234086), _1234082))], (25957 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234082), _1234086)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234084), _1234086)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234086), _1234084)))], (47217 ^ _775828) ^ [_1717627, _1717629, _1717631, _1717633] : [-(hAPP(hAPP(c_List_Otake(_1717627), hAPP(c_Nat_OSuc, _1717629)), hAPP(hAPP(c_List_Olist_OCons(_1717627), _1717631), _1717633)) = hAPP(hAPP(c_List_Olist_OCons(_1717627), _1717631), hAPP(hAPP(c_List_Otake(_1717627), _1717629), _1717633)))], (17285 ^ _775828) ^ [_1071570, _1071572, _1071574, _1071576] : [class_Int_Onumber__ring(_1071570), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071570), hAPP(c_Int_Onumber__class_Onumber__of(_1071570), _1071572)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071570), _1071574), hAPP(c_Int_Onumber__class_Onumber__of(_1071570), _1071576))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071570), hAPP(c_Int_Onumber__class_Onumber__of(_1071570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071572), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071576)))), _1071574))], (27242 ^ _775828) ^ [_1257894, _1257896, _1257898] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257894, tc_HOL_Obool)), _1257896), _1257898) = hAPP(c_Set_OCollect(_1257894), hAPP(hAPP(c_COMBS(_1257894, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1257894), c_fconj), hAPP(hAPP(c_COMBC(_1257894, tc_fun(_1257894, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257894)), _1257896))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1257894), c_fNot), hAPP(hAPP(c_COMBC(_1257894, tc_fun(_1257894, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257894)), _1257898)))))], (33519 ^ _775828) ^ [_1397731, _1397733, _1397735, _1397737, _1397739] : [class_Groups_Ocomm__monoid__mult(_1397731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397733), _1397735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397733, tc_HOL_Obool)), _1397737), _1397735)), 33533 ^ _775828 : [(33536 ^ _775828) ^ [] : [hAPP(_1397739, 33532 ^ [_1397731, _1397733, _1397735, _1397737, _1397739]) = c_Groups_Oone__class_Oone(_1397731)], (33534 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397733), 33532 ^ [_1397731, _1397733, _1397735, _1397737, _1397739]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1397733, tc_HOL_Obool)), _1397735), _1397737))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397733, _1397731), _1397739), _1397737) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397733, _1397731), _1397739), _1397735))], (24923 ^ _775828) ^ [] : [-(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)))], (8176 ^ _775828) ^ [_907190, _907192, _907194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907190), _907192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907192), _907194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _907190), _907194)))], (2688 ^ _775828) ^ [_815683, _815685, _815687, _815689, _815691, _815693, _815695, _815697, _815699, _815701, _815703, _815705, _815707, _815709] : [-(c_New__Random__Sequence_Opos__decr__bind(_815709, _815705, _815701, _815697, _815693, _815689, _815685) = c_New__Random__Sequence_Opos__decr__bind(_815707, _815703, _815699, _815695, _815691, _815687, _815683)), _815709 = _815707, _815705 = _815703, _815701 = _815699, _815697 = _815695, _815693 = _815691, _815689 = _815687, _815685 = _815683], (13591 ^ _775828) ^ [_1001678, _1001680, _1001682, _1001684, _1001686] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_1001678, _1001680), _1001682, _1001684, _1001686)), 13592 ^ _775828 : [(13593 ^ _775828) ^ [_1001733] : [c_Natural_Oevaln(_1001678, _1001682, _1001684, _1001733), c_Natural_Oevaln(_1001680, _1001733, _1001684, _1001686)]]], (33208 ^ _775828) ^ [_1390803, _1390805, _1390807, _1390809, _1390811] : [class_Groups_Ocomm__monoid__mult(_1390803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390805), _1390807)), -(hBOOL(hAPP(hAPP(c_member(_1390805), _1390809), _1390807))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390805, _1390803), _1390811), hAPP(hAPP(c_Set_Oinsert(_1390805), _1390809), _1390807)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390803), hAPP(_1390811, _1390809)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390805, _1390803), _1390811), _1390807)))], (27238 ^ _775828) ^ [_1257796, _1257798] : [-(hAPP(c_Set_OCollect(_1257796), hAPP(hAPP(c_COMBC(_1257796, tc_fun(_1257796, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257796)), _1257798)) = _1257798)], (25405 ^ _775828) ^ [_1223949, _1223951] : [_1223949 = _1223951, -(hAPP(c_Code__Numeral_Onat__of, _1223949) = hAPP(c_Code__Numeral_Onat__of, _1223951))], (22202 ^ _775828) ^ [_1161680, _1161682] : [class_Fields_Olinordered__field__inverse__zero(_1161680), class_Int_Onumber__ring(_1161680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161680), c_Groups_Ozero__class_Ozero(_1161680)), _1161682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161680), c_Groups_Ozero__class_Ozero(_1161680)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161680), _1161682), hAPP(c_Int_Onumber__class_Onumber__of(_1161680), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (16084 ^ _775828) ^ [_1048256, _1048258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048256), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048258), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048256), _1048258)))], (18509 ^ _775828) ^ [_1094162] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1094162), c_Int_OMin) = c_Int_Osucc(_1094162))], (22840 ^ _775828) ^ [_1173166, _1173168, _1173170, _1173172, _1173174] : [class_Fields_Olinordered__field(_1173166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173166), c_Groups_Ozero__class_Ozero(_1173166)), _1173168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173166), _1173168), _1173170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173166), c_Groups_Ozero__class_Ozero(_1173166)), _1173172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173166), _1173172), _1173174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173166), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173166), _1173168), _1173174)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173166), _1173170), _1173172))))], (51044 ^ _775828) ^ [_1803536, _1803538] : [class_Lattices_Olattice(_1803536), -(class_Lattices_Osemilattice__inf(tc_fun(_1803538, _1803536)))], (13206 ^ _775828) ^ [_994406, _994408, _994410, _994412, _994414, _994416] : [c_Com_Ocom_OCond(_994406, _994408, _994410) = c_Com_Ocom_OCond(_994412, _994414, _994416), 13209 ^ _775828 : [(13214 ^ _775828) ^ [] : [-(_994410 = _994416)], (13212 ^ _775828) ^ [] : [-(_994408 = _994414)], (13210 ^ _775828) ^ [] : [-(_994406 = _994412)]]], (38430 ^ _775828) ^ [_1505959, _1505961, _1505963] : [_1505963 = hAPP(c_COMBK(tc_Option_Ooption(_1505961), _1505959), c_Option_Ooption_ONone(_1505961)), -(c_Map_Odom(_1505959, _1505961, _1505963) = c_Orderings_Obot__class_Obot(tc_fun(_1505959, tc_HOL_Obool)))], (13819 ^ _775828) ^ [_1005996, _1005998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1005996), _1005998)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005996, _1005998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1005996), _1005998))], (44184 ^ _775828) ^ [_1641113, _1641115, _1641117, _1641119] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641113, tc_fun(_1641115, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1641113, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1641115, tc_HOL_Obool), tc_fun(_1641115, tc_HOL_Obool), _1641113), hAPP(c_COMBC(_1641115, tc_fun(_1641115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1641115))), _1641117)), _1641119)), -(hBOOL(hAPP(hAPP(c_member(_1641115), _1641119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641113, tc_fun(_1641115, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1641113, tc_HOL_Obool))), _1641117))))], (18994 ^ _775828) ^ [_1102754, _1102756, _1102758, _1102760] : [-(hAPP(c_Product__Type_Osnd(_1102754, _1102756), hAPP(hAPP(c_Product__Type_OPair(_1102754, _1102756), _1102758), _1102760)) = _1102760)], (25383 ^ _775828) ^ [_1223568, _1223570] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1223568, _1223570) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1223568), hAPP(c_Code__Numeral_Onat__of, _1223570))))], (15290 ^ _775828) ^ [_1032648, _1032650, _1032652, _1032654] : [class_Divides_Oring__div(_1032648), -(c_Divides_Odiv__class_Omod(_1032648, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032648), _1032650), _1032652), _1032654) = c_Divides_Odiv__class_Omod(_1032648, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032648), c_Divides_Odiv__class_Omod(_1032648, _1032650, _1032654)), _1032652), _1032654))], (49071 ^ _775828) ^ [_1761193, _1761195, _1761197, _1761199, _1761201] : [class_Groups_Omonoid__add(_1761193), class_Groups_Oordered__ab__semigroup__add(_1761193), 49081 ^ _775828 : [(49084 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761193), hAPP(_1761199, 49080 ^ [_1761193, _1761195, _1761197, _1761199, _1761201])), hAPP(_1761201, 49080 ^ [_1761193, _1761195, _1761197, _1761199, _1761201])))], (49082 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761195), 49080 ^ [_1761193, _1761195, _1761197, _1761199, _1761201]), hAPP(c_List_Oset(_1761195), _1761197))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761193), hAPP(c_List_Omonoid__add__class_Olistsum(_1761193), hAPP(hAPP(c_List_Omap(_1761195, _1761193), _1761199), _1761197))), hAPP(c_List_Omonoid__add__class_Olistsum(_1761193), hAPP(hAPP(c_List_Omap(_1761195, _1761193), _1761201), _1761197)))))], (34263 ^ _775828) ^ [_1413568, _1413570, _1413572, _1413574] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413568, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413568, tc_HOL_Obool)), _1413570), _1413572)), _1413574) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413568, tc_HOL_Obool)), _1413570), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413568, tc_HOL_Obool)), _1413572), _1413574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413568, tc_HOL_Obool)), _1413574), _1413570)))], (5891 ^ _775828) ^ [_869667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869667), _869667))], (49680 ^ _775828) ^ [_1774669, _1774671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774669), _1774671)), -(c_List_Oupt(_1774669, hAPP(c_Nat_OSuc, _1774671)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1774669, _1774671)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1774671), c_List_Olist_ONil(tc_Nat_Onat))))], (7627 ^ _775828) ^ [_897531, _897533, _897535] : [class_Rings_Oidom(_897531), 7630 ^ _775828 : [(7631 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897531), _897533), _897533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897531), _897535), _897535), -(_897533 = _897535), -(_897533 = hAPP(c_Groups_Ouminus__class_Ouminus(_897531), _897535))], (7641 ^ _775828) ^ [] : [7642 ^ _775828 : [(7645 ^ _775828) ^ [] : [_897533 = hAPP(c_Groups_Ouminus__class_Ouminus(_897531), _897535)], (7643 ^ _775828) ^ [] : [_897533 = _897535]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897531), _897533), _897533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897531), _897535), _897535))]]], (15093 ^ _775828) ^ [_1029021, _1029023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029023)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1029021)), hAPP(c_Int_Onat, _1029023)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1029021, _1029023)))], (4362 ^ _775828) ^ [_842456, _842458, _842460, _842462] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_842462, _842458) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_842460, _842456)), _842462 = _842460, _842458 = _842456], (23982 ^ _775828) ^ [_1195758, _1195760, _1195762, _1195764] : [class_Orderings_Olinorder(_1195758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195758), _1195760), _1195762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195758), _1195760), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195758), _1195762), _1195764))))], (33837 ^ _775828) ^ [_1404715, _1404717, _1404719, _1404721] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404715, tc_HOL_Obool)), _1404717), _1404719), _1404721)), -(hBOOL(hAPP(_1404717, _1404721)))], (46944 ^ _775828) ^ [_1710275, _1710277, _1710279] : [46946 ^ _775828 : [(46949 ^ _775828) ^ [] : [hBOOL(hAPP(_1710279, hAPP(hAPP(c_List_Onth(_1710275), _1710277), 46945 ^ [_1710275, _1710277, _1710279])))], (46947 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46945 ^ [_1710275, _1710277, _1710279]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710275)), _1710277))))]], 46950 ^ _775828 : [(46951 ^ _775828) ^ [_1710477] : [hBOOL(hAPP(hAPP(c_member(_1710275), _1710477), hAPP(c_List_Oset(_1710275), _1710277))), -(hBOOL(hAPP(_1710279, _1710477)))]]], (24759 ^ _775828) ^ [_1211223, _1211225, _1211227] : [24761 ^ _775828 : [(24764 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1211223), 24760 ^ [_1211223, _1211225, _1211227]), c_Wellfounded_Oacc(_1211223, _1211227)))], (24762 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1211223, _1211223)), hAPP(hAPP(c_Product__Type_OPair(_1211223, _1211223), 24760 ^ [_1211223, _1211225, _1211227]), _1211225)), _1211227)))]], -(hBOOL(hAPP(hAPP(c_member(_1211223), _1211225), c_Wellfounded_Oacc(_1211223, _1211227))))], (37817 ^ _775828) ^ [_1492328, _1492330, _1492332, _1492334, _1492336] : [class_Groups_Oordered__ab__group__add(_1492328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492330), _1492332)), 37827 ^ _775828 : [(37830 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1492328), c_Groups_Ozero__class_Ozero(_1492328)), hAPP(_1492334, 37826 ^ [_1492328, _1492330, _1492332, _1492334, _1492336])))], (37828 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492330), 37826 ^ [_1492328, _1492330, _1492332, _1492334, _1492336]), _1492332)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492330, _1492328), _1492334), _1492332) = c_Groups_Ozero__class_Ozero(_1492328), hBOOL(hAPP(hAPP(c_member(_1492330), _1492336), _1492332)), -(hAPP(_1492334, _1492336) = c_Groups_Ozero__class_Ozero(_1492328))], (38136 ^ _775828) ^ [_1499321, _1499323, _1499325] : [class_Orderings_Oorder(_1499321), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499321, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1499321, _1499323), _1499325)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499321), _1499325)) = c_Orderings_Obot__class_Obot(tc_fun(_1499321, tc_HOL_Obool)))], (6732 ^ _775828) ^ [_882618] : [_882618 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882618) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36932 ^ _775828) ^ [_1470208, _1470210, _1470212, _1470214] : [class_Rings_Oring__1(_1470208), -(hAPP(c_Int_Oring__1__class_Oof__int(_1470208), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470210, tc_Int_Oint), _1470212), _1470214)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470210, _1470208), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1470208, _1470210), c_Int_Oring__1__class_Oof__int(_1470208)), _1470212)), _1470214))], (25797 ^ _775828) ^ [_1231762, _1231764] : [25804 ^ _775828 : [(25807 ^ _775828) ^ [] : [_1231762 = _1231764], (25805 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231762), _1231764)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231762), _1231764)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231764), _1231762)))], (51272 ^ _775828) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (12510 ^ _775828) ^ [_982265, _982267] : [12511 ^ _775828 : [(12514 ^ _775828) ^ [] : [_982265 = _982267], (12512 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982265), _982267))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982265), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _982267), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48169 ^ _775828) ^ [_1739154, _1739156] : [-(c_List_Olistrel(_1739154, c_Transitive__Closure_Ortrancl(_1739154, _1739156)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739154), c_List_Olistrel1(_1739154, _1739156)))], (42746 ^ _775828) ^ [_1607924, _1607926, _1607928] : [-(hAPP(c_Fun_Ocomp(_1607924, _1607926, _1607924, _1607928), c_Fun_Oid(_1607924)) = _1607928)], (27367 ^ _775828) ^ [_1261202, _1261204, _1261206, _1261208] : [hBOOL(hAPP(c_Predicate_ORangeP(_1261202, _1261204, hAPP(hAPP(c_COMBC(_1261202, tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_fun(_1261204, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261204, tc_fun(tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_fun(_1261204, tc_HOL_Obool)), _1261202), c_COMBC(_1261204, tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261204, tc_prod(_1261202, _1261204)), tc_fun(_1261204, tc_fun(tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_HOL_Obool)), _1261202), hAPP(c_COMBB(tc_prod(_1261202, _1261204), tc_fun(tc_fun(tc_prod(_1261202, _1261204), tc_HOL_Obool), tc_HOL_Obool), _1261204), c_member(tc_prod(_1261202, _1261204)))), c_Product__Type_OPair(_1261202, _1261204)))), _1261206)), _1261208)), -(hBOOL(hAPP(hAPP(c_member(_1261204), _1261208), hAPP(c_Relation_ORange(_1261202, _1261204), _1261206))))], (49554 ^ _775828) ^ [_1771908, _1771910] : [-(c_Random_Oselect__weight(_1771908, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1771908), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1771908, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1771908, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1771908)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1771910)) = c_Random_Oselect__weight(_1771908, _1771910))], (29565 ^ _775828) ^ [_1312275, _1312277] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312275, tc_HOL_Obool)), _1312277), _1312277) = c_Orderings_Obot__class_Obot(tc_fun(_1312275, tc_HOL_Obool)))], (2188 ^ _775828) ^ [_807785, _807787, _807789, _807791] : [-(c_Nat__Transfer_Otsub(_807791, _807787) = c_Nat__Transfer_Otsub(_807789, _807785)), _807791 = _807789, _807787 = _807785], (4640 ^ _775828) ^ [_846727, _846729] : [_846729 = _846727, -(c_Int_Onumber__class_Onumber__of(_846729) = c_Int_Onumber__class_Onumber__of(_846727))], (38486 ^ _775828) ^ [_1507583, _1507585, _1507587] : [c_Equiv__Relations_Oequiv(_1507583, _1507585, _1507587), -(hAPP(hAPP(c_Relation_Orel__comp(_1507583, _1507583, _1507583), hAPP(c_Relation_Oconverse(_1507583, _1507583), _1507587)), _1507587) = _1507587)], (40967 ^ _775828) ^ [_1564656, _1564658, _1564660, _1564662, _1564664, _1564666] : [hBOOL(hAPP(hAPP(c_member(_1564656), _1564658), _1564660)), 40970 ^ _775828 : [(40977 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564656), _1564662), _1564660))), -(hAPP(c_Set_Ovimage(_1564664, _1564656, hAPP(hAPP(c_COMBC(_1564664, _1564656, _1564656), hAPP(hAPP(c_COMBC(_1564664, _1564656, tc_fun(_1564656, _1564656)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1564656, tc_fun(_1564656, _1564656)), _1564664), c_If(_1564656)), hAPP(hAPP(c_COMBC(_1564664, tc_fun(_1564664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564664)), _1564666))), _1564658)), _1564662)), _1564660) = _1564666)], (40971 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564656), _1564662), _1564660)), -(hAPP(c_Set_Ovimage(_1564664, _1564656, hAPP(hAPP(c_COMBC(_1564664, _1564656, _1564656), hAPP(hAPP(c_COMBC(_1564664, _1564656, tc_fun(_1564656, _1564656)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1564656, tc_fun(_1564656, _1564656)), _1564664), c_If(_1564656)), hAPP(hAPP(c_COMBC(_1564664, tc_fun(_1564664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564664)), _1564666))), _1564658)), _1564662)), _1564660) = c_Orderings_Otop__class_Otop(tc_fun(_1564664, tc_HOL_Obool)))]]], (2536 ^ _775828) ^ [_813215, _813217] : [_813217 = _813215, -(c_DSequence_Osingle(_813217) = c_DSequence_Osingle(_813215))], (47255 ^ _775828) ^ [_1718514, _1718516, _1718518, _1718520, _1718522] : [-(_1718514 = _1718516), -(hAPP(hAPP(c_List_Onth(_1718518), hAPP(hAPP(c_List_Olist__update(_1718518, _1718520), _1718514), _1718522)), _1718516) = hAPP(hAPP(c_List_Onth(_1718518), _1718520), _1718516))], (43342 ^ _775828) ^ [_1622701, _1622703, _1622705, _1622707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622701, _1622701)), hAPP(hAPP(c_Product__Type_OPair(_1622701, _1622701), _1622703), _1622705)), c_Transitive__Closure_Otrancl(_1622701, _1622707))), 43346 ^ _775828 : [(43349 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622701, _1622701)), hAPP(hAPP(c_Product__Type_OPair(_1622701, _1622701), 43345 ^ [_1622701, _1622703, _1622705, _1622707]), _1622705)), _1622707)))], (43347 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622701, _1622701)), hAPP(hAPP(c_Product__Type_OPair(_1622701, _1622701), _1622703), 43345 ^ [_1622701, _1622703, _1622705, _1622707])), c_Transitive__Closure_Ortrancl(_1622701, _1622707))))]]], (51440 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (40921 ^ _775828) ^ [_1563430, _1563432, _1563434] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563430, _1563430)), hAPP(hAPP(c_Product__Type_OPair(_1563430, _1563430), _1563432), _1563432)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1563430, _1563430), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1563434))))], (32943 ^ _775828) ^ [_1385547, _1385549, _1385551] : [class_Groups_Ocomm__monoid__mult(_1385547), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385549, _1385547), hAPP(c_COMBK(_1385547, _1385549), c_Groups_Oone__class_Oone(_1385547))), _1385551) = c_Groups_Oone__class_Oone(_1385547))], (28091 ^ _775828) ^ [_1279260, _1279262] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1279260, _1279262), 28092 ^ [_1279260, _1279262])), -(c_Wellfounded_OwfP(_1279260, _1279262))], (41426 ^ _775828) ^ [_1577120, _1577122, _1577124, _1577126, _1577128, _1577130] : [hBOOL(hAPP(hAPP(c_member(_1577120), _1577122), _1577124)), 41429 ^ _775828 : [(41436 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1577126, tc_HOL_Obool)), _1577128), _1577130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577126, _1577120), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1577126, _1577120), _1577128), hAPP(c_COMBK(tc_fun(_1577120, tc_HOL_Obool), _1577126), _1577124))), hAPP(hAPP(c_Product__Type_OSigma(_1577126, _1577120), _1577130), hAPP(c_COMBK(tc_fun(_1577120, tc_HOL_Obool), _1577126), _1577124)))))], (41430 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577126, _1577120), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1577126, _1577120), _1577128), hAPP(c_COMBK(tc_fun(_1577120, tc_HOL_Obool), _1577126), _1577124))), hAPP(hAPP(c_Product__Type_OSigma(_1577126, _1577120), _1577130), hAPP(c_COMBK(tc_fun(_1577120, tc_HOL_Obool), _1577126), _1577124)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1577126, tc_HOL_Obool)), _1577128), _1577130)))]]], (7421 ^ _775828) ^ [_894271, _894273, _894275, _894277] : [-(c_Option_Ooption_Ooption__rec(_894271, _894273, _894275, _894277, c_Option_Ooption_ONone(_894273)) = _894275)], (22912 ^ _775828) ^ [_1174522, _1174524, _1174526, _1174528] : [class_Fields_Olinordered__field__inverse__zero(_1174522), 22915 ^ _775828 : [(22916 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174524), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174522), _1174526), _1174528))), 22919 ^ _775828 : [(22926 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), c_Groups_Ozero__class_Ozero(_1174522)), _1174528))), 22929 ^ _775828 : [(22936 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174528), c_Groups_Ozero__class_Ozero(_1174522)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174524), c_Groups_Ozero__class_Ozero(_1174522))))], (22930 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174528), c_Groups_Ozero__class_Ozero(_1174522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174522), _1174524), _1174528))))]]], (22920 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), c_Groups_Ozero__class_Ozero(_1174522)), _1174528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174522), _1174524), _1174528)), _1174526)))]]], (22942 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174524), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174522), _1174526), _1174528)))), 22945 ^ _775828 : [(22948 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174522), _1174524), _1174528)), _1174526))], (22946 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), c_Groups_Ozero__class_Ozero(_1174522)), _1174528)))]], 22949 ^ _775828 : [(22952 ^ _775828) ^ [] : [22953 ^ _775828 : [(22956 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174522), _1174524), _1174528)))], (22954 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174528), c_Groups_Ozero__class_Ozero(_1174522))))]], 22957 ^ _775828 : [(22960 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174524), c_Groups_Ozero__class_Ozero(_1174522)))], (22958 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), _1174528), c_Groups_Ozero__class_Ozero(_1174522)))]]], (22950 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174522), c_Groups_Ozero__class_Ozero(_1174522)), _1174528))]]]]], (5298 ^ _775828) ^ [_856814, _856816] : [_856816 = _856814, -(c_List_Olist_OCons(_856816) = c_List_Olist_OCons(_856814))], (47381 ^ _775828) ^ [_1721110, _1721112, _1721114, _1721116] : [hAPP(hAPP(c_List_Olist__update(_1721110, _1721112), _1721114), _1721116) = c_List_Olist_ONil(_1721110), -(_1721112 = c_List_Olist_ONil(_1721110))], (10094 ^ _775828) ^ [_939185, _939187, _939189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939185), _939187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939189), _939187))))], (44579 ^ _775828) ^ [_1651613, _1651615, _1651617, _1651619] : [hBOOL(hAPP(hAPP(c_member(_1651613), _1651615), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651613, tc_HOL_Obool), _1651617))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1651613, tc_HOL_Obool)), _1651619), _1651617)), -(hBOOL(hAPP(hAPP(c_member(_1651613), _1651615), _1651619)))], (29583 ^ _775828) ^ [_1312709, _1312711, _1312713] : [hBOOL(hAPP(hAPP(c_member(_1312709), _1312711), _1312713)), -(hAPP(hAPP(c_Set_Oinsert(_1312709), _1312711), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312709, tc_HOL_Obool)), _1312713), hAPP(hAPP(c_Set_Oinsert(_1312709), _1312711), c_Orderings_Obot__class_Obot(tc_fun(_1312709, tc_HOL_Obool))))) = _1312713)], (33178 ^ _775828) ^ [_1390094, _1390096, _1390098, _1390100, _1390102] : [class_Groups_Ocomm__monoid__mult(_1390094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390096), _1390098)), 33185 ^ _775828 : [(33192 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390096), _1390100), _1390098))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390096, _1390094), hAPP(hAPP(c_COMBC(_1390096, _1390094, _1390094), hAPP(hAPP(c_COMBS(_1390096, _1390094, tc_fun(_1390094, _1390094)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1390094, tc_fun(_1390094, _1390094)), _1390096), c_If(_1390094)), hAPP(c_fequal, _1390100))), _1390102)), c_Groups_Oone__class_Oone(_1390094))), _1390098) = c_Groups_Oone__class_Oone(_1390094))], (33186 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1390096), _1390100), _1390098)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390096, _1390094), hAPP(hAPP(c_COMBC(_1390096, _1390094, _1390094), hAPP(hAPP(c_COMBS(_1390096, _1390094, tc_fun(_1390094, _1390094)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1390094, tc_fun(_1390094, _1390094)), _1390096), c_If(_1390094)), hAPP(c_fequal, _1390100))), _1390102)), c_Groups_Oone__class_Oone(_1390094))), _1390098) = hAPP(_1390102, _1390100))]]], (51144 ^ _775828) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51078 ^ _775828) ^ [_1803981, _1803983] : [class_Lattices_Olattice(_1803981), -(class_Lattices_Olattice(tc_fun(_1803983, _1803981)))], (48870 ^ _775828) ^ [_1756191, _1756193, _1756195] : [class_Orderings_Olinorder(_1756191), -(c_Big__Operators_Olinorder__class_OMin(_1756191, hAPP(c_List_Oset(_1756191), hAPP(hAPP(c_List_Olist_OCons(_1756191), _1756193), _1756195))) = hAPP(c_List_Ofoldl(_1756191, _1756191, c_Orderings_Oord__class_Omin(_1756191), _1756193), _1756195))], (19608 ^ _775828) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (48723 ^ _775828) ^ [_1753122, _1753124, _1753126] : [-(c_List_Orotate(_1753122, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1753124), _1753126)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1753122), tc_List_Olist(_1753122), tc_List_Olist(_1753122), c_List_Orotate(_1753122, _1753124)), c_List_Orotate(_1753122, _1753126)))], (38238 ^ _775828) ^ [_1502135, _1502137, _1502139] : [class_Orderings_Olinorder(_1502135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1502135), _1502137), _1502139)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502135, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1502135, _1502137, _1502139)), hAPP(c_SetInterval_Oord__class_OatLeast(_1502135), _1502139)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502135), _1502137))], (29659 ^ _775828) ^ [_1314215, _1314217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1314215, tc_HOL_Obool)), _1314217), c_Orderings_Obot__class_Obot(tc_fun(_1314215, tc_HOL_Obool))))], (28830 ^ _775828) ^ [_1294492, _1294494, _1294496] : [28831 ^ _775828 : [(28832 ^ _775828) ^ [_1294546] : [hBOOL(hAPP(_1294492, _1294546))]], _1294494 = c_Hilbert__Choice_OEps(_1294496, _1294492), -(hBOOL(hAPP(_1294492, _1294494)))], (49221 ^ _775828) ^ [_1764003, _1764005, _1764007, _1764009] : [49223 ^ _775828 : [(49226 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764007, 49222 ^ [_1764003, _1764005, _1764007, _1764009])), hAPP(_1764009, 49222 ^ [_1764003, _1764005, _1764007, _1764009])))], (49224 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764003), 49222 ^ [_1764003, _1764005, _1764007, _1764009]), hAPP(c_List_Oset(_1764003), _1764005))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1764003, _1764007, _1764005)), c_List_Olist_Olist__size(_1764003, _1764009, _1764005))))], (16747 ^ _775828) ^ [_1061091, _1061093] : [16748 ^ _775828 : [(16751 ^ _775828) ^ [] : [_1061093 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16749 ^ _775828) ^ [] : [-(_1061091 = 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)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1061091)), _1061093))))], (15994 ^ _775828) ^ [_1046581, _1046583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046581)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046583), _1046581)), _1046581) = _1046583)], (36359 ^ _775828) ^ [_1458490, _1458492, _1458494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1458490), _1458492)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458492), _1458494)) = 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, _1458490), _1458492)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458492), _1458494))))], (25417 ^ _775828) ^ [_1224140, _1224142] : [_1224140 = _1224142, -(hAPP(c_Code__Numeral_Onat__of, _1224140) = hAPP(c_Code__Numeral_Onat__of, _1224142))], (45620 ^ _775828) ^ [_1675381, _1675383, _1675385, _1675387, _1675389] : [-(c_Map_Omap__comp(_1675381, _1675383, _1675385, hAPP(c_COMBK(tc_Option_Ooption(_1675383), _1675381), c_Option_Ooption_ONone(_1675383)), _1675387, _1675389) = c_Option_Ooption_ONone(_1675383))], (21174 ^ _775828) ^ [_1142426, _1142428, _1142430, _1142432] : [class_Rings_Odivision__ring(_1142426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142426), _1142428), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142426), _1142430), _1142432)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142426), _1142428), _1142430)), _1142432))], (48781 ^ _775828) ^ [_1754423, _1754425, _1754427, _1754429] : [class_Groups_Osemigroup__add(_1754423), -(hAPP(c_List_Ofoldl(_1754423, _1754423, c_Groups_Oplus__class_Oplus(_1754423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1754423), _1754425), _1754427)), _1754429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1754423), _1754425), hAPP(c_List_Ofoldl(_1754423, _1754423, c_Groups_Oplus__class_Oplus(_1754423), _1754427), _1754429)))], (21858 ^ _775828) ^ [_1154924, _1154926, _1154928, _1154930] : [class_Fields_Olinordered__field__inverse__zero(_1154924), class_Int_Onumber(_1154924), 21865 ^ _775828 : [(21866 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154926), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154924), _1154928), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)))), 21869 ^ _775828 : [(21876 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), c_Groups_Ozero__class_Ozero(_1154924)), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)))), 21879 ^ _775828 : [(21886 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)), c_Groups_Ozero__class_Ozero(_1154924)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154926), c_Groups_Ozero__class_Ozero(_1154924))))], (21880 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)), c_Groups_Ozero__class_Ozero(_1154924))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154924), _1154926), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)))))]]], (21870 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), c_Groups_Ozero__class_Ozero(_1154924)), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154924), _1154926), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))), _1154928)))]]], (21892 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154926), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154924), _1154928), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))))), 21895 ^ _775828 : [(21898 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154924), _1154926), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))), _1154928))], (21896 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), c_Groups_Ozero__class_Ozero(_1154924)), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))))]], 21899 ^ _775828 : [(21902 ^ _775828) ^ [] : [21903 ^ _775828 : [(21906 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154924), _1154926), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930))))], (21904 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)), c_Groups_Ozero__class_Ozero(_1154924))))]], 21907 ^ _775828 : [(21910 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), _1154926), c_Groups_Ozero__class_Ozero(_1154924)))], (21908 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)), c_Groups_Ozero__class_Ozero(_1154924)))]]], (21900 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), c_Groups_Ozero__class_Ozero(_1154924)), hAPP(c_Int_Onumber__class_Onumber__of(_1154924), _1154930)))]]]]], (16102 ^ _775828) ^ [_1048621, _1048623, _1048625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048621), _1048623)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048625), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048623), _1048621))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048625), _1048621)), hAPP(c_Nat_OSuc, _1048623)))], (50838 ^ _775828) ^ [_1799146, _1799148, _1799150] : [hBOOL(hAPP(c_List_Odistinct(_1799146), _1799148)), hBOOL(hAPP(hAPP(c_member(_1799146), _1799150), hAPP(c_List_Oset(_1799146), _1799148))), -(c_List_OtakeWhile(_1799146, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1799146), c_fNot), hAPP(hAPP(c_COMBC(_1799146, _1799146, tc_HOL_Obool), c_fequal), _1799150)), hAPP(c_List_Orev(_1799146), _1799148)) = hAPP(c_List_Orev(_1799146), hAPP(c_List_Otl(_1799146), c_List_OdropWhile(_1799146, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1799146), c_fNot), hAPP(hAPP(c_COMBC(_1799146, _1799146, tc_HOL_Obool), c_fequal), _1799150)), _1799148))))], (38308 ^ _775828) ^ [_1503353] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1503353)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1503353))], (46371 ^ _775828) ^ [_1693977, _1693979, _1693981, _1693983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693977), tc_List_Olist(_1693977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693977), tc_List_Olist(_1693977)), _1693979), _1693981)), c_List_Olistrel(_1693977, _1693983))), 46374 ^ _775828 : [(46377 ^ _775828) ^ [_1694313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693977, _1693977)), _1694313), hAPP(c_List_Oset(tc_prod(_1693977, _1693977)), hAPP(hAPP(c_List_Ozip(_1693977, _1693977), _1693979), _1693981)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1693977, _1693977, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1693977, tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_fun(_1693977, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1693977, tc_fun(tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_fun(_1693977, tc_HOL_Obool)), _1693977), c_COMBC(_1693977, tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1693977, tc_prod(_1693977, _1693977)), tc_fun(_1693977, tc_fun(tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_HOL_Obool)), _1693977), hAPP(c_COMBB(tc_prod(_1693977, _1693977), tc_fun(tc_fun(tc_prod(_1693977, _1693977), tc_HOL_Obool), tc_HOL_Obool), _1693977), c_member(tc_prod(_1693977, _1693977)))), c_Product__Type_OPair(_1693977, _1693977)))), _1693983)), _1694313)))], (46375 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693977)), _1693979) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693977)), _1693981))]]], (50836 ^ _775828) ^ [_1799103, _1799105] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1799103), _1799105) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1799103)), c_List_Oembed__list(_1799105))))], (33083 ^ _775828) ^ [_1387996, _1387998, _1388000, _1388002, _1388004] : [class_Groups_Ocomm__monoid__mult(_1387996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387998), _1388000)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387998, _1387996), hAPP(hAPP(c_COMBS(_1387998, _1387996, _1387996), hAPP(hAPP(c_COMBB(_1387996, tc_fun(_1387996, _1387996), _1387998), c_Groups_Otimes__class_Otimes(_1387996)), _1388002)), _1388004)), _1388000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387996), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387998, _1387996), _1388002), _1388000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387998, _1387996), _1388004), _1388000)))], (19284 ^ _775828) ^ [_1107466, _1107468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107466), _1107468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107466), c_Int_OPls)))], (21560 ^ _775828) ^ [_1149104, _1149106] : [hAPP(c_Nat_OSuc, _1149104) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149106), -(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(_1149106))), 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)), _1149104))))))], (47675 ^ _775828) ^ [_1727460, _1727462, _1727464, _1727466, _1727468, _1727470, _1727472] : [-(hBOOL(hAPP(hAPP(c_member(_1727460), _1727462), hAPP(c_List_Oset(_1727460), hAPP(hAPP(c_List_Otake(_1727460), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727464)), _1727466)), _1727468))))), -(c_Map_Omap__upds(_1727460, _1727464, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1727460, tc_Option_Ooption(_1727464)), _1727470), _1727462), hAPP(c_Option_Ooption_OSome(_1727464), _1727472)), _1727468, _1727466) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1727460, tc_Option_Ooption(_1727464)), c_Map_Omap__upds(_1727460, _1727464, _1727470, _1727468, _1727466)), _1727462), hAPP(c_Option_Ooption_OSome(_1727464), _1727472)))], (1350 ^ _775828) ^ [_795321, _795323] : [-(class_Smallcheck_Osmall(_795321)), _795323 = _795321, class_Smallcheck_Osmall(_795323)], (45351 ^ _775828) ^ [_1669159, _1669161, _1669163, _1669165, _1669167] : [hAPP(c_Map_Omap__add(_1669159, _1669161, _1669163, _1669165), _1669167) = c_Option_Ooption_ONone(_1669161), 45354 ^ _775828 : [(45357 ^ _775828) ^ [] : [-(hAPP(_1669163, _1669167) = c_Option_Ooption_ONone(_1669161))], (45355 ^ _775828) ^ [] : [-(hAPP(_1669165, _1669167) = c_Option_Ooption_ONone(_1669161))]]], (21548 ^ _775828) ^ [_1148837, _1148839] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148837) = hAPP(c_Nat_OSuc, _1148839), -(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(_1148837))), 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)), _1148839))))))], (25461 ^ _775828) ^ [_1224912, _1224914] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1224912), _1224914) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224912)), hAPP(c_Code__Numeral_Onat__of, _1224914))))], (51262 ^ _775828) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (13184 ^ _775828) ^ [_993986, _993988, _993990, _993992, _993994, _993996] : [c_Com_Ocom_OCond(_993986, _993988, _993990) = c_Com_Ocom_OLocal(_993992, _993994, _993996)], (25515 ^ _775828) ^ [_1226323, _1226325, _1226327, _1226329, _1226331, _1226333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1226329, _1226329)), hAPP(hAPP(c_Product__Type_OPair(_1226329, _1226329), hAPP(_1226333, _1226325)), hAPP(_1226333, _1226327))), _1226331)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1226323, _1226323)), hAPP(hAPP(c_Product__Type_OPair(_1226323, _1226323), _1226325), _1226327)), hAPP(hAPP(c_Relation_Oinv__image(_1226329, _1226323), _1226331), _1226333))))], (42822 ^ _775828) ^ [_1609901, _1609903, _1609905, _1609907, _1609909, _1609911] : [class_Groups_Ocomm__monoid__mult(_1609901), c_Fun_Oinj__on(_1609903, _1609905, _1609907, _1609909), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1609905, _1609901), _1609911), hAPP(c_Set_Oimage(_1609903, _1609905, _1609907), _1609909)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1609903, _1609901), hAPP(c_Fun_Ocomp(_1609905, _1609901, _1609903, _1609911), _1609907)), _1609909))], (5609 ^ _775828) ^ [_864837, _864839, _864841, _864843, _864845] : [5612 ^ _775828 : [(5618 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_864845, 5610 ^ [_864837, _864839, _864841, _864843, _864845]), 5614 ^ [_864837, _864839, _864841, _864843, _864845]))], (5616 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_864843, 5611 ^ [_864837, _864839, _864841, _864843, _864845], _864839, 5614 ^ [_864837, _864839, _864841, _864843, _864845]))], (5613 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_864841, 5610 ^ [_864837, _864839, _864841, _864843, _864845]), 5611 ^ [_864837, _864839, _864841, _864843, _864845])))]], -(c_Hoare__Mirabelle_Otriple__valid(_864837, _864839, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864837), _864841), _864843), _864845)))], (45546 ^ _775828) ^ [_1673751, _1673753, _1673755, _1673757, _1673759, _1673761, _1673763] : [hAPP(_1673751, _1673753) = hAPP(c_Option_Ooption_OSome(_1673755), _1673757), -(c_Map_Omap__comp(_1673755, _1673759, _1673761, _1673763, _1673751, _1673753) = hAPP(_1673763, _1673757))], (12213 ^ _775828) ^ [_977086, _977088, _977090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977086), _977088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977088), _977090))))], (42400 ^ _775828) ^ [_1599443, _1599445] : [-(c_Relation_Osingle__valued(_1599443, _1599443, c_Relation_OId__on(_1599443, _1599445)))], (20096 ^ _775828) ^ [_1121047] : [-(c_Int_OBit0(_1121047) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121047), _1121047))], (44633 ^ _775828) ^ [_1653059, _1653061, _1653063, _1653065] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653059, tc_fun(_1653061, tc_HOL_Obool)), _1653063), _1653065) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653061, tc_HOL_Obool), hAPP(c_Set_Oimage(_1653059, tc_fun(_1653061, tc_HOL_Obool), _1653065), _1653063)))], (44791 ^ _775828) ^ [_1656980, _1656982, _1656984] : [class_Complete__Lattice_Ocomplete__lattice(_1656980), class_Orderings_Olinorder(_1656980), 44798 ^ _775828 : [(44808 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656980), c_Complete__Lattice_OInf__class_OInf(_1656980, _1656982)), _1656984))), 44809 ^ _775828 : [(44810 ^ _775828) ^ [_1657286] : [hBOOL(hAPP(hAPP(c_member(_1656980), _1657286), _1656982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656980), _1657286), _1656984))]]], (44799 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656980), c_Complete__Lattice_OInf__class_OInf(_1656980, _1656982)), _1656984)), 44803 ^ _775828 : [(44806 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1656980), 44802 ^ [_1656980, _1656982, _1656984]), _1656984)))], (44804 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656980), 44802 ^ [_1656980, _1656982, _1656984]), _1656982)))]]]]], (21046 ^ _775828) ^ [_1137828, _1137830, _1137832, _1137834] : [class_Groups_Ouminus(_1137828), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1137830, _1137828)), _1137832), _1137834) = hAPP(c_Groups_Ouminus__class_Ouminus(_1137828), hAPP(_1137832, _1137834)))], (45961 ^ _775828) ^ [_1683291, _1683293, _1683295, _1683297] : [-(hBOOL(hAPP(hAPP(c_member(_1683291), _1683293), hAPP(c_List_Oset(_1683291), _1683295)))), hBOOL(hAPP(hAPP(c_member(_1683291), _1683293), hAPP(c_List_Oset(_1683291), c_List_Oremove1(_1683291, _1683297, _1683295))))], (51122 ^ _775828) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (23626 ^ _775828) ^ [_1189263, _1189265, _1189267, _1189269] : [-(hAPP(c_Nat_Onat_Onat__rec(_1189263, _1189265, _1189267), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1189269)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1189263), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1189269))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1189263, _1189263), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1189263, tc_fun(_1189263, _1189263)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189263, tc_fun(_1189263, _1189263)), tc_Int_Oint), c_If(_1189263)), c_Nat__Numeral_Oneg)), _1189265)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1189263, _1189263), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1189263, _1189263), tc_Int_Oint), _1189267), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1189263, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1189263, _1189265, _1189267)), c_Int_Onat)))))], (31759 ^ _775828) ^ [_1361498, _1361500, _1361502, _1361504, _1361506] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1361498, _1361498)), hAPP(hAPP(c_Product__Type_OPair(_1361498, _1361498), _1361500), _1361502)), c_Transitive__Closure_Ortrancl(_1361498, _1361504))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1361498, _1361498)), hAPP(hAPP(c_Product__Type_OPair(_1361498, _1361498), _1361502), _1361506)), c_Transitive__Closure_Otrancl(_1361498, _1361504))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361498, _1361498)), hAPP(hAPP(c_Product__Type_OPair(_1361498, _1361498), _1361500), _1361506)), c_Transitive__Closure_Otrancl(_1361498, _1361504))))], (11394 ^ _775828) ^ [_963000, _963002, _963004] : [class_Groups_Oordered__comm__monoid__add(_963000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963000), _963002), c_Groups_Ozero__class_Ozero(_963000))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963000), _963004), c_Groups_Ozero__class_Ozero(_963000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963000), _963002), _963004)), c_Groups_Ozero__class_Ozero(_963000))))], (28603 ^ _775828) ^ [_1289548, _1289550, _1289552, _1289554] : [class_Lattices_Osemilattice__sup(_1289548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289548), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289548), _1289550), _1289552)), _1289554)), 28610 ^ _775828 : [(28613 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289548), _1289552), _1289554)))], (28611 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289548), _1289550), _1289554)))]]], (13740 ^ _775828) ^ [_1004693, _1004695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004695, _1004693)), _1004693)))], (10051 ^ _775828) ^ [_938462, _938464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938462), _938464)), -(_938464 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938462), 10054 ^ [_938462, _938464]))], (36960 ^ _775828) ^ [_1471144, _1471146, _1471148, _1471150, _1471152] : [class_Rings_Osemiring__0(_1471144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471144), _1471146), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471148, _1471144), _1471150), _1471152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471148, _1471144), hAPP(hAPP(c_COMBB(_1471144, _1471144, _1471148), hAPP(c_Groups_Otimes__class_Otimes(_1471144), _1471146)), _1471150)), _1471152))], (36635 ^ _775828) ^ [_1464199, _1464201, _1464203] : [class_Orderings_Olinorder(_1464199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1464199), _1464201), _1464203)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464199, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1464199), _1464201)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1464199, _1464201, _1464203)) = hAPP(c_SetInterval_Oord__class_OatMost(_1464199), _1464203))], (50501 ^ _775828) ^ [_1791759, _1791761, _1791763, _1791765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1791759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791761)), _1791763))), -(hAPP(c_List_Orev(_1791761), hAPP(hAPP(c_List_Olist__update(_1791761, _1791763), _1791759), _1791765)) = hAPP(hAPP(c_List_Olist__update(_1791761, hAPP(c_List_Orev(_1791761), _1791763)), 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(_1791761)), _1791763)), _1791759)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1791765))], (48409 ^ _775828) ^ [_1746194, _1746196, _1746198] : [hBOOL(hAPP(c_List_Odistinct(_1746194), _1746196)), -(hBOOL(hAPP(c_List_Odistinct(_1746194), hAPP(hAPP(c_List_Odrop(_1746194), _1746198), _1746196))))], (15478 ^ _775828) ^ [_1036202, _1036204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1036202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036204), _1036202))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1036204), _1036202) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036204), _1036202)), _1036202)))], (46694 ^ _775828) ^ [_1704164, _1704166, _1704168, _1704170, _1704172] : [class_Rings_Osemiring__0(_1704164), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704164), hAPP(hAPP(c_List_Omap(_1704166, _1704164), hAPP(hAPP(c_COMBB(_1704164, _1704164, _1704166), hAPP(c_Groups_Otimes__class_Otimes(_1704164), _1704168)), _1704170)), _1704172)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1704164), _1704168), hAPP(c_List_Omonoid__add__class_Olistsum(_1704164), hAPP(hAPP(c_List_Omap(_1704166, _1704164), _1704170), _1704172))))], (39812 ^ _775828) ^ [_1538306, _1538308] : [hAPP(c_Int_ORep__Integ, _1538306) = hAPP(c_Int_ORep__Integ, _1538308), -(_1538306 = _1538308)], (34229 ^ _775828) ^ [_1412773, _1412775, _1412777, _1412779] : [hBOOL(hAPP(hAPP(c_member(_1412773), _1412775), _1412777)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412773, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1412773), _1412775), _1412779)), _1412777) = hAPP(hAPP(c_Set_Oinsert(_1412773), _1412775), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412773, tc_HOL_Obool)), _1412779), _1412777)))], (19156 ^ _775828) ^ [_1105499] : [class_Int_Onumber__ring(_1105499), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105499), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1105499))], (29110 ^ _775828) ^ [_1302951, _1302953] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302951, _1302951)), hAPP(hAPP(c_Product__Type_OPair(_1302951, _1302951), 29111 ^ [_1302951, _1302953]), 29111 ^ [_1302951, _1302953])), c_Transitive__Closure_Otrancl(_1302951, _1302953)))), -(c_Wellfounded_Oacyclic(_1302951, _1302953))], (49373 ^ _775828) ^ [_1767291, _1767293, _1767295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1767291, tc_HOL_Obool)), hAPP(c_List_Oset(_1767291), hAPP(c_List_Ofilter(_1767291, _1767293), _1767295))), hAPP(c_List_Oset(_1767291), _1767295))))], (14417 ^ _775828) ^ [_1017209, _1017211, _1017213, _1017215, _1017217] : [c_Com_Ocom_OWhile(_1017209, _1017211) = c_Com_Ocom_OCall(_1017213, _1017215, _1017217)], (4160 ^ _775828) ^ [_839361, _839363, _839365, _839367, _839369, _839371, _839373, _839375] : [-(c_Map_Orestrict__map(_839375, _839371, _839367, _839363) = c_Map_Orestrict__map(_839373, _839369, _839365, _839361)), _839375 = _839373, _839371 = _839369, _839367 = _839365, _839363 = _839361], (31613 ^ _775828) ^ [_1357859, _1357861, _1357863] : [-(c_Transitive__Closure_Ortrancl(_1357859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1357859, _1357859), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1357859, _1357861)), c_Transitive__Closure_Ortrancl(_1357859, _1357863))) = c_Transitive__Closure_Ortrancl(_1357859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1357859, _1357859), tc_HOL_Obool)), _1357861), _1357863)))], (36697 ^ _775828) ^ [_1465339, _1465341, _1465343] : [class_Orderings_Olinorder(_1465339), 36700 ^ _775828 : [(36707 ^ _775828) ^ [] : [_1465341 = _1465343, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1465339), _1465341) = hAPP(c_SetInterval_Oord__class_OlessThan(_1465339), _1465343))], (36701 ^ _775828) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1465339), _1465341) = hAPP(c_SetInterval_Oord__class_OlessThan(_1465339), _1465343), -(_1465341 = _1465343)]]], (34211 ^ _775828) ^ [_1412441, _1412443, _1412445, _1412447] : [hBOOL(hAPP(hAPP(c_member(_1412441), _1412443), _1412445)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412441, tc_HOL_Obool)), _1412445), hAPP(hAPP(c_Set_Oinsert(_1412441), _1412443), _1412447)) = hAPP(hAPP(c_Set_Oinsert(_1412441), _1412443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412441, tc_HOL_Obool)), _1412445), _1412447)))], (47685 ^ _775828) ^ [_1727655, _1727657, _1727659, _1727661, _1727663, _1727665] : [-(hBOOL(hAPP(hAPP(c_member(_1727655), _1727657), hAPP(c_List_Oset(_1727655), _1727659)))), -(hAPP(c_Map_Omap__upds(_1727655, _1727661, _1727663, _1727659, _1727665), _1727657) = hAPP(_1727663, _1727657))], (38003 ^ _775828) ^ [_1496287, _1496289] : [-(hAPP(c_Relation_OImage(_1496287, _1496287, c_Relation_OId(_1496287)), _1496289) = _1496289)], (17111 ^ _775828) ^ [_1068160, _1068162, _1068164] : [class_Int_Onumber__ring(_1068160), -(hAPP(c_Int_Onumber__class_Onumber__of(_1068160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068162), _1068164)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068160), hAPP(c_Int_Onumber__class_Onumber__of(_1068160), _1068162)), hAPP(c_Int_Onumber__class_Onumber__of(_1068160), _1068164)))], (12161 ^ _775828) ^ [_976205, _976207, _976209, _976211] : [class_Groups_Ouminus(_976205), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_976207, _976205)), _976209), _976211) = hAPP(c_Groups_Ouminus__class_Ouminus(_976205), hAPP(_976209, _976211)))], (17745 ^ _775828) ^ [_1079790, _1079792] : [class_Groups_Omonoid__mult(_1079790), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079790), _1079792), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1079792)], (32411 ^ _775828) ^ [_1374620, _1374622, _1374624] : [class_Orderings_Olinorder(_1374620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374620), _1374622)), hBOOL(hAPP(hAPP(c_member(_1374620), _1374624), _1374622)), 32422 ^ _775828 : [(32429 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374620, tc_HOL_Obool)), _1374622), hAPP(hAPP(c_Set_Oinsert(_1374620), _1374624), c_Orderings_Obot__class_Obot(tc_fun(_1374620, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374620, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1374620, _1374622) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374620), _1374624), c_Big__Operators_Olinorder__class_OMin(_1374620, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374620, tc_HOL_Obool)), _1374622), hAPP(hAPP(c_Set_Oinsert(_1374620), _1374624), c_Orderings_Obot__class_Obot(tc_fun(_1374620, tc_HOL_Obool)))))))], (32423 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374620, tc_HOL_Obool)), _1374622), hAPP(hAPP(c_Set_Oinsert(_1374620), _1374624), c_Orderings_Obot__class_Obot(tc_fun(_1374620, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374620, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1374620, _1374622) = _1374624)]]], (48894 ^ _775828) ^ [_1756719, _1756721, _1756723, _1756725] : [class_Complete__Lattice_Ocomplete__lattice(_1756719), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1756721, _1756719), hAPP(c_List_Oset(_1756721), _1756723)), _1756725) = hAPP(c_List_Ofoldl(_1756719, _1756721, hAPP(c_COMBC(_1756721, _1756719, _1756719), hAPP(hAPP(c_COMBB(_1756719, tc_fun(_1756719, _1756719), _1756721), c_Lattices_Osemilattice__sup__class_Osup(_1756719)), _1756725)), c_Orderings_Obot__class_Obot(_1756719)), _1756723))], (20066 ^ _775828) ^ [_1120598] : [c_Int_OPls = c_Int_OBit0(_1120598), -(c_Int_OPls = _1120598)], (7735 ^ _775828) ^ [_899288, _899290, _899292] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899288)), _899290) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899288)), _899292), -(_899290 = _899292)], (19958 ^ _775828) ^ [_1118521, _1118523] : [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), _1118521))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1118523)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1118521))) = 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), _1118523), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118521)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (2002 ^ _775828) ^ [_804938, _804940, _804942, _804944, _804946, _804948, _804950, _804952, _804954, _804956] : [-(c_Product__Type_Oprod_Oprod__rec(_804956, _804952, _804948, _804944, _804940) = c_Product__Type_Oprod_Oprod__rec(_804954, _804950, _804946, _804942, _804938)), _804956 = _804954, _804952 = _804950, _804948 = _804946, _804944 = _804942, _804940 = _804938], (24188 ^ _775828) ^ [_1199461, _1199463, _1199465] : [class_Orderings_Olinorder(_1199461), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199461), _1199463), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199461), _1199463), _1199465)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199461), _1199463), _1199465))], (29117 ^ _775828) ^ [_1303025, _1303027, _1303029, _1303031, _1303033, _1303035] : [c_Hoare__Mirabelle_Ohoare__derivs(_1303025, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1303025), tc_HOL_Obool)), _1303027), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1303025), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025))), hAPP(hAPP(c_COMBB(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1303025)), _1303029)), c_Com_Ocom_OBODY)), _1303031)), _1303033)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1303025), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025))), hAPP(hAPP(c_COMBB(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1303025, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1303025))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1303025)), _1303029)), 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))), _1303031)), _1303033)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1303035), _1303033)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1303025, _1303027, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1303025)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1303025), hAPP(_1303029, _1303035)), hAPP(c_Com_Ocom_OBODY, _1303035)), hAPP(_1303031, _1303035))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1303025), tc_HOL_Obool)))))], (13470 ^ _775828) ^ [_999418, _999420, _999422, _999424, _999426, _999428] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_999418, _999420, _999422), _999424, _999426, _999428)), 13471 ^ _775828 : [(13478 ^ _775828) ^ [] : [-(hBOOL(hAPP(_999418, _999424))), c_Natural_Oevaln(_999422, _999424, _999426, _999428)], (13472 ^ _775828) ^ [] : [hBOOL(hAPP(_999418, _999424)), c_Natural_Oevaln(_999420, _999424, _999426, _999428)]]], (20162 ^ _775828) ^ [_1122202, _1122204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122202), _1122204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1122202)), c_Int_OBit1(_1122204))))], (32353 ^ _775828) ^ [_1373443, _1373445, _1373447] : [class_Orderings_Olinorder(_1373443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373443), _1373445)), -(hBOOL(hAPP(hAPP(c_member(_1373443), _1373447), _1373445))), -(_1373445 = c_Orderings_Obot__class_Obot(tc_fun(_1373443, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1373443, hAPP(hAPP(c_Set_Oinsert(_1373443), _1373447), _1373445)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373443), _1373447), c_Big__Operators_Olinorder__class_OMax(_1373443, _1373445)))], (16639 ^ _775828) ^ [_1059057, _1059059, _1059061, _1059063] : [-(hBOOL(hAPP(hAPP(c_member(_1059057), _1059059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059057, tc_HOL_Obool)), _1059061), _1059063)))), hBOOL(hAPP(hAPP(c_member(_1059057), _1059059), _1059061)), -(hBOOL(hAPP(hAPP(c_member(_1059057), _1059059), _1059063)))], (44637 ^ _775828) ^ [_1653173, _1653175] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653173, tc_HOL_Obool), _1653175) = hAPP(c_Set_OCollect(_1653173), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1653173, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1653173), c_HOL_OAll(tc_fun(_1653173, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1653173, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1653173, tc_HOL_Obool), tc_HOL_Obool), _1653173), hAPP(c_COMBS(tc_fun(_1653173, 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(_1653173, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1653173, tc_HOL_Obool), tc_fun(tc_fun(_1653173, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1653173, tc_HOL_Obool))), _1653175)))), c_member(_1653173)))))], (45830 ^ _775828) ^ [_1680346, _1680348, _1680350] : [hBOOL(hAPP(c_List_Odistinct(_1680346), hAPP(hAPP(c_List_Omap(tc_prod(_1680346, _1680348), _1680346), c_Product__Type_Ofst(_1680346, _1680348)), _1680350))), -(hAPP(c_List_Oset(tc_prod(_1680346, _1680348)), _1680350) = hAPP(c_Set_OCollect(tc_prod(_1680346, _1680348)), hAPP(c_Product__Type_Oprod_Oprod__case(_1680346, _1680348, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1680346, tc_fun(_1680348, tc_Option_Ooption(_1680348)), tc_fun(_1680348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1680348), tc_HOL_Obool), tc_fun(tc_fun(_1680348, tc_Option_Ooption(_1680348)), tc_fun(_1680348, tc_HOL_Obool)), _1680346), c_COMBB(tc_Option_Ooption(_1680348), tc_HOL_Obool, _1680348)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1680348), tc_fun(tc_Option_Ooption(_1680348), tc_HOL_Obool), _1680346), c_fequal), c_Map_Omap__of(_1680346, _1680348, _1680350)))), c_Option_Ooption_OSome(_1680348)))))], (20108 ^ _775828) ^ [_1121275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1121275)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121275), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46913 ^ _775828) ^ [_1709508, _1709510, _1709512, _1709514, _1709516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709508), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709510)), _1709512))), -(hAPP(hAPP(c_List_Onth(_1709514), hAPP(hAPP(c_List_Omap(_1709510, _1709514), _1709516), _1709512)), _1709508) = hAPP(_1709516, hAPP(hAPP(c_List_Onth(_1709510), _1709512), _1709508)))], (45309 ^ _775828) ^ [_1668302, _1668304, _1668306, _1668308, _1668310, _1668312] : [hAPP(c_Map_Omap__add(_1668302, _1668304, _1668306, _1668308), _1668310) = hAPP(c_Option_Ooption_OSome(_1668304), _1668312), -(hAPP(_1668308, _1668310) = hAPP(c_Option_Ooption_OSome(_1668304), _1668312)), 45316 ^ _775828 : [(45319 ^ _775828) ^ [] : [-(hAPP(_1668306, _1668310) = hAPP(c_Option_Ooption_OSome(_1668304), _1668312))], (45317 ^ _775828) ^ [] : [-(hAPP(_1668308, _1668310) = c_Option_Ooption_ONone(_1668304))]]], (19784 ^ _775828) ^ [_1115671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1115671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1115671)))], (30385 ^ _775828) ^ [_1331066, _1331068] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331066), _1331068)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1331066, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1331066, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1331066, tc_HOL_Obool), tc_fun(_1331066, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1331066, tc_HOL_Obool))), _1331068)))))], (31933 ^ _775828) ^ [_1366200, _1366202, _1366204] : [class_Lattices_Olattice(_1366200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366200), _1366202)), hBOOL(hAPP(hAPP(c_member(_1366200), _1366204), _1366202)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1366200), _1366204), c_Big__Operators_Olattice__class_OInf__fin(_1366200, _1366202)) = _1366204)], (4810 ^ _775828) ^ [_849308, _849310] : [_849310 = _849308, -(c_Groups_Oone__class_Oone(_849310) = c_Groups_Oone__class_Oone(_849308))], (3584 ^ _775828) ^ [_830271, _830273, _830275, _830277, _830279, _830281, _830283, _830285] : [-(c_New__Random__Sequence_Oneg__map(_830285, _830281, _830277, _830273) = c_New__Random__Sequence_Oneg__map(_830283, _830279, _830275, _830271)), _830285 = _830283, _830281 = _830279, _830277 = _830275, _830273 = _830271], (34803 ^ _775828) ^ [_1425206, _1425208, _1425210] : [class_Orderings_Olinorder(_1425206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425206), _1425208)), -(_1425208 = c_Orderings_Obot__class_Obot(tc_fun(_1425206, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425206), _1425210)), -(_1425210 = c_Orderings_Obot__class_Obot(tc_fun(_1425206, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425206, tc_HOL_Obool)), _1425208), _1425210) = c_Orderings_Obot__class_Obot(tc_fun(_1425206, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1425206, c_Orderings_Oord__class_Omin(_1425206), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425206, tc_HOL_Obool)), _1425208), _1425210)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1425206), c_Big__Operators_Olattice_OInf__fin(_1425206, c_Orderings_Oord__class_Omin(_1425206), _1425208)), c_Big__Operators_Olattice_OInf__fin(_1425206, c_Orderings_Oord__class_Omin(_1425206), _1425210)))], (10732 ^ _775828) ^ [_951163, _951165] : [class_Groups_Ocomm__monoid__mult(_951163), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951163), c_Groups_Oone__class_Oone(_951163)), _951165) = _951165)], (39572 ^ _775828) ^ [_1531685, _1531687, _1531689, _1531691] : [-(_1531685 = c_Orderings_Obot__class_Obot(tc_fun(_1531687, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531687, tc_fun(_1531689, tc_HOL_Obool)), _1531685), hAPP(c_COMBK(tc_fun(_1531689, tc_HOL_Obool), _1531687), _1531691)) = _1531691)], (5583 ^ _775828) ^ [_864294] : [hAPP(c_Nat_OSuc, _864294) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13953 ^ _775828) ^ [_1008570, _1008572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008570)), -(c_SMT_Oz3mod(_1008572, _1008570) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008572, _1008570))], (19188 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (28020 ^ _775828) ^ [_1277127, _1277129] : [-(c_FunDef_Oreduction__pair(_1277127, _1277129)), c_Wellfounded_Owf(_1277127, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool), tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool)), _1277129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1277127, _1277127, _1277127), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool), tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool)), _1277129)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool), tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool)), _1277129))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool), tc_fun(tc_prod(_1277127, _1277127), tc_HOL_Obool)), _1277129)))], (48157 ^ _775828) ^ [_1738866, _1738868, _1738870, _1738872] : [hBOOL(hAPP(hAPP(c_member(_1738866), _1738868), c_Wellfounded_Oacc(_1738866, _1738870))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738866)), _1738872), c_Wellfounded_Oacc(tc_List_Olist(_1738866), c_List_Olistrel1(_1738866, _1738870)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738866)), hAPP(hAPP(c_List_Olist_OCons(_1738866), _1738868), _1738872)), c_Wellfounded_Oacc(tc_List_Olist(_1738866), c_List_Olistrel1(_1738866, _1738870)))))], (31841 ^ _775828) ^ [_1363484, _1363486, _1363488, _1363490] : [c_Wellfounded_Oacyclic(_1363484, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1363484, _1363484)), hAPP(hAPP(c_Product__Type_OPair(_1363484, _1363484), _1363486), _1363488)), _1363490)), 31844 ^ _775828 : [(31847 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1363484, _1363484)), hAPP(hAPP(c_Product__Type_OPair(_1363484, _1363484), _1363488), _1363486)), c_Transitive__Closure_Ortrancl(_1363484, _1363490)))], (31845 ^ _775828) ^ [] : [-(c_Wellfounded_Oacyclic(_1363484, _1363490))]]], (14155 ^ _775828) ^ [_1012473, _1012475] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1012473, _1012475)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1012475)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8110 ^ _775828) ^ [_906168, _906170] : [-(hBOOL(hAPP(_906168, hAPP(c_Int_Onat, _906170)))), 8114 ^ _775828 : [(8117 ^ _775828) ^ [] : [hBOOL(hAPP(_906168, 8113 ^ [_906168, _906170]))], (8115 ^ _775828) ^ [] : [-(_906170 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8113 ^ [_906168, _906170]))]], 8118 ^ _775828 : [(8121 ^ _775828) ^ [] : [hBOOL(hAPP(_906168, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8119 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _906170), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (47337 ^ _775828) ^ [_1720095, _1720097, _1720099, _1720101, _1720103, _1720105] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1720095, _1720097), hAPP(hAPP(c_List_Ozip(_1720095, _1720097), _1720099), _1720101)), _1720103), _1720105) = hAPP(hAPP(c_List_Ozip(_1720095, _1720097), hAPP(hAPP(c_List_Olist__update(_1720095, _1720099), _1720103), hAPP(c_Product__Type_Ofst(_1720095, _1720097), _1720105))), hAPP(hAPP(c_List_Olist__update(_1720097, _1720101), _1720103), hAPP(c_Product__Type_Osnd(_1720095, _1720097), _1720105))))], (22414 ^ _775828) ^ [_1165719, _1165721, _1165723] : [class_Fields_Olinordered__field__inverse__zero(_1165719), -(hAPP(c_Groups_Oabs__class_Oabs(_1165719), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165719), _1165721), _1165723)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165719), hAPP(c_Groups_Oabs__class_Oabs(_1165719), _1165721)), hAPP(c_Groups_Oabs__class_Oabs(_1165719), _1165723)))], (14818 ^ _775828) ^ [_1023724, _1023726, _1023728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023724)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023728), _1023724)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023726), _1023728)), _1023724))], (29559 ^ _775828) ^ [_1312156, _1312158] : [_1312158 = c_Orderings_Obot__class_Obot(tc_fun(_1312156, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312156, tc_HOL_Obool)), _1312158), c_Orderings_Obot__class_Obot(tc_fun(_1312156, tc_HOL_Obool)))))], (47871 ^ _775828) ^ [_1732223, _1732225, _1732227, _1732229, _1732231] : [-(hAPP(hAPP(c_List_Omap(_1732223, _1732225), _1732227), hAPP(hAPP(c_List_Oappend(_1732223), _1732229), _1732231)) = hAPP(hAPP(c_List_Oappend(_1732225), hAPP(hAPP(c_List_Omap(_1732223, _1732225), _1732227), _1732229)), hAPP(hAPP(c_List_Omap(_1732223, _1732225), _1732227), _1732231)))], (43514 ^ _775828) ^ [_1626567, _1626569, _1626571, _1626573, _1626575, _1626577, _1626579, _1626581] : [class_Groups_Ocomm__monoid__add(_1626567), c_Fun_Oinj__on(_1626569, _1626571, _1626573, _1626575), _1626577 = hAPP(c_Set_Oimage(_1626569, _1626571, _1626573), _1626575), 43528 ^ _775828 : [(43531 ^ _775828) ^ [] : [hAPP(_1626579, 43527 ^ [_1626567, _1626569, _1626571, _1626573, _1626575, _1626577, _1626579, _1626581]) = hAPP(_1626581, hAPP(_1626573, 43527 ^ [_1626567, _1626569, _1626571, _1626573, _1626575, _1626577, _1626579, _1626581]))], (43529 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626569), 43527 ^ [_1626567, _1626569, _1626571, _1626573, _1626575, _1626577, _1626579, _1626581]), _1626575)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626571, _1626567), _1626581), _1626577) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626569, _1626567), _1626579), _1626575))], (40117 ^ _775828) ^ [_1544975, _1544977, _1544979, _1544981, _1544983] : [-(hAPP(c_Set_Oimage(_1544975, _1544977, hAPP(hAPP(c_COMBB(_1544979, _1544977, _1544975), _1544981), _1544983)), c_Orderings_Otop__class_Otop(tc_fun(_1544975, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1544979, _1544977, _1544981), hAPP(c_Set_Oimage(_1544975, _1544979, _1544983), c_Orderings_Otop__class_Otop(tc_fun(_1544975, tc_HOL_Obool)))))], (34417 ^ _775828) ^ [_1417320, _1417322, _1417324] : [class_Lattices_Olattice(_1417320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417320), _1417322)), -(_1417324 = c_Orderings_Obot__class_Obot(tc_fun(_1417320, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417320, tc_HOL_Obool)), _1417324), _1417322)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417320), c_Big__Operators_Olattice__class_OInf__fin(_1417320, _1417324)), c_Big__Operators_Olattice__class_OInf__fin(_1417320, _1417322)) = c_Big__Operators_Olattice__class_OInf__fin(_1417320, _1417322))], (980 ^ _775828) ^ [_790696, _790698] : [-(class_Groups_Oordered__ab__group__add__abs(_790696)), _790698 = _790696, class_Groups_Oordered__ab__group__add__abs(_790698)], (44000 ^ _775828) ^ [_1636249, _1636251, _1636253, _1636255, _1636257] : [c_Finite__Set_Ofun__left__comm(_1636249, _1636251, _1636253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636249), _1636255)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1636249, _1636251, _1636253, _1636257, _1636255), hAPP(hAPP(c_Finite__Set_Ofold(_1636249, _1636251, _1636253), _1636257), _1636255))))], (13911 ^ _775828) ^ [_1007778, _1007780, _1007782, _1007784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007780), _1007782)), -(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), _1007782), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007784, _1007778))), _1007780))))], (15472 ^ _775828) ^ [_1036043, _1036045, _1036047] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036045), _1036047)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036043), _1036045)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036043), _1036047)))], (40616 ^ _775828) ^ [_1556621, _1556623, _1556625] : [c_Equiv__Relations_Oequivp(_1556621, _1556623), -(hBOOL(hAPP(hAPP(_1556623, _1556625), _1556625)))], (39518 ^ _775828) ^ [_1530462, _1530464, _1530466, _1530468, _1530470] : [hBOOL(hAPP(hAPP(c_member(_1530462), _1530464), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530466, tc_fun(_1530462, tc_HOL_Obool)), _1530468), _1530470))), 39522 ^ _775828 : [(39525 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530462), _1530464), hAPP(_1530470, 39521 ^ [_1530462, _1530464, _1530466, _1530468, _1530470]))))], (39523 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530466), 39521 ^ [_1530462, _1530464, _1530466, _1530468, _1530470]), _1530468)))]]], (10031 ^ _775828) ^ [_938086, _938088, _938090] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938086, tc_HOL_Obool)), _938088) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938086, tc_HOL_Obool)), _938090), -(_938088 = _938090)], (39052 ^ _775828) ^ [_1519250, _1519252, _1519254, _1519256, _1519258, _1519260] : [c_Fun_Oinj__on(_1519250, _1519252, _1519254, _1519256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519250, tc_HOL_Obool)), _1519258), _1519256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519250, tc_HOL_Obool)), _1519260), _1519256)), -(hAPP(c_Set_Oimage(_1519250, _1519252, _1519254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519250, tc_HOL_Obool)), _1519258), _1519260)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519252, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1519250, _1519252, _1519254), _1519258)), hAPP(c_Set_Oimage(_1519250, _1519252, _1519254), _1519260)))], (28215 ^ _775828) ^ [_1281762, _1281764] : [class_Lattices_Osemilattice__sup(_1281762), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281762), _1281764), _1281764) = _1281764)], (47369 ^ _775828) ^ [_1720877, _1720879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1720877), _1720879)), -(c_List_Oupto(_1720879, _1720877) = c_List_Olist_ONil(tc_Int_Oint))], (13060 ^ _775828) ^ [_991732, _991734, _991736, _991738, _991740, _991742] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_991732, _991734, _991736), _991738, _991740, _991742), 13065 ^ _775828 : [(13068 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_991734, _991738, _991740, _991742))], (13066 ^ _775828) ^ [] : [-(hBOOL(hAPP(_991732, _991738)))]], 13069 ^ _775828 : [(13072 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_991736, _991738, _991740, _991742))], (13070 ^ _775828) ^ [] : [hBOOL(hAPP(_991732, _991738))]]], (20984 ^ _775828) ^ [_1136797] : [-(_1136797 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 20987 ^ _775828 : [(20994 ^ _775828) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1136797, 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, _1136797) = 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), _1136797), 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)))], (20988 ^ _775828) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1136797, 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, _1136797) = 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), _1136797), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (51056 ^ _775828) ^ [_1803694, _1803696] : [class_Lattices_Oboolean__algebra(_1803694), -(class_Lattices_Oboolean__algebra(tc_fun(_1803696, _1803694)))], (35353 ^ _775828) ^ [_1439194, _1439196, _1439198] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1439194, tc_HOL_Obool)), _1439196), hAPP(c_Set_OPow(_1439194), _1439198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439194, tc_HOL_Obool)), _1439196), _1439198)))], (33288 ^ _775828) ^ [_1392497, _1392499, _1392501, _1392503] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1392497, tc_Option_Ooption(_1392499)), hAPP(c_COMBK(tc_Option_Ooption(_1392499), _1392497), c_Option_Ooption_ONone(_1392499))), _1392501), c_Option_Ooption_ONone(_1392499)), _1392503) = c_Option_Ooption_ONone(_1392499))], (49333 ^ _775828) ^ [_1766379, _1766381] : [-(_1766379 = c_List_Olist_ONil(_1766381)), -(hAPP(hAPP(c_List_Oappend(_1766381), c_List_Obutlast(_1766381, _1766379)), hAPP(hAPP(c_List_Olist_OCons(_1766381), c_List_Olast(_1766381, _1766379)), c_List_Olist_ONil(_1766381))) = _1766379)], (16069 ^ _775828) ^ [_1047948, _1047950, _1047952] : [-(hBOOL(hAPP(_1047948, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047950), _1047952)))), 16072 ^ _775828 : [(16075 ^ _775828) ^ [] : [hBOOL(hAPP(_1047948, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16073 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047950), _1047952)))]], 16077 ^ _775828 : [(16080 ^ _775828) ^ [] : [hBOOL(hAPP(_1047948, 16076 ^ [_1047948, _1047950, _1047952]))], (16078 ^ _775828) ^ [] : [-(_1047950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047952), 16076 ^ [_1047948, _1047950, _1047952]))]]], (1980 ^ _775828) ^ [_804549, _804551, _804553, _804555, _804557, _804559, _804561, _804563, _804565, _804567] : [-(c_Product__Type_Oprod_Oprod__size(_804567, _804563, _804559, _804555, _804551) = c_Product__Type_Oprod_Oprod__size(_804565, _804561, _804557, _804553, _804549)), _804567 = _804565, _804563 = _804561, _804559 = _804557, _804555 = _804553, _804551 = _804549], (27875 ^ _775828) ^ [_1274287, _1274289, _1274291, _1274293] : [c_Wellfounded_Owf(_1274287, _1274289), c_Wellfounded_Owf(_1274291, _1274293), -(c_Wellfounded_Owf(tc_prod(_1274287, _1274291), c_Wellfounded_Olex__prod(_1274287, _1274291, _1274289, _1274293)))], (4480 ^ _775828) ^ [_844209, _844211, _844213, _844215] : [-(c_Product__Type_OPair(_844215, _844211) = c_Product__Type_OPair(_844213, _844209)), _844215 = _844213, _844211 = _844209], (25122 ^ _775828) ^ [_1219243, _1219245, _1219247, _1219249] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1219243, _1219245)), c_Nitpick_Opair__box_OPairBox(_1219243, _1219245, _1219247, _1219249)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31849 ^ _775828) ^ [_1363679, _1363681, _1363683, _1363685] : [-(c_Wellfounded_Oacyclic(_1363679, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1363679, _1363679)), hAPP(hAPP(c_Product__Type_OPair(_1363679, _1363679), _1363681), _1363683)), _1363685))), c_Wellfounded_Oacyclic(_1363679, _1363685), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1363679, _1363679)), hAPP(hAPP(c_Product__Type_OPair(_1363679, _1363679), _1363683), _1363681)), c_Transitive__Closure_Ortrancl(_1363679, _1363685))))], (29935 ^ _775828) ^ [_1320707, _1320709, _1320711, _1320713, _1320715] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1320707, _1320709, hAPP(hAPP(c_COMBC(_1320707, tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_fun(_1320709, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1320709, tc_fun(tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_fun(_1320709, tc_HOL_Obool)), _1320707), c_COMBC(_1320709, tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1320709, tc_prod(_1320707, _1320709)), tc_fun(_1320709, tc_fun(tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_HOL_Obool)), _1320707), hAPP(c_COMBB(tc_prod(_1320707, _1320709), tc_fun(tc_fun(tc_prod(_1320707, _1320709), tc_HOL_Obool), tc_HOL_Obool), _1320709), c_member(tc_prod(_1320707, _1320709)))), c_Product__Type_OPair(_1320707, _1320709)))), _1320711)), _1320713), _1320715)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1320709, _1320707)), hAPP(hAPP(c_Product__Type_OPair(_1320709, _1320707), _1320713), _1320715)), hAPP(c_Relation_Oconverse(_1320707, _1320709), _1320711))))], (27537 ^ _775828) ^ [_1265174, _1265176] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1265174), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265176))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1265174), _1265176)))], (13805 ^ _775828) ^ [_1005766, _1005768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005766)), 13808 ^ _775828 : [(13811 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005768, _1005766)), _1005766)))], (13809 ^ _775828) ^ [] : [-(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, _1005768, _1005766))))]]], (1650 ^ _775828) ^ [_799071, _799073] : [-(class_Rings_Osemiring__1(_799071)), _799073 = _799071, class_Rings_Osemiring__1(_799073)], (44125 ^ _775828) ^ [_1638825, _1638827, _1638829, _1638831] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1638829), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638825, tc_fun(_1638829, tc_HOL_Obool)), _1638827), _1638831)))), 44126 ^ _775828 : [(44127 ^ _775828) ^ [_1638899] : [hBOOL(hAPP(hAPP(c_member(_1638825), _1638899), _1638827)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638829), hAPP(_1638831, _1638899)))]]], (734 ^ _775828) ^ [_787013, _787015, _787017, _787019, _787021, _787023] : [-(c_Finite__Set_Ofolding__one(_787021, _787017, _787013)), c_Finite__Set_Ofolding__one(_787023, _787019, _787015), _787023 = _787021, _787019 = _787017, _787015 = _787013], (15390 ^ _775828) ^ [_1034487, _1034489, _1034491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034487), _1034489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034487), _1034491)), 15397 ^ _775828 : [(15404 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034489), _1034491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034489), _1034487)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034491), _1034487))))], (15398 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034489), _1034487)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034491), _1034487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034489), _1034491)))]]], (36914 ^ _775828) ^ [_1469671, _1469673, _1469675, _1469677] : [class_Groups_Oab__group__add(_1469671), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469673, _1469671), hAPP(hAPP(c_COMBB(_1469671, _1469671, _1469673), c_Groups_Ouminus__class_Ouminus(_1469671)), _1469675)), _1469677) = hAPP(c_Groups_Ouminus__class_Ouminus(_1469671), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469673, _1469671), _1469675), _1469677)))], (12383 ^ _775828) ^ [_980136, _980138, _980140] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980138), _980140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980136), _980138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980136), _980140)))], (26778 ^ _775828) ^ [_1249018, _1249020, _1249022, _1249024] : [class_Orderings_Oorder(_1249018), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1249018, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249020), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249022), _1249024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249018), hAPP(_1249020, _1249022)), hAPP(_1249020, _1249024))))], (9125 ^ _775828) ^ [_921695, _921697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921695)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _921695), _921697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _921695)), hAPP(c_Int_Onat, _921697)))], (46903 ^ _775828) ^ [_1709229, _1709231, _1709233, _1709235, _1709237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709229), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709231)), _1709233))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709229), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709235)), _1709237))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1709231, _1709235)), hAPP(hAPP(c_List_Ozip(_1709231, _1709235), _1709233), _1709237)), _1709229) = hAPP(hAPP(c_Product__Type_OPair(_1709231, _1709235), hAPP(hAPP(c_List_Onth(_1709231), _1709233), _1709229)), hAPP(hAPP(c_List_Onth(_1709235), _1709237), _1709229)))], (14233 ^ _775828) ^ [_1013672, _1013674] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013672, _1013674)), _1013672)))], (51178 ^ _775828) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51486 ^ _775828) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (20566 ^ _775828) ^ [_1129241, _1129243, _1129245] : [class_Rings_Olinordered__idom(_1129241), 20569 ^ _775828 : [(20578 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129241), hAPP(hAPP(c_Power_Opower__class_Opower(_1129241), _1129243), 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(_1129241), _1129245), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1129241)), _1129243 = c_Groups_Ozero__class_Ozero(_1129241), _1129245 = c_Groups_Ozero__class_Ozero(_1129241)], (20570 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129241), hAPP(hAPP(c_Power_Opower__class_Opower(_1129241), _1129243), 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(_1129241), _1129245), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1129241), 20573 ^ _775828 : [(20576 ^ _775828) ^ [] : [-(_1129245 = c_Groups_Ozero__class_Ozero(_1129241))], (20574 ^ _775828) ^ [] : [-(_1129243 = c_Groups_Ozero__class_Ozero(_1129241))]]]]], (36107 ^ _775828) ^ [_1454017, _1454019, _1454021] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454017), _1454019))), 36110 ^ _775828 : [(36117 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454021), _1454019))), -(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)), _1454017)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454021), _1454019)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (36111 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454021), _1454019)), -(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)), _1454017)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454021), _1454019)) = 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))))]]], (17997 ^ _775828) ^ [_1084243, _1084245, _1084247, _1084249] : [class_Rings_Olinordered__semidom(_1084243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084245), _1084247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084243), c_Groups_Oone__class_Oone(_1084243)), _1084249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084243), hAPP(hAPP(c_Power_Opower__class_Opower(_1084243), _1084249), _1084245)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084243), _1084249), _1084247))))], (15878 ^ _775828) ^ [_1043847, _1043849, _1043851] : [class_Rings_Oring__1(_1043847), hBOOL(hAPP(hAPP(c_member(_1043847), _1043849), c_Int_Oring__1__class_OInts(_1043847))), hBOOL(hAPP(hAPP(c_member(_1043847), _1043851), c_Int_Oring__1__class_OInts(_1043847))), -(hBOOL(hAPP(hAPP(c_member(_1043847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043847), _1043849), _1043851)), c_Int_Oring__1__class_OInts(_1043847))))], (47083 ^ _775828) ^ [_1713595, _1713597, _1713599, _1713601] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713595) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1713597), hAPP(hAPP(c_List_Olist_OCons(_1713597), _1713599), _1713601)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713595)) = hAPP(hAPP(c_List_Onth(_1713597), _1713601), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713595)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (21192 ^ _775828) ^ [_1142823, _1142825, _1142827] : [class_Rings_Odivision__ring(_1142823), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1142823), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142823), _1142825), _1142827)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142823), hAPP(c_Groups_Ouminus__class_Ouminus(_1142823), _1142825)), _1142827))], (17187 ^ _775828) ^ [_1069670, _1069672, _1069674] : [class_Groups_Oordered__ab__group__add__abs(_1069670), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069670), hAPP(c_Groups_Oabs__class_Oabs(_1069670), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069670), _1069672), _1069674))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069670), hAPP(c_Groups_Oabs__class_Oabs(_1069670), _1069672)), hAPP(c_Groups_Oabs__class_Oabs(_1069670), _1069674)))))], (14524 ^ _775828) ^ [_1018969] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018969, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1018969)], (30139 ^ _775828) ^ [_1325260, _1325262, _1325264, _1325266] : [-(c_Nitpick_Ofold__graph_H(_1325260, _1325262, _1325264, _1325266, c_Orderings_Obot__class_Obot(tc_fun(_1325260, tc_HOL_Obool)), _1325266))], (5845 ^ _775828) ^ [_868938, _868940, _868942] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _868938, _868940, _868942), -(_868942 = _868938)], (50740 ^ _775828) ^ [_1797416] : [-(c_List_Oremdups(_1797416, c_List_Olist_ONil(_1797416)) = c_List_Olist_ONil(_1797416))], (2394 ^ _775828) ^ [_810936, _810938, _810940, _810942] : [-(c_Nitpick_Ouminus__frac(_810942, _810938) = c_Nitpick_Ouminus__frac(_810940, _810936)), _810942 = _810940, _810938 = _810936], (24825 ^ _775828) ^ [_1212600, _1212602, _1212604] : [-(c_Nitpick_Oplus__frac(_1212600, _1212602, _1212604) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1212600), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1212600), _1212602), hAPP(c_Nitpick_Odenom(_1212600), _1212604))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1212600), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1212600), tc_Int_Oint), c_Nitpick_Ofrac(_1212600)), 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(_1212600), _1212602))), 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(_1212600), _1212602))))), 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(_1212600), _1212604))), 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(_1212600), _1212604)))))), c_COMBI(tc_Int_Oint))))], (6999 ^ _775828) ^ [_886697, _886699] : [class_Rings_Omult__zero(_886697), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_886697), _886699), c_Groups_Ozero__class_Ozero(_886697)) = c_Groups_Ozero__class_Ozero(_886697))], (42430 ^ _775828) ^ [_1599939, _1599941, _1599943, _1599945, _1599947, _1599949] : [c_Relation_Osingle__valued(_1599939, _1599941, _1599943), hBOOL(hAPP(hAPP(c_member(tc_prod(_1599939, _1599941)), hAPP(hAPP(c_Product__Type_OPair(_1599939, _1599941), _1599945), _1599947)), _1599943)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1599939, _1599941)), hAPP(hAPP(c_Product__Type_OPair(_1599939, _1599941), _1599945), _1599949)), _1599943)), -(_1599947 = _1599949)], (19710 ^ _775828) ^ [_1114449, _1114451] : [c_Int_Oiszero(_1114449, hAPP(c_Int_Onumber__class_Onumber__of(_1114449), c_Int_OBit1(_1114451))), class_Int_Onumber__ring(_1114449), class_Int_Oring__char__0(_1114449)], (29631 ^ _775828) ^ [_1313603, _1313605, _1313607] : [hBOOL(hAPP(_1313603, _1313605)), -(hAPP(c_Set_OCollect(_1313607), hAPP(hAPP(c_COMBS(_1313607, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1313607), c_fconj), hAPP(hAPP(c_COMBC(_1313607, _1313607, tc_HOL_Obool), c_fequal), _1313605))), _1313603)) = hAPP(hAPP(c_Set_Oinsert(_1313607), _1313605), c_Orderings_Obot__class_Obot(tc_fun(_1313607, tc_HOL_Obool))))], (36623 ^ _775828) ^ [_1463913, _1463915, _1463917, _1463919] : [class_Orderings_Olinorder(_1463913), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463913, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1463913), _1463915)), c_SetInterval_Oord__class_OatLeastAtMost(_1463913, _1463917, _1463919)) = c_SetInterval_Oord__class_OatLeastAtMost(_1463913, _1463917, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1463913), _1463915), _1463919)))], (46682 ^ _775828) ^ [_1703804, _1703806, _1703808] : [class_Groups_Omonoid__add(_1703804), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1703804), hAPP(hAPP(c_List_Olist_OCons(_1703804), _1703806), _1703808)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1703804), _1703806), hAPP(c_List_Omonoid__add__class_Olistsum(_1703804), _1703808)))], (5537 ^ _775828) ^ [_863504, _863506] : [_863504 = _863506, -(hAPP(c_Com_Ocom_OBODY, _863504) = hAPP(c_Com_Ocom_OBODY, _863506))], (6115 ^ _775828) ^ [_872926, _872928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872928), hAPP(c_Nat_OSuc, _872926))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872926), _872928))], (47992 ^ _775828) ^ [_1734856, _1734858, _1734860] : [-(hAPP(hAPP(c_List_Oappend(_1734856), _1734858), _1734860) = c_List_Olist_ONil(_1734856)), _1734858 = c_List_Olist_ONil(_1734856), _1734860 = c_List_Olist_ONil(_1734856)], (44409 ^ _775828) ^ [_1647658] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647658, tc_HOL_Obool) = c_Set_OBall(_1647658))], (49205 ^ _775828) ^ [_1763637, _1763639, _1763641] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763637)), _1763639), c_List_Olists(_1763637, _1763641)))), 49206 ^ _775828 : [(49209 ^ _775828) ^ [_1763765, _1763767] : [_1763639 = hAPP(hAPP(c_List_Olist_OCons(_1763637), _1763767), _1763765), hBOOL(hAPP(hAPP(c_member(_1763637), _1763767), _1763641)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763637)), _1763765), c_List_Olists(_1763637, _1763641)))], (49207 ^ _775828) ^ [] : [_1763639 = c_List_Olist_ONil(_1763637)]]], (4704 ^ _775828) ^ [_847709, _847711] : [_847711 = _847709, -(c_Finite__Set_Ofinite(_847711) = c_Finite__Set_Ofinite(_847709))], (9095 ^ _775828) ^ [_921279, _921281] : [hAPP(c_Int_Onat, _921279) = _921281, 9098 ^ _775828 : [(9105 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921279))), -(_921281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9099 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921279)), -(_921279 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921281))]]], (46119 ^ _775828) ^ [_1687581, _1687583, _1687585] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687581)), _1687583) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687581)), _1687585)), _1687583 = _1687585], (45747 ^ _775828) ^ [_1678532, _1678534, _1678536, _1678538, _1678540] : [hAPP(hAPP(c_List_Omap(_1678532, _1678534), _1678536), _1678538) = hAPP(hAPP(c_List_Omap(_1678532, _1678534), _1678536), _1678540), c_Fun_Oinj__on(_1678532, _1678534, _1678536, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1678532, tc_HOL_Obool)), hAPP(c_List_Oset(_1678532), _1678538)), hAPP(c_List_Oset(_1678532), _1678540))), -(_1678538 = _1678540)], (20210 ^ _775828) ^ [_1123040, _1123042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123040), _1123042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1123040)), c_Int_OBit0(_1123042))))], (34505 ^ _775828) ^ [_1419219, _1419221, _1419223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1419219), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419219, tc_HOL_Obool)), _1419221), _1419223))), -(hAPP(c_Finite__Set_Ocard(_1419219), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419219, tc_HOL_Obool)), _1419221), _1419223)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1419219), _1419221)), hAPP(c_Finite__Set_Ocard(_1419219), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419219, tc_HOL_Obool)), _1419221), _1419223))))], (7391 ^ _775828) ^ [_893708, _893710] : [class_Rings_Ocomm__semiring__1(_893708), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_893708), _893710), c_Groups_Ozero__class_Ozero(_893708)) = c_Groups_Ozero__class_Ozero(_893708))], (15142 ^ _775828) ^ [_1030019, _1030021, _1030023] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030019), _1030021)), _1030023) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030019), _1030023)), _1030021))], (39626 ^ _775828) ^ [_1533163, _1533165, _1533167, _1533169, _1533171] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533163, tc_fun(_1533165, tc_HOL_Obool)), _1533167), hAPP(hAPP(c_COMBS(_1533163, tc_fun(_1533165, tc_HOL_Obool), tc_fun(_1533165, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533165, tc_HOL_Obool), tc_fun(tc_fun(_1533165, tc_HOL_Obool), tc_fun(_1533165, tc_HOL_Obool)), _1533163), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533165, tc_HOL_Obool))), _1533169)), _1533171)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533165, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533163, tc_fun(_1533165, tc_HOL_Obool)), _1533167), _1533169)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533163, tc_fun(_1533165, tc_HOL_Obool)), _1533167), _1533171)))], (25054 ^ _775828) ^ [_1217895, _1217897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1217895), _1217897)), -(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)), _1217895)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1217897))))], (28795 ^ _775828) ^ [_1293902, _1293904] : [28796 ^ _775828 : [(28797 ^ _775828) ^ [_1293948] : [hBOOL(hAPP(_1293902, _1293948))]], -(hBOOL(hAPP(_1293902, c_Hilbert__Choice_OEps(_1293904, _1293902))))], (13607 ^ _775828) ^ [_1002067, _1002069, _1002071, _1002073, _1002075, _1002077] : [c_Com_Ocom_OLocal(_1002067, _1002069, _1002071) = c_Com_Ocom_OCall(_1002073, _1002075, _1002077)], (16431 ^ _775828) ^ [_1055271, _1055273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1055271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055271), _1055273)), -(c_Divides_Odivmod__nat(_1055273, _1055271) = 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), _1055273), _1055271)), _1055271))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055273), _1055271), _1055271)))], (11903 ^ _775828) ^ [_971726, _971728, _971730] : [class_Groups_Oordered__comm__monoid__add(_971726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971726), _971728), c_Groups_Ozero__class_Ozero(_971726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971726), _971730), c_Groups_Ozero__class_Ozero(_971726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971726), _971728), _971730)), c_Groups_Ozero__class_Ozero(_971726))))], (20632 ^ _775828) ^ [_1130226, _1130228, _1130230] : [class_Rings_Ocomm__semiring__1(_1130226), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1130226), _1130228), 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)))), _1130230)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130226), hAPP(hAPP(c_Power_Opower__class_Opower(_1130226), _1130228), _1130230)), hAPP(hAPP(c_Power_Opower__class_Opower(_1130226), _1130228), _1130230)))], (26423 ^ _775828) ^ [_1242494, _1242496, _1242498, _1242500, _1242502] : [class_Rings_Ocomm__semiring__1(_1242494), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242494), hAPP(hAPP(c_Power_Opower__class_Opower(_1242494), _1242496), _1242498)), _1242500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242502), _1242498)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242494), hAPP(hAPP(c_Power_Opower__class_Opower(_1242494), _1242496), _1242502)), _1242500)))], (48385 ^ _775828) ^ [_1745668, _1745670, _1745672, _1745674] : [-(hAPP(hAPP(c_List_Otake(_1745668), _1745670), hAPP(hAPP(c_List_Odrop(_1745668), _1745672), _1745674)) = hAPP(hAPP(c_List_Odrop(_1745668), _1745672), hAPP(hAPP(c_List_Otake(_1745668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745670), _1745672)), _1745674)))], (2216 ^ _775828) ^ [_808235, _808237] : [_808237 = _808235, -(c_Nitpick_Ozero__frac(_808237) = c_Nitpick_Ozero__frac(_808235))], (41530 ^ _775828) ^ [_1579377, _1579379] : [class_Orderings_Olinorder(_1579377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579377), _1579379)), -(c_Big__Operators_Olinorder__class_OMax(_1579377, _1579379) = hAPP(c_Finite__Set_Ofold1(_1579377, c_Orderings_Oord__class_Omax(_1579377)), _1579379))], (24046 ^ _775828) ^ [_1196845, _1196847, _1196849, _1196851] : [class_Orderings_Olinorder(_1196845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196845), _1196847), _1196849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196845), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196845), _1196847), _1196851)), _1196849)))], (49339 ^ _775828) ^ [_1766462, _1766464, _1766466, _1766468] : [hAPP(hAPP(c_List_Oappend(_1766462), _1766464), hAPP(hAPP(c_List_Olist_OCons(_1766462), _1766466), c_List_Olist_ONil(_1766462))) = _1766468, 49342 ^ _775828 : [(49347 ^ _775828) ^ [] : [-(c_List_Olast(_1766462, _1766468) = _1766466)], (49345 ^ _775828) ^ [] : [-(c_List_Obutlast(_1766462, _1766468) = _1766464)], (49343 ^ _775828) ^ [] : [_1766468 = c_List_Olist_ONil(_1766462)]]], (23616 ^ _775828) ^ [_1189198, _1189200] : [-(c_Divides_Odivmod__nat(_1189200, _1189198) = 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), _1189200), _1189198), _1189198))), -(_1189198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189200), _1189198)))], (12574 ^ _775828) ^ [] : [-(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))], (11827 ^ _775828) ^ [_970360] : [class_Rings_Osemiring__1(_970360), -(hBOOL(hAPP(hAPP(c_member(_970360), c_Groups_Oone__class_Oone(_970360)), c_Nat_Osemiring__1__class_ONats(_970360))))], (8092 ^ _775828) ^ [_905856] : [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, _905856)))))], (49881 ^ _775828) ^ [_1778002, _1778004] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1778002, _1778004))))], (49156 ^ _775828) ^ [_1762553, _1762555] : [-(_1762553 = c_List_Olist_ONil(_1762555)), -(c_List_Olast(_1762555, _1762553) = hAPP(hAPP(c_List_Onth(_1762555), _1762553), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762555)), _1762553)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (18497 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (29719 ^ _775828) ^ [_1315635, _1315637] : [class_Orderings_Obot(_1315635), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315635), c_Orderings_Obot__class_Obot(_1315635)), _1315637)))], (33749 ^ _775828) ^ [_1402727, _1402729, _1402731] : [class_Lattices_Osemilattice__inf(_1402727), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402727), _1402729), _1402731) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402727), _1402731), _1402729))], (7995 ^ _775828) ^ [_903989, _903991, _903993, _903995] : [class_Rings_Ocomm__semiring__1(_903989), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903989), _903991), _903993)), _903995) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903989), _903991), _903995)), _903993))], (49817 ^ _775828) ^ [_1777048] : [-(c_List_Oupt(_1777048, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (45097 ^ _775828) ^ [_1663712, _1663714, _1663716, _1663718, _1663720, _1663722] : [-(_1663712 = c_Orderings_Obot__class_Obot(tc_fun(_1663714, tc_HOL_Obool))), 45103 ^ _775828 : [(45106 ^ _775828) ^ [] : [c_Fun_Oinj__on(_1663716, _1663718, _1663720, hAPP(_1663722, 45102 ^ [_1663712, _1663714, _1663716, _1663718, _1663720, _1663722]))], (45104 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663714), 45102 ^ [_1663712, _1663714, _1663716, _1663718, _1663720, _1663722]), _1663712)))]], -(c_Fun_Oinj__on(_1663716, _1663718, _1663720, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663714, tc_fun(_1663716, tc_HOL_Obool)), _1663712), _1663722)))], (50507 ^ _775828) ^ [_1791958, _1791960, _1791962, _1791964] : [-(c_List_Oconcat(_1791958, hAPP(hAPP(c_List_Omap(_1791960, tc_List_Olist(_1791958)), hAPP(hAPP(c_COMBC(_1791960, tc_List_Olist(_1791958), tc_List_Olist(_1791958)), hAPP(hAPP(c_COMBB(_1791958, tc_fun(tc_List_Olist(_1791958), tc_List_Olist(_1791958)), _1791960), c_List_Olist_OCons(_1791958)), _1791962)), c_List_Olist_ONil(_1791958))), _1791964)) = hAPP(hAPP(c_List_Omap(_1791960, _1791958), _1791962), _1791964))], (48102 ^ _775828) ^ [_1737121, _1737123, _1737125, _1737127] : [-(c_List_Osublist(_1737121, hAPP(hAPP(c_List_Oappend(_1737121), _1737123), _1737125), _1737127) = hAPP(hAPP(c_List_Oappend(_1737121), c_List_Osublist(_1737121, _1737123, _1737127)), c_List_Osublist(_1737121, _1737125, 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(_1737121)), _1737123)))), _1737127)))))], (25194 ^ _775828) ^ [_1220379, _1220381] : [-(c_HOL_OThe(_1220379, hAPP(hAPP(c_COMBC(_1220379, _1220379, tc_HOL_Obool), c_fequal), _1220381)) = _1220381)], (45688 ^ _775828) ^ [_1677155, _1677157, _1677159, _1677161, _1677163, _1677165] : [-(hAPP(hAPP(c_Option_Omap(_1677155, _1677157), _1677159), hAPP(hAPP(c_Option_Omap(_1677161, _1677155), _1677163), _1677165)) = hAPP(hAPP(c_Option_Omap(_1677161, _1677157), hAPP(c_Fun_Ocomp(_1677155, _1677157, _1677161, _1677159), _1677163)), _1677165))], (36467 ^ _775828) ^ [_1460744, _1460746, _1460748, _1460750] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1460744), _1460746)), 36470 ^ _775828 : [(36471 ^ _775828) ^ [_1460898] : [36473 ^ _775828 : [(36479 ^ _775828) ^ [] : [-(_1460898 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36475 ^ [_1460744, _1460746, _1460748, _1460750, _1460898]), 36472 ^ [_1460744, _1460746, _1460748, _1460750, _1460898]))], (36477 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36475 ^ [_1460744, _1460746, _1460748, _1460750, _1460898]), _1460748)))], (36474 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36472 ^ [_1460744, _1460746, _1460748, _1460750, _1460898]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1460746))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1460744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1460898), _1460750))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1460744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1460898), _1460746)), _1460750))))]]], (25349 ^ _775828) ^ [_1222960, _1222962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222960), _1222962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1222960)), hAPP(c_Code__Numeral_Oof__nat, _1222962))))], (42990 ^ _775828) ^ [_1613832, _1613834, _1613836, _1613838, _1613840, _1613842, _1613844, _1613846, _1613848, _1613850, _1613852] : [c_Finite__Set_Ofolding(_1613832, _1613834, _1613836, _1613838), -(hAPP(c_Fun_Ocomp(_1613840, _1613842, _1613844, _1613846), hAPP(c_Fun_Ocomp(_1613848, _1613840, _1613844, _1613850), _1613852)) = hAPP(c_Fun_Ocomp(_1613848, _1613842, _1613844, hAPP(c_Fun_Ocomp(_1613840, _1613842, _1613848, _1613846), _1613850)), _1613852))], (51180 ^ _775828) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (4720 ^ _775828) ^ [_847943, _847945] : [_847945 = _847943, -(c_SetInterval_Oord__class_OatMost(_847945) = c_SetInterval_Oord__class_OatMost(_847943))], (38532 ^ _775828) ^ [_1508442, _1508444, _1508446, _1508448, _1508450, _1508452] : [-(hBOOL(hAPP(hAPP(c_member(_1508442), _1508444), _1508446))), -(hAPP(c_Fun_Ooverride__on(_1508442, _1508448, _1508450, _1508452, _1508446), _1508444) = hAPP(_1508450, _1508444))], (45321 ^ _775828) ^ [_1668538, _1668540, _1668542, _1668544, _1668546, _1668548] : [hAPP(c_Map_Omap__add(_1668538, _1668540, _1668542, _1668544), _1668546) = hAPP(c_Option_Ooption_OSome(_1668540), _1668548), -(hAPP(_1668544, _1668546) = hAPP(c_Option_Ooption_OSome(_1668540), _1668548)), 45328 ^ _775828 : [(45331 ^ _775828) ^ [] : [-(hAPP(_1668542, _1668546) = hAPP(c_Option_Ooption_OSome(_1668540), _1668548))], (45329 ^ _775828) ^ [] : [-(hAPP(_1668544, _1668546) = c_Option_Ooption_ONone(_1668540))]]], (11102 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5843 ^ _775828) ^ [_868911, _868913] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _868911, _868913, _868911))], (29799 ^ _775828) ^ [_1317339, _1317341, _1317343, _1317345] : [-(hBOOL(hAPP(hAPP(c_member(_1317339), _1317341), _1317343))), 29802 ^ _775828 : [(29809 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317339, tc_HOL_Obool)), _1317343), _1317345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317339, tc_HOL_Obool)), _1317343), hAPP(hAPP(c_Set_Oinsert(_1317339), _1317341), _1317345))))], (29803 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317339, tc_HOL_Obool)), _1317343), hAPP(hAPP(c_Set_Oinsert(_1317339), _1317341), _1317345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317339, tc_HOL_Obool)), _1317343), _1317345)))]]], (2682 ^ _775828) ^ [_815598, _815600] : [_815600 = _815598, -(c_Code__Numeral_OSuc__code__numeral(_815600) = c_Code__Numeral_OSuc__code__numeral(_815598))], (15410 ^ _775828) ^ [_1034840, _1034842, _1034844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034840), _1034842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1034840), _1034844)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034842), _1034840)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034844), _1034840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034842), _1034844))], (40758 ^ _775828) ^ [_1559448, _1559450, _1559452] : [c_Wellfounded_Owf(_1559448, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1559448, _1559448), tc_HOL_Obool), _1559450), _1559452)), -(c_Wellfounded_Owf(_1559448, _1559452))], (34299 ^ _775828) ^ [_1414678, _1414680, _1414682, _1414684] : [hBOOL(hAPP(hAPP(c_member(_1414678), _1414680), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414678, tc_HOL_Obool)), _1414682), hAPP(c_Set_OCollect(_1414678), _1414684)))), 34302 ^ _775828 : [(34305 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1414684, _1414680)))], (34303 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1414678), _1414680), _1414682)))]]], (30722 ^ _775828) ^ [_1337685, _1337687, _1337689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337685), _1337687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1337685), _1337687)), hAPP(c_Finite__Set_Ocard(_1337685), hAPP(hAPP(c_Set_Oinsert(_1337685), _1337689), _1337687)))))], (25561 ^ _775828) ^ [_1227774, _1227776] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227776), _1227774))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227774), _1227776)))], (14904 ^ _775828) ^ [_1025567, _1025569, _1025571, _1025573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025569), _1025571)), -(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), _1025571), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025573, _1025567))), _1025569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025571), _1025567))))], (23224 ^ _775828) ^ [_1180345, _1180347, _1180349, _1180351] : [class_Fields_Ofield(_1180345), -(_1180347 = c_Groups_Ozero__class_Ozero(_1180345)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180345), _1180349), _1180347)), _1180351) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180345), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180345), _1180349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180345), _1180347), _1180351))), _1180347))], (49548 ^ _775828) ^ [_1771695, _1771697, _1771699] : [-(c_List_Omap__filter(_1771695, _1771697, _1771699, c_List_Olist_ONil(_1771695)) = c_List_Olist_ONil(_1771697))], (46450 ^ _775828) ^ [_1697529, _1697531, _1697533, _1697535, _1697537, _1697539] : [-(hAPP(hAPP(c_List_Ozip(_1697529, _1697531), hAPP(hAPP(c_List_Olist_OCons(_1697529), _1697533), _1697535)), hAPP(hAPP(c_List_Olist_OCons(_1697531), _1697537), _1697539)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1697529, _1697531)), hAPP(hAPP(c_Product__Type_OPair(_1697529, _1697531), _1697533), _1697537)), hAPP(hAPP(c_List_Ozip(_1697529, _1697531), _1697535), _1697539)))], (13286 ^ _775828) ^ [_995721, _995723, _995725, _995727] : [class_Divides_Osemiring__div(_995721), -(c_Divides_Odiv__class_Omod(_995721, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995721), c_Divides_Odiv__class_Omod(_995721, _995723, _995725)), _995727), _995725) = c_Divides_Odiv__class_Omod(_995721, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995721), _995723), _995727), _995725))], (32159 ^ _775828) ^ [_1370270, _1370272, _1370274] : [class_Orderings_Olinorder(_1370270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370270), _1370272)), hBOOL(hAPP(hAPP(c_member(_1370270), _1370274), _1370272)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370270), _1370274), c_Big__Operators_Olinorder__class_OMax(_1370270, _1370272)) = c_Big__Operators_Olinorder__class_OMax(_1370270, _1370272))], (1460 ^ _775828) ^ [_796696, _796698] : [-(class_Groups_Ocancel__semigroup__add(_796696)), _796698 = _796696, class_Groups_Ocancel__semigroup__add(_796698)], (47075 ^ _775828) ^ [_1713335, _1713337] : [-(hAPP(c_List_Oset(_1713335), _1713337) = hAPP(c_Set_OCollect(_1713335), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1713335), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1713335, 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)), _1713335), 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)), _1713335), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1713335, tc_fun(tc_Nat_Onat, _1713335), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1713335, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1713335), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1713335), c_COMBB(_1713335, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1713335), _1713337))))), 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(_1713335)), _1713337))))))], (23194 ^ _775828) ^ [_1179811, _1179813, _1179815, _1179817] : [class_Fields_Ofield(_1179811), -(_1179813 = c_Groups_Ozero__class_Ozero(_1179811)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179811), _1179815), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179811), _1179817), _1179813)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179811), _1179813), _1179815)), _1179817)), _1179813))], (15630 ^ _775828) ^ [_1039140, _1039142, _1039144] : [class_Groups_Oab__group__add(_1039140), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039140), _1039142), _1039144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039140), _1039142), hAPP(c_Groups_Ouminus__class_Ouminus(_1039140), _1039144)))], (9643 ^ _775828) ^ [_930899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _930899), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _930899)))], (18267 ^ _775828) ^ [_1089702, _1089704, _1089706, _1089708, _1089710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1089702, _1089704)), hAPP(_1089702, _1089706))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1089708, _1089708)), hAPP(hAPP(c_Product__Type_OPair(_1089708, _1089708), _1089704), _1089706)), c_Wellfounded_Omlex__prod(_1089708, _1089702, _1089710))))], (1520 ^ _775828) ^ [_797446, _797448] : [-(class_Rings_Oordered__semiring(_797446)), _797448 = _797446, class_Rings_Oordered__semiring(_797448)], (13718 ^ _775828) ^ [_1004340, _1004342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004340, _1004342)), _1004340)))], (25463 ^ _775828) ^ [_1224958, _1224960] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1224958), _1224960) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224958)), hAPP(c_Code__Numeral_Onat__of, _1224960))))], (49799 ^ _775828) ^ [_1776757, _1776759, _1776761] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1776757), c_List_Oupt(_1776759, _1776761)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1776759), _1776757), _1776761))], (29473 ^ _775828) ^ [_1310468, _1310470, _1310472] : [hAPP(hAPP(c_Set_Oinsert(_1310468), _1310470), c_Orderings_Obot__class_Obot(tc_fun(_1310468, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1310468), _1310472), c_Orderings_Obot__class_Obot(tc_fun(_1310468, tc_HOL_Obool))), -(_1310470 = _1310472)], (10778 ^ _775828) ^ [_952054, _952056, _952058, _952060] : [hBOOL(hAPP(hAPP(c_member(_952054), _952056), _952058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952054, tc_HOL_Obool)), _952058), _952060)), -(hBOOL(hAPP(hAPP(c_member(_952054), _952056), _952060)))], (45582 ^ _775828) ^ [_1674587, _1674589, _1674591, _1674593, _1674595] : [c_Fun_Oinj__on(_1674587, _1674589, _1674591, c_Orderings_Otop__class_Otop(tc_fun(_1674587, tc_HOL_Obool))), 45585 ^ _775828 : [(45592 ^ _775828) ^ [] : [_1674593 = _1674595, -(hAPP(hAPP(c_List_Omap(_1674587, _1674589), _1674591), _1674593) = hAPP(hAPP(c_List_Omap(_1674587, _1674589), _1674591), _1674595))], (45586 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Omap(_1674587, _1674589), _1674591), _1674593) = hAPP(hAPP(c_List_Omap(_1674587, _1674589), _1674591), _1674595), -(_1674593 = _1674595)]]], (28890 ^ _775828) ^ [_1297518, _1297520, _1297522, _1297524, _1297526] : [c_Hoare__Mirabelle_Ohoare__derivs(_1297518, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1297518), tc_HOL_Obool)), _1297520), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1297518), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), hAPP(hAPP(c_COMBB(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1297518)), _1297522)), c_Com_Ocom_OBODY)), _1297524)), _1297526)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1297518), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), hAPP(hAPP(c_COMBB(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1297518)), _1297522)), 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))), _1297524)), _1297526)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1297518, _1297520, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1297518), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), hAPP(hAPP(c_COMBB(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1297518, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1297518))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1297518)), _1297522)), c_Com_Ocom_OBODY)), _1297524)), _1297526)))], (21672 ^ _775828) ^ [] : [-(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))], (19928 ^ _775828) ^ [_1117889, _1117891] : [class_Int_Onumber__ring(_1117889), -(hAPP(c_Int_Onumber__class_Onumber__of(_1117889), c_Int_Opred(_1117891)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117889), hAPP(c_Groups_Ouminus__class_Ouminus(_1117889), c_Groups_Oone__class_Oone(_1117889))), hAPP(c_Int_Onumber__class_Onumber__of(_1117889), _1117891)))], (47014 ^ _775828) ^ [_1712121, _1712123, _1712125, _1712127] : [hBOOL(hAPP(c_List_Odistinct(_1712121), _1712123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712125), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712121)), _1712123))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712127), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712121)), _1712123))), 47025 ^ _775828 : [(47032 ^ _775828) ^ [] : [_1712125 = _1712127, -(hAPP(hAPP(c_List_Onth(_1712121), _1712123), _1712125) = hAPP(hAPP(c_List_Onth(_1712121), _1712123), _1712127))], (47026 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Onth(_1712121), _1712123), _1712125) = hAPP(hAPP(c_List_Onth(_1712121), _1712123), _1712127), -(_1712125 = _1712127)]]], (51270 ^ _775828) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (37540 ^ _775828) ^ [_1485371, _1485373, _1485375, _1485377, _1485379] : [class_Groups_Ocomm__monoid__add(_1485371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485373), _1485375)), hBOOL(hAPP(hAPP(c_member(_1485373), _1485377), _1485375)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485373, _1485371), _1485379), _1485375) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1485371), hAPP(_1485379, _1485377)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485373, _1485371), _1485379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485373, tc_HOL_Obool)), _1485375), hAPP(hAPP(c_Set_Oinsert(_1485373), _1485377), c_Orderings_Obot__class_Obot(tc_fun(_1485373, tc_HOL_Obool)))))))], (6832 ^ _775828) ^ [_884072, _884074] : [hAPP(c_Option_Ooption_OSome(_884072), _884074) = c_Option_Ooption_ONone(_884072)], (11682 ^ _775828) ^ [_967696, _967698] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967696), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967696), _967698)))))], (35365 ^ _775828) ^ [_1439466, _1439468, _1439470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439466, tc_HOL_Obool)), _1439468), _1439470)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1439466, tc_HOL_Obool)), _1439468), hAPP(c_Set_OPow(_1439466), _1439470))))], (14772 ^ _775828) ^ [_1022937, _1022939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022937), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022939), _1022937)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022937), _1022939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47877 ^ _775828) ^ [_1732413, _1732415, _1732417, _1732419] : [-(hAPP(hAPP(c_List_Oappend(_1732413), hAPP(hAPP(c_List_Oappend(_1732413), _1732415), _1732417)), _1732419) = hAPP(hAPP(c_List_Oappend(_1732413), _1732415), hAPP(hAPP(c_List_Oappend(_1732413), _1732417), _1732419)))], (5156 ^ _775828) ^ [_854705, _854707, _854709, _854711, _854713, _854715] : [-(c_List_OtakeWhile(_854715, _854711, _854707) = c_List_OtakeWhile(_854713, _854709, _854705)), _854715 = _854713, _854711 = _854709, _854707 = _854705], (7941 ^ _775828) ^ [_902980, _902982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _902980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _902982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902982), _902980))))], (6005 ^ _775828) ^ [_871265, _871267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _871265)), hAPP(c_Nat_OSuc, _871267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871265), _871267)))], (9583 ^ _775828) ^ [_929902] : [-(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), _929902))))], (40861 ^ _775828) ^ [_1562042, _1562044] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1562042, _1562042), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1562044) = c_Relation_OId(_1562042))], (5761 ^ _775828) ^ [_867642, _867644, _867646, _867648] : [c_Natural_Oevaln(_867642, _867644, _867646, _867648), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_867642), _867644), _867648)))], (24453 ^ _775828) ^ [] : [-(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)))))], (20500 ^ _775828) ^ [_1128097] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1128097))), 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), _1128097), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (41294 ^ _775828) ^ [_1573202, _1573204, _1573206, _1573208] : [hAPP(hAPP(c_Product__Type_OSigma(_1573202, _1573204), _1573206), hAPP(c_COMBK(tc_fun(_1573204, tc_HOL_Obool), _1573202), _1573208)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1573202, _1573204), tc_HOL_Obool)), -(_1573206 = c_Orderings_Obot__class_Obot(tc_fun(_1573202, tc_HOL_Obool))), -(_1573208 = c_Orderings_Obot__class_Obot(tc_fun(_1573204, tc_HOL_Obool)))], (28373 ^ _775828) ^ [_1285198, _1285200, _1285202, _1285204] : [28377 ^ _775828 : [(28380 ^ _775828) ^ [] : [hBOOL(hAPP(_1285204, 28376 ^ [_1285198, _1285200, _1285202, _1285204]))], (28378 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285198), 28376 ^ [_1285198, _1285200, _1285202, _1285204]), _1285200)))]], 28382 ^ _775828 : [(28385 ^ _775828) ^ [] : [hBOOL(hAPP(_1285204, 28381 ^ [_1285198, _1285200, _1285202, _1285204]))], (28383 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285198), 28381 ^ [_1285198, _1285200, _1285202, _1285204]), _1285202)))]], 28386 ^ _775828 : [(28387 ^ _775828) ^ [_1285531] : [hBOOL(hAPP(hAPP(c_member(_1285198), _1285531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285198, tc_HOL_Obool)), _1285200), _1285202))), -(hBOOL(hAPP(_1285204, _1285531)))]]], (20464 ^ _775828) ^ [_1127457, _1127459] : [class_Rings_Oring__1(_1127457), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127457), hAPP(c_Groups_Ouminus__class_Ouminus(_1127457), _1127459)), 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(_1127457), _1127459), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (28197 ^ _775828) ^ [_1281421, _1281423, _1281425, _1281427] : [-(hAPP(c_Relation_Oconverse(_1281421, _1281423), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1281421, _1281423), tc_HOL_Obool)), _1281425), _1281427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1281423, _1281421), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1281421, _1281423), _1281425)), hAPP(c_Relation_Oconverse(_1281421, _1281423), _1281427)))], (12939 ^ _775828) ^ [_989518, _989520, _989522, _989524, _989526] : [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), _989518), _989520)), _989522)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989518), _989524)), _989526))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _989522), _989518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _989526), _989518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989520), _989524)))], (48008 ^ _775828) ^ [_1735132, _1735134, _1735136] : [_1735136 = c_List_Olist_ONil(_1735134), -(_1735132 = hAPP(hAPP(c_List_Oappend(_1735134), _1735136), _1735132))], (6841 ^ _775828) ^ [_884159, _884161] : [_884159 = c_Option_Ooption_ONone(_884161), 6844 ^ _775828 : [(6845 ^ _775828) ^ [_884231] : [_884159 = hAPP(c_Option_Ooption_OSome(_884161), _884231)]]], (6442 ^ _775828) ^ [_878273, _878275, _878277] : [class_Orderings_Opreorder(_878273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878273), _878275), _878277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878273), _878277), _878275))], (24551 ^ _775828) ^ [_1207110, _1207112] : [c_Nat__Transfer_Ois__nat(_1207110), c_Nat__Transfer_Ois__nat(_1207112), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1207110, _1207112)))], (26019 ^ _775828) ^ [_1235284, _1235286] : [_1235286 = _1235284, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235284), _1235286)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235286), _1235284)))], (48104 ^ _775828) ^ [_1737200, _1737202, _1737204, _1737206, _1737208, _1737210, _1737212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1737200, _1737200)), hAPP(hAPP(c_Product__Type_OPair(_1737200, _1737200), _1737202), _1737204)), _1737206)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737200), tc_List_Olist(_1737200))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737200), tc_List_Olist(_1737200)), hAPP(hAPP(c_List_Oappend(_1737200), _1737208), hAPP(hAPP(c_List_Olist_OCons(_1737200), _1737202), _1737210))), hAPP(hAPP(c_List_Oappend(_1737200), _1737208), hAPP(hAPP(c_List_Olist_OCons(_1737200), _1737204), _1737212)))), c_List_Olexord(_1737200, _1737206))))], (48225 ^ _775828) ^ [_1740908, _1740910, _1740912, _1740914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740908), tc_List_Olist(_1740908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740908), tc_List_Olist(_1740908)), _1740910), _1740912)), c_List_Olistrel1(_1740908, hAPP(c_Relation_Oconverse(_1740908, _1740908), _1740914)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740908), tc_List_Olist(_1740908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740908), tc_List_Olist(_1740908)), _1740910), _1740912)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1740908), tc_List_Olist(_1740908)), c_List_Olistrel1(_1740908, _1740914)))))], (3832 ^ _775828) ^ [_834095, _834097, _834099, _834101, _834103, _834105] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_834105, _834101, _834097) = c_Smallcheck_Ofull__small__class_Ofull__small(_834103, _834099, _834095)), _834105 = _834103, _834101 = _834099, _834097 = _834095], (36407 ^ _775828) ^ [_1459633, _1459635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459633), _1459635))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459633), hAPP(c_Nat_OSuc, _1459635)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (12435 ^ _775828) ^ [_980976, _980978] : [class_Rings_Olinordered__idom(_980976), 12438 ^ _775828 : [(12445 ^ _775828) ^ [] : [_980978 = c_Groups_Ozero__class_Ozero(_980976), -(c_Groups_Osgn__class_Osgn(_980976, _980978) = c_Groups_Ozero__class_Ozero(_980976))], (12439 ^ _775828) ^ [] : [c_Groups_Osgn__class_Osgn(_980976, _980978) = c_Groups_Ozero__class_Ozero(_980976), -(_980978 = c_Groups_Ozero__class_Ozero(_980976))]]], (48425 ^ _775828) ^ [_1746582, _1746584, _1746586] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746582)), hAPP(hAPP(c_List_Odrop(_1746582), _1746584), _1746586)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746582)), _1746586)), _1746584))], (44105 ^ _775828) ^ [_1638375, _1638377, _1638379, _1638381, _1638383, _1638385, _1638387, _1638389] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638375, tc_fun(_1638377, tc_fun(_1638379, tc_HOL_Obool))), _1638381), _1638383), _1638385), _1638387)), -(hBOOL(hAPP(hAPP(hAPP(_1638383, _1638389), _1638385), _1638387))), hBOOL(hAPP(hAPP(c_member(_1638375), _1638389), _1638381))], (42579 ^ _775828) ^ [_1604142, _1604144, _1604146, _1604148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1604142), _1604144)), 42585 ^ _775828 : [(42588 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1604146), hAPP(_1604148, 42584 ^ [_1604142, _1604144, _1604146, _1604148])))], (42586 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604142), 42584 ^ [_1604142, _1604144, _1604146, _1604148]), _1604144)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1604146), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1604142, tc_fun(_1604146, tc_HOL_Obool)), _1604144), _1604148))))], (11693 ^ _775828) ^ [_967902, _967904] : [11694 ^ _775828 : [(11695 ^ _775828) ^ [_967955] : [_967904 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967902), _967955))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967902), _967904)))], (2648 ^ _775828) ^ [_815063, _815065, _815067, _815069, _815071, _815073, _815075, _815077] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_815077, _815073, _815069, _815065) = c_New__Random__Sequence_Opos__not__random__dseq(_815075, _815071, _815067, _815063)), _815077 = _815075, _815073 = _815071, _815069 = _815067, _815065 = _815063], (3712 ^ _775828) ^ [_832243, _832245, _832247, _832249] : [-(c_HOL_OThe(_832249, _832245) = c_HOL_OThe(_832247, _832243)), _832249 = _832247, _832245 = _832243], (6422 ^ _775828) ^ [_878035, _878037, _878039] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _878037))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_878035, _878037, _878039))))], (41008 ^ _775828) ^ [_1565868, _1565870, _1565872] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565868, _1565868)), _1565870), c_Transitive__Closure_Otrancl(_1565868, _1565872)))), 41009 ^ _775828 : [(41010 ^ _775828) ^ [_1565947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1565947)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565868, _1565868)), _1565870), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1565868, _1565868), tc_HOL_Obool), _1565947), _1565872)))]]], (51126 ^ _775828) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (4414 ^ _775828) ^ [_843222, _843224, _843226, _843228] : [-(c_Wellfounded_Oacc(_843228, _843224) = c_Wellfounded_Oacc(_843226, _843222)), _843228 = _843226, _843224 = _843222], (47473 ^ _775828) ^ [_1722713, _1722715, _1722717] : [-(hAPP(hAPP(c_List_Otake(_1722713), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1722713), _1722715), _1722717)) = hAPP(hAPP(c_List_Olist_OCons(_1722713), _1722715), c_List_Olist_ONil(_1722713)))], (6225 ^ _775828) ^ [_874827, _874829, _874831, _874833] : [class_Orderings_Oorder(_874827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874827), hAPP(_874829, 6230 ^ [_874827, _874829, _874831, _874833])), hAPP(_874829, hAPP(c_Nat_OSuc, 6230 ^ [_874827, _874829, _874831, _874833])))), 6233 ^ _775828 : [(6240 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874831), _874833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874827), hAPP(_874829, _874831)), hAPP(_874829, _874833))))], (6234 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874827), hAPP(_874829, _874831)), hAPP(_874829, _874833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874831), _874833)))]]], (26567 ^ _775828) ^ [_1245230, _1245232, _1245234, _1245236] : [class_Rings_Ocomm__ring(_1245230), class_Rings_Odvd(_1245230), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245230), _1245232), _1245234)), 26578 ^ _775828 : [(26585 ^ _775828) ^ [_1245656, _1245658] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245230), _1245232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245230), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1245230), _1245658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245230), _1245656), _1245234))), _1245236))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245230), _1245232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245230), _1245658), _1245236))))], (26579 ^ _775828) ^ [_1245483, _1245485] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245230), _1245232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245230), _1245485), _1245236))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245230), _1245232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245230), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1245230), _1245485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245230), _1245483), _1245234))), _1245236))))]]], (35153 ^ _775828) ^ [_1434492, _1434494, _1434496, _1434498, _1434500, _1434502, _1434504] : [c_Finite__Set_Ofolding__image__simple(_1434492, _1434494, _1434496, _1434498, _1434500, _1434502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434494), _1434504)), -(hAPP(_1434502, _1434504) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1434492, _1434494, _1434496), _1434500), _1434498), _1434504))], (40549 ^ _775828) ^ [_1554600, _1554602, _1554604, _1554606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554600, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554600, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40550 ^ [_1554600, _1554602, _1554604, _1554606])), _1554602)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554600, 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), 40550 ^ [_1554600, _1554602, _1554604, _1554606]), _1554604))), _1554606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554600, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554600, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1554602)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554600, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1554606))))], (51358 ^ _775828) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (2350 ^ _775828) ^ [_810260, _810262] : [_810262 = _810260, -(c_Nitpick_Ofrac(_810262) = c_Nitpick_Ofrac(_810260))], (50736 ^ _775828) ^ [_1797350] : [-(c_List_Oembed__list(_1797350) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1797350))], (39434 ^ _775828) ^ [_1528137, _1528139, _1528141, _1528143, _1528145] : [39436 ^ _775828 : [(39442 ^ _775828) ^ [] : [hBOOL(hAPP(_1528145, 39438 ^ [_1528137, _1528139, _1528141, _1528143, _1528145]))], (39440 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528137), 39438 ^ [_1528137, _1528139, _1528141, _1528143, _1528145]), hAPP(_1528143, 39435 ^ [_1528137, _1528139, _1528141, _1528143, _1528145]))))], (39437 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528139), 39435 ^ [_1528137, _1528139, _1528141, _1528143, _1528145]), _1528141)))]], 39443 ^ _775828 : [(39444 ^ _775828) ^ [_1528447] : [hBOOL(hAPP(hAPP(c_member(_1528137), _1528447), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528139, tc_fun(_1528137, tc_HOL_Obool)), _1528141), _1528143))), -(hBOOL(hAPP(_1528145, _1528447)))]]], (10300 ^ _775828) ^ [_942984, _942986, _942988, _942990] : [class_Rings_Ocomm__semiring__1(_942984), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942984), _942986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942984), _942988), _942990)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942984), _942988), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942984), _942986), _942990)))], (17143 ^ _775828) ^ [_1068788, _1068790, _1068792] : [class_Rings_Oring__1(_1068788), hBOOL(hAPP(hAPP(c_member(_1068788), _1068790), c_Int_Oring__1__class_OInts(_1068788))), -(hBOOL(hAPP(hAPP(c_member(_1068788), hAPP(hAPP(c_Power_Opower__class_Opower(_1068788), _1068790), _1068792)), c_Int_Oring__1__class_OInts(_1068788))))], (1280 ^ _775828) ^ [_794446, _794448] : [-(class_Lattices_Odistrib__lattice(_794446)), _794448 = _794446, class_Lattices_Odistrib__lattice(_794448)], (35759 ^ _775828) ^ [_1447337, _1447339, _1447341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447337)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447339), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1447341)), 35766 ^ _775828 : [(35767 ^ _775828) ^ [_1447545] : [35769 ^ _775828 : [(35775 ^ _775828) ^ [] : [-(_1447545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35771 ^ [_1447337, _1447339, _1447341, _1447545]), 35768 ^ [_1447337, _1447339, _1447341, _1447545]))], (35773 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35771 ^ [_1447337, _1447339, _1447341, _1447545]), _1447341)))], (35770 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35768 ^ [_1447337, _1447339, _1447341, _1447545]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1447337))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1447545), _1447339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447545), _1447337)), _1447339)))]]], (38516 ^ _775828) ^ [_1508097, _1508099, _1508101, _1508103] : [c_Equiv__Relations_Oequiv(_1508097, _1508099, _1508101), hBOOL(hAPP(hAPP(c_member(_1508097), _1508103), _1508099)), -(hBOOL(hAPP(hAPP(c_member(_1508097), _1508103), hAPP(c_Relation_OImage(_1508097, _1508097, _1508101), hAPP(hAPP(c_Set_Oinsert(_1508097), _1508103), c_Orderings_Obot__class_Obot(tc_fun(_1508097, tc_HOL_Obool)))))))], (44882 ^ _775828) ^ [_1658776, _1658778, _1658780] : [class_Complete__Lattice_Ocomplete__lattice(_1658776), -(c_Complete__Lattice_OSup__class_OSup(_1658776, hAPP(hAPP(c_Set_Oinsert(_1658776), _1658778), _1658780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1658776), _1658778), c_Complete__Lattice_OSup__class_OSup(_1658776, _1658780)))], (50738 ^ _775828) ^ [_1797378, _1797380] : [-(hAPP(c_List_Oset(_1797378), c_List_Oremdups(_1797378, _1797380)) = hAPP(c_List_Oset(_1797378), _1797380))], (16296 ^ _775828) ^ [_1052619, _1052621, _1052623, _1052625, _1052627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052619), _1052621)), 16299 ^ _775828 : [(16306 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052625), 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), _1052621), _1052619)), _1052623)), _1052627))), -(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), _1052619), _1052623)), _1052625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052621), _1052623)), _1052627))))], (16300 ^ _775828) ^ [] : [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), _1052619), _1052623)), _1052625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052621), _1052623)), _1052627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052625), 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), _1052621), _1052619)), _1052623)), _1052627))))]]], (17241 ^ _775828) ^ [_1070739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1070739)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1070739 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48369 ^ _775828) ^ [_1745361, _1745363] : [-(hAPP(hAPP(c_List_Odrop(_1745361), _1745363), c_List_Olist_ONil(_1745361)) = c_List_Olist_ONil(_1745361))], (5396 ^ _775828) ^ [_858277, _858279, _858281, _858283, _858285, _858287] : [-(c_COMBS(_858287, _858283, _858279) = c_COMBS(_858285, _858281, _858277)), _858287 = _858285, _858283 = _858281, _858279 = _858277], (12105 ^ _775828) ^ [_975381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _975381)))], (30517 ^ _775828) ^ [_1333440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1333440)), 30521 ^ _775828 : [(30522 ^ _775828) ^ [_1333520] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1333520), _1333440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1333520), 30520 ^ [_1333440])))]]], (9183 ^ _775828) ^ [_922669, _922671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922669)), 9186 ^ _775828 : [(9193 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922669), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _922669)), _922671)))], (9187 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _922669)), _922671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922669), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922671))))]]], (16595 ^ _775828) ^ [_1058138] : [class_Rings_Olinordered__idom(_1058138), -(hAPP(c_Groups_Oabs__class_Oabs(_1058138), c_Groups_Oone__class_Oone(_1058138)) = c_Groups_Oone__class_Oone(_1058138))], (6406 ^ _775828) ^ [_877724, _877726, _877728, _877730] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_877724, _877726), _877728, _877730, hAPP(hAPP(hAPP(c_Natural_Oupdate, _877728), _877724), hAPP(_877726, _877728))))], (44818 ^ _775828) ^ [_1657440, _1657442] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1657440, tc_HOL_Obool), hAPP(c_Set_OPow(_1657440), _1657442)) = _1657442)], (9501 ^ _775828) ^ [_928503, _928505] : [class_Rings_Olinordered__ring(_928503), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928503), c_Groups_Ozero__class_Ozero(_928503)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928503), _928505), _928505))))], (24128 ^ _775828) ^ [_1198341, _1198343] : [class_Orderings_Olinorder(_1198341), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198341), _1198343), _1198343) = _1198343)], (23602 ^ _775828) ^ [_1188954, _1188956, _1188958] : [-(hAPP(c_Nat_Onat_Onat__rec(_1188954, _1188956, _1188958), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1188956)], (39640 ^ _775828) ^ [_1533975, _1533977, _1533979, _1533981, _1533983, _1533985] : [class_Complete__Lattice_Ocomplete__lattice(_1533975), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533977, tc_fun(_1533979, _1533975)), _1533981), _1533983), _1533985) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533977, _1533975), _1533981), hAPP(hAPP(c_COMBC(_1533977, _1533979, _1533975), _1533983), _1533985)))], (29373 ^ _775828) ^ [_1308483, _1308485, _1308487, _1308489] : [hBOOL(hAPP(hAPP(c_member(_1308483), _1308485), _1308487)), -(hBOOL(hAPP(hAPP(c_member(_1308483), _1308485), hAPP(hAPP(c_Set_Oinsert(_1308483), _1308489), _1308487))))], (12705 ^ _775828) ^ [_985595, _985597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985597)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _985595)), hAPP(c_Int_Onat, _985597)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _985595), _985597)))], (2982 ^ _775828) ^ [_820642, _820644] : [_820644 = _820642, -(c_Wellfounded_Omeasure(_820644) = c_Wellfounded_Omeasure(_820642))], (46688 ^ _775828) ^ [_1703933, _1703935, _1703937, _1703939, _1703941] : [class_Groups_Ocomm__monoid__add(_1703933), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1703933), hAPP(hAPP(c_List_Omap(_1703935, _1703933), hAPP(hAPP(c_COMBS(_1703935, _1703933, _1703933), hAPP(hAPP(c_COMBB(_1703933, tc_fun(_1703933, _1703933), _1703935), c_Groups_Oplus__class_Oplus(_1703933)), _1703937)), _1703939)), _1703941)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1703933), hAPP(c_List_Omonoid__add__class_Olistsum(_1703933), hAPP(hAPP(c_List_Omap(_1703935, _1703933), _1703937), _1703941))), hAPP(c_List_Omonoid__add__class_Olistsum(_1703933), hAPP(hAPP(c_List_Omap(_1703935, _1703933), _1703939), _1703941))))], (33933 ^ _775828) ^ [_1407042, _1407044, _1407046, _1407048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407042, tc_HOL_Obool)), _1407044), _1407046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407042, tc_HOL_Obool)), _1407044), _1407048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1407042, tc_HOL_Obool)), _1407044), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407042, tc_HOL_Obool)), _1407046), _1407048))))], (24545 ^ _775828) ^ [_1207025, _1207027] : [c_Nat__Transfer_Ois__nat(_1207025), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207025), _1207027)))], (14433 ^ _775828) ^ [_1017587, _1017589] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017587, _1017589)) = _1017589, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1017587), _1017589) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30696 ^ _775828) ^ [_1337230, _1337232] : [-(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), _1337230)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1337232))))))], (20446 ^ _775828) ^ [_1127168, _1127170] : [class_Groups_Omonoid__mult(_1127168), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127168), _1127170), 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(_1127168), _1127170), _1127170))], (8525 ^ _775828) ^ [_912669] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _912669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912669)))], (46041 ^ _775828) ^ [_1685254, _1685256, _1685258, _1685260] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685254, _1685254)), hAPP(hAPP(c_Product__Type_OPair(_1685254, _1685254), _1685256), _1685258)), hAPP(c_List_Oset(tc_prod(_1685254, _1685254)), hAPP(hAPP(c_List_Ozip(_1685254, _1685254), _1685260), _1685260))))), hBOOL(hAPP(hAPP(c_member(_1685254), _1685256), hAPP(c_List_Oset(_1685254), _1685260))), _1685256 = _1685258], (25381 ^ _775828) ^ [_1223523, _1223525, _1223527, _1223529] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1223523, _1223525, _1223527, _1223529) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1223523, _1223525), _1223527), _1223529)))], (8417 ^ _775828) ^ [_910996, _910998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _910996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _910998)), 8424 ^ _775828 : [(8431 ^ _775828) ^ [] : [_910996 = _910998, -(hAPP(c_Int_Onat, _910996) = hAPP(c_Int_Onat, _910998))], (8425 ^ _775828) ^ [] : [hAPP(c_Int_Onat, _910996) = hAPP(c_Int_Onat, _910998), -(_910996 = _910998)]]], (42946 ^ _775828) ^ [_1612828, _1612830, _1612832, _1612834, _1612836] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1612828, _1612830, _1612832), _1612834), _1612836))), hBOOL(hAPP(hAPP(_1612830, _1612834), _1612836)), hBOOL(hAPP(_1612832, _1612836))], (42156 ^ _775828) ^ [_1594423, _1594425, _1594427] : [c_Relation_Orefl__on(_1594423, _1594425, hAPP(c_Relation_Oconverse(_1594423, _1594423), _1594427)), -(c_Relation_Orefl__on(_1594423, _1594425, _1594427))], (44976 ^ _775828) ^ [_1660794, _1660796] : [class_Complete__Lattice_Ocomplete__lattice(_1660794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660794), _1660796)), -(_1660796 = c_Orderings_Obot__class_Obot(tc_fun(_1660794, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1660794, _1660796) = c_Complete__Lattice_OInf__class_OInf(_1660794, _1660796))], (770 ^ _775828) ^ [_787551, _787553, _787555, _787557, _787559, _787561, _787563, _787565, _787567, _787569, _787571, _787573] : [-(c_Finite__Set_Ofolding__image__simple__idem(_787571, _787567, _787563, _787559, _787555, _787551)), c_Finite__Set_Ofolding__image__simple__idem(_787573, _787569, _787565, _787561, _787557, _787553), _787573 = _787571, _787569 = _787567, _787565 = _787563, _787561 = _787559, _787557 = _787555, _787553 = _787551], (7929 ^ _775828) ^ [_902705, _902707, _902709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902707), _902709)), -(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, _902705)), _902707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902705)), _902709))))], (29753 ^ _775828) ^ [_1316150, _1316152] : [class_Lattices_Obounded__lattice__bot(_1316150), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316150), c_Orderings_Obot__class_Obot(_1316150)), _1316152) = _1316152)], (40105 ^ _775828) ^ [_1544756, _1544758] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544756), c_Orderings_Otop__class_Otop(tc_fun(_1544756, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544758), c_Orderings_Otop__class_Otop(tc_fun(_1544758, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544756, _1544758)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1544756, _1544758), tc_HOL_Obool)))))], (1960 ^ _775828) ^ [_804243, _804245] : [_804245 = _804243, -(c_Int_Oring__1__class_OInts(_804245) = c_Int_Oring__1__class_OInts(_804243))], (11538 ^ _775828) ^ [_965521] : [class_Rings_Olinordered__semidom(_965521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965521), c_Groups_Oone__class_Oone(_965521)), c_Groups_Ozero__class_Ozero(_965521)))], (41322 ^ _775828) ^ [_1573975, _1573977, _1573979, _1573981, _1573983] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1573975, _1573977), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1573975, tc_HOL_Obool)), _1573979), _1573981)), hAPP(c_COMBK(tc_fun(_1573977, tc_HOL_Obool), _1573975), _1573983)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573975, _1573977), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1573975, _1573977), _1573979), hAPP(c_COMBK(tc_fun(_1573977, tc_HOL_Obool), _1573975), _1573983))), hAPP(hAPP(c_Product__Type_OSigma(_1573975, _1573977), _1573981), hAPP(c_COMBK(tc_fun(_1573977, tc_HOL_Obool), _1573975), _1573983))))], (36966 ^ _775828) ^ [_1471307, _1471309, _1471311, _1471313, _1471315] : [class_Groups_Ocomm__monoid__add(_1471307), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471309, _1471307), hAPP(hAPP(c_COMBS(_1471309, _1471307, _1471307), hAPP(hAPP(c_COMBB(_1471307, tc_fun(_1471307, _1471307), _1471309), c_Groups_Oplus__class_Oplus(_1471307)), _1471311)), _1471313)), _1471315) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1471307), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471309, _1471307), _1471311), _1471315)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471309, _1471307), _1471313), _1471315)))], (19760 ^ _775828) ^ [_1115277] : [class_Int_Onumber__ring(_1115277), -(c_Groups_Oone__class_Oone(_1115277) = hAPP(c_Int_Onumber__class_Onumber__of(_1115277), c_Int_OBit1(c_Int_OPls)))], (12143 ^ _775828) ^ [_975894, _975896] : [class_Lattices_Oab__semigroup__idem__mult(_975894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975894), _975896), _975896) = _975896)], (33719 ^ _775828) ^ [_1402204, _1402206, _1402208, _1402210] : [-(hAPP(c_Relation_Oconverse(_1402204, _1402206), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1402204, _1402206), tc_HOL_Obool)), _1402208), _1402210)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1402206, _1402204), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1402204, _1402206), _1402208)), hAPP(c_Relation_Oconverse(_1402204, _1402206), _1402210)))], (44683 ^ _775828) ^ [_1654760, _1654762, _1654764] : [c_Equiv__Relations_Oequiv(_1654760, _1654762, _1654764), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654760, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1654760), _1654762), _1654764)) = _1654762)], (40313 ^ _775828) ^ [_1548545, _1548547, _1548549, _1548551] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548545, tc_fun(_1548547, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1548545, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1548547, tc_HOL_Obool), tc_fun(_1548547, tc_HOL_Obool), _1548545), hAPP(c_COMBC(_1548547, tc_fun(_1548547, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548547))), _1548549)), _1548551)), -(hBOOL(hAPP(hAPP(c_member(_1548547), _1548551), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548545, tc_fun(_1548547, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1548545, tc_HOL_Obool))), _1548549))))], (40041 ^ _775828) ^ [_1543598, _1543600, _1543602, _1543604, _1543606] : [c_Fun_Oinj__on(_1543598, _1543600, _1543602, c_Orderings_Otop__class_Otop(tc_fun(_1543598, tc_HOL_Obool))), 40044 ^ _775828 : [(40051 ^ _775828) ^ [] : [_1543604 = _1543606, -(hAPP(_1543602, _1543604) = hAPP(_1543602, _1543606))], (40045 ^ _775828) ^ [] : [hAPP(_1543602, _1543604) = hAPP(_1543602, _1543606), -(_1543604 = _1543606)]]], (30129 ^ _775828) ^ [_1324987, _1324989, _1324991, _1324993] : [hAPP(hAPP(c_Relation_Orel__comp(_1324987, _1324987, _1324987), _1324989), _1324991) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324987, _1324987), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1324987, _1324987, _1324987), _1324989), _1324993) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324987, _1324987), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1324987, _1324987, _1324987), _1324989), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1324987, _1324987), tc_HOL_Obool)), _1324991), _1324993)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324987, _1324987), tc_HOL_Obool)))], (30409 ^ _775828) ^ [_1331567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1331567)), 30413 ^ _775828 : [(30414 ^ _775828) ^ [_1331647] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331647), _1331567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1331647), 30412 ^ [_1331567])))]]], (6017 ^ _775828) ^ [_871477, _871479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871477), hAPP(c_Nat_OSuc, _871479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871477), _871479))), -(_871477 = _871479)], (20028 ^ _775828) ^ [_1119914, _1119916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1119914)), c_Int_OBit0(_1119916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119914), _1119916)))], (3880 ^ _775828) ^ [_834843, _834845, _834847, _834849, _834851, _834853, _834855, _834857, _834859, _834861, _834863, _834865] : [-(c_Map_Omap__comp(_834865, _834861, _834857, _834853, _834849, _834845) = c_Map_Omap__comp(_834863, _834859, _834855, _834851, _834847, _834843)), _834865 = _834863, _834861 = _834859, _834857 = _834855, _834853 = _834851, _834849 = _834847, _834845 = _834843], (6053 ^ _775828) ^ [_871990, _871992] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871990), _871992))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871990), hAPP(c_Nat_OSuc, _871992))), -(_871992 = _871990)], (43804 ^ _775828) ^ [_1632530, _1632532, _1632534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1632530), _1632532)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632530, tc_HOL_Obool)), _1632534), _1632532) = hAPP(hAPP(c_Finite__Set_Ofold(_1632530, tc_fun(_1632530, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1632530, tc_HOL_Obool), tc_fun(tc_fun(_1632530, tc_HOL_Obool), tc_fun(_1632530, tc_HOL_Obool)), _1632530), hAPP(c_COMBC(tc_fun(_1632530, tc_HOL_Obool), tc_fun(_1632530, tc_HOL_Obool), tc_fun(_1632530, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1632530, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1632530, tc_fun(_1632530, tc_HOL_Obool), tc_fun(_1632530, tc_HOL_Obool)), c_Set_Oinsert(_1632530)), c_Orderings_Obot__class_Obot(tc_fun(_1632530, tc_HOL_Obool))))), _1632534), _1632532))], (22362 ^ _775828) ^ [_1164633, _1164635, _1164637, _1164639] : [class_Fields_Olinordered__field(_1164633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164633), c_Groups_Ozero__class_Ozero(_1164633)), _1164635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164633), _1164637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164633), _1164639), _1164635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164633), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164633), _1164637), _1164635)), _1164639)))], (47417 ^ _775828) ^ [_1721735, _1721737] : [-(c_List_Olistrelp(_1721735, _1721737, c_List_Olist_ONil(_1721735), c_List_Olist_ONil(_1721735)))], (49041 ^ _775828) ^ [_1760537, _1760539, _1760541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760537), tc_List_Olist(_1760537))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760537), tc_List_Olist(_1760537)), c_List_Olist_ONil(_1760537)), _1760539)), c_List_Olexord(_1760537, _1760541))), -(_1760539 = hAPP(hAPP(c_List_Olist_OCons(_1760537), 49044 ^ [_1760537, _1760539, _1760541]), 49045 ^ [_1760537, _1760539, _1760541]))], (46073 ^ _775828) ^ [_1686228, _1686230, _1686232, _1686234, _1686236, _1686238] : [-(hAPP(hAPP(c_List_Ozip(_1686228, _1686230), hAPP(hAPP(c_List_Omap(_1686232, _1686228), _1686234), _1686236)), _1686238) = hAPP(hAPP(c_List_Omap(tc_prod(_1686232, _1686230), tc_prod(_1686228, _1686230)), hAPP(c_Product__Type_Oprod_Oprod__case(_1686232, _1686230, tc_prod(_1686228, _1686230)), hAPP(hAPP(c_COMBB(_1686228, tc_fun(_1686230, tc_prod(_1686228, _1686230)), _1686232), c_Product__Type_OPair(_1686228, _1686230)), _1686234))), hAPP(hAPP(c_List_Ozip(_1686232, _1686230), _1686236), _1686238)))], (4548 ^ _775828) ^ [_845263, _845265, _845267, _845269, _845271, _845273, _845275, _845277] : [-(c_List_Omap__filter(_845277, _845273, _845269, _845265) = c_List_Omap__filter(_845275, _845271, _845267, _845263)), _845277 = _845275, _845273 = _845271, _845269 = _845267, _845265 = _845263], (23444 ^ _775828) ^ [_1185162] : [-(c_Divides_Oadjust(_1185162) = 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)), _1185162))))), 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)), _1185162))))), 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))))))))], (18595 ^ _775828) ^ [_1095427] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1095427), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1095427))], (15452 ^ _775828) ^ [_1035598, _1035600, _1035602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035598), _1035600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035602), _1035600)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035602), _1035598))))], (30119 ^ _775828) ^ [_1324714, _1324716, _1324718, _1324720] : [hAPP(hAPP(c_Relation_Orel__comp(_1324714, _1324714, _1324714), _1324716), _1324718) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324714, _1324714), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1324714, _1324714, _1324714), _1324720), _1324718) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324714, _1324714), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1324714, _1324714, _1324714), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1324714, _1324714), tc_HOL_Obool)), _1324716), _1324720)), _1324718) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1324714, _1324714), tc_HOL_Obool)))], (37588 ^ _775828) ^ [_1486491, _1486493, _1486495] : [class_Fields_Ofield(_1486491), -(_1486493 = c_Groups_Oone__class_Oone(_1486491)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486491), hAPP(c_Power_Opower__class_Opower(_1486491), _1486493)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1486495)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1486491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1486491), hAPP(hAPP(c_Power_Opower__class_Opower(_1486491), _1486493), _1486495)), c_Groups_Oone__class_Oone(_1486491))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1486491), _1486493), c_Groups_Oone__class_Oone(_1486491))))], (35121 ^ _775828) ^ [_1433801, _1433803, _1433805, _1433807, _1433809, _1433811] : [hBOOL(hAPP(hAPP(_1433801, _1433803), _1433805)), hBOOL(hAPP(hAPP(_1433807, _1433803), _1433805)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433809, tc_fun(_1433811, tc_HOL_Obool))), _1433801), _1433807), _1433803), _1433805)))], (23572 ^ _775828) ^ [_1188176, _1188178, _1188180, _1188182, _1188184] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188176, _1188178, tc_HOL_Obool), _1188180), hAPP(hAPP(c_Product__Type_OPair(_1188176, _1188178), _1188182), _1188184))), -(hBOOL(hAPP(hAPP(_1188180, _1188182), _1188184)))], (50361 ^ _775828) ^ [_1788109, _1788111] : [-(hAPP(c_List_Orev(_1788109), _1788111) = hAPP(c_List_Ofoldl(tc_List_Olist(_1788109), _1788109, hAPP(c_COMBC(_1788109, tc_List_Olist(_1788109), tc_List_Olist(_1788109)), c_List_Olist_OCons(_1788109)), c_List_Olist_ONil(_1788109)), _1788111))], (33657 ^ _775828) ^ [_1400587, _1400589, _1400591] : [c_Wellfounded_Owf(_1400587, _1400589), -(c_Wellfounded_Owf(_1400587, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1400587, _1400587), tc_HOL_Obool)), _1400591), _1400589)))], (19728 ^ _775828) ^ [_1114719, _1114721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1114719)), _1114721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114719), _1114721)))], (5034 ^ _775828) ^ [_852832, _852834, _852836, _852838, _852840, _852842] : [-(c_Finite__Set_Ofold(_852842, _852838, _852834) = c_Finite__Set_Ofold(_852840, _852836, _852832)), _852842 = _852840, _852838 = _852836, _852834 = _852832], (28149 ^ _775828) ^ [_1280333, _1280335, _1280337, _1280339] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280333, tc_HOL_Obool)), _1280335), _1280337), _1280339)), -(hBOOL(hAPP(_1280335, _1280339))), -(hBOOL(hAPP(_1280337, _1280339)))], (51164 ^ _775828) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (29297 ^ _775828) ^ [_1307221, _1307223] : [-(c_Option_Oset(_1307221, hAPP(c_Option_Ooption_OSome(_1307221), _1307223)) = hAPP(hAPP(c_Set_Oinsert(_1307221), _1307223), c_Orderings_Obot__class_Obot(tc_fun(_1307221, tc_HOL_Obool))))], (12592 ^ _775828) ^ [_983554, _983556] : [class_Rings_Oring__1(_983554), -(hBOOL(hAPP(hAPP(c_member(_983554), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_983554), _983556)), c_Int_Oring__1__class_OInts(_983554))))], (13724 ^ _775828) ^ [_1004439, _1004441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004441)), -(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, _1004439, _1004441))))], (17877 ^ _775828) ^ [_1081973, _1081975, _1081977] : [class_Power_Opower(_1081973), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081973), _1081975), hAPP(c_Nat_OSuc, _1081977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081973), _1081975), hAPP(hAPP(c_Power_Opower__class_Opower(_1081973), _1081975), _1081977)))], (2552 ^ _775828) ^ [_813449, _813451, _813453, _813455, _813457, _813459, _813461, _813463, _813465, _813467] : [-(c_Nitpick_Opair__box_Opair__box__case(_813467, _813463, _813459, _813455, _813451) = c_Nitpick_Opair__box_Opair__box__case(_813465, _813461, _813457, _813453, _813449)), _813467 = _813465, _813463 = _813461, _813459 = _813457, _813455 = _813453, _813451 = _813449], (31329 ^ _775828) ^ [_1351612, _1351614, _1351616] : [class_Orderings_Olinorder(_1351612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351612), _1351614)), -(_1351614 = c_Orderings_Obot__class_Obot(tc_fun(_1351612, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351612), _1351616)), -(_1351616 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[-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1073894, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1073894, tc_HOL_Obool)), _1073896), _1073898)), _1073898) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1073894, tc_HOL_Obool)), _1073896), _1073898))], (11532 ^ _775828) ^ [_965416, _965418] : [class_Groups_Ogroup__add(_965416), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965416), _965418), hAPP(c_Groups_Ouminus__class_Ouminus(_965416), _965418)) = c_Groups_Ozero__class_Ozero(_965416))], (4838 ^ _775828) ^ [_849782, _849784] : [_849784 = _849782, -(c_Orderings_Oord__class_Omax(_849784) = c_Orderings_Oord__class_Omax(_849782))], (23636 ^ _775828) ^ [_1189598, _1189600] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1189598)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1189600)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1189600))), 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[hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1327073, tc_fun(_1327075, tc_HOL_Obool))), _1327077), _1327079))], (6210 ^ _775828) ^ [_874509, _874511, _874513, _874515] : [class_Orderings_Oorder(_874509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874509), hAPP(_874511, 6215 ^ [_874509, _874511, _874513, _874515])), hAPP(_874511, hAPP(c_Nat_OSuc, 6215 ^ [_874509, _874511, _874513, _874515])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874513), _874515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874509), hAPP(_874511, _874513)), hAPP(_874511, _874515))))], (5150 ^ _775828) ^ [_854620, _854622] : [_854622 = _854620, -(c_Groups_Oplus__class_Oplus(_854622) = c_Groups_Oplus__class_Oplus(_854620))], (19720 ^ _775828) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (27974 ^ _775828) ^ [_1276128, _1276130] : [c_Wellfounded_Owf(_1276128, _1276130), 27977 ^ _775828 : [(27978 ^ _775828) ^ [_1276197] : [-(hBOOL(hAPP(hAPP(c_member(_1276128), 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hAPP(c_Finite__Set_Ocard(_1429302), _1429304)), hAPP(c_Finite__Set_Ocard(_1429302), _1429306)))], (15972 ^ _775828) ^ [_1046164, _1046166, _1046168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046164), _1046166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046168), _1046166)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046168), _1046164))))], (44896 ^ _775828) ^ [_1659133] : [class_Complete__Lattice_Ocomplete__lattice(_1659133), -(c_Complete__Lattice_OSup__class_OSup(_1659133, c_Orderings_Otop__class_Otop(tc_fun(_1659133, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1659133))], (50734 ^ _775828) ^ [_1797294, _1797296, _1797298, _1797300] : [-(c_List_Oremdups(_1797294, hAPP(hAPP(c_List_Omap(_1797296, _1797294), _1797298), c_List_Oremdups(_1797296, _1797300))) = c_List_Oremdups(_1797294, hAPP(hAPP(c_List_Omap(_1797296, _1797294), _1797298), _1797300)))], (37216 ^ _775828) ^ [_1477036, _1477038, _1477040, _1477042, _1477044, _1477046, _1477048] : [class_Groups_Ocomm__monoid__add(_1477036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477038), _1477040)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477042), _1477044)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477038, _1477036), hAPP(hAPP(c_COMBS(_1477038, tc_fun(_1477042, tc_HOL_Obool), _1477036), hAPP(hAPP(c_COMBB(tc_fun(_1477042, _1477036), tc_fun(tc_fun(_1477042, tc_HOL_Obool), _1477036), _1477038), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477042, _1477036)), _1477046)), hAPP(hAPP(c_COMBB(tc_fun(_1477042, tc_HOL_Obool), tc_fun(_1477042, tc_HOL_Obool), _1477038), c_Set_OCollect(_1477042)), hAPP(hAPP(c_COMBB(tc_fun(_1477042, tc_HOL_Obool), tc_fun(_1477042, tc_HOL_Obool), _1477038), hAPP(c_COMBS(_1477042, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, 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tc_HOL_Obool), c_member(_1477038)), _1477040)))), hAPP(c_COMBC(_1477038, _1477042, tc_HOL_Obool), _1477048))))), _1477044))], (46432 ^ _775828) ^ [_1696944, _1696946, _1696948] : [-(hAPP(c_List_Olexn(_1696944, _1696946), hAPP(c_Nat_OSuc, _1696948)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1696944), tc_List_Olist(_1696944)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1696944, tc_List_Olist(_1696944)), tc_prod(_1696944, tc_List_Olist(_1696944))), tc_prod(tc_List_Olist(_1696944), tc_List_Olist(_1696944)), c_Product__Type_Omap__pair(tc_prod(_1696944, tc_List_Olist(_1696944)), tc_List_Olist(_1696944), tc_prod(_1696944, tc_List_Olist(_1696944)), tc_List_Olist(_1696944), hAPP(c_Product__Type_Oprod_Oprod__case(_1696944, tc_List_Olist(_1696944), tc_List_Olist(_1696944)), c_List_Olist_OCons(_1696944)), hAPP(c_Product__Type_Oprod_Oprod__case(_1696944, tc_List_Olist(_1696944), tc_List_Olist(_1696944)), c_List_Olist_OCons(_1696944)))), c_Wellfounded_Olex__prod(_1696944, tc_List_Olist(_1696944), _1696946, hAPP(c_List_Olexn(_1696944, _1696946), _1696948)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1696944), tc_List_Olist(_1696944))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1696944), tc_List_Olist(_1696944), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696944), tc_fun(tc_List_Olist(_1696944), tc_HOL_Obool), tc_fun(tc_List_Olist(_1696944), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1696944), tc_HOL_Obool), tc_fun(tc_List_Olist(_1696944), tc_HOL_Obool)), tc_List_Olist(_1696944)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1696944))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1696944)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696944), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696944)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696944)))), hAPP(c_Nat_OSuc, _1696948))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696944), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696944)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696944)))), hAPP(c_Nat_OSuc, _1696948)))))))], (5593 ^ _775828) ^ [_864469] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _864469)], (7649 ^ _775828) ^ [_897850, _897852, _897854] : [class_Rings_Oring(_897850), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897850), hAPP(c_Groups_Ouminus__class_Ouminus(_897850), _897852)), hAPP(c_Groups_Ouminus__class_Ouminus(_897850), _897854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897850), _897852), _897854))], (51456 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (32597 ^ _775828) ^ [_1378239, _1378241] : [class_Lattices_Olattice(_1378239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378239), _1378241)), -(_1378241 = c_Orderings_Obot__class_Obot(tc_fun(_1378239, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378239), c_Big__Operators_Olattice__class_OInf__fin(_1378239, _1378241)), c_Big__Operators_Olattice__class_OSup__fin(_1378239, _1378241))))], (15326 ^ _775828) ^ [_1033419, _1033421] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033419), _1033421) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033421), _1033419) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1033419 = _1033421)], (28814 ^ _775828) ^ [_1294226, _1294228] : [-(c_Hilbert__Choice_OEps(_1294226, hAPP(hAPP(c_COMBC(_1294226, _1294226, tc_HOL_Obool), c_fequal), _1294228)) = _1294228)], (15336 ^ _775828) ^ [_1033572] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033572), _1033572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40798 ^ _775828) ^ [_1560398, _1560400, _1560402, _1560404, _1560406] : [-(hAPP(c_Set_Ovimage(_1560398, _1560400, _1560402), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1560400, tc_HOL_Obool)), _1560404), _1560406)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1560398, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1560398, _1560400, _1560402), _1560404)), hAPP(c_Set_Ovimage(_1560398, _1560400, _1560402), _1560406)))], (38027 ^ _775828) ^ [_1496895, _1496897, _1496899, _1496901, _1496903] : [-(hAPP(c_Relation_OImage(_1496895, _1496897, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496895, _1496897), tc_HOL_Obool)), _1496899), _1496901)), _1496903) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496897, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496895, _1496897, _1496899), _1496903)), hAPP(c_Relation_OImage(_1496895, _1496897, _1496901), _1496903)))], (12485 ^ _775828) ^ [_981824, _981826, _981828] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981826)), _981828)) = 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), _981824), _981826))), _981828))], (13746 ^ _775828) ^ [_1004807, _1004809] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004807, _1004809) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1004807 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1004809), 13749 ^ [_1004807, _1004809]))], (41562 ^ _775828) ^ [_1580013, _1580015, _1580017, _1580019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1580013), _1580015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580013, _1580013), tc_HOL_Obool)), _1580017), hAPP(hAPP(c_Product__Type_OSigma(_1580013, _1580013), _1580015), hAPP(c_COMBK(tc_fun(_1580013, tc_HOL_Obool), _1580013), _1580015)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1580013, tc_HOL_Obool)), _1580019), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1580013), _1580015), _1580017))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1580013), _1580019)))], (5316 ^ _775828) ^ [_857069, _857071, _857073, _857075] : [-(tc_fun(_857075, _857071) = tc_fun(_857073, _857069)), _857075 = _857073, _857071 = _857069], (5927 ^ _775828) ^ [_870162, _870164, _870166, _870168] : [c_Com_Ocom_OAss(_870162, _870164) = c_Com_Ocom_OAss(_870166, _870168), 5930 ^ _775828 : [(5933 ^ _775828) ^ [] : [-(_870164 = _870168)], (5931 ^ _775828) ^ [] : [-(_870162 = _870166)]]], (2516 ^ _775828) ^ [_812909, _812911, _812913, _812915, _812917, _812919] : [-(c_Random__Sequence_Oempty(_812919, _812915, _812911) = c_Random__Sequence_Oempty(_812917, _812913, _812909)), _812919 = _812917, _812915 = _812913, _812911 = _812909], (28315 ^ _775828) ^ [_1283953, _1283955, _1283957, _1283959] : [28316 ^ _775828 : [(28317 ^ _775828) ^ [_1284063] : [hBOOL(hAPP(hAPP(c_member(_1283953), _1284063), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283953, tc_HOL_Obool)), _1283955), _1283957))), hBOOL(hAPP(_1283959, _1284063))]], 28325 ^ _775828 : [(28328 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1283959, 28324 ^ [_1283953, _1283955, _1283957, _1283959])))], (28326 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1283953), 28324 ^ [_1283953, _1283955, _1283957, _1283959]), _1283955)))]], 28330 ^ _775828 : [(28333 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1283959, 28329 ^ [_1283953, _1283955, _1283957, _1283959])))], (28331 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1283953), 28329 ^ [_1283953, _1283955, _1283957, _1283959]), _1283957)))]]], (29181 ^ _775828) ^ [_1304699, _1304701] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304699, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1304699, tc_HOL_Obool))), _1304701) = _1304701)], (25485 ^ _775828) ^ [_1225462, _1225464] : 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_902198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902196), _902198))))], (28769 ^ _775828) ^ [_1293406, _1293408, _1293410] : [c_Wellfounded_Owf(_1293406, _1293408), hBOOL(hAPP(hAPP(c_member(tc_prod(_1293406, _1293406)), hAPP(hAPP(c_Product__Type_OPair(_1293406, _1293406), hAPP(_1293410, hAPP(c_Nat_OSuc, 28772 ^ [_1293406, _1293408, _1293410]))), hAPP(_1293410, 28772 ^ [_1293406, _1293408, _1293410]))), _1293408))], (124 ^ _775828) ^ [_777520, _777522, _777524, _777526, _777528, _777530] : [-(c_Nitpick_Oless__frac(_777528, _777524, _777520)), c_Nitpick_Oless__frac(_777530, _777526, _777522), _777530 = _777528, _777526 = _777524, _777522 = _777520], (51284 ^ _775828) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (5999 ^ _775828) ^ [_871229] : [-(_871229 = 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)), _871229)))], (26469 ^ _775828) ^ [_1243342, _1243344, _1243346] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243342), _1243344)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243342), _1243346))), -(_1243342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243344), _1243346)))], (8035 ^ _775828) ^ [_904916, _904918, _904920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _904916)), 8038 ^ _775828 : [(8045 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904918), _904920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904916), _904918)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904916), _904920))))], (8039 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904916), _904918)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _904916), _904920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904918), _904920)))]]], (26437 ^ _775828) ^ [_1242761, _1242763, _1242765, _1242767] : [class_Divides_Osemiring__div(_1242761), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242761), _1242763), _1242765)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1242761), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242761), _1242765), _1242763)), _1242767) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242761), hAPP(hAPP(c_Power_Opower__class_Opower(_1242761), _1242765), _1242767)), hAPP(hAPP(c_Power_Opower__class_Opower(_1242761), _1242763), _1242767)))], (20052 ^ _775828) ^ [_1120360, _1120362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120360)), c_Int_OBit0(_1120362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120360), _1120362)))], (5304 ^ _775828) ^ [_856899, _856901] : [_856901 = _856899, -(c_List_Olist_ONil(_856901) = c_List_Olist_ONil(_856899))], (47587 ^ _775828) ^ [_1725015, _1725017, _1725019, _1725021] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1725015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1725017), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1725015)), hAPP(hAPP(c_List_Olist_OCons(_1725017), _1725019), _1725021)) = c_List_Olist_ONil(_1725017))], (36487 ^ _775828) ^ [_1461208, _1461210, _1461212, _1461214] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461208), _1461210)), 36490 ^ _775828 : [(36491 ^ _775828) ^ [_1461362] : [36493 ^ _775828 : [(36499 ^ _775828) ^ [] : [-(_1461362 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36495 ^ [_1461208, _1461210, _1461212, _1461214, _1461362]), 36492 ^ [_1461208, _1461210, _1461212, _1461214, _1461362]))], (36497 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36495 ^ [_1461208, _1461210, _1461212, _1461214, _1461362]), _1461212)))], (36494 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36492 ^ [_1461208, _1461210, _1461212, _1461214, _1461362]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1461210))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461208), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461362), _1461214))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461208), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461362), _1461210)), _1461214))))]]], (47739 ^ _775828) ^ [_1729097, _1729099, _1729101, _1729103, _1729105] : [-(hAPP(hAPP(c_List_Oappend(_1729097), _1729099), hAPP(hAPP(c_List_Olist_OCons(_1729097), _1729101), c_List_Olist_ONil(_1729097))) = hAPP(hAPP(c_List_Oappend(_1729097), _1729103), hAPP(hAPP(c_List_Olist_OCons(_1729097), _1729105), c_List_Olist_ONil(_1729097)))), _1729099 = _1729103, _1729101 = _1729105], (2056 ^ _775828) ^ [_805795, _805797, _805799, _805801, _805803, _805805, _805807, _805809] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_805809, _805805, _805801, _805797) = c_Nat_Osemiring__1__class_Oof__nat__aux(_805807, _805803, _805799, _805795)), _805809 = _805807, _805805 = _805803, _805801 = _805799, _805797 = _805795], (44038 ^ _775828) ^ [_1636940, _1636942, _1636944, _1636946, _1636948, _1636950, _1636952] : [c_Finite__Set_Ofun__left__comm(_1636940, _1636942, _1636944), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1636940, _1636942, _1636944, _1636946, _1636948), _1636950)), hBOOL(hAPP(hAPP(c_member(_1636940), _1636952), _1636948)), 44050 ^ _775828 : [(44053 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1636940, _1636942, _1636944, _1636946, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1636940, tc_HOL_Obool)), _1636948), hAPP(hAPP(c_Set_Oinsert(_1636940), _1636952), c_Orderings_Obot__class_Obot(tc_fun(_1636940, tc_HOL_Obool))))), 44049 ^ [_1636940, _1636942, _1636944, _1636946, _1636948, _1636950, _1636952])))], (44051 ^ _775828) ^ [] : [-(_1636950 = hAPP(hAPP(_1636944, _1636952), 44049 ^ [_1636940, _1636942, _1636944, _1636946, _1636948, _1636950, _1636952]))]]], (16497 ^ _775828) ^ [_1056447, _1056449, _1056451] : [class_Int_Onumber(_1056447), 16500 ^ _775828 : [(16507 ^ _775828) ^ [] : [_1056451 = hAPP(c_Int_Onumber__class_Onumber__of(_1056447), _1056449), -(hAPP(c_Int_Onumber__class_Onumber__of(_1056447), _1056449) = _1056451)], (16501 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1056447), _1056449) = _1056451, -(_1056451 = hAPP(c_Int_Onumber__class_Onumber__of(_1056447), _1056449))]]], (30752 ^ _775828) ^ [_1338254, _1338256, _1338258, _1338260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338254), _1338256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1338258), hAPP(c_Set_Oimage(_1338254, _1338258, _1338260), _1338256))), hAPP(c_Finite__Set_Ocard(_1338254), _1338256))))], (49467 ^ _775828) ^ [_1769223, _1769225, _1769227, _1769229, _1769231] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769223)), hAPP(c_List_Ofilter(_1769223, _1769225), hAPP(hAPP(c_List_Omap(_1769227, _1769223), _1769229), _1769231))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769227)), hAPP(c_List_Ofilter(_1769227, hAPP(c_Fun_Ocomp(_1769223, tc_HOL_Obool, _1769227, _1769225), _1769229)), _1769231)))], (29777 ^ _775828) ^ [_1316786, _1316788, _1316790, _1316792, _1316794] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1316786, _1316788, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1316786)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1316786), hAPP(hAPP(c_COMBC(_1316786, 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)), _1316786), 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)), _1316786), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1316790))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1316792))), c_Com_Ocom_OWhile(_1316792, _1316794)), _1316790)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1316786), tc_HOL_Obool)))))], (33290 ^ _775828) ^ [_1392557, _1392559, _1392561, _1392563, _1392565] : [class_Groups_Ocomm__monoid__mult(_1392557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392559), _1392561)), hBOOL(hAPP(hAPP(c_member(_1392559), _1392563), _1392561)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392559, _1392557), _1392565), _1392561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392557), hAPP(_1392565, _1392563)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392559, _1392557), _1392565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392559, tc_HOL_Obool)), _1392561), hAPP(hAPP(c_Set_Oinsert(_1392559), _1392563), c_Orderings_Obot__class_Obot(tc_fun(_1392559, tc_HOL_Obool)))))))], (45931 ^ _775828) ^ [_1682780, _1682782] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1682780), _1682782) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1682780, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1682782), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (39491 ^ _775828) ^ [_1529920, _1529922, _1529924, _1529926, _1529928] : [class_Complete__Lattice_Ocomplete__lattice(_1529920), class_Orderings_Olinorder(_1529920), 39498 ^ _775828 : [(39508 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1529920), _1529922), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529924, _1529920), _1529926), _1529928)))), 39509 ^ _775828 : [(39510 ^ _775828) ^ [_1530268] : [hBOOL(hAPP(hAPP(c_member(_1529924), _1530268), _1529926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1529920), _1529922), hAPP(_1529928, _1530268)))]]], (39499 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1529920), _1529922), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529924, _1529920), _1529926), _1529928))), 39503 ^ _775828 : [(39506 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1529920), _1529922), hAPP(_1529928, 39502 ^ [_1529920, _1529922, _1529924, _1529926, _1529928]))))], (39504 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529924), 39502 ^ [_1529920, _1529922, _1529924, _1529926, _1529928]), _1529926)))]]]]], (6722 ^ _775828) ^ [] : [-(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)))], (48695 ^ _775828) ^ [_1752497, _1752499, _1752501, _1752503] : [-(hAPP(c_List_Orotate(_1752497, _1752499), hAPP(c_List_Orotate(_1752497, _1752501), _1752503)) = hAPP(c_List_Orotate(_1752497, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752499), _1752501)), _1752503))], (46426 ^ _775828) ^ [_1696561, _1696563, _1696565, _1696567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696561), tc_List_Olist(_1696561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696561), tc_List_Olist(_1696561)), _1696565), _1696567)), c_List_Olistrel(_1696561, _1696563))), -(c_List_Olistrelp(_1696561, hAPP(hAPP(c_COMBC(_1696561, tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_fun(_1696561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1696561, tc_fun(tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_fun(_1696561, tc_HOL_Obool)), _1696561), c_COMBC(_1696561, tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1696561, tc_prod(_1696561, _1696561)), tc_fun(_1696561, tc_fun(tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_HOL_Obool)), _1696561), hAPP(c_COMBB(tc_prod(_1696561, _1696561), tc_fun(tc_fun(tc_prod(_1696561, _1696561), tc_HOL_Obool), tc_HOL_Obool), _1696561), c_member(tc_prod(_1696561, _1696561)))), c_Product__Type_OPair(_1696561, _1696561)))), _1696563), _1696565, _1696567))], (48719 ^ _775828) ^ [_1753006, _1753008, _1753010] : [-(hAPP(c_List_Otl(_1753006), hAPP(hAPP(c_List_Oappend(_1753006), _1753008), _1753010)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1753006), _1753006, hAPP(c_List_Otl(_1753006), _1753010), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1753006), tc_List_Olist(_1753006)), _1753006), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753006), tc_List_Olist(_1753006), tc_List_Olist(_1753006)), c_List_Oappend(_1753006)), _1753010))), _1753008))], (36797 ^ _775828) ^ [_1467079, _1467081, _1467083] : [class_Orderings_Olinorder(_1467079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467079), _1467081), _1467083)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467079, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1467079), _1467081)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1467079, _1467081), _1467083)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1467079), _1467083))], (48361 ^ _775828) ^ [_1745086, _1745088, _1745090, _1745092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745086), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745088)), _1745090))), -(hAPP(hAPP(c_List_Olist__update(_1745088, _1745090), _1745086), _1745092) = hAPP(hAPP(c_List_Oappend(_1745088), hAPP(hAPP(c_List_Otake(_1745088), _1745086), _1745090)), hAPP(hAPP(c_List_Olist_OCons(_1745088), _1745092), hAPP(hAPP(c_List_Odrop(_1745088), hAPP(c_Nat_OSuc, _1745086)), _1745090))))], (47583 ^ _775828) ^ [_1724848, _1724850] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1724848), tc_List_Olist(_1724848), c_List_Olistrel(_1724848, _1724850)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724848)), c_List_Olist_ONil(_1724848)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724848), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724848)), c_List_Olist_ONil(_1724848)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724848), tc_HOL_Obool))))], (8915 ^ _775828) ^ [_918438, _918440, _918442] : [class_Orderings_Olinorder(_918438), 8918 ^ _775828 : [(8925 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918438), _918442), _918440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918438), _918440), _918442))], (8919 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918438), _918440), _918442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918438), _918442), _918440)))]]], (50411 ^ _775828) ^ [_1789123, _1789125, _1789127] : [_1789125 = hAPP(c_List_Orev(_1789123), _1789127), -(hAPP(c_List_Orev(_1789123), _1789125) = _1789127)], (30057 ^ _775828) ^ [_1323655, _1323657] : [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)))), _1323655, _1323657) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323655), _1323657)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323657), _1323655)))], (5434 ^ _775828) ^ [_858838, _858840] : [_858840 = _858838, -(v_P(_858840) = v_P(_858838))], (7971 ^ _775828) ^ [_903451, _903453, _903455] : [class_Rings_Ocomm__semiring__1(_903451), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903451), _903453), _903455) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903451), _903455), _903453))], (10622 ^ _775828) ^ [_948960, _948962, _948964, _948966] : [class_Rings_Ocomm__semiring__1(_948960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948960), _948962), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948960), _948964), _948966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948960), _948962), _948964)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948960), _948962), _948966)))], (36343 ^ _775828) ^ [_1458183] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458183), hAPP(c_Nat_OSuc, _1458183)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1458183), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (41384 ^ _775828) ^ [_1576105, _1576107, _1576109, _1576111, _1576113, _1576115] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576105, _1576107)), hAPP(hAPP(c_Product__Type_OPair(_1576105, _1576107), _1576109), _1576111)), hAPP(hAPP(c_Product__Type_OSigma(_1576105, _1576107), _1576113), _1576115))), -(hBOOL(hAPP(hAPP(c_member(_1576107), _1576111), hAPP(_1576115, _1576109))))], (30870 ^ _775828) ^ [_1340615, _1340617, _1340619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340615), _1340617)), -(hBOOL(hAPP(hAPP(c_member(_1340615), _1340619), _1340617))), -(hAPP(c_Finite__Set_Ocard(_1340615), hAPP(hAPP(c_Set_Oinsert(_1340615), _1340619), _1340617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1340615), _1340617)))], (31531 ^ _775828) ^ [_1355816, _1355818] : [class_Orderings_Olinorder(_1355816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355816), _1355818)), -(_1355818 = c_Orderings_Obot__class_Obot(tc_fun(_1355816, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1355816), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355816), 31544 ^ [_1355816, _1355818]), 31545 ^ [_1355816, _1355818])), hAPP(hAPP(c_Set_Oinsert(_1355816), 31544 ^ [_1355816, _1355818]), hAPP(hAPP(c_Set_Oinsert(_1355816), 31545 ^ [_1355816, _1355818]), c_Orderings_Obot__class_Obot(tc_fun(_1355816, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1355816), c_Big__Operators_Olattice_OInf__fin(_1355816, c_Orderings_Oord__class_Omin(_1355816), _1355818)), _1355818)))], (28521 ^ _775828) ^ [_1288099, _1288101, _1288103, _1288105] : [class_Lattices_Osemilattice__sup(_1288099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288099), _1288101), _1288103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288099), _1288101), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288099), _1288103), _1288105))))], (45161 ^ _775828) ^ [_1665058, _1665060, _1665062] : [45163 ^ _775828 : [(45166 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1665058), _1665062), 45162 ^ [_1665058, _1665060, _1665062]))], (45164 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1665058, tc_HOL_Obool)), 45162 ^ [_1665058, _1665060, _1665062]), _1665060)))]], -(hBOOL(hAPP(hAPP(c_member(_1665058), _1665062), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665058, tc_HOL_Obool), _1665060))))], (48207 ^ _775828) ^ [_1740380, _1740382, _1740384] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740380), tc_List_Olist(_1740380))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1740380), tc_List_Olist(_1740380)), _1740382), c_List_Olist_ONil(_1740380))), c_List_Olistrel1(_1740380, _1740384)))], (31373 ^ _775828) ^ [_1352346, _1352348, _1352350] : [class_Orderings_Olinorder(_1352346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352346), _1352348)), -(hBOOL(hAPP(hAPP(c_member(_1352346), _1352350), _1352348))), -(_1352348 = c_Orderings_Obot__class_Obot(tc_fun(_1352346, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1352346, c_Orderings_Oord__class_Omin(_1352346), hAPP(hAPP(c_Set_Oinsert(_1352346), _1352350), _1352348)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1352346), _1352350), c_Big__Operators_Olattice_OInf__fin(_1352346, c_Orderings_Oord__class_Omin(_1352346), _1352348)))], (27264 ^ _775828) ^ [_1258663, _1258665, _1258667] : [c_Relation_Ototal__on(_1258663, _1258665, _1258667), -(c_Relation_Ototal__on(_1258663, _1258665, hAPP(c_Relation_Oconverse(_1258663, _1258663), _1258667)))], (49937 ^ _775828) ^ [_1778831, _1778833, _1778835, _1778837, _1778839] : [class_Orderings_Olinorder(_1778831), 49940 ^ _775828 : [(49947 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1778831, hAPP(hAPP(c_List_Omap(_1778833, _1778831), _1778835), _1778839)), -(c_List_Olinorder__class_Osorted(_1778831, hAPP(hAPP(c_List_Omap(_1778833, _1778831), _1778835), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1778833, _1778831, _1778835), _1778837), _1778839))))], (49941 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1778831, hAPP(hAPP(c_List_Omap(_1778833, _1778831), _1778835), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1778833, _1778831, _1778835), _1778837), _1778839))), -(c_List_Olinorder__class_Osorted(_1778831, hAPP(hAPP(c_List_Omap(_1778833, _1778831), _1778835), _1778839)))]]], (12353 ^ _775828) ^ [_979577, _979579, _979581] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979577), _979579)), _979581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979579), _979581)))], (40245 ^ _775828) ^ [_1547302] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547302, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1547302, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1547302, tc_HOL_Obool)))], (28077 ^ _775828) ^ [_1279026] : [-(c_Wellfounded_OwfP(_1279026, hAPP(c_COMBK(tc_fun(_1279026, tc_HOL_Obool), _1279026), hAPP(c_COMBK(tc_HOL_Obool, _1279026), c_fFalse))))], (10656 ^ _775828) ^ [_949696, _949698, _949700, _949702] : [class_Rings_Ocomm__semiring__1(_949696), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949696), _949698), _949700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949696), _949702), _949700)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949696), _949698), _949702)), _949700))], (33921 ^ _775828) ^ [_1406715, _1406717, _1406719, _1406721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406715, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1406715, _1406717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1406715, _1406717), tc_HOL_Obool)), _1406719), _1406721))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406715, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1406715, _1406717), _1406719)), hAPP(c_Relation_ODomain(_1406715, _1406717), _1406721)))))], (41649 ^ _775828) ^ [_1582159, _1582161, _1582163] : [class_Lattices_Oab__semigroup__idem__mult(_1582159), -(_1582161 = c_Orderings_Obot__class_Obot(tc_fun(_1582159, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582159), _1582161)), -(hAPP(c_Finite__Set_Ofold1(_1582159, c_Groups_Otimes__class_Otimes(_1582159)), hAPP(hAPP(c_Set_Oinsert(_1582159), _1582163), _1582161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1582159), _1582163), hAPP(c_Finite__Set_Ofold1(_1582159, c_Groups_Otimes__class_Otimes(_1582159)), _1582161)))], (31315 ^ _775828) ^ [_1351377, _1351379, _1351381] : [class_Orderings_Olinorder(_1351377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351377), _1351379)), hBOOL(hAPP(hAPP(c_member(_1351377), _1351381), _1351379)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351377), _1351381), c_Big__Operators_Olattice_OSup__fin(_1351377, c_Orderings_Oord__class_Omax(_1351377), _1351379)) = _1351381)], (29104 ^ _775828) ^ [_1302823, _1302825] : [c_Wellfounded_Oacyclic(_1302823, _1302825), 29107 ^ _775828 : [(29108 ^ _775828) ^ [_1302908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302823, _1302823)), hAPP(hAPP(c_Product__Type_OPair(_1302823, _1302823), _1302908), _1302908)), c_Transitive__Closure_Otrancl(_1302823, _1302825)))]]], (9598 ^ _775828) ^ [_930140] : [9599 ^ _775828 : [(9600 ^ _775828) ^ [_930197] : [hBOOL(hAPP(_930140, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930197)))]], 9602 ^ _775828 : [(9605 ^ _775828) ^ [] : [-(hBOOL(hAPP(_930140, 9601 ^ [_930140])))], (9603 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9601 ^ [_930140])))]]], (29038 ^ _775828) ^ [_1301499, _1301501, _1301503, _1301505] : [c_Hoare__Mirabelle_Ohoare__derivs(_1301499, _1301501, _1301503), c_Hoare__Mirabelle_Ohoare__derivs(_1301499, _1301505, _1301501), -(c_Hoare__Mirabelle_Ohoare__derivs(_1301499, _1301505, _1301503))], (26980 ^ _775828) ^ [_1252483, _1252485] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252483), _1252485)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252483)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252485))))], (18205 ^ _775828) ^ [_1088307, _1088309, _1088311, _1088313] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1088307, _1088309, _1088311), _1088313), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1088309)], (46113 ^ _775828) ^ [_1687491] : [class_Orderings_Olinorder(_1687491), -(c_Finite__Set_Ofun__left__comm(_1687491, tc_List_Olist(_1687491), c_List_Olinorder__class_Oinsort__key(_1687491, _1687491, c_COMBI(_1687491))))], (30690 ^ _775828) ^ [_1336869, _1336871, _1336873, _1336875] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336869), hAPP(c_Set_OCollect(_1336869), _1336871))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1336873), hAPP(c_Set_OCollect(_1336873), hAPP(hAPP(c_COMBB(tc_fun(_1336869, tc_HOL_Obool), tc_HOL_Obool, _1336873), c_HOL_OEx(_1336869)), hAPP(hAPP(c_COMBC(_1336873, tc_fun(_1336869, tc_HOL_Obool), tc_fun(_1336869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1336869, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1336869, tc_HOL_Obool), tc_fun(_1336869, tc_HOL_Obool)), _1336873), c_COMBS(_1336869, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1336869, tc_HOL_Obool), tc_fun(_1336869, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1336873), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1336869), c_fconj)), hAPP(hAPP(c_COMBC(_1336873, tc_fun(_1336869, _1336873), tc_fun(_1336869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1336873, tc_HOL_Obool), tc_fun(tc_fun(_1336869, _1336873), tc_fun(_1336869, tc_HOL_Obool)), _1336873), c_COMBB(_1336873, tc_HOL_Obool, _1336869)), c_fequal)), _1336875)))), _1336871))))))], (45292 ^ _775828) ^ [_1667868, _1667870, _1667872, _1667874] : [class_Rings_Olinordered__semidom(_1667868), 45298 ^ _775828 : [(45301 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1667868), c_Groups_Ozero__class_Ozero(_1667868)), hAPP(_1667874, 45297 ^ [_1667868, _1667870, _1667872, _1667874])))], (45299 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667870), 45297 ^ [_1667868, _1667870, _1667872, _1667874]), _1667872)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1667868), c_Groups_Ozero__class_Ozero(_1667868)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1667870, _1667868), _1667874), _1667872))))], (19196 ^ _775828) ^ [] : [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)], (43628 ^ _775828) ^ [_1629052, _1629054, _1629056, _1629058] : [class_Orderings_Olinorder(_1629052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629052), _1629054)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1629052, _1629052, c_Orderings_Oord__class_Omax(_1629052)), _1629056), hAPP(hAPP(c_Set_Oinsert(_1629052), _1629058), _1629054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1629052), _1629058), hAPP(hAPP(c_Finite__Set_Ofold(_1629052, _1629052, c_Orderings_Oord__class_Omax(_1629052)), _1629056), _1629054)))], (9205 ^ _775828) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (51266 ^ _775828) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (27443 ^ _775828) ^ [_1263230, _1263232] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1263230), 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)))), _1263232)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263230), _1263232)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263232), _1263230)))], (38082 ^ _775828) ^ [_1498045, _1498047, _1498049, _1498051, _1498053] : [-(hBOOL(hAPP(hAPP(c_member(_1498045), _1498047), hAPP(c_Relation_OImage(_1498049, _1498045, _1498051), _1498053)))), 38083 ^ _775828 : [(38084 ^ _775828) ^ [_1498131] : [hBOOL(hAPP(hAPP(c_member(_1498049), _1498131), _1498053)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1498049, _1498045)), hAPP(hAPP(c_Product__Type_OPair(_1498049, _1498045), _1498131), _1498047)), _1498051))]]], (19462 ^ _775828) ^ [_1110310] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110310), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110310)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1110310)))], (2902 ^ _775828) ^ [_819372, _819374] : [_819374 = _819372, -(c_Divides_Odiv__class_Odiv(_819374) = c_Divides_Odiv__class_Odiv(_819372))], (48403 ^ _775828) ^ [_1746089, _1746091] : [hBOOL(hAPP(c_List_Odistinct(_1746089), _1746091)), -(hBOOL(hAPP(c_List_Odistinct(_1746089), hAPP(c_List_Orotate1(_1746089), _1746091))))], (360 ^ _775828) ^ [_781078, _781080, _781082, _781084, _781086, _781088, _781090, _781092, _781094, _781096] : [-(c_Big__Operators_Ocomm__monoid__big(_781094, _781090, _781086, _781082, _781078)), c_Big__Operators_Ocomm__monoid__big(_781096, _781092, _781088, _781084, _781080), _781096 = _781094, _781092 = _781090, _781088 = _781086, _781084 = _781082, _781080 = _781078], (8625 ^ _775828) ^ [_914174, _914176, _914178] : [hBOOL(hAPP(hAPP(c_member(_914174), _914176), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_914174, tc_HOL_Obool)), _914178))), hBOOL(hAPP(hAPP(c_member(_914174), _914176), _914178))], (48237 ^ _775828) ^ [_1741372, _1741374, _1741376, _1741378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741372), tc_List_Olist(_1741372))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741372), tc_List_Olist(_1741372)), _1741374), _1741376)), c_List_Olistrel(_1741372, _1741378))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741372), tc_List_Olist(_1741372))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741372), tc_List_Olist(_1741372)), _1741374), _1741376)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1741372), c_List_Olistrel1(_1741372, _1741378)))))], (8519 ^ _775828) ^ [_912621] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _912621))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _912621)) = _912621)], (27435 ^ _775828) ^ [_1263085, _1263087] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1263085), 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)))), _1263087))), 27438 ^ _775828 : [(27441 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263087), _1263085))], (27439 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263085), _1263087)))]]], (240 ^ _775828) ^ [_779310, _779312, _779314, _779316, _779318, _779320] : [-(c_Relation_Ototal__on(_779318, _779314, _779310)), c_Relation_Ototal__on(_779320, _779316, _779312), _779320 = _779318, _779316 = _779314, _779312 = _779310], (51586 ^ _775828) ^ [_1809263, _1809265] : [hBOOL(hAPP(hAPP(c_fdisj, _1809263), _1809265)), -(hBOOL(_1809263)), -(hBOOL(_1809265))], (31783 ^ _775828) ^ [_1362180, _1362182] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1362180, _1362180), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1362180, _1362182)), c_Relation_OId(_1362180)) = c_Transitive__Closure_Ortrancl(_1362180, _1362182))], (47928 ^ _775828) ^ [_1733592, _1733594, _1733596, _1733598] : [_1733594 = _1733598, -(hAPP(hAPP(c_List_Oappend(_1733592), _1733594), _1733596) = hAPP(hAPP(c_List_Oappend(_1733592), _1733598), _1733596))], (27918 ^ _775828) ^ [_1275056, _1275058, _1275060, _1275062, _1275064, _1275066, _1275068] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1275056, _1275058, _1275060, _1275062, _1275064), _1275066), _1275068))), 27919 ^ _775828 : [(27920 ^ _775828) ^ [_1275127] : [hBOOL(hAPP(hAPP(_1275062, _1275066), _1275127)), hBOOL(hAPP(hAPP(_1275064, _1275127), _1275068))]]], (33821 ^ _775828) ^ [_1404287, _1404289, _1404291, _1404293, _1404295] : [class_Lattices_Olattice(_1404287), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404289, _1404287)), _1404291), _1404293), _1404295) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404287), hAPP(_1404291, _1404295)), hAPP(_1404293, _1404295)))], (38208 ^ _775828) ^ [_1501232, _1501234, _1501236, _1501238] : [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), _1501232), _1501234)), 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), _1501236), _1501238)), 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), _1501232), _1501238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501236), _1501234))))], (18389 ^ _775828) ^ [_1091848, _1091850, _1091852, _1091854, _1091856, _1091858, _1091860] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091848, _1091850), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091852), _1091854))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1091856, _1091850), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1091858), _1091860))), -(_1091850 = 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), _1091848), _1091856), _1091850), 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), _1091852), _1091858)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091854), _1091860)), _1091850))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091854), _1091860), _1091850)))))], (49897 ^ _775828) ^ [_1778227, _1778229] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1778227), _1778229)) = c_List_Oupt(_1778227, _1778229))], (19944 ^ _775828) ^ [_1118257, _1118259] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118257)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118259)) = 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)))), _1118257)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118259)))], (36605 ^ _775828) ^ [_1463603, _1463605, _1463607] : [class_Orderings_Oorder(_1463603), 36608 ^ _775828 : [(36615 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1463603), _1463605), _1463607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463603, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1463603), _1463605)), hAPP(c_SetInterval_Oord__class_OatMost(_1463603), _1463607))))], (36609 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463603, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1463603), _1463605)), hAPP(c_SetInterval_Oord__class_OatMost(_1463603), _1463607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1463603), _1463605), _1463607)))]]], (47519 ^ _775828) ^ [_1723709, _1723711, _1723713] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723709), tc_List_Olist(_1723709))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723709), tc_List_Olist(_1723709)), c_List_Olist_ONil(_1723709)), _1723711)), c_List_Olex(_1723709, _1723713)))], (23494 ^ _775828) ^ [_1186586, _1186588] : [_1186586 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1186586, _1186588) = 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)))], (47397 ^ _775828) ^ [_1721402, _1721404, _1721406, _1721408, _1721410] : [-(hAPP(hAPP(c_List_Olist__update(_1721402, hAPP(hAPP(c_List_Olist__update(_1721402, _1721404), _1721406), _1721408)), _1721406), _1721410) = hAPP(hAPP(c_List_Olist__update(_1721402, _1721404), _1721406), _1721410))], (38369 ^ _775828) ^ [_1504657, _1504659] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504657), _1504659)), -(_1504659 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1504657, 38373 ^ [_1504657, _1504659]), 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)), 38372 ^ [_1504657, _1504659]))))], (13180 ^ _775828) ^ [_993865, _993867, _993869, _993871, _993873] : [c_Com_Ocom_OCond(_993865, _993867, _993869) = c_Com_Ocom_OSemi(_993871, _993873)], (9523 ^ _775828) ^ [_928886, _928888] : [class_Groups_Olinordered__ab__group__add(_928886), 9526 ^ _775828 : [(9533 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928886), _928888), c_Groups_Ozero__class_Ozero(_928886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928886), _928888), hAPP(c_Groups_Ouminus__class_Ouminus(_928886), _928888))))], (9527 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928886), _928888), hAPP(c_Groups_Ouminus__class_Ouminus(_928886), _928888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928886), _928888), c_Groups_Ozero__class_Ozero(_928886))))]]], (39377 ^ _775828) ^ [_1526497, _1526499, _1526501, _1526503, _1526505, _1526507, _1526509] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1526497, _1526499, _1526501, _1526503, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1526497, tc_HOL_Obool)), _1526505), hAPP(hAPP(c_Set_Oinsert(_1526497), _1526507), c_Orderings_Obot__class_Obot(tc_fun(_1526497, tc_HOL_Obool))))), _1526509)), hBOOL(hAPP(hAPP(c_member(_1526497), _1526507), _1526505)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1526497, _1526499, _1526501, _1526503, _1526505), hAPP(hAPP(_1526501, _1526507), _1526509))))], (21168 ^ _775828) ^ [_1142267, _1142269, _1142271, _1142273] : [class_Rings_Odivision__ring(_1142267), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142267), _1142269), _1142271)), _1142273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142267), _1142269), _1142273)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142267), _1142271), _1142273)))], (13406 ^ _775828) ^ [_998288, _998290] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _998288, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _998290)) = 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), _998288), _998290)))], (47922 ^ _775828) ^ [_1733483, _1733485, _1733487, _1733489] : [hAPP(hAPP(c_List_Oappend(_1733483), _1733485), _1733487) = hAPP(hAPP(c_List_Oappend(_1733483), _1733489), _1733487), -(_1733485 = _1733489)], (48331 ^ _775828) ^ [_1744154, _1744156, _1744158, _1744160] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744154), tc_List_Olist(_1744154))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744154), tc_List_Olist(_1744154)), _1744156), _1744158)), c_List_Olistrel1(_1744154, _1744160)))), 48332 ^ _775828 : [(48333 ^ _775828) ^ [_1744287, _1744289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1744154, _1744154)), hAPP(hAPP(c_Product__Type_OPair(_1744154, _1744154), hAPP(hAPP(c_List_Onth(_1744154), _1744156), _1744287)), _1744289)), _1744160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744287), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744154)), _1744156))), _1744158 = hAPP(hAPP(c_List_Olist__update(_1744154, _1744156), _1744287), _1744289)]]], (14373 ^ _775828) ^ [_1016267, _1016269, _1016271] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1016267, _1016269)), _1016271), _1016271))), 14374 ^ _775828 : [(14377 ^ _775828) ^ [_1016367] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1016269), _1016271), _1016367)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1016267, _1016269)), _1016367), _1016271))], (14375 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1016267, _1016271)))]]], (47731 ^ _775828) ^ [_1728920, _1728922, _1728924, _1728926, _1728928] : [hAPP(hAPP(c_List_Oappend(_1728920), _1728922), hAPP(hAPP(c_List_Olist_OCons(_1728920), _1728924), c_List_Olist_ONil(_1728920))) = hAPP(hAPP(c_List_Oappend(_1728920), _1728926), hAPP(hAPP(c_List_Olist_OCons(_1728920), _1728928), c_List_Olist_ONil(_1728920))), 47734 ^ _775828 : [(47737 ^ _775828) ^ [] : [-(_1728924 = _1728928)], (47735 ^ _775828) ^ [] : [-(_1728922 = _1728926)]]], (36629 ^ _775828) ^ [_1464056, _1464058, _1464060, _1464062] : [class_Orderings_Olinorder(_1464056), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464056, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1464056, _1464058, _1464060)), hAPP(c_SetInterval_Oord__class_OatMost(_1464056), _1464062)) = c_SetInterval_Oord__class_OatLeastAtMost(_1464056, _1464058, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1464056), _1464060), _1464062)))], (9957 ^ _775828) ^ [_936690, _936692, _936694] : [class_Lattices_Oboolean__algebra(_936690), 9960 ^ _775828 : [(9967 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936690), _936694), _936692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936690), hAPP(c_Groups_Ouminus__class_Ouminus(_936690), _936692)), hAPP(c_Groups_Ouminus__class_Ouminus(_936690), _936694))))], (9961 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936690), hAPP(c_Groups_Ouminus__class_Ouminus(_936690), _936692)), hAPP(c_Groups_Ouminus__class_Ouminus(_936690), _936694))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936690), _936694), _936692)))]]], (28902 ^ _775828) ^ [_1298159, _1298161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1298159), _1298161)), -(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), _1298159), _1298161)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (37792 ^ _775828) ^ [_1491808, _1491810, _1491812, _1491814, _1491816, _1491818] : [class_Groups_Oordered__ab__group__add(_1491808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491810), _1491812)), 37802 ^ _775828 : [(37805 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1491808), c_Groups_Ozero__class_Ozero(_1491808)), hAPP(_1491814, 37801 ^ [_1491808, _1491810, _1491812, _1491814, _1491816, _1491818])))], (37803 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491810), 37801 ^ [_1491808, _1491810, _1491812, _1491814, _1491816, _1491818]), _1491812)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491810, _1491808), _1491814), _1491812) = _1491816, hBOOL(hAPP(hAPP(c_member(_1491810), _1491818), _1491812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1491808), hAPP(_1491814, _1491818)), _1491816)))], (44659 ^ _775828) ^ [_1653941, _1653943] : [-(hAPP(c_Relation_OField(_1653941), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1653941, _1653941), tc_HOL_Obool), _1653943)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1653941, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1653941, _1653941), tc_HOL_Obool), tc_fun(_1653941, tc_HOL_Obool), c_Relation_OField(_1653941)), _1653943)))], (47817 ^ _775828) ^ [_1730793, _1730795, _1730797, _1730799, _1730801, _1730803] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730793)), _1730795) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730797)), _1730799), -(c_Map_Omap__upds(_1730793, _1730797, _1730801, _1730795, hAPP(hAPP(c_List_Oappend(_1730797), _1730799), _1730803)) = c_Map_Omap__upds(_1730793, _1730797, _1730801, _1730795, _1730799))], (38514 ^ _775828) ^ [_1508057, _1508059, _1508061, _1508063] : [-(c_Fun_Ooverride__on(_1508057, _1508059, _1508061, _1508063, c_Orderings_Obot__class_Obot(tc_fun(_1508057, tc_HOL_Obool))) = _1508061)], (46712 ^ _775828) ^ [_1704675, _1704677, _1704679, _1704681, _1704683] : [class_Groups_Oab__group__add(_1704675), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704675), hAPP(hAPP(c_List_Omap(_1704677, _1704675), hAPP(hAPP(c_COMBS(_1704677, _1704675, _1704675), hAPP(hAPP(c_COMBB(_1704675, tc_fun(_1704675, _1704675), _1704677), c_Groups_Ominus__class_Ominus(_1704675)), _1704679)), _1704681)), _1704683)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1704675), hAPP(c_List_Omonoid__add__class_Olistsum(_1704675), hAPP(hAPP(c_List_Omap(_1704677, _1704675), _1704679), _1704683))), hAPP(c_List_Omonoid__add__class_Olistsum(_1704675), hAPP(hAPP(c_List_Omap(_1704677, _1704675), _1704681), _1704683))))], (6203 ^ _775828) ^ [_874414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _874414)), -(_874414 = hAPP(c_Nat_OSuc, 6206 ^ [_874414]))], (28309 ^ _775828) ^ [_1283726, _1283728, _1283730] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283726, tc_HOL_Obool)), _1283728), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283726, tc_HOL_Obool)), _1283728), _1283730)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283726, tc_HOL_Obool)), _1283728), _1283730))], (13400 ^ _775828) ^ [_998152, _998154, _998156] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998152), c_Divides_Odiv__class_Omod(tc_Int_Oint, _998154, _998156)), _998156) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998152), _998154), _998156))], (21636 ^ _775828) ^ [_1150450, _1150452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150450)), hAPP(c_Nat_OSuc, _1150452))), -(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(_1150450))), 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)), _1150452)))))], (42109 ^ _775828) ^ [_1593132, _1593134, _1593136, _1593138, _1593140, _1593142, _1593144, _1593146] : [c_Fun_Oinj__on(_1593132, _1593134, _1593136, _1593138), c_Fun_Oinj__on(_1593140, _1593142, _1593144, _1593146), -(c_Fun_Oinj__on(tc_prod(_1593132, _1593140), tc_prod(_1593134, _1593142), c_Product__Type_Omap__pair(_1593132, _1593134, _1593140, _1593142, _1593136, _1593144), hAPP(hAPP(c_Product__Type_OSigma(_1593132, _1593140), _1593138), hAPP(c_COMBK(tc_fun(_1593140, tc_HOL_Obool), _1593132), _1593146))))], (19116 ^ _775828) ^ [_1104986] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1104986) = _1104986)], (50996 ^ _775828) ^ [_1802754, _1802756] : [hBOOL(hAPP(c_List_Odistinct(_1802754), _1802756)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1802754, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802754), tc_fun(_1802754, tc_HOL_Obool)), c_List_Oset(_1802754)), c_Enum_Osublists(_1802754, _1802756)))))], (30758 ^ _775828) ^ [_1338387, _1338389, _1338391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338387), _1338389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1338387, tc_HOL_Obool)), _1338391), _1338389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1338387), _1338391)), hAPP(c_Finite__Set_Ocard(_1338387), _1338389))))], (34223 ^ _775828) ^ [_1412681, _1412683, _1412685, _1412687] : [-(hBOOL(hAPP(hAPP(c_member(_1412681), _1412683), _1412685))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412681, tc_HOL_Obool)), _1412685), hAPP(hAPP(c_Set_Oinsert(_1412681), _1412683), _1412687)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412681, tc_HOL_Obool)), _1412685), _1412687))], (11408 ^ _775828) ^ [_963255, _963257, _963259] : [class_Groups_Oordered__comm__monoid__add(_963255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963255), c_Groups_Ozero__class_Ozero(_963255)), _963257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963255), c_Groups_Ozero__class_Ozero(_963255)), _963259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963255), c_Groups_Ozero__class_Ozero(_963255)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963255), _963257), _963259))))], (37052 ^ _775828) ^ [_1473368, _1473370, _1473372, _1473374, _1473376] : [class_Groups_Ocomm__monoid__add(_1473368), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473368), _1473370), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473372), _1473374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473376), _1473374))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473368), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1473368, tc_Nat_Onat), _1473370), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1473374))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1473372, _1473376)))], (7409 ^ _775828) ^ [_894029, _894031, _894033] : [_894033 = hAPP(c_Option_Ooption_OSome(_894029), _894031), -(hBOOL(hAPP(hAPP(c_member(_894029), _894031), c_Option_Oset(_894029, _894033))))], (24719 ^ _775828) ^ [_1210207, _1210209, _1210211] : [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), _1210207), _1210209))), -(hBOOL(hAPP(hAPP(_1210211, _1210207), _1210209))), 24726 ^ _775828 : [(24729 ^ _775828) ^ [] : [-(24725 ^ [_1210207, _1210209, _1210211] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1210211, 24725 ^ [_1210207, _1210209, _1210211]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 24724 ^ [_1210207, _1210209, _1210211], 24725 ^ [_1210207, _1210209, _1210211]))))], (24735 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1210211, 24724 ^ [_1210207, _1210209, _1210211]), 24725 ^ [_1210207, _1210209, _1210211]))], (24727 ^ _775828) ^ [] : [-(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), 24724 ^ [_1210207, _1210209, _1210211]), 24725 ^ [_1210207, _1210209, _1210211]))))]]], (51418 ^ _775828) ^ [_1807315, _1807317] : [-(class_Smallcheck_Osmall(tc_prod(_1807315, _1807317))), class_Smallcheck_Osmall(_1807315), class_Smallcheck_Osmall(_1807317)], (3662 ^ _775828) ^ [_831490, _831492, _831494, _831496] : [-(c_Lazy__Sequence_Ohb__single(_831496, _831492) = c_Lazy__Sequence_Ohb__single(_831494, _831490)), _831496 = _831494, _831492 = _831490], (34261 ^ _775828) ^ [_1413493, _1413495, _1413497] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413493, tc_HOL_Obool)), _1413495), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413493, tc_HOL_Obool)), _1413497), _1413495)) = c_Orderings_Obot__class_Obot(tc_fun(_1413493, tc_HOL_Obool)))], (10082 ^ _775828) ^ [_938987, _938989] : [_938987 = _938989, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938987), _938989)))], (16513 ^ _775828) ^ [_1056688] : [-(c_Divides_Odivmod__nat(_1056688, 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)), _1056688))], (31787 ^ _775828) ^ [_1362283, _1362285, _1362287, _1362289] : [-(hBOOL(hAPP(hAPP(c_member(_1362283), _1362285), hAPP(c_Relation_ODomain(_1362283, _1362283), _1362287)))), 31790 ^ _775828 : [(31797 ^ _775828) ^ [] : [_1362285 = _1362289, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1362283, _1362283)), hAPP(hAPP(c_Product__Type_OPair(_1362283, _1362283), _1362285), _1362289)), c_Transitive__Closure_Ortrancl(_1362283, _1362287))))], (31791 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362283, _1362283)), hAPP(hAPP(c_Product__Type_OPair(_1362283, _1362283), _1362285), _1362289)), c_Transitive__Closure_Ortrancl(_1362283, _1362287))), -(_1362285 = _1362289)]]], (13396 ^ _775828) ^ [_998074] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _998074, _998074) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29705 ^ _775828) ^ [_1315368, _1315370] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1315368, tc_HOL_Obool)), _1315370)), -(hBOOL(hAPP(hAPP(c_member(_1315368), _1315370), c_Orderings_Obot__class_Obot(tc_fun(_1315368, tc_HOL_Obool)))))], (31813 ^ _775828) ^ [_1362800, _1362802, _1362804, _1362806] : [hBOOL(hAPP(hAPP(c_member(_1362800), _1362802), c_Wellfounded_Oacc(_1362800, _1362804))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1362800, _1362800)), hAPP(hAPP(c_Product__Type_OPair(_1362800, _1362800), _1362806), _1362802)), c_Transitive__Closure_Ortrancl(_1362800, _1362804))), -(hBOOL(hAPP(hAPP(c_member(_1362800), _1362806), c_Wellfounded_Oacc(_1362800, _1362804))))], (16973 ^ _775828) ^ [_1065293, _1065295, _1065297] : [class_Rings_Ocomm__semiring__1(_1065293), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065293), _1065295), hAPP(c_Nat_OSuc, _1065297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065293), _1065295), hAPP(hAPP(c_Power_Opower__class_Opower(_1065293), _1065295), _1065297)))], (14213 ^ _775828) ^ [_1013357, _1013359, _1013361, _1013363] : [-(c_Com_Ocom_OWhile(_1013357, _1013359) = c_Com_Ocom_OWhile(_1013361, _1013363)), _1013357 = _1013361, _1013359 = _1013363], (34103 ^ _775828) ^ [_1410112, _1410114, _1410116, _1410118] : [class_Lattices_Osemilattice__inf(_1410112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410112), _1410114), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410112), _1410116), _1410118))), 34110 ^ _775828 : [(34113 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410112), _1410114), _1410118)))], (34111 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410112), _1410114), _1410116)))]]], (49261 ^ _775828) ^ [_1764993, _1764995, _1764997] : [-(_1764993 = c_List_Olist_ONil(_1764995)), -(c_List_Obutlast(_1764995, hAPP(hAPP(c_List_Oappend(_1764995), _1764997), _1764993)) = hAPP(hAPP(c_List_Oappend(_1764995), _1764997), c_List_Obutlast(_1764995, _1764993)))], (22434 ^ _775828) ^ [_1166127, _1166129, _1166131, _1166133] : [class_Fields_Olinordered__field__inverse__zero(_1166127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166127), _1166129), _1166131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166127), c_Groups_Ozero__class_Ozero(_1166127)), _1166133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166127), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166127), _1166129), _1166133)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166127), _1166131), _1166133))))], (15842 ^ _775828) ^ [_1043077, _1043079, _1043081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043077), _1043079)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043079), _1043077)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043081), _1043079)), _1043077))], (32479 ^ _775828) ^ [_1376076, _1376078] : [class_Orderings_Olinorder(_1376076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376076), _1376078)), -(_1376078 = c_Orderings_Obot__class_Obot(tc_fun(_1376076, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1376076), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376076), 32492 ^ [_1376076, _1376078]), 32493 ^ [_1376076, _1376078])), hAPP(hAPP(c_Set_Oinsert(_1376076), 32492 ^ [_1376076, _1376078]), hAPP(hAPP(c_Set_Oinsert(_1376076), 32493 ^ [_1376076, _1376078]), c_Orderings_Obot__class_Obot(tc_fun(_1376076, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1376076), c_Big__Operators_Olinorder__class_OMin(_1376076, _1376078)), _1376078)))], (17797 ^ _775828) ^ [_1080673, _1080675, _1080677] : [class_Power_Opower(_1080673), class_Rings_Omult__zero(_1080673), class_Rings_Ono__zero__divisors(_1080673), class_Rings_Ozero__neq__one(_1080673), 17812 ^ _775828 : [(17821 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1080673), _1080675), _1080677) = c_Groups_Ozero__class_Ozero(_1080673)), _1080675 = c_Groups_Ozero__class_Ozero(_1080673), -(_1080677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17813 ^ _775828) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1080673), _1080675), _1080677) = c_Groups_Ozero__class_Ozero(_1080673), 17816 ^ _775828 : [(17819 ^ _775828) ^ [] : [_1080677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17817 ^ _775828) ^ [] : [-(_1080675 = c_Groups_Ozero__class_Ozero(_1080673))]]]]], (19406 ^ _775828) ^ [_1109388, _1109390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109388), c_Int_OPls))), 19409 ^ _775828 : [(19416 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109390), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109390)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1109388), _1109390)))], (19410 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109390), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109390)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109388))]]], (15488 ^ _775828) ^ [_1036350, _1036352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1036350)), 15491 ^ _775828 : [(15498 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036352), _1036350))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1036352), _1036350) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036352), _1036350)), _1036350)))], (15492 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036352), _1036350)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1036352), _1036350) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24248 ^ _775828) ^ [_1200905, _1200907, _1200909, _1200911] : [class_Orderings_Olinorder(_1200905), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200905), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200905), _1200907), _1200909)), _1200911) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200905), _1200907), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200905), _1200909), _1200911)))], (50776 ^ _775828) ^ [_1797969, _1797971, _1797973] : [hBOOL(hAPP(c_List_Odistinct(_1797969), _1797971)), -(c_List_Oremove1(_1797969, _1797973, c_List_Oremdups(_1797969, _1797971)) = c_List_Oremdups(_1797969, c_List_Oremove1(_1797969, _1797973, _1797971)))], (39622 ^ _775828) ^ [_1532997, _1532999, _1533001, _1533003, _1533005, _1533007] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532997, tc_fun(_1532999, tc_HOL_Obool)), _1533001), hAPP(hAPP(c_COMBB(_1533003, tc_fun(_1532999, tc_HOL_Obool), _1532997), _1533005), _1533007)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533003, tc_fun(_1532999, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1532997, _1533003, _1533007), _1533001)), _1533005))], (51242 ^ _775828) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (47647 ^ _775828) ^ [_1726521, _1726523, _1726525, _1726527, _1726529] : [-(hAPP(hAPP(c_List_Ozip(_1726521, _1726523), _1726525), hAPP(hAPP(c_List_Olist_OCons(_1726523), _1726527), _1726529)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1726521, _1726523)), _1726521, c_List_Olist_ONil(tc_prod(_1726521, _1726523)), hAPP(hAPP(c_COMBC(_1726521, tc_fun(tc_List_Olist(_1726521), tc_List_Olist(tc_prod(_1726521, _1726523))), tc_fun(tc_List_Olist(_1726521), tc_List_Olist(tc_prod(_1726521, _1726523)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1726521, _1726523)), tc_List_Olist(tc_prod(_1726521, _1726523))), tc_fun(tc_fun(tc_List_Olist(_1726521), tc_List_Olist(tc_prod(_1726521, _1726523))), tc_fun(tc_List_Olist(_1726521), tc_List_Olist(tc_prod(_1726521, _1726523)))), _1726521), c_COMBB(tc_List_Olist(tc_prod(_1726521, _1726523)), tc_List_Olist(tc_prod(_1726521, _1726523)), tc_List_Olist(_1726521))), hAPP(hAPP(c_COMBB(tc_prod(_1726521, _1726523), tc_fun(tc_List_Olist(tc_prod(_1726521, _1726523)), tc_List_Olist(tc_prod(_1726521, _1726523))), _1726521), c_List_Olist_OCons(tc_prod(_1726521, _1726523))), hAPP(hAPP(c_COMBC(_1726521, _1726523, tc_prod(_1726521, _1726523)), c_Product__Type_OPair(_1726521, _1726523)), _1726527)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1726521), tc_List_Olist(_1726523), tc_List_Olist(tc_prod(_1726521, _1726523))), c_List_Ozip(_1726521, _1726523)), _1726529))), _1726525))], (3916 ^ _775828) ^ [_835477, _835479, _835481, _835483, _835485, _835487] : [-(c_Map_Oran(_835487, _835483, _835479) = c_Map_Oran(_835485, _835481, _835477)), _835487 = _835485, _835483 = _835481, _835479 = _835477], (7939 ^ _775828) ^ [_902934, _902936] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902934), _902936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902934)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902936)))], (50271 ^ _775828) ^ [_1786023, _1786025] : [_1786025 = c_List_Olist_ONil(_1786023), -(hAPP(c_List_Orev(_1786023), _1786025) = c_List_Olist_ONil(_1786023))], (44677 ^ _775828) ^ [_1654611, _1654613, _1654615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1654611, tc_HOL_Obool), tc_HOL_Obool)), _1654613), _1654615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654611, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654611, tc_HOL_Obool), _1654613)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654611, tc_HOL_Obool), _1654615))))], (48429 ^ _775828) ^ [_1746680, _1746682, _1746684, _1746686] : [-(hAPP(hAPP(c_List_Odrop(_1746680), hAPP(c_Nat_OSuc, _1746682)), hAPP(hAPP(c_List_Olist_OCons(_1746680), _1746684), _1746686)) = hAPP(hAPP(c_List_Odrop(_1746680), _1746682), _1746686))], (24447 ^ _775828) ^ [_1205143, _1205145] : [class_Orderings_Olinorder(_1205143), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205143), _1205145), _1205145) = _1205145)], (15164 ^ _775828) ^ [_1030383, _1030385, _1030387] : [class_Rings_Oring__1(_1030383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030385), _1030387)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030387), _1030385)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030383), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030383), _1030387)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030383), _1030385)))], (44365 ^ _775828) ^ [_1646213, _1646215, _1646217, _1646219, _1646221] : [_1646213 = c_Orderings_Obot__class_Obot(tc_fun(_1646215, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646217, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646215, tc_fun(_1646217, tc_HOL_Obool)), _1646213), _1646219)), _1646221) = _1646221)], (11789 ^ _775828) ^ [_969658, _969660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969658)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969658), _969660)))], (42540 ^ _775828) ^ [_1603022, _1603024, _1603026] : [42542 ^ _775828 : [(42545 ^ _775828) ^ [] : [hBOOL(hAPP(_1603024, 42541 ^ [_1603022, _1603024, _1603026]))], (42543 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603022), 42541 ^ [_1603022, _1603024, _1603026]), _1603026)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1603022, _1603024), _1603026)))], (7935 ^ _775828) ^ [_902842, _902844] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902842)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902844)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902842), _902844)))], (44075 ^ _775828) ^ [_1637740, _1637742, _1637744, _1637746, _1637748, _1637750] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637740, tc_fun(_1637742, tc_HOL_Obool)), _1637744), _1637746), _1637748)), hBOOL(hAPP(hAPP(c_member(_1637740), _1637750), _1637744)), -(hBOOL(hAPP(hAPP(_1637746, _1637750), _1637748)))], (3986 ^ _775828) ^ [_836630, _836632, _836634, _836636, _836638, _836640, _836642, _836644] : [-(c_Wellfounded_Olex__prod(_836644, _836640, _836636, _836632) = c_Wellfounded_Olex__prod(_836642, _836638, _836634, _836630)), _836644 = _836642, _836640 = _836638, _836636 = _836634, _836632 = _836630], (51224 ^ _775828) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (38200 ^ _775828) ^ [] : [-(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))))))], (48046 ^ _775828) ^ [_1735792, _1735794] : [-(hAPP(hAPP(c_List_Oappend(_1735792), c_List_Olist_ONil(_1735792)), _1735794) = _1735794)], (46831 ^ _775828) ^ [_1707459, _1707461, _1707463, _1707465, _1707467] : [class_Orderings_Olinorder(_1707459), hBOOL(hAPP(c_List_Odistinct(_1707461), _1707463)), -(hBOOL(hAPP(c_List_Odistinct(_1707461), c_List_Olinorder__class_Oinsort__insert__key(_1707461, _1707459, _1707465, _1707467, _1707463))))], (3620 ^ _775828) ^ [_830873, _830875] : [_830875 = _830873, -(tc_Lazy__Sequence_Olazy__sequence(_830875) = tc_Lazy__Sequence_Olazy__sequence(_830873))], (46562 ^ _775828) ^ [_1699968, _1699970, _1699972, _1699974, _1699976, _1699978] : [-(_1699968 = _1699970), -(hAPP(c_Map_Omap__of(_1699972, _1699974, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1699972, _1699974)), hAPP(hAPP(c_Product__Type_OPair(_1699972, _1699974), _1699968), _1699976)), _1699978)), _1699970) = hAPP(c_Map_Omap__of(_1699972, _1699974, _1699978), _1699970))], (8785 ^ _775828) ^ [_916570, _916572, _916574] : [class_Orderings_Oorder(_916570), -(_916572 = _916574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916570), _916572), _916574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916570), _916572), _916574)))], (15470 ^ _775828) ^ [_1035986, _1035988, _1035990] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035986), _1035988)), _1035990) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035986), _1035990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035988), _1035990)))], (41404 ^ _775828) ^ [_1576645, _1576647, _1576649, _1576651, _1576653, _1576655] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576645, _1576647)), hAPP(hAPP(c_Product__Type_OPair(_1576645, _1576647), _1576649), _1576651)), hAPP(hAPP(c_Product__Type_OSigma(_1576645, _1576647), _1576653), _1576655)))), hBOOL(hAPP(hAPP(c_member(_1576645), _1576649), _1576653)), hBOOL(hAPP(hAPP(c_member(_1576647), _1576651), hAPP(_1576655, _1576649)))], (11745 ^ _775828) ^ [_968874, _968876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968874), _968876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968874)), _968876)))], (40849 ^ _775828) ^ [_1561661, _1561663, _1561665] : [40850 ^ _775828 : [(40851 ^ _775828) ^ [_1561737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561661, _1561661)), _1561663), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561661, _1561661), tc_HOL_Obool), _1561737), _1561665)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561661, _1561661)), _1561663), c_Transitive__Closure_Ortrancl(_1561661, _1561665))))], (28187 ^ _775828) ^ [_1281054, _1281056, _1281058, _1281060, _1281062, _1281064] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1281054, _1281056, _1281058), _1281060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1281056, _1281058), tc_HOL_Obool)), _1281062), _1281064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1281054, _1281058), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1281054, _1281056, _1281058), _1281060), _1281062)), hAPP(hAPP(c_Relation_Orel__comp(_1281054, _1281056, _1281058), _1281060), _1281064)))], (50601 ^ _775828) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (44397 ^ _775828) ^ [_1647116, _1647118, _1647120, _1647122, _1647124] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1647116, tc_fun(_1647118, tc_HOL_Obool)), _1647120), hAPP(hAPP(c_COMBB(tc_fun(_1647118, tc_HOL_Obool), tc_fun(_1647118, tc_HOL_Obool), _1647116), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647118, tc_HOL_Obool)), _1647122)), _1647124)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647118, tc_HOL_Obool)), _1647122), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647116, tc_fun(_1647118, tc_HOL_Obool)), _1647120), _1647124)))], (14722 ^ _775828) ^ [_1022116, _1022118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022116), _1022118)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022116), _1022118) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51444 ^ _775828) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (28233 ^ _775828) ^ [_1282053, _1282055, _1282057] : [class_Lattices_Olattice(_1282053), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282053), _1282055), _1282057) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282053), _1282057), _1282055))], (29080 ^ _775828) ^ [_1302202, _1302204] : [-(hAPP(c_Relation_ORange(_1302202, _1302202), c_Transitive__Closure_Otrancl(_1302202, _1302204)) = hAPP(c_Relation_ORange(_1302202, _1302202), _1302204))], (1816 ^ _775828) ^ [_801967, _801969, _801971, _801973, _801975, _801977, _801979, _801981] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_801981, _801977, _801973, _801969) = c_Hoare__Mirabelle_Otriple_Otriple__case(_801979, _801975, _801971, _801967)), _801981 = _801979, _801977 = _801975, _801973 = _801971, _801969 = _801967], (25509 ^ _775828) ^ [_1226136, _1226138, _1226140, _1226142, _1226144, _1226146] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1226136, _1226136)), hAPP(hAPP(c_Product__Type_OPair(_1226136, _1226136), _1226138), _1226140)), hAPP(hAPP(c_Relation_Oinv__image(_1226142, _1226136), _1226144), _1226146))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1226142, _1226142)), hAPP(hAPP(c_Product__Type_OPair(_1226142, _1226142), hAPP(_1226146, _1226138)), hAPP(_1226146, _1226140))), _1226144)))], (36075 ^ _775828) ^ [_1453358, _1453360] : [c_Wellfounded_Owf(_1453358, _1453360), -(c_Wellfounded_Owf(tc_List_Olist(_1453358), c_List_Olex(_1453358, _1453360)))], (13618 ^ _775828) ^ [_1002307, _1002309, _1002311, _1002313] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_1002307, _1002309)), _1002311), _1002313))), 13619 ^ _775828 : [(13620 ^ _775828) ^ [_1002375] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1002307), _1002311), _1002375)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1002309), _1002375), _1002313))]]], (43434 ^ _775828) ^ [_1624922, _1624924, _1624926, _1624928, _1624930, _1624932] : [class_Groups_Oab__semigroup__mult(_1624922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624924), _1624926)), 43444 ^ _775828 : [(43447 ^ _775828) ^ [] : [hAPP(_1624928, 43443 ^ [_1624922, _1624924, _1624926, _1624928, _1624930, _1624932]) = hAPP(_1624930, 43443 ^ [_1624922, _1624924, _1624926, _1624928, _1624930, _1624932])], (43445 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624924), 43443 ^ [_1624922, _1624924, _1624926, _1624928, _1624930, _1624932]), _1624926)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1624922, _1624924, c_Groups_Otimes__class_Otimes(_1624922)), _1624928), _1624932), _1624926) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1624922, _1624924, c_Groups_Otimes__class_Otimes(_1624922)), _1624930), _1624932), _1624926))], (31691 ^ _775828) ^ [_1359837, _1359839] : [-(c_Transitive__Closure_Ortrancl(_1359837, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1359837, _1359837), tc_HOL_Obool)), _1359839), c_Relation_OId(_1359837))) = c_Transitive__Closure_Ortrancl(_1359837, _1359839))], (9167 ^ _775828) ^ [_922416, _922418] : [class_Rings_Olinordered__idom(_922416), 9170 ^ _775828 : [(9177 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922416), c_Groups_Ozero__class_Ozero(_922416)), hAPP(c_Int_Oring__1__class_Oof__int(_922416), _922418))))], (9171 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922416), c_Groups_Ozero__class_Ozero(_922416)), hAPP(c_Int_Oring__1__class_Oof__int(_922416), _922418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922418)))]]], (18911 ^ _775828) ^ [_1101141, _1101143, _1101145] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1101141, _1101143), _1101145))), _1101141 = 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), _1101145)), _1101143)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1101145)), 18918 ^ _775828 : [(18921 ^ _775828) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1101145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18919 ^ _775828) ^ [] : [-(_1101143 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 18922 ^ _775828 : [(18925 ^ _775828) ^ [] : [18926 ^ _775828 : [(18929 ^ _775828) ^ [] : [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), _1101145))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1101145)), _1101143))], (18927 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101143)))]], 18934 ^ _775828 : [(18937 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101143), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1101145))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1101145)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18935 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101143))]]], (18923 ^ _775828) ^ [] : [_1101143 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (30347 ^ _775828) ^ [_1330255, _1330257, _1330259] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330255), _1330257)), hBOOL(hAPP(hAPP(c_member(_1330255), _1330259), _1330257)), -(hAPP(c_Finite__Set_Ocard(_1330255), _1330257) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330255, tc_HOL_Obool)), _1330257), hAPP(hAPP(c_Set_Oinsert(_1330255), _1330259), c_Orderings_Obot__class_Obot(tc_fun(_1330255, tc_HOL_Obool)))))))], (17441 ^ _775828) ^ [_1074584, _1074586] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1074584), _1074586) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1074586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1074584 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51232 ^ _775828) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (6131 ^ _775828) ^ [_873263] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _873263), _873263)))], (34381 ^ _775828) ^ [_1416504, _1416506, _1416508, _1416510] : [class_Orderings_Oorder(_1416504), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416504, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1416504, _1416506, _1416508)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1416504, _1416508, _1416510)) = c_Orderings_Obot__class_Obot(tc_fun(_1416504, tc_HOL_Obool)))], (33643 ^ _775828) ^ [_1400316, _1400318] : [class_Lattices_Obounded__lattice__bot(_1400316), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1400316), _1400318), c_Orderings_Obot__class_Obot(_1400316)) = c_Orderings_Obot__class_Obot(_1400316))], (15710 ^ _775828) ^ [_1040647, _1040649] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040647), _1040649)), hAPP(c_Nat_OSuc, _1040647))))], (17635 ^ _775828) ^ [_1077761, _1077763, _1077765] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077761)))), 17638 ^ _775828 : [(17645 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077763)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077761)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077763)), _1077765)) = 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), _1077761), _1077763))), _1077765))], (17639 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077763))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077761)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077763)), _1077765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077761)), _1077765))]]], (48697 ^ _775828) ^ [_1752550, _1752552, _1752554, _1752556, _1752558] : [-(hAPP(c_List_Orotate(_1752550, _1752552), hAPP(hAPP(c_List_Omap(_1752554, _1752550), _1752556), _1752558)) = hAPP(hAPP(c_List_Omap(_1752554, _1752550), _1752556), hAPP(c_List_Orotate(_1752554, _1752552), _1752558)))], (18503 ^ _775828) ^ [_1094080] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1094080) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094080))], (15324 ^ _775828) ^ [_1033368, _1033370, _1033372] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1033368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033370), _1033372)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1033368), _1033370)), _1033372))], (8591 ^ _775828) ^ [_913614, _913616] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913614) = _913616), _913614 = hAPP(c_Int_Onat, _913616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913616))], (28966 ^ _775828) ^ [_1299784, _1299786, _1299788, _1299790, _1299792, _1299794] : [hBOOL(hAPP(hAPP(_1299784, _1299786), _1299788)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299790, tc_fun(_1299792, tc_HOL_Obool))), _1299784), _1299794), _1299786), _1299788)))], (15648 ^ _775828) ^ [_1039497] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039497), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1039497)], (51170 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (17513 ^ _775828) ^ [_1075721, _1075723] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075721)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075721)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075723)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075721)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075723))))], (45933 ^ _775828) ^ [_1682823, _1682825] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1682823, _1682825) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1682823), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1682825)))], (22702 ^ _775828) ^ [_1170925, _1170927, _1170929, _1170931] : [class_Fields_Ofield__inverse__zero(_1170925), -(_1170927 = c_Groups_Ozero__class_Ozero(_1170925)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170925), _1170929), _1170927)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170925), _1170931), _1170927)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170925), _1170929), _1170931))], (23174 ^ _775828) ^ [_1179455, _1179457, _1179459, _1179461] : [class_Fields_Ofield(_1179455), -(_1179457 = c_Groups_Ozero__class_Ozero(_1179455)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179455), _1179459), _1179457)), _1179461) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179455), _1179459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179455), _1179457), _1179461))), _1179457))], (33266 ^ _775828) ^ [_1391928, _1391930, _1391932, _1391934, _1391936] : [hAPP(_1391928, _1391930) = hAPP(c_Option_Ooption_OSome(_1391932), _1391934), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1391936, tc_Option_Ooption(_1391932)), _1391928), _1391930), hAPP(c_Option_Ooption_OSome(_1391932), _1391934)) = _1391928)], (25773 ^ _775828) ^ [_1231362, _1231364] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231362), _1231364)), 25778 ^ _775828 : [(25781 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231364), _1231362))], (25779 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231362), _1231364)))]], -(_1231362 = _1231364)], (35421 ^ _775828) ^ [_1441150, _1441152, _1441154] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1441150, tc_HOL_Obool)), _1441154), hAPP(c_Set_OPow(_1441150), _1441152))), -(hBOOL(hAPP(c_Predicate_OPowp(_1441150, hAPP(hAPP(c_COMBC(_1441150, tc_fun(_1441150, tc_HOL_Obool), tc_HOL_Obool), c_member(_1441150)), _1441152)), _1441154)))], (43734 ^ _775828) ^ [_1631213, _1631215, _1631217] : [class_Lattices_Oab__semigroup__idem__mult(_1631213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631213), _1631215)), -(hAPP(c_Finite__Set_Ofold1(_1631213, c_Groups_Otimes__class_Otimes(_1631213)), hAPP(hAPP(c_Set_Oinsert(_1631213), _1631217), _1631215)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631213, _1631213, c_Groups_Otimes__class_Otimes(_1631213)), _1631217), _1631215))], (1000 ^ _775828) ^ [_790946, _790948] : [-(class_Rings_Oring__1__no__zero__divisors(_790946)), _790948 = _790946, class_Rings_Oring__1__no__zero__divisors(_790948)], (8327 ^ _775828) ^ [_909580, _909582, _909584, _909586] : [class_Orderings_Oorder(_909580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909580), _909582), _909584)), _909582 = _909586, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909580), _909586), _909584)))], (35611 ^ _775828) ^ [_1444510, _1444512] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1444510, _1444512)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1444512)), _1444510))], (19828 ^ _775828) ^ [] : [-(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)))))], (30213 ^ _775828) ^ [_1326493, _1326495, _1326497, _1326499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326493), _1326495)), 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)), _1326493), _1326497)), 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)), _1326495), _1326499)), 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)), _1326495), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326497), _1326499))), c_FunDef_Omin__strict)))], (32523 ^ _775828) ^ [_1377026, _1377028] : [class_Lattices_Olattice(_1377026), -(c_Big__Operators_Olattice__class_OSup__fin(_1377026, hAPP(hAPP(c_Set_Oinsert(_1377026), _1377028), c_Orderings_Obot__class_Obot(tc_fun(_1377026, tc_HOL_Obool)))) = _1377028)], (20376 ^ _775828) ^ [_1125945] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1125945)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1125945)))], (33815 ^ _775828) ^ [_1404144, _1404146, _1404148, _1404150] : [class_Lattices_Osemilattice__inf(_1404144), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404144), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404144), _1404146), _1404148)), _1404150) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404144), _1404146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404144), _1404148), _1404150)))], (16681 ^ _775828) ^ [_1059999, _1060001] : [class_Rings_Ocomm__semiring__1(_1059999), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1059999), _1060001), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1060001)], (29147 ^ _775828) ^ [_1304017, _1304019] : [c_Wellfounded_Oacyclic(_1304017, hAPP(c_Set_OCollect(tc_prod(_1304017, _1304017)), hAPP(c_Product__Type_Oprod_Oprod__case(_1304017, _1304017, tc_HOL_Obool), c_Predicate_Oconversep(_1304017, _1304017, _1304019)))), -(c_Wellfounded_Oacyclic(_1304017, hAPP(c_Set_OCollect(tc_prod(_1304017, _1304017)), hAPP(c_Product__Type_Oprod_Oprod__case(_1304017, _1304017, tc_HOL_Obool), _1304019))))], (11246 ^ _775828) ^ [_960377, _960379, _960381, _960383] : [class_Groups_Oordered__comm__monoid__add(_960377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960377), c_Groups_Ozero__class_Ozero(_960377)), _960379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960377), _960381), _960383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960377), _960381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960377), _960379), _960383))))], (40527 ^ _775828) ^ [] : [-(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))))], (33669 ^ _775828) ^ [_1400822, _1400824, _1400826, _1400828] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400822, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1400822, tc_fun(_1400822, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400822)), _1400824)), hAPP(hAPP(c_COMBC(_1400822, tc_fun(_1400822, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400822)), _1400826)), _1400828)), -(hBOOL(hAPP(hAPP(c_member(_1400822), _1400828), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400822, tc_HOL_Obool)), _1400824), _1400826))))], (40684 ^ _775828) ^ [_1557862, _1557864, _1557866, _1557868, _1557870, _1557872] : [c_Typedef_Otype__definition(_1557862, _1557864, _1557866, _1557868, _1557870), -(hAPP(_1557868, hAPP(_1557866, _1557872)) = _1557872)], (17439 ^ _775828) ^ [_1074534] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1074534)))], (45967 ^ _775828) ^ [_1683414, _1683416, _1683418, _1683420] : [-(_1683414 = _1683416), 45970 ^ _775828 : [(45977 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1683418), _1683414), hAPP(c_List_Oset(_1683418), _1683420))), -(hBOOL(hAPP(hAPP(c_member(_1683418), _1683414), hAPP(c_List_Oset(_1683418), c_List_Oremove1(_1683418, _1683416, _1683420)))))], (45971 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1683418), _1683414), hAPP(c_List_Oset(_1683418), c_List_Oremove1(_1683418, _1683416, _1683420)))), -(hBOOL(hAPP(hAPP(c_member(_1683418), _1683414), hAPP(c_List_Oset(_1683418), _1683420))))]]], (14403 ^ _775828) ^ [_1016824, _1016826, _1016828] : [c_Com_Ocom_OWhile(_1016824, _1016826) = hAPP(c_Com_Ocom_OBODY, _1016828)], (51230 ^ _775828) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (19778 ^ _775828) ^ [_1115558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115558), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1115558)), c_Int_OPls)))], (24501 ^ _775828) ^ [_1206446, _1206448] : [c_Nat__Transfer_Ois__nat(_1206446), c_Nat__Transfer_Ois__nat(_1206448), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1206446), _1206448)))], (12598 ^ _775828) ^ [_983657, _983659] : [class_Rings_Olinordered__idom(_983657), 12601 ^ _775828 : [(12608 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983657), _983659), c_Groups_Ozero__class_Ozero(_983657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983657), c_Groups_Osgn__class_Osgn(_983657, _983659)), c_Groups_Ozero__class_Ozero(_983657))))], (12602 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983657), c_Groups_Osgn__class_Osgn(_983657, _983659)), c_Groups_Ozero__class_Ozero(_983657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983657), _983659), c_Groups_Ozero__class_Ozero(_983657))))]]], (20790 ^ _775828) ^ [_1133522, _1133524, _1133526] : [class_Rings_Olinordered__idom(_1133522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133522), _1133524), c_Groups_Ozero__class_Ozero(_1133522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133522), hAPP(hAPP(c_Power_Opower__class_Opower(_1133522), _1133524), 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)))), _1133526)))), c_Groups_Ozero__class_Ozero(_1133522))))], (37554 ^ _775828) ^ [_1485696, _1485698, _1485700, _1485702, _1485704] : [class_Groups_Oab__group__add(_1485696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485698), _1485700)), 37561 ^ _775828 : [(37568 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485698), _1485702), _1485700))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485698, _1485696), _1485704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485698, tc_HOL_Obool)), _1485700), hAPP(hAPP(c_Set_Oinsert(_1485698), _1485702), c_Orderings_Obot__class_Obot(tc_fun(_1485698, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485698, _1485696), _1485704), _1485700))], (37562 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1485698), _1485702), _1485700)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485698, _1485696), _1485704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485698, tc_HOL_Obool)), _1485700), hAPP(hAPP(c_Set_Oinsert(_1485698), _1485702), c_Orderings_Obot__class_Obot(tc_fun(_1485698, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1485696), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485698, _1485696), _1485704), _1485700)), hAPP(_1485704, _1485702)))]]], (46452 ^ _775828) ^ [_1697616, _1697618, _1697620] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1697616, tc_HOL_Obool)), hAPP(c_List_Oset(_1697616), _1697618)), hAPP(c_List_Oset(_1697616), hAPP(hAPP(c_List_Olist_OCons(_1697616), _1697620), _1697618)))))], (19042 ^ _775828) ^ [_1103774, _1103776, _1103778] : [19044 ^ _775828 : [(19047 ^ _775828) ^ [] : [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(_1103776, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19043 ^ [_1103774, _1103776, _1103778]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1103776, 19043 ^ [_1103774, _1103776, _1103778])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19045 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19043 ^ [_1103774, _1103776, _1103778]), _1103774)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1103776, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1103778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103778), hAPP(_1103776, _1103774))), 19057 ^ _775828 : [(19060 ^ _775828) ^ [] : [-(hAPP(_1103776, 19056 ^ [_1103774, _1103776, _1103778]) = _1103778)], (19058 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19056 ^ [_1103774, _1103776, _1103778]), _1103774)))]]], (46730 ^ _775828) ^ [_1705212, _1705214] : [class_Groups_Ocomm__monoid__add(_1705212), hBOOL(hAPP(c_List_Odistinct(_1705212), _1705214)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705212), _1705214) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1705212, _1705212), c_COMBI(_1705212)), hAPP(c_List_Oset(_1705212), _1705214)))], (51360 ^ _775828) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (46580 ^ _775828) ^ [_1700438, _1700440, _1700442, _1700444] : [-(c_Map_Omap__of(_1700438, _1700440, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1700438, _1700440)), _1700442), _1700444)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1700438, tc_Option_Ooption(_1700440)), c_Map_Omap__of(_1700438, _1700440, _1700444)), hAPP(c_Product__Type_Ofst(_1700438, _1700440), _1700442)), hAPP(c_Option_Ooption_OSome(_1700440), hAPP(c_Product__Type_Osnd(_1700438, _1700440), _1700442))))], (42087 ^ _775828) ^ [_1592517, _1592519, _1592521, _1592523, _1592525, _1592527] : [-(c_Product__Type_Omap__pair(_1592517, _1592519, _1592521, _1592523, _1592525, _1592527) = hAPP(c_Product__Type_Oprod_Oprod__case(_1592517, _1592521, tc_prod(_1592519, _1592523)), hAPP(hAPP(c_COMBC(_1592517, tc_fun(_1592521, _1592523), tc_fun(_1592521, tc_prod(_1592519, _1592523))), hAPP(hAPP(c_COMBB(tc_fun(_1592523, tc_prod(_1592519, _1592523)), tc_fun(tc_fun(_1592521, _1592523), tc_fun(_1592521, tc_prod(_1592519, _1592523))), _1592517), c_COMBB(_1592523, tc_prod(_1592519, _1592523), _1592521)), hAPP(hAPP(c_COMBB(_1592519, tc_fun(_1592523, tc_prod(_1592519, _1592523)), _1592517), c_Product__Type_OPair(_1592519, _1592523)), _1592525))), _1592527)))], (29333 ^ _775828) ^ [_1307777, _1307779, _1307781] : [-(hBOOL(hAPP(hAPP(c_member(_1307777), _1307779), hAPP(hAPP(c_Set_Oinsert(_1307777), _1307779), _1307781))))], (7875 ^ _775828) ^ [_901661, 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hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _862164))), _862166)))], (13260 ^ _775828) ^ [_995264, _995266] : [class_Divides_Osemiring__div(_995264), -(c_Divides_Odiv__class_Omod(_995264, _995266, c_Groups_Ozero__class_Ozero(_995264)) = _995266)], (50527 ^ _775828) ^ [_1792382, _1792384, _1792386] : [class_Orderings_Olinorder(_1792382), c_List_Olinorder__class_Osorted(_1792382, hAPP(c_List_Orev(_1792382), _1792384)), 50534 ^ _775828 : [(50541 ^ _775828) ^ [] : [-(_1792384 = c_List_Olist_ONil(_1792382)), -(c_List_Ofoldr(_1792382, _1792382, c_Orderings_Oord__class_Omax(_1792382), _1792384, _1792386) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1792382), hAPP(hAPP(c_List_Onth(_1792382), _1792384), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1792386))], (50535 ^ _775828) ^ [] : [_1792384 = c_List_Olist_ONil(_1792382), -(c_List_Ofoldr(_1792382, _1792382, c_Orderings_Oord__class_Omax(_1792382), _1792384, _1792386) = _1792386)]]], (14415 ^ _775828) ^ [_1017150, _1017152, _1017154, _1017156, _1017158] : [c_Com_Ocom_OCall(_1017150, _1017152, _1017154) = c_Com_Ocom_OWhile(_1017156, _1017158)], (14303 ^ _775828) ^ [_1014955, _1014957, _1014959, _1014961, _1014963] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014955, _1014957), _1014959, _1014961, _1014963)), 14304 ^ _775828 : [(14311 ^ _775828) ^ [] : [hBOOL(hAPP(_1014955, _1014959)), 14314 ^ _775828 : [(14315 ^ _775828) ^ [_1015165] : [c_Natural_Oevaln(_1014957, _1014959, _1014961, _1015165), c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014955, _1014957), _1015165, _1014961, _1014963)]]], (14305 ^ _775828) ^ [] : [_1014963 = _1014959, -(hBOOL(hAPP(_1014955, _1014959)))]]], (42922 ^ _775828) ^ [_1612087, _1612089, _1612091, _1612093, _1612095] : [c_Hoare__Mirabelle_Ohoare__valids(_1612087, _1612089, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1612087)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1612087), c_Hoare__Mirabelle_Opeek__and(_1612087, _1612091, _1612093)), _1612095), _1612091)), 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_775828 : [(48519 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1748368), hAPP(hAPP(c_List_Odrop(_1748368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748374)), _1748370)), _1748372) = _1748376)], (48517 ^ _775828) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1748368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748374)), _1748370) = _1748374)]]], (48505 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748370)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748374))), 48508 ^ _775828 : [(48511 ^ _775828) ^ [] : [-(_1748372 = hAPP(hAPP(c_List_Oappend(_1748368), hAPP(hAPP(c_List_Odrop(_1748368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748370)), _1748374)), _1748376))], (48509 ^ _775828) ^ [] : [-(_1748370 = hAPP(hAPP(c_List_Otake(_1748368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748368)), _1748370)), _1748374))]]]]], (23354 ^ _775828) ^ 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^ _775828 : [(22474 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), _1166398), c_Groups_Ozero__class_Ozero(_1166396))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), c_Groups_Ozero__class_Ozero(_1166396)), _1166400))], (22468 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), c_Groups_Ozero__class_Ozero(_1166396)), _1166398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), _1166400), c_Groups_Ozero__class_Ozero(_1166396)))]]], (22452 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166396), _1166398), _1166400)), c_Groups_Ozero__class_Ozero(_1166396))), 22457 ^ _775828 : [(22460 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), _1166400), c_Groups_Ozero__class_Ozero(_1166396))))], (22458 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), c_Groups_Ozero__class_Ozero(_1166396)), _1166398)))]], 22461 ^ _775828 : [(22464 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), c_Groups_Ozero__class_Ozero(_1166396)), _1166400)))], (22462 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166396), _1166398), c_Groups_Ozero__class_Ozero(_1166396))))]]]]], (48731 ^ _775828) ^ [_1753291, _1753293, _1753295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753291)), _1753293)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1753291, _1753295), _1753293) = _1753293)], (23462 ^ _775828) ^ [_1185684, _1185686, _1185688] : [-(hAPP(c_Product__Type_Osnd(_1185684, _1185686), _1185688) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185684, _1185686, _1185686), hAPP(c_COMBK(tc_fun(_1185686, _1185686), _1185684), c_COMBI(_1185686))), _1185688))], (20544 ^ _775828) ^ [_1128907, _1128909] : [class_Rings_Olinordered__idom(_1128907), 20547 ^ _775828 : [(20554 ^ _775828) ^ [] : [-(_1128909 = c_Groups_Ozero__class_Ozero(_1128907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128907), c_Groups_Ozero__class_Ozero(_1128907)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128907), _1128909), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20548 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128907), c_Groups_Ozero__class_Ozero(_1128907)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128907), _1128909), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1128909 = c_Groups_Ozero__class_Ozero(_1128907)]]], (36249 ^ _775828) ^ [_1456521, _1456523] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1456521), _1456523)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1456521)), hAPP(c_Nat_OSuc, _1456523)))], (35625 ^ _775828) ^ [_1444821, _1444823] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1444821), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1444823) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1444821, _1444823))], (48657 ^ _775828) ^ [_1751766, _1751768, _1751770] : [-(hAPP(c_List_Otl(_1751766), hAPP(hAPP(c_List_Odrop(_1751766), _1751768), _1751770)) = hAPP(hAPP(c_List_Odrop(_1751766), _1751768), hAPP(c_List_Otl(_1751766), _1751770)))], (28643 ^ _775828) ^ [_1290334, _1290336, _1290338, _1290340] : [hBOOL(hAPP(hAPP(c_member(_1290334), _1290336), _1290338)), -(hBOOL(hAPP(hAPP(c_member(_1290334), _1290336), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290334, tc_HOL_Obool)), _1290338), _1290340))))], (34621 ^ _775828) ^ [_1421642, _1421644, _1421646, _1421648, _1421650] : [class_Groups_Ocomm__monoid__mult(_1421642), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421644), _1421646)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421644), _1421648)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421644, tc_HOL_Obool)), _1421646), _1421648) = c_Orderings_Obot__class_Obot(tc_fun(_1421644, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421644, _1421642), _1421650), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421644, tc_HOL_Obool)), _1421646), _1421648)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421642), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421644, _1421642), _1421650), _1421646)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421644, _1421642), _1421650), _1421648)))], (23638 ^ _775828) ^ [_1189670, _1189672, _1189674, _1189676] : [class_Orderings_Olinorder(_1189670), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189670), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1189670), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189670), _1189672), _1189674)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189670), _1189672), _1189676))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189670), _1189672), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1189670), _1189674), _1189676)))))], (34255 ^ _775828) ^ [_1413360, _1413362, _1413364] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413360, tc_HOL_Obool)), _1413362), _1413364) = c_Orderings_Obot__class_Obot(tc_fun(_1413360, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413360, tc_HOL_Obool)), _1413362), _1413364) = _1413362)], (19804 ^ _775828) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (38492 ^ _775828) ^ [_1507696, _1507698, _1507700] : [hAPP(hAPP(c_Relation_Orel__comp(_1507696, _1507696, _1507696), hAPP(c_Relation_Oconverse(_1507696, _1507696), _1507698)), _1507698) = _1507698, hAPP(c_Relation_ODomain(_1507696, _1507696), _1507698) = _1507700, -(c_Equiv__Relations_Oequiv(_1507696, _1507700, _1507698))], (40802 ^ _775828) ^ [_1560516, _1560518, _1560520, _1560522, _1560524, _1560526] : [-(hAPP(c_Set_Ovimage(_1560516, _1560518, _1560520), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1560522, tc_fun(_1560518, tc_HOL_Obool)), _1560524), _1560526)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1560522, tc_fun(_1560516, tc_HOL_Obool)), _1560524), hAPP(hAPP(c_COMBB(tc_fun(_1560518, tc_HOL_Obool), tc_fun(_1560516, tc_HOL_Obool), _1560522), c_Set_Ovimage(_1560516, _1560518, _1560520)), _1560526)))], (27725 ^ _775828) ^ [_1269286, _1269288, _1269290] : [-(hAPP(c_Relation_ODomain(_1269286, _1269288), hAPP(c_Set_OCollect(tc_prod(_1269286, _1269288)), hAPP(c_Product__Type_Oprod_Oprod__case(_1269286, _1269288, tc_HOL_Obool), _1269290))) = hAPP(c_Set_OCollect(_1269286), hAPP(hAPP(c_COMBB(tc_fun(_1269288, tc_HOL_Obool), tc_HOL_Obool, _1269286), c_HOL_OEx(_1269288)), _1269290)))], (33611 ^ _775828) ^ [_1399674, _1399676, _1399678, _1399680, _1399682] : [-(c_Map_Orestrict__map(_1399674, _1399676, c_Map_Orestrict__map(_1399674, _1399676, _1399678, _1399680), _1399682) = c_Map_Orestrict__map(_1399674, _1399676, _1399678, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399674, tc_HOL_Obool)), _1399680), _1399682)))], (40355 ^ _775828) ^ [_1549555, _1549557, _1549559] : [-(c_Map_Odom(_1549555, _1549557, hAPP(hAPP(c_COMBB(_1549557, tc_Option_Ooption(_1549557), _1549555), c_Option_Ooption_OSome(_1549557)), _1549559)) = c_Orderings_Otop__class_Otop(tc_fun(_1549555, tc_HOL_Obool)))], (40325 ^ _775828) ^ [_1548989, _1548991, _1548993, _1548995, _1548997] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548989), hAPP(c_Set_Oimage(_1548991, _1548989, _1548993), c_Orderings_Otop__class_Otop(tc_fun(_1548991, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548995), hAPP(c_Set_Oimage(_1548991, _1548995, hAPP(hAPP(c_COMBB(_1548989, _1548995, _1548991), _1548997), _1548993)), c_Orderings_Otop__class_Otop(tc_fun(_1548991, tc_HOL_Obool))))))], (29535 ^ _775828) ^ [_1311703, _1311705, _1311707] : [class_Orderings_Obot(_1311703), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1311705, _1311703)), _1311707) = c_Orderings_Obot__class_Obot(_1311703))], (51326 ^ _775828) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (26335 ^ _775828) ^ [_1240718, _1240720, _1240722, _1240724] : [class_Divides_Osemiring__div(_1240718), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240718), _1240720), _1240722)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240718), _1240724), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240718), _1240722), _1240720)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240718), _1240724), _1240722)), _1240720))], (11773 ^ _775828) ^ [] : [-(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))))], (34 ^ _775828) ^ [_776281, _776283, _776285, _776287, _776289, _776291, _776293, _776295] : [-(c_Natural_Oevaln(_776293, _776289, _776285, _776281)), c_Natural_Oevaln(_776295, _776291, _776287, _776283), _776295 = _776293, _776291 = _776289, _776287 = _776285, _776283 = _776281], (33917 ^ _775828) ^ [_1406492, _1406494, _1406496, _1406498] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406492, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406492, tc_HOL_Obool)), _1406494), _1406496)), _1406498) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406492, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406492, tc_HOL_Obool)), _1406494), _1406498)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406492, tc_HOL_Obool)), _1406496), _1406498)))], (40770 ^ _775828) ^ [_1559721, _1559723, _1559725, _1559727] : [-(hAPP(_1559721, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1559723, _1559723), _1559725), _1559721), _1559727)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1559723, _1559723), _1559725), _1559721), hAPP(_1559721, _1559727)))], (35325 ^ _775828) ^ [_1438364, _1438366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1438364), _1438366)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1438364, tc_HOL_Obool)), hAPP(c_Set_OPow(_1438364), _1438366)) = 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(_1438364), _1438366)))], (15892 ^ _775828) ^ [_1044102, _1044104] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044102), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044102), _1044104))], (42168 ^ _775828) ^ [_1594611, _1594613] : [-(c_Relation_Orefl__on(_1594611, c_Orderings_Otop__class_Otop(tc_fun(_1594611, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1594611, _1594613)))], (39766 ^ _775828) ^ [_1537184, _1537186, _1537188, _1537190, _1537192, _1537194, _1537196, _1537198, _1537200, _1537202] : [c_Equiv__Relations_Oequiv(_1537184, _1537186, _1537188), c_Equiv__Relations_Oequiv(_1537190, _1537192, _1537194), c_Equiv__Relations_Ocongruent2(_1537184, _1537190, tc_fun(_1537196, tc_HOL_Obool), _1537188, _1537194, _1537198), hBOOL(hAPP(hAPP(c_member(_1537184), _1537200), _1537186)), hBOOL(hAPP(hAPP(c_member(_1537190), _1537202), _1537192)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537184, tc_fun(_1537196, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1537184, _1537184, _1537188), hAPP(hAPP(c_Set_Oinsert(_1537184), _1537200), c_Orderings_Obot__class_Obot(tc_fun(_1537184, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1537190, tc_fun(_1537196, tc_HOL_Obool)), tc_fun(_1537196, tc_HOL_Obool), _1537184), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537190, tc_fun(_1537196, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1537190, _1537190, _1537194), hAPP(hAPP(c_Set_Oinsert(_1537190), _1537202), c_Orderings_Obot__class_Obot(tc_fun(_1537190, tc_HOL_Obool)))))), _1537198)) = hAPP(hAPP(_1537198, _1537200), _1537202))], (19816 ^ _775828) ^ [_1116068, _1116070] : [class_Groups_Omonoid__mult(_1116068), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1116068), _1116070), 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(_1116068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116068), _1116070), _1116070)), _1116070))], (36879 ^ _775828) ^ [_1468949, _1468951, _1468953, _1468955] : [class_Groups_Oordered__ab__group__add__abs(_1468949), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468949), hAPP(c_Groups_Oabs__class_Oabs(_1468949), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468951, _1468949), _1468953), _1468955))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468951, _1468949), hAPP(hAPP(c_COMBB(_1468949, _1468949, _1468951), c_Groups_Oabs__class_Oabs(_1468949)), _1468953)), _1468955))))], (51068 ^ _775828) ^ [_1803852, _1803854] : [-(class_Finite__Set_Ofinite(tc_fun(_1803852, _1803854))), class_Finite__Set_Ofinite(_1803852), class_Finite__Set_Ofinite(_1803854)], (45686 ^ _775828) ^ [_1677084, _1677086, _1677088, _1677090, _1677092] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1677084), tc_Option_Ooption(_1677086), tc_Option_Ooption(_1677088), hAPP(c_Option_Omap(_1677084, _1677086), _1677090)), hAPP(c_Option_Omap(_1677088, _1677084), _1677092)) = hAPP(c_Option_Omap(_1677088, _1677086), hAPP(c_Fun_Ocomp(_1677084, _1677086, _1677088, _1677090), _1677092)))], (25929 ^ _775828) ^ [_1233818, _1233820, _1233822] : [_1233818 = _1233820, 25940 ^ _775828 : [(25943 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233822), _1233818))], (25941 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233818), _1233822)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233820), _1233822)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233822), _1233820)))], (46812 ^ _775828) ^ [_1707135] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1707135) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46815 ^ _775828 : [(46816 ^ _775828) ^ [_1707210] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1707210), hAPP(c_List_Oset(tc_Nat_Onat), _1707135))), -(_1707210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15898 ^ _775828) ^ [_1044228] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1044228)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1044228)], (7201 ^ _775828) ^ [_890438, _890440, _890442, _890444] : [class_Rings_Olinordered__ring__strict(_890438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890438), c_Groups_Ozero__class_Ozero(_890438)), _890440)), 7208 ^ _775828 : [(7215 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890438), _890442), _890444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890438), _890440), _890442)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890438), _890440), _890444))))], (7209 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890438), _890440), _890442)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_890438), _890440), _890444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890438), _890442), _890444)))]]], (2422 ^ _775828) ^ [_811386, _811388, _811390, _811392] : [-(c_Random_Oinc__shift(_811392, _811388) = c_Random_Oinc__shift(_811390, _811386)), _811392 = _811390, _811388 = _811386], (27280 ^ _775828) ^ [_1259033, _1259035, _1259037, _1259039, _1259041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1259035, _1259033)), hAPP(hAPP(c_Product__Type_OPair(_1259035, _1259033), _1259039), _1259037)), _1259041)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1259033, _1259035)), hAPP(hAPP(c_Product__Type_OPair(_1259033, _1259035), _1259037), _1259039)), hAPP(c_Relation_Oconverse(_1259035, _1259033), _1259041))))], (12971 ^ _775828) ^ [_990106, _990108, _990110] : [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), _990106), _990108)), _990110))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990110), _990106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990108)))], (6901 ^ _775828) ^ [_885072, _885074, _885076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _885072), _885074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885076)), -(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), _885076)), _885072)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _885076)), _885074))))], (7385 ^ _775828) ^ [_893607, _893609, _893611] : [_893609 = _893611, -(hAPP(c_Option_Ooption_OSome(_893607), _893609) = hAPP(c_Option_Ooption_OSome(_893607), _893611))], (40157 ^ _775828) ^ [_1545664, _1545666] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545664, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1545664, tc_HOL_Obool))), _1545666) = _1545666)], (24525 ^ _775828) ^ [_1206759, _1206761] : [c_Nat__Transfer_Ois__nat(_1206759), c_Nat__Transfer_Ois__nat(_1206761), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206759, _1206761)))], (3748 ^ _775828) ^ [_832783, _832785] : [_832785 = _832783, -(c_HOL_OAll(_832785) = c_HOL_OAll(_832783))], (48064 ^ _775828) ^ [_1736297, _1736299, _1736301] : [-(hBOOL(hAPP(c_List_Odistinct(_1736297), hAPP(hAPP(c_List_Oappend(_1736297), _1736299), _1736301)))), hBOOL(hAPP(c_List_Odistinct(_1736297), _1736299)), hBOOL(hAPP(c_List_Odistinct(_1736297), _1736301)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1736297, tc_HOL_Obool)), hAPP(c_List_Oset(_1736297), _1736299)), hAPP(c_List_Oset(_1736297), _1736301)) = c_Orderings_Obot__class_Obot(tc_fun(_1736297, tc_HOL_Obool))], (44858 ^ _775828) ^ [_1658341, _1658343, _1658345] : [class_Complete__Lattice_Ocomplete__lattice(_1658341), hBOOL(hAPP(hAPP(c_member(_1658341), _1658343), _1658345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658341), c_Complete__Lattice_OInf__class_OInf(_1658341, _1658345)), _1658343)))], (28275 ^ _775828) ^ [_1282932, _1282934, _1282936, _1282938] : [class_Lattices_Osemilattice__sup(_1282932), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282932), _1282934), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282932), _1282936), _1282938)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282932), _1282936), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282932), _1282934), _1282938)))], (30397 ^ _775828) ^ [_1331335, _1331337, _1331339] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331335), hAPP(hAPP(c_Set_Oinsert(_1331335), _1331337), _1331339))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331335), _1331339)))], (19438 ^ _775828) ^ [_1109934, _1109936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109934), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109934)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109936)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1109934), _1109936)))], (40389 ^ _775828) ^ [_1550162, _1550164] : [-(c_Fun_Oinj__on(tc_fun(_1550162, _1550164), tc_fun(tc_prod(_1550162, _1550164), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1550162, _1550164), tc_HOL_Obool), tc_fun(tc_prod(_1550162, _1550164), tc_HOL_Obool), tc_fun(_1550162, _1550164)), c_Set_OCollect(tc_prod(_1550162, _1550164))), hAPP(hAPP(c_COMBB(tc_fun(_1550162, tc_fun(_1550164, tc_HOL_Obool)), tc_fun(tc_prod(_1550162, _1550164), tc_HOL_Obool), tc_fun(_1550162, _1550164)), c_Product__Type_Oprod_Oprod__case(_1550162, _1550164, tc_HOL_Obool)), hAPP(c_COMBB(_1550164, tc_fun(_1550164, tc_HOL_Obool), _1550162), hAPP(c_COMBC(_1550164, _1550164, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1550162, _1550164), tc_HOL_Obool))))], (48707 ^ _775828) ^ [_1752801, _1752803, _1752805] : [-(_1752801 = c_List_Olist_ONil(_1752803)), -(hAPP(c_List_Otl(_1752803), hAPP(hAPP(c_List_Oappend(_1752803), _1752801), _1752805)) = hAPP(hAPP(c_List_Oappend(_1752803), hAPP(c_List_Otl(_1752803), _1752801)), _1752805))], (40339 ^ _775828) ^ [_1549314, _1549316] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1549314, _1549316)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1549314, _1549316), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1549316), c_Orderings_Otop__class_Otop(tc_fun(_1549316, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1549314), c_Orderings_Otop__class_Otop(tc_fun(_1549314, tc_HOL_Obool)))))], (8559 ^ _775828) ^ [_913169] : [hAPP(c_Int_Onat, _913169) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _913169), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25879 ^ _775828) ^ [_1233051, _1233053, _1233055] : [_1233051 = _1233053, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233053), _1233055)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233051), _1233055)))], (6262 ^ _775828) ^ [_875566, _875568, _875570, _875572, _875574] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_875566, _875568), _875570, _875572, _875574), -(_875574 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _875570), _875566), hAPP(_875568, _875570)))], (47841 ^ _775828) ^ [_1731437, _1731439, _1731441, _1731443, _1731445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731439)), _1731441))), -(hAPP(hAPP(c_List_Olist__update(_1731439, hAPP(hAPP(c_List_Oappend(_1731439), _1731441), _1731443)), _1731437), _1731445) = hAPP(hAPP(c_List_Oappend(_1731439), hAPP(hAPP(c_List_Olist__update(_1731439, _1731441), _1731437), _1731445)), _1731443))], (47823 ^ _775828) ^ [_1730946, _1730948, _1730950, _1730952, _1730954] : [-(hAPP(hAPP(c_List_Olist__update(_1730946, hAPP(hAPP(c_List_Oappend(_1730946), _1730948), hAPP(hAPP(c_List_Olist_OCons(_1730946), _1730950), _1730952))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730946)), _1730948)), _1730954) = hAPP(hAPP(c_List_Oappend(_1730946), _1730948), hAPP(hAPP(c_List_Olist_OCons(_1730946), _1730954), _1730952)))], (28860 ^ _775828) ^ [_1295590, _1295592, _1295594, _1295596, _1295598, _1295600] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1295590, _1295592)), hAPP(hAPP(c_Product__Type_OPair(_1295590, _1295592), _1295598), _1295600)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool)), _1295594), _1295596))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295590, tc_fun(_1295592, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1295590, tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_fun(_1295592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295592, tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_fun(_1295592, tc_HOL_Obool)), _1295590), c_COMBC(_1295592, tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295592, tc_prod(_1295590, _1295592)), tc_fun(_1295592, tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), _1295590), hAPP(c_COMBB(tc_prod(_1295590, _1295592), tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool), _1295592), c_member(tc_prod(_1295590, _1295592)))), c_Product__Type_OPair(_1295590, _1295592)))), _1295594)), hAPP(hAPP(c_COMBC(_1295590, tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_fun(_1295592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295592, tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_fun(_1295592, tc_HOL_Obool)), _1295590), c_COMBC(_1295592, tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295592, tc_prod(_1295590, _1295592)), tc_fun(_1295592, tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool)), _1295590), hAPP(c_COMBB(tc_prod(_1295590, _1295592), tc_fun(tc_fun(tc_prod(_1295590, _1295592), tc_HOL_Obool), tc_HOL_Obool), _1295592), c_member(tc_prod(_1295590, _1295592)))), c_Product__Type_OPair(_1295590, _1295592)))), _1295596)), _1295598), _1295600)))], (30039 ^ _775828) ^ [_1323331, _1323333] : [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)))), _1323331, _1323333), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323331), _1323333)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323333), _1323331)))], (44437 ^ _775828) ^ [_1648514, _1648516, _1648518, _1648520, _1648522] : [_1648514 = c_Orderings_Obot__class_Obot(tc_fun(_1648516, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648516, tc_fun(_1648518, tc_HOL_Obool)), _1648514), hAPP(hAPP(c_COMBB(tc_fun(_1648518, tc_HOL_Obool), tc_fun(_1648518, tc_HOL_Obool), _1648516), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648518, tc_HOL_Obool)), _1648520)), _1648522)) = c_Orderings_Otop__class_Otop(tc_fun(_1648518, tc_HOL_Obool)))], (45647 ^ _775828) ^ [_1675949, _1675951, _1675953, _1675955, _1675957] : [-(c_Map_Omap__of(_1675949, _1675951, hAPP(hAPP(c_List_Omap(tc_prod(_1675949, _1675953), tc_prod(_1675949, _1675951)), hAPP(c_Product__Type_Oprod_Oprod__case(_1675949, _1675953, tc_prod(_1675949, _1675951)), hAPP(hAPP(c_COMBC(_1675949, tc_fun(_1675953, _1675951), tc_fun(_1675953, tc_prod(_1675949, _1675951))), hAPP(hAPP(c_COMBB(tc_fun(_1675951, tc_prod(_1675949, _1675951)), tc_fun(tc_fun(_1675953, _1675951), tc_fun(_1675953, tc_prod(_1675949, _1675951))), _1675949), c_COMBB(_1675951, tc_prod(_1675949, _1675951), _1675953)), c_Product__Type_OPair(_1675949, _1675951))), _1675955))), _1675957)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1675953), tc_Option_Ooption(_1675951), _1675949, hAPP(c_Option_Omap(_1675953, _1675951), _1675955)), c_Map_Omap__of(_1675949, _1675953, _1675957)))], (29999 ^ _775828) ^ [_1322642] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1322642, _1322642) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1322642), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (13520 ^ _775828) ^ [_1000394, _1000396, _1000398, _1000400, _1000402] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1000394, _1000396, _1000398)), _1000400), _1000402)), 13525 ^ _775828 : [(13528 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000396), _1000400), _1000402)))], (13526 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1000394, _1000400)))]], 13529 ^ _775828 : [(13532 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000398), _1000400), _1000402)))], (13530 ^ _775828) ^ [] : [hBOOL(hAPP(_1000394, _1000400))]]], (33923 ^ _775828) ^ [_1406797, _1406799, _1406801, _1406803, _1406805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406797, tc_HOL_Obool)), _1406799), _1406801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406797, tc_HOL_Obool)), _1406803), _1406805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406797, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406797, tc_HOL_Obool)), _1406799), _1406803)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406797, tc_HOL_Obool)), _1406801), _1406805))))], (29223 ^ _775828) ^ [_1305672, _1305674, _1305676] : [-(hAPP(c_Set_Oimage(_1305672, _1305674, _1305676), c_Orderings_Obot__class_Obot(tc_fun(_1305672, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1305674, tc_HOL_Obool)))], (43259 ^ _775828) ^ [_1620027, _1620029, _1620031] : [-(hAPP(c_New__DSequence_Oneg__single(_1620027, _1620029), _1620031) = c_Lazy__Sequence_Ohb__single(_1620027, _1620029))], (37022 ^ _775828) ^ [_1472531, _1472533, _1472535, _1472537, _1472539] : [class_Groups_Ocomm__monoid__add(_1472531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472533), _1472535)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472533, _1472531), hAPP(hAPP(c_COMBS(_1472533, _1472531, _1472531), hAPP(hAPP(c_COMBB(_1472531, tc_fun(_1472531, _1472531), _1472533), c_Groups_Oplus__class_Oplus(_1472531)), _1472537)), _1472539)), _1472535) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1472531), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472533, _1472531), _1472537), _1472535)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472533, _1472531), _1472539), _1472535)))], (49511 ^ _775828) ^ [_1770744, _1770746] : [-(c_List_Ofoldr(tc_List_Olist(_1770744), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1770744)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1770744))), c_List_Otranspose(_1770744, _1770746), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1770744))), hAPP(c_List_Ofilter(tc_List_Olist(_1770744), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1770744)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1770744), tc_List_Olist(_1770744), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1770744)))), _1770746)))], (13558 ^ _775828) ^ [_1001084, _1001086, _1001088] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1001084, _1001086, _1001088)))), hBOOL(hAPP(c_Com_OWT, _1001086)), hBOOL(hAPP(c_Com_OWT, _1001088))], (5577 ^ _775828) ^ [_864190, _864192, _864194, _864196] : [c_Natural_Oevaln(_864190, _864192, _864194, _864196), -(c_Natural_Oevaln(_864190, _864192, hAPP(c_Nat_OSuc, _864194), _864196))], (20978 ^ _775828) ^ [_1136721] : [_1136721 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1136721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (860 ^ _775828) ^ [_788968, _788970, _788972, _788974, _788976, _788978] : [-(c_Equiv__Relations_Oequiv(_788976, _788972, _788968)), c_Equiv__Relations_Oequiv(_788978, _788974, _788970), _788978 = _788976, _788974 = _788972, _788970 = _788968], (43377 ^ _775828) ^ [_1623562, _1623564] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623562), _1623564)), 43383 ^ _775828 : [(43386 ^ _775828) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43384 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623562), 43382 ^ [_1623562, _1623564]), _1623564)))]], -(hAPP(c_Finite__Set_Ocard(_1623562), _1623564) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28483 ^ _775828) ^ [_1287463, _1287465, _1287467] : [class_Lattices_Osemilattice__sup(_1287463), 28486 ^ _775828 : [(28493 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287463), _1287465), _1287467) = _1287467, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287463), _1287465), _1287467)))], (28487 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287463), _1287465), _1287467)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287463), _1287465), _1287467) = _1287467)]]], (50619 ^ _775828) ^ [_1795060, _1795062, _1795064] : [c_List_OtakeWhile(_1795060, _1795062, _1795064) = _1795064, 50622 ^ _775828 : [(50623 ^ _775828) ^ [_1795147] : [hBOOL(hAPP(hAPP(c_member(_1795060), _1795147), hAPP(c_List_Oset(_1795060), _1795064))), -(hBOOL(hAPP(_1795062, _1795147)))]]], (1190 ^ _775828) ^ [_793321, _793323] : [-(class_Rings_Oring(_793321)), _793323 = _793321, class_Rings_Oring(_793323)], (45598 ^ _775828) ^ [_1674898, _1674900, _1674902] : [c_Fun_Oinj__on(tc_List_Olist(_1674898), tc_List_Olist(_1674900), hAPP(c_List_Omap(_1674898, _1674900), _1674902), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674898), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1674898, _1674900, _1674902, c_Orderings_Otop__class_Otop(tc_fun(_1674898, tc_HOL_Obool))))], (10964 ^ _775828) ^ [_955254, _955256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955256)), _955254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955254), _955256))], (1230 ^ _775828) ^ [_793821, _793823] : [-(class_Complete__Lattice_Ocomplete__lattice(_793821)), _793823 = _793821, class_Complete__Lattice_Ocomplete__lattice(_793823)], (34873 ^ _775828) ^ [_1426568, _1426570, _1426572] : [class_Orderings_Olinorder(_1426568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426568), _1426570)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426568), _1426572)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426568, tc_HOL_Obool)), _1426570), _1426572) = c_Orderings_Obot__class_Obot(tc_fun(_1426568, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1426568), c_Big__Operators_Olattice_OSup__fin(_1426568, c_Orderings_Oord__class_Omax(_1426568), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426568, tc_HOL_Obool)), _1426570), _1426572))), c_Big__Operators_Olattice_OSup__fin(_1426568, c_Orderings_Oord__class_Omax(_1426568), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426568, tc_HOL_Obool)), _1426570), _1426572))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1426568), c_Big__Operators_Olattice_OSup__fin(_1426568, c_Orderings_Oord__class_Omax(_1426568), _1426570)), c_Big__Operators_Olattice_OSup__fin(_1426568, c_Orderings_Oord__class_Omax(_1426568), _1426572)))], (13104 ^ _775828) ^ [_992475, _992477, _992479, _992481, _992483] : [hBOOL(hAPP(_992475, _992477)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_992479), _992477), _992481)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_992475, _992479, _992483)), _992477), _992481)))], (14439 ^ _775828) ^ [_1017686, _1017688] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017686, _1017688)) = _1017688), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1017686), _1017688) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017686, _1017688)))], (29237 ^ _775828) ^ [_1305965, _1305967, _1305969, _1305971] : [c_Hoare__Mirabelle_Ohoare__derivs(_1305965, _1305967, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1305965)), _1305969), _1305971)), 29240 ^ _775828 : [(29243 ^ _775828) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1305965, _1305967, _1305971))], (29241 ^ _775828) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1305965, _1305967, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1305965)), _1305969), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1305965), tc_HOL_Obool)))))]]], (49459 ^ _775828) ^ [_1768952, _1768954, _1768956] : [-(c_List_Opartition(_1768952, _1768954, _1768956) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768952), tc_List_Olist(_1768952)), hAPP(c_List_Ofilter(_1768952, _1768954), _1768956)), hAPP(c_List_Ofilter(_1768952, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1768952, c_fNot), _1768954)), _1768956)))], (39375 ^ _775828) ^ [_1526397, _1526399, _1526401, _1526403, _1526405] : [-(hAPP(c_Fun_Othe__inv__into(_1526397, _1526399, _1526401, _1526403), _1526405) = c_HOL_OThe(_1526397, hAPP(hAPP(c_COMBS(_1526397, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526397), c_fconj), hAPP(hAPP(c_COMBC(_1526397, tc_fun(_1526397, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526397)), _1526401))), hAPP(hAPP(c_COMBC(_1526397, _1526399, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1526399, tc_fun(_1526399, tc_HOL_Obool), _1526397), c_fequal), _1526403)), _1526405))))], (31615 ^ _775828) ^ [_1357926, _1357928] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1357926, _1357926, _1357926), _1357928), c_Transitive__Closure_Ortrancl(_1357926, _1357928)) = hAPP(hAPP(c_Relation_Orel__comp(_1357926, _1357926, _1357926), c_Transitive__Closure_Ortrancl(_1357926, _1357928)), _1357928))], (20186 ^ _775828) ^ [_1122612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1122612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1122612))))], (4372 ^ _775828) ^ [_842605, _842607] : [_842607 = _842605, -(c_Lattices_Osemilattice__inf__class_Oinf(_842607) = c_Lattices_Osemilattice__inf__class_Oinf(_842605))], (51216 ^ _775828) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (37400 ^ _775828) ^ [_1481872, _1481874, _1481876, _1481878, _1481880] : [class_Groups_Ocomm__monoid__add(_1481872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481874), _1481876)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481874, _1481872), _1481878), hAPP(hAPP(c_Set_Oinsert(_1481874), _1481880), _1481876)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1481872), hAPP(_1481878, _1481880)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481874, _1481872), _1481878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1481874, tc_HOL_Obool)), _1481876), hAPP(hAPP(c_Set_Oinsert(_1481874), _1481880), c_Orderings_Obot__class_Obot(tc_fun(_1481874, tc_HOL_Obool)))))))], (34457 ^ _775828) ^ [_1417983, _1417985, _1417987, _1417989, _1417991] : [class_Groups_Ocomm__monoid__mult(_1417983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417985), _1417987)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417985), _1417989)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417983), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417985, _1417983), _1417991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417985, tc_HOL_Obool)), _1417987), _1417989))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417985, _1417983), _1417991), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417985, tc_HOL_Obool)), _1417987), _1417989))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417983), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417985, _1417983), _1417991), _1417987)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417985, _1417983), _1417991), _1417989)))], (1040 ^ _775828) ^ [_791446, _791448] : [-(class_Groups_Oordered__ab__group__add(_791446)), _791448 = _791446, class_Groups_Oordered__ab__group__add(_791448)], (29661 ^ _775828) ^ [_1314255] : [-(hAPP(c_Relation_OField(_1314255), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1314255, _1314255), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1314255, tc_HOL_Obool)))], (19062 ^ _775828) ^ [_1104230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104230), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104230)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (40786 ^ _775828) ^ [_1560058, _1560060, _1560062, _1560064] : [-(hAPP(c_Set_Ovimage(_1560058, _1560060, _1560062), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1560060, tc_HOL_Obool)), _1560064)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1560058, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1560058, _1560060, _1560062), _1560064)))], (1070 ^ _775828) ^ [_791821, _791823] : [-(class_Rings_Olinordered__idom(_791821)), _791823 = _791821, class_Rings_Olinordered__idom(_791823)], (13765 ^ _775828) ^ [_1005113, _1005115] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005113), _1005115) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005113, _1005115) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17259 ^ _775828) ^ [_1071094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1071094) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071094))], (10928 ^ _775828) ^ [_954702, _954704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954702)), hAPP(c_Nat_OSuc, _954704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954702), _954704)))], (15174 ^ _775828) ^ [_1030582, _1030584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030582), _1030584)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030584)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030582)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030584), _1030582)))], (51222 ^ _775828) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (21390 ^ _775828) ^ [_1146285, _1146287] : [class_Rings_Osemiring__1(_1146285), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1146285), _1146287) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1146285, hAPP(hAPP(c_COMBC(_1146285, _1146285, _1146285), c_Groups_Oplus__class_Oplus(_1146285)), c_Groups_Oone__class_Oone(_1146285)), _1146287, c_Groups_Ozero__class_Ozero(_1146285)))], (25425 ^ _775828) ^ [_1224260] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1224260)) = _1224260)], (28872 ^ _775828) ^ [_1296398, _1296400, _1296402] : [-(hAPP(c_Relation_OField(_1296398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1296398, _1296398), tc_HOL_Obool)), _1296400), _1296402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296398, tc_HOL_Obool)), hAPP(c_Relation_OField(_1296398), _1296400)), hAPP(c_Relation_OField(_1296398), _1296402)))], (2666 ^ _775828) ^ [_815364, _815366] : [_815366 = _815364, -(c_New__DSequence_Opos__not__seq(_815366) = c_New__DSequence_Opos__not__seq(_815364))], (31611 ^ _775828) ^ [_1357816, _1357818] : [-(c_Transitive__Closure_Ortrancl(_1357816, hAPP(c_Relation_Oconverse(_1357816, _1357816), _1357818)) = hAPP(c_Relation_Oconverse(_1357816, _1357816), c_Transitive__Closure_Ortrancl(_1357816, _1357818)))], (13580 ^ _775828) ^ [_1001464, _1001466, _1001468, _1001470] : [c_Com_Ocom_OCond(_1001464, _1001466, _1001468) = hAPP(c_Com_Ocom_OBODY, _1001470)], (19252 ^ _775828) ^ [_1106912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106912), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25583 ^ _775828) ^ [_1228165, _1228167, _1228169] : [class_Rings_Olinordered__idom(_1228165), hAPP(c_Groups_Oabs__class_Oabs(_1228165), _1228167) = hAPP(c_Groups_Oabs__class_Oabs(_1228165), _1228169), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228165), _1228167), _1228169)))], (26703 ^ _775828) ^ [_1247815, _1247817, _1247819] : [class_Rings_Ocomm__semiring__1(_1247815), 26708 ^ _775828 : [(26711 ^ _775828) ^ [] : [_1247819 = c_Groups_Oone__class_Oone(_1247815)], (26709 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247817))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1247815), _1247819), hAPP(hAPP(c_Power_Opower__class_Opower(_1247815), _1247819), _1247817))))], (10324 ^ _775828) ^ [_943526, _943528] : [class_Rings_Ocomm__semiring__1(_943526), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943526), _943528), _943528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943526), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943526), c_Groups_Oone__class_Oone(_943526)), c_Groups_Oone__class_Oone(_943526))), _943528))], (41396 ^ _775828) ^ [_1576448, _1576450, _1576452, _1576454, _1576456, _1576458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576448, _1576450)), hAPP(hAPP(c_Product__Type_OPair(_1576448, _1576450), _1576452), _1576454)), hAPP(hAPP(c_Product__Type_OSigma(_1576448, _1576450), _1576456), _1576458))), 41399 ^ _775828 : [(41402 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576450), _1576454), hAPP(_1576458, _1576452))))], (41400 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576448), _1576452), _1576456)))]]], (8751 ^ _775828) ^ [_916035, _916037, _916039] : [class_Orderings_Opreorder(_916035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916035), _916037), _916039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916035), _916037), _916039)))], (49523 ^ _775828) ^ [_1771076, _1771078, _1771080, _1771082, _1771084] : [-(c_List_Omap__filter(_1771076, _1771078, _1771080, hAPP(hAPP(c_List_Olist_OCons(_1771076), _1771082), _1771084)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1771078), _1771078, c_List_Omap__filter(_1771076, _1771078, _1771080, _1771084), hAPP(hAPP(c_COMBC(_1771078, tc_List_Olist(_1771078), tc_List_Olist(_1771078)), c_List_Olist_OCons(_1771078)), c_List_Omap__filter(_1771076, _1771078, _1771080, _1771084))), hAPP(_1771080, _1771082)))], (50451 ^ _775828) ^ [_1789915, _1789917, _1789919] : [-(hAPP(c_List_Orotate(_1789915, _1789917), hAPP(c_List_Orev(_1789915), _1789919)) = hAPP(c_List_Orev(_1789915), hAPP(c_List_Orotate(_1789915, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789915)), _1789919)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1789917, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789915)), _1789919)))), _1789919)))], (16328 ^ _775828) ^ [_1053410, _1053412] : [_1053410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053410), _1053412) = _1053412)], (19432 ^ _775828) ^ [_1109829, _1109831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109829), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109829)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109831)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22218 ^ _775828) ^ [_1161965, _1161967, _1161969, _1161971] : [class_Fields_Olinordered__field__inverse__zero(_1161965), 22221 ^ _775828 : [(22222 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161967), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161965), _1161969), _1161971))), 22225 ^ _775828 : [(22232 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), c_Groups_Ozero__class_Ozero(_1161965)), _1161971))), 22235 ^ _775828 : [(22242 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), _1161971), c_Groups_Ozero__class_Ozero(_1161965)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161967), c_Groups_Ozero__class_Ozero(_1161965))))], (22236 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), _1161971), c_Groups_Ozero__class_Ozero(_1161965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161965), _1161967), _1161971))))]]], (22226 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), c_Groups_Ozero__class_Ozero(_1161965)), _1161971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161965), _1161967), _1161971)), _1161969)))]]], (22248 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161967), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161965), _1161969), _1161971)))), 22251 ^ _775828 : [(22254 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161965), _1161967), _1161971)), _1161969))], (22252 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), c_Groups_Ozero__class_Ozero(_1161965)), _1161971)))]], 22255 ^ _775828 : [(22258 ^ _775828) ^ [] : [22259 ^ _775828 : [(22262 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161965), _1161967), _1161971)))], (22260 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), _1161971), c_Groups_Ozero__class_Ozero(_1161965))))]], 22263 ^ _775828 : [(22266 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161965), _1161967), c_Groups_Ozero__class_Ozero(_1161965)))], (22264 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), _1161971), c_Groups_Ozero__class_Ozero(_1161965)))]]], (22256 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161965), c_Groups_Ozero__class_Ozero(_1161965)), _1161971))]]]]], (6162 ^ _775828) ^ [_873759, _873761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873759), hAPP(c_Nat_OSuc, _873761))), -(_873759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6170 ^ _775828 : [(6173 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 6169 ^ [_873759, _873761]), _873761)))], (6171 ^ _775828) ^ [] : [-(_873759 = hAPP(c_Nat_OSuc, 6169 ^ [_873759, _873761]))]]], (44449 ^ _775828) ^ [_1648809, _1648811, _1648813, _1648815, _1648817] : [_1648809 = c_Orderings_Obot__class_Obot(tc_fun(_1648811, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648813, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648811, tc_fun(_1648813, tc_HOL_Obool)), _1648809), _1648815)), _1648817) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648813, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1648813, tc_HOL_Obool))), _1648817))], (34403 ^ _775828) ^ [_1417112, _1417114, _1417116] : [class_Lattices_Olattice(_1417112), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417112), _1417114)), -(_1417114 = c_Orderings_Obot__class_Obot(tc_fun(_1417112, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1417112, hAPP(hAPP(c_Set_Oinsert(_1417112), _1417116), _1417114)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417112), _1417116), c_Big__Operators_Olattice__class_OInf__fin(_1417112, _1417114)))], (34317 ^ _775828) ^ [_1415048, _1415050, _1415052] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415048, tc_HOL_Obool)), _1415050), _1415052) = hAPP(c_Set_OCollect(_1415048), hAPP(hAPP(c_COMBS(_1415048, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1415048), c_fconj), hAPP(hAPP(c_COMBC(_1415048, tc_fun(_1415048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415048)), _1415050))), hAPP(hAPP(c_COMBC(_1415048, tc_fun(_1415048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415048)), _1415052))))], (47365 ^ _775828) ^ [_1720791, _1720793, _1720795] : [-(hAPP(hAPP(c_List_Ozip(_1720791, _1720793), _1720795), c_List_Olist_ONil(_1720793)) = c_List_Olist_ONil(tc_prod(_1720791, _1720793)))], (11140 ^ _775828) ^ [_958307, _958309, _958311] : [11141 ^ _775828 : [(11144 ^ _775828) ^ [] : [_958309 = _958311], (11142 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958307, tc_HOL_Obool)), _958309), _958311))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958307, tc_HOL_Obool)), _958309), _958311)))], (20408 ^ _775828) ^ [_1126580] : [class_Int_Onumber__ring(_1126580), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126580), c_Groups_Oone__class_Oone(_1126580)), c_Groups_Oone__class_Oone(_1126580)) = hAPP(c_Int_Onumber__class_Onumber__of(_1126580), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (41550 ^ _775828) ^ [_1579697, _1579699] : [class_Orderings_Olinorder(_1579697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579697), _1579699)), -(c_Big__Operators_Olattice_OSup__fin(_1579697, c_Orderings_Oord__class_Omax(_1579697), _1579699) = hAPP(c_Finite__Set_Ofold1(_1579697, c_Orderings_Oord__class_Omax(_1579697)), _1579699))], (42089 ^ _775828) ^ [_1592640, _1592642, _1592644, _1592646, _1592648, _1592650, _1592652, _1592654, _1592656, _1592658] : [hAPP(c_Set_Oimage(_1592640, _1592642, _1592644), _1592646) = _1592648, hAPP(c_Set_Oimage(_1592650, _1592652, _1592654), _1592656) = _1592658, -(hAPP(c_Set_Oimage(tc_prod(_1592640, _1592650), tc_prod(_1592642, _1592652), c_Product__Type_Omap__pair(_1592640, _1592642, _1592650, _1592652, _1592644, _1592654)), hAPP(hAPP(c_Product__Type_OSigma(_1592640, _1592650), _1592646), hAPP(c_COMBK(tc_fun(_1592650, tc_HOL_Obool), _1592640), _1592656))) = hAPP(hAPP(c_Product__Type_OSigma(_1592642, _1592652), _1592648), hAPP(c_COMBK(tc_fun(_1592652, tc_HOL_Obool), _1592642), _1592658)))], (30858 ^ _775828) ^ [_1340273, _1340275, _1340277] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340273), _1340275)), -(hAPP(c_Finite__Set_Ocard(_1340273), hAPP(hAPP(c_Set_Oinsert(_1340273), _1340277), _1340275)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1340273), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340273, tc_HOL_Obool)), _1340275), hAPP(hAPP(c_Set_Oinsert(_1340273), _1340277), c_Orderings_Obot__class_Obot(tc_fun(_1340273, tc_HOL_Obool)))))))], (27425 ^ _775828) ^ [_1262836, _1262838, _1262840, _1262842] : [27426 ^ _775828 : [(27427 ^ _775828) ^ [_1262890] : [hBOOL(hAPP(hAPP(_1262840, _1262890), _1262842))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1262836, _1262838, _1262840), _1262842)))], (47307 ^ _775828) ^ [_1719446, _1719448, _1719450, _1719452] : [c_List_Olist_ONil(_1719446) = hAPP(hAPP(c_List_Omap(_1719448, _1719446), _1719450), _1719452), -(_1719452 = c_List_Olist_ONil(_1719448))], (50423 ^ _775828) ^ [_1789373, _1789375] : [-(hAPP(c_List_Oset(_1789373), hAPP(c_List_Orev(_1789373), _1789375)) = hAPP(c_List_Oset(_1789373), _1789375))], (33103 ^ _775828) ^ [_1388530, _1388532, _1388534, _1388536, _1388538] : [class_Rings_Ocomm__semiring__1(_1388530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388532), _1388534)), hBOOL(hAPP(hAPP(c_member(_1388532), _1388536), _1388534)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1388530), hAPP(_1388538, _1388536)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388532, _1388530), _1388538), _1388534))))], (51260 ^ _775828) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (24296 ^ _775828) ^ [_1202005, _1202007, _1202009, _1202011] : [class_Groups_Oordered__ab__group__add(_1202005), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202005), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202005), _1202007), _1202009)), _1202011) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202005), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202005), _1202007), _1202011)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202005), _1202009), _1202011)))], (44225 ^ _775828) ^ [_1642287, _1642289, _1642291, _1642293] : [44227 ^ _775828 : [(44230 ^ _775828) ^ [] : [hAPP(_1642293, 44226 ^ [_1642287, _1642289, _1642291, _1642293]) = c_Orderings_Otop__class_Otop(tc_fun(_1642289, tc_HOL_Obool))], (44228 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1642287), 44226 ^ [_1642287, _1642289, _1642291, _1642293]), _1642291)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642287, tc_fun(_1642289, tc_HOL_Obool)), _1642291), _1642293) = c_Orderings_Otop__class_Otop(tc_fun(_1642289, tc_HOL_Obool)))], (1966 ^ _775828) ^ [_804328, _804330, _804332, _804334, _804336, _804338] : [-(c_Power_Opower_Opower(_804338, _804334, _804330) = c_Power_Opower_Opower(_804336, _804332, _804328)), _804338 = _804336, _804334 = _804332, _804330 = _804328], (7857 ^ _775828) ^ [_901339, _901341] : [-(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), _901339), _901341)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901341))], (34089 ^ _775828) ^ [_1409841, _1409843, _1409845, _1409847, _1409849] : [class_Lattices_Osemilattice__inf(_1409841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409841), _1409843), _1409845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409841), _1409847), _1409849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409841), _1409843), _1409847)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409841), _1409845), _1409849))))], (37390 ^ _775828) ^ [_1481461, _1481463, _1481465, _1481467, _1481469, _1481471] : [class_Groups_Ocomm__monoid__add(_1481461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481463), _1481465)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481463, _1481461), _1481467), _1481465) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481469, _1481461), hAPP(hAPP(c_COMBB(tc_fun(_1481463, tc_HOL_Obool), _1481461, _1481469), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481463, _1481461), _1481467)), hAPP(hAPP(c_COMBB(tc_fun(_1481463, tc_HOL_Obool), tc_fun(_1481463, tc_HOL_Obool), _1481469), c_Set_OCollect(_1481463)), hAPP(hAPP(c_COMBB(tc_fun(_1481463, tc_HOL_Obool), tc_fun(_1481463, tc_HOL_Obool), _1481469), hAPP(c_COMBS(_1481463, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1481463), c_fconj), hAPP(hAPP(c_COMBC(_1481463, tc_fun(_1481463, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481463)), _1481465)))), hAPP(c_COMBC(_1481463, _1481469, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1481469, tc_fun(_1481469, tc_HOL_Obool), _1481463), c_fequal), _1481471)))))), hAPP(c_Set_Oimage(_1481463, _1481469, _1481471), _1481465)))], (12309 ^ _775828) ^ [_978802, _978804, _978806] : [_978802 = _978804, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978806, tc_HOL_Obool)), _978804), _978802)))], (42458 ^ _775828) ^ [_1600614, _1600616, _1600618] : [42461 ^ _775828 : [(42467 ^ _775828) ^ [] : [42460 ^ [_1600614, _1600616, _1600618] = 42463 ^ [_1600614, _1600616, _1600618]], (42465 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600614, _1600616)), hAPP(hAPP(c_Product__Type_OPair(_1600614, _1600616), 42459 ^ [_1600614, _1600616, _1600618]), 42463 ^ [_1600614, _1600616, _1600618])), _1600618)))], (42462 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600614, _1600616)), hAPP(hAPP(c_Product__Type_OPair(_1600614, _1600616), 42459 ^ [_1600614, _1600616, _1600618]), 42460 ^ [_1600614, _1600616, _1600618])), _1600618)))]], -(c_Relation_Osingle__valued(_1600614, _1600616, _1600618))], (46648 ^ _775828) ^ [_1703058, _1703060, _1703062, _1703064] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1703058), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1703060), _1703062)))), -(hAPP(c_Random_Opick(_1703060, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1703060)), _1703062), _1703064)), _1703058) = hAPP(c_Random_Opick(_1703060, _1703064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1703058), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1703060), _1703062))))], (20474 ^ _775828) ^ [_1127641, _1127643, _1127645] : [class_Groups_Omonoid__mult(_1127641), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127641), _1127643), 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)))), _1127645)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1127641), hAPP(hAPP(c_Power_Opower__class_Opower(_1127641), _1127643), _1127645)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (15128 ^ _775828) ^ [_1029700, _1029702] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029700), _1029702)), _1029702) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029700), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029700, _1029702)))], (3578 ^ _775828) ^ [_830186, _830188] : [_830188 = _830186, -(c_New__Random__Sequence_Opos__single(_830188) = c_New__Random__Sequence_Opos__single(_830186))], (6787 ^ _775828) ^ [_883364, _883366] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883364) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _883366), -(_883364 = _883366)], (29779 ^ _775828) ^ [_1316882, _1316884, _1316886, _1316888, _1316890] : [-(c_Predicate_Oconversep(_1316882, _1316884, c_Predicate_Opred__comp(_1316882, _1316886, _1316884, _1316888, _1316890)) = c_Predicate_Opred__comp(_1316884, _1316886, _1316882, c_Predicate_Oconversep(_1316886, _1316884, _1316890), c_Predicate_Oconversep(_1316882, _1316886, _1316888)))], (26447 ^ _775828) ^ [_1243002] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243002), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1243002 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33977 ^ _775828) ^ [_1407920, _1407922, _1407924] : [class_Lattices_Osemilattice__inf(_1407920), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407920), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407920), _1407922), _1407924)), _1407924)))], (26487 ^ _775828) ^ [_1243637, _1243639, _1243641] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243639), _1243641))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243637), _1243641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243641), _1243639)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243637), _1243639)))], (25022 ^ _775828) ^ [_1216900, _1216902] : [-(hAPP(c_Set_Oimage(_1216900, _1216900, c_COMBI(_1216900)), _1216902) = _1216902)], (33913 ^ _775828) ^ [_1406324, _1406326, _1406328, _1406330] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406324, tc_HOL_Obool)), _1406326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406324, tc_HOL_Obool)), _1406328), _1406330)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406324, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406324, tc_HOL_Obool)), _1406326), _1406328)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406324, tc_HOL_Obool)), _1406326), _1406330)))], (16757 ^ _775828) ^ [_1061271, _1061273] : [class_Groups_Oordered__ab__group__add__abs(_1061271), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061271), c_Groups_Ozero__class_Ozero(_1061271)), hAPP(c_Groups_Oabs__class_Oabs(_1061271), _1061273))))], (16583 ^ _775828) ^ [_1057870, _1057872, _1057874] : [class_Rings_Olinordered__idom(_1057870), -(hAPP(c_Groups_Oabs__class_Oabs(_1057870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057870), _1057872), _1057874)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057870), hAPP(c_Groups_Oabs__class_Oabs(_1057870), _1057872)), hAPP(c_Groups_Oabs__class_Oabs(_1057870), _1057874)))], (21612 ^ _775828) ^ [_1149980] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149980))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1149980)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23482 ^ _775828) ^ [_1186206, _1186208] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186206), _1186208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1186206)), _1186208)))], (7443 ^ _775828) ^ [_894629, _894631] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894629), _894631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894631), _894629))], (45763 ^ _775828) ^ [_1678837, _1678839, _1678841, _1678843] : [c_Fun_Oinj__on(_1678837, _1678839, _1678841, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1678837, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1678837), tc_fun(_1678837, tc_HOL_Obool), c_List_Oset(_1678837)), _1678843))), -(c_Fun_Oinj__on(tc_List_Olist(_1678837), tc_List_Olist(_1678839), hAPP(c_List_Omap(_1678837, _1678839), _1678841), _1678843))], (47191 ^ _775828) ^ [_1717013, _1717015, _1717017, _1717019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717013), _1717015)), -(hAPP(hAPP(c_List_Onth(_1717017), hAPP(hAPP(c_List_Otake(_1717017), _1717015), _1717019)), _1717013) = hAPP(hAPP(c_List_Onth(_1717017), _1717019), _1717013))], (40485 ^ _775828) ^ [_1552321, _1552323, _1552325, _1552327] : [hAPP(c_Set_Oimage(_1552321, _1552323, _1552325), c_Orderings_Otop__class_Otop(tc_fun(_1552321, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1552323, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552323, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1552323, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1552321, _1552323, _1552325), _1552327))), hAPP(c_Set_Oimage(_1552321, _1552323, _1552325), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1552321, tc_HOL_Obool)), _1552327)))))], (30395 ^ _775828) ^ [_1331285] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331285), c_Orderings_Obot__class_Obot(tc_fun(_1331285, tc_HOL_Obool)))))], (46365 ^ _775828) ^ [_1693911, _1693913] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1693911), _1693913))), -(c_Nitpick_Ocard_H(_1693911, _1693913) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29335 ^ _775828) ^ [_1307840, _1307842, _1307844, _1307846] : [hBOOL(hAPP(hAPP(c_member(_1307840), _1307842), hAPP(hAPP(c_Set_Oinsert(_1307840), _1307844), _1307846))), -(_1307842 = _1307844), -(hBOOL(hAPP(hAPP(c_member(_1307840), _1307842), _1307846)))], (24579 ^ _775828) ^ [_1207558, _1207560, _1207562] : [hBOOL(hAPP(hAPP(c_member(_1207558), _1207560), c_Wellfounded_Oacc(_1207558, _1207562))), 24582 ^ _775828 : [(24583 ^ _775828) ^ [_1207672] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1207558, _1207558)), hAPP(hAPP(c_Product__Type_OPair(_1207558, _1207558), _1207672), _1207560)), _1207562)), -(hBOOL(hAPP(hAPP(c_member(_1207558), _1207672), c_Wellfounded_Oacc(_1207558, _1207562))))]]], (1220 ^ _775828) ^ [_793696, _793698] : [-(class_Orderings_Owellorder(_793696)), _793698 = _793696, class_Orderings_Owellorder(_793698)], (9405 ^ _775828) ^ [_926813, _926815, _926817] : [class_Rings_Oordered__cancel__semiring(_926813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926813), c_Groups_Ozero__class_Ozero(_926813)), _926815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926813), _926817), c_Groups_Ozero__class_Ozero(_926813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926813), _926815), _926817)), c_Groups_Ozero__class_Ozero(_926813))))], (37276 ^ _775828) ^ [_1478686, _1478688, _1478690, _1478692, _1478694] : [class_Groups_Ocomm__monoid__add(_1478686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478688), _1478690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478688), _1478692)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478688, _1478686), _1478694), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478688, tc_HOL_Obool)), _1478690), _1478692))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478688, _1478686), _1478694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478688, tc_HOL_Obool)), _1478690), _1478692))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478688, _1478686), _1478694), _1478690)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478688, _1478686), _1478694), _1478692)))], (3362 ^ _775828) ^ [_826706, _826708, _826710, _826712, _826714, _826716] : [-(c_Predicate_ODomainP(_826716, _826712, _826708) = c_Predicate_ODomainP(_826714, _826710, _826706)), _826716 = _826714, _826712 = _826710, _826708 = _826706], (14938 ^ _775828) ^ [_1026223, _1026225, _1026227] : [-(hBOOL(hAPP(_1026223, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1026225, _1026227)))), 14941 ^ _775828 : [(14944 ^ _775828) ^ [] : [hBOOL(hAPP(_1026223, _1026225))], (14942 ^ _775828) ^ [] : [-(_1026227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14945 ^ _775828 : [(14950 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14948 ^ [_1026223, _1026225, _1026227]), _1026227)))], (14952 ^ _775828) ^ [] : [-(_1026225 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026227), 14947 ^ [_1026223, _1026225, _1026227])), 14948 ^ [_1026223, _1026225, _1026227]))], (14954 ^ _775828) ^ [] : [hBOOL(hAPP(_1026223, 14948 ^ [_1026223, _1026225, _1026227]))], (14946 ^ _775828) ^ [] : [_1026227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23906 ^ _775828) ^ [_1194417, _1194419, _1194421, _1194423] : [class_Orderings_Olinorder(_1194417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194417), _1194419), _1194421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194417), _1194419), _1194423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194417), _1194419), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194417), _1194421), _1194423))))], (33250 ^ _775828) ^ [_1391611, _1391613, _1391615, _1391617, _1391619, _1391621, _1391623] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1391611, tc_Option_Ooption(_1391613)), _1391615), _1391617), hAPP(c_Option_Ooption_OSome(_1391613), _1391619)), _1391621) = hAPP(c_Option_Ooption_OSome(_1391613), _1391623)), 33251 ^ _775828 : [(33258 ^ _775828) ^ [] : [-(_1391621 = _1391617), hAPP(_1391615, _1391621) = hAPP(c_Option_Ooption_OSome(_1391613), _1391623)], (33252 ^ _775828) ^ [] : [_1391621 = _1391617, _1391619 = _1391623]]], (36523 ^ _775828) ^ [_1461983, _1461985, _1461987, _1461989] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461983), _1461985)), 36526 ^ _775828 : [(36527 ^ _775828) ^ [_1462141] : [36529 ^ _775828 : [(36535 ^ _775828) ^ [] : [-(_1462141 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36531 ^ [_1461983, _1461985, _1461987, _1461989, _1462141]), 36528 ^ [_1461983, _1461985, _1461987, _1461989, _1462141]))], (36533 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36531 ^ [_1461983, _1461985, _1461987, _1461989, _1462141]), _1461987)))], (36530 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36528 ^ [_1461983, _1461985, _1461987, _1461989, _1462141]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1461985))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462141), _1461989)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462141), _1461985)), _1461989)))]]], (27657 ^ _775828) ^ [_1267580, _1267582, _1267584, _1267586] : [-(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), _1267580, _1267582)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267584, _1267586)))), 27658 ^ _775828 : [(27661 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267584), _1267580)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267582), _1267586))], (27659 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1267580), _1267582)))]]], (16334 ^ _775828) ^ [_1053493, _1053495] : [-(_1053493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053493), _1053495) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053493), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1053495)))], (1540 ^ _775828) ^ [_797696, _797698] : [-(class_Groups_Ocomm__monoid__add(_797696)), _797698 = _797696, class_Groups_Ocomm__monoid__add(_797698)], (4434 ^ _775828) ^ [_843520, _843522, _843524, _843526] : [-(c_List_Olexord(_843526, _843522) = c_List_Olexord(_843524, _843520)), _843526 = _843524, _843522 = _843520], (16543 ^ _775828) ^ [_1057162, _1057164] : [class_Groups_Oordered__ab__group__add__abs(_1057162), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057162), _1057164), hAPP(c_Groups_Oabs__class_Oabs(_1057162), _1057164))))], (35023 ^ _775828) ^ [_1430586, _1430588, _1430590, _1430592] : [-(c_Predicate_Oconversep(_1430586, _1430588, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430586, tc_fun(_1430588, tc_HOL_Obool))), _1430590), _1430592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430588, tc_fun(_1430586, tc_HOL_Obool))), c_Predicate_Oconversep(_1430586, _1430588, _1430590)), c_Predicate_Oconversep(_1430586, _1430588, _1430592)))], (16208 ^ _775828) ^ [_1050998, _1051000] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050998, _1051000) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1050998), _1051000)), _1051000)))], (27783 ^ _775828) ^ [_1270716, _1270718, _1270720] : [-(hAPP(c_Relation_ODomain(_1270716, _1270718), hAPP(c_Relation_Oconverse(_1270718, _1270716), _1270720)) = hAPP(c_Relation_ORange(_1270718, _1270716), _1270720))], (33693 ^ _775828) ^ [_1401509, _1401511, _1401513, _1401515] : [hBOOL(hAPP(hAPP(c_member(_1401509), _1401511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401509, tc_HOL_Obool)), _1401513), _1401515))), 33696 ^ _775828 : [(33699 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401509), _1401511), _1401515)))], (33697 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401509), _1401511), _1401513)))]]], (6156 ^ _775828) ^ [_873657] : [_873657 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873657), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (21336 ^ _775828) ^ [_1145293, _1145295, _1145297] : [class_Rings_Odivision__ring(_1145293), -(_1145295 = c_Groups_Ozero__class_Ozero(_1145293)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145293), hAPP(c_Groups_Ouminus__class_Ouminus(_1145293), _1145297)), hAPP(c_Groups_Ouminus__class_Ouminus(_1145293), _1145295)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145293), _1145297), _1145295))], (47379 ^ _775828) ^ [_1721048, _1721050, _1721052] : [-(hAPP(c_Map_Omap__of(_1721048, _1721050, c_List_Olist_ONil(tc_prod(_1721048, _1721050))), _1721052) = c_Option_Ooption_ONone(_1721050))], (35597 ^ _775828) ^ [_1444256, _1444258, _1444260] : [class_Groups_Oordered__ab__group__add(_1444256), -(hAPP(c_Set_Oimage(_1444256, _1444256, c_Groups_Ouminus__class_Ouminus(_1444256)), c_SetInterval_Oord__class_OatLeastAtMost(_1444256, _1444258, _1444260)) = c_SetInterval_Oord__class_OatLeastAtMost(_1444256, hAPP(c_Groups_Ouminus__class_Ouminus(_1444256), _1444260), hAPP(c_Groups_Ouminus__class_Ouminus(_1444256), _1444258)))], (32391 ^ _775828) ^ [_1374150, _1374152, _1374154] : [class_Orderings_Olinorder(_1374150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374150), _1374152)), 32398 ^ _775828 : [(32405 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374150, tc_HOL_Obool)), _1374152), hAPP(hAPP(c_Set_Oinsert(_1374150), _1374154), c_Orderings_Obot__class_Obot(tc_fun(_1374150, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374150, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1374150, hAPP(hAPP(c_Set_Oinsert(_1374150), _1374154), _1374152)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374150), _1374154), c_Big__Operators_Olinorder__class_OMax(_1374150, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374150, tc_HOL_Obool)), _1374152), hAPP(hAPP(c_Set_Oinsert(_1374150), _1374154), c_Orderings_Obot__class_Obot(tc_fun(_1374150, tc_HOL_Obool)))))))], (32399 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374150, tc_HOL_Obool)), _1374152), hAPP(hAPP(c_Set_Oinsert(_1374150), _1374154), c_Orderings_Obot__class_Obot(tc_fun(_1374150, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374150, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1374150, hAPP(hAPP(c_Set_Oinsert(_1374150), _1374154), _1374152)) = _1374154)]]], (17117 ^ _775828) ^ [_1068295, _1068297, _1068299] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1068295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068297), _1068299)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1068295), _1068297)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1068295), _1068299)))], (14397 ^ _775828) ^ [_1016716, _1016718] : [hBOOL(hAPP(c_Com_OWT, _1016718)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1016716, _1016718))))], (35505 ^ _775828) ^ [_1442753, _1442755, _1442757] : [class_Orderings_Oorder(_1442753), 35508 ^ _775828 : [(35515 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442753), _1442755), _1442757))), -(c_Orderings_Obot__class_Obot(tc_fun(_1442753, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1442753, _1442755, _1442757))], (35509 ^ _775828) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1442753, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1442753, _1442755, _1442757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442753), _1442755), _1442757))]]], (43002 ^ _775828) ^ [_1614140, _1614142, _1614144, _1614146, _1614148, _1614150, _1614152, _1614154] : [c_Finite__Set_Ofolding(_1614140, _1614142, _1614144, _1614146), -(hAPP(c_Fun_Ocomp(_1614142, _1614142, _1614148, hAPP(_1614144, _1614150)), hAPP(c_Fun_Ocomp(_1614142, _1614142, _1614148, hAPP(_1614144, _1614152)), _1614154)) = hAPP(c_Fun_Ocomp(_1614142, _1614142, _1614148, hAPP(_1614144, _1614152)), hAPP(c_Fun_Ocomp(_1614142, _1614142, _1614148, hAPP(_1614144, _1614150)), _1614154)))], (20598 ^ _775828) ^ [_1129803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1129803), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1129803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1129803 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25435 ^ _775828) ^ [_1224438, _1224440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224438)), hAPP(c_Code__Numeral_Onat__of, _1224440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1224438), _1224440)))], (25677 ^ _775828) ^ [_1229744, _1229746, _1229748, _1229750] : [class_Divides_Osemiring__div(_1229744), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229744), _1229746), c_Divides_Odiv__class_Omod(_1229744, _1229748, _1229750))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229744), _1229746), _1229750)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229744), _1229746), _1229748)))], (14758 ^ _775828) ^ [_1022692, _1022694, _1022696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022692), 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)), _1022694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022694), _1022696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022692), _1022694)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022692), _1022696))))], (44614 ^ _775828) ^ [_1652552, _1652554, _1652556, _1652558, _1652560, _1652562, _1652564] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652552, tc_fun(_1652554, tc_fun(_1652556, tc_HOL_Obool))), _1652558), _1652560), _1652562), _1652564)), 44617 ^ _775828 : [(44618 ^ _775828) ^ [_1652680] : [hBOOL(hAPP(hAPP(c_member(_1652552), _1652680), _1652558)), -(hBOOL(hAPP(hAPP(hAPP(_1652560, _1652680), _1652562), _1652564)))]]], (24831 ^ _775828) ^ [_1212893, _1212895, _1212897, _1212899] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1212893, _1212895, _1212897, tc_prod(_1212895, _1212897)), _1212899), c_Product__Type_OPair(_1212895, _1212897)) = _1212899)], (45612 ^ _775828) ^ [_1675193] : [-(hAPP(c_List_Omap(_1675193, _1675193), c_COMBI(_1675193)) = c_Fun_Oid(tc_List_Olist(_1675193)))], (51142 ^ _775828) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (44423 ^ _775828) ^ [_1647979, _1647981, _1647983, _1647985] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647979, tc_fun(_1647981, tc_HOL_Obool)), _1647983), _1647985) = hAPP(c_Set_OCollect(_1647981), hAPP(hAPP(c_COMBB(tc_fun(_1647979, tc_HOL_Obool), tc_HOL_Obool, _1647981), c_HOL_OAll(_1647979)), hAPP(hAPP(c_COMBB(tc_fun(_1647979, tc_HOL_Obool), tc_fun(_1647979, tc_HOL_Obool), _1647981), hAPP(c_COMBS(_1647979, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1647979), c_fimplies), hAPP(hAPP(c_COMBC(_1647979, tc_fun(_1647979, tc_HOL_Obool), tc_HOL_Obool), c_member(_1647979)), _1647983)))), hAPP(hAPP(c_COMBC(_1647981, tc_fun(_1647979, tc_fun(_1647981, tc_HOL_Obool)), tc_fun(_1647979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1647981, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1647979, tc_fun(_1647981, tc_HOL_Obool)), tc_fun(_1647979, tc_HOL_Obool)), _1647981), c_COMBB(tc_fun(_1647981, tc_HOL_Obool), tc_HOL_Obool, _1647979)), c_member(_1647981))), _1647985)))))], (50986 ^ _775828) ^ [_1802468, _1802470, _1802472] : [-(c_Enum_On__lists(_1802468, hAPP(c_Nat_OSuc, _1802470), _1802472) = c_List_Oconcat(tc_List_Olist(_1802468), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802468), tc_List_Olist(tc_List_Olist(_1802468))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1802468), tc_List_Olist(_1802468), tc_List_Olist(tc_List_Olist(_1802468))), hAPP(hAPP(c_COMBB(tc_fun(_1802468, tc_List_Olist(_1802468)), tc_fun(tc_List_Olist(_1802468), tc_List_Olist(tc_List_Olist(_1802468))), tc_List_Olist(_1802468)), c_List_Omap(_1802468, tc_List_Olist(_1802468))), hAPP(c_COMBC(_1802468, tc_List_Olist(_1802468), tc_List_Olist(_1802468)), c_List_Olist_OCons(_1802468)))), _1802472)), c_Enum_On__lists(_1802468, _1802470, _1802472))))], (11973 ^ _775828) ^ [_973039, _973041, _973043] : [class_Rings_Olinordered__idom(_973039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973039), c_Groups_Ozero__class_Ozero(_973039)), _973041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973039), c_Groups_Ozero__class_Ozero(_973039)), _973043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973039), _973043), c_Groups_Oone__class_Oone(_973039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973039), _973043), _973041)), _973041)))], (28085 ^ _775828) ^ [_1279168, _1279170] : [c_Wellfounded_OwfP(_1279168, _1279170), 28088 ^ _775828 : [(28089 ^ _775828) ^ [_1279232] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1279168, _1279170), _1279232)))]]], (42770 ^ _775828) ^ [_1608562, _1608564, _1608566, _1608568, _1608570, _1608572, _1608574, _1608576] : [hAPP(c_Fun_Ocomp(_1608562, _1608564, _1608566, _1608568), _1608570) = hAPP(c_Fun_Ocomp(_1608572, _1608564, _1608566, _1608574), _1608576), 42773 ^ _775828 : [(42774 ^ _775828) ^ [_1608677] : [-(hAPP(_1608568, hAPP(_1608570, _1608677)) = hAPP(_1608574, hAPP(_1608576, _1608677)))]]], (25503 ^ _775828) ^ [_1225849, _1225851, _1225853, _1225855, _1225857, _1225859, _1225861] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1225849, _1225851, _1225853, _1225855), _1225857), _1225859), _1225861) = c_New__DSequence_Opos__bind(_1225849, _1225851, hAPP(hAPP(hAPP(_1225853, _1225857), _1225859), _1225861), hAPP(hAPP(c_COMBC(_1225849, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1225851))), hAPP(hAPP(c_COMBC(_1225849, 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(_1225851)))), hAPP(hAPP(c_COMBC(_1225849, 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(_1225851))))), _1225855), _1225857)), _1225859)), _1225861)))], (44930 ^ _775828) ^ [_1659970, _1659972, _1659974] : [class_Complete__Lattice_Ocomplete__lattice(_1659970), -(c_Complete__Lattice_OSup__class_OSup(_1659970, hAPP(hAPP(c_Set_Oinsert(_1659970), _1659972), hAPP(hAPP(c_Set_Oinsert(_1659970), _1659974), c_Orderings_Obot__class_Obot(tc_fun(_1659970, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1659970), _1659972), _1659974))], (42776 ^ _775828) ^ [_1608716, _1608718, _1608720, _1608722, _1608724, _1608726] : [-(hAPP(hAPP(c_Fun_Ocomp(_1608716, _1608718, _1608720, _1608722), _1608724), _1608726) = hAPP(_1608722, hAPP(_1608724, _1608726)))], (878 ^ _775828) ^ [_789237, _789239, _789241, _789243, _789245, _789247] : [-(c_Relation_Orefl__on(_789245, _789241, _789237)), c_Relation_Orefl__on(_789247, _789243, _789239), _789247 = _789245, _789243 = _789241, _789239 = _789237], (15051 ^ _775828) ^ [_1028239, _1028241, _1028243] : [-(hBOOL(hAPP(_1028239, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028241), _1028243)))), 15052 ^ _775828 : [(15059 ^ _775828) ^ [_1028407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028243), _1028407)), _1028241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028243), hAPP(c_Nat_OSuc, _1028407)))), hBOOL(hAPP(_1028239, _1028407))], (15053 ^ _775828) ^ [] : [_1028243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1028239, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (13010 ^ _775828) ^ [_990872, _990874, _990876] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_990872, _990874, _990876)) = 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), _990874)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _990876))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33915 ^ _775828) ^ [_1406408, _1406410, _1406412, _1406414] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406408, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406408, tc_HOL_Obool)), _1406410), _1406412)), _1406414) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406408, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406408, tc_HOL_Obool)), _1406410), _1406414)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406408, tc_HOL_Obool)), _1406412), _1406414)))], (2100 ^ _775828) ^ [_806479, _806481, _806483, _806485] : [-(c_Divides_Odivmod__int(_806485, _806481) = c_Divides_Odivmod__int(_806483, _806479)), _806485 = _806483, _806481 = _806479], (49321 ^ _775828) ^ [_1766173, _1766175, _1766177, _1766179] : [_1766173 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766175)), _1766177)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1766175, hAPP(hAPP(c_List_Olist__update(_1766175, _1766177), _1766173), _1766179)) = c_List_Obutlast(_1766175, _1766177))], (28185 ^ _775828) ^ [_1280963, _1280965, _1280967, _1280969, _1280971, _1280973] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1280963, _1280965, _1280967), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1280963, _1280965), tc_HOL_Obool)), _1280969), _1280971)), _1280973) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1280963, _1280967), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1280963, _1280965, _1280967), _1280969), _1280973)), hAPP(hAPP(c_Relation_Orel__comp(_1280963, _1280965, _1280967), _1280971), _1280973)))], (13965 ^ _775828) ^ [_1008709, _1008711, _1008713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008709)), 13968 ^ _775828 : [(13969 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1008711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008713), _1008709)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008713, _1008709))), 13972 ^ _775828 : [(13973 ^ _775828) ^ [_1008910, _1008912] : [-(hBOOL(hAPP(hAPP(_1008711, _1008912), _1008910))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008910), _1008709)), _1008713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008709), _1008912)), _1008910)]]], (13987 ^ _775828) ^ [] : [13990 ^ _775828 : [(13993 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13989 ^ [_1008709, _1008711, _1008713]), _1008709)))], (13995 ^ _775828) ^ [] : [-(_1008713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008709), 13988 ^ [_1008709, _1008711, _1008713])), 13989 ^ [_1008709, _1008711, _1008713]))], (13997 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1008711, 13988 ^ [_1008709, _1008711, _1008713]), 13989 ^ [_1008709, _1008711, _1008713]))], (13991 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13989 ^ [_1008709, _1008711, _1008713])))]], -(hBOOL(hAPP(hAPP(_1008711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008713), _1008709)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008713, _1008709))))]]], (23368 ^ _775828) ^ [_1183150, _1183152] : [class_Rings_Oring__1(_1183150), 23371 ^ _775828 : [(23378 ^ _775828) ^ [] : [-(_1183152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23381 ^ _775828 : [(23388 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183152), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1183150), _1183152) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1183150), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1183150, _1183150)), tc_fun(tc_Int_Oint, _1183150)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1183150, _1183150), _1183150), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1183150, _1183150)), tc_fun(tc_Int_Oint, _1183150)), tc_Int_Oint), c_COMBB(tc_fun(_1183150, _1183150), _1183150, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1183150, tc_fun(tc_fun(_1183150, _1183150), _1183150), tc_Int_Oint), c_HOL_OLet(_1183150, _1183150)), c_Int_Oring__1__class_Oof__int(_1183150)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1183150, _1183150), tc_fun(_1183150, _1183150)), hAPP(hAPP(c_COMBB(tc_fun(_1183150, tc_fun(_1183150, _1183150)), tc_fun(tc_fun(_1183150, _1183150), tc_fun(_1183150, _1183150)), tc_Int_Oint), c_COMBS(_1183150, _1183150, _1183150)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1183150, _1183150), tc_fun(_1183150, tc_fun(_1183150, _1183150))), hAPP(hAPP(c_COMBB(tc_fun(_1183150, tc_fun(_1183150, _1183150)), tc_fun(tc_fun(_1183150, _1183150), tc_fun(_1183150, tc_fun(_1183150, _1183150))), tc_Int_Oint), c_COMBB(_1183150, tc_fun(_1183150, _1183150), _1183150)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1183150, tc_fun(_1183150, _1183150)), tc_Int_Oint), c_If(_1183150)), 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(_1183150, _1183150, _1183150), c_Groups_Oplus__class_Oplus(_1183150)), c_COMBI(_1183150))))), hAPP(hAPP(c_COMBC(_1183150, _1183150, _1183150), hAPP(hAPP(c_COMBB(_1183150, tc_fun(_1183150, _1183150), _1183150), c_Groups_Oplus__class_Oplus(_1183150)), hAPP(hAPP(c_COMBS(_1183150, _1183150, _1183150), c_Groups_Oplus__class_Oplus(_1183150)), c_COMBI(_1183150)))), c_Groups_Oone__class_Oone(_1183150))))), c_Divides_Odivmod__int(_1183152, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (23382 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183152), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1183150), _1183152) = hAPP(c_Groups_Ouminus__class_Ouminus(_1183150), hAPP(c_Int_Oring__1__class_Oof__int(_1183150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183152))))]]], (23372 ^ _775828) ^ [] : [_1183152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1183150), _1183152) = c_Groups_Ozero__class_Ozero(_1183150))]]], (14608 ^ _775828) ^ [_1020367, _1020369] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1020367), _1020369) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1020369 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14617 ^ _775828 : [(14620 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020367), _1020369)))], (14618 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020367)))]], 14621 ^ _775828 : [(14624 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020369), _1020367)))], (14622 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020367), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (12467 ^ _775828) ^ [_981482, _981484, _981486, _981488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981482), _981484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981486), _981488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981482), _981486)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981484), _981488))))], (5585 ^ _775828) ^ [_864329] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _864329)], (35947 ^ _775828) ^ [_1450903, _1450905, _1450907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450903)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1450905), _1450907)), 35954 ^ _775828 : [(35955 ^ _775828) ^ [_1451093] : [35957 ^ _775828 : [(35963 ^ _775828) ^ [] : [-(_1451093 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35959 ^ [_1450903, _1450905, _1450907, _1451093]), 35956 ^ [_1450903, _1450905, _1450907, _1451093]))], (35961 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35959 ^ [_1450903, _1450905, _1450907, _1451093]), _1450907)))], (35958 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35956 ^ [_1450903, _1450905, _1450907, _1451093]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450903))))]], -(_1451093 = _1450905), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1451093), _1450903) = _1450905]]], (20368 ^ _775828) ^ [_1125811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125811), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1125811)), c_Int_OMin)))], (25821 ^ _775828) ^ [_1232151, _1232153] : [-(_1232151 = _1232153), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232151), _1232153)), 25828 ^ _775828 : [(25831 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232153), _1232151))], (25829 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232151), _1232153)))]]], (25741 ^ _775828) ^ [_1230829, _1230831, _1230833, _1230835] : [class_Rings_Ocomm__semiring__1(_1230829), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230829), _1230831), _1230833)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230829), _1230833), _1230835)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230829), _1230831), _1230835)))], (44301 ^ _775828) ^ [_1644397, _1644399, _1644401, _1644403, _1644405] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644397, tc_HOL_Obool)), _1644399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644401, tc_fun(_1644397, tc_HOL_Obool)), _1644403), _1644405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644401, tc_fun(_1644397, tc_HOL_Obool)), _1644403), hAPP(hAPP(c_COMBB(tc_fun(_1644397, tc_HOL_Obool), tc_fun(_1644397, tc_HOL_Obool), _1644401), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644397, tc_HOL_Obool)), _1644399)), _1644405)))], (10088 ^ _775828) ^ [_939074, _939076, _939078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939074), _939076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939076), _939078))))], (19118 ^ _775828) ^ [_1105012] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1105012) = c_Int_OPls)], (31409 ^ _775828) ^ [_1352844, _1352846, _1352848] : [class_Orderings_Olinorder(_1352844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352844), _1352846)), 31416 ^ _775828 : [(31423 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352844, tc_HOL_Obool)), _1352846), hAPP(hAPP(c_Set_Oinsert(_1352844), _1352848), c_Orderings_Obot__class_Obot(tc_fun(_1352844, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352844, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1352844, c_Orderings_Oord__class_Omin(_1352844), hAPP(hAPP(c_Set_Oinsert(_1352844), _1352848), _1352846)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1352844), _1352848), c_Big__Operators_Olattice_OInf__fin(_1352844, c_Orderings_Oord__class_Omin(_1352844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352844, tc_HOL_Obool)), _1352846), hAPP(hAPP(c_Set_Oinsert(_1352844), _1352848), c_Orderings_Obot__class_Obot(tc_fun(_1352844, tc_HOL_Obool)))))))], (31417 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352844, tc_HOL_Obool)), _1352846), hAPP(hAPP(c_Set_Oinsert(_1352844), _1352848), c_Orderings_Obot__class_Obot(tc_fun(_1352844, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352844, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1352844, c_Orderings_Oord__class_Omin(_1352844), hAPP(hAPP(c_Set_Oinsert(_1352844), _1352848), _1352846)) = _1352848)]]], (15352 ^ _775828) ^ [_1033867, _1033869, _1033871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033867), _1033869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033867), _1033871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033871), _1033869)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033871), _1033867))))], (33865 ^ _775828) ^ [_1405207, _1405209, _1405211, _1405213] : [class_Lattices_Osemilattice__inf(_1405207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405207), _1405209), _1405211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405207), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1405207), _1405213), _1405209)), _1405211)))], (7951 ^ _775828) ^ [_903139, _903141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _903139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _903141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _903139), _903141))))], (40897 ^ _775828) ^ [_1562917, _1562919, _1562921, _1562923] : [-(hAPP(c_Set_Oimage(_1562917, _1562919, _1562921), hAPP(c_Set_Ovimage(_1562917, _1562919, _1562921), _1562923)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562919, tc_HOL_Obool)), _1562923), hAPP(c_Set_Oimage(_1562917, _1562919, _1562921), c_Orderings_Otop__class_Otop(tc_fun(_1562917, tc_HOL_Obool)))))], (31927 ^ _775828) ^ [_1366069, _1366071, _1366073] : [class_Groups_Oordered__ab__group__add(_1366069), -(hAPP(c_Set_Oimage(_1366069, _1366069, c_Groups_Ouminus__class_Ouminus(_1366069)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1366069, _1366071, _1366073)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1366069, hAPP(c_Groups_Ouminus__class_Ouminus(_1366069), _1366073), hAPP(c_Groups_Ouminus__class_Ouminus(_1366069), _1366071)))], (1710 ^ _775828) ^ [_799821, _799823] : [-(class_Groups_Ominus(_799821)), _799823 = _799821, class_Groups_Ominus(_799823)], (34041 ^ _775828) ^ [_1409021, _1409023, _1409025] : [class_Lattices_Osemilattice__inf(_1409021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409021), _1409023), _1409025)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409021), _1409023), _1409025) = _1409023)], (51244 ^ _775828) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51338 ^ _775828) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (25188 ^ _775828) ^ [_1220294] : [c_Nat__Transfer_Onat__set(_1220294), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1220294)) = _1220294)], (39282 ^ _775828) ^ [_1524462, _1524464, _1524466, _1524468] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1524462, _1524464, _1524466, _1524468, c_Orderings_Obot__class_Obot(tc_fun(_1524462, tc_HOL_Obool))), _1524468)))], (9377 ^ _775828) ^ [_926303, _926305, _926307] : [class_Rings_Oordered__cancel__semiring(_926303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926303), _926305), c_Groups_Ozero__class_Ozero(_926303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926303), c_Groups_Ozero__class_Ozero(_926303)), _926307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926303), _926305), _926307)), c_Groups_Ozero__class_Ozero(_926303))))], (8437 ^ _775828) ^ [_911281, _911283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911283)), 8444 ^ _775828 : [(8451 ^ _775828) ^ [] : [_911281 = _911283, -(hAPP(c_Int_Onat, _911281) = hAPP(c_Int_Onat, _911283))], (8445 ^ _775828) ^ [] : [hAPP(c_Int_Onat, _911281) = hAPP(c_Int_Onat, _911283), -(_911281 = _911283)]]], (30305 ^ _775828) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (51114 ^ _775828) ^ [_1804455, _1804457] : [class_Groups_Ominus(_1804455), -(class_Groups_Ominus(tc_fun(_1804457, _1804455)))], (10570 ^ _775828) ^ [_947956, _947958, _947960, _947962] : [class_Groups_Oordered__cancel__ab__semigroup__add(_947956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947956), _947958), _947960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947956), _947962), _947958)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947956), _947962), _947960))))], (5505 ^ _775828) ^ [_862868, _862870, _862872, _862874] : [_862868 = _862870, 5510 ^ _775828 : [(5513 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_862872), _862874), _862870)))], (5511 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_862872), _862874), _862868)))]], 5514 ^ _775828 : [(5517 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_862872), _862874), _862870))], (5515 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_862872), _862874), _862868))]]], (15714 ^ _775828) ^ [_1040723, _1040725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040723), _1040725)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040723), _1040725) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46298 ^ _775828) ^ [_1692241, _1692243, _1692245, _1692247, _1692249] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692241)), _1692243) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692245)), _1692247), 46301 ^ _775828 : [(46308 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692241), _1692249), hAPP(c_List_Oset(_1692241), _1692243)))), -(hAPP(c_Map_Omap__of(_1692241, _1692245, hAPP(hAPP(c_List_Ozip(_1692241, _1692245), _1692243), _1692247)), _1692249) = c_Option_Ooption_ONone(_1692245))], (46302 ^ _775828) ^ [] : [hAPP(c_Map_Omap__of(_1692241, _1692245, hAPP(hAPP(c_List_Ozip(_1692241, _1692245), _1692243), _1692247)), _1692249) = c_Option_Ooption_ONone(_1692245), hBOOL(hAPP(hAPP(c_member(_1692241), _1692249), hAPP(c_List_Oset(_1692241), _1692243)))]]], (25449 ^ _775828) ^ [_1224701, _1224703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1224701)), hAPP(c_Code__Numeral_Onat__of, _1224703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1224701), _1224703)))], (38047 ^ _775828) ^ [_1497288, _1497290, _1497292] : [class_Orderings_Oorder(_1497288), 38050 ^ _775828 : [(38057 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497288), _1497292), _1497290)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497288, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1497288), _1497290)), hAPP(c_SetInterval_Oord__class_OatLeast(_1497288), _1497292))))], (38051 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497288, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1497288), _1497290)), hAPP(c_SetInterval_Oord__class_OatLeast(_1497288), _1497292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497288), _1497292), _1497290)))]]], (49566 ^ _775828) ^ [_1772338, _1772340, _1772342, _1772344, _1772346] : [-(hAPP(hAPP(c_List_Omap(_1772338, _1772340), _1772342), hAPP(c_List_Ofilter(_1772338, _1772344), _1772346)) = c_List_Omap__filter(_1772338, _1772340, hAPP(hAPP(c_COMBC(_1772338, tc_Option_Ooption(_1772340), tc_Option_Ooption(_1772340)), hAPP(hAPP(c_COMBS(_1772338, tc_Option_Ooption(_1772340), tc_fun(tc_Option_Ooption(_1772340), tc_Option_Ooption(_1772340))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1772340), tc_fun(tc_Option_Ooption(_1772340), tc_Option_Ooption(_1772340))), _1772338), c_If(tc_Option_Ooption(_1772340))), _1772344)), hAPP(hAPP(c_COMBB(_1772340, tc_Option_Ooption(_1772340), _1772338), c_Option_Ooption_OSome(_1772340)), _1772342))), c_Option_Ooption_ONone(_1772340)), _1772346))], (41943 ^ _775828) ^ [_1588776, _1588778, _1588780, _1588782, _1588784, _1588786] : [class_Groups_Ocomm__monoid__add(_1588776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588778), _1588780)), 41953 ^ _775828 : [(41956 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1588782), hAPP(_1588784, 41952 ^ [_1588776, _1588778, _1588780, _1588782, _1588784, _1588786])))], (41954 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588778), 41952 ^ [_1588776, _1588778, _1588780, _1588782, _1588784, _1588786]), _1588780)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1588778, _1588776), hAPP(hAPP(c_COMBS(_1588778, tc_fun(_1588782, tc_HOL_Obool), _1588776), hAPP(hAPP(c_COMBB(tc_fun(_1588782, _1588776), tc_fun(tc_fun(_1588782, tc_HOL_Obool), _1588776), _1588778), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1588782, _1588776)), _1588786)), _1588784)), _1588780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1588778, _1588782), _1588776), hAPP(c_Product__Type_Oprod_Oprod__case(_1588778, _1588782, _1588776), _1588786)), hAPP(hAPP(c_Product__Type_OSigma(_1588778, _1588782), _1588780), _1588784)))], (28972 ^ _775828) ^ [_1299917, _1299919, _1299921, _1299923, _1299925, _1299927] : [hBOOL(hAPP(hAPP(_1299917, _1299919), _1299921)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299923, tc_fun(_1299925, tc_HOL_Obool))), _1299927), _1299917), _1299919), _1299921)))], (47269 ^ _775828) ^ [_1718759, _1718761, _1718763] : [hAPP(hAPP(c_List_Otake(_1718759), _1718761), _1718763) = c_List_Olist_ONil(_1718759), -(_1718761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1718763 = c_List_Olist_ONil(_1718759))], (45507 ^ _775828) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (41901 ^ _775828) ^ [_1587775, _1587777, _1587779, _1587781] : [class_Groups_Ocomm__monoid__add(_1587775), c_Fun_Oinj__on(_1587777, _1587775, _1587779, _1587781), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1587777, _1587775), _1587779), _1587781) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1587775, _1587775), c_Fun_Oid(_1587775)), hAPP(c_Set_Oimage(_1587777, _1587775, _1587779), _1587781)))], (21119 ^ _775828) ^ [_1141375, _1141377, _1141379] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1141375, _1141377), _1141379)), 21122 ^ _775828 : [(21123 ^ _775828) ^ [_1141460] : [hBOOL(hAPP(hAPP(_1141377, _1141460), _1141379)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1141375, _1141377), _1141460)))]]], (5745 ^ _775828) ^ [_867376, _867378, _867380] : [_867378 = _867380, -(hBOOL(hAPP(hAPP(c_member(_867376), _867378), hAPP(c_fequal, _867380))))], (39245 ^ _775828) ^ [_1523750, _1523752] : [-(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)), _1523750), _1523752))], (23160 ^ _775828) ^ [_1179208, _1179210, _1179212, _1179214, _1179216] : [class_Fields_Ofield(_1179208), -(_1179210 = c_Groups_Ozero__class_Ozero(_1179208)), -(_1179212 = c_Groups_Ozero__class_Ozero(_1179208)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179208), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179208), _1179214), _1179210)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179208), _1179216), _1179212)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179208), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179208), _1179214), _1179212)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179208), _1179216), _1179210))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179208), _1179210), _1179212)))], (26399 ^ _775828) ^ [_1242036, _1242038, _1242040, _1242042] : [class_Rings_Ocomm__semiring__1(_1242036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242038), _1242040)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242036), hAPP(hAPP(c_Power_Opower__class_Opower(_1242036), _1242042), _1242038)), hAPP(hAPP(c_Power_Opower__class_Opower(_1242036), _1242042), _1242040))))], (42778 ^ _775828) ^ [_1608766, _1608768, _1608770, _1608772, _1608774, _1608776, _1608778, _1608780, _1608782, _1608784, _1608786] : [hAPP(_1608766, hAPP(_1608768, _1608770)) = hAPP(_1608772, hAPP(_1608774, _1608776)), -(hAPP(hAPP(c_Fun_Ocomp(_1608778, _1608780, _1608782, _1608766), _1608768), _1608770) = hAPP(hAPP(c_Fun_Ocomp(_1608784, _1608780, _1608786, _1608772), _1608774), _1608776))], (43764 ^ _775828) ^ [_1631778, _1631780, _1631782] : [class_Orderings_Olinorder(_1631778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631778), _1631780)), -(c_Big__Operators_Olinorder__class_OMin(_1631778, hAPP(hAPP(c_Set_Oinsert(_1631778), _1631782), _1631780)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631778, _1631778, c_Orderings_Oord__class_Omin(_1631778)), _1631782), _1631780))], (50449 ^ _775828) ^ [_1789849, _1789851, _1789853] : [-(hAPP(c_List_Orev(_1789849), hAPP(hAPP(c_List_Odrop(_1789849), _1789851), _1789853)) = hAPP(hAPP(c_List_Otake(_1789849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789849)), _1789853)), _1789851)), hAPP(c_List_Orev(_1789849), _1789853)))], (23278 ^ _775828) ^ [_1181401, _1181403, _1181405, _1181407] : [class_Fields_Olinordered__field__inverse__zero(_1181401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181401), _1181403), _1181405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181401), _1181407), c_Groups_Ozero__class_Ozero(_1181401))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181401), c_Groups_Ozero__class_Ozero(_1181401)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181401), _1181403), _1181405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181401), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181401), _1181407), _1181403)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181401), _1181407), _1181405))))], (19662 ^ _775828) ^ [_1113677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1113677)))], (45616 ^ _775828) ^ [_1675264, _1675266, _1675268, _1675270, _1675272, _1675274, _1675276] : [-(c_List_Ofoldr(_1675264, _1675266, _1675268, hAPP(hAPP(c_List_Omap(_1675270, _1675264), _1675272), _1675274), _1675276) = c_List_Ofoldr(_1675270, _1675266, hAPP(c_Fun_Ocomp(_1675264, tc_fun(_1675266, _1675266), _1675270, _1675268), _1675272), _1675274, _1675276))], (44497 ^ _775828) ^ [_1649939, _1649941, _1649943, _1649945, _1649947] : [_1649939 = c_Orderings_Obot__class_Obot(tc_fun(_1649941, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649941, tc_fun(_1649943, tc_HOL_Obool)), _1649939), hAPP(hAPP(c_COMBB(tc_fun(_1649943, tc_HOL_Obool), tc_fun(_1649943, tc_HOL_Obool), _1649941), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1649943, tc_HOL_Obool)), _1649945)), _1649947)) = c_Orderings_Otop__class_Otop(tc_fun(_1649943, tc_HOL_Obool)))], (51384 ^ _775828) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (47585 ^ _775828) ^ [_1724925, _1724927] : [-(c_List_Oset__Cons(_1724925, _1724927, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724925)), c_List_Olist_ONil(_1724925)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724925), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1724925, tc_List_Olist(_1724925), hAPP(hAPP(c_COMBC(_1724925, tc_List_Olist(_1724925), tc_List_Olist(_1724925)), c_List_Olist_OCons(_1724925)), c_List_Olist_ONil(_1724925))), _1724927))], (51190 ^ _775828) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (48463 ^ _775828) ^ [_1747487, _1747489, _1747491, _1747493] : [hAPP(hAPP(c_List_Oappend(_1747487), _1747489), _1747491) = _1747493, 48466 ^ _775828 : [(48469 ^ _775828) ^ [] : [-(_1747491 = hAPP(hAPP(c_List_Odrop(_1747487), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747487)), _1747489)), _1747493))], (48467 ^ _775828) ^ [] : [-(_1747489 = hAPP(hAPP(c_List_Otake(_1747487), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747487)), _1747489)), _1747493))]]], (14286 ^ _775828) ^ [_1014670, _1014672, _1014674, _1014676, _1014678] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014670, _1014672), _1014674, _1014676, _1014678), 14291 ^ _775828 : [(14294 ^ _775828) ^ [] : [hBOOL(hAPP(_1014670, _1014674))], (14292 ^ _775828) ^ [] : [-(_1014678 = _1014674)]], 14295 ^ _775828 : [(14301 ^ _775828) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1014670, _1014672), 14297 ^ [_1014670, _1014672, _1014674, _1014676, _1014678], _1014676, _1014678))], (14299 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_1014672, _1014674, _1014676, 14297 ^ [_1014670, _1014672, _1014674, _1014676, _1014678]))], (14296 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1014670, _1014674)))]]], (11833 ^ _775828) ^ [_970455, _970457, _970459] : [class_Groups_Oordered__comm__monoid__add(_970455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970455), c_Groups_Ozero__class_Ozero(_970455)), _970457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970455), c_Groups_Ozero__class_Ozero(_970455)), _970459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970455), c_Groups_Ozero__class_Ozero(_970455)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970455), _970457), _970459))))], (51050 ^ _775828) ^ [_1803615, _1803617] : [class_Lattices_Odistrib__lattice(_1803615), -(class_Lattices_Odistrib__lattice(tc_fun(_1803617, _1803615)))], (30457 ^ _775828) ^ [_1332458, _1332460, _1332462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332458, tc_HOL_Obool)), _1332460), _1332462)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332458), _1332462)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332458), _1332460)))], (15216 ^ _775828) ^ [_1031307, _1031309, _1031311] : [class_Groups_Oab__group__add(_1031307), 15219 ^ _775828 : [(15226 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031307), _1031309), _1031311) = c_Groups_Ozero__class_Ozero(_1031307), -(_1031309 = _1031311)], (15220 ^ _775828) ^ [] : [_1031309 = _1031311, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031307), _1031309), _1031311) = c_Groups_Ozero__class_Ozero(_1031307))]]], (44709 ^ _775828) ^ [_1655389, _1655391, _1655393] : [44711 ^ _775828 : [(44714 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655389, tc_HOL_Obool)), 44710 ^ [_1655389, _1655391, _1655393]), _1655393) = c_Orderings_Obot__class_Obot(tc_fun(_1655389, tc_HOL_Obool))], (44712 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1655389, tc_HOL_Obool)), 44710 ^ [_1655389, _1655391, _1655393]), _1655391)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655389, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1655389, tc_HOL_Obool), _1655391)), _1655393) = c_Orderings_Obot__class_Obot(tc_fun(_1655389, tc_HOL_Obool)))], (17915 ^ _775828) ^ [_1082762, _1082764, _1082766, _1082768] : [class_Rings_Olinordered__semidom(_1082762), hAPP(hAPP(c_Power_Opower__class_Opower(_1082762), _1082764), hAPP(c_Nat_OSuc, _1082766)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1082762), _1082768), hAPP(c_Nat_OSuc, _1082766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082762), c_Groups_Ozero__class_Ozero(_1082762)), _1082764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082762), c_Groups_Ozero__class_Ozero(_1082762)), _1082768)), -(_1082764 = _1082768)], (27248 ^ _775828) ^ [_1258188] : [-(c_Int_Oint__ge__less__than2(_1258188) = 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), _1258188)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (45470 ^ _775828) ^ [_1671700, _1671702] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1671700), _1671702) = c_Smallcheck_Osmall_H(_1671700, hAPP(c_Code__Numeral_Oint__of, _1671702), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1671702))))], (17519 ^ _775828) ^ [_1075800, _1075802] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075800))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075800)), _1075802) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075802))], (18203 ^ _775828) ^ [_1088274, _1088276] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088274, _1088276), c_Divides_Odivmod__nat(_1088274, _1088276))))], (35213 ^ _775828) ^ [_1435749, _1435751, _1435753, _1435755, _1435757] : [class_Groups_Ocomm__monoid__mult(_1435749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435751), _1435753)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435751), _1435755)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435749), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435749, _1435751, c_Groups_Otimes__class_Otimes(_1435749)), _1435757), c_Groups_Oone__class_Oone(_1435749)), _1435753)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435749, _1435751, c_Groups_Otimes__class_Otimes(_1435749)), _1435757), c_Groups_Oone__class_Oone(_1435749)), _1435755)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435749), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435749, _1435751, c_Groups_Otimes__class_Otimes(_1435749)), _1435757), c_Groups_Oone__class_Oone(_1435749)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1435751, tc_HOL_Obool)), _1435753), _1435755))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435749, _1435751, c_Groups_Otimes__class_Otimes(_1435749)), _1435757), c_Groups_Oone__class_Oone(_1435749)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435751, tc_HOL_Obool)), _1435753), _1435755))))], (13394 ^ _775828) ^ [_998047] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _998047) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3518 ^ _775828) ^ [_829198, _829200, _829202, _829204, _829206, _829208, _829210, _829212] : [-(c_Random__Sequence_Obind(_829212, _829208, _829204, _829200) = c_Random__Sequence_Obind(_829210, _829206, _829202, _829198)), _829212 = _829210, _829208 = _829206, _829204 = _829202, _829200 = _829198], (48427 ^ _775828) ^ [_1746637, _1746639, _1746641] : [-(hAPP(hAPP(c_List_Odrop(_1746637), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1746637), _1746639), _1746641)) = _1746641)], (14237 ^ _775828) ^ [_1013759, _1013761, _1013763] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013759, _1013761)), _1013763) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013759), _1013763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013761), _1013763)))], (7715 ^ _775828) ^ [_898972, _898974, _898976] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898972), _898974) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898976), _898974), -(_898972 = _898976), -(_898974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10162 ^ _775828) ^ [_940404, _940406, _940408, _940410] : [class_Groups_Ocancel__semigroup__add(_940404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940404), _940406), _940408) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940404), _940410), _940408), -(_940406 = _940410)], (27513 ^ _775828) ^ [_1264708, _1264710, _1264712] : [c_Relation_Ototal__on(_1264708, _1264710, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1264708, _1264708), tc_HOL_Obool)), _1264712), c_Relation_OId(_1264708))), -(c_Relation_Ototal__on(_1264708, _1264710, _1264712))], (33384 ^ _775828) ^ [_1394612, _1394614, _1394616, _1394618, _1394620, _1394622] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394612, tc_Option_Ooption(_1394614)), c_Map_Orestrict__map(_1394612, _1394614, _1394616, _1394618)), _1394620), _1394622) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1394612, tc_Option_Ooption(_1394614)), c_Map_Orestrict__map(_1394612, _1394614, _1394616, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394612, tc_HOL_Obool)), _1394618), hAPP(hAPP(c_Set_Oinsert(_1394612), _1394620), c_Orderings_Obot__class_Obot(tc_fun(_1394612, tc_HOL_Obool)))))), _1394620), _1394622))], (5774 ^ _775828) ^ [_867866, _867868, _867870] : [5775 ^ _775828 : [(5776 ^ _775828) ^ [_867916] : [c_Natural_Oevaln(_867866, _867868, _867916, _867870)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_867866), _867868), _867870)))], (34573 ^ _775828) ^ [_1420660, _1420662, _1420664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420660, _1420660), tc_HOL_Obool)), c_Relation_OId(_1420660)), _1420662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420660, _1420660), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1420660, _1420660, _1420660), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1420660, _1420660), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1420660, _1420664)), _1420662)), _1420664)), _1420662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420660, _1420660), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1420660, _1420664)), _1420662)))], (11304 ^ _775828) ^ [_961356, _961358] : [class_Groups_Olinordered__ab__group__add(_961356), 11307 ^ _775828 : [(11314 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961356), _961358), c_Groups_Ozero__class_Ozero(_961356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961356), _961358), _961358)), c_Groups_Ozero__class_Ozero(_961356))))], (11308 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961356), _961358), _961358)), c_Groups_Ozero__class_Ozero(_961356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961356), _961358), c_Groups_Ozero__class_Ozero(_961356))))]]], (44246 ^ _775828) ^ [_1642737, _1642739, _1642741] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642737, tc_fun(_1642739, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1642737, tc_HOL_Obool))), _1642741) = c_Orderings_Otop__class_Otop(tc_fun(_1642739, tc_HOL_Obool)))], (5833 ^ _775828) ^ [_868743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _868743), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38332 ^ _775828) ^ [_1503830, _1503832] : [class_Groups_Oordered__ab__group__add(_1503830), -(hAPP(c_Set_Oimage(_1503830, _1503830, c_Groups_Ouminus__class_Ouminus(_1503830)), hAPP(c_SetInterval_Oord__class_OlessThan(_1503830), _1503832)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503830), hAPP(c_Groups_Ouminus__class_Ouminus(_1503830), _1503832)))], (39411 ^ _775828) ^ [_1527349, _1527351, _1527353, _1527355, _1527357] : [-(hAPP(c_Relation_Oconverse(_1527349, _1527351), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527353, tc_fun(tc_prod(_1527349, _1527351), tc_HOL_Obool)), _1527355), _1527357)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527353, tc_fun(tc_prod(_1527351, _1527349), tc_HOL_Obool)), _1527355), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527349, _1527351), tc_HOL_Obool), tc_fun(tc_prod(_1527351, _1527349), tc_HOL_Obool), _1527353), c_Relation_Oconverse(_1527349, _1527351)), _1527357)))], (3754 ^ _775828) ^ [_832868, _832870] : [_832870 = _832868, -(c_Relation_OField(_832870) = c_Relation_OField(_832868))], (12773 ^ _775828) ^ [_986679, _986681] : [class_Int_Oring__char__0(_986679), hBOOL(hAPP(hAPP(c_member(_986679), _986681), c_Int_Oring__1__class_OInts(_986679))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986679), c_Groups_Oone__class_Oone(_986679)), _986681)), _986681) = c_Groups_Ozero__class_Ozero(_986679)], (7937 ^ _775828) ^ [_902888, _902890] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902888)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _902890)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _902888), _902890)))], (2478 ^ _775828) ^ [_812310, _812312, _812314, _812316] : [-(c_Divides_Odivmod__nat(_812316, _812312) = c_Divides_Odivmod__nat(_812314, _812310)), _812316 = _812314, _812312 = _812310], (21624 ^ _775828) ^ [_1150139, _1150141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150139)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150141))), -(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(_1150141))), 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), _1150139)), c_Int_Onat))))))], (19830 ^ _775828) ^ [_1116280, _1116282] : [class_Int_Onumber__ring(_1116280), class_Rings_Olinordered__idom(_1116280), 19837 ^ _775828 : [(19844 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1116282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116280), c_Groups_Oone__class_Oone(_1116280)), hAPP(c_Int_Onumber__class_Onumber__of(_1116280), _1116282))))], (19838 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116280), c_Groups_Oone__class_Oone(_1116280)), hAPP(c_Int_Onumber__class_Onumber__of(_1116280), _1116282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1116282)))]]], (4660 ^ _775828) ^ [_847033, _847035] : [_847035 = _847033, -(c_SetInterval_Oord__class_OlessThan(_847035) = c_SetInterval_Oord__class_OlessThan(_847033))], (50094 ^ _775828) ^ [_1781907, _1781909] : [class_Orderings_Olinorder(_1781907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1781907), _1781909)), 50101 ^ _775828 : [(50106 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1781907), c_List_Olinorder__class_Osorted__list__of__set(_1781907, _1781909))))], (50104 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781907, c_List_Olinorder__class_Osorted__list__of__set(_1781907, _1781909)))], (50102 ^ _775828) ^ [] : [-(hAPP(c_List_Oset(_1781907), c_List_Olinorder__class_Osorted__list__of__set(_1781907, _1781909)) = _1781909)]]], (27130 ^ _775828) ^ [_1255134, _1255136] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255134))), _1255136)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255134), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255136))))], (48249 ^ _775828) ^ [_1741790, _1741792, _1741794, _1741796, _1741798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1741790, _1741790)), hAPP(hAPP(c_Product__Type_OPair(_1741790, _1741790), _1741792), _1741794)), _1741796)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741790), tc_List_Olist(_1741790))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741790), tc_List_Olist(_1741790)), hAPP(hAPP(c_List_Olist_OCons(_1741790), _1741792), _1741798)), hAPP(hAPP(c_List_Olist_OCons(_1741790), _1741794), _1741798))), c_List_Olistrel1(_1741790, _1741796))))], (50259 ^ _775828) ^ [_1785820, _1785822] : [_1785822 = c_List_Olist_ONil(_1785820), -(c_List_Olist_ONil(_1785820) = hAPP(c_List_Orev(_1785820), _1785822))], (45454 ^ _775828) ^ [_1671414, _1671416, _1671418] : [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)), _1671414), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1671416), _1671418)))), 45457 ^ _775828 : [(45464 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1671416), _1671418))), -(c_Smallcheck_Osmall_H(_1671414, _1671416, _1671418) = 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(_1671414, _1671416, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1671418), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1671414, _1671418)))], (45458 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1671416), _1671418)), -(c_Smallcheck_Osmall_H(_1671414, _1671416, _1671418) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (30778 ^ _775828) ^ [_1338733, _1338735, _1338737, _1338739] : [_1338733 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1338735, _1338737), 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)), _1338739))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338735), _1338733)))], (21510 ^ _775828) ^ [_1148212, _1148214, _1148216, _1148218] : [class_Fields_Ofield__inverse__zero(_1148212), class_Int_Onumber(_1148212), 21517 ^ _775828 : [(21518 ^ _775828) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148212), _1148214), hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216)) = _1148218, 21521 ^ _775828 : [(21528 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216) = c_Groups_Ozero__class_Ozero(_1148212), -(_1148218 = c_Groups_Ozero__class_Ozero(_1148212))], (21522 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216) = c_Groups_Ozero__class_Ozero(_1148212)), -(_1148214 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148212), _1148218), hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216)))]]], (21534 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148212), _1148214), hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216)) = _1148218), 21537 ^ _775828 : [(21540 ^ _775828) ^ [] : [_1148214 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148212), _1148218), hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216))], (21538 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216) = c_Groups_Ozero__class_Ozero(_1148212)]], 21541 ^ _775828 : [(21544 ^ _775828) ^ [] : [_1148218 = c_Groups_Ozero__class_Ozero(_1148212)], (21542 ^ _775828) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1148212), _1148216) = c_Groups_Ozero__class_Ozero(_1148212))]]]]], (35331 ^ _775828) ^ [_1438491, _1438493, _1438495, _1438497, _1438499] : [35334 ^ _775828 : [(35337 ^ _775828) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1438493, _1438495, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1438493)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1438493), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1438493), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 35333 ^ [_1438491, _1438493, _1438495, _1438497, _1438499]))), _1438497), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1438493), hAPP(_1438499, 35332 ^ [_1438491, _1438493, _1438495, _1438497, _1438499])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1438493), tc_HOL_Obool))))], (35335 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1438491, 35332 ^ [_1438491, _1438493, _1438495, _1438497, _1438499]), 35333 ^ [_1438491, _1438493, 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c_Groups_Ozero__class_Ozero(_927913))))]]]]], (16607 ^ _775828) ^ [_1058334, _1058336, _1058338, _1058340] : [class_Rings_Ocomm__semiring__1(_1058334), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1058334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058334), _1058336), _1058338)), _1058340) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058334), hAPP(hAPP(c_Power_Opower__class_Opower(_1058334), _1058336), _1058340)), hAPP(hAPP(c_Power_Opower__class_Opower(_1058334), _1058338), _1058340)))], (498 ^ _775828) ^ [_783309, _783311, _783313, _783315, _783317, _783319] : [-(c_Big__Operators_Osemilattice__big(_783317, _783313, _783309)), c_Big__Operators_Osemilattice__big(_783319, _783315, _783311), _783319 = _783317, _783315 = _783313, _783311 = _783309], (37314 ^ _775828) ^ [_1479559, _1479561, _1479563, _1479565] : [class_Groups_Ocomm__monoid__add(_1479559), 37317 ^ _775828 : [(37324 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479561), _1479563))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479561, _1479559), _1479565), _1479563) = c_Groups_Ozero__class_Ozero(_1479559))], (37318 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1479561), _1479563)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479561, _1479559), _1479565), _1479563) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1479559, _1479561, c_Groups_Oplus__class_Oplus(_1479559)), _1479565), c_Groups_Ozero__class_Ozero(_1479559)), _1479563))]]], (29577 ^ _775828) ^ [_1312632, _1312634, _1312636] : [-(hBOOL(hAPP(hAPP(c_member(_1312632), _1312634), _1312636))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312632, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1312632), _1312634), _1312636)), hAPP(hAPP(c_Set_Oinsert(_1312632), _1312634), c_Orderings_Obot__class_Obot(tc_fun(_1312632, tc_HOL_Obool)))) = _1312636)], (7431 ^ _775828) ^ [_894442, _894444] : [_894444 = c_Option_Ooption_ONone(_894442), -(c_Option_Ois__none(_894442, _894444))], (38196 ^ _775828) ^ [_1500807, _1500809, _1500811, _1500813] : [-(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), _1500807), _1500809)), 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), _1500811), _1500813)), 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), _1500807), _1500811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1500809), _1500813))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1500807), _1500813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1500809), _1500811)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (3456 ^ _775828) ^ [_828221, _828223] : [_828223 = _828221, -(c_Nitpick_ORep__Frac(_828223) = c_Nitpick_ORep__Frac(_828221))], (46640 ^ _775828) ^ [_1702834, _1702836, _1702838] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702834)), c_List_Osublist(_1702834, _1702836, _1702838)) = 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(_1702834)), _1702836)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1702838)))))], (27869 ^ _775828) ^ [_1274188, _1274190, _1274192, _1274194] : [c_Wellfounded_Owf(_1274188, _1274190), -(c_Wellfounded_Owf(_1274192, hAPP(hAPP(c_Relation_Oinv__image(_1274188, _1274192), _1274190), _1274194)))], (25196 ^ _775828) ^ [_1220429] : [c_Nat__Transfer_Onat__set(_1220429), 25199 ^ _775828 : [(25200 ^ _775828) ^ [_1220495] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1220495), _1220429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220495)))]]], (47247 ^ _775828) ^ [_1718327, _1718329, _1718331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718327), tc_List_Olist(_1718327))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718327), tc_List_Olist(_1718327)), c_List_Olist_ONil(_1718327)), _1718329)), c_List_Olistrel(_1718327, _1718331))), -(_1718329 = c_List_Olist_ONil(_1718327))], (28465 ^ _775828) ^ [_1287142, _1287144, _1287146] : [class_Lattices_Osemilattice__sup(_1287142), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287142), _1287144), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287142), _1287144), _1287146))))], (4078 ^ _775828) ^ [_838086, _838088] : [_838088 = _838086, -(c_Random_Orange(_838088) = c_Random_Orange(_838086))], (39082 ^ _775828) ^ [_1519875, _1519877, _1519879, _1519881, _1519883, _1519885] : [c_Fun_Oinj__on(_1519875, _1519877, _1519879, _1519881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1519875, _1519877, _1519879), _1519881)), _1519883)), c_Fun_Oinj__on(_1519877, _1519875, _1519885, _1519883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519875, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1519877, _1519875, _1519885), _1519883)), _1519881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519875), _1519881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519877), _1519883)), -(hAPP(c_Finite__Set_Ocard(_1519875), _1519881) = hAPP(c_Finite__Set_Ocard(_1519877), _1519883))], (30838 ^ _775828) ^ [_1339847, _1339849, _1339851] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339847), _1339849)), -(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(_1339847), _1339851)), hAPP(c_Finite__Set_Ocard(_1339847), _1339849))), hAPP(c_Finite__Set_Ocard(_1339847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339847, tc_HOL_Obool)), _1339851), _1339849)))))], (25028 ^ _775828) ^ [_1217077, _1217079, _1217081, _1217083] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1217077, _1217079, _1217081, c_Code__Numeral_OSuc__code__numeral(_1217083)) = hAPP(hAPP(_1217081, _1217083), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1217077, _1217079, _1217081, _1217083)))], (14536 ^ _775828) ^ [_1019247, _1019249, _1019251, _1019253] : [class_Divides_Osemiring__div(_1019247), -(_1019249 = c_Groups_Ozero__class_Ozero(_1019247)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019247), _1019249), _1019251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019247), _1019249), _1019253)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019247), _1019251), _1019253))], (36821 ^ _775828) ^ [_1467574, _1467576] : [class_Orderings_Olinorder(_1467574), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467574, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1467574), _1467576)), hAPP(hAPP(c_Set_Oinsert(_1467574), _1467576), c_Orderings_Obot__class_Obot(tc_fun(_1467574, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1467574), _1467576))], (49049 ^ _775828) ^ [_1760720, _1760722, _1760724] : [49050 ^ _775828 : [(49051 ^ _775828) ^ [_1760809, _1760811] : [_1760722 = hAPP(hAPP(c_List_Olist_OCons(_1760720), _1760811), _1760809)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760720), tc_List_Olist(_1760720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760720), tc_List_Olist(_1760720)), c_List_Olist_ONil(_1760720)), _1760722)), c_List_Olexord(_1760720, _1760724))))], (33827 ^ _775828) ^ [_1404424, _1404426] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404424, tc_HOL_Obool)), _1404426), _1404426) = _1404426)], (24350 ^ _775828) ^ [_1203144, _1203146] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1203144), hAPP(c_Nat_OSuc, _1203146)) = 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)), _1203146)), _1203144))], (32765 ^ _775828) ^ [_1381630, _1381632, _1381634, _1381636] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381630), _1381632)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381634), _1381636)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1381630, _1381634)), c_Sum__Type_OPlus(_1381630, _1381634, _1381632, _1381636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1381630), _1381632)), hAPP(c_Finite__Set_Ocard(_1381634), _1381636)))], (36841 ^ _775828) ^ [_1467933, _1467935, _1467937] : [class_Orderings_Olinorder(_1467933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467933), _1467935), _1467937)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467933, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1467933), _1467935)), c_SetInterval_Oord__class_OatLeastAtMost(_1467933, _1467935, _1467937)) = hAPP(c_SetInterval_Oord__class_OatMost(_1467933), _1467937))], (37448 ^ _775828) ^ [_1483103, _1483105, _1483107, _1483109] : [-(hBOOL(hAPP(hAPP(c_member(_1483103), _1483105), _1483107))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483103, tc_Nat_Onat), _1483109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1483103, tc_HOL_Obool)), _1483107), hAPP(hAPP(c_Set_Oinsert(_1483103), _1483105), c_Orderings_Obot__class_Obot(tc_fun(_1483103, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483103, tc_Nat_Onat), _1483109), _1483107))], (3014 ^ _775828) ^ [_821118, _821120, _821122, _821124, _821126, _821128] : [-(c_FunDef_Oin__rel(_821128, _821124, _821120) = c_FunDef_Oin__rel(_821126, _821122, _821118)), _821128 = _821126, _821124 = _821122, _821120 = _821118], (8503 ^ _775828) ^ [_912348, _912350, _912352] : [class_Rings_Olinordered__semidom(_912348), 8506 ^ _775828 : [(8513 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _912350), _912352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912348), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_912348), _912350)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_912348), _912352))))], (8507 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912348), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_912348), _912350)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_912348), _912352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _912350), _912352)))]]], (9419 ^ _775828) ^ [_927068, _927070, _927072] : [class_Rings_Oordered__cancel__semiring(_927068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927068), c_Groups_Ozero__class_Ozero(_927068)), _927070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927068), c_Groups_Ozero__class_Ozero(_927068)), _927072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927068), c_Groups_Ozero__class_Ozero(_927068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927068), _927070), _927072))))], (16389 ^ _775828) ^ [_1054450, _1054452, _1054454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1054452), 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), _1054452), _1054454))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1054450))), _1054454)))], (26872 ^ _775828) ^ [_1250603, _1250605, _1250607] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250603), _1250605)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250603), _1250607)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1250603), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1250605, _1250607))))], (13456 ^ _775828) ^ [_999186, _999188, _999190, _999192, _999194, _999196] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_999186, _999188, _999190), _999192, _999194, _999196), 13461 ^ _775828 : [(13464 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_999188, _999192, _999194, _999196))], (13462 ^ _775828) ^ [] : [-(hBOOL(hAPP(_999186, _999192)))]], 13465 ^ _775828 : [(13468 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_999190, _999192, _999194, _999196))], (13466 ^ _775828) ^ [] : [hBOOL(hAPP(_999186, _999192))]]], (40654 ^ _775828) ^ [_1557352] : [-(c_Equiv__Relations_Oequivp(_1557352, c_fequal))], (43692 ^ _775828) ^ [_1630412, _1630414, _1630416, _1630418] : [class_Lattices_Osemilattice__inf(_1630412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630412), _1630414)), hBOOL(hAPP(hAPP(c_member(_1630412), _1630416), _1630414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630412), hAPP(hAPP(c_Finite__Set_Ofold(_1630412, _1630412, c_Lattices_Osemilattice__inf__class_Oinf(_1630412)), _1630418), _1630414)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1630412), _1630416), _1630418))))], (12614 ^ _775828) ^ [_983925, _983927] : [class_Rings_Olinordered__idom(_983925), 12617 ^ _775828 : [(12624 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983925), c_Groups_Ozero__class_Ozero(_983925)), _983927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983925), c_Groups_Ozero__class_Ozero(_983925)), c_Groups_Osgn__class_Osgn(_983925, _983927))))], (12618 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983925), c_Groups_Ozero__class_Ozero(_983925)), c_Groups_Osgn__class_Osgn(_983925, _983927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983925), c_Groups_Ozero__class_Ozero(_983925)), _983927)))]]], (28824 ^ _775828) ^ [_1294388, _1294390] : [28825 ^ _775828 : [(28826 ^ _775828) ^ [_1294434] : [hBOOL(hAPP(_1294388, _1294434))]], -(hBOOL(hAPP(_1294388, c_Hilbert__Choice_OEps(_1294390, _1294388))))], (30810 ^ _775828) ^ [_1339315, _1339317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1339315), _1339317))), 30813 ^ _775828 : [(30816 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339315), _1339317)))], (30814 ^ _775828) ^ [] : [_1339317 = c_Orderings_Obot__class_Obot(tc_fun(_1339315, tc_HOL_Obool))]]], (17193 ^ _775828) ^ [_1069823, _1069825, _1069827, _1069829, _1069831] : [class_Groups_Oordered__ab__group__add__abs(_1069823), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069823), hAPP(c_Groups_Oabs__class_Oabs(_1069823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069823), _1069825), _1069827)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069823), _1069829), _1069831)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069823), hAPP(c_Groups_Oabs__class_Oabs(_1069823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069823), _1069825), _1069829))), hAPP(c_Groups_Oabs__class_Oabs(_1069823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1069823), _1069827), _1069831))))))], (32435 ^ _775828) ^ [_1375126, _1375128, _1375130] : [class_Orderings_Olinorder(_1375126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375126), _1375128)), hBOOL(hAPP(hAPP(c_member(_1375126), _1375130), _1375128)), 32446 ^ _775828 : [(32453 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375126, tc_HOL_Obool)), _1375128), hAPP(hAPP(c_Set_Oinsert(_1375126), _1375130), c_Orderings_Obot__class_Obot(tc_fun(_1375126, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375126, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1375126, _1375128) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375126), _1375130), c_Big__Operators_Olinorder__class_OMax(_1375126, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375126, tc_HOL_Obool)), _1375128), hAPP(hAPP(c_Set_Oinsert(_1375126), _1375130), c_Orderings_Obot__class_Obot(tc_fun(_1375126, tc_HOL_Obool)))))))], (32447 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375126, tc_HOL_Obool)), _1375128), hAPP(hAPP(c_Set_Oinsert(_1375126), _1375130), c_Orderings_Obot__class_Obot(tc_fun(_1375126, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375126, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1375126, _1375128) = _1375130)]]], (48667 ^ _775828) ^ [_1751964, _1751966, _1751968] : [_1751968 = c_List_Olist_ONil(_1751964), -(hAPP(c_List_Orotate(_1751964, _1751966), _1751968) = c_List_Olist_ONil(_1751964))], (5499 ^ _775828) ^ [_862779, _862781, _862783] : [c_Hoare__Mirabelle_Otriple__valid(_862779, hAPP(c_Nat_OSuc, _862781), _862783), -(c_Hoare__Mirabelle_Otriple__valid(_862779, _862781, _862783))], (45787 ^ _775828) ^ [_1679489, _1679491, _1679493] : [-(c_Map_Odom(_1679489, _1679491, c_Map_Omap__of(_1679489, _1679491, _1679493)) = hAPP(c_Set_Oimage(tc_prod(_1679489, _1679491), _1679489, c_Product__Type_Ofst(_1679489, _1679491)), hAPP(c_List_Oset(tc_prod(_1679489, _1679491)), _1679493)))], (26992 ^ _775828) ^ [_1252714, _1252716] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252714)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252716))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252714), _1252716)))], (29217 ^ _775828) ^ [_1305555, _1305557, _1305559, _1305561] : [_1305561 = c_Orderings_Obot__class_Obot(tc_fun(_1305555, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1305555, _1305557, _1305559), _1305561) = c_Orderings_Obot__class_Obot(tc_fun(_1305557, tc_HOL_Obool)))], (44166 ^ _775828) ^ [_1639888, _1639890, _1639892, _1639894, _1639896, _1639898] : [hBOOL(hAPP(hAPP(c_member(_1639888), _1639890), _1639892)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639888, tc_fun(_1639894, tc_HOL_Obool)), _1639892), hAPP(hAPP(c_COMBB(tc_fun(_1639894, tc_HOL_Obool), tc_fun(_1639894, tc_HOL_Obool), _1639888), hAPP(c_Set_Oinsert(_1639894), _1639896)), _1639898)) = hAPP(hAPP(c_Set_Oinsert(_1639894), _1639896), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639888, tc_fun(_1639894, tc_HOL_Obool)), _1639892), _1639898)))], (12518 ^ _775828) ^ [_982414] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _982414)), _982414) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45935 ^ _775828) ^ [_1682876] : [c_List_Onat__list(_1682876), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1682876)))], (51308 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (34031 ^ _775828) ^ [_1408842, _1408844, _1408846, _1408848] : [class_Lattices_Osemilattice__inf(_1408842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408842), _1408844), _1408846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408842), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408842), _1408848), _1408844)), _1408846)))], (27561 ^ _775828) ^ [_1265648, _1265650, _1265652, _1265654] : [hBOOL(hAPP(hAPP(c_member(_1265648), _1265650), c_SetInterval_Oord_OatLeast(_1265648, _1265652, _1265654))), -(hBOOL(hAPP(hAPP(_1265652, _1265654), _1265650)))], (44665 ^ _775828) ^ [_1654155, _1654157, _1654159] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654155, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654155, tc_HOL_Obool), _1654157)), _1654159) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654155, tc_HOL_Obool), tc_fun(_1654155, tc_HOL_Obool)), _1654157), hAPP(hAPP(c_COMBC(tc_fun(_1654155, tc_HOL_Obool), tc_fun(_1654155, tc_HOL_Obool), tc_fun(_1654155, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654155, tc_HOL_Obool))), _1654159)))], (12576 ^ _775828) ^ [_983286] : [class_Rings_Oring__1(_983286), -(hBOOL(hAPP(hAPP(c_member(_983286), c_Groups_Oone__class_Oone(_983286)), c_Int_Oring__1__class_OInts(_983286))))], (37010 ^ _775828) ^ [_1472313, _1472315, _1472317] : [class_Groups_Ocomm__monoid__add(_1472313), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472315, _1472313), _1472317), c_Orderings_Obot__class_Obot(tc_fun(_1472315, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1472313))], (25100 ^ _775828) ^ [_1218716, _1218718, _1218720, _1218722, _1218724, _1218726] : [-(c_Nitpick_Opair__box_OPairBox(_1218716, _1218718, _1218720, _1218722) = c_Nitpick_Opair__box_OPairBox(_1218716, _1218718, _1218724, _1218726)), _1218720 = _1218724, _1218722 = _1218726], (38398 ^ _775828) ^ [_1505357, _1505359, _1505361, _1505363] : [hBOOL(hAPP(hAPP(c_member(_1505357), _1505359), c_Map_Odom(_1505357, _1505361, _1505363))), hAPP(_1505363, _1505359) = c_Option_Ooption_ONone(_1505361)], (24677 ^ _775828) ^ [_1209410] : [-(c_Nitpick_Oone__frac(_1209410) = c_Nitpick_OAbs__Frac(_1209410, 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))))], (49624 ^ _775828) ^ [_1773620, _1773622] : [class_Orderings_Olinorder(_1773620), -(_1773622 = c_List_Olist_ONil(_1773620)), c_List_Olinorder__class_Osorted(_1773620, _1773622), -(c_List_Olinorder__class_Osorted(_1773620, c_List_Obutlast(_1773620, _1773622)))], (17137 ^ _775828) ^ [_1068681, _1068683] : [class_Rings_Olinordered__idom(_1068681), -(hAPP(c_Groups_Oabs__class_Oabs(_1068681), _1068683) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068681), _1068683), c_Groups_Osgn__class_Osgn(_1068681, _1068683)))], (10628 ^ _775828) ^ [_949119, _949121, _949123, _949125, _949127] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_949119), 10631 ^ _775828 : [(10632 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949121), _949125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949123), _949127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949121), _949127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949123), _949125)), -(_949121 = _949123), -(_949125 = _949127)], (10642 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949121), _949125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949123), _949127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949121), _949127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949119), _949123), _949125))), 10645 ^ _775828 : [(10648 ^ _775828) ^ [] : [_949125 = _949127], (10646 ^ _775828) ^ [] : [_949121 = _949123]]]]], (10738 ^ _775828) ^ [_951258, _951260] : [class_Groups_Omonoid__mult(_951258), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951258), c_Groups_Oone__class_Oone(_951258)), _951260) = _951260)], (33711 ^ _775828) ^ [_1401879, _1401881, _1401883, _1401885] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401879, tc_HOL_Obool)), _1401881), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401879, tc_HOL_Obool)), _1401883), _1401885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401879, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401879, tc_HOL_Obool)), _1401881), _1401883)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401879, tc_HOL_Obool)), _1401881), _1401885)))], (6885 ^ _775828) ^ [_884810, _884812] : [class_Rings_Olinordered__idom(_884810), 6888 ^ _775828 : [(6895 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _884812), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884810), hAPP(c_Int_Oring__1__class_Oof__int(_884810), _884812)), c_Groups_Ozero__class_Ozero(_884810))))], (6889 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884810), hAPP(c_Int_Oring__1__class_Oof__int(_884810), _884812)), c_Groups_Ozero__class_Ozero(_884810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _884812), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32019 ^ _775828) ^ [_1368103, _1368105] : [class_Orderings_Olinorder(_1368103), -(c_Big__Operators_Olinorder__class_OMax(_1368103, hAPP(hAPP(c_Set_Oinsert(_1368103), _1368105), c_Orderings_Obot__class_Obot(tc_fun(_1368103, tc_HOL_Obool)))) = _1368105)], (15602 ^ _775828) ^ [_1038519, _1038521, _1038523, _1038525, _1038527, _1038529] : [class_Rings_Oring(_1038519), 15605 ^ _775828 : [(15612 ^ _775828) ^ [] : [_1038525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038519), _1038527), _1038521)), _1038523)), _1038529), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), _1038521), _1038523)), _1038525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), _1038527), _1038523)), _1038529))], (15606 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), _1038521), _1038523)), _1038525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), _1038527), _1038523)), _1038529), -(_1038525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038519), _1038527), _1038521)), _1038523)), _1038529))]]], (40491 ^ _775828) ^ [_1552516, _1552518] : [-(c_List_Olex(_1552516, _1552518) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1552516), tc_List_Olist(_1552516)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1552516, _1552518)))], (50387 ^ _775828) ^ [_1788691, _1788693] : [class_Groups_Ocomm__monoid__add(_1788691), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1788691), hAPP(c_List_Orev(_1788691), _1788693)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1788691), _1788693))], (10264 ^ _775828) ^ [_942134, _942136, _942138] : [_942136 = _942138, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942134), _942136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942134), _942138))], (30728 ^ _775828) ^ [_1337818, _1337820, _1337822] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337818), _1337820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1337818, tc_HOL_Obool)), _1337822), _1337820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1337818), _1337822)), hAPP(c_Finite__Set_Ocard(_1337818), _1337820))))], (49236 ^ _775828) ^ [_1764406, _1764408, _1764410, _1764412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764408)), _1764410))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764408)), _1764412))), 49246 ^ _775828 : [(49249 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Onth(_1764408), _1764410), 49245 ^ [_1764406, _1764408, _1764410, _1764412]) = hAPP(hAPP(c_List_Onth(_1764408), _1764412), 49245 ^ [_1764406, _1764408, _1764410, _1764412])], (49247 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49245 ^ [_1764406, _1764408, _1764410, _1764412]), _1764406)))]], -(hAPP(hAPP(c_List_Otake(_1764408), _1764406), _1764410) = hAPP(hAPP(c_List_Otake(_1764408), _1764406), _1764412))], (25359 ^ _775828) ^ [_1223153, _1223155] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1223153)), hAPP(c_Code__Numeral_Oof__nat, _1223155)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223153), _1223155)))], (14199 ^ _775828) ^ [_1013130, _1013132] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1013130, _1013132))), -(hBOOL(hAPP(c_Com_OWT, _1013132)))], (44371 ^ _775828) ^ [_1646346, _1646348, _1646350, _1646352, _1646354] : [-(_1646346 = c_Orderings_Obot__class_Obot(tc_fun(_1646348, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646350, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646348, tc_fun(_1646350, tc_HOL_Obool)), _1646346), _1646352)), _1646354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646348, tc_fun(_1646350, tc_HOL_Obool)), _1646346), hAPP(hAPP(c_COMBC(_1646348, tc_fun(_1646350, tc_HOL_Obool), tc_fun(_1646350, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1646350, tc_HOL_Obool), tc_fun(tc_fun(_1646350, tc_HOL_Obool), tc_fun(_1646350, tc_HOL_Obool)), _1646348), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646350, tc_HOL_Obool))), _1646352)), _1646354)))], (40075 ^ _775828) ^ [_1544133] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544133), c_Orderings_Otop__class_Otop(tc_fun(_1544133, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1544133)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1544133), tc_HOL_Obool)))))], (22746 ^ _775828) ^ [_1171581, _1171583, _1171585, _1171587] : [class_Fields_Ofield__inverse__zero(_1171581), 22749 ^ _775828 : [(22750 ^ _775828) ^ [] : [_1171583 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171581), _1171585), _1171587), 22753 ^ _775828 : [(22760 ^ _775828) ^ [] : [_1171587 = c_Groups_Ozero__class_Ozero(_1171581), -(_1171583 = c_Groups_Ozero__class_Ozero(_1171581))], (22754 ^ _775828) ^ [] : [-(_1171587 = c_Groups_Ozero__class_Ozero(_1171581)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171581), _1171583), _1171587) = _1171585)]]], (22766 ^ _775828) ^ [] : [-(_1171583 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171581), _1171585), _1171587)), 22769 ^ _775828 : [(22772 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171581), _1171583), _1171587) = _1171585], (22770 ^ _775828) ^ [] : [_1171587 = c_Groups_Ozero__class_Ozero(_1171581)]], 22773 ^ _775828 : [(22776 ^ _775828) ^ [] : [_1171583 = c_Groups_Ozero__class_Ozero(_1171581)], (22774 ^ _775828) ^ [] : [-(_1171587 = c_Groups_Ozero__class_Ozero(_1171581))]]]]], (39864 ^ _775828) ^ [_1539298, _1539300, _1539302, _1539304, _1539306, _1539308, _1539310, _1539312, _1539314] : [c_Equiv__Relations_Oequiv(_1539298, _1539300, _1539302), c_Equiv__Relations_Oequiv(_1539304, _1539306, _1539308), c_Equiv__Relations_Ocongruent2(_1539298, _1539304, tc_fun(_1539310, tc_HOL_Obool), _1539302, _1539308, _1539312), hBOOL(hAPP(hAPP(c_member(_1539304), _1539314), _1539306)), -(c_Equiv__Relations_Ocongruent(_1539298, tc_fun(_1539310, tc_HOL_Obool), _1539302, hAPP(hAPP(c_COMBB(tc_fun(_1539304, tc_fun(_1539310, tc_HOL_Obool)), tc_fun(_1539310, tc_HOL_Obool), _1539298), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539304, tc_fun(_1539310, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1539304, _1539304, _1539308), hAPP(hAPP(c_Set_Oinsert(_1539304), _1539314), c_Orderings_Obot__class_Obot(tc_fun(_1539304, tc_HOL_Obool)))))), _1539312)))], (23590 ^ _775828) ^ [_1188650, _1188652, _1188654, _1188656, _1188658, _1188660] : [hAPP(c_Product__Type_Oapsnd(_1188650, _1188652, _1188654, _1188656), _1188658) = hAPP(c_Product__Type_Oapsnd(_1188650, _1188652, _1188654, _1188660), _1188658), -(hAPP(_1188656, hAPP(c_Product__Type_Osnd(_1188654, _1188650), _1188658)) = hAPP(_1188660, hAPP(c_Product__Type_Osnd(_1188654, _1188650), _1188658)))], (41823 ^ _775828) ^ [_1585338, _1585340, _1585342] : [class_Groups_Oab__semigroup__mult(_1585338), -(_1585340 = c_Orderings_Obot__class_Obot(tc_fun(_1585338, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585338), _1585340)), -(hBOOL(hAPP(hAPP(c_member(_1585338), _1585342), _1585340))), -(hAPP(c_Finite__Set_Ofold1(_1585338, c_Groups_Otimes__class_Otimes(_1585338)), hAPP(hAPP(c_Set_Oinsert(_1585338), _1585342), _1585340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1585338), _1585342), hAPP(c_Finite__Set_Ofold1(_1585338, c_Groups_Otimes__class_Otimes(_1585338)), _1585340)))], (10136 ^ _775828) ^ [_939922, _939924, _939926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939922), _939924)), _939926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939924), _939926)))], (9363 ^ _775828) ^ [_926048, _926050, _926052] : [class_Rings_Oordered__ring(_926048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926048), _926050), c_Groups_Ozero__class_Ozero(_926048))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926048), _926052), c_Groups_Ozero__class_Ozero(_926048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926048), c_Groups_Ozero__class_Ozero(_926048)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926048), _926050), _926052))))], (13216 ^ _775828) ^ [_994553, _994555, _994557, _994559, _994561, _994563] : [-(c_Com_Ocom_OCond(_994553, _994555, _994557) = c_Com_Ocom_OCond(_994559, _994561, _994563)), _994553 = _994559, _994555 = _994561, _994557 = _994563], (43706 ^ _775828) ^ [_1630679, _1630681, _1630683, _1630685] : [class_Orderings_Olinorder(_1630679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630679), _1630681)), hBOOL(hAPP(hAPP(c_member(_1630679), _1630683), _1630681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630679), hAPP(hAPP(c_Finite__Set_Ofold(_1630679, _1630679, c_Orderings_Oord__class_Omin(_1630679)), _1630685), _1630681)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1630679), _1630683), _1630685))))], (50367 ^ _775828) ^ [_1788260, _1788262, _1788264] : [-(hAPP(c_List_Orev(_1788260), hAPP(hAPP(c_List_Oappend(_1788260), _1788262), _1788264)) = hAPP(hAPP(c_List_Oappend(_1788260), hAPP(c_List_Orev(_1788260), _1788264)), hAPP(c_List_Orev(_1788260), _1788262)))], (5170 ^ _775828) ^ [_854926, _854928] : [_854928 = _854926, -(c_Groups_Ozero__class_Ozero(_854928) = c_Groups_Ozero__class_Ozero(_854926))], (36873 ^ _775828) ^ [_1468626, _1468628, _1468630, _1468632] : [class_Rings_Ocomm__semiring__1(_1468626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1468626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468626), c_Groups_Oone__class_Oone(_1468626)), c_Groups_Oone__class_Oone(_1468626))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468626), hAPP(hAPP(c_COMBB(_1468626, _1468626, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1468626), _1468628)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1468626, _1468626), hAPP(hAPP(c_COMBB(_1468626, tc_fun(_1468626, _1468626), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1468626)), c_Nat_Osemiring__1__class_Oof__nat(_1468626))), _1468630))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468632))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1468626), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468626), _1468632)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468626), _1468628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468626), _1468628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1468626), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468626), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1468632), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1468630)))))], (13114 ^ _775828) ^ [_992656, _992658, _992660, _992662, _992664] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_992656, _992658, _992660)), _992662), _992664)), 13119 ^ _775828 : [(13122 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_992658), _992662), _992664)))], (13120 ^ _775828) ^ [] : [-(hBOOL(hAPP(_992656, _992662)))]], 13123 ^ _775828 : [(13126 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_992660), _992662), _992664)))], (13124 ^ _775828) ^ [] : [hBOOL(hAPP(_992656, _992662))]]], (49529 ^ _775828) ^ [_1771290, _1771292] : [c_List_Otranspose(_1771290, _1771292) = c_List_Olist_ONil(tc_List_Olist(_1771290)), 49532 ^ _775828 : [(49533 ^ _775828) ^ [_1771385] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771290)), _1771385), hAPP(c_List_Oset(tc_List_Olist(_1771290)), _1771292))), -(_1771385 = c_List_Olist_ONil(_1771290))]]], (43360 ^ _775828) ^ [_1623221, _1623223, _1623225, _1623227] : [class_Groups_Ocomm__monoid__mult(_1623221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623223), _1623225)), 43370 ^ _775828 : [(43373 ^ _775828) ^ [] : [hAPP(_1623227, 43369 ^ [_1623221, _1623223, _1623225, _1623227]) = c_Groups_Oone__class_Oone(_1623221)], (43371 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623223), 43369 ^ [_1623221, _1623223, _1623225, _1623227]), _1623225)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1623221, _1623223, c_Groups_Otimes__class_Otimes(_1623221)), _1623227), c_Groups_Oone__class_Oone(_1623221)), _1623225) = c_Groups_Oone__class_Oone(_1623221))], (48767 ^ _775828) ^ [_1754071, _1754073, _1754075, _1754077, _1754079, _1754081, _1754083] : [-(hAPP(c_List_Ofoldl(_1754071, _1754073, _1754075, _1754077), hAPP(hAPP(c_List_Omap(_1754079, _1754073), _1754081), _1754083)) = hAPP(c_List_Ofoldl(_1754071, _1754079, hAPP(hAPP(c_COMBC(_1754071, tc_fun(_1754079, _1754073), tc_fun(_1754079, _1754071)), hAPP(hAPP(c_COMBB(tc_fun(_1754073, _1754071), tc_fun(tc_fun(_1754079, _1754073), tc_fun(_1754079, _1754071)), _1754071), c_COMBB(_1754073, _1754071, _1754079)), _1754075)), _1754081), _1754077), _1754083))], (9433 ^ _775828) ^ [_927323, _927325, _927327] : [class_Rings_Olinordered__ring__strict(_927323), 9436 ^ _775828 : [(9451 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927323), _927325), _927327)), c_Groups_Ozero__class_Ozero(_927323)))), 9452 ^ _775828 : [(9459 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), _927325), c_Groups_Ozero__class_Ozero(_927323))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), c_Groups_Ozero__class_Ozero(_927323)), _927327))], (9453 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), c_Groups_Ozero__class_Ozero(_927323)), _927325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), _927327), c_Groups_Ozero__class_Ozero(_927323)))]]], (9437 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927323), _927325), _927327)), c_Groups_Ozero__class_Ozero(_927323))), 9442 ^ _775828 : [(9445 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), _927327), c_Groups_Ozero__class_Ozero(_927323))))], (9443 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), c_Groups_Ozero__class_Ozero(_927323)), _927325)))]], 9446 ^ _775828 : [(9449 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), c_Groups_Ozero__class_Ozero(_927323)), _927327)))], (9447 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927323), _927325), c_Groups_Ozero__class_Ozero(_927323))))]]]]], (18209 ^ _775828) ^ [_1088406, _1088408, _1088410, _1088412] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088406, _1088408), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1088410), _1088412))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1088406, _1088408) = _1088412)], (22780 ^ _775828) ^ [_1172075, _1172077, _1172079] : [class_Fields_Olinordered__field(_1172075), -(_1172077 = c_Groups_Ozero__class_Ozero(_1172075)), -(hAPP(c_Groups_Oabs__class_Oabs(_1172075), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172075), _1172079), _1172077)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172075), hAPP(c_Groups_Oabs__class_Oabs(_1172075), _1172079)), hAPP(c_Groups_Oabs__class_Oabs(_1172075), _1172077)))], (2 ^ _775828) ^ [_775855] : [-(_775855 = _775855)], (13254 ^ _775828) ^ [_995173, _995175] : [class_Divides_Osemiring__div(_995173), -(c_Divides_Odiv__class_Omod(_995173, c_Groups_Ozero__class_Ozero(_995173), _995175) = c_Groups_Ozero__class_Ozero(_995173))], (10282 ^ _775828) ^ [_942555, _942557, _942559, _942561] : [class_Rings_Ocomm__semiring__1(_942555), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942555), _942557), _942559)), _942561) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942555), _942557), _942561)), _942559))], (12751 ^ _775828) ^ [_986329, _986331] : [class_Rings_Olinordered__idom(_986329), 12754 ^ _775828 : [(12761 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986329), c_Groups_Ozero__class_Ozero(_986329)), _986331)), -(c_Groups_Osgn__class_Osgn(_986329, _986331) = c_Groups_Oone__class_Oone(_986329))], (12755 ^ _775828) ^ [] : [c_Groups_Osgn__class_Osgn(_986329, _986331) = c_Groups_Oone__class_Oone(_986329), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986329), c_Groups_Ozero__class_Ozero(_986329)), _986331)))]]], (24841 ^ _775828) ^ [_1213172, _1213174, _1213176] : [-(c_Nitpick_Otimes__frac(_1213172, _1213174, _1213176) = hAPP(hAPP(c_Nitpick_Ofrac(_1213172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1213172), _1213174)), hAPP(c_Nitpick_Onum(_1213172), _1213176))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1213172), _1213174)), hAPP(c_Nitpick_Odenom(_1213172), _1213176))))], (51288 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (30365 ^ _775828) ^ [_1330627, _1330629, _1330631, _1330633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330627), _1330629)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330631), hAPP(c_Set_Oimage(_1330627, _1330631, _1330633), _1330629))))], (20456 ^ _775828) ^ [_1127325] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127325), 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, _1127325)))], (43138 ^ _775828) ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159] : [class_Groups_Ocomm__monoid__add(_1617149), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617151), _1617153)), 43148 ^ _775828 : [(43149 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617151), 43147 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159]), _1617153)))], (43154 ^ _775828) ^ [] : [43147 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159] = 43150 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159]], (43158 ^ _775828) ^ [] : [hAPP(_1617157, hAPP(_1617155, 43147 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159])) = c_Groups_Ozero__class_Ozero(_1617149)], (43156 ^ _775828) ^ [] : [-(hAPP(_1617155, 43147 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159]) = hAPP(_1617155, 43150 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159]))], (43152 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617151), 43150 ^ [_1617149, _1617151, _1617153, _1617155, _1617157, _1617159]), _1617153)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1617159, _1617149), _1617157), hAPP(c_Set_Oimage(_1617151, _1617159, _1617155), _1617153)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1617151, _1617149), hAPP(c_Fun_Ocomp(_1617159, _1617149, _1617151, _1617157), _1617155)), _1617153))], (49029 ^ _775828) ^ [_1760180, _1760182, _1760184] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760180)), _1760182), c_List_Olists(_1760180, c_Wellfounded_Oacc(_1760180, _1760184)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760180)), _1760182), c_Wellfounded_Oacc(tc_List_Olist(_1760180), c_List_Olistrel1(_1760180, _1760184)))))], (2198 ^ _775828) ^ [_807934, _807936, _807938, _807940, _807942, _807944, _807946, _807948] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_807948, _807944, _807940, _807936) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_807946, _807942, _807938, _807934)), _807948 = _807946, _807944 = _807942, _807940 = _807938, _807936 = _807934], (51436 ^ _775828) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (46488 ^ _775828) ^ [_1698403, _1698405, _1698407, _1698409, _1698411, _1698413] : [-(c_List_Olistrelp(_1698403, _1698405, hAPP(hAPP(c_List_Olist_OCons(_1698403), _1698407), _1698409), hAPP(hAPP(c_List_Olist_OCons(_1698403), _1698411), _1698413))), hBOOL(hAPP(hAPP(_1698405, _1698407), _1698411)), c_List_Olistrelp(_1698403, _1698405, _1698409, _1698413)], (15071 ^ _775828) ^ [_1028637, _1028639, _1028641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1028637)), 15074 ^ _775828 : [(15075 ^ _775828) ^ [] : [-(_1028639 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028641), _1028637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028637), _1028639)), _1028641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028637), hAPP(c_Nat_OSuc, _1028639))))], (15085 ^ _775828) ^ [] : [_1028639 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028641), _1028637), 15088 ^ _775828 : [(15091 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028637), hAPP(c_Nat_OSuc, _1028639)))))], (15089 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028637), _1028639)), _1028641)))]]]]], (8647 ^ _775828) ^ [_914560, _914562, _914564, _914566] : [class_Orderings_Opreorder(_914560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914560), _914562), _914564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914560), _914564), _914566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914560), _914562), _914566)))], (21660 ^ _775828) ^ [_1151036, _1151038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151036)), hAPP(c_Nat_OSuc, _1151038))), -(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(_1151036))), 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)), _1151038)))))], (16991 ^ _775828) ^ [_1065686, _1065688, _1065690, _1065692] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065686), hAPP(c_Int_Onumber__class_Onumber__of(_1065686), _1065688)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065686), _1065690), _1065692)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065686), hAPP(c_Int_Onumber__class_Onumber__of(_1065686), _1065688)), _1065690)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065686), hAPP(c_Int_Onumber__class_Onumber__of(_1065686), _1065688)), _1065692))), class_Int_Onumber(_1065686), class_Rings_Oring(_1065686)], (13402 ^ _775828) ^ [_998203, _998205] : [-(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, _998203, _998205)), _998205) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _998203), _998205))], (6869 ^ _775828) ^ [_884557, _884559] : [class_Rings_Olinordered__idom(_884557), 6872 ^ _775828 : [(6879 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _884559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884557), c_Groups_Ozero__class_Ozero(_884557)), hAPP(c_Int_Oring__1__class_Oof__int(_884557), _884559))))], (6873 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884557), c_Groups_Ozero__class_Ozero(_884557)), hAPP(c_Int_Oring__1__class_Oof__int(_884557), _884559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _884559)))]]], (26311 ^ _775828) ^ [_1240242, _1240244, _1240246, _1240248] : [class_Divides_Osemiring__div(_1240242), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240242), _1240244), _1240246)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240242), _1240244), _1240248)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240242), _1240246), _1240248)), _1240244) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240242), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240242), _1240246), _1240244)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1240242), _1240248), _1240244)))], (48521 ^ _775828) ^ [_1748881, _1748883, _1748885, _1748887, _1748889] : [-(hAPP(hAPP(c_List_Oappend(_1748881), _1748883), _1748885) = hAPP(hAPP(c_List_Oappend(_1748881), _1748887), _1748889)), 48524 ^ _775828 : [(48527 ^ _775828) ^ [] : [_1748883 = hAPP(hAPP(c_List_Otake(_1748881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748883)), _1748887), _1748885 = hAPP(hAPP(c_List_Oappend(_1748881), hAPP(hAPP(c_List_Odrop(_1748881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748883)), _1748887)), _1748889)], (48525 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748883)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748887))))]], 48532 ^ _775828 : [(48535 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Otake(_1748881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748887)), _1748883) = _1748887, hAPP(hAPP(c_List_Oappend(_1748881), hAPP(hAPP(c_List_Odrop(_1748881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748887)), _1748883)), _1748885) = _1748889], (48533 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748883)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748881)), _1748887)))]]], (23516 ^ _775828) ^ [_1187033, _1187035] : [_1187033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1187033, _1187035) = 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)))], (21618 ^ _775828) ^ [_1150069] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150069)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1150069)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150069)), 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)))))], (18741 ^ _775828) ^ [_1097937, _1097939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1097937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097939), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1097937), _1097939) = 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), _1097937), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1097939)))))], (40698 ^ _775828) ^ [_1558094, _1558096, _1558098, _1558100, _1558102, _1558104] : [c_Typedef_Otype__definition(_1558094, _1558096, _1558098, _1558100, _1558102), hBOOL(hAPP(hAPP(c_member(_1558096), _1558104), _1558102)), -(hAPP(_1558098, hAPP(_1558100, _1558104)) = _1558104)], (29295 ^ _775828) ^ [_1307150, _1307152, _1307154, _1307156, _1307158] : [-(hAPP(c_Relation_ORange(_1307150, _1307152), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1307150, _1307152)), hAPP(hAPP(c_Product__Type_OPair(_1307150, _1307152), _1307154), _1307156)), _1307158)) = hAPP(hAPP(c_Set_Oinsert(_1307152), _1307156), hAPP(c_Relation_ORange(_1307150, _1307152), _1307158)))], (42521 ^ _775828) ^ [_1602652, _1602654] : [42523 ^ _775828 : [(42526 ^ _775828) ^ [] : [hBOOL(hAPP(_1602652, hAPP(c_Int_OAbs__Integ, 42522 ^ [_1602652, _1602654])))], (42524 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42522 ^ [_1602652, _1602654]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1602652, _1602654)))], (20046 ^ _775828) ^ [_1120238, _1120240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120238), _1120240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120238)), c_Int_OBit0(_1120240))))], (26285 ^ _775828) ^ [_1239835, _1239837, _1239839] : [class_Divides_Osemiring__div(_1239835), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239835), _1239837), _1239839)), -(c_Divides_Odiv__class_Omod(_1239835, _1239839, _1239837) = c_Groups_Ozero__class_Ozero(_1239835))], (43598 ^ _775828) ^ [_1628383, _1628385, _1628387, _1628389] : [class_Lattices_Osemilattice__sup(_1628383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628383), _1628385)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628383, _1628383, c_Lattices_Osemilattice__sup__class_Osup(_1628383)), _1628387), hAPP(hAPP(c_Set_Oinsert(_1628383), _1628389), _1628385)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1628383), _1628389), hAPP(hAPP(c_Finite__Set_Ofold(_1628383, _1628383, c_Lattices_Osemilattice__sup__class_Osup(_1628383)), _1628387), _1628385)))], (41374 ^ _775828) ^ [_1575839, _1575841] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575839, _1575841), c_Orderings_Otop__class_Otop(tc_fun(_1575839, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1575841, tc_HOL_Obool), _1575839), c_Orderings_Otop__class_Otop(tc_fun(_1575841, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1575839, _1575841), tc_HOL_Obool)))], (28731 ^ _775828) ^ [_1292397, _1292399, _1292401] : [c_Wellfounded_Owf(_1292397, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292397, _1292397), tc_HOL_Obool)), _1292399), _1292401)), -(c_Wellfounded_Owf(_1292397, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292397, _1292397), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292397, _1292397), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1292397, _1292397, _1292397), _1292399), _1292399)), hAPP(hAPP(c_Relation_Orel__comp(_1292397, _1292397, _1292397), _1292401), _1292399))), _1292401)))], (22322 ^ _775828) ^ [_1163871, _1163873, _1163875, _1163877] : [class_Fields_Olinordered__field(_1163871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163871), c_Groups_Ozero__class_Ozero(_1163871)), _1163873)), 22329 ^ _775828 : [(22336 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163871), _1163875), _1163873)), _1163877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163871), _1163875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163871), _1163877), _1163873))))], (22330 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163871), _1163875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163871), _1163877), _1163873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163871), _1163875), _1163873)), _1163877)))]]], (24815 ^ _775828) ^ [_1212530, _1212532] : [-(c_Random_Olog(_1212530, _1212532) = 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(_1212530, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1212532), _1212530)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1212530), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1212532), _1212530)))], (24110 ^ _775828) ^ [_1197932, _1197934, _1197936, _1197938] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1197932), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197932), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197932), _1197934), _1197936)), _1197938) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197932), _1197934), _1197938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197932), _1197936), _1197938)))], (32087 ^ _775828) ^ [_1369183, _1369185] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1369183, _1369185)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1369185), _1369183))], (7083 ^ _775828) ^ [_888272, _888274, _888276] : [class_Rings_Olinordered__ring__strict(_888272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888272), _888274), c_Groups_Ozero__class_Ozero(_888272))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888272), _888276), c_Groups_Ozero__class_Ozero(_888272))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888272), c_Groups_Ozero__class_Ozero(_888272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888272), _888274), _888276))))], (41809 ^ _775828) ^ [_1585064, _1585066, _1585068, _1585070, _1585072] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585064, _1585064)), hAPP(hAPP(c_Product__Type_OPair(_1585064, _1585064), _1585066), _1585068)), c_Transitive__Closure_Ortrancl(_1585064, _1585070))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585064, _1585064), tc_HOL_Obool)), _1585070), hAPP(hAPP(c_Product__Type_OSigma(_1585064, _1585064), _1585072), hAPP(c_COMBK(tc_fun(_1585064, tc_HOL_Obool), _1585064), _1585072)))), -(_1585066 = _1585068), -(hBOOL(hAPP(hAPP(c_member(_1585064), _1585066), _1585072)))], (34347 ^ _775828) ^ [_1415623, _1415625, _1415627] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415623, tc_HOL_Obool)), _1415625), _1415627) = c_Orderings_Obot__class_Obot(tc_fun(_1415623, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415623, tc_HOL_Obool)), _1415625), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1415623, tc_HOL_Obool)), _1415627))))], (6726 ^ _775828) ^ [_882541] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _882541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_882541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18841 ^ _775828) ^ [_1099757, _1099759, _1099761, _1099763, _1099765] : [-(c_Product__Type_Oprod_Oprod__size(_1099757, _1099759, _1099761, _1099763, _1099765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1099761, hAPP(c_Product__Type_Ofst(_1099757, _1099759), _1099765))), hAPP(_1099763, hAPP(c_Product__Type_Osnd(_1099757, _1099759), _1099765)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17895 ^ _775828) ^ [_1082354, _1082356, _1082358] : [class_Rings_Olinordered__idom(_1082354), -(hAPP(c_Groups_Oabs__class_Oabs(_1082354), hAPP(hAPP(c_Power_Opower__class_Opower(_1082354), hAPP(c_Groups_Ouminus__class_Ouminus(_1082354), _1082356)), _1082358)) = hAPP(c_Groups_Oabs__class_Oabs(_1082354), hAPP(hAPP(c_Power_Opower__class_Opower(_1082354), _1082356), _1082358)))], (16755 ^ _775828) ^ [_1061227, _1061229] : [-(c_Divides_Odivmod__nat(_1061227, _1061229) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1061227), _1061229)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1061227, _1061229)))], (6246 ^ _775828) ^ [_875245, _875247, _875249] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_875245, _875247, _875249))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _875247))))], (28745 ^ _775828) ^ [_1292894, _1292896, _1292898] : [-(hAPP(c_Set_OCollect(_1292894), hAPP(hAPP(c_COMBS(_1292894, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1292894), c_fimplies), _1292896)), _1292898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292894, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1292894, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1292894), _1292896))), hAPP(c_Set_OCollect(_1292894), _1292898)))], (33715 ^ _775828) ^ [_1402036, _1402038, _1402040, _1402042] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402036, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402036, tc_HOL_Obool)), _1402038), _1402040)), _1402042) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402036, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402036, tc_HOL_Obool)), _1402038), _1402042)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402036, tc_HOL_Obool)), _1402040), _1402042)))], (1100 ^ _775828) ^ [_792196, _792198] : [-(class_Rings_Ocomm__ring__1(_792196)), _792198 = _792196, class_Rings_Ocomm__ring__1(_792198)], (16763 ^ _775828) ^ [_1061374, _1061376] : [class_Groups_Oordered__ab__group__add__abs(_1061374), 16766 ^ _775828 : [(16773 ^ _775828) ^ [] : [_1061376 = c_Groups_Ozero__class_Ozero(_1061374), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061374), hAPP(c_Groups_Oabs__class_Oabs(_1061374), _1061376)), c_Groups_Ozero__class_Ozero(_1061374))))], (16767 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061374), hAPP(c_Groups_Oabs__class_Oabs(_1061374), _1061376)), c_Groups_Ozero__class_Ozero(_1061374))), -(_1061376 = c_Groups_Ozero__class_Ozero(_1061374))]]], (5521 ^ _775828) ^ [_863189, _863191, _863193, _863195, _863197, _863199] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_863189, _863191, _863193, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_863189), _863195), _863197), _863199)) = hAPP(hAPP(hAPP(_863193, _863195), _863197), _863199))], (39700 ^ _775828) ^ [_1535552, _1535554] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535552, tc_fun(_1535552, tc_HOL_Obool)), _1535554), hAPP(hAPP(c_COMBC(_1535552, tc_fun(_1535552, tc_HOL_Obool), tc_fun(_1535552, tc_HOL_Obool)), c_Set_Oinsert(_1535552)), c_Orderings_Obot__class_Obot(tc_fun(_1535552, tc_HOL_Obool)))) = _1535554)], (11260 ^ _775828) ^ [_960630, _960632, _960634] : [class_Groups_Oordered__comm__monoid__add(_960630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960630), c_Groups_Ozero__class_Ozero(_960630)), _960632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960630), c_Groups_Ozero__class_Ozero(_960630)), _960634)), 11271 ^ _775828 : [(11280 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960630), _960632), _960634) = c_Groups_Ozero__class_Ozero(_960630)), _960632 = c_Groups_Ozero__class_Ozero(_960630), _960634 = c_Groups_Ozero__class_Ozero(_960630)], (11272 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960630), _960632), _960634) = c_Groups_Ozero__class_Ozero(_960630), 11275 ^ _775828 : [(11278 ^ _775828) ^ [] : [-(_960634 = c_Groups_Ozero__class_Ozero(_960630))], (11276 ^ _775828) ^ [] : [-(_960632 = c_Groups_Ozero__class_Ozero(_960630))]]]]], (45536 ^ _775828) ^ [_1673511, _1673513, _1673515, _1673517, _1673519, _1673521, _1673523] : [-(c_Map_Omap__comp(_1673511, _1673513, _1673515, _1673517, _1673519, _1673521) = hAPP(c_Option_Ooption_OSome(_1673513), _1673523)), 45537 ^ _775828 : [(45538 ^ _775828) ^ [_1673589] : [hAPP(_1673519, _1673521) = hAPP(c_Option_Ooption_OSome(_1673511), _1673589), hAPP(_1673517, _1673589) = hAPP(c_Option_Ooption_OSome(_1673513), _1673523)]]], (43120 ^ _775828) ^ [_1616776, _1616778, _1616780, _1616782, _1616784, _1616786] : [c_Finite__Set_Ofolding(_1616776, _1616778, _1616780, _1616782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616776), _1616784)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616776), _1616786)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1616776, tc_HOL_Obool)), _1616784), _1616786) = c_Orderings_Obot__class_Obot(tc_fun(_1616776, tc_HOL_Obool)), -(hAPP(_1616782, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616776, tc_HOL_Obool)), _1616784), _1616786)) = hAPP(c_Fun_Ocomp(_1616778, _1616778, _1616778, hAPP(_1616782, _1616784)), hAPP(_1616782, _1616786)))], (50828 ^ _775828) ^ [_1798907, _1798909] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798907)), c_List_Oremdups(_1798907, _1798909)) = hAPP(c_Finite__Set_Ocard(_1798907), hAPP(c_List_Oset(_1798907), _1798909)))], (46867 ^ _775828) ^ [_1708121, _1708123, _1708125] : [class_Orderings_Olinorder(_1708121), -(hBOOL(hAPP(hAPP(c_member(_1708121), _1708123), hAPP(c_List_Oset(_1708121), _1708125)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1708121, _1708121, c_COMBI(_1708121), _1708123, _1708125) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708121, _1708121, c_COMBI(_1708121)), _1708123), _1708125))], (12524 ^ _775828) ^ [_982507, _982509] : [_982507 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982507), _982509), -(_982509 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_982507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31619 ^ _775828) ^ [_1358021, _1358023, _1358025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358021, _1358021), tc_HOL_Obool)), _1358023), _1358025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1358021, _1358021), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1358021, _1358023)), c_Transitive__Closure_Ortrancl(_1358021, _1358025))))], (38422 ^ _775828) ^ [_1505775, _1505777, _1505779, _1505781] : [-(c_Map_Odom(_1505775, _1505777, c_Map_Orestrict__map(_1505775, _1505777, _1505779, _1505781)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505775, tc_HOL_Obool)), c_Map_Odom(_1505775, _1505777, _1505779)), _1505781))], (35407 ^ _775828) ^ [_1440596, _1440598] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1440596), _1440598)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1440596, tc_HOL_Obool)), hAPP(c_Set_OPow(_1440596), _1440598))))], (26075 ^ _775828) ^ [_1236209, _1236211, _1236213] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236209), _1236211)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236211), _1236209))), 26090 ^ _775828 : [(26093 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236213), _1236209))], (26091 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236209), _1236213)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236211), _1236213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236213), _1236211)))], (38160 ^ _775828) ^ [_1499865, _1499867] : [class_Groups_Oordered__ab__group__add(_1499865), -(hAPP(c_Set_Oimage(_1499865, _1499865, c_Groups_Ouminus__class_Ouminus(_1499865)), hAPP(c_SetInterval_Oord__class_OatMost(_1499865), _1499867)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1499865), hAPP(c_Groups_Ouminus__class_Ouminus(_1499865), _1499867)))], (34905 ^ _775828) ^ [_1427211, _1427213, _1427215] : [class_Lattices_Olattice(_1427211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427211), _1427213)), hBOOL(hAPP(hAPP(c_member(_1427211), _1427215), _1427213)), 34916 ^ _775828 : [(34923 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427211, tc_HOL_Obool)), _1427213), hAPP(hAPP(c_Set_Oinsert(_1427211), _1427215), c_Orderings_Obot__class_Obot(tc_fun(_1427211, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1427211, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1427211, _1427213) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427211), _1427215), c_Big__Operators_Olattice__class_OInf__fin(_1427211, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427211, tc_HOL_Obool)), _1427213), hAPP(hAPP(c_Set_Oinsert(_1427211), _1427215), c_Orderings_Obot__class_Obot(tc_fun(_1427211, tc_HOL_Obool)))))))], (34917 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427211, tc_HOL_Obool)), _1427213), hAPP(hAPP(c_Set_Oinsert(_1427211), _1427215), c_Orderings_Obot__class_Obot(tc_fun(_1427211, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1427211, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1427211, _1427213) = _1427215)]]], (31991 ^ _775828) ^ [_1367703, _1367705] : [class_Groups_Olinordered__ab__group__add(_1367703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367703), _1367705)), -(_1367705 = c_Orderings_Obot__class_Obot(tc_fun(_1367703, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367703), c_Big__Operators_Olinorder__class_OMax(_1367703, _1367705)) = c_Big__Operators_Olinorder__class_OMin(_1367703, hAPP(c_Set_Oimage(_1367703, _1367703, c_Groups_Ouminus__class_Ouminus(_1367703)), _1367705)))], (49363 ^ _775828) ^ [_1766901, _1766903, _1766905, _1766907] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766901)), _1766903))), c_List_Ofoldr(tc_List_Olist(_1766905), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1766905)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1766905))), _1766907, 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(_1766901)), _1766903)), c_List_Ofoldr(tc_List_Olist(_1766905), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1766905)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1766905), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1766905)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1766905)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1766905), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1766905)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1766905), tc_List_Olist(_1766905), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1766905)))), _1766907), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (4766 ^ _775828) ^ [_848632, _848634, _848636, _848638, _848640, _848642] : [-(c_Divides_Odiv__class_Omod(_848642, _848638, _848634) = c_Divides_Odiv__class_Omod(_848640, _848636, _848632)), _848642 = _848640, _848638 = _848636, _848634 = _848632], (10360 ^ _775828) ^ [_944216, _944218] : [class_Rings_Osemiring__1(_944216), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_944216), hAPP(c_Nat_OSuc, _944218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944216), c_Groups_Oone__class_Oone(_944216)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_944216), _944218)))], (42800 ^ _775828) ^ [_1609367, _1609369, _1609371, _1609373, _1609375] : [hAPP(c_Set_Oimage(_1609367, _1609369, _1609371), c_Orderings_Otop__class_Otop(tc_fun(_1609367, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1609369, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1609369, _1609373, _1609375), c_Orderings_Otop__class_Otop(tc_fun(_1609369, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1609373, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1609367, _1609373, hAPP(c_Fun_Ocomp(_1609369, _1609373, _1609367, _1609375), _1609371)), c_Orderings_Otop__class_Otop(tc_fun(_1609367, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1609373, tc_HOL_Obool)))], (21052 ^ _775828) ^ [_1137963, _1137965, _1137967] : [hAPP(hAPP(c_COMBC(_1137963, tc_fun(_1137963, tc_HOL_Obool), tc_HOL_Obool), c_member(_1137963)), _1137965) = hAPP(hAPP(c_COMBC(_1137963, tc_fun(_1137963, tc_HOL_Obool), tc_HOL_Obool), c_member(_1137963)), _1137967), -(_1137965 = _1137967)], (1320 ^ _775828) ^ [_794946, _794948] : [-(class_Orderings_Obot(_794946)), _794948 = _794946, class_Orderings_Obot(_794948)], (26165 ^ _775828) ^ [_1237753, _1237755, _1237757] : [class_Rings_Ocomm__semiring__1(_1237753), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237753), _1237755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237753), _1237755), _1237757))))], (26998 ^ _775828) ^ [_1252825, _1252827] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252825), _1252827)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1252825), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1252827), _1252825)) = _1252827)], (36920 ^ _775828) ^ [_1469820, _1469822, _1469824] : [class_Groups_Ocomm__monoid__add(_1469820), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469822, _1469820), hAPP(c_COMBK(_1469820, _1469822), c_Groups_Ozero__class_Ozero(_1469820))), _1469824) = c_Groups_Ozero__class_Ozero(_1469820))], (18731 ^ _775828) ^ [_1097750] : [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), _1097750))), -(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), _1097750)) = 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), _1097750))))], (19468 ^ _775828) ^ [_1110365, _1110367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1110365)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110367)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110365)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110367), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1110365))))], (35471 ^ _775828) ^ [_1442252, _1442254] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442252, _1442254)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1442252), hAPP(c_Nat_OSuc, _1442254)))], (39201 ^ _775828) ^ [_1522766, _1522768, _1522770, _1522772, _1522774, _1522776] : [c_Fun_Oinj__on(_1522766, _1522768, _1522770, _1522772), hBOOL(hAPP(hAPP(c_member(_1522768), _1522774), hAPP(c_Set_Oimage(_1522766, _1522768, _1522770), _1522772))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522766, tc_HOL_Obool)), _1522772), _1522776)), -(hBOOL(hAPP(hAPP(c_member(_1522766), hAPP(c_Fun_Othe__inv__into(_1522766, _1522768, _1522772, _1522770), _1522774)), _1522776)))], (51318 ^ _775828) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (36101 ^ _775828) ^ [_1453865, _1453867, _1453869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1453865), _1453867)), -(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)), _1453865)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1453869), _1453867)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1453869), _1453865)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1453867), _1453865)))], (51450 ^ _775828) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (32863 ^ _775828) ^ [_1383620, _1383622, _1383624, _1383626, _1383628, _1383630] : [-(_1383620 = _1383622), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383624, _1383626), _1383628), _1383622), _1383630), _1383620) = hAPP(_1383628, _1383620))], (14239 ^ _775828) ^ [_1013812, _1013814] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1013812)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1013814)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013812), _1013814))], (33731 ^ _775828) ^ [_1402408, _1402410, _1402412, _1402414, _1402416] : [class_Lattices_Olattice(_1402408), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402410, _1402408)), _1402412), _1402414), _1402416) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1402408), hAPP(_1402412, _1402416)), hAPP(_1402414, _1402416)))], (90 ^ _775828) ^ [_777077, _777079] : [-(class_Fields_Olinordered__field__inverse__zero(_777077)), _777079 = _777077, class_Fields_Olinordered__field__inverse__zero(_777079)], (24535 ^ _775828) ^ [_1206890, _1206892] : [c_Nat__Transfer_Ois__nat(_1206890), c_Nat__Transfer_Ois__nat(_1206892), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206890), _1206892)))], (49686 ^ _775828) ^ [_1774792, _1774794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774792), _1774794))), -(c_List_Oupt(_1774792, hAPP(c_Nat_OSuc, _1774794)) = c_List_Olist_ONil(tc_Nat_Onat))], (51198 ^ _775828) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (9025 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (44653 ^ _775828) ^ [_1653830, _1653832] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1653830), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1653830, tc_HOL_Obool), _1653832))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1653830, tc_HOL_Obool)), _1653832)))], (46752 ^ _775828) ^ [_1705672, _1705674, _1705676, _1705678] : [class_Groups_Ocomm__monoid__add(_1705672), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1705672), _1705674), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1705676, _1705678))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1705672), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1705672), _1705674), c_List_Oupto(_1705676, _1705678))))], (50648 ^ _775828) ^ [_1795643, _1795645, _1795647, _1795649, _1795651] : [-(hBOOL(hAPP(_1795643, _1795645))), -(c_List_OtakeWhile(_1795647, _1795643, hAPP(hAPP(c_List_Oappend(_1795647), _1795649), hAPP(hAPP(c_List_Olist_OCons(_1795647), _1795645), _1795651))) = c_List_OtakeWhile(_1795647, _1795643, _1795649))], (31079 ^ _775828) ^ [_1345434, _1345436, _1345438, _1345440, _1345442] : [c_Finite__Set_Ofolding__one(_1345434, _1345436, _1345438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345434), _1345440)), 31086 ^ _775828 : [(31093 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345434, tc_HOL_Obool)), _1345440), hAPP(hAPP(c_Set_Oinsert(_1345434), _1345442), c_Orderings_Obot__class_Obot(tc_fun(_1345434, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345434, tc_HOL_Obool))), -(hAPP(_1345438, hAPP(hAPP(c_Set_Oinsert(_1345434), _1345442), _1345440)) = hAPP(hAPP(_1345436, _1345442), hAPP(_1345438, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345434, tc_HOL_Obool)), _1345440), hAPP(hAPP(c_Set_Oinsert(_1345434), _1345442), c_Orderings_Obot__class_Obot(tc_fun(_1345434, tc_HOL_Obool)))))))], (31087 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345434, tc_HOL_Obool)), _1345440), hAPP(hAPP(c_Set_Oinsert(_1345434), _1345442), c_Orderings_Obot__class_Obot(tc_fun(_1345434, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345434, tc_HOL_Obool)), -(hAPP(_1345438, hAPP(hAPP(c_Set_Oinsert(_1345434), _1345442), _1345440)) = _1345442)]]], (10690 ^ _775828) ^ [_950460, _950462, _950464, _950466] : [class_Rings_Ocomm__semiring(_950460), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950460), _950462), _950464)), _950466) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950460), _950462), _950466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950460), _950464), _950466)))], (41256 ^ _775828) ^ [_1572095, _1572097, _1572099, _1572101, _1572103, _1572105, _1572107, _1572109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572095, _1572097), tc_HOL_Obool)), _1572099), hAPP(hAPP(c_Product__Type_OSigma(_1572095, _1572097), _1572101), hAPP(c_COMBK(tc_fun(_1572097, tc_HOL_Obool), _1572095), _1572103)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572097, _1572105), tc_HOL_Obool)), _1572107), hAPP(hAPP(c_Product__Type_OSigma(_1572097, _1572105), _1572103), hAPP(c_COMBK(tc_fun(_1572105, tc_HOL_Obool), _1572097), _1572109)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572095, _1572105), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1572095, _1572097, _1572105), _1572099), _1572107)), hAPP(hAPP(c_Product__Type_OSigma(_1572095, _1572105), _1572101), hAPP(c_COMBK(tc_fun(_1572105, tc_HOL_Obool), _1572095), _1572109)))))], (204 ^ _775828) ^ [_778764, _778766, _778768, _778770, _778772, _778774, _778776, _778778] : [-(c_Orderings_Oorder_Omono(_778776, _778772, _778768, _778764)), c_Orderings_Oorder_Omono(_778778, _778774, _778770, _778766), _778778 = _778776, _778774 = _778772, _778770 = _778768, _778766 = _778764], (45900 ^ _775828) ^ [_1682074, _1682076, _1682078, _1682080, _1682082] : [hBOOL(hAPP(c_List_Odistinct(_1682074), hAPP(hAPP(c_List_Omap(tc_prod(_1682074, _1682076), _1682074), c_Product__Type_Ofst(_1682074, _1682076)), _1682078))), 45903 ^ _775828 : [(45910 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1682074, _1682076)), hAPP(hAPP(c_Product__Type_OPair(_1682074, _1682076), _1682082), _1682080)), hAPP(c_List_Oset(tc_prod(_1682074, _1682076)), _1682078))), -(hAPP(c_Option_Ooption_OSome(_1682076), _1682080) = hAPP(c_Map_Omap__of(_1682074, _1682076, _1682078), _1682082))], (45904 ^ _775828) ^ [] : [hAPP(c_Option_Ooption_OSome(_1682076), _1682080) = hAPP(c_Map_Omap__of(_1682074, _1682076, _1682078), _1682082), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682074, _1682076)), hAPP(hAPP(c_Product__Type_OPair(_1682074, _1682076), _1682082), _1682080)), hAPP(c_List_Oset(tc_prod(_1682074, _1682076)), _1682078))))]]], (49497 ^ _775828) ^ [_1769940, _1769942] : [-(c_List_Opartition(_1769940, _1769942, c_List_Olist_ONil(_1769940)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769940), tc_List_Olist(_1769940)), c_List_Olist_ONil(_1769940)), c_List_Olist_ONil(_1769940)))], (36663 ^ _775828) ^ [_1464751, _1464753, _1464755] : [class_Orderings_Olinorder(_1464751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1464751), _1464753), _1464755)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464751, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1464751), _1464753)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1464751, _1464753, _1464755)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1464751), _1464755))], (40407 ^ _775828) ^ [_1550593, _1550595, _1550597, _1550599] : [c_Fun_Oinj__on(_1550593, _1550595, _1550597, c_Orderings_Otop__class_Otop(tc_fun(_1550593, tc_HOL_Obool))), 40410 ^ _775828 : [(40424 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550595), _1550599), hAPP(c_Set_Oimage(_1550593, _1550595, _1550597), c_Orderings_Otop__class_Otop(tc_fun(_1550593, tc_HOL_Obool)))))), 40425 ^ _775828 : [(40426 ^ _775828) ^ [_1550996] : [_1550599 = hAPP(_1550597, _1550996), 40430 ^ _775828 : [(40433 ^ _775828) ^ [] : [40429 ^ [_1550593, _1550595, _1550597, _1550599, _1550996] = _1550996], (40431 ^ _775828) ^ [] : [-(_1550599 = hAPP(_1550597, 40429 ^ [_1550593, _1550595, _1550597, _1550599, _1550996]))]]]]], (40411 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550595), _1550599), hAPP(c_Set_Oimage(_1550593, _1550595, _1550597), c_Orderings_Otop__class_Otop(tc_fun(_1550593, tc_HOL_Obool))))), 40415 ^ _775828 : [(40418 ^ _775828) ^ [_1550858] : [_1550599 = hAPP(_1550597, _1550858), -(_1550858 = 40414 ^ [_1550593, _1550595, _1550597, _1550599])], (40416 ^ _775828) ^ [] : [-(_1550599 = hAPP(_1550597, 40414 ^ [_1550593, _1550595, _1550597, _1550599]))]]]]], (20266 ^ _775828) ^ [_1124034] : [-(c_Int_Opred(c_Int_OBit0(_1124034)) = c_Int_OBit1(c_Int_Opred(_1124034)))], (47313 ^ _775828) ^ [_1719549, _1719551, _1719553, _1719555] : [_1719555 = c_List_Olist_ONil(_1719551), -(c_List_Olist_ONil(_1719549) = hAPP(hAPP(c_List_Omap(_1719551, _1719549), _1719553), _1719555))], (19550 ^ _775828) ^ [_1111821, _1111823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111821), _1111823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111821)), c_Int_OBit1(_1111823))))], (51252 ^ _775828) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (47405 ^ _775828) ^ [_1721536, _1721538] : [-(c_List_Oremove1(_1721536, _1721538, c_List_Olist_ONil(_1721536)) = c_List_Olist_ONil(_1721536))], (41540 ^ _775828) ^ [_1579534, _1579536] : [class_Orderings_Olinorder(_1579534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579534), _1579536)), -(c_Big__Operators_Olattice_OInf__fin(_1579534, c_Orderings_Oord__class_Omin(_1579534), _1579536) = hAPP(c_Finite__Set_Ofold1(_1579534, c_Orderings_Oord__class_Omin(_1579534)), _1579536))], (46672 ^ _775828) ^ [_1703509, _1703511, _1703513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1703509, tc_HOL_Obool)), hAPP(c_List_Oset(_1703509), c_List_Osublist(_1703509, _1703511, _1703513))), hAPP(c_List_Oset(_1703509), _1703511))))], (36011 ^ _775828) ^ [_1452169, _1452171] : [c_Wellfounded_Owf(_1452169, _1452171), -(c_Wellfounded_Owf(tc_List_Olist(_1452169), c_List_Olenlex(_1452169, _1452171)))], (182 ^ _775828) ^ [_778411, _778413, _778415, _778417, _778419, _778421, _778423, _778425] : [-(c_Orderings_Oorder_Ostrict__mono(_778423, _778419, _778415, _778411)), c_Orderings_Oorder_Ostrict__mono(_778425, _778421, _778417, _778413), _778425 = _778423, _778421 = _778419, _778417 = _778415, _778413 = _778411], (33959 ^ _775828) ^ [_1407599, _1407601, _1407603] : [class_Lattices_Olattice(_1407599), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407599), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407599), _1407601), _1407603)), _1407601)))], (29655 ^ _775828) ^ [_1314104, _1314106] : [-(hAPP(c_Set_OCollect(_1314104), hAPP(hAPP(c_COMBC(_1314104, _1314104, tc_HOL_Obool), c_fequal), _1314106)) = hAPP(hAPP(c_Set_Oinsert(_1314104), _1314106), c_Orderings_Obot__class_Obot(tc_fun(_1314104, tc_HOL_Obool))))], (34495 ^ _775828) ^ [_1418962, _1418964, _1418966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1418962), _1418964)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418962), _1418966)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1418962), _1418964)), hAPP(c_Finite__Set_Ocard(_1418962), _1418966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1418962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418962, tc_HOL_Obool)), _1418964), _1418966))), hAPP(c_Finite__Set_Ocard(_1418962), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418962, tc_HOL_Obool)), _1418964), _1418966))))], (27993 ^ _775828) ^ [_1276483, _1276485, _1276487, _1276489] : [hBOOL(hAPP(c_Predicate_ODomainP(_1276483, _1276485, _1276487), _1276489)), -(hBOOL(hAPP(hAPP(_1276487, _1276489), 27996 ^ [_1276483, _1276485, _1276487, _1276489])))], (44908 ^ _775828) ^ [_1659319] : [class_Complete__Lattice_Ocomplete__lattice(_1659319), -(c_Complete__Lattice_OInf__class_OInf(_1659319, c_Orderings_Otop__class_Otop(tc_fun(_1659319, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1659319))], (24899 ^ _775828) ^ [_1214329, _1214331, _1214333, _1214335, _1214337] : [-(_1214329 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1214331, _1214333, _1214329, _1214335), _1214337) = hAPP(hAPP(c_Product__Type_Oscomp(_1214333, _1214331, _1214333, tc_prod(_1214331, _1214333)), hAPP(_1214335, _1214337)), c_Random_Oiterate(_1214331, _1214333, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1214329), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1214335)))], (41192 ^ _775828) ^ [_1570404, _1570406, _1570408, _1570410, _1570412] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1570404, _1570406, hAPP(hAPP(c_Set_Oinsert(_1570404), _1570408), _1570410)), _1570412)), 41197 ^ _775828 : [(41202 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1570404), 41195 ^ [_1570404, _1570406, _1570408, _1570410, _1570412]), 41196 ^ [_1570404, _1570406, _1570408, _1570410, _1570412]))], (41200 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1570404, _1570404, _1570406, 41195 ^ [_1570404, _1570406, _1570408, _1570410, _1570412], 41196 ^ [_1570404, _1570406, _1570408, _1570410, _1570412]), _1570412)))], (41198 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1570404), _1570408), _1570410) = hAPP(hAPP(c_Set_Oinsert(_1570404), 41195 ^ [_1570404, _1570406, _1570408, _1570410, _1570412]), 41196 ^ [_1570404, _1570406, _1570408, _1570410, _1570412]))]]], (44890 ^ _775828) ^ [_1659026, _1659028] : [class_Complete__Lattice_Ocomplete__lattice(_1659026), -(c_Complete__Lattice_OInf__class_OInf(_1659026, hAPP(hAPP(c_Set_Oinsert(_1659026), _1659028), c_Orderings_Obot__class_Obot(tc_fun(_1659026, tc_HOL_Obool)))) = _1659028)], (28191 ^ _775828) ^ [_1281217, _1281219, _1281221] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281217, tc_HOL_Obool)), _1281219), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281217, tc_HOL_Obool)), _1281221), _1281219)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281217, tc_HOL_Obool)), _1281219), _1281221))], (51258 ^ _775828) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (29637 ^ _775828) ^ [_1313776, _1313778, _1313780] : [-(hBOOL(hAPP(_1313776, _1313778))), -(hAPP(c_Set_OCollect(_1313780), hAPP(hAPP(c_COMBS(_1313780, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1313780), c_fconj), hAPP(hAPP(c_COMBC(_1313780, _1313780, tc_HOL_Obool), c_fequal), _1313778))), _1313776)) = c_Orderings_Obot__class_Obot(tc_fun(_1313780, tc_HOL_Obool)))], (51276 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (13486 ^ _775828) ^ [_999705, _999707, _999709, _999711] : [hAPP(c_Com_Ocom_OBODY, _999705) = c_Com_Ocom_OLocal(_999707, _999709, _999711)], (39609 ^ _775828) ^ [_1532573, _1532575, _1532577, _1532579, _1532581] : [39611 ^ _775828 : [(39614 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532573, tc_HOL_Obool)), hAPP(_1532579, 39610 ^ [_1532573, _1532575, _1532577, _1532579, _1532581])), _1532581))], (39612 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532575), 39610 ^ [_1532573, _1532575, _1532577, _1532579, _1532581]), _1532577)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532573, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1532575, tc_fun(_1532573, tc_HOL_Obool)), _1532577), _1532579)), _1532581)))], (13632 ^ _775828) ^ [_1002632, _1002634] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_1002632, _1002634))), 13635 ^ _775828 : [(13638 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1002634)))], (13636 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1002632)))]]], (29153 ^ _775828) ^ [_1304158, _1304160] : [c_Wellfounded_Oacyclic(_1304158, hAPP(c_Set_OCollect(tc_prod(_1304158, _1304158)), hAPP(c_Product__Type_Oprod_Oprod__case(_1304158, _1304158, tc_HOL_Obool), _1304160))), -(c_Wellfounded_Oacyclic(_1304158, hAPP(c_Set_OCollect(tc_prod(_1304158, _1304158)), hAPP(c_Product__Type_Oprod_Oprod__case(_1304158, _1304158, tc_HOL_Obool), c_Predicate_Oconversep(_1304158, _1304158, _1304160)))))], (34217 ^ _775828) ^ [_1412608, _1412610, _1412612, _1412614] : [-(hBOOL(hAPP(hAPP(c_member(_1412608), _1412610), _1412612))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412608, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1412608), _1412610), _1412614)), _1412612) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412608, tc_HOL_Obool)), _1412614), _1412612))], (36719 ^ _775828) ^ [_1465675] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1465675)) = _1465675)], (51020 ^ _775828) ^ [_1803220, _1803222] : [class_Complete__Lattice_Ocomplete__lattice(_1803220), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1803222, _1803220)))], (23442 ^ _775828) ^ [_1185044, _1185046, _1185048, _1185050, _1185052] : [-(c_Nat_Onat_Onat__case(_1185044, _1185046, _1185048, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1185050)), _1185052)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1185044), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1185050))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1185044, _1185044), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1185044, tc_fun(_1185044, _1185044)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1185044, tc_fun(_1185044, _1185044)), tc_Int_Oint), c_If(_1185044)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1185044, _1185046, _1185048, _1185052))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1185044, tc_Int_Oint), _1185048), 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)), _1185052)))))], (5879 ^ _775828) ^ [_869482, _869484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869482), _869484)), _869482 = _869484], (18455 ^ _775828) ^ [_1093333, _1093335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093335)), -(c_Divides_OposDivAlg(_1093333, _1093335) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1093333), _1093335)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1093333, _1093335)))], (3228 ^ _775828) ^ [_824617, _824619, _824621, _824623, _824625, _824627, _824629, _824631, _824633, _824635] : [-(c_Fun_Ooverride__on(_824635, _824631, _824627, _824623, _824619) = c_Fun_Ooverride__on(_824633, _824629, _824625, _824621, _824617)), _824635 = _824633, _824631 = _824629, _824627 = _824625, _824623 = _824621, _824619 = _824617], (25301 ^ _775828) ^ [_1222092, _1222094, _1222096, _1222098, _1222100] : [hBOOL(hAPP(_1222092, hAPP(hAPP(c_Product__Type_OPair(_1222094, _1222096), _1222098), _1222100))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1222094, _1222096, tc_HOL_Obool, _1222092), _1222098), _1222100)))], (51334 ^ _775828) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (9571 ^ _775828) ^ [_929696, _929698] : [class_Rings_Olinordered__semidom(_929696), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929696), c_Groups_Ozero__class_Ozero(_929696)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929696), _929698))))], (5422 ^ _775828) ^ [_858668, _858670] : [_858670 = _858668, -(c_Option_Othe(_858670) = c_Option_Othe(_858668))], (41292 ^ _775828) ^ [_1573132, _1573134, _1573136] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1573132, _1573134), c_Orderings_Obot__class_Obot(tc_fun(_1573132, tc_HOL_Obool))), _1573136) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1573132, _1573134), tc_HOL_Obool)))], (20750 ^ _775828) ^ [_1132740, _1132742] : [-(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), _1132740)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1132742))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1132740))) = 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), _1132742)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132740)))], (43824 ^ _775828) ^ [_1633019, _1633021, _1633023, _1633025] : [class_Complete__Lattice_Ocomplete__lattice(_1633019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633021), _1633023)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1633021, _1633019), _1633023), _1633025) = hAPP(hAPP(c_Finite__Set_Ofold(_1633021, _1633019, hAPP(hAPP(c_COMBB(_1633019, tc_fun(_1633019, _1633019), _1633021), c_Lattices_Osemilattice__sup__class_Osup(_1633019)), _1633025)), c_Orderings_Obot__class_Obot(_1633019)), _1633023))], (31769 ^ _775828) ^ [_1361771, _1361773, _1361775, _1361777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1361771, _1361771)), hAPP(hAPP(c_Product__Type_OPair(_1361771, _1361771), _1361773), _1361775)), c_Transitive__Closure_Ortrancl(_1361771, _1361777))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361771, _1361771)), hAPP(hAPP(c_Product__Type_OPair(_1361771, _1361771), _1361775), _1361773)), c_Transitive__Closure_Ortrancl(_1361771, hAPP(c_Relation_Oconverse(_1361771, _1361771), _1361777)))))], (33911 ^ _775828) ^ [_1406240, _1406242, _1406244, _1406246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406240, tc_HOL_Obool)), _1406242), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406240, tc_HOL_Obool)), _1406244), _1406246)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406240, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406240, tc_HOL_Obool)), _1406242), _1406244)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406240, tc_HOL_Obool)), _1406242), _1406246)))], (44297 ^ _775828) ^ [_1644085, _1644087, _1644089, _1644091, _1644093, _1644095, _1644097] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644085, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644087, tc_fun(_1644085, tc_HOL_Obool)), _1644089), _1644091)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644093, tc_fun(_1644085, tc_HOL_Obool)), _1644095), _1644097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644087, tc_fun(_1644085, tc_HOL_Obool)), _1644089), hAPP(hAPP(c_COMBB(tc_fun(_1644093, tc_fun(_1644085, tc_HOL_Obool)), tc_fun(_1644085, tc_HOL_Obool), _1644087), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644093, tc_fun(_1644085, tc_HOL_Obool)), _1644095)), hAPP(hAPP(c_COMBC(_1644087, tc_fun(_1644093, tc_fun(_1644085, tc_HOL_Obool)), tc_fun(_1644093, tc_fun(_1644085, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1644085, tc_HOL_Obool), tc_fun(_1644085, tc_HOL_Obool)), tc_fun(tc_fun(_1644093, tc_fun(_1644085, tc_HOL_Obool)), tc_fun(_1644093, tc_fun(_1644085, tc_HOL_Obool))), _1644087), c_COMBB(tc_fun(_1644085, tc_HOL_Obool), tc_fun(_1644085, tc_HOL_Obool), _1644093)), hAPP(hAPP(c_COMBB(tc_fun(_1644085, tc_HOL_Obool), tc_fun(tc_fun(_1644085, tc_HOL_Obool), tc_fun(_1644085, tc_HOL_Obool)), _1644087), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644085, tc_HOL_Obool))), _1644091))), _1644097))))], (44926 ^ _775828) ^ [_1659816, _1659818, _1659820] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659816, tc_HOL_Obool)), _1659818), _1659820) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1659816, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1659816, tc_HOL_Obool)), _1659818), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1659816, tc_HOL_Obool)), _1659820), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1659816, tc_HOL_Obool), tc_HOL_Obool))))))], (1936 ^ _775828) ^ [_803873, _803875, _803877, _803879, _803881, _803883] : [-(c_Com_Ocom_OLocal(_803883, _803879, _803875) = c_Com_Ocom_OLocal(_803881, _803877, _803873)), _803883 = _803881, _803879 = _803877, _803875 = _803873], (8947 ^ _775828) ^ [_918856, _918858, _918860] : [class_Groups_Oordered__ab__group__add(_918856), 8950 ^ _775828 : [(8957 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918856), _918860), hAPP(c_Groups_Ouminus__class_Ouminus(_918856), _918858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918856), _918858), hAPP(c_Groups_Ouminus__class_Ouminus(_918856), _918860))))], (8951 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918856), _918858), hAPP(c_Groups_Ouminus__class_Ouminus(_918856), _918860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918856), _918860), hAPP(c_Groups_Ouminus__class_Ouminus(_918856), _918858))))]]], (10306 ^ _775828) ^ [_943127, _943129, _943131] : [class_Rings_Ocomm__semiring__1(_943127), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943127), _943129), _943131) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943127), _943131), _943129))], (44741 ^ _775828) ^ [_1656086, _1656088, _1656090] : [class_Complete__Lattice_Ocomplete__lattice(_1656086), 44744 ^ _775828 : [(44745 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656086), _1656088), c_Complete__Lattice_OInf__class_OInf(_1656086, _1656090))), 44748 ^ _775828 : [(44749 ^ _775828) ^ [_1656244] : [hBOOL(hAPP(hAPP(c_member(_1656086), _1656244), _1656090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656086), _1656088), _1656244)))]]], (44755 ^ _775828) ^ [] : [44757 ^ _775828 : [(44760 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656086), _1656088), 44756 ^ [_1656086, _1656088, _1656090]))], (44758 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656086), 44756 ^ [_1656086, _1656088, _1656090]), _1656090)))]], 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c_Groups_Ozero__class_Ozero(_1479364)), _1479368))], (2530 ^ _775828) ^ [_813130, _813132] : [_813132 = _813130, -(c_DSequence_Oempty(_813132) = c_DSequence_Oempty(_813130))], (37176 ^ _775828) ^ [_1475988, _1475990, _1475992, _1475994, _1475996] : [class_Groups_Ocomm__monoid__add(_1475988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475990), _1475992)), 37183 ^ _775828 : [(37190 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475990), _1475994), _1475992))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475990, _1475988), hAPP(hAPP(c_COMBC(_1475990, _1475988, _1475988), hAPP(hAPP(c_COMBS(_1475990, _1475988, tc_fun(_1475988, _1475988)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1475988, tc_fun(_1475988, _1475988)), _1475990), c_If(_1475988)), hAPP(c_fequal, _1475994))), _1475996)), c_Groups_Ozero__class_Ozero(_1475988))), _1475992) = c_Groups_Ozero__class_Ozero(_1475988))], (37184 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1475990), _1475994), _1475992)), 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_790821, class_Groups_Olinordered__ab__group__add(_790823)], (51376 ^ _775828) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (6400 ^ _775828) ^ [_877621, _877623] : [class_Rings_Osemiring__1(_877621), -(hBOOL(hAPP(hAPP(c_member(_877621), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877621), _877623)), c_Nat_Osemiring__1__class_ONats(_877621))))], (32057 ^ _775828) ^ [_1368699, _1368701, _1368703] : [class_Orderings_Oorder(_1368699), 32060 ^ _775828 : [(32067 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368699), _1368701), _1368703))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1368699, _1368701, _1368703) = c_Orderings_Obot__class_Obot(tc_fun(_1368699, tc_HOL_Obool)))], (32061 ^ _775828) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1368699, _1368701, _1368703) = c_Orderings_Obot__class_Obot(tc_fun(_1368699, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368699), _1368701), _1368703))]]], (19602 ^ _775828) ^ [_1112697] : [c_Int_OMin = _1112697, -(c_Int_OMin = c_Int_OBit1(_1112697))], (29497 ^ _775828) ^ [_1310903, _1310905, _1310907, _1310909, _1310911] : [hAPP(hAPP(c_Set_Oinsert(_1310903), _1310905), hAPP(hAPP(c_Set_Oinsert(_1310903), _1310907), c_Orderings_Obot__class_Obot(tc_fun(_1310903, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1310903), _1310909), hAPP(hAPP(c_Set_Oinsert(_1310903), _1310911), c_Orderings_Obot__class_Obot(tc_fun(_1310903, tc_HOL_Obool)))), 29502 ^ _775828 : [(29505 ^ _775828) ^ [] : [-(_1310907 = _1310911)], (29503 ^ _775828) ^ [] : [-(_1310905 = _1310909)]], 29506 ^ _775828 : [(29509 ^ _775828) ^ [] : [-(_1310907 = _1310909)], (29507 ^ _775828) ^ [] : [-(_1310905 = _1310911)]]], (31987 ^ _775828) ^ [_1367641, _1367643] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1367641, _1367643))))], (4388 ^ _775828) ^ [_842839, _842841, _842843, _842845] : [-(c_Product__Type_OSigma(_842845, _842841) = c_Product__Type_OSigma(_842843, _842839)), _842845 = _842843, _842841 = _842839], (25042 ^ _775828) ^ [_1217664, _1217666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1217664), _1217666)), -(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)), _1217664)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1217666))))], (23596 ^ _775828) ^ [_1188799, _1188801, _1188803, _1188805, _1188807, _1188809] : [hAPP(_1188805, hAPP(c_Product__Type_Osnd(_1188803, _1188799), _1188807)) = hAPP(_1188809, hAPP(c_Product__Type_Osnd(_1188803, _1188799), _1188807)), -(hAPP(c_Product__Type_Oapsnd(_1188799, _1188801, _1188803, _1188805), _1188807) = hAPP(c_Product__Type_Oapsnd(_1188799, _1188801, _1188803, _1188809), _1188807))], (51374 ^ _775828) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (27501 ^ _775828) ^ [_1264450, _1264452, _1264454] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1264450, _1264450)), hAPP(hAPP(c_Product__Type_OPair(_1264450, _1264450), _1264452), _1264454)), c_Relation_OId(_1264450))), -(_1264452 = _1264454)], (31147 ^ _775828) ^ [_1347505, _1347507, _1347509] : [class_Orderings_Olinorder(_1347505), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347505), _1347507)), -(_1347507 = c_Orderings_Obot__class_Obot(tc_fun(_1347505, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347505), _1347509)), -(_1347509 = c_Orderings_Obot__class_Obot(tc_fun(_1347505, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347505), c_Big__Operators_Olattice_OInf__fin(_1347505, c_Orderings_Oord__class_Omin(_1347505), _1347507)), c_Big__Operators_Olattice_OInf__fin(_1347505, c_Orderings_Oord__class_Omin(_1347505), _1347509)) = c_Big__Operators_Olattice_OInf__fin(_1347505, c_Orderings_Oord__class_Omin(_1347505), hAPP(c_Set_OCollect(_1347505), hAPP(hAPP(c_COMBB(tc_fun(_1347505, 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tc_HOL_Obool), tc_fun(_1347505, tc_HOL_Obool)), _1347505), c_COMBS(_1347505, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1347505, tc_fun(_1347505, tc_HOL_Obool)), tc_fun(_1347505, tc_fun(_1347505, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1347505), hAPP(c_COMBB(tc_fun(_1347505, tc_HOL_Obool), tc_fun(_1347505, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1347505), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1347505), c_fconj))), hAPP(hAPP(c_COMBC(_1347505, tc_fun(_1347505, tc_fun(_1347505, _1347505)), tc_fun(_1347505, tc_fun(_1347505, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1347505, _1347505), tc_fun(_1347505, tc_HOL_Obool)), tc_fun(tc_fun(_1347505, tc_fun(_1347505, _1347505)), tc_fun(_1347505, tc_fun(_1347505, tc_HOL_Obool))), _1347505), c_COMBB(tc_fun(_1347505, _1347505), tc_fun(_1347505, tc_HOL_Obool), _1347505)), hAPP(hAPP(c_COMBB(tc_fun(_1347505, tc_HOL_Obool), tc_fun(tc_fun(_1347505, _1347505), tc_fun(_1347505, tc_HOL_Obool)), _1347505), c_COMBB(_1347505, tc_HOL_Obool, _1347505)), c_fequal))), c_Orderings_Oord__class_Omax(_1347505)))))), hAPP(hAPP(c_COMBC(_1347505, tc_fun(_1347505, tc_HOL_Obool), tc_fun(_1347505, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1347505, tc_HOL_Obool), tc_fun(_1347505, tc_HOL_Obool)), _1347505), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1347505)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1347505), c_fconj), hAPP(hAPP(c_COMBC(_1347505, tc_fun(_1347505, tc_HOL_Obool), tc_HOL_Obool), c_member(_1347505)), _1347507)))), hAPP(hAPP(c_COMBC(_1347505, tc_fun(_1347505, tc_HOL_Obool), tc_HOL_Obool), c_member(_1347505)), _1347509))))))))], (40855 ^ _775828) ^ [_1561825, _1561827, _1561829, _1561831] : [-(hAPP(c_Set_Ovimage(_1561825, _1561827, _1561829), _1561831) = hAPP(c_Set_OCollect(_1561825), hAPP(hAPP(c_COMBC(_1561825, tc_fun(_1561827, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1561827, tc_fun(tc_fun(_1561827, tc_HOL_Obool), tc_HOL_Obool), _1561825), c_member(_1561827)), _1561829)), _1561831)))], (9697 ^ _775828) ^ [_931829, _931831, _931833, _931835] : [class_Rings_Olinordered__semiring__strict(_931829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931829), _931831), _931833)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931829), _931831), _931835))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931829), c_Groups_Ozero__class_Ozero(_931829)), _931831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931829), _931833), _931835)))], (350 ^ _775828) ^ [_780953, _780955] : [-(class_Fields_Ofield__inverse__zero(_780953)), _780955 = _780953, class_Fields_Ofield__inverse__zero(_780955)], (30493 ^ _775828) ^ [_1333074, _1333076] : [class_Finite__Set_Ofinite(_1333074), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333074), _1333076)))], (51430 ^ _775828) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (45622 ^ _775828) ^ [_1675458, _1675460, _1675462, _1675464, _1675466, _1675468] : [c_Map_Omap__comp(_1675458, _1675460, _1675462, _1675464, _1675466, _1675468) = c_Option_Ooption_ONone(_1675460), -(hAPP(_1675466, _1675468) = c_Option_Ooption_ONone(_1675458)), 45630 ^ _775828 : [(45633 ^ _775828) ^ [] : [-(hAPP(_1675464, 45629 ^ [_1675458, _1675460, _1675462, _1675464, _1675466, _1675468]) = c_Option_Ooption_ONone(_1675460))], (45631 ^ _775828) ^ [] : [-(hAPP(_1675466, _1675468) = hAPP(c_Option_Ooption_OSome(_1675458), 45629 ^ [_1675458, _1675460, _1675462, _1675464, _1675466, _1675468]))]]], (37016 ^ _775828) ^ [_1472422, _1472424, _1472426] : [class_Groups_Ocomm__monoid__add(_1472422), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472424, _1472422), _1472426), c_Orderings_Obot__class_Obot(tc_fun(_1472424, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1472422))], (41083 ^ _775828) ^ [_1567585, _1567587, _1567589, _1567591] : [c_Wellfounded_Omax__extp(_1567585, _1567587, _1567589, _1567591), 41086 ^ _775828 : [(41089 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567585), _1567591)))], (41091 ^ _775828) ^ [] : [_1567591 = c_Orderings_Obot__class_Obot(tc_fun(_1567585, tc_HOL_Obool))], (41093 ^ _775828) ^ [_1567801] : [hBOOL(hAPP(hAPP(c_member(_1567585), _1567801), _1567589)), 41097 ^ _775828 : [(41100 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1567587, _1567801), 41096 ^ [_1567585, _1567587, _1567589, _1567591, _1567801])))], (41098 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567585), 41096 ^ [_1567585, _1567587, _1567589, _1567591, _1567801]), _1567591)))]]], (41087 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567585), _1567589)))]]], (15988 ^ _775828) ^ [_1046476, _1046478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046476)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046476), _1046478)), _1046476) = _1046478)], (5632 ^ _775828) ^ [_865383, _865385, _865387, _865389] : [_865383 = _865385, 5635 ^ _775828 : [(5642 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_865387), _865385), _865389)), -(hBOOL(hAPP(hAPP(c_member(_865387), _865383), _865389)))], (5636 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_865387), _865383), _865389)), -(hBOOL(hAPP(hAPP(c_member(_865387), _865385), _865389)))]]], (39630 ^ _775828) ^ [_1533374, _1533376, _1533378, _1533380, _1533382] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533374, tc_fun(_1533376, tc_HOL_Obool)), _1533378), hAPP(hAPP(c_COMBC(_1533374, tc_fun(_1533376, tc_HOL_Obool), tc_fun(_1533376, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533376, tc_HOL_Obool), tc_fun(tc_fun(_1533376, tc_HOL_Obool), tc_fun(_1533376, tc_HOL_Obool)), _1533374), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533376, tc_HOL_Obool))), _1533380)), _1533382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533376, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533374, tc_fun(_1533376, tc_HOL_Obool)), _1533378), _1533380)), _1533382))], (45562 ^ _775828) ^ [_1674123, _1674125, _1674127, _1674129, _1674131] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1674123), tc_List_Olist(_1674125), tc_List_Olist(_1674127), hAPP(c_List_Omap(_1674123, _1674125), _1674129)), hAPP(c_List_Omap(_1674127, _1674123), _1674131)) = hAPP(c_List_Omap(_1674127, _1674125), hAPP(c_Fun_Ocomp(_1674123, _1674125, _1674127, _1674129), _1674131)))], (40437 ^ _775828) ^ [_1551224, _1551226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551224), c_Orderings_Otop__class_Otop(tc_fun(_1551224, tc_HOL_Obool)))), c_Fun_Oinj__on(_1551224, _1551224, _1551226, c_Orderings_Otop__class_Otop(tc_fun(_1551224, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1551224, _1551224, _1551226), c_Orderings_Otop__class_Otop(tc_fun(_1551224, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551224, tc_HOL_Obool)))], (46331 ^ _775828) ^ [_1692930, _1692932, _1692934] : [hBOOL(hAPP(hAPP(c_member(_1692930), _1692932), hAPP(c_List_Oset(_1692930), _1692934))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692930)), c_List_Oremove1(_1692930, _1692932, _1692934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692930)), _1692934)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11684 ^ _775828) ^ [_967735, _967737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967735), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967737), _967735)))))], (10798 ^ _775828) ^ [_952424] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952424) = _952424)], (38650 ^ _775828) ^ [_1511171, _1511173, _1511175, _1511177, _1511179, _1511181, _1511183] : [c_Equiv__Relations_Oequiv(_1511171, _1511173, _1511175), hBOOL(hAPP(hAPP(c_member(tc_fun(_1511171, tc_HOL_Obool)), _1511177), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511171), _1511173), _1511175))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1511171, tc_HOL_Obool)), _1511179), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511171), _1511173), _1511175))), hBOOL(hAPP(hAPP(c_member(_1511171), _1511181), _1511177)), hBOOL(hAPP(hAPP(c_member(_1511171), _1511183), _1511179)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1511171, _1511171)), hAPP(hAPP(c_Product__Type_OPair(_1511171, _1511171), _1511181), _1511183)), _1511175)), -(_1511177 = _1511179)], (47395 ^ _775828) ^ [_1721362, _1721364, _1721366] : [-(hAPP(hAPP(c_List_Olist__update(_1721362, c_List_Olist_ONil(_1721362)), _1721364), _1721366) = c_List_Olist_ONil(_1721362))], (42646 ^ _775828) ^ [_1605732, _1605734, _1605736] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1605732, _1605734, _1605736)), 42648 ^ _775828 : [(42649 ^ _775828) ^ [_1605878] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1605732)), _1605878), _1605734)), -(c_Hoare__Mirabelle_Otriple__valid(_1605732, 42647 ^ [_1605732, _1605734, _1605736], _1605878))], (42658 ^ _775828) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1605732, 42647 ^ [_1605732, _1605734, _1605736], 42654 ^ [_1605732, _1605734, _1605736])], (42656 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1605732)), 42654 ^ [_1605732, _1605734, _1605736]), _1605736)))]]], (41204 ^ _775828) ^ [_1570795, _1570797, _1570799, _1570801, _1570803] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1570795, _1570797, hAPP(hAPP(c_Set_Oinsert(_1570795), _1570799), _1570801)), _1570803))), 41205 ^ _775828 : [(41206 ^ _775828) ^ [_1570899, _1570901] : [hAPP(hAPP(c_Set_Oinsert(_1570795), _1570799), _1570801) = hAPP(hAPP(c_Set_Oinsert(_1570795), _1570901), _1570899), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1570795, _1570795, _1570797, _1570901, _1570899), _1570803)), -(hBOOL(hAPP(hAPP(c_member(_1570795), _1570901), _1570899)))]]], (46343 ^ _775828) ^ [_1693145, _1693147, _1693149, _1693151] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693145)), _1693147) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693149)), _1693151), hBOOL(hAPP(c_List_Odistinct(_1693145), _1693147)), -(c_Map_Odom(_1693145, _1693149, c_Map_Omap__of(_1693145, _1693149, hAPP(hAPP(c_List_Ozip(_1693145, _1693149), _1693147), _1693151))) = hAPP(c_List_Oset(_1693145), _1693147))], (4298 ^ _775828) ^ [_841482, _841484, _841486, _841488] : [-(c_Big__Operators_Olattice__class_OInf__fin(_841488, _841484) = c_Big__Operators_Olattice__class_OInf__fin(_841486, _841482)), _841488 = _841486, _841484 = _841482], (20290 ^ _775828) ^ [_1124376] : [-(c_Int_Osucc(c_Int_OBit1(_1124376)) = c_Int_OBit0(c_Int_Osucc(_1124376)))], (47827 ^ _775828) ^ [_1731085, _1731087, _1731089, _1731091, _1731093, _1731095] : [hAPP(hAPP(c_List_Olist_OCons(_1731085), _1731087), _1731089) = _1731091, _1731093 = hAPP(hAPP(c_List_Oappend(_1731085), _1731089), _1731095), -(hAPP(hAPP(c_List_Olist_OCons(_1731085), _1731087), _1731093) = hAPP(hAPP(c_List_Oappend(_1731085), _1731091), _1731095))], (5326 ^ _775828) ^ [_857218, _857220, _857222, _857224] : [-(tc_sum(_857224, _857220) = tc_sum(_857222, _857218)), _857224 = _857222, _857220 = _857218], (29611 ^ _775828) ^ [_1313354, _1313356] : [-(hBOOL(hAPP(_1313356, 29612 ^ [_1313354, _1313356]))), -(hAPP(c_Set_OCollect(_1313354), _1313356) = c_Orderings_Obot__class_Obot(tc_fun(_1313354, tc_HOL_Obool)))], (24589 ^ _775828) ^ [_1207811, _1207813, _1207815] : [24591 ^ _775828 : [(24594 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1207811), 24590 ^ [_1207811, _1207813, _1207815]), c_Wellfounded_Oacc(_1207811, _1207815)))], (24592 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1207811, _1207811)), hAPP(hAPP(c_Product__Type_OPair(_1207811, _1207811), 24590 ^ [_1207811, _1207813, _1207815]), _1207813)), _1207815)))]], -(hBOOL(hAPP(hAPP(c_member(_1207811), _1207813), c_Wellfounded_Oacc(_1207811, _1207815))))], (38226 ^ _775828) ^ [_1501838, _1501840, _1501842, _1501844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501838), _1501844)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501842), _1501840))), -(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), _1501838), _1501840)), 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), _1501842), _1501844)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (14854 ^ _775828) ^ [_1024506, _1024508, _1024510] : [class_Divides_Osemiring__div(_1024506), -(_1024508 = c_Groups_Ozero__class_Ozero(_1024506)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024506), _1024508), _1024510)), _1024508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024506), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024506), _1024510), _1024508)), c_Groups_Oone__class_Oone(_1024506)))], (47861 ^ _775828) ^ [_1731914, _1731916, _1731918, _1731920, _1731922, _1731924] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731914)), _1731916) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731918)), _1731920), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731914)), _1731922) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731918)), _1731924), -(hAPP(hAPP(c_List_Ozip(_1731914, _1731918), hAPP(hAPP(c_List_Oappend(_1731914), _1731916), _1731922)), hAPP(hAPP(c_List_Oappend(_1731918), _1731920), _1731924)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1731914, _1731918)), hAPP(hAPP(c_List_Ozip(_1731914, _1731918), _1731916), _1731920)), hAPP(hAPP(c_List_Ozip(_1731914, _1731918), _1731922), _1731924)))], (42864 ^ _775828) ^ [_1610738, _1610740, _1610742, _1610744, _1610746] : [class_Groups_Ocomm__monoid__mult(_1610738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610740), _1610742)), c_Fun_Oinj__on(_1610740, _1610740, _1610744, _1610742), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1610740, _1610738), _1610746), hAPP(c_Set_Oimage(_1610740, _1610740, _1610744), _1610742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1610740, _1610738), hAPP(c_Fun_Ocomp(_1610740, _1610738, _1610740, _1610746), _1610744)), _1610742))], (39452 ^ _775828) ^ [_1528664, _1528666] : [-(c_Relation_OId__on(_1528664, _1528666) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528664, tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool)), _1528666), hAPP(hAPP(c_COMBC(_1528664, tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool), tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1528664, _1528664), tc_fun(tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool), tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool)), _1528664), c_Set_Oinsert(tc_prod(_1528664, _1528664))), hAPP(hAPP(c_COMBS(_1528664, _1528664, tc_prod(_1528664, _1528664)), c_Product__Type_OPair(_1528664, _1528664)), c_COMBI(_1528664)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528664, _1528664), tc_HOL_Obool)))))], (50894 ^ _775828) ^ [_1800356, _1800358, _1800360] : [-(c_List_OdropWhile(_1800356, _1800358, _1800360) = c_List_Olist_ONil(_1800356)), hBOOL(hAPP(_1800358, hAPP(c_List_Ohd(_1800356), c_List_OdropWhile(_1800356, _1800358, _1800360))))], (39126 ^ _775828) ^ [_1520891, _1520893, _1520895, _1520897, _1520899] : [c_Fun_Oinj__on(_1520891, _1520893, _1520895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520891, tc_HOL_Obool)), _1520897), _1520899)), 39129 ^ _775828 : [(39134 ^ _775828) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520893, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1520891, _1520893, _1520895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520891, tc_HOL_Obool)), _1520897), _1520899))), hAPP(c_Set_Oimage(_1520891, _1520893, _1520895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520891, tc_HOL_Obool)), _1520899), _1520897))) = c_Orderings_Obot__class_Obot(tc_fun(_1520893, tc_HOL_Obool)))], (39132 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1520891, _1520893, _1520895, _1520899))], (39130 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1520891, _1520893, _1520895, _1520897))]]], (10318 ^ _775828) ^ [_943381, _943383, _943385] : [class_Rings_Ocomm__semiring__1(_943381), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943381), _943383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943381), _943385), _943383)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943381), _943385), c_Groups_Oone__class_Oone(_943381))), _943383))], (28996 ^ _775828) ^ [_1300388, _1300390] : [-(c_Transitive__Closure_Otrancl(_1300388, hAPP(c_Relation_Oconverse(_1300388, _1300388), _1300390)) = hAPP(c_Relation_Oconverse(_1300388, _1300388), c_Transitive__Closure_Otrancl(_1300388, _1300390)))], (22804 ^ _775828) ^ [_1172488, _1172490, _1172492] : [class_Fields_Olinordered__field(_1172488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172488), c_Groups_Ozero__class_Ozero(_1172488)), _1172490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172488), _1172492), c_Groups_Ozero__class_Ozero(_1172488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172488), _1172490), _1172492)), c_Groups_Ozero__class_Ozero(_1172488))))], (46616 ^ _775828) ^ [_1702056, _1702058, _1702060, _1702062, _1702064] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702056), tc_List_Olist(_1702056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702056), tc_List_Olist(_1702056)), _1702058), hAPP(hAPP(c_List_Olist_OCons(_1702056), _1702060), _1702062))), c_List_Olistrel(_1702056, _1702064))), 46621 ^ _775828 : [(46626 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702056), tc_List_Olist(_1702056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702056), tc_List_Olist(_1702056)), 46620 ^ [_1702056, _1702058, _1702060, _1702062, _1702064]), _1702062)), c_List_Olistrel(_1702056, _1702064))))], (46624 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1702056, _1702056)), hAPP(hAPP(c_Product__Type_OPair(_1702056, _1702056), 46619 ^ [_1702056, _1702058, _1702060, _1702062, _1702064]), _1702060)), _1702064)))], (46622 ^ _775828) ^ [] : [-(_1702058 = hAPP(hAPP(c_List_Olist_OCons(_1702056), 46619 ^ [_1702056, _1702058, _1702060, _1702062, _1702064]), 46620 ^ [_1702056, _1702058, _1702060, _1702062, _1702064]))]]], (19394 ^ _775828) ^ [_1109176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1109176)), -(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), _1109176))))], (46724 ^ _775828) ^ [_1705047, _1705049, _1705051, _1705053] : [class_Groups_Oab__group__add(_1705047), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1705047), hAPP(c_List_Omonoid__add__class_Olistsum(_1705047), hAPP(hAPP(c_List_Omap(_1705049, _1705047), _1705051), _1705053))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1705047), hAPP(hAPP(c_List_Omap(_1705049, _1705047), hAPP(c_Fun_Ocomp(_1705047, _1705047, _1705049, c_Groups_Ouminus__class_Ouminus(_1705047)), _1705051)), _1705053)))], (50371 ^ _775828) ^ [_1788387, _1788389] : [hBOOL(hAPP(c_List_Odistinct(_1788387), hAPP(c_List_Orev(_1788387), _1788389))), -(hBOOL(hAPP(c_List_Odistinct(_1788387), _1788389)))], (32211 ^ _775828) ^ [_1371158, _1371160, _1371162] : [class_Orderings_Olinorder(_1371158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371158), _1371160)), -(_1371160 = c_Orderings_Obot__class_Obot(tc_fun(_1371158, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1371158, hAPP(hAPP(c_Set_Oinsert(_1371158), _1371162), _1371160)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371158), _1371162), c_Big__Operators_Olinorder__class_OMin(_1371158, _1371160)))], (44234 ^ _775828) ^ [_1642532, _1642534, _1642536, _1642538] : [_1642532 = c_Orderings_Obot__class_Obot(tc_fun(_1642534, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642534, tc_fun(_1642536, tc_HOL_Obool)), _1642532), hAPP(c_COMBK(tc_fun(_1642536, tc_HOL_Obool), _1642534), _1642538)) = c_Orderings_Otop__class_Otop(tc_fun(_1642536, tc_HOL_Obool)))], (37000 ^ _775828) ^ [_1472189, _1472191, _1472193, _1472195] : [class_Groups_Ocomm__monoid__add(_1472189), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1472191), _1472193))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472191, _1472189), _1472195), _1472193) = c_Groups_Ozero__class_Ozero(_1472189))], (17491 ^ _775828) ^ [_1075305, _1075307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1075305)), -(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), _1075305), _1075307))))], (51328 ^ _775828) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (51182 ^ _775828) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (4584 ^ _775828) ^ [_845819, _845821, _845823, _845825, _845827, _845829] : [-(c_List_Osublist(_845829, _845825, _845821) = c_List_Osublist(_845827, _845823, _845819)), _845829 = _845827, _845825 = _845823, _845821 = _845819], (49770 ^ _775828) ^ [_1776232, _1776234, _1776236] : [class_Orderings_Olinorder(_1776232), 49773 ^ _775828 : [(49786 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1776232, hAPP(hAPP(c_List_Olist_OCons(_1776232), _1776234), _1776236))), c_List_Olinorder__class_Osorted(_1776232, _1776236), 49792 ^ _775828 : [(49795 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1776232), _1776234), 49791 ^ [_1776232, _1776234, _1776236]))], (49793 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776232), 49791 ^ [_1776232, _1776234, _1776236]), hAPP(c_List_Oset(_1776232), _1776236))))]]], (49774 ^ _775828) ^ [] : [c_List_Olinorder__class_Osorted(_1776232, hAPP(hAPP(c_List_Olist_OCons(_1776232), _1776234), _1776236)), 49777 ^ _775828 : [(49780 ^ _775828) ^ [_1776418] : [hBOOL(hAPP(hAPP(c_member(_1776232), _1776418), hAPP(c_List_Oset(_1776232), _1776236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1776232), _1776234), _1776418)))], (49778 ^ _775828) ^ [] : [-(c_List_Olinorder__class_Osorted(_1776232, _1776236))]]]]], (16883 ^ _775828) ^ [_1063615, _1063617, _1063619] : [class_Groups_Oordered__ab__group__add__abs(_1063615), 16886 ^ _775828 : [(16895 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), hAPP(c_Groups_Oabs__class_Oabs(_1063615), _1063617)), _1063619))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), _1063617), _1063619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), hAPP(c_Groups_Ouminus__class_Ouminus(_1063615), _1063617)), _1063619))], (16887 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), hAPP(c_Groups_Oabs__class_Oabs(_1063615), _1063617)), _1063619)), 16890 ^ _775828 : [(16893 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), hAPP(c_Groups_Ouminus__class_Ouminus(_1063615), _1063617)), _1063619)))], (16891 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063615), _1063617), _1063619)))]]]]], (32707 ^ _775828) ^ [_1380579, _1380581, _1380583, _1380585] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1380579, _1380583)), c_Sum__Type_OPlus(_1380579, _1380583, _1380581, _1380585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1380579), _1380581)), hAPP(c_Finite__Set_Ocard(_1380583), _1380585))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380579), _1380581)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380583), _1380585))], (23844 ^ _775828) ^ [_1193357, _1193359, _1193361, _1193363] : [class_Orderings_Olinorder(_1193357), 23847 ^ _775828 : [(23856 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193357), _1193361), _1193363)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), _1193361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), _1193363))], (23848 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193357), _1193361), _1193363))), 23851 ^ _775828 : [(23854 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), _1193363)))], (23852 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193357), _1193359), _1193361)))]]]]], (10530 ^ _775828) ^ [_947200, _947202] : [class_Groups_Ocomm__monoid__add(_947200), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947200), _947202), c_Groups_Ozero__class_Ozero(_947200)) = _947202)], (25030 ^ _775828) ^ [_1217139, _1217141, _1217143, _1217145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1217139), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1217141, _1217143, _1217139, _1217145) = 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(_1217141)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1217141)))], (25527 ^ _775828) ^ [_1227183, _1227185, _1227187] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227183), _1227185)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227183), _1227187))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1227183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227185), _1227187)))], (15276 ^ _775828) ^ [_1032311, _1032313, _1032315] : [class_Groups_Oab__group__add(_1032311), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032311), _1032313), _1032315)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032311), _1032315), _1032313))], (6358 ^ _775828) ^ [_876907] : [class_Rings_Osemiring__1(_876907), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_876907), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_876907))], (4726 ^ _775828) ^ [_848028, _848030, _848032, _848034, _848036, _848038] : [-(c_List_Olinorder__class_Oinsort__key(_848038, _848034, _848030) = c_List_Olinorder__class_Oinsort__key(_848036, _848032, _848028)), _848038 = _848036, _848034 = _848032, _848030 = _848028], (48187 ^ _775828) ^ [_1739708, _1739710, _1739712, _1739714, _1739716] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739708), tc_List_Olist(_1739708))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739708), tc_List_Olist(_1739708)), _1739710), _1739712)), c_List_Olistrel1(_1739708, _1739714))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739708), tc_List_Olist(_1739708))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739708), tc_List_Olist(_1739708)), hAPP(hAPP(c_List_Olist_OCons(_1739708), _1739716), _1739710)), hAPP(hAPP(c_List_Olist_OCons(_1739708), _1739716), _1739712))), c_List_Olistrel1(_1739708, _1739714))))], (11727 ^ _775828) ^ [_968567, _968569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968567)), _968569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968567), _968569)))], (51226 ^ _775828) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (38614 ^ _775828) ^ [_1510249, _1510251, _1510253, _1510255, _1510257] : [c_Equiv__Relations_Oequiv(_1510249, _1510251, _1510253), hBOOL(hAPP(hAPP(c_member(tc_prod(_1510249, _1510249)), hAPP(hAPP(c_Product__Type_OPair(_1510249, _1510249), _1510255), _1510257)), _1510253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510249, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510249, _1510249, _1510253), hAPP(hAPP(c_Set_Oinsert(_1510249), _1510255), c_Orderings_Obot__class_Obot(tc_fun(_1510249, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1510249, _1510249, _1510253), hAPP(hAPP(c_Set_Oinsert(_1510249), _1510257), c_Orderings_Obot__class_Obot(tc_fun(_1510249, tc_HOL_Obool)))))))], (14509 ^ _775828) ^ [_1018728, _1018730] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018728, _1018730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1018728 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018730), 14512 ^ [_1018728, _1018730]))], (11807 ^ _775828) ^ [_969994, _969996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969994), _969996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969994)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969996))))], (40662 ^ _775828) ^ [_1557488, _1557490, _1557492, _1557494, _1557496] : [c_Typedef_Otype__definition(_1557488, _1557490, _1557492, _1557494, _1557496), -(hAPP(c_Set_Oimage(_1557488, _1557490, _1557492), c_Orderings_Otop__class_Otop(tc_fun(_1557488, tc_HOL_Obool))) = _1557496)], (1670 ^ _775828) ^ [_799321, _799323] : [-(class_Rings_Omult__zero(_799321)), _799323 = _799321, class_Rings_Omult__zero(_799323)], (32885 ^ _775828) ^ [_1384068, _1384070, _1384072, _1384074, _1384076] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1384068, tc_Option_Ooption(_1384070)), _1384072), _1384074), hAPP(c_Option_Ooption_OSome(_1384070), _1384076)) = hAPP(c_COMBK(tc_Option_Ooption(_1384070), _1384068), c_Option_Ooption_ONone(_1384070))], (47215 ^ _775828) ^ [_1717572, _1717574, _1717576] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717572)), hAPP(hAPP(c_List_Otake(_1717572), _1717574), _1717576)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717572)), _1717576)), _1717574))], (45566 ^ _775828) ^ [_1674265, _1674267, _1674269, _1674271, _1674273] : [hAPP(hAPP(c_List_Omap(_1674265, _1674267), _1674269), _1674271) = hAPP(hAPP(c_List_Omap(_1674265, _1674267), _1674269), _1674273), c_Fun_Oinj__on(_1674265, _1674267, _1674269, c_Orderings_Otop__class_Otop(tc_fun(_1674265, tc_HOL_Obool))), -(_1674271 = _1674273)], (50359 ^ _775828) ^ [_1788046, _1788048, _1788050, _1788052] : [-(hAPP(hAPP(c_List_Omap(_1788046, _1788048), _1788050), c_List_Oconcat(_1788046, _1788052)) = c_List_Oconcat(_1788048, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1788046), tc_List_Olist(_1788048)), hAPP(c_List_Omap(_1788046, _1788048), _1788050)), _1788052)))], (49371 ^ _775828) ^ [_1767239, _1767241, _1767243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767239)), hAPP(c_List_Ofilter(_1767239, _1767241), _1767243))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767239)), _1767243))))], (32299 ^ _775828) ^ [_1372592, _1372594, _1372596] : [class_Orderings_Olinorder(_1372592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372592), _1372594)), -(_1372594 = c_Orderings_Obot__class_Obot(tc_fun(_1372592, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372592), _1372596)), -(_1372596 = c_Orderings_Obot__class_Obot(tc_fun(_1372592, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1372592, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372592, tc_HOL_Obool)), _1372594), _1372596)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372592), c_Big__Operators_Olinorder__class_OMax(_1372592, _1372594)), c_Big__Operators_Olinorder__class_OMax(_1372592, _1372596)))], (24497 ^ _775828) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (43052 ^ _775828) ^ [_1615329, _1615331, _1615333, _1615335, _1615337, _1615339, _1615341, _1615343] : [c_Finite__Set_Ofolding(_1615329, _1615331, _1615333, _1615335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615329), _1615337)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615329), _1615339)), -(hAPP(c_Fun_Ocomp(_1615331, _1615331, _1615341, hAPP(_1615335, _1615339)), hAPP(c_Fun_Ocomp(_1615331, _1615331, _1615341, hAPP(_1615335, _1615337)), _1615343)) = hAPP(c_Fun_Ocomp(_1615331, _1615331, _1615341, hAPP(_1615335, _1615337)), hAPP(c_Fun_Ocomp(_1615331, _1615331, _1615341, hAPP(_1615335, _1615339)), _1615343)))], (40556 ^ _775828) ^ [_1554930, _1554932, _1554934, _1554936] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554930, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40557 ^ [_1554930, _1554932, _1554934, _1554936])), _1554932) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554930, 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), 40557 ^ [_1554930, _1554932, _1554934, _1554936]), _1554934))), _1554936), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554930, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1554932) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1554930, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1554936))], (3178 ^ _775828) ^ [_823856, _823858, _823860, _823862, _823864, _823866] : [-(c_Partial__Function_Oflat__lub(_823866, _823862, _823858) = c_Partial__Function_Oflat__lub(_823864, _823860, _823856)), _823866 = _823864, _823862 = _823860, _823858 = _823856], (19240 ^ _775828) ^ [_1106720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106720), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106720))], (7923 ^ _775828) ^ [_902574, _902576, _902578] : [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, _902574)), _902576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902574)), _902578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902576), _902578)))], (40668 ^ _775828) ^ [_1557601, _1557603, _1557605, _1557607, _1557609, _1557611, _1557613] : [c_Typedef_Otype__definition(_1557601, _1557603, _1557605, _1557607, _1557609), 40671 ^ _775828 : [(40678 ^ _775828) ^ [] : [_1557611 = _1557613, -(hAPP(_1557605, _1557611) = hAPP(_1557605, _1557613))], (40672 ^ _775828) ^ [] : [hAPP(_1557605, _1557611) = hAPP(_1557605, _1557613), -(_1557611 = _1557613)]]], (48549 ^ _775828) ^ [_1749640, _1749642, _1749644, _1749646] : [-(hAPP(c_List_Orotate1(_1749640), c_List_Olist_ONil(_1749640)) = c_List_Olist_ONil(_1749640))], (10524 ^ _775828) ^ [_947105, _947107] : [class_Groups_Omonoid__add(_947105), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947105), _947107), c_Groups_Ozero__class_Ozero(_947105)) = _947107)], (33593 ^ _775828) ^ [_1399310, _1399312, _1399314, _1399316] : [hBOOL(hAPP(hAPP(c_member(_1399310), _1399312), _1399314)), hBOOL(hAPP(hAPP(c_member(_1399310), _1399312), _1399316)), -(hBOOL(hAPP(hAPP(c_member(_1399310), _1399312), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399310, tc_HOL_Obool)), _1399314), _1399316))))], (24386 ^ _775828) ^ [_1203844, _1203846, _1203848, _1203850, _1203852] : [-(hAPP(c_Product__Type_Ofst(_1203844, _1203846), hAPP(c_Product__Type_Oapfst(_1203848, _1203844, _1203846, _1203850), _1203852)) = hAPP(_1203850, hAPP(c_Product__Type_Ofst(_1203848, _1203846), _1203852)))], (18489 ^ _775828) ^ [_1093903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093903)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1093903) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1093903), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29941 ^ _775828) ^ [_1321090, _1321092, _1321094, _1321096, _1321098] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1321092, _1321090)), hAPP(hAPP(c_Product__Type_OPair(_1321092, _1321090), _1321096), _1321098)), hAPP(c_Relation_Oconverse(_1321090, _1321092), _1321094))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1321090, _1321092, hAPP(hAPP(c_COMBC(_1321090, tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_fun(_1321092, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1321092, tc_fun(tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_fun(_1321092, tc_HOL_Obool)), _1321090), c_COMBC(_1321092, tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1321092, tc_prod(_1321090, _1321092)), tc_fun(_1321092, tc_fun(tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_HOL_Obool)), _1321090), hAPP(c_COMBB(tc_prod(_1321090, _1321092), tc_fun(tc_fun(tc_prod(_1321090, _1321092), tc_HOL_Obool), tc_HOL_Obool), _1321092), c_member(tc_prod(_1321090, _1321092)))), c_Product__Type_OPair(_1321090, _1321092)))), _1321094)), _1321096), _1321098)))], (26389 ^ _775828) ^ [_1241839, _1241841, _1241843] : [class_Divides_Oring__div(_1241839), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241839), _1241841), _1241843)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241839), hAPP(c_Groups_Ouminus__class_Ouminus(_1241839), _1241843)), _1241841) = hAPP(c_Groups_Ouminus__class_Ouminus(_1241839), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241839), _1241843), _1241841)))], (46470 ^ _775828) ^ [_1698044, _1698046, _1698048, _1698050, _1698052] : [-(hAPP(hAPP(c_List_Olist_OCons(_1698044), _1698046), _1698048) = hAPP(hAPP(c_List_Olist_OCons(_1698044), _1698050), _1698052)), _1698046 = _1698050, _1698048 = _1698052], (20216 ^ _775828) ^ [_1123147, _1123149] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1123147)), c_Int_OBit1(_1123149)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123147), _1123149)))], (18725 ^ _775828) ^ [_1097633] : [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), _1097633))), -(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), _1097633)) = 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), _1097633))))], (43228 ^ _775828) ^ [_1619259, _1619261, _1619263, _1619265, _1619267, _1619269, _1619271, _1619273] : [class_Groups_Ocomm__monoid__mult(_1619259), c_Fun_Oinj__on(_1619261, _1619263, _1619265, _1619267), _1619269 = hAPP(c_Set_Oimage(_1619261, _1619263, _1619265), _1619267), 43242 ^ _775828 : [(43245 ^ _775828) ^ [] : [hAPP(_1619271, 43241 ^ [_1619259, _1619261, _1619263, _1619265, _1619267, _1619269, _1619271, _1619273]) = hAPP(hAPP(c_Fun_Ocomp(_1619263, _1619259, _1619261, _1619273), _1619265), 43241 ^ [_1619259, _1619261, _1619263, _1619265, _1619267, _1619269, _1619271, _1619273])], (43243 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619261), 43241 ^ [_1619259, _1619261, _1619263, _1619265, _1619267, _1619269, _1619271, _1619273]), _1619267)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1619263, _1619259), _1619273), _1619269) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1619261, _1619259), _1619271), _1619267))], (44252 ^ _775828) ^ [_1642947, _1642949, _1642951, _1642953, _1642955] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642947, tc_fun(_1642949, tc_HOL_Obool)), _1642951), hAPP(hAPP(c_COMBB(tc_fun(_1642949, tc_HOL_Obool), tc_fun(_1642949, tc_HOL_Obool), _1642947), hAPP(c_Set_Oinsert(_1642949), _1642953)), _1642955)) = hAPP(hAPP(c_Set_Oinsert(_1642949), _1642953), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642947, tc_fun(_1642949, tc_HOL_Obool)), _1642951), _1642955)))], (5555 ^ _775828) ^ [_863849] : [_863849 = hAPP(c_Nat_OSuc, _863849)], (27334 ^ _775828) ^ [_1260353, _1260355, _1260357, _1260359] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1260353, _1260353)), hAPP(hAPP(c_Product__Type_OPair(_1260353, _1260353), _1260355), _1260357)), c_Relation_OId__on(_1260353, _1260359)))), _1260355 = _1260357, hBOOL(hAPP(hAPP(c_member(_1260353), _1260355), _1260359))], (18465 ^ _775828) ^ [_1093508, _1093510] : [-(c_Divides_Odivmod__int(_1093508, _1093510) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1093508), _1093510)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1093508, _1093510)))], (29917 ^ _775828) ^ [_1320102, _1320104] : [_1320104 = c_Option_Ooption_ONone(_1320102), -(c_Option_Oset(_1320102, _1320104) = c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool)))], (42363 ^ _775828) ^ [_1598559] : [class_Lattices_Osemilattice__sup(_1598559), -(c_Finite__Set_Ofun__left__comm__idem(_1598559, _1598559, c_Lattices_Osemilattice__sup__class_Osup(_1598559)))], (50265 ^ _775828) ^ [_1785932, _1785934] : [hAPP(c_List_Orev(_1785932), _1785934) = c_List_Olist_ONil(_1785932), -(_1785934 = c_List_Olist_ONil(_1785932))], (35415 ^ _775828) ^ [_1441005, _1441007, _1441009] : [hBOOL(hAPP(c_Predicate_OPowp(_1441005, hAPP(hAPP(c_COMBC(_1441005, tc_fun(_1441005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1441005)), _1441007)), _1441009)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1441005, tc_HOL_Obool)), _1441009), hAPP(c_Set_OPow(_1441005), _1441007))))], (11056 ^ _775828) ^ [_956827, _956829, _956831, _956833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956827), _956829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956831), _956833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956827), _956831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956829), _956833))))], (16022 ^ _775828) ^ [_1047069, _1047071, _1047073] : [hBOOL(hAPP(_1047069, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047071), _1047073))), 16025 ^ _775828 : [(16032 ^ _775828) ^ [_1047254] : [_1047071 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047073), _1047254), -(hBOOL(hAPP(_1047069, _1047254)))], (16026 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047071), _1047073)), -(hBOOL(hAPP(_1047069, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (3202 ^ _775828) ^ [_824226, _824228] : [_824228 = _824226, -(c_Wellfounded_Ofinite__psubset(_824228) = c_Wellfounded_Ofinite__psubset(_824226))], (24659 ^ _775828) ^ [_1209159, _1209161] : [-(c_Nitpick_Oint__lcm(_1209159, _1209161) = 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), _1209159)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1209161)))))], (31591 ^ _775828) ^ [_1357371, _1357373, _1357375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1357371, _1357371)), _1357373), _1357375)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1357371, _1357371)), _1357373), c_Transitive__Closure_Ortrancl(_1357371, _1357375))))], (44846 ^ _775828) ^ [_1658134, _1658136, _1658138] : [class_Complete__Lattice_Ocomplete__lattice(_1658134), hBOOL(hAPP(hAPP(c_member(_1658134), _1658136), _1658138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658134), _1658136), c_Complete__Lattice_OSup__class_OSup(_1658134, _1658138))))], (632 ^ _775828) ^ [_785400, _785402, _785404, _785406, _785408, _785410, _785412, _785414, _785416, _785418] : [-(c_Finite__Set_Ofolding__image(_785416, _785412, _785408, _785404, _785400)), c_Finite__Set_Ofolding__image(_785418, _785414, _785410, _785406, _785402), _785418 = _785416, _785414 = _785412, _785410 = _785408, _785406 = _785404, _785402 = _785400], (32225 ^ _775828) ^ [_1371366, _1371368, _1371370] : [class_Orderings_Olinorder(_1371366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371366), _1371368)), -(_1371368 = c_Orderings_Obot__class_Obot(tc_fun(_1371366, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1371366, hAPP(hAPP(c_Set_Oinsert(_1371366), _1371370), _1371368)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371366), _1371370), c_Big__Operators_Olinorder__class_OMax(_1371366, _1371368)))], (44888 ^ _775828) ^ [_1658897, _1658899, _1658901, _1658903, _1658905] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658897, tc_fun(_1658899, tc_HOL_Obool)), _1658901), hAPP(hAPP(c_COMBS(_1658897, tc_fun(_1658899, tc_HOL_Obool), tc_fun(_1658899, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1658899, tc_HOL_Obool), tc_fun(tc_fun(_1658899, tc_HOL_Obool), tc_fun(_1658899, tc_HOL_Obool)), _1658897), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658899, tc_HOL_Obool))), _1658903)), _1658905)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1658899, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658899, tc_HOL_Obool), hAPP(c_Set_Oimage(_1658897, tc_fun(_1658899, tc_HOL_Obool), _1658903), _1658901))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658899, tc_HOL_Obool), hAPP(c_Set_Oimage(_1658897, tc_fun(_1658899, tc_HOL_Obool), _1658905), _1658901))))], (34175 ^ _775828) ^ [_1411663, _1411665] : [class_Lattices_Oboolean__algebra(_1411663), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411663), _1411665), hAPP(c_Groups_Ouminus__class_Ouminus(_1411663), _1411665)) = c_Orderings_Obot__class_Obot(_1411663))], (28589 ^ _775828) ^ [_1289277, _1289279, _1289281, _1289283, _1289285] : [class_Lattices_Osemilattice__sup(_1289277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289277), _1289279), _1289281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289277), _1289283), _1289285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289277), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289277), _1289279), _1289283)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289277), _1289281), _1289285))))], (19850 ^ _775828) ^ [_1116585, _1116587] : [class_Int_Onumber__ring(_1116585), class_Rings_Olinordered__idom(_1116585), 19857 ^ _775828 : [(19864 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116587), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116585), hAPP(c_Int_Onumber__class_Onumber__of(_1116585), _1116587)), c_Groups_Oone__class_Oone(_1116585))))], (19858 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116585), hAPP(c_Int_Onumber__class_Onumber__of(_1116585), _1116587)), c_Groups_Oone__class_Oone(_1116585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116587), c_Int_OBit1(c_Int_OPls))))]]], (21690 ^ _775828) ^ [_1151672, _1151674, _1151676, _1151678] : [class_Fields_Olinordered__field__inverse__zero(_1151672), class_Int_Onumber(_1151672), 21697 ^ _775828 : [(21698 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151672), _1151674), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))), _1151678)), 21701 ^ _775828 : [(21708 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)))), 21711 ^ _775828 : [(21718 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)), c_Groups_Ozero__class_Ozero(_1151672)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), _1151678)))], (21712 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)), c_Groups_Ozero__class_Ozero(_1151672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151672), _1151678), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))), _1151674)))]]], (21702 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), _1151674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151672), _1151678), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)))))]]], (21724 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151672), _1151674), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))), _1151678))), 21727 ^ _775828 : [(21730 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), _1151674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151672), _1151678), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))))], (21728 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))))]], 21731 ^ _775828 : [(21734 ^ _775828) ^ [] : [21735 ^ _775828 : [(21738 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151672), _1151678), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676))), _1151674))], (21736 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)), c_Groups_Ozero__class_Ozero(_1151672))))]], 21739 ^ _775828 : [(21742 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), _1151678))], (21740 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)), c_Groups_Ozero__class_Ozero(_1151672)))]]], (21732 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151672), c_Groups_Ozero__class_Ozero(_1151672)), hAPP(c_Int_Onumber__class_Onumber__of(_1151672), _1151676)))]]]]], (12855 ^ _775828) ^ [_987930, _987932, _987934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987930)), _987930 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987930), _987934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987932), _987930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _987934)))], (30403 ^ _775828) ^ [_1331442, _1331444, _1331446] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331442), _1331446)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331442), hAPP(hAPP(c_Set_Oinsert(_1331442), _1331444), _1331446))))], (51492 ^ _775828) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (33117 ^ _775828) ^ [_1388787, _1388789, _1388791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1388787), _1388789)), 33120 ^ _775828 : [(33121 ^ _775828) ^ [] : [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(_1388787, tc_Nat_Onat), _1388791), _1388789))), 33124 ^ _775828 : [(33125 ^ _775828) ^ [_1388955] : [hBOOL(hAPP(hAPP(c_member(_1388787), _1388955), _1388789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1388791, _1388955))))]]], (33131 ^ _775828) ^ [] : [33133 ^ _775828 : [(33136 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1388791, 33132 ^ [_1388787, _1388789, _1388791])))], (33134 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388787), 33132 ^ [_1388787, _1388789, _1388791]), _1388789)))]], -(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(_1388787, tc_Nat_Onat), _1388791), _1388789))))]]], (6296 ^ _775828) ^ [_876027, _876029, _876031] : [class_Orderings_Olinorder(_876027), 6299 ^ _775828 : [(6300 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876027), _876029), _876031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876027), _876031), _876029))), -(_876029 = _876031)], (6310 ^ _775828) ^ [] : [6311 ^ _775828 : [(6314 ^ _775828) ^ [] : [_876029 = _876031], (6312 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876027), _876031), _876029))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876027), _876029), _876031))]]], (42696 ^ _775828) ^ [_1606977, _1606979, _1606981, _1606983, _1606985, _1606987] : [c_Fun_Oinj__on(_1606977, _1606979, hAPP(c_Fun_Ocomp(_1606981, _1606979, _1606977, _1606983), _1606985), _1606987), -(c_Fun_Oinj__on(_1606981, _1606979, _1606983, hAPP(c_Set_Oimage(_1606977, _1606981, _1606985), _1606987)))], (20324 ^ _775828) ^ [_1125042, _1125044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1125042)), c_Int_OBit0(_1125044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125042), _1125044)))], (48964 ^ _775828) ^ [_1758594, _1758596, _1758598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1758594, tc_HOL_Obool)), _1758596), _1758598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1758594), tc_HOL_Obool)), c_List_Olists(_1758594, _1758596)), c_List_Olists(_1758594, _1758598))))], (37242 ^ _775828) ^ [_1478027, _1478029, _1478031] : [class_Groups_Ocomm__monoid__add(_1478027), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1478027), _1478029), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1478031))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478027), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1478027), _1478029), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1478031))), hAPP(_1478029, hAPP(c_Nat_OSuc, _1478031))))], (43270 ^ _775828) ^ [_1620260, _1620262, _1620264, _1620266, _1620268] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620260, _1620260)), hAPP(hAPP(c_Product__Type_OPair(_1620260, _1620260), _1620262), _1620264)), c_Transitive__Closure_Ortrancl(_1620260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620260, _1620260), tc_HOL_Obool)), _1620266), _1620268)))), 43276 ^ _775828 : [(43282 ^ _775828) ^ [] : [43275 ^ [_1620260, _1620262, _1620264, _1620266, _1620268] = 43278 ^ [_1620260, _1620262, _1620264, _1620266, _1620268]], (43280 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620260, _1620260)), hAPP(hAPP(c_Product__Type_OPair(_1620260, _1620260), 43275 ^ [_1620260, _1620262, _1620264, _1620266, _1620268]), 43278 ^ [_1620260, _1620262, _1620264, _1620266, _1620268])), _1620268)))], (43277 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620260, _1620260)), hAPP(hAPP(c_Product__Type_OPair(_1620260, _1620260), _1620262), 43275 ^ [_1620260, _1620262, _1620264, _1620266, _1620268])), c_Transitive__Closure_Ortrancl(_1620260, _1620266))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620260, _1620260)), hAPP(hAPP(c_Product__Type_OPair(_1620260, _1620260), _1620262), _1620264)), c_Transitive__Closure_Ortrancl(_1620260, _1620266))))], (39632 ^ _775828) ^ [_1533483, _1533485, _1533487, _1533489, _1533491] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533483, tc_HOL_Obool)), _1533485), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533487, tc_fun(_1533483, tc_HOL_Obool)), _1533489), _1533491)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533487, tc_fun(_1533483, tc_HOL_Obool)), _1533489), hAPP(hAPP(c_COMBB(tc_fun(_1533483, tc_HOL_Obool), tc_fun(_1533483, tc_HOL_Obool), _1533487), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533483, tc_HOL_Obool)), _1533485)), _1533491)))], (25393 ^ _775828) ^ [_1223771, _1223773, _1223775, _1223777, _1223779] : [-(_1223771 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1223773, _1223775, _1223777, _1223779), _1223771) = c_Lazy__Sequence_Obind(_1223773, _1223775, hAPP(_1223777, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1223771), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1223773, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1223775)), _1223779), _1223771)))], (44206 ^ _775828) ^ [_1641807, _1641809, _1641811, _1641813] : [44208 ^ _775828 : [(44211 ^ _775828) ^ [] : [hAPP(_1641813, 44207 ^ [_1641807, _1641809, _1641811, _1641813]) = c_Orderings_Otop__class_Otop(tc_fun(_1641807, tc_HOL_Obool))], (44209 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1641809), 44207 ^ [_1641807, _1641809, _1641811, _1641813]), _1641811)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1641807, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641809, tc_fun(_1641807, tc_HOL_Obool)), _1641811), _1641813))], (23550 ^ _775828) ^ [_1187562, _1187564, _1187566, _1187568, _1187570] : [-(hAPP(c_Nat_Onat_Onat__rec(_1187562, _1187564, _1187566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1187568)), _1187570)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1187562), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1187568))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1187562, _1187562), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1187562, tc_fun(_1187562, _1187562)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1187562, tc_fun(_1187562, _1187562)), tc_Int_Oint), c_If(_1187562)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1187562, _1187564, _1187566), _1187570))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1187562, _1187562), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1187562, _1187562), tc_Int_Oint), _1187566), 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)), _1187570))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1187562, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1187562, _1187564, _1187566)), 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)), _1187570))))))], (40099 ^ _775828) ^ [_1544631, _1544633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1544631, _1544633)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1544631, _1544633), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544633), c_Orderings_Otop__class_Otop(tc_fun(_1544633, tc_HOL_Obool)))))], (49255 ^ _775828) ^ [_1764888, _1764890, _1764892] : [_1764888 = c_List_Olist_ONil(_1764890), -(c_List_Obutlast(_1764890, hAPP(hAPP(c_List_Oappend(_1764890), _1764892), _1764888)) = c_List_Obutlast(_1764890, _1764892))], (31687 ^ _775828) ^ [_1359743, _1359745] : [-(c_Transitive__Closure_Ortrancl(_1359743, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1359743, _1359743), tc_HOL_Obool)), _1359745), c_Relation_OId(_1359743))) = c_Transitive__Closure_Ortrancl(_1359743, _1359745))], (9909 ^ _775828) ^ [_935909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935909)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_935909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23490 ^ _775828) ^ [_1186360, _1186362] : [-(c_Divides_Odivmod__int__rel(_1186360, _1186362) = 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, _1186360))), 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), _1186362)))))), 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)), _1186362))), 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)), _1186362))))), 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)), _1186362)))), 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), _1186362))), 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))))))))], (45170 ^ _775828) ^ [_1665274, _1665276, _1665278, _1665280] : [class_Lattices_Osemilattice__inf(_1665274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1665274), _1665276)), 45180 ^ _775828 : [(45183 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665274), _1665278), 45179 ^ [_1665274, _1665276, _1665278, _1665280]))], (45181 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665274), 45179 ^ [_1665274, _1665276, _1665278, _1665280]), _1665276)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1665274), _1665278), _1665280)), hAPP(hAPP(c_Finite__Set_Ofold(_1665274, _1665274, c_Lattices_Osemilattice__inf__class_Oinf(_1665274)), _1665280), _1665276))))], (42812 ^ _775828) ^ [_1609688, _1609690, _1609692, _1609694, _1609696, _1609698] : [class_Groups_Ocomm__monoid__add(_1609688), c_Fun_Oinj__on(_1609690, _1609692, _1609694, _1609696), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1609692, _1609688), _1609698), hAPP(c_Set_Oimage(_1609690, _1609692, _1609694), _1609696)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1609690, _1609688), hAPP(c_Fun_Ocomp(_1609692, _1609688, _1609690, _1609698), _1609694)), _1609696))], (10011 ^ _775828) ^ [_937574] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _937574)))], (24779 ^ _775828) ^ [_1211760, _1211762, _1211764, _1211766] : [24781 ^ _775828 : [(24786 ^ _775828) ^ [] : [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(_1211764, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24780 ^ [_1211760, _1211762, _1211764, _1211766]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1211764, 24780 ^ [_1211760, _1211762, _1211764, _1211766])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24784 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24780 ^ [_1211760, _1211762, _1211764, _1211766]), _1211762)))], (24782 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1211760), 24780 ^ [_1211760, _1211762, _1211764, _1211766])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211760), _1211762)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1211764, _1211760)), _1211766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211766), hAPP(_1211764, _1211762))), 24800 ^ _775828 : [(24805 ^ _775828) ^ [] : [-(hAPP(_1211764, 24799 ^ [_1211760, _1211762, _1211764, _1211766]) = _1211766)], (24803 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 24799 ^ [_1211760, _1211762, _1211764, _1211766]), _1211762)))], (24801 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1211760), 24799 ^ [_1211760, _1211762, _1211764, _1211766])))]]], (25293 ^ _775828) ^ [_1221990, _1221992] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1221990), _1221992))), -(c_Quickcheck_Obeyond(_1221990, _1221992) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (47571 ^ _775828) ^ [_1724730, _1724732] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724732)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724730), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724732)) = c_List_Olist_ONil(tc_Int_Oint))], (40732 ^ _775828) ^ [_1558684, _1558686, _1558688, _1558690] : [c_Fun_Oinj__on(_1558684, _1558686, _1558688, c_Orderings_Otop__class_Otop(tc_fun(_1558684, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558684, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1558684, _1558686, _1558688), hAPP(hAPP(c_Set_Oinsert(_1558686), _1558690), c_Orderings_Obot__class_Obot(tc_fun(_1558686, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1558684), c_HOL_OThe(_1558684, hAPP(hAPP(c_COMBC(_1558684, _1558686, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1558686, tc_fun(_1558686, tc_HOL_Obool), _1558684), c_fequal), _1558688)), _1558690))), c_Orderings_Obot__class_Obot(tc_fun(_1558684, tc_HOL_Obool))))))], (47599 ^ _775828) ^ [_1725227, _1725229, _1725231, _1725233] : [hBOOL(hAPP(c_List_Odistinct(_1725227), _1725229)), -(hBOOL(hAPP(hAPP(c_member(_1725227), _1725231), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1725227, tc_HOL_Obool)), hAPP(c_List_Oset(_1725227), _1725229)), hAPP(hAPP(c_Set_Oinsert(_1725227), hAPP(hAPP(c_List_Onth(_1725227), _1725229), _1725233)), c_Orderings_Obot__class_Obot(tc_fun(_1725227, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1725227), hAPP(hAPP(c_List_Olist__update(_1725227, _1725229), _1725233), _1725231))))], (17119 ^ _775828) ^ [_1068352, _1068354] : [class_Int_Onumber__ring(_1068352), -(hAPP(c_Int_Onumber__class_Onumber__of(_1068352), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068354)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1068352), hAPP(c_Int_Onumber__class_Onumber__of(_1068352), _1068354)))], (40175 ^ _775828) ^ [_1545984, _1545986] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545984, tc_HOL_Obool)), _1545986), c_Orderings_Otop__class_Otop(tc_fun(_1545984, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545984, tc_HOL_Obool)))], (49465 ^ _775828) ^ [_1769140, _1769142, _1769144] : [-(hAPP(c_List_Oset(_1769140), hAPP(c_List_Ofilter(_1769140, _1769142), _1769144)) = hAPP(c_Set_OCollect(_1769140), hAPP(hAPP(c_COMBS(_1769140, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1769140), c_fconj), hAPP(hAPP(c_COMBC(_1769140, tc_fun(_1769140, tc_HOL_Obool), tc_HOL_Obool), c_member(_1769140)), hAPP(c_List_Oset(_1769140), _1769144)))), _1769142)))], (49433 ^ _775828) ^ [_1768427, _1768429, _1768431, _1768433] : [-(hBOOL(hAPP(_1768427, _1768429))), -(c_List_Oremove1(_1768431, _1768429, hAPP(c_List_Ofilter(_1768431, _1768427), _1768433)) = hAPP(c_List_Ofilter(_1768431, _1768427), _1768433))], (2988 ^ _775828) ^ [_820727, _820729, _820731, _820733, _820735, _820737] : [-(c_Wellfounded_Omlex__prod(_820737, _820733, _820729) = c_Wellfounded_Omlex__prod(_820735, _820731, _820727)), _820737 = _820735, _820733 = _820731, _820729 = _820727], (4978 ^ _775828) ^ [_851994, _851996, _851998, _852000] : [-(c_List_Olast(_852000, _851996) = c_List_Olast(_851998, _851994)), _852000 = _851998, _851996 = _851994], (30141 ^ _775828) ^ [_1325298, _1325300, _1325302, _1325304] : [-(c_Nitpick_Ofold__graph_H(_1325298, _1325300, _1325302, _1325304, c_Orderings_Obot__class_Obot(tc_fun(_1325298, tc_HOL_Obool)), _1325304))], (50611 ^ _775828) ^ [_1794875, _1794877, _1794879, _1794881] : [hBOOL(hAPP(hAPP(c_member(_1794875), _1794877), hAPP(c_List_Oset(_1794875), c_List_OtakeWhile(_1794875, _1794879, _1794881)))), 50614 ^ _775828 : [(50617 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1794879, _1794877)))], (50615 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794875), _1794877), hAPP(c_List_Oset(_1794875), _1794881))))]]], (20348 ^ _775828) ^ [_1125473, _1125475] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1125473)), _1125475) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125473), _1125475))), _1125475))], (20098 ^ _775828) ^ [_1121078, _1121080] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1121078)), _1121080) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121078), _1121080)))], (51002 ^ _775828) ^ [_1802891, _1802893, _1802895] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1802891))), c_Enum_On__lists(_1802891, _1802893, _1802895)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802891)), _1802895)), _1802893))], (39454 ^ _775828) ^ [_1528788, _1528790, _1528792, _1528794, _1528796, _1528798] : [class_Complete__Lattice_Ocomplete__lattice(_1528788), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528790, _1528788), _1528792), hAPP(hAPP(c_COMBB(tc_fun(_1528794, _1528788), _1528788, _1528790), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528794, _1528788), _1528796)), _1528798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528794, _1528788), _1528796), hAPP(hAPP(c_COMBB(tc_fun(_1528790, _1528788), _1528788, _1528794), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528790, _1528788), _1528792)), hAPP(c_COMBC(_1528790, _1528794, _1528788), _1528798))))], (24612 ^ _775828) ^ [_1208316, _1208318] : [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), _1208316), _1208318))), 24615 ^ _775828 : [(24622 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208318), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24625 ^ _775828 : [(24634 ^ _775828) ^ [] : [-(c_Nitpick_Onorm__frac(_1208316, _1208318) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1208316), _1208318)), 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), _1208316))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1208318)))), -(_1208316 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1208318 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24626 ^ _775828) ^ [] : [24627 ^ _775828 : [(24630 ^ _775828) ^ [] : [_1208318 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24628 ^ _775828) ^ [] : [_1208316 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1208316, _1208318) = 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)))]]], (24616 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208318), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1208316, _1208318) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208316), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208318)))]]], (42351 ^ _775828) ^ [_1598401] : [class_Lattices_Oab__semigroup__idem__mult(_1598401), -(c_Finite__Set_Ofun__left__comm__idem(_1598401, _1598401, c_Groups_Otimes__class_Otimes(_1598401)))], (33639 ^ _775828) ^ [_1400224, _1400226] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400224, tc_HOL_Obool)), _1400226), c_Orderings_Obot__class_Obot(tc_fun(_1400224, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1400224, tc_HOL_Obool)))], (3028 ^ _775828) ^ [_821339, _821341, _821343, _821345, _821347, _821349, _821351, _821353] : [-(c_Recdef_Osame__fst(_821353, _821349, _821345, _821341) = c_Recdef_Osame__fst(_821351, _821347, _821343, _821339)), _821353 = _821351, _821349 = _821347, _821345 = _821343, _821341 = _821339], (11038 ^ _775828) ^ [_956436, _956438, _956440, _956442] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956436), _956438)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956440), _956438)), _956442)) = 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), _956436), _956440)), _956438)), _956442))], (48661 ^ _775828) ^ [_1751869, _1751871, _1751873] : [hAPP(c_List_Orotate(_1751869, _1751871), _1751873) = c_List_Olist_ONil(_1751869), -(_1751873 = c_List_Olist_ONil(_1751869))], (5549 ^ _775828) ^ [_863725, _863727, _863729, _863731] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863725)), _863727, _863729, _863731), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _863725), _863727, hAPP(c_Nat_OSuc, _863729), _863731))], (49527 ^ _775828) ^ [_1771232, _1771234] : [-(c_List_Otranspose(_1771232, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1771232)), c_List_Olist_ONil(_1771232)), _1771234)) = c_List_Otranspose(_1771232, _1771234))], (40638 ^ _775828) ^ [_1557023, _1557025] : [-(c_Equiv__Relations_Oequivp(_1557023, _1557025)), 40643 ^ _775828 : [(40646 ^ _775828) ^ [] : [hAPP(_1557025, 40639 ^ [_1557023, _1557025]) = hAPP(_1557025, 40640 ^ [_1557023, _1557025])], (40644 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1557025, 40639 ^ [_1557023, _1557025]), 40640 ^ [_1557023, _1557025])))]], 40647 ^ _775828 : [(40650 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1557025, 40639 ^ [_1557023, _1557025]), 40640 ^ [_1557023, _1557025]))], (40648 ^ _775828) ^ [] : [-(hAPP(_1557025, 40639 ^ [_1557023, _1557025]) = hAPP(_1557025, 40640 ^ [_1557023, _1557025]))]]], (45803 ^ _775828) ^ [] : [c_Com_OWT__bodies, 45806 ^ _775828 : [(45807 ^ _775828) ^ [_1679897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1679897), 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)), _1679897)))]]], (46901 ^ _775828) ^ [_1709004, _1709006, _1709008, _1709010] : [-(hAPP(c_List_Oset(tc_prod(_1709004, _1709006)), hAPP(hAPP(c_List_Ozip(_1709004, _1709006), _1709008), _1709010)) = hAPP(c_Set_OCollect(tc_prod(_1709004, _1709006)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1709004, _1709006)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1709004, _1709006), 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(_1709004, _1709006)), 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(_1709004, _1709006)), 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(_1709004, _1709006), tc_fun(tc_Nat_Onat, tc_prod(_1709004, _1709006)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1709004, _1709006), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1709004, _1709006)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1709004, _1709006)), c_COMBB(tc_prod(_1709004, _1709006), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1709006, tc_prod(_1709004, _1709006)), hAPP(hAPP(c_COMBB(_1709004, tc_fun(_1709006, tc_prod(_1709004, _1709006)), tc_Nat_Onat), c_Product__Type_OPair(_1709004, _1709006)), hAPP(c_List_Onth(_1709004), _1709008))), hAPP(c_List_Onth(_1709006), _1709010)))))), 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(_1709004)), _1709008)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709006)), _1709010)))))))], (5695 ^ _775828) ^ [_866503, _866505, _866507] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _866503)), _866505), _866507)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _866503))), _866505), _866507)))], (17575 ^ _775828) ^ [_1076693, _1076695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076693)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1076693)), _1076695) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076693), _1076695)))], (24122 ^ _775828) ^ [_1198250, _1198252] : [class_Orderings_Olinorder(_1198250), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198250), _1198252), _1198252) = _1198252)], (47984 ^ _775828) ^ [_1734727, _1734729, _1734731] : [hAPP(hAPP(c_List_Oappend(_1734727), _1734729), _1734731) = c_List_Olist_ONil(_1734727), 47987 ^ _775828 : [(47990 ^ _775828) ^ [] : [-(_1734731 = c_List_Olist_ONil(_1734727))], (47988 ^ _775828) ^ [] : [-(_1734729 = c_List_Olist_ONil(_1734727))]]], (15662 ^ _775828) ^ [_1039746, _1039748, _1039750] : [-(_1039746 = 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), _1039746), _1039748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039746), _1039750)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039748), _1039750))], (45448 ^ _775828) ^ [_1671344, _1671346, _1671348] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1671344), _1671346))), -(c_Smallcheck_Osmall_H(_1671348, _1671344, _1671346) = 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(_1671348, _1671344, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1671346), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1671348, _1671346)))], (24146 ^ _775828) ^ [_1198650, _1198652, _1198654] : [class_Orderings_Olinorder(_1198650), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198650), _1198652), _1198654) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198650), _1198654), _1198652))], (17737 ^ _775828) ^ [_1079623] : [-(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), _1079623)) = 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), _1079623))))], (7495 ^ _775828) ^ [_895440, _895442] : [class_Groups_Ogroup__add(_895440), -(hAPP(c_Groups_Ouminus__class_Ouminus(_895440), hAPP(c_Groups_Ouminus__class_Ouminus(_895440), _895442)) = _895442)], (27395 ^ _775828) ^ [_1262274, _1262276] : [-(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)))), _1262274)) = 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)))), _1262276))), 27397 ^ _775828 : [(27400 ^ _775828) ^ [] : [27401 ^ _775828 : [(27404 ^ _775828) ^ [] : [hBOOL(hAPP(_1262276, 27396 ^ [_1262274, _1262276]))], (27402 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1262274, 27396 ^ [_1262274, _1262276])))]], 27405 ^ _775828 : [(27408 ^ _775828) ^ [] : [hBOOL(hAPP(_1262274, 27396 ^ [_1262274, _1262276]))], (27406 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1262276, 27396 ^ [_1262274, _1262276])))]]], (27398 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27396 ^ [_1262274, _1262276])))]]], (25321 ^ _775828) ^ [_1222426, _1222428] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1222426)), hAPP(c_Code__Numeral_Oof__nat, _1222428)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222426), _1222428)))], (29901 ^ _775828) ^ [_1319631, _1319633, _1319635] : [-(hAPP(hAPP(c_Set_Oinsert(_1319631), _1319633), _1319635) = hAPP(c_Set_OCollect(_1319631), hAPP(hAPP(c_COMBS(_1319631, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1319631), c_fdisj), hAPP(hAPP(c_COMBC(_1319631, _1319631, tc_HOL_Obool), c_fequal), _1319633))), hAPP(hAPP(c_COMBC(_1319631, tc_fun(_1319631, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319631)), _1319635))))], (50363 ^ _775828) ^ [_1788164, _1788166] : [-(c_List_Oconcat(_1788164, _1788166) = hAPP(c_List_Ofoldl(tc_List_Olist(_1788164), tc_List_Olist(_1788164), c_List_Oappend(_1788164), c_List_Olist_ONil(_1788164)), _1788166))], (41366 ^ _775828) ^ [_1575472, _1575474] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575472, _1575472), tc_HOL_Obool)), c_Relation_OId__on(_1575472, _1575474)), hAPP(hAPP(c_Product__Type_OSigma(_1575472, _1575472), _1575474), hAPP(c_COMBK(tc_fun(_1575472, tc_HOL_Obool), _1575472), _1575474)))))], (47367 ^ _775828) ^ [_1720834, _1720836, _1720838] : [-(hAPP(hAPP(c_List_Ozip(_1720834, _1720836), c_List_Olist_ONil(_1720834)), _1720838) = c_List_Olist_ONil(tc_prod(_1720834, _1720836)))], (38005 ^ _775828) ^ [_1496321, _1496323, _1496325, _1496327, _1496329] : [-(hAPP(c_Relation_OImage(_1496321, _1496323, _1496325), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496321, tc_HOL_Obool)), _1496327), _1496329)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496323, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496321, _1496323, _1496325), _1496327)), hAPP(c_Relation_OImage(_1496321, _1496323, _1496325), _1496329)))], (46071 ^ _775828) ^ [_1686086, _1686088, _1686090, _1686092, _1686094, _1686096] : [-(hAPP(hAPP(c_List_Ozip(_1686086, _1686088), _1686090), hAPP(hAPP(c_List_Omap(_1686092, _1686088), _1686094), _1686096)) = hAPP(hAPP(c_List_Omap(tc_prod(_1686086, _1686092), tc_prod(_1686086, _1686088)), hAPP(c_Product__Type_Oprod_Oprod__case(_1686086, _1686092, tc_prod(_1686086, _1686088)), hAPP(hAPP(c_COMBC(_1686086, tc_fun(_1686092, _1686088), tc_fun(_1686092, tc_prod(_1686086, _1686088))), hAPP(hAPP(c_COMBB(tc_fun(_1686088, tc_prod(_1686086, _1686088)), tc_fun(tc_fun(_1686092, _1686088), tc_fun(_1686092, tc_prod(_1686086, _1686088))), _1686086), c_COMBB(_1686088, tc_prod(_1686086, _1686088), _1686092)), c_Product__Type_OPair(_1686086, _1686088))), _1686094))), hAPP(hAPP(c_List_Ozip(_1686086, _1686092), _1686090), _1686096)))], (38102 ^ _775828) ^ [_1498512, _1498514, _1498516, _1498518, _1498520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498512, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1498514, _1498512, _1498516), _1498518)), _1498520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498514, tc_HOL_Obool)), _1498518), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498514, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1498512, _1498514, hAPP(c_Relation_Oconverse(_1498514, _1498512), _1498516)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498512, tc_HOL_Obool)), _1498520))))))], (18697 ^ _775828) ^ [_1096972, _1096974, _1096976, _1096978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1096972), _1096974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1096976), _1096978)), -(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), _1096972), _1096976)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1096974), _1096978))), c_FunDef_Opair__leq)))], (17719 ^ _775828) ^ [_1079260, _1079262] : [class_Groups_Omonoid__mult(_1079260), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079260), c_Groups_Oone__class_Oone(_1079260)), _1079262) = c_Groups_Oone__class_Oone(_1079260))], (25645 ^ _775828) ^ [_1229208, _1229210, _1229212] : [class_Rings_Ocomm__ring__1(_1229208), 25648 ^ _775828 : [(25655 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229208), _1229210), _1229212)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229208), hAPP(c_Groups_Ouminus__class_Ouminus(_1229208), _1229210)), _1229212)))], (25649 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229208), hAPP(c_Groups_Ouminus__class_Ouminus(_1229208), _1229210)), _1229212)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229208), _1229210), _1229212)))]]], (17889 ^ _775828) ^ [_1082199, _1082201, _1082203, _1082205] : [class_Groups_Omonoid__mult(_1082199), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082199), _1082201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1082203), _1082205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082199), hAPP(hAPP(c_Power_Opower__class_Opower(_1082199), _1082201), _1082203)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082199), _1082201), _1082205)))], (28876 ^ _775828) ^ [_1296571, _1296573, _1296575] : [-(c_Hilbert__Choice_OEps(tc_prod(_1296571, _1296573), _1296575) = c_Hilbert__Choice_OEps(tc_prod(_1296571, _1296573), hAPP(c_Product__Type_Oprod_Oprod__case(_1296571, _1296573, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1296573, tc_prod(_1296571, _1296573)), tc_fun(_1296573, tc_HOL_Obool), _1296571), hAPP(c_COMBB(tc_prod(_1296571, _1296573), tc_HOL_Obool, _1296573), _1296575)), c_Product__Type_OPair(_1296571, _1296573)))))], (19734 ^ _775828) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (24410 ^ _775828) ^ [_1204446] : [class_Orderings_Olinorder(_1204446), -(c_Orderings_Oord_Omin(_1204446, hAPP(c_COMBC(_1204446, _1204446, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1204446))) = c_Orderings_Oord__class_Omax(_1204446))], (21250 ^ _775828) ^ [_1143999, _1144001, _1144003, _1144005] : [class_Rings_Odivision__ring(_1143999), -(_1144001 = c_Groups_Ozero__class_Ozero(_1143999)), 21257 ^ _775828 : [(21264 ^ _775828) ^ [] : [_1144003 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143999), _1144005), _1144001), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143999), _1144003), _1144001) = _1144005)], (21258 ^ _775828) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143999), _1144003), _1144001) = _1144005, -(_1144003 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143999), _1144005), _1144001))]]], (28783 ^ _775828) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (11070 ^ _775828) ^ [_957073, _957075, _957077, _957079] : [class_Orderings_Oord(_957073), 11073 ^ _775828 : [(11082 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957075, _957073)), _957077), _957079))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957075, _957073)), _957077), _957079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957075, _957073)), _957079), _957077)))], (11074 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957075, _957073)), _957077), _957079)), 11077 ^ _775828 : [(11080 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957075, _957073)), _957079), _957077))], (11078 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957075, _957073)), _957077), _957079)))]]]]], (12637 ^ _775828) ^ [_984327, _984329] : [12638 ^ _775828 : [(12639 ^ _775828) ^ [_984383] : [_984329 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984327), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _984383)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984327), _984329)))], (30227 ^ _775828) ^ [_1326774, _1326776, _1326778, _1326780] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326774), _1326776)), 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)), _1326778), _1326774)), 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)), _1326780), _1326776)), 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)), _1326778), _1326780)), _1326776)), c_FunDef_Omax__strict)))], (5204 ^ _775828) ^ [_855415, _855417] : [_855417 = _855415, -(c_List_Onth(_855417) = c_List_Onth(_855415))], (51158 ^ _775828) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (23456 ^ _775828) ^ [_1185512, _1185514, _1185516, _1185518, _1185520, _1185522] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185512, _1185514, _1185516), _1185518), hAPP(hAPP(c_Product__Type_OPair(_1185512, _1185514), _1185520), _1185522)) = hAPP(hAPP(_1185518, _1185520), _1185522))], (23656 ^ _775828) ^ [_1190123, _1190125, _1190127] : [class_Orderings_Olinorder(_1190123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190123), _1190125), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190123), _1190127), _1190125))))], (31961 ^ _775828) ^ [_1366915, _1366917, _1366919] : [class_Groups_Olinordered__ab__semigroup__add(_1366915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366915), _1366917)), -(_1366917 = c_Orderings_Obot__class_Obot(tc_fun(_1366915, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366915), _1366919), c_Big__Operators_Olinorder__class_OMin(_1366915, _1366917)) = c_Big__Operators_Olinorder__class_OMin(_1366915, hAPP(c_Set_OCollect(_1366915), hAPP(hAPP(c_COMBB(tc_fun(_1366915, tc_HOL_Obool), tc_HOL_Obool, _1366915), c_HOL_OEx(_1366915)), hAPP(hAPP(c_COMBC(_1366915, tc_fun(_1366915, tc_HOL_Obool), tc_fun(_1366915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366915, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1366915, tc_HOL_Obool), tc_fun(_1366915, tc_HOL_Obool)), _1366915), c_COMBS(_1366915, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366915, tc_HOL_Obool), tc_fun(_1366915, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1366915), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366915), c_fconj)), hAPP(hAPP(c_COMBC(_1366915, tc_fun(_1366915, _1366915), tc_fun(_1366915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366915, tc_HOL_Obool), tc_fun(tc_fun(_1366915, _1366915), tc_fun(_1366915, tc_HOL_Obool)), _1366915), c_COMBB(_1366915, tc_HOL_Obool, _1366915)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1366915), _1366919))))), hAPP(hAPP(c_COMBC(_1366915, tc_fun(_1366915, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366915)), _1366917))))))], (2760 ^ _775828) ^ [_816959, _816961] : [_816961 = _816959, -(c_Lazy__Sequence_Ohit__bound(_816961) = c_Lazy__Sequence_Ohit__bound(_816959))], (13925 ^ _775828) ^ [_1008025, _1008027, _1008029, _1008031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008027), _1008029)), -(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), _1008029), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008031, _1008025))), _1008027)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008029), _1008025))))], (46851 ^ _775828) ^ [_1707797, _1707799, _1707801] : [class_Orderings_Olinorder(_1707797), -(hAPP(c_List_Oset(_1707797), c_List_Olinorder__class_Oinsort__insert__key(_1707797, _1707797, c_COMBI(_1707797), _1707799, _1707801)) = hAPP(hAPP(c_Set_Oinsert(_1707797), _1707799), hAPP(c_List_Oset(_1707797), _1707801)))], (20458 ^ _775828) ^ [_1127360] : [class_Rings_Osemiring__1(_1127360), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127360), c_Groups_Oone__class_Oone(_1127360)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1127360))], (5410 ^ _775828) ^ [_858498, _858500] : [_858500 = _858498, -(tc_Hoare__Mirabelle_Otriple(_858500) = tc_Hoare__Mirabelle_Otriple(_858498))], (19556 ^ _775828) ^ [_1111943, _1111945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1111943)), c_Int_OBit1(_1111945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111943), _1111945)))], (9939 ^ _775828) ^ [_936390] : [-(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), _936390))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46207 ^ _775828) ^ [_1689503, _1689505, _1689507, _1689509] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689503)), _1689505) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689507)), _1689509), -(hAPP(hAPP(c_List_Omap(tc_prod(_1689503, _1689507), _1689507), c_Product__Type_Osnd(_1689503, _1689507)), hAPP(hAPP(c_List_Ozip(_1689503, _1689507), _1689505), _1689509)) = _1689509)], (13603 ^ _775828) ^ [_1001940, _1001942, _1001944, _1001946, _1001948] : [c_Com_Ocom_OLocal(_1001940, _1001942, _1001944) = c_Com_Ocom_OAss(_1001946, _1001948)], (51204 ^ _775828) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (33439 ^ _775828) ^ [_1396107, _1396109, _1396111] : [class_Orderings_Olinorder(_1396107), hAPP(_1396109, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396107), 33444 ^ [_1396107, _1396109, _1396111]), 33445 ^ [_1396107, _1396109, _1396111])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396107), hAPP(_1396109, 33444 ^ [_1396107, _1396109, _1396111])), hAPP(_1396109, 33445 ^ [_1396107, _1396109, _1396111])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396107), _1396111)), -(_1396111 = c_Orderings_Obot__class_Obot(tc_fun(_1396107, tc_HOL_Obool))), -(hAPP(_1396109, c_Big__Operators_Olattice_OInf__fin(_1396107, c_Orderings_Oord__class_Omin(_1396107), _1396111)) = c_Big__Operators_Olattice_OInf__fin(_1396107, c_Orderings_Oord__class_Omin(_1396107), hAPP(c_Set_Oimage(_1396107, _1396107, _1396109), _1396111)))], (50609 ^ _775828) ^ [_1794801, _1794803, _1794805, _1794807, _1794809] : [-(hAPP(hAPP(c_List_Ozip(_1794801, _1794803), c_List_OtakeWhile(_1794801, _1794805, _1794807)), _1794809) = c_List_OtakeWhile(tc_prod(_1794801, _1794803), hAPP(c_Fun_Ocomp(_1794801, tc_HOL_Obool, tc_prod(_1794801, _1794803), _1794805), c_Product__Type_Ofst(_1794801, _1794803)), hAPP(hAPP(c_List_Ozip(_1794801, _1794803), _1794807), _1794809)))], (46025 ^ _775828) ^ [_1684580, _1684582] : [-(hAPP(hAPP(c_List_Ozip(_1684580, _1684580), _1684582), _1684582) = hAPP(hAPP(c_List_Omap(_1684580, tc_prod(_1684580, _1684580)), hAPP(hAPP(c_COMBS(_1684580, _1684580, tc_prod(_1684580, _1684580)), c_Product__Type_OPair(_1684580, _1684580)), c_COMBI(_1684580))), _1684582))], (48852 ^ _775828) ^ [_1755818, _1755820] : [class_Complete__Lattice_Ocomplete__lattice(_1755818), -(c_Complete__Lattice_OInf__class_OInf(_1755818, hAPP(c_List_Oset(_1755818), _1755820)) = hAPP(c_List_Ofoldl(_1755818, _1755818, c_Lattices_Osemilattice__inf__class_Oinf(_1755818), c_Orderings_Otop__class_Otop(_1755818)), _1755820))], (28012 ^ _775828) ^ [_1276838, _1276840] : [c_FunDef_Oreduction__pair(_1276838, _1276840), 28015 ^ _775828 : [(28018 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1276838, _1276838, _1276838), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool), tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool)), _1276840)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool), tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool)), _1276840))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool), tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool)), _1276840))))], (28016 ^ _775828) ^ [] : [-(c_Wellfounded_Owf(_1276838, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool), tc_fun(tc_prod(_1276838, _1276838), tc_HOL_Obool)), _1276840)))]]], (50848 ^ _775828) ^ [_1799437, _1799439, _1799441] : [hBOOL(hAPP(c_List_Odistinct(_1799437), _1799439)), hBOOL(hAPP(hAPP(c_member(_1799437), _1799441), hAPP(c_List_Oset(_1799437), _1799439))), -(c_List_OdropWhile(_1799437, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1799437), c_fNot), hAPP(hAPP(c_COMBC(_1799437, _1799437, tc_HOL_Obool), c_fequal), _1799441)), hAPP(c_List_Orev(_1799437), _1799439)) = hAPP(hAPP(c_List_Olist_OCons(_1799437), _1799441), hAPP(c_List_Orev(_1799437), c_List_OtakeWhile(_1799437, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1799437), c_fNot), hAPP(hAPP(c_COMBC(_1799437, _1799437, tc_HOL_Obool), c_fequal), _1799441)), _1799439))))], (29847 ^ _775828) ^ [_1318342, _1318344, _1318346, _1318348] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318342, tc_HOL_Obool)), _1318344), hAPP(hAPP(c_Set_Oinsert(_1318342), _1318346), _1318348)))), 29850 ^ _775828 : [(29853 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318342, tc_HOL_Obool)), _1318344), _1318348))], (29851 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318342), _1318346), _1318348)))]], 29854 ^ _775828 : [(29857 ^ _775828) ^ [] : [29858 ^ _775828 : [(29861 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318342, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318342, tc_HOL_Obool)), _1318344), hAPP(hAPP(c_Set_Oinsert(_1318342), _1318346), c_Orderings_Obot__class_Obot(tc_fun(_1318342, tc_HOL_Obool))))), _1318348))], (29859 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318342), _1318346), _1318344)))]], 29862 ^ _775828 : [(29865 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318342, tc_HOL_Obool)), _1318344), _1318348))], (29863 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1318342), _1318346), _1318344))]]], (29855 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1318342), _1318346), _1318348))]]], (36413 ^ _775828) ^ [_1459685, _1459687, _1459689, _1459691] : [class_Orderings_Olinorder(_1459685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1459685), _1459687), _1459689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459685), _1459689), _1459691)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459685, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1459685, _1459687, _1459689)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459685, _1459689), _1459691)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1459685, _1459687, _1459691))], (46969 ^ _775828) ^ [_1710899, _1710901, _1710903] : [-(_1710899 = _1710901), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710903)), _1710899) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710903)), _1710901), 46975 ^ _775828 : [(46978 ^ _775828) ^ [] : [hAPP(hAPP(c_List_Onth(_1710903), _1710899), 46974 ^ [_1710899, _1710901, _1710903]) = hAPP(hAPP(c_List_Onth(_1710903), _1710901), 46974 ^ [_1710899, _1710901, _1710903])], (46976 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46974 ^ [_1710899, _1710901, _1710903]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710903)), _1710899))))]]], (39235 ^ _775828) ^ [_1523553, _1523555, _1523557, _1523559, _1523561, _1523563] : [hBOOL(hAPP(hAPP(c_member(_1523553), _1523555), _1523557)), hBOOL(hAPP(hAPP(_1523559, _1523555), _1523561)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523553, tc_fun(_1523563, tc_HOL_Obool)), _1523557), _1523559), _1523561)))], (35379 ^ _775828) ^ [_1439782, _1439784, _1439786] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1439782, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1439782, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1439782), _1439784)), hAPP(c_Set_OPow(_1439782), _1439786))), hAPP(c_Set_OPow(_1439782), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439782, tc_HOL_Obool)), _1439784), _1439786)))))], (51236 ^ _775828) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (14556 ^ _775828) ^ [_1019571, _1019573, _1019575] : [class_Divides_Osemiring__div(_1019571), -(_1019573 = c_Groups_Ozero__class_Ozero(_1019571)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019571), _1019573), _1019575)), _1019573) = _1019575)], (15103 ^ _775828) ^ [_1029194, _1029196, _1029198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029194)), 15109 ^ _775828 : [(15112 ^ _775828) ^ [] : [hBOOL(hAPP(_1029196, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15108 ^ [_1029194, _1029196, _1029198]), _1029194)))], (15110 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1029196, 15108 ^ [_1029194, _1029196, _1029198])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029198)), 15117 ^ _775828 : [(15118 ^ _775828) ^ [_1029483] : [hBOOL(hAPP(_1029196, _1029483)), -(hBOOL(hAPP(_1029196, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1029483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029198), _1029194)))))]]], (32871 ^ _775828) ^ [_1383730, _1383732, _1383734, _1383736, _1383738, _1383740] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383730, _1383732), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383730, _1383732), _1383734), _1383736), _1383738)), _1383736), _1383740) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383730, _1383732), _1383734), _1383736), _1383740))], (4378 ^ _775828) ^ [_842690, _842692, _842694, _842696] : [-(c_Fun_Ofun__upd(_842696, _842692) = c_Fun_Ofun__upd(_842694, _842690)), _842696 = _842694, _842692 = _842690], (27723 ^ _775828) ^ [_1268838, _1268840, _1268842, _1268844, _1268846] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1268838, _1268840, _1268842), _1268844), _1268846) = hAPP(c_Set_OCollect(tc_prod(_1268838, _1268842)), hAPP(c_Product__Type_Oprod_Oprod__case(_1268838, _1268842, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1268842, tc_fun(_1268840, tc_HOL_Obool)), tc_fun(_1268842, tc_HOL_Obool), _1268838), hAPP(c_COMBB(tc_fun(_1268840, tc_HOL_Obool), tc_HOL_Obool, _1268842), c_HOL_OEx(_1268840))), hAPP(hAPP(c_COMBC(_1268838, tc_fun(_1268842, tc_fun(_1268840, tc_HOL_Obool)), tc_fun(_1268842, tc_fun(_1268840, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268840, tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), tc_fun(tc_fun(_1268842, tc_fun(_1268840, tc_HOL_Obool)), tc_fun(_1268842, tc_fun(_1268840, tc_HOL_Obool))), _1268838), c_COMBB(tc_fun(_1268840, tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool), _1268842)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1268840, tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), _1268838), c_COMBS(_1268840, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_HOL_Obool), tc_fun(_1268840, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1268838), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268840), c_fconj)), hAPP(hAPP(c_COMBC(_1268838, tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_fun(tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), _1268838), c_COMBC(_1268840, tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_prod(_1268838, _1268840)), tc_fun(_1268840, tc_fun(tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_HOL_Obool)), _1268838), hAPP(c_COMBB(tc_prod(_1268838, _1268840), tc_fun(tc_fun(tc_prod(_1268838, _1268840), tc_HOL_Obool), tc_HOL_Obool), _1268840), c_member(tc_prod(_1268838, _1268840)))), c_Product__Type_OPair(_1268838, _1268840)))), _1268844))))), hAPP(hAPP(c_COMBC(_1268842, tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_fun(tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_fun(_1268840, tc_HOL_Obool)), _1268842), c_COMBC(_1268840, tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268840, tc_prod(_1268840, _1268842)), tc_fun(_1268840, tc_fun(tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_HOL_Obool)), _1268842), hAPP(c_COMBB(tc_prod(_1268840, _1268842), tc_fun(tc_fun(tc_prod(_1268840, _1268842), tc_HOL_Obool), tc_HOL_Obool), _1268840), c_member(tc_prod(_1268840, _1268842)))), hAPP(c_COMBC(_1268840, _1268842, tc_prod(_1268840, _1268842)), c_Product__Type_OPair(_1268840, _1268842))))), _1268846))))))], (26515 ^ _775828) ^ [_1244115, _1244117, _1244119] : [class_Rings_Odvd(_1244115), class_Rings_Osemiring__0(_1244115), 26522 ^ _775828 : [(26532 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1244117, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244115), _1244119), 26539 ^ [_1244115, _1244117, _1244119])))), 26533 ^ _775828 : [(26534 ^ _775828) ^ [_1244444] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244115), _1244119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244115), _1244444), c_Groups_Ozero__class_Ozero(_1244115)))), hBOOL(hAPP(_1244117, _1244444))]]], (26523 ^ _775828) ^ [] : [26524 ^ _775828 : [(26525 ^ _775828) ^ [_1244307] : [hBOOL(hAPP(_1244117, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244115), _1244119), _1244307)))]], 26527 ^ _775828 : [(26530 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1244117, 26526 ^ [_1244115, _1244117, _1244119])))], (26528 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244115), _1244119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244115), 26526 ^ [_1244115, _1244117, _1244119]), c_Groups_Ozero__class_Ozero(_1244115)))))]]]]], (40788 ^ _775828) ^ [_1560117, _1560119, _1560121, _1560123] : [-(hAPP(c_Set_Ovimage(_1560117, _1560119, _1560121), hAPP(c_Set_OCollect(_1560119), _1560123)) = hAPP(c_Set_OCollect(_1560117), hAPP(hAPP(c_COMBB(_1560119, tc_HOL_Obool, _1560117), _1560123), _1560121)))], (24284 ^ _775828) ^ [_1201762] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1201762), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27757 ^ _775828) ^ [_1270072, _1270074, _1270076, _1270078, _1270080, _1270082, _1270084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1270072, _1270074), tc_HOL_Obool)), _1270076), _1270078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1270074, _1270080), tc_HOL_Obool)), _1270082), _1270084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1270072, _1270080), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1270072, _1270074, _1270080), _1270076), _1270082)), hAPP(hAPP(c_Relation_Orel__comp(_1270072, _1270074, _1270080), _1270078), _1270084))))], (27232 ^ _775828) ^ [_1257687, _1257689, _1257691] : [hBOOL(hAPP(_1257691, _1257689)), -(hBOOL(hAPP(hAPP(c_member(_1257687), _1257689), hAPP(c_Set_OCollect(_1257687), _1257691))))], (12805 ^ _775828) ^ [_987139, _987141] : [class_Groups_Osgn__if(_987139), 12808 ^ _775828 : [(12815 ^ _775828) ^ [] : [-(_987141 = c_Groups_Ozero__class_Ozero(_987139)), 12818 ^ _775828 : [(12825 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987139), c_Groups_Ozero__class_Ozero(_987139)), _987141))), -(c_Groups_Osgn__class_Osgn(_987139, _987141) = hAPP(c_Groups_Ouminus__class_Ouminus(_987139), c_Groups_Oone__class_Oone(_987139)))], (12819 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987139), c_Groups_Ozero__class_Ozero(_987139)), _987141)), -(c_Groups_Osgn__class_Osgn(_987139, _987141) = c_Groups_Oone__class_Oone(_987139))]]], (12809 ^ _775828) ^ [] : [_987141 = c_Groups_Ozero__class_Ozero(_987139), -(c_Groups_Osgn__class_Osgn(_987139, _987141) = c_Groups_Ozero__class_Ozero(_987139))]]], (46051 ^ _775828) ^ [_1685489, _1685491, _1685493, _1685495, _1685497, _1685499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685489, _1685491)), hAPP(hAPP(c_Product__Type_OPair(_1685489, _1685491), _1685493), _1685495)), hAPP(c_List_Oset(tc_prod(_1685489, _1685491)), hAPP(hAPP(c_List_Ozip(_1685489, _1685491), _1685497), _1685499)))), -(hBOOL(hAPP(hAPP(c_member(_1685489), _1685493), hAPP(c_List_Oset(_1685489), _1685497))))], (45238 ^ _775828) ^ [_1666679, _1666681, _1666683, _1666685, _1666687, _1666689, _1666691, _1666693] : [c_Finite__Set_Ofolding__image__simple__idem(_1666679, _1666681, _1666683, _1666685, _1666687, _1666689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1666681), _1666691)), -(hAPP(_1666689, hAPP(hAPP(c_Set_Oinsert(_1666681), _1666693), _1666691)) = hAPP(hAPP(_1666683, hAPP(_1666687, _1666693)), hAPP(_1666689, _1666691)))], (20840 ^ _775828) ^ [_1134479, _1134481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134479)), 20843 ^ _775828 : [(20850 ^ _775828) ^ [] : [-(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), _1134481), _1134479)))), -(c_Divides_OnegDivAlg(_1134481, _1134479) = hAPP(c_Divides_Oadjust(_1134479), c_Divides_OnegDivAlg(_1134481, 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)))), _1134479))))], (20844 ^ _775828) ^ [] : [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), _1134481), _1134479))), -(c_Divides_OnegDivAlg(_1134481, _1134479) = 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), _1134481), _1134479)))]]], (7595 ^ _775828) ^ [_896965, _896967, _896969] : [class_Groups_Oordered__ab__group__add(_896965), 7598 ^ _775828 : [(7605 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896965), hAPP(c_Groups_Ouminus__class_Ouminus(_896965), _896969)), _896967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896965), hAPP(c_Groups_Ouminus__class_Ouminus(_896965), _896967)), _896969)))], (7599 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896965), hAPP(c_Groups_Ouminus__class_Ouminus(_896965), _896967)), _896969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_896965), hAPP(c_Groups_Ouminus__class_Ouminus(_896965), _896969)), _896967)))]]], (51268 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (40115 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (40923 ^ _775828) ^ [_1563503, _1563505, _1563507, _1563509] : [hBOOL(hAPP(hAPP(c_member(_1563503), _1563505), _1563507)), -(hAPP(c_Set_Ovimage(_1563509, _1563503, hAPP(c_COMBK(_1563503, _1563509), _1563505)), _1563507) = c_Orderings_Otop__class_Otop(tc_fun(_1563509, tc_HOL_Obool)))], (23644 ^ _775828) ^ [_1189843, _1189845, _1189847, _1189849] : [class_Orderings_Olinorder(_1189843), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189843), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1189843), _1189845), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189843), _1189847), _1189849))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189843), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1189843), _1189845), _1189847)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1189843), _1189845), _1189849)))))], (50439 ^ _775828) ^ [_1789686, _1789688] : [-(_1789686 = c_List_Olist_ONil(_1789688)), -(hAPP(c_List_Ohd(_1789688), hAPP(c_List_Orev(_1789688), _1789686)) = c_List_Olast(_1789688, _1789686))], (14984 ^ _775828) ^ [_1027090, _1027092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027090)), -(c_SMT_Oz3div(_1027092, _1027090) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027092), _1027090))], (27388 ^ _775828) ^ [_1262109, _1262111, _1262113, _1262115] : [hBOOL(hAPP(hAPP(c_member(_1262109), _1262111), hAPP(c_Relation_ORange(_1262113, _1262109), _1262115))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1262113, _1262109)), hAPP(hAPP(c_Product__Type_OPair(_1262113, _1262109), 27391 ^ [_1262109, _1262111, _1262113, _1262115]), _1262111)), _1262115)))], (50629 ^ _775828) ^ [_1795256, _1795258, _1795260] : [50631 ^ _775828 : [(50634 ^ _775828) ^ [] : [hBOOL(hAPP(_1795258, 50630 ^ [_1795256, _1795258, _1795260]))], (50632 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795256), 50630 ^ [_1795256, _1795258, _1795260]), hAPP(c_List_Oset(_1795256), _1795260))))]], -(c_List_OtakeWhile(_1795256, _1795258, _1795260) = _1795260)], (30738 ^ _775828) ^ [_1338009, _1338011, _1338013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338009), _1338011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338009, tc_HOL_Obool)), _1338013), _1338011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1338009), _1338011)), hAPP(c_Finite__Set_Ocard(_1338009), _1338013))), -(_1338013 = _1338011)], (42744 ^ _775828) ^ [_1607887, _1607889, _1607891] : [-(hAPP(c_Fun_Ocomp(_1607887, _1607887, _1607889, c_Fun_Oid(_1607887)), _1607891) = _1607891)], (23634 ^ _775828) ^ [_1189532, _1189534] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1189532)), hAPP(c_Nat_OSuc, _1189534)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1189532))), 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, _1189534))), 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)), _1189534)))))], (29575 ^ _775828) ^ [_1312569, _1312571, _1312573] : [-(hAPP(hAPP(c_Set_Oinsert(_1312569), _1312571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312569, tc_HOL_Obool)), _1312573), hAPP(hAPP(c_Set_Oinsert(_1312569), _1312571), c_Orderings_Obot__class_Obot(tc_fun(_1312569, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1312569), _1312571), _1312573))], (17409 ^ _775828) ^ [_1073954] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073954) = _1073954)], (5008 ^ _775828) ^ [_852441, _852443] : [_852443 = _852441, -(c_Nat_Osemiring__1__class_Oof__nat(_852443) = c_Nat_Osemiring__1__class_Oof__nat(_852441))], (27166 ^ _775828) ^ [_1255903, _1255905, _1255907] : [c_Relation_Ototal__on(_1255903, _1255905, _1255907), 27169 ^ _775828 : [(27170 ^ _775828) ^ [_1256047] : [hBOOL(hAPP(hAPP(c_member(_1255903), _1256047), _1255905)), 27173 ^ _775828 : [(27174 ^ _775828) ^ [_1256187] : [hBOOL(hAPP(hAPP(c_member(_1255903), _1256187), _1255905)), -(_1256047 = _1256187), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1255903, _1255903)), hAPP(hAPP(c_Product__Type_OPair(_1255903, _1255903), _1256047), _1256187)), _1255907))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1255903, _1255903)), hAPP(hAPP(c_Product__Type_OPair(_1255903, _1255903), _1256187), _1256047)), _1255907)))]]]]], (38988 ^ _775828) ^ [_1518022, _1518024, _1518026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518022), _1518024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518022, tc_HOL_Obool)), _1518024), hAPP(c_Set_Oimage(_1518022, _1518022, _1518026), _1518024))), -(c_Fun_Oinj__on(_1518022, _1518022, _1518026, _1518024))], (12673 ^ _775828) ^ [_985038, _985040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _985038), c_Groups_Oone__class_Oone(tc_Int_Oint))), _985040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985038), _985040)))], (50642 ^ _775828) ^ [_1795544, _1795546, _1795548] : [hBOOL(hAPP(c_List_Odistinct(_1795544), _1795546)), -(hBOOL(hAPP(c_List_Odistinct(_1795544), c_List_OtakeWhile(_1795544, _1795548, _1795546))))], (2488 ^ _775828) ^ [_812459, _812461, _812463, _812465] : [-(c_Divides_Odivmod__nat__rel(_812465, _812461) = c_Divides_Odivmod__nat__rel(_812463, _812459)), _812465 = _812463, _812461 = _812459], (38186 ^ _775828) ^ [_1500527, _1500529, _1500531, _1500533] : [-(hAPP(c_Relation_OImage(_1500527, _1500529, _1500531), hAPP(hAPP(c_Set_Oinsert(_1500527), _1500533), c_Orderings_Obot__class_Obot(tc_fun(_1500527, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1500529), hAPP(hAPP(c_COMBC(_1500529, tc_fun(tc_prod(_1500527, _1500529), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1500527, _1500529), tc_fun(tc_fun(tc_prod(_1500527, _1500529), tc_HOL_Obool), tc_HOL_Obool), _1500529), c_member(tc_prod(_1500527, _1500529))), hAPP(c_Product__Type_OPair(_1500527, _1500529), _1500533))), _1500531)))], (43618 ^ _775828) ^ [_1628829, _1628831, _1628833, _1628835] : [class_Orderings_Olinorder(_1628829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628829), _1628831)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628829, _1628829, c_Orderings_Oord__class_Omin(_1628829)), _1628833), hAPP(hAPP(c_Set_Oinsert(_1628829), _1628835), _1628831)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1628829), _1628835), hAPP(hAPP(c_Finite__Set_Ofold(_1628829, _1628829, c_Orderings_Oord__class_Omin(_1628829)), _1628833), _1628831)))], (38296 ^ _775828) ^ [_1503131, _1503133] : [class_Orderings_Olinorder(_1503131), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1503131, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503131), _1503133)) = hAPP(c_SetInterval_Oord__class_OatMost(_1503131), _1503133))], (5811 ^ _775828) ^ [_868451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _868451))))], (14592 ^ _775828) ^ [_1020133, _1020135] : [class_Divides_Osemiring__div(_1020133), -(_1020135 = c_Groups_Ozero__class_Ozero(_1020133)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020133), _1020135), _1020135) = c_Groups_Oone__class_Oone(_1020133))], (17357 ^ _775828) ^ [_1072955, _1072957, _1072959, _1072961] : [class_Rings_Olinordered__semidom(_1072955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072957), _1072959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072955), c_Groups_Ozero__class_Ozero(_1072955)), _1072961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072955), _1072961), c_Groups_Oone__class_Oone(_1072955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072955), hAPP(hAPP(c_Power_Opower__class_Opower(_1072955), _1072961), _1072959)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072955), _1072961), _1072957))))], (5246 ^ _775828) ^ [_856040, _856042, _856044, _856046] : [-(c_List_Omap(_856046, _856042) = c_List_Omap(_856044, _856040)), _856046 = _856044, _856042 = _856040], (31301 ^ _775828) ^ [_1351142, _1351144, _1351146] : [class_Orderings_Olinorder(_1351142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351142), _1351144)), hBOOL(hAPP(hAPP(c_member(_1351142), _1351146), _1351144)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351142), _1351146), c_Big__Operators_Olattice_OInf__fin(_1351142, c_Orderings_Oord__class_Omin(_1351142), _1351144)) = _1351146)], (38794 ^ _775828) ^ [_1514345, _1514347, _1514349] : [-(c_Fun_Oinj__on(_1514345, _1514347, _1514349, c_Orderings_Obot__class_Obot(tc_fun(_1514345, tc_HOL_Obool))))], (4094 ^ _775828) ^ [_838320, _838322, _838324, _838326] : [-(c_Random_Oselect(_838326, _838322) = c_Random_Oselect(_838324, _838320)), _838326 = _838324, _838322 = _838320], (35521 ^ _775828) ^ [_1442972, _1442974, _1442976] : [class_Orderings_Oorder(_1442972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442972), _1442974), _1442976)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1442972, _1442976, _1442974) = c_Orderings_Obot__class_Obot(tc_fun(_1442972, tc_HOL_Obool)))], (45519 ^ _775828) ^ [_1673091, _1673093, _1673095, _1673097, _1673099, _1673101] : [-(c_Map_Omap__comp(_1673091, _1673093, _1673095, _1673097, _1673099, _1673101) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1673093), _1673091, c_Option_Ooption_ONone(_1673093), _1673097), hAPP(_1673099, _1673101)))], (26143 ^ _775828) ^ [_1237378, _1237380, _1237382, _1237384] : [class_Rings_Ocomm__semiring__1(_1237378), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237378), _1237380), _1237382)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237378), hAPP(hAPP(c_Power_Opower__class_Opower(_1237378), _1237380), _1237384)), hAPP(hAPP(c_Power_Opower__class_Opower(_1237378), _1237382), _1237384))))], (20106 ^ _775828) ^ [_1121238] : [c_Int_OBit0(_1121238) = c_Int_OMin], (47669 ^ _775828) ^ [_1727263, _1727265, _1727267, _1727269, _1727271, _1727273, _1727275] : [hBOOL(hAPP(hAPP(c_member(_1727263), _1727265), hAPP(c_List_Oset(_1727263), hAPP(hAPP(c_List_Otake(_1727263), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727267)), _1727269)), _1727271)))), -(c_Map_Omap__upds(_1727263, _1727267, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1727263, tc_Option_Ooption(_1727267)), _1727273), _1727265), hAPP(c_Option_Ooption_OSome(_1727267), _1727275)), _1727271, _1727269) = c_Map_Omap__upds(_1727263, _1727267, _1727273, _1727271, _1727269))], (42662 ^ _775828) ^ [_1606133, _1606135, _1606137] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1606133), c_Map_Odom(_1606133, _1606135, _1606137))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1606133), c_Orderings_Otop__class_Otop(tc_fun(_1606133, tc_HOL_Obool))))), -(hAPP(_1606137, 42669 ^ [_1606133, _1606135, _1606137]) = c_Option_Ooption_ONone(_1606135))], (48177 ^ _775828) ^ [_1739344, _1739346] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1739344), tc_List_Olist(_1739344)), tc_HOL_Obool)), c_List_Olistrel1(_1739344, c_Transitive__Closure_Ortrancl(_1739344, _1739346))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1739344), c_List_Olistrel1(_1739344, _1739346)))))], (24424 ^ _775828) ^ [] : [-(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))], (37032 ^ _775828) ^ [_1472798, _1472800] : [-(hAPP(c_Finite__Set_Ocard(_1472798), _1472800) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472798, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1472798), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1472800))], (7321 ^ _775828) ^ [_892548, _892550] : [class_Int_Oring__char__0(_892548), 7324 ^ _775828 : [(7331 ^ _775828) ^ [] : [_892550 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_892548) = hAPP(c_Int_Oring__1__class_Oof__int(_892548), _892550))], (7325 ^ _775828) ^ [] : [c_Groups_Ozero__class_Ozero(_892548) = hAPP(c_Int_Oring__1__class_Oof__int(_892548), _892550), -(_892550 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (226 ^ _775828) ^ [_779117, _779119, _779121, _779123] : [-(c_Relation_Oirrefl(_779121, _779117)), c_Relation_Oirrefl(_779123, _779119), _779123 = _779121, _779119 = _779117], (29433 ^ _775828) ^ [_1309696, _1309698, _1309700, _1309702, _1309704] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1309696, _1309698, _1309700), _1309702), _1309704)), -(hBOOL(hAPP(hAPP(_1309700, _1309704), _1309702)))], (21554 ^ _775828) ^ [_1148960, _1148962] : [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(_1148960))), 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)), _1148962))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148960) = hAPP(c_Nat_OSuc, _1148962))], (30185 ^ _775828) ^ [_1325931, _1325933, _1325935, _1325937] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1325931), _1325933)), 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)), _1325931), _1325935)), 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)), _1325933), _1325937)), 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)), _1325933), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1325935), _1325937))), c_FunDef_Omin__weak)))], (9921 ^ _775828) ^ [_936104, _936106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936104)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936106)))), 9924 ^ _775828 : [(9927 ^ _775828) ^ [] : [-(_936106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9925 ^ _775828) ^ [] : [-(_936104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4566 ^ _775828) ^ [_845564, _845566] : [_845566 = _845564, -(c_If(_845566) = c_If(_845564))], (34359 ^ _775828) ^ [_1415915, _1415917, _1415919, _1415921, _1415923] : [class_Orderings_Olinorder(_1415915), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415915, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1415915, _1415917, _1415919)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1415915, _1415921, _1415923)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1415915, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415915), _1415917), _1415921), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415915), _1415919), _1415923)))], (49311 ^ _775828) ^ [_1765920, _1765922, _1765924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765920), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765922)), _1765924))), -(hAPP(hAPP(c_List_Otake(_1765922), _1765920), c_List_Obutlast(_1765922, _1765924)) = hAPP(hAPP(c_List_Otake(_1765922), _1765920), _1765924))], (4468 ^ _775828) ^ [_844039, _844041] : [_844041 = _844039, -(c_Set_Oinsert(_844041) = c_Set_Oinsert(_844039))], (4490 ^ _775828) ^ [_844358, _844360, _844362, _844364, _844366, _844368] : [-(c_List_Opartition(_844368, _844364, _844360) = c_List_Opartition(_844366, _844362, _844358)), _844368 = _844366, _844364 = _844362, _844360 = _844358], (48739 ^ _775828) ^ [_1753456, _1753458, _1753460] : [-(hAPP(c_List_Otl(_1753456), hAPP(hAPP(c_List_Otake(_1753456), _1753458), _1753460)) = hAPP(hAPP(c_List_Otake(_1753456), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1753458), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1753456), _1753460)))], (15744 ^ _775828) ^ [_1041291, _1041293] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041291), _1041293))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041293), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041291), _1041293)) = _1041291)], (6428 ^ _775828) ^ [_878138, _878140, _878142] : [class_Orderings_Olinorder(_878138), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878138), _878140), _878142))), -(_878140 = _878142), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878138), _878142), _878140)))], (38438 ^ _775828) ^ [_1506122, _1506124, _1506126] : [-(c_Map_Odom(_1506122, _1506124, _1506126) = hAPP(c_Set_OCollect(_1506122), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506122), c_fNot), hAPP(hAPP(c_COMBC(_1506122, tc_Option_Ooption(_1506124), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1506124), tc_fun(tc_Option_Ooption(_1506124), tc_HOL_Obool), _1506122), c_fequal), _1506126)), c_Option_Ooption_ONone(_1506124)))))], (51388 ^ _775828) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (42194 ^ _775828) ^ [_1595107, _1595109, _1595111, _1595113] : [c_Relation_Orefl__on(_1595107, _1595109, _1595111), hBOOL(hAPP(hAPP(c_member(_1595107), _1595113), _1595109)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595107, _1595107)), hAPP(hAPP(c_Product__Type_OPair(_1595107, _1595107), _1595113), _1595113)), _1595111)))], (35187 ^ _775828) ^ [_1435282, _1435284, _1435286, _1435288] : [class_Groups_Ocomm__monoid__mult(_1435282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435284), _1435286)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1435284, _1435282), _1435288), _1435286) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435282, _1435284, c_Groups_Otimes__class_Otimes(_1435282)), _1435288), c_Groups_Oone__class_Oone(_1435282)), _1435286))], (41747 ^ _775828) ^ [_1583936, _1583938, _1583940] : [class_Orderings_Olinorder(_1583936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583936), _1583938)), -(_1583938 = c_Orderings_Obot__class_Obot(tc_fun(_1583936, tc_HOL_Obool))), 41758 ^ _775828 : [(41768 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1583936), hAPP(c_Finite__Set_Ofold1(_1583936, c_Orderings_Oord__class_Omin(_1583936)), _1583938)), _1583940))), 41769 ^ _775828 : [(41770 ^ _775828) ^ [_1584325] : [hBOOL(hAPP(hAPP(c_member(_1583936), _1584325), _1583938)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1583936), _1584325), _1583940))]]], (41759 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1583936), hAPP(c_Finite__Set_Ofold1(_1583936, c_Orderings_Oord__class_Omin(_1583936)), _1583938)), _1583940)), 41763 ^ _775828 : [(41766 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1583936), 41762 ^ [_1583936, _1583938, _1583940]), _1583940)))], (41764 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583936), 41762 ^ [_1583936, _1583938, _1583940]), _1583938)))]]]]], (38726 ^ _775828) ^ [_1512759, _1512761, _1512763, _1512765, _1512767, _1512769, _1512771] : [c_Equiv__Relations_Oequiv(_1512759, _1512761, _1512763), hBOOL(hAPP(hAPP(c_member(tc_fun(_1512759, tc_HOL_Obool)), _1512765), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512759), _1512761), _1512763))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1512759, tc_HOL_Obool)), _1512767), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512759), _1512761), _1512763))), hBOOL(hAPP(hAPP(c_member(_1512759), _1512769), _1512765)), hBOOL(hAPP(hAPP(c_member(_1512759), _1512771), _1512767)), 38745 ^ _775828 : [(38752 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1512759, _1512759)), hAPP(hAPP(c_Product__Type_OPair(_1512759, _1512759), _1512769), _1512771)), _1512763)), -(_1512765 = _1512767)], (38746 ^ _775828) ^ [] : [_1512765 = _1512767, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1512759, _1512759)), hAPP(hAPP(c_Product__Type_OPair(_1512759, _1512759), _1512769), _1512771)), _1512763)))]]], (15338 ^ _775828) ^ [_1033601] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033601), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1033601)], (18207 ^ _775828) ^ [_1088346, _1088348, _1088350, _1088352, _1088354] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1088346, _1088348, _1088350), _1088352), hAPP(c_Nat_OSuc, _1088354)) = hAPP(hAPP(_1088350, _1088352), hAPP(hAPP(c_Power_Opower_Opower(_1088346, _1088348, _1088350), _1088352), _1088354)))], (10684 ^ _775828) ^ [_950267, _950269, _950271, _950273, _950275] : [class_Rings_Osemiring(_950267), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950267), _950269), _950271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950267), _950273), _950271)), _950275)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950267), _950269), _950273)), _950271)), _950275))], (35082 ^ _775828) ^ [_1432863, _1432865, _1432867, _1432869, _1432871] : [class_Groups_Ocomm__monoid__mult(_1432863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432865), _1432867)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432865), _1432869)), 35096 ^ _775828 : [(35099 ^ _775828) ^ [] : [hAPP(_1432871, 35095 ^ [_1432863, _1432865, _1432867, _1432869, _1432871]) = c_Groups_Oone__class_Oone(_1432863)], (35097 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432865), 35095 ^ [_1432863, _1432865, _1432867, _1432869, _1432871]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432865, tc_HOL_Obool)), _1432867), _1432869))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432865, _1432863), _1432871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432865, tc_HOL_Obool)), _1432867), _1432869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432863), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432865, _1432863), _1432871), _1432867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432865, _1432863), _1432871), _1432869)))], (40225 ^ _775828) ^ [_1546934, _1546936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1546934, tc_HOL_Obool)), _1546936), c_Orderings_Otop__class_Otop(tc_fun(_1546934, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1546934, tc_HOL_Obool)))], (19738 ^ _775828) ^ [_1114871] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114871), c_Int_OMin) = c_Int_Opred(_1114871))], (19680 ^ _775828) ^ [_1113944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1113944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113944))))], (10019 ^ _775828) ^ [_937768, _937770, _937772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937768, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937768, tc_HOL_Obool)), _937770)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937768, tc_HOL_Obool)), _937772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937768, tc_HOL_Obool)), _937772), _937770)))], (14165 ^ _775828) ^ [_1012594, _1012596, _1012598, _1012600, _1012602, _1012604] : [hBOOL(hAPP(_1012594, _1012596)), c_Natural_Oevaln(_1012598, _1012596, _1012600, _1012602), c_Natural_Oevaln(c_Com_Ocom_OWhile(_1012594, _1012598), _1012602, _1012600, _1012604), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_1012594, _1012598), _1012596, _1012600, _1012604))], (50043 ^ _775828) ^ [_1780865, _1780867, _1780869, _1780871] : [class_Groups_Ocomm__monoid__add(_1780865), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1780865), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1780865), _1780867), c_List_Oupt(_1780869, _1780871))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1780865), _1780867), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1780869, _1780871))))], (33020 ^ _775828) ^ [_1386974, _1386976, _1386978] : [class_Groups_Ocomm__monoid__mult(_1386974), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386976, _1386974), _1386978), c_Orderings_Obot__class_Obot(tc_fun(_1386976, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1386974))], (25112 ^ _775828) ^ [_1218961, _1218963, _1218965, _1218967] : [-(c_HOL_OThe(tc_prod(_1218961, _1218963), hAPP(c_Product__Type_Oprod_Oprod__case(_1218961, _1218963, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1218961, tc_fun(_1218963, tc_HOL_Obool), tc_fun(_1218963, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1218963, tc_HOL_Obool), tc_fun(_1218963, tc_HOL_Obool)), _1218961), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1218963)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1218961), c_fconj), hAPP(c_fequal, _1218965)))), hAPP(c_fequal, _1218967)))) = hAPP(hAPP(c_Product__Type_OPair(_1218961, _1218963), _1218965), _1218967))], (46396 ^ _775828) ^ [_1695444, _1695446, _1695448] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695444), tc_List_Olist(_1695444))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695444), tc_List_Olist(_1695444)), _1695446), _1695446)), c_List_Olistrel(_1695444, c_Transitive__Closure_Ortrancl(_1695444, _1695448)))))], (22964 ^ _775828) ^ [_1175475, _1175477, _1175479, _1175481] : [class_Fields_Olinordered__field__inverse__zero(_1175475), 22967 ^ _775828 : [(22968 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175475), _1175477), _1175479)), _1175481)), 22971 ^ _775828 : [(22978 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175479))), 22981 ^ _775828 : [(22988 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175479), c_Groups_Ozero__class_Ozero(_1175475)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175481)))], (22982 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175479), c_Groups_Ozero__class_Ozero(_1175475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175475), _1175481), _1175479)), _1175477)))]]], (22972 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175475), _1175481), _1175479))))]]], (22994 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175475), _1175477), _1175479)), _1175481))), 22997 ^ _775828 : [(23000 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175475), _1175481), _1175479)))], (22998 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175479)))]], 23001 ^ _775828 : [(23004 ^ _775828) ^ [] : [23005 ^ _775828 : [(23008 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175475), _1175481), _1175479)), _1175477))], (23006 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175479), c_Groups_Ozero__class_Ozero(_1175475))))]], 23009 ^ _775828 : [(23012 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175481))], (23010 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), _1175479), c_Groups_Ozero__class_Ozero(_1175475)))]]], (23002 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175475), c_Groups_Ozero__class_Ozero(_1175475)), _1175479))]]]]], (29451 ^ _775828) ^ [_1310049, _1310051, _1310053, _1310055, _1310057] : [hBOOL(hAPP(hAPP(_1310053, _1310057), _1310055)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1310049, _1310051, _1310053), _1310055), _1310057)))], (15282 ^ _775828) ^ [_1032430, _1032432, _1032434] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1032430), _1032432)), _1032434) = 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), _1032430), _1032434)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032432), _1032434))), 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, _1032430, _1032434)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1032432, _1032434))), _1032434)))], (6767 ^ _775828) ^ [_883099, _883101] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _883099), _883101))), -(_883099 = _883101), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _883101), _883099)))], (4246 ^ _775828) ^ [_840716, _840718] : [_840718 = _840716, -(c_Fun_Oid(_840718) = c_Fun_Oid(_840716))], (32857 ^ _775828) ^ [_1383511, _1383513, _1383515, _1383517, _1383519, _1383521] : [_1383511 = _1383513, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1383515, _1383517), _1383519), _1383513), _1383521), _1383511) = _1383521)], (45349 ^ _775828) ^ [_1669078, _1669080, _1669082, _1669084, _1669086] : [-(hAPP(c_Map_Omap__add(_1669078, _1669080, _1669082, _1669084), _1669086) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1669080), _1669080, hAPP(_1669082, _1669086), c_Option_Ooption_OSome(_1669080)), hAPP(_1669084, _1669086)))], (15712 ^ _775828) ^ [_1040686, _1040688] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040686), _1040688)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24164 ^ _775828) ^ [_1198977, _1198979, _1198981] : [class_Orderings_Olinorder(_1198977), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198977), _1198979), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198977), _1198979), _1198981)) = _1198979)], (8619 ^ _775828) ^ [_914050, _914052, _914054] : [hBOOL(hAPP(hAPP(c_member(_914050), _914052), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_914050, tc_HOL_Obool)), _914054))), hBOOL(hAPP(hAPP(c_member(_914050), _914052), _914054))], (10900 ^ _775828) ^ [_954270] : [_954270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954270), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18713 ^ _775828) ^ [_1097333, _1097335, _1097337, _1097339] : [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), _1097333), _1097335)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1097337), _1097339))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1097333), _1097339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1097337), _1097335))], (44559 ^ _775828) ^ [_1651219, _1651221, _1651223, _1651225] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1651219, tc_HOL_Obool)), _1651221), _1651223)), hBOOL(hAPP(hAPP(c_member(_1651219), _1651225), _1651221)), -(hBOOL(hAPP(hAPP(c_member(_1651219), _1651225), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1651219, tc_HOL_Obool), _1651223))))], (42083 ^ _775828) ^ [_1592433, _1592435, _1592437, _1592439] : [-(c_Product__Type_Oapfst(_1592433, _1592435, _1592437, _1592439) = c_Product__Type_Omap__pair(_1592433, _1592435, _1592437, _1592437, _1592439, c_Fun_Oid(_1592437)))], (36230 ^ _775828) ^ [_1456177, _1456179] : [36238 ^ _775828 : [(36241 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1456179, 36237 ^ [_1456177, _1456179])))], (36239 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 36237 ^ [_1456177, _1456179]), _1456177)))]], 36231 ^ _775828 : [(36232 ^ _775828) ^ [_1456245] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1456245), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1456177))), hBOOL(hAPP(_1456179, _1456245))]]], (51282 ^ _775828) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (30315 ^ _775828) ^ [_1329265, _1329267, _1329269, _1329271] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1329265, tc_HOL_Obool), tc_fun(_1329265, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1329265, tc_HOL_Obool), tc_fun(_1329265, tc_HOL_Obool)), _1329269), _1329271)), c_Wellfounded_Omax__ext(_1329265, _1329267))), -(c_Wellfounded_Omax__extp(_1329265, hAPP(hAPP(c_COMBC(_1329265, tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_fun(_1329265, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1329265, tc_fun(tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_fun(_1329265, tc_HOL_Obool)), _1329265), c_COMBC(_1329265, tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1329265, tc_prod(_1329265, _1329265)), tc_fun(_1329265, tc_fun(tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_HOL_Obool)), _1329265), hAPP(c_COMBB(tc_prod(_1329265, _1329265), tc_fun(tc_fun(tc_prod(_1329265, _1329265), tc_HOL_Obool), tc_HOL_Obool), _1329265), c_member(tc_prod(_1329265, _1329265)))), c_Product__Type_OPair(_1329265, _1329265)))), _1329267), _1329269, _1329271))], (50315 ^ _775828) ^ [_1786962, _1786964, _1786966] : [hAPP(c_List_Orev(_1786962), _1786964) = hAPP(hAPP(c_List_Olist_OCons(_1786962), _1786966), c_List_Olist_ONil(_1786962)), -(_1786964 = hAPP(hAPP(c_List_Olist_OCons(_1786962), _1786966), c_List_Olist_ONil(_1786962)))], (50455 ^ _775828) ^ [_1790214, _1790216, _1790218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790214), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790216)), _1790218))), -(hAPP(hAPP(c_List_Onth(_1790216), hAPP(c_List_Orev(_1790216), _1790218)), _1790214) = hAPP(hAPP(c_List_Onth(_1790216), _1790218), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790216)), _1790218)), hAPP(c_Nat_OSuc, _1790214))))], (19742 ^ _775828) ^ [_1114930, _1114932] : [class_Int_Onumber__ring(_1114930), -(hAPP(c_Int_Onumber__class_Onumber__of(_1114930), c_Int_OBit1(_1114932)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114930), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114930), c_Groups_Oone__class_Oone(_1114930)), hAPP(c_Int_Onumber__class_Onumber__of(_1114930), _1114932))), hAPP(c_Int_Onumber__class_Onumber__of(_1114930), _1114932)))], (15368 ^ _775828) ^ [_1034114, _1034116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034114), _1034116)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1034114, _1034116) = _1034114)], (29471 ^ _775828) ^ [_1310441] : [-(c_Predicate_Oconversep(_1310441, _1310441, c_fequal) = c_fequal)], (18573 ^ _775828) ^ [_1095108, _1095110] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095108), _1095110) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 18574 ^ _775828 : [(18581 ^ _775828) ^ [] : [_1095108 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1095110 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (18575 ^ _775828) ^ [] : [_1095108 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1095110 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (37667 ^ _775828) ^ [_1488738, _1488740, _1488742] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1488738), _1488740), _1488742) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1488738), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1488738, tc_Int_Oint), _1488740), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1488742))), class_Groups_Ocomm__monoid__add(_1488738), class_Groups_Ocomm__monoid__mult(_1488738)], (13688 ^ _775828) ^ [_1003785, _1003787, _1003789] : [class_Divides_Osemiring__div(_1003785), -(c_Divides_Odiv__class_Omod(_1003785, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003785), _1003787), _1003789), _1003789) = c_Groups_Ozero__class_Ozero(_1003785))], (3098 ^ _775828) ^ [_822476, _822478, _822480, _822482, _822484, _822486, _822488, _822490] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_822490, _822486, _822482, _822478) = c_SetInterval_Oord_OgreaterThanLessThan(_822488, _822484, _822480, _822476)), _822490 = _822488, _822486 = _822484, _822482 = _822480, _822478 = _822476], (31739 ^ _775828) ^ [_1360958, _1360960, _1360962, _1360964, _1360966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1360958, _1360958)), hAPP(hAPP(c_Product__Type_OPair(_1360958, _1360958), _1360960), _1360962)), c_Transitive__Closure_Ortrancl(_1360958, _1360964))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1360958, _1360958)), hAPP(hAPP(c_Product__Type_OPair(_1360958, _1360958), _1360962), _1360966)), _1360964)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360958, _1360958)), hAPP(hAPP(c_Product__Type_OPair(_1360958, _1360958), _1360960), _1360966)), c_Transitive__Closure_Otrancl(_1360958, _1360964))))], (30716 ^ _775828) ^ [_1337586, _1337588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1337586), _1337588))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337586), _1337588)))], (29179 ^ _775828) ^ [_1304659, _1304661] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304659, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1304659, tc_HOL_Obool))), _1304661)))], (29413 ^ _775828) ^ [_1309264, _1309266, _1309268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309264, tc_HOL_Obool)), _1309266), hAPP(hAPP(c_Set_Oinsert(_1309264), _1309268), _1309266))))], (8001 ^ _775828) ^ [_904132, _904134, _904136, _904138, _904140] : [class_Rings_Ocomm__semiring__1(_904132), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), _904134), _904136)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), _904138), _904140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), _904134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), _904136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904132), _904138), _904140))))], (51302 ^ _775828) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (24260 ^ _775828) ^ [_1201207, _1201209, _1201211, _1201213] : [class_Orderings_Olinorder(_1201207), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201207), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201207), _1201209), _1201211)), _1201213) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201207), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201207), _1201209), _1201213)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201207), _1201211), _1201213)))], (10744 ^ _775828) ^ [_951353, _951355, _951357] : [class_Groups_Ogroup__add(_951353), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951353), hAPP(c_Groups_Ouminus__class_Ouminus(_951353), _951355)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951353), _951355), _951357)) = _951357)], (48916 ^ _775828) ^ [_1757260, _1757262, _1757264, _1757266, _1757268] : [hBOOL(hAPP(hAPP(c_member(_1757260), _1757262), hAPP(c_List_Oset(_1757260), _1757264))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757266), hAPP(_1757268, _1757262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757266), c_List_Olist_Olist__size(_1757260, _1757268, _1757264))))], (51366 ^ _775828) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (36589 ^ _775828) ^ [_1463335, _1463337, _1463339] : [class_Orderings_Oord(_1463335), 36592 ^ _775828 : [(36599 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1463335), _1463337), _1463339)), -(hBOOL(hAPP(hAPP(c_member(_1463335), _1463337), hAPP(c_SetInterval_Oord__class_OatMost(_1463335), _1463339))))], (36593 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463335), _1463337), hAPP(c_SetInterval_Oord__class_OatMost(_1463335), _1463339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1463335), _1463337), _1463339)))]]], (15678 ^ _775828) ^ [_1040066, _1040068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040066), _1040068)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040066), _1040068)))], (13488 ^ _775828) ^ [_999759, _999761, _999763, _999765] : [c_Com_Ocom_OLocal(_999759, _999761, _999763) = hAPP(c_Com_Ocom_OBODY, _999765)], (28079 ^ _775828) ^ [_1279064, _1279066, _1279068] : [c_Wellfounded_OwfP(_1279064, _1279066), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1279064, _1279066), _1279068)))], (18217 ^ _775828) ^ [_1088548, _1088550, _1088552, _1088554] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1088548, _1088550), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1088552), _1088554))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1088548), _1088550) = _1088552)], (694 ^ _775828) ^ [_786391, _786393, _786395, _786397, _786399, _786401, _786403, _786405] : [-(c_Finite__Set_Ofolding(_786403, _786399, _786395, _786391)), c_Finite__Set_Ofolding(_786405, _786401, _786397, _786393), _786405 = _786403, _786401 = _786399, _786397 = _786395, _786393 = _786391], (18707 ^ _775828) ^ [_1097175, _1097177, _1097179, _1097181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1097175), _1097177)), -(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), _1097175), _1097179)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1097177), _1097181))), c_FunDef_Opair__leq)))], (46029 ^ _775828) ^ [_1684710, _1684712, _1684714, _1684716, _1684718, _1684720, _1684722, _1684724] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1684710, _1684712), _1684714), _1684716), hAPP(hAPP(c_List_Ozip(_1684710, _1684712), _1684718), hAPP(hAPP(c_List_Omap(_1684720, _1684712), _1684722), _1684724))) = hAPP(hAPP(c_List_Omap(tc_prod(_1684710, _1684720), _1684714), hAPP(c_Product__Type_Oprod_Oprod__case(_1684710, _1684720, _1684714), hAPP(hAPP(c_COMBB(tc_fun(_1684720, tc_prod(_1684710, _1684712)), tc_fun(_1684720, _1684714), _1684710), hAPP(c_COMBB(tc_prod(_1684710, _1684712), _1684714, _1684720), _1684716)), hAPP(hAPP(c_COMBC(_1684710, tc_fun(_1684720, _1684712), tc_fun(_1684720, tc_prod(_1684710, _1684712))), hAPP(hAPP(c_COMBB(tc_fun(_1684712, tc_prod(_1684710, _1684712)), tc_fun(tc_fun(_1684720, _1684712), tc_fun(_1684720, tc_prod(_1684710, _1684712))), _1684710), c_COMBB(_1684712, tc_prod(_1684710, _1684712), _1684720)), c_Product__Type_OPair(_1684710, _1684712))), _1684722)))), hAPP(hAPP(c_List_Ozip(_1684710, _1684720), _1684718), _1684724)))], (6268 ^ _775828) ^ [_875683, _875685] : [class_Orderings_Opreorder(_875683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875683), _875685), _875685))], (6830 ^ _775828) ^ [_884028, _884030] : [c_Option_Ooption_ONone(_884028) = hAPP(c_Option_Ooption_OSome(_884028), _884030)], (41594 ^ _775828) ^ [_1581111, _1581113, _1581115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1581111), _1581113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581111, _1581111), tc_HOL_Obool)), _1581115), hAPP(hAPP(c_Product__Type_OSigma(_1581111, _1581111), _1581113), hAPP(c_COMBK(tc_fun(_1581111, tc_HOL_Obool), _1581111), _1581113)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1581111, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1581111), _1581113), _1581115))))], (27755 ^ _775828) ^ [_1269997, _1269999, _1270001, _1270003, _1270005, _1270007, _1270009] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1269997, _1269999, _1270001), hAPP(hAPP(c_Relation_Orel__comp(_1269997, _1270003, _1269999), _1270005), _1270007)), _1270009) = hAPP(hAPP(c_Relation_Orel__comp(_1269997, _1270003, _1270001), _1270005), hAPP(hAPP(c_Relation_Orel__comp(_1270003, _1269999, _1270001), _1270007), _1270009)))], (6452 ^ _775828) ^ [_878433, _878435, _878437, _878439] : [class_Orderings_Oorder(_878433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878433), _878435), _878437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878433), _878439), _878435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878433), _878439), _878437)))], (15854 ^ _775828) ^ [_1043325, _1043327, _1043329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043325), _1043327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043329), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043327), _1043329)), _1043325))))], (49895 ^ _775828) ^ [_1778199, _1778201] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1778199, _1778201)))], (13378 ^ _775828) ^ [_997739, _997741, _997743] : [class_Divides_Oring__div(_997739), -(c_Divides_Odiv__class_Omod(_997739, hAPP(c_Groups_Ouminus__class_Ouminus(_997739), _997741), _997743) = c_Divides_Odiv__class_Omod(_997739, hAPP(c_Groups_Ouminus__class_Ouminus(_997739), c_Divides_Odiv__class_Omod(_997739, _997741, _997743)), _997743))], (42629 ^ _775828) ^ [_1605342, _1605344, _1605346] : [c_Hoare__Mirabelle_Ohoare__valids(_1605342, _1605344, _1605346), 42632 ^ _775828 : [(42633 ^ _775828) ^ [_1605451] : [42635 ^ _775828 : [(42638 ^ _775828) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1605342, _1605451, 42634 ^ [_1605342, _1605344, _1605346, _1605451])], (42636 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1605342)), 42634 ^ [_1605342, _1605344, _1605346, _1605451]), _1605344)))]], 42639 ^ _775828 : [(42640 ^ _775828) ^ [_1605623] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1605342)), _1605623), _1605346)), -(c_Hoare__Mirabelle_Otriple__valid(_1605342, _1605451, _1605623))]]]]], (24875 ^ _775828) ^ [_1213843, _1213845, _1213847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1213843), c_Nitpick_Oplus__frac(_1213843, _1213845, c_Nitpick_Ouminus__frac(_1213843, _1213847)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1213843, _1213845, _1213847))], (31975 ^ _775828) ^ [_1367401, _1367403, _1367405] : [class_Orderings_Olinorder(_1367401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367401), _1367403), _1367405)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367401, tc_HOL_Obool)), 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_1064484))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064480), hAPP(c_Int_Onumber__class_Onumber__of(_1064480), _1064484)), hAPP(c_Int_Onumber__class_Onumber__of(_1064480), _1064482)))]]], (8761 ^ _775828) ^ [_916194, _916196, _916198] : [class_Orderings_Olinorder(_916194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916194), _916196), _916198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916194), _916198), _916196))], (12721 ^ _775828) ^ [_985863, _985865] : [class_Int_Oring__char__0(_985863), hBOOL(hAPP(hAPP(c_member(_985863), _985865), c_Int_Oring__1__class_OInts(_985863))), 12728 ^ _775828 : [(12735 ^ _775828) ^ [] : [_985865 = c_Groups_Ozero__class_Ozero(_985863), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985863), _985865), _985865) = c_Groups_Ozero__class_Ozero(_985863))], (12729 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985863), _985865), _985865) = c_Groups_Ozero__class_Ozero(_985863), -(_985865 = c_Groups_Ozero__class_Ozero(_985863))]]], (8265 ^ _775828) ^ [_908623, _908625, _908627] : [class_Orderings_Oorder(_908623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908623), _908625), _908627)), 8272 ^ _775828 : [(8279 ^ _775828) ^ [] : [_908627 = _908625, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908623), _908627), _908625)))], (8273 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908623), _908627), _908625)), -(_908627 = _908625)]]], (17607 ^ _775828) ^ [_1077210, _1077212] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077210) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077212)), 17610 ^ _775828 : [(17613 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077212)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17611 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077210))))]], 17614 ^ _775828 : [(17617 ^ _775828) ^ [] : [17618 ^ _775828 : [(17621 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077210) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17619 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077212))))]], 17622 ^ _775828 : [(17625 ^ _775828) ^ [] : [_1077210 = _1077212], (17623 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077212)))]]], (17615 ^ _775828) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077210)))]]], (30253 ^ _775828) ^ [] : [-(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, 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582979), _1582983), hAPP(c_Finite__Set_Ofold1(_1582979, c_Orderings_Oord__class_Omin(_1582979)), _1582981))), 41709 ^ _775828 : [(41710 ^ _775828) ^ [_1583272] : [hBOOL(hAPP(hAPP(c_member(_1582979), _1583272), _1582981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582979), _1582983), _1583272)))]]], (41716 ^ _775828) ^ [] : [41718 ^ _775828 : [(41721 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582979), _1582983), 41717 ^ [_1582979, _1582981, _1582983]))], (41719 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582979), 41717 ^ [_1582979, _1582981, _1582983]), _1582981)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582979), _1582983), hAPP(c_Finite__Set_Ofold1(_1582979, c_Orderings_Oord__class_Omin(_1582979)), _1582981))))]]], (27348 ^ _775828) ^ [_1260621, _1260623] : [-(c_Relation_OId__on(_1260621, _1260623) = hAPP(c_Product__Type_Oprod_Oprod__case(_1260621, _1260621, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1260621, tc_HOL_Obool, tc_fun(_1260621, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260621, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1260621, tc_HOL_Obool)), _1260621), c_COMBC(_1260621, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260621, tc_HOL_Obool), tc_fun(_1260621, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1260621), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260621), c_fconj)), c_fequal))), _1260623)))], (3698 ^ _775828) ^ [_832022, _832024, _832026, _832028, _832030, _832032] : [-(c_Finite__Set_Ofold__image(_832032, _832028, _832024) = c_Finite__Set_Ofold__image(_832030, _832026, _832022)), _832032 = _832030, _832028 = _832026, _832024 = _832022], (19938 ^ _775828) ^ [_1118114, _1118116] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1118114, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118116)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1118114, 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)))), _1118116)))], (47321 ^ _775828) ^ [_1719698, _1719700, _1719702, _1719704, _1719706, _1719708] : [-(hAPP(hAPP(c_List_Omap(_1719698, _1719700), _1719702), hAPP(hAPP(c_List_Olist__update(_1719698, _1719704), _1719706), _1719708)) = hAPP(hAPP(c_List_Olist__update(_1719700, hAPP(hAPP(c_List_Omap(_1719698, _1719700), _1719702), _1719704)), _1719706), hAPP(_1719702, _1719708)))], (29597 ^ _775828) ^ [_1313041, _1313043, _1313045] : [_1313045 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1313041, _1313043), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1313041, _1313043), _1313045) = c_Orderings_Obot__class_Obot(tc_fun(_1313041, tc_HOL_Obool)))], (44431 ^ _775828) ^ [_1648369, _1648371, _1648373, _1648375, _1648377] : [-(_1648369 = c_Orderings_Obot__class_Obot(tc_fun(_1648371, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648371, tc_fun(_1648373, tc_HOL_Obool)), _1648369), hAPP(hAPP(c_COMBC(_1648371, tc_fun(_1648373, tc_HOL_Obool), tc_fun(_1648373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648373, tc_HOL_Obool), tc_fun(tc_fun(_1648373, tc_HOL_Obool), tc_fun(_1648373, tc_HOL_Obool)), _1648371), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648373, tc_HOL_Obool))), _1648375)), _1648377)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648373, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648371, tc_fun(_1648373, tc_HOL_Obool)), _1648369), _1648375)), _1648377))], (35483 ^ _775828) ^ [_1442453, _1442455] : [c_Nat__Transfer_Ois__nat(_1442453), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1442453, _1442455)))], (42418 ^ _775828) ^ [_1599746, _1599748, _1599750, _1599752, _1599754] : [c_Relation_Osingle__valued(_1599746, _1599748, _1599750), c_Relation_Osingle__valued(_1599748, _1599752, _1599754), -(c_Relation_Osingle__valued(_1599746, _1599752, hAPP(hAPP(c_Relation_Orel__comp(_1599746, _1599748, _1599752), _1599750), _1599754)))], (35413 ^ _775828) ^ [_1440707, _1440709] : [-(hAPP(c_Set_OPow(_1440707), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1440707, tc_HOL_Obool)), _1440709)) = hAPP(c_Set_OCollect(tc_fun(_1440707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1440707, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1440707, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1440707, tc_HOL_Obool), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1440707, tc_HOL_Obool)), c_COMBS(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1440707, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1440707, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1440707, tc_HOL_Obool), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_fun(_1440707, tc_HOL_Obool)), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_fun(_1440707, tc_HOL_Obool)), tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1440707, tc_HOL_Obool)), c_COMBB(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1440707, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1440707, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440707, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1440707, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1440707, tc_HOL_Obool)), _1440709)), c_Set_OPow(_1440707))))))], (50919 ^ _775828) ^ [_1800872, _1800874, _1800876, _1800878, _1800880] : [hBOOL(hAPP(hAPP(c_member(_1800872), _1800874), hAPP(c_List_Oset(_1800872), _1800876))), -(hBOOL(hAPP(_1800878, _1800874))), -(c_List_OdropWhile(_1800872, _1800878, hAPP(hAPP(c_List_Oappend(_1800872), _1800876), _1800880)) = hAPP(hAPP(c_List_Oappend(_1800872), c_List_OdropWhile(_1800872, _1800878, _1800876)), _1800880))], (41058 ^ _775828) ^ [_1567101, _1567103, _1567105, _1567107, _1567109] : [class_Groups_Ocomm__monoid__add(_1567101), class_Groups_Ocomm__monoid__mult(_1567101), _1567103 = _1567105, c_Nat__Transfer_Onat__set(_1567105), 41076 ^ _775828 : [(41079 ^ _775828) ^ [] : [hAPP(_1567107, 41075 ^ [_1567101, _1567103, _1567105, _1567107, _1567109]) = hAPP(_1567109, 41075 ^ [_1567101, _1567103, _1567105, _1567107, _1567109])], (41077 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41075 ^ [_1567101, _1567103, _1567105, _1567107, _1567109])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1567101), _1567107), _1567103) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1567101), _1567109), _1567105))], (47705 ^ _775828) ^ [_1728095, _1728097, _1728099, _1728101, _1728103, _1728105, _1728107] : [-(hBOOL(hAPP(hAPP(c_member(_1728095), _1728097), hAPP(c_List_Oset(_1728095), _1728099)))), -(c_Map_Omap__upds(_1728095, _1728101, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1728095, tc_Option_Ooption(_1728101)), _1728103), _1728097), hAPP(c_Option_Ooption_OSome(_1728101), _1728105)), _1728099, _1728107) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1728095, tc_Option_Ooption(_1728101)), c_Map_Omap__upds(_1728095, _1728101, _1728103, _1728099, _1728107)), _1728097), hAPP(c_Option_Ooption_OSome(_1728101), _1728105)))], (10025 ^ _775828) ^ [_937915, _937917, _937919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937915, tc_HOL_Obool)), _937919), _937917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937915, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937915, tc_HOL_Obool)), _937917)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_937915, tc_HOL_Obool)), _937919))))], (26187 ^ _775828) ^ [_1238146, _1238148, _1238150, _1238152] : [class_Rings_Ocomm__semiring__1(_1238146), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238146), _1238148), _1238150)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238146), _1238148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238146), _1238152), _1238150))))], (49835 ^ _775828) ^ [_1777298, _1777300] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1777298, _1777300)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1777298), _1777300))], (44256 ^ _775828) ^ [_1643125, _1643127, _1643129, _1643131] : [-(hAPP(c_Set_OPow(_1643125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643127, tc_fun(_1643125, tc_HOL_Obool)), _1643129), _1643131)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643127, tc_fun(tc_fun(_1643125, tc_HOL_Obool), tc_HOL_Obool)), _1643129), hAPP(hAPP(c_COMBB(tc_fun(_1643125, tc_HOL_Obool), tc_fun(tc_fun(_1643125, tc_HOL_Obool), tc_HOL_Obool), _1643127), c_Set_OPow(_1643125)), _1643131)))], (50882 ^ _775828) ^ [_1800185, _1800187, _1800189] : [class_Orderings_Olinorder(_1800185), c_List_Olinorder__class_Osorted(_1800185, _1800187), -(c_List_Olinorder__class_Osorted(_1800185, c_List_OdropWhile(_1800185, _1800189, _1800187)))], (19474 ^ _775828) ^ [_1110492, _1110494] : [class_Int_Onumber__ring(_1110492), 19477 ^ _775828 : [(19484 ^ _775828) ^ [] : [c_Int_Oiszero(_1110492, hAPP(c_Int_Onumber__class_Onumber__of(_1110492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1110492), _1110494) = c_Groups_Oone__class_Oone(_1110492))], (19478 ^ _775828) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1110492), _1110494) = c_Groups_Oone__class_Oone(_1110492), -(c_Int_Oiszero(_1110492, hAPP(c_Int_Onumber__class_Onumber__of(_1110492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (20010 ^ _775828) ^ [_1119589, _1119591] : [_1119589 = _1119591, -(c_Int_OBit0(_1119589) = c_Int_OBit0(_1119591))], (49301 ^ _775828) ^ [_1765647, _1765649, _1765651, _1765653] : [49302 ^ _775828 : [(49305 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1765647), _1765649), hAPP(c_List_Oset(_1765647), c_List_Obutlast(_1765647, _1765653))))], (49303 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1765647), _1765649), hAPP(c_List_Oset(_1765647), c_List_Obutlast(_1765647, _1765651))))]], -(hBOOL(hAPP(hAPP(c_member(_1765647), _1765649), hAPP(c_List_Oset(_1765647), c_List_Obutlast(_1765647, hAPP(hAPP(c_List_Oappend(_1765647), _1765651), _1765653))))))], (1440 ^ _775828) ^ [_796446, _796448] : [-(class_Rings_Oordered__cancel__semiring(_796446)), _796448 = _796446, class_Rings_Oordered__cancel__semiring(_796448)], (45719 ^ _775828) ^ [_1677883, _1677885, _1677887, _1677889, _1677891] : [-(hAPP(hAPP(c_Option_Omap(_1677883, _1677885), _1677887), _1677889) = hAPP(c_Option_Ooption_OSome(_1677885), _1677891)), 45720 ^ _775828 : [(45721 ^ _775828) ^ [_1677951] : [_1677889 = hAPP(c_Option_Ooption_OSome(_1677883), _1677951), hAPP(_1677887, _1677951) = _1677891]]], (35383 ^ _775828) ^ [_1439920, _1439922, _1439924, _1439926, _1439928] : [hAPP(c_Set_Oimage(_1439920, _1439922, _1439924), _1439926) = _1439928, -(hAPP(c_Set_Oimage(tc_fun(_1439920, tc_HOL_Obool), tc_fun(_1439922, tc_HOL_Obool), c_Set_Oimage(_1439920, _1439922, _1439924)), hAPP(c_Set_OPow(_1439920), _1439926)) = hAPP(c_Set_OPow(_1439922), _1439928))], (28449 ^ _775828) ^ [_1286816, _1286818, _1286820] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286816, tc_HOL_Obool)), _1286818), _1286820) = _1286820, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286816, tc_HOL_Obool)), _1286818), _1286820)))], (31125 ^ _775828) ^ [_1346388, _1346390, _1346392] : [class_Orderings_Olinorder(_1346388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346388), _1346390)), -(_1346390 = c_Orderings_Obot__class_Obot(tc_fun(_1346388, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346388), _1346392)), -(_1346392 = c_Orderings_Obot__class_Obot(tc_fun(_1346388, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346388), c_Big__Operators_Olattice_OSup__fin(_1346388, c_Orderings_Oord__class_Omax(_1346388), _1346390)), c_Big__Operators_Olattice_OSup__fin(_1346388, c_Orderings_Oord__class_Omax(_1346388), _1346392)) = c_Big__Operators_Olattice_OSup__fin(_1346388, c_Orderings_Oord__class_Omax(_1346388), hAPP(c_Set_OCollect(_1346388), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_HOL_Obool), tc_HOL_Obool, _1346388), c_HOL_OEx(_1346388)), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool)), tc_fun(_1346388, tc_HOL_Obool), _1346388), hAPP(c_COMBB(tc_fun(_1346388, tc_HOL_Obool), tc_HOL_Obool, _1346388), c_HOL_OEx(_1346388))), hAPP(hAPP(c_COMBC(_1346388, tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool)), tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_fun(tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool))), tc_fun(tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool)), tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool))), _1346388), c_COMBS(_1346388, tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_fun(_1346388, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1346388, tc_fun(tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool))), _1346388), hAPP(c_COMBB(tc_fun(_1346388, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool)), _1346388), c_COMBS(_1346388, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool)), tc_fun(_1346388, tc_fun(_1346388, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1346388), hAPP(c_COMBB(tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1346388), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1346388), c_fconj))), hAPP(hAPP(c_COMBC(_1346388, tc_fun(_1346388, tc_fun(_1346388, _1346388)), tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1346388, _1346388), tc_fun(_1346388, tc_HOL_Obool)), tc_fun(tc_fun(_1346388, tc_fun(_1346388, _1346388)), tc_fun(_1346388, tc_fun(_1346388, tc_HOL_Obool))), _1346388), c_COMBB(tc_fun(_1346388, _1346388), tc_fun(_1346388, tc_HOL_Obool), _1346388)), hAPP(hAPP(c_COMBB(tc_fun(_1346388, tc_HOL_Obool), tc_fun(tc_fun(_1346388, _1346388), tc_fun(_1346388, tc_HOL_Obool)), _1346388), c_COMBB(_1346388, tc_HOL_Obool, _1346388)), c_fequal))), c_Orderings_Oord__class_Omin(_1346388)))))), hAPP(hAPP(c_COMBC(_1346388, tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1346388, tc_HOL_Obool), tc_fun(_1346388, tc_HOL_Obool)), _1346388), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1346388)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1346388), c_fconj), hAPP(hAPP(c_COMBC(_1346388, tc_fun(_1346388, tc_HOL_Obool), tc_HOL_Obool), c_member(_1346388)), _1346390)))), hAPP(hAPP(c_COMBC(_1346388, tc_fun(_1346388, tc_HOL_Obool), tc_HOL_Obool), c_member(_1346388)), _1346392))))))))], (4136 ^ _775828) ^ [_838991, _838993, _838995, _838997, _838999, _839001] : [-(c_List_Oset__Cons(_839001, _838997, _838993) = c_List_Oset__Cons(_838999, _838995, _838991)), _839001 = _838999, _838997 = _838995, _838993 = _838991], (70 ^ _775828) ^ [_776827, _776829] : [-(class_Rings_Odivision__ring__inverse__zero(_776827)), _776829 = _776827, class_Rings_Odivision__ring__inverse__zero(_776829)], (3682 ^ _775828) ^ [_831788, _831790, _831792, _831794] : [-(c_Wellfounded_Omax__ext(_831794, _831790) = c_Wellfounded_Omax__ext(_831792, _831788)), _831794 = _831792, _831790 = _831788], (43535 ^ _775828) ^ [_1627059, _1627061, _1627063, _1627065, _1627067, _1627069, _1627071, _1627073] : [class_Groups_Ocomm__monoid__add(_1627059), class_Orderings_Oord(_1627061), _1627063 = _1627065, _1627067 = _1627069, 43553 ^ _775828 : [(43558 ^ _775828) ^ [] : [hAPP(_1627071, 43552 ^ [_1627059, _1627061, _1627063, _1627065, _1627067, _1627069, _1627071, _1627073]) = hAPP(_1627073, 43552 ^ [_1627059, _1627061, _1627063, _1627065, _1627067, _1627069, _1627071, _1627073])], (43556 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1627061), 43552 ^ [_1627059, _1627061, _1627063, _1627065, _1627067, _1627069, _1627071, _1627073]), _1627069)))], (43554 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1627061), _1627065), 43552 ^ [_1627059, _1627061, _1627063, _1627065, _1627067, _1627069, _1627071, _1627073])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1627061, _1627059), _1627071), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1627061, _1627063), _1627067)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1627061, _1627059), _1627073), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1627061, _1627065), _1627069)))], (44141 ^ _775828) ^ [_1639250, _1639252, _1639254, _1639256, _1639258] : [hBOOL(hAPP(hAPP(c_member(_1639250), _1639252), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639254, tc_fun(_1639250, tc_HOL_Obool)), _1639256), _1639258))), 44144 ^ _775828 : [(44145 ^ _775828) ^ [_1639374] : [hBOOL(hAPP(hAPP(c_member(_1639254), _1639374), _1639256)), -(hBOOL(hAPP(hAPP(c_member(_1639250), _1639252), hAPP(_1639258, _1639374))))]]], (19234 ^ _775828) ^ [_1106633] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106633), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106633), c_Int_OPls)))], (22396 ^ _775828) ^ [_1165284, _1165286, _1165288, _1165290, _1165292] : [class_Fields_Ofield__inverse__zero(_1165284), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165284), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165284), _1165286), _1165288)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165284), _1165290), _1165292)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165284), _1165286), _1165290)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165284), _1165288), _1165292)))], (11951 ^ _775828) ^ [_972664, _972666, _972668] : [class_Rings_Olinordered__ring__strict(_972664), 11954 ^ _775828 : [(11955 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972664), c_Groups_Ozero__class_Ozero(_972664)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972664), _972666), _972666)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972664), _972668), _972668)))), _972666 = c_Groups_Ozero__class_Ozero(_972664), _972668 = c_Groups_Ozero__class_Ozero(_972664)], (11965 ^ _775828) ^ [] : [11966 ^ _775828 : [(11969 ^ _775828) ^ [] : [-(_972668 = c_Groups_Ozero__class_Ozero(_972664))], (11967 ^ _775828) ^ [] : [-(_972666 = c_Groups_Ozero__class_Ozero(_972664))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972664), c_Groups_Ozero__class_Ozero(_972664)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972664), _972666), _972666)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972664), _972668), _972668)))))]]], (41893 ^ _775828) ^ [_1587641, _1587643] : [-(c_Product__Type_Oapsnd(_1587641, _1587641, _1587643, c_Fun_Oid(_1587641)) = c_Fun_Oid(tc_prod(_1587643, _1587641)))], (16841 ^ _775828) ^ [_1062720, _1062722, _1062724] : [class_Groups_Oordered__ab__group__add__abs(_1062720), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062720), hAPP(c_Groups_Oabs__class_Oabs(_1062720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062720), hAPP(c_Groups_Oabs__class_Oabs(_1062720), _1062722)), hAPP(c_Groups_Oabs__class_Oabs(_1062720), _1062724)))), hAPP(c_Groups_Oabs__class_Oabs(_1062720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062720), _1062722), _1062724)))))], (47457 ^ _775828) ^ [_1722431, _1722433] : [-(_1722433 = c_List_Olist_ONil(_1722431)), -(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(_1722431)), _1722433))))], (7069 ^ _775828) ^ [_888003, _888005, _888007, _888009] : [class_Rings_Olinordered__semiring__strict(_888003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888003), _888005), _888007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888003), c_Groups_Ozero__class_Ozero(_888003)), _888009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888003), _888005), _888009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_888003), _888007), _888009))))], (38188 ^ _775828) ^ [_1500630, _1500632, _1500634] : [class_Rings_Oring__1(_1500630), -(hAPP(c_Int_Oring__1__class_Oof__int(_1500630), 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), _1500632), _1500634)), 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(_1500630), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1500630), _1500632)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1500630), _1500634)))], (10990 ^ _775828) ^ [_955647, _955649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955647), _955649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955647), _955649)))], (34283 ^ _775828) ^ [_1414221, _1414223] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414221, tc_HOL_Obool)), _1414223), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414221, tc_HOL_Obool)), _1414223)) = c_Orderings_Obot__class_Obot(tc_fun(_1414221, tc_HOL_Obool)))], (13298 ^ _775828) ^ [_995991, _995993, _995995, _995997] : [class_Divides_Osemiring__div(_995991), -(c_Divides_Odiv__class_Omod(_995991, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995991), _995993), _995995), _995997) = c_Divides_Odiv__class_Omod(_995991, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995991), c_Divides_Odiv__class_Omod(_995991, _995993, _995997)), c_Divides_Odiv__class_Omod(_995991, _995995, _995997)), _995997))], (49182 ^ _775828) ^ [_1763161, _1763163, _1763165] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763161, _1763161)), hAPP(hAPP(c_Product__Type_OPair(_1763161, _1763161), 49183 ^ [_1763161, _1763163, _1763165]), 49183 ^ [_1763161, _1763163, _1763165])), _1763163))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763161), tc_List_Olist(_1763161))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763161), tc_List_Olist(_1763161)), _1763165), _1763165)), c_List_Olexord(_1763161, _1763163)))], (47319 ^ _775828) ^ [_1719658, _1719660, _1719662] : [-(hAPP(hAPP(c_List_Omap(_1719658, _1719660), _1719662), c_List_Olist_ONil(_1719658)) = c_List_Olist_ONil(_1719660))], (1780 ^ _775828) ^ [_800692, _800694, _800696, _800698, _800700, _800702] : [-(c_Hoare__Mirabelle_Otriple__valid(_800700, _800696, _800692)), c_Hoare__Mirabelle_Otriple__valid(_800702, _800698, _800694), _800702 = _800700, _800698 = _800696, _800694 = _800692], (19422 ^ _775828) ^ [_1109661, _1109663] : [class_Int_Onumber__ring(_1109661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1109663)), -(hBOOL(hAPP(hAPP(c_member(_1109661), hAPP(c_Int_Onumber__class_Onumber__of(_1109661), _1109663)), c_Nat_Osemiring__1__class_ONats(_1109661))))], (36657 ^ _775828) ^ 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hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1093702), _1093706))), c_FunDef_Opair__less)))], (46155 ^ _775828) ^ [_1688376, _1688378, _1688380, _1688382] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688376)), hAPP(hAPP(c_List_Omap(_1688378, _1688376), _1688380), _1688382)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688378)), _1688382))], (10192 ^ _775828) ^ [_940905, _940907, _940909, _940911] : [class_Groups_Ocancel__semigroup__add(_940905), 10195 ^ _775828 : [(10202 ^ _775828) ^ [] : [_940907 = _940911, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940905), _940907), _940909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940905), _940911), _940909))], (10196 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940905), _940907), _940909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940905), _940911), _940909), -(_940907 = _940911)]]], (28711 ^ _775828) ^ [_1291843, _1291845, _1291847, _1291849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291843, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1291843, tc_HOL_Obool)), _1291845), _1291847)), _1291849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291843, tc_HOL_Obool)), _1291845), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291843, tc_HOL_Obool)), _1291847), _1291849))))], (9321 ^ _775828) ^ [_925241, _925243, _925245, _925247] : [class_Rings_Oordered__comm__semiring(_925241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925241), _925243), _925245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925241), c_Groups_Ozero__class_Ozero(_925241)), _925247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925241), _925247), _925243)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925241), _925247), _925245))))], (10702 ^ _775828) ^ [_950701] : [class_Rings_Ozero__neq__one(_950701), c_Groups_Ozero__class_Ozero(_950701) = c_Groups_Oone__class_Oone(_950701)], (47463 ^ _775828) ^ [_1722480, _1722482, _1722484, _1722486, _1722488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722480, tc_HOL_Obool)), hAPP(c_List_Oset(_1722480), _1722482)), _1722484)), hBOOL(hAPP(hAPP(c_member(_1722480), _1722486), _1722484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722480, tc_HOL_Obool)), hAPP(c_List_Oset(_1722480), hAPP(hAPP(c_List_Olist__update(_1722480, _1722482), _1722488), _1722486))), _1722484)))], (32759 ^ _775828) ^ [_1381517, _1381519, _1381521, _1381523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1381517, _1381519)), c_Sum__Type_OPlus(_1381517, _1381519, _1381521, _1381523))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1381519), _1381523)))], (46642 ^ _775828) ^ [_1702915, _1702917, _1702919, _1702921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1702915), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1702917), _1702919))), -(hAPP(c_Random_Opick(_1702917, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1702917)), _1702919), _1702921)), _1702915) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1702917), _1702919))], (27477 ^ _775828) ^ [_1263963, _1263965, _1263967, _1263969] : [hBOOL(hAPP(hAPP(c_member(_1263963), _1263965), c_SetInterval_Oord_OlessThan(_1263963, _1263967, _1263969))), -(hBOOL(hAPP(hAPP(_1263967, _1263965), _1263969)))], (50433 ^ _775828) ^ [_1789639, _1789641] : [-(_1789639 = c_List_Olist_ONil(_1789641)), -(c_List_Olast(_1789641, hAPP(c_List_Orev(_1789641), _1789639)) = hAPP(c_List_Ohd(_1789641), _1789639))], (6738 ^ _775828) ^ [_882713] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882713))), -(hAPP(c_Com_Obody, _882713) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6741 ^ [_882713]))], (34279 ^ _775828) ^ [_1414088, _1414090, _1414092, _1414094] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414088, tc_HOL_Obool)), _1414090), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414088, tc_HOL_Obool)), _1414092), _1414094)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414088, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414088, tc_HOL_Obool)), _1414090), _1414092)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414088, tc_HOL_Obool)), _1414090), _1414094)))], (35288 ^ _775828) ^ [_1437540, _1437542, _1437544] : [class_Lattices_Olattice(_1437540), hAPP(_1437542, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437540), 35293 ^ [_1437540, _1437542, _1437544]), 35294 ^ [_1437540, _1437542, _1437544])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437540), hAPP(_1437542, 35293 ^ [_1437540, _1437542, _1437544])), hAPP(_1437542, 35294 ^ [_1437540, _1437542, _1437544])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437540), _1437544)), -(_1437544 = c_Orderings_Obot__class_Obot(tc_fun(_1437540, tc_HOL_Obool))), -(hAPP(_1437542, c_Big__Operators_Olattice__class_OInf__fin(_1437540, _1437544)) = c_Big__Operators_Olattice__class_OInf__fin(_1437540, hAPP(c_Set_Oimage(_1437540, _1437540, _1437542), _1437544)))], (45377 ^ _775828) ^ [_1669661, _1669663, _1669665, _1669667, _1669669] : [-(hBOOL(hAPP(hAPP(c_member(_1669661), _1669663), c_Map_Odom(_1669661, _1669665, _1669667)))), -(hAPP(c_Map_Omap__add(_1669661, _1669665, _1669667, _1669669), _1669663) = hAPP(_1669669, _1669663))], (40766 ^ _775828) ^ [_1559613, _1559615, _1559617] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1559613, _1559613, _1559613), _1559615), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1559613, _1559613), tc_HOL_Obool), _1559617), _1559615)) = hAPP(hAPP(c_Relation_Orel__comp(_1559613, _1559613, _1559613), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1559613, _1559613), tc_HOL_Obool), _1559617), _1559615)), _1559615))], (34387 ^ _775828) ^ [_1416631, _1416633, _1416635, _1416637, _1416639, _1416641] : [-(hAPP(c_Set_Oimage(_1416631, _1416633, hAPP(hAPP(c_COMBS(_1416631, _1416633, _1416633), hAPP(hAPP(c_COMBS(_1416631, _1416633, tc_fun(_1416633, _1416633)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1416633, tc_fun(_1416633, _1416633)), _1416631), c_If(_1416633)), _1416635)), _1416637)), _1416639)), _1416641) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416633, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1416631, _1416633, _1416637), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416631, tc_HOL_Obool)), _1416641), hAPP(c_Set_OCollect(_1416631), _1416635)))), hAPP(c_Set_Oimage(_1416631, _1416633, _1416639), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416631, tc_HOL_Obool)), _1416641), hAPP(c_Set_OCollect(_1416631), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1416631), c_fNot), _1416635))))))], (39547 ^ _775828) ^ [_1531074, _1531076, _1531078, _1531080] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1531074, tc_fun(_1531076, tc_HOL_Obool)), _1531078), _1531080) = c_Orderings_Obot__class_Obot(tc_fun(_1531076, tc_HOL_Obool)), 39550 ^ _775828 : [(39551 ^ _775828) ^ [_1531190] : [hBOOL(hAPP(hAPP(c_member(_1531074), _1531190), _1531078)), -(hAPP(_1531080, _1531190) = c_Orderings_Obot__class_Obot(tc_fun(_1531076, tc_HOL_Obool)))]]], (25237 ^ _775828) ^ [_1221032, _1221034] : [c_Nat__Transfer_Onat__set(_1221032), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1221034), _1221032)), -(c_Nat__Transfer_Ois__nat(_1221034))], (36401 ^ _775828) ^ [_1459510, _1459512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459510), _1459512)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459510), hAPP(c_Nat_OSuc, _1459512)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1459512), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459510), _1459512)))], (386 ^ _775828) ^ [_781523, _781525] : [-(class_Fields_Ofield(_781523)), _781525 = _781523, class_Fields_Ofield(_781525)], (160 ^ _775828) ^ [_778058, _778060, _778062, _778064, _778066, _778068, _778070, _778072] : [-(c_Nat__Transfer_Otransfer__morphism(_778070, _778066, _778062, _778058)), c_Nat__Transfer_Otransfer__morphism(_778072, _778068, _778064, _778060), _778072 = _778070, _778068 = _778066, _778064 = _778062, _778060 = _778058], (9781 ^ _775828) ^ [_933443, _933445, _933447, _933449, _933451] : [class_Rings_Olinordered__semiring__strict(_933443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933443), _933445), _933447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933443), _933449), _933451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933443), c_Groups_Ozero__class_Ozero(_933443)), _933445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933443), c_Groups_Ozero__class_Ozero(_933443)), _933449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933443), _933445), _933449)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933443), _933447), _933451))))], (2596 ^ _775828) ^ [_814227, _814229, _814231, _814233, _814235, _814237, _814239, _814241] : [-(c_Nitpick_Opair__box_OPairBox(_814241, _814237, _814233, _814229) = c_Nitpick_Opair__box_OPairBox(_814239, _814235, _814231, _814227)), _814241 = _814239, _814237 = _814235, _814233 = _814231, _814229 = _814227], (45874 ^ _775828) ^ [_1681437, _1681439, _1681441, _1681443, _1681445] : [hBOOL(hAPP(c_List_Odistinct(_1681437), hAPP(hAPP(c_List_Omap(tc_prod(_1681437, _1681439), _1681437), c_Product__Type_Ofst(_1681437, _1681439)), _1681441))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1681437, _1681439)), hAPP(hAPP(c_Product__Type_OPair(_1681437, _1681439), _1681443), _1681445)), hAPP(c_List_Oset(tc_prod(_1681437, _1681439)), _1681441))), -(hAPP(c_Map_Omap__of(_1681437, _1681439, _1681441), _1681443) = hAPP(c_Option_Ooption_OSome(_1681439), _1681445))], (21566 ^ _775828) ^ [_1149227, _1149229] : [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(_1149229))), 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)), _1149227))))), -(hAPP(c_Nat_OSuc, _1149227) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1149229))], (5352 ^ _775828) ^ [_857601, _857603] : [_857603 = _857601, -(c_COMBI(_857603) = c_COMBI(_857601))], (51152 ^ _775828) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (5342 ^ _775828) ^ [_857452, _857454, _857456, _857458] : [-(tc_prod(_857458, _857454) = tc_prod(_857456, _857452)), _857458 = _857456, _857454 = _857452], (9889 ^ _775828) ^ [_935516, _935518, _935520, _935522] : [class_Rings_Olinordered__ring__strict(_935516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935516), c_Groups_Ozero__class_Ozero(_935516)), _935518)), 9896 ^ _775828 : [(9903 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935516), _935520), _935522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935516), _935518), _935520)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935516), _935518), _935522))))], (9897 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935516), _935518), _935520)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935516), _935518), _935522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935516), _935520), _935522)))]]], (11847 ^ _775828) ^ [_970710, _970712, _970714] : [class_Groups_Oordered__comm__monoid__add(_970710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970710), c_Groups_Ozero__class_Ozero(_970710)), _970712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970710), c_Groups_Ozero__class_Ozero(_970710)), _970714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970710), c_Groups_Ozero__class_Ozero(_970710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970710), _970712), _970714))))], (1500 ^ _775828) ^ [_797196, _797198] : [-(class_Groups_Ocomm__monoid__mult(_797196)), _797198 = _797196, class_Groups_Ocomm__monoid__mult(_797198)], (28399 ^ _775828) ^ [_1285773, _1285775, _1285777, _1285779] : [hBOOL(hAPP(_1285773, _1285775)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285777, tc_HOL_Obool)), _1285779), _1285773), _1285775)))], (1510 ^ _775828) ^ [_797321, _797323] : [-(class_Groups_Oab__semigroup__add(_797321)), _797323 = _797321, class_Groups_Oab__semigroup__add(_797323)], (43918 ^ _775828) ^ [_1634534, _1634536, _1634538, _1634540, _1634542, _1634544] : [c_Finite__Set_Ofun__left__comm(_1634534, _1634536, _1634538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634534), _1634540)), hBOOL(hAPP(hAPP(c_member(_1634534), _1634542), _1634540)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1634534, _1634536, _1634538), _1634544), _1634540) = hAPP(hAPP(_1634538, _1634542), hAPP(hAPP(c_Finite__Set_Ofold(_1634534, _1634536, _1634538), _1634544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634534, tc_HOL_Obool)), _1634540), hAPP(hAPP(c_Set_Oinsert(_1634534), _1634542), c_Orderings_Obot__class_Obot(tc_fun(_1634534, tc_HOL_Obool)))))))], (30537 ^ _775828) ^ [_1333806, _1333808, _1333810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1333806, _1333808)), _1333810)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333808), hAPP(c_Relation_ORange(_1333806, _1333808), _1333810))))], (20890 ^ _775828) ^ [_1135331] : [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), _1135331))), 20893 ^ _775828 : [(20900 ^ _775828) ^ [] : [-(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), _1135331)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1135331)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1135331)), 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), _1135331)))))], (20894 ^ _775828) ^ [] : [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), _1135331))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1135331)) = 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)))]]], (26045 ^ _775828) ^ [_1235703, _1235705, _1235707] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235703), _1235705)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235705), _1235703))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235705), _1235707)), 26056 ^ _775828 : [(26059 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235707), _1235703))], (26057 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235703), _1235707)))]]], (12325 ^ _775828) ^ [_979098, _979100, _979102] : [_979098 = _979100, 12328 ^ _775828 : [(12331 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979102, tc_HOL_Obool)), _979100), _979098)))], (12329 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979102, tc_HOL_Obool)), _979098), _979100)))]]], (51508 ^ _775828) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (51212 ^ _775828) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (27256 ^ _775828) ^ [_1258495, _1258497, _1258499, _1258501] : [-(hAPP(c_Relation_Oconverse(_1258495, _1258495), hAPP(hAPP(c_Relation_Oinv__image(_1258497, _1258495), _1258499), _1258501)) = hAPP(hAPP(c_Relation_Oinv__image(_1258497, _1258495), hAPP(c_Relation_Oconverse(_1258497, _1258497), _1258499)), _1258501))], (46157 ^ _775828) ^ [_1688428, _1688430, _1688432, _1688434, _1688436, _1688438, _1688440] : [hAPP(hAPP(c_List_Omap(_1688428, _1688430), _1688432), _1688434) = hAPP(hAPP(c_List_Omap(_1688436, _1688430), _1688438), _1688440), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688428)), _1688434) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688436)), _1688440))], (47593 ^ _775828) ^ [_1725138, _1725140, _1725142, _1725144] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1725138) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1725140), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1725138)), hAPP(hAPP(c_List_Olist_OCons(_1725140), _1725142), _1725144)) = hAPP(hAPP(c_List_Olist_OCons(_1725140), _1725142), hAPP(hAPP(c_List_Otake(_1725140), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1725138)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1725144)))], (28952 ^ _775828) ^ [_1299438, _1299440, _1299442, _1299444, _1299446, _1299448] : [28953 ^ _775828 : [(28956 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1299444, _1299440), _1299442))], (28954 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(_1299438, _1299440), _1299442))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299446, tc_fun(_1299448, tc_HOL_Obool))), _1299444), _1299438), _1299440), _1299442)))], (30579 ^ _775828) ^ [_1334648, _1334650, _1334652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334648), hAPP(c_Set_OCollect(_1334648), hAPP(hAPP(c_COMBS(_1334648, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1334648), c_fdisj), _1334650)), _1334652)))), 30582 ^ _775828 : [(30585 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334648), hAPP(c_Set_OCollect(_1334648), _1334652))))], (30583 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334648), hAPP(c_Set_OCollect(_1334648), _1334650))))]]], (33348 ^ _775828) ^ [_1393966, _1393968, _1393970, _1393972, _1393974] : [hBOOL(hAPP(hAPP(c_member(_1393966), _1393968), _1393970)), -(hAPP(c_Map_Orestrict__map(_1393966, _1393972, _1393974, _1393970), _1393968) = hAPP(_1393974, _1393968))], (15264 ^ _775828) ^ [_1032093, _1032095, _1032097] : [class_Groups_Ogroup__add(_1032093), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032093), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032093), _1032095), _1032097)), _1032097) = _1032095)], (23214 ^ _775828) ^ [_1180167, _1180169, _1180171, _1180173] : [class_Fields_Ofield(_1180167), -(_1180169 = c_Groups_Ozero__class_Ozero(_1180167)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180167), _1180171), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180167), _1180173), _1180169)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180167), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180167), _1180169), _1180171)), _1180173)), _1180169))], (48615 ^ _775828) ^ [_1751271, _1751273, _1751275] : [-(_1751271 = c_List_Olist_ONil(_1751273)), -(hAPP(c_List_Ohd(_1751273), hAPP(hAPP(c_List_Oappend(_1751273), _1751271), _1751275)) = hAPP(c_List_Ohd(_1751273), _1751271))], (42908 ^ _775828) ^ [_1611722] : [-(c_Nitpick_Odenom(_1611722) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1611722, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1611722)))], (36695 ^ _775828) ^ [_1465311] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1465311))))], (25068 ^ _775828) ^ [_1218155, _1218157] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1218155), _1218157)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218155)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218157))))], (48717 ^ _775828) ^ [_1752957, _1752959, _1752961] : [-(hAPP(c_List_Orotate1(_1752957), hAPP(c_List_Orotate(_1752957, _1752959), _1752961)) = hAPP(c_List_Orotate(_1752957, _1752959), hAPP(c_List_Orotate1(_1752957), _1752961)))], (35163 ^ _775828) ^ [_1434689, _1434691, _1434693, _1434695, _1434697] : [class_Groups_Ocomm__monoid__mult(_1434689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434691), _1434693)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1434689, _1434691, c_Groups_Otimes__class_Otimes(_1434689)), hAPP(hAPP(c_COMBS(_1434691, _1434689, _1434689), hAPP(hAPP(c_COMBB(_1434689, tc_fun(_1434689, _1434689), _1434691), c_Groups_Otimes__class_Otimes(_1434689)), _1434695)), _1434697)), c_Groups_Oone__class_Oone(_1434689)), _1434693) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434689), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1434689, _1434691, c_Groups_Otimes__class_Otimes(_1434689)), _1434695), c_Groups_Oone__class_Oone(_1434689)), _1434693)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1434689, _1434691, c_Groups_Otimes__class_Otimes(_1434689)), _1434697), c_Groups_Oone__class_Oone(_1434689)), _1434693)))], (45696 ^ _775828) ^ [_1677416, _1677418, _1677420, _1677422] : [hAPP(hAPP(c_Option_Omap(_1677416, _1677418), _1677420), _1677422) = c_Option_Ooption_ONone(_1677418), -(_1677422 = c_Option_Ooption_ONone(_1677416))], (48900 ^ _775828) ^ [_1756890, _1756892, _1756894, _1756896] : [class_Complete__Lattice_Ocomplete__lattice(_1756890), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756892, _1756890), hAPP(c_List_Oset(_1756892), _1756894)), _1756896) = hAPP(c_List_Ofoldl(_1756890, _1756892, hAPP(c_COMBC(_1756892, _1756890, _1756890), hAPP(hAPP(c_COMBB(_1756890, tc_fun(_1756890, _1756890), _1756892), c_Lattices_Osemilattice__inf__class_Oinf(_1756890)), _1756896)), c_Orderings_Otop__class_Otop(_1756890)), _1756894))], (36723 ^ _775828) ^ [] : [-(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)))], (27344 ^ _775828) ^ [_1260550, _1260552] : [-(hAPP(c_Relation_ORange(_1260550, _1260550), c_Relation_OId__on(_1260550, _1260552)) = _1260552)], (51314 ^ _775828) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (42043 ^ _775828) ^ [_1591311, _1591313, _1591315, _1591317, _1591319] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591311, _1591313)), _1591315), hAPP(hAPP(c_Product__Type_OSigma(_1591311, _1591313), _1591317), _1591319))), 42047 ^ _775828 : [(42053 ^ _775828) ^ [] : [-(_1591315 = hAPP(hAPP(c_Product__Type_OPair(_1591311, _1591313), 42046 ^ [_1591311, _1591313, _1591315, _1591317, _1591319]), 42049 ^ [_1591311, _1591313, _1591315, _1591317, _1591319]))], (42051 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591313), 42049 ^ [_1591311, _1591313, _1591315, _1591317, _1591319]), hAPP(_1591319, 42046 ^ [_1591311, _1591313, _1591315, _1591317, _1591319]))))], (42048 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591311), 42046 ^ [_1591311, _1591313, _1591315, _1591317, _1591319]), _1591317)))]]], (23142 ^ _775828) ^ [_1178849, _1178851, _1178853, _1178855] : [class_Fields_Olinordered__field(_1178849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178849), _1178851), _1178853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178849), _1178855), c_Groups_Ozero__class_Ozero(_1178849))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178849), c_Groups_Ozero__class_Ozero(_1178849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178849), _1178851), _1178853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178849), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178849), _1178855), _1178851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178849), _1178855), _1178853))))], (18409 ^ _775828) ^ [_1092385, _1092387, _1092389, _1092391] : [_1092385 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1092387), _1092389)), _1092391), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1092385, _1092387), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1092389), _1092391)))), 18416 ^ _775828 : [(18419 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092391), _1092387))], (18417 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092387)))]], 18424 ^ _775828 : [(18427 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092387), _1092391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092391), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18425 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092387))]]], (27298 ^ _775828) ^ [_1259548] : [-(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)))), _1259548))))], (48775 ^ _775828) ^ [_1754286, _1754288, _1754290] : [class_Groups_Omonoid__add(_1754286), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1754286), _1754288), hAPP(c_List_Ofoldl(_1754286, _1754286, c_Groups_Oplus__class_Oplus(_1754286), c_Groups_Ozero__class_Ozero(_1754286)), _1754290)) = hAPP(c_List_Ofoldl(_1754286, _1754286, c_Groups_Oplus__class_Oplus(_1754286), _1754288), _1754290))], (43974 ^ _775828) ^ [_1635706, _1635708, _1635710, _1635712, _1635714] : [c_Finite__Set_Ofun__left__comm(_1635706, _1635708, _1635710), -(hAPP(c_Fun_Ocomp(_1635708, _1635708, _1635708, hAPP(_1635710, _1635712)), hAPP(_1635710, _1635714)) = hAPP(c_Fun_Ocomp(_1635708, _1635708, _1635708, hAPP(_1635710, _1635714)), hAPP(_1635710, _1635712)))], (15362 ^ _775828) ^ [_1034050, _1034052] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034050), _1034052))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1034050, _1034052) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034050), _1034052), _1034052))], (8051 ^ _775828) ^ [_905217, _905219, _905221] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _905217), _905219) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _905217), _905221), -(_905217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_905219 = _905221)], (12520 ^ _775828) ^ [_982446] : [-(hAPP(c_Nat_OSuc, _982446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982446), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (38472 ^ _775828) ^ [_1507230, _1507232, _1507234, _1507236, _1507238] : [c_Equiv__Relations_Oequiv(_1507230, _1507232, _1507234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507230, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1507230, _1507230, _1507234), hAPP(hAPP(c_Set_Oinsert(_1507230), _1507236), c_Orderings_Obot__class_Obot(tc_fun(_1507230, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1507230, _1507230, _1507234), hAPP(hAPP(c_Set_Oinsert(_1507230), _1507238), c_Orderings_Obot__class_Obot(tc_fun(_1507230, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1507230), _1507236), _1507232)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507230, _1507230)), hAPP(hAPP(c_Product__Type_OPair(_1507230, _1507230), _1507238), _1507236)), _1507234)))], (17725 ^ _775828) ^ [_1079359, _1079361, _1079363] : [class_Rings_Osemiring__1(_1079359), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1079359), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1079361), _1079363)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079359), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1079359), _1079361)), _1079363))], (33406 ^ _775828) ^ [_1395289, _1395291, _1395293, _1395295] : [-(c_Map_Orestrict__map(_1395289, _1395291, _1395293, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1395289, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1395289), _1395295), c_Orderings_Obot__class_Obot(tc_fun(_1395289, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1395289, tc_Option_Ooption(_1395291)), _1395293), _1395295), c_Option_Ooption_ONone(_1395291)))], (39415 ^ _775828) ^ [_1527545, _1527547, _1527549, _1527551, _1527553, _1527555, _1527557] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527545, _1527547, _1527549), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527551, tc_fun(tc_prod(_1527545, _1527547), tc_HOL_Obool)), _1527553), _1527555)), _1527557) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527551, tc_fun(tc_prod(_1527545, _1527549), tc_HOL_Obool)), _1527553), hAPP(hAPP(c_COMBC(_1527551, tc_fun(tc_prod(_1527547, _1527549), tc_HOL_Obool), tc_fun(tc_prod(_1527545, _1527549), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527545, _1527547), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1527547, _1527549), tc_HOL_Obool), tc_fun(tc_prod(_1527545, _1527549), tc_HOL_Obool)), _1527551), c_Relation_Orel__comp(_1527545, _1527547, _1527549)), _1527555)), _1527557)))], (29511 ^ _775828) ^ [_1311165, _1311167, _1311169, _1311171, _1311173] : [-(hAPP(hAPP(c_Set_Oinsert(_1311165), _1311167), hAPP(hAPP(c_Set_Oinsert(_1311165), _1311169), c_Orderings_Obot__class_Obot(tc_fun(_1311165, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1311165), _1311171), hAPP(hAPP(c_Set_Oinsert(_1311165), _1311173), c_Orderings_Obot__class_Obot(tc_fun(_1311165, tc_HOL_Obool))))), 29512 ^ _775828 : [(29519 ^ _775828) ^ [] : [_1311167 = _1311173, _1311169 = _1311171], (29513 ^ _775828) ^ [] : [_1311167 = _1311171, _1311169 = _1311173]]], (44718 ^ _775828) ^ [_1655652, _1655654, _1655656] : [class_Complete__Lattice_Ocomplete__lattice(_1655652), 44721 ^ _775828 : [(44722 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655652), c_Complete__Lattice_OSup__class_OSup(_1655652, _1655654)), _1655656)), 44725 ^ _775828 : [(44726 ^ _775828) ^ [_1655810] : [hBOOL(hAPP(hAPP(c_member(_1655652), _1655810), _1655654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655652), _1655810), _1655656)))]]], (44732 ^ _775828) ^ [] : [44734 ^ _775828 : [(44737 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655652), 44733 ^ [_1655652, _1655654, _1655656]), _1655656))], (44735 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655652), 44733 ^ [_1655652, _1655654, _1655656]), _1655654)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1655652), c_Complete__Lattice_OSup__class_OSup(_1655652, _1655654)), _1655656)))]]], (23544 ^ _775828) ^ [_1187509, _1187511] : [-(_1187509 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1187509, _1187511) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1187509), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1187511)))], (13668 ^ _775828) ^ [_1003283, _1003285, _1003287, _1003289, _1003291, _1003293] : [c_Com_Ocom_OCall(_1003283, _1003285, _1003287) = c_Com_Ocom_OCond(_1003289, _1003291, _1003293)], (23566 ^ _775828) ^ [_1188047, _1188049, _1188051, _1188053, _1188055] : [hBOOL(hAPP(hAPP(_1188047, _1188049), _1188051)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188053, _1188055, tc_HOL_Obool), _1188047), hAPP(hAPP(c_Product__Type_OPair(_1188053, _1188055), _1188049), _1188051))))], (20538 ^ _775828) ^ [_1128798, _1128800] : [class_Rings_Olinordered__idom(_1128798), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128798), c_Groups_Ozero__class_Ozero(_1128798)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128798), _1128800), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (44115 ^ _775828) ^ [_1638602, _1638604, _1638606, _1638608, _1638610, _1638612, _1638614, _1638616] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638602, tc_fun(_1638604, tc_fun(_1638606, tc_HOL_Obool))), _1638608), _1638610), _1638612), _1638614)), hBOOL(hAPP(hAPP(c_member(_1638602), _1638616), _1638608)), -(hBOOL(hAPP(hAPP(hAPP(_1638610, _1638616), _1638612), _1638614)))], (40159 ^ _775828) ^ [_1545705, _1545707] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545705, tc_HOL_Obool)), _1545707), c_Orderings_Otop__class_Otop(tc_fun(_1545705, tc_HOL_Obool))) = _1545707)], (10502 ^ _775828) ^ [_946769, _946771] : [class_Groups_Ocomm__monoid__add(_946769), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946769), c_Groups_Ozero__class_Ozero(_946769)), _946771) = _946771)], (12303 ^ _775828) ^ [_978703, _978705, _978707] : [_978703 = _978705, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978707, tc_HOL_Obool)), _978703), _978705)))], (51032 ^ _775828) ^ [_1803378, _1803380] : [class_Lattices_Obounded__lattice(_1803378), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1803380, _1803378)))], (6123 ^ _775828) ^ [_873095, _873097, _873099] : [hAPP(c_Com_Ocom_OBODY, _873095) = c_Com_Ocom_OAss(_873097, _873099)], (21082 ^ _775828) ^ [_1139986, _1139988, _1139990, _1139992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool)), _1139990), _1139992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139986, tc_fun(_1139988, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1139986, tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_fun(_1139988, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139988, tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_fun(_1139988, tc_HOL_Obool)), _1139986), c_COMBC(_1139988, tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139988, tc_prod(_1139986, _1139988)), tc_fun(_1139988, tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), _1139986), hAPP(c_COMBB(tc_prod(_1139986, _1139988), tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool), _1139988), c_member(tc_prod(_1139986, _1139988)))), c_Product__Type_OPair(_1139986, _1139988)))), _1139990)), hAPP(hAPP(c_COMBC(_1139986, tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_fun(_1139988, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139988, tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_fun(_1139988, tc_HOL_Obool)), _1139986), c_COMBC(_1139988, tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1139988, tc_prod(_1139986, _1139988)), tc_fun(_1139988, tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool)), _1139986), hAPP(c_COMBB(tc_prod(_1139986, _1139988), tc_fun(tc_fun(tc_prod(_1139986, _1139988), tc_HOL_Obool), tc_HOL_Obool), _1139988), c_member(tc_prod(_1139986, _1139988)))), c_Product__Type_OPair(_1139986, _1139988)))), _1139992))))], (7173 ^ _775828) ^ [_889928, _889930, _889932] : [class_Rings_Olinordered__semiring__strict(_889928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889928), c_Groups_Ozero__class_Ozero(_889928)), _889930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889928), _889932), c_Groups_Ozero__class_Ozero(_889928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_889928), _889930), _889932)), c_Groups_Ozero__class_Ozero(_889928))))], (15924 ^ _775828) ^ [_1044847, _1044849, _1044851, _1044853, _1044855, _1044857] : [class_Rings_Oordered__ring(_1044847), 15927 ^ _775828 : [(15934 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044847), _1044849), _1044855)), _1044851)), _1044853)), _1044857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), _1044849), _1044851)), _1044853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), _1044855), _1044851)), _1044857))))], (15928 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), _1044849), _1044851)), _1044853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), _1044855), _1044851)), _1044857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044847), _1044849), _1044855)), _1044851)), _1044853)), _1044857)))]]], (29541 ^ _775828) ^ [_1311818, _1311820, _1311822] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1311818, _1311818, hAPP(hAPP(c_COMBB(tc_fun(_1311818, tc_HOL_Obool), tc_fun(_1311818, tc_HOL_Obool), _1311818), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1311818), c_fNot)), 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c_Groups_Ozero__class_Ozero(_1160373)), _1160379)))], (22156 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160373), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377)), c_Groups_Ozero__class_Ozero(_1160373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160373), _1160379), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))), _1160375)))]]], (22146 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160373), c_Groups_Ozero__class_Ozero(_1160373)), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160373), _1160375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160373), _1160379), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377)))))]]], (22168 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160373), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160373), _1160375), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))), _1160379))), 22171 ^ _775828 : [(22174 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160373), _1160375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160373), _1160379), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))))], (22172 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160373), c_Groups_Ozero__class_Ozero(_1160373)), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))))]], 22175 ^ _775828 : [(22178 ^ _775828) ^ [] : [22179 ^ _775828 : [(22182 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160373), _1160379), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377))), _1160375))], (22180 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160373), hAPP(c_Int_Onumber__class_Onumber__of(_1160373), _1160377)), c_Groups_Ozero__class_Ozero(_1160373))))]], 22183 ^ 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c_Lattices_Osemilattice__inf__class_Oinf(_1633672)), _1633676), _1633674))], (40578 ^ _775828) ^ [_1555569, _1555571] : [c_Equiv__Relations_Oequiv(_1555569, c_Orderings_Otop__class_Otop(tc_fun(_1555569, tc_HOL_Obool)), _1555571), -(c_Equiv__Relations_Oequivp(_1555569, hAPP(hAPP(c_COMBC(_1555569, tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_fun(_1555569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555569, tc_fun(tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_fun(_1555569, tc_HOL_Obool)), _1555569), c_COMBC(_1555569, tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555569, tc_prod(_1555569, _1555569)), tc_fun(_1555569, tc_fun(tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_HOL_Obool)), _1555569), hAPP(c_COMBB(tc_prod(_1555569, _1555569), tc_fun(tc_fun(tc_prod(_1555569, _1555569), tc_HOL_Obool), tc_HOL_Obool), _1555569), c_member(tc_prod(_1555569, 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-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863616)), _863618, _863620, _863622))], (21162 ^ _775828) ^ [_1142168, _1142170] : [class_Rings_Odivision__ring(_1142168), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142168), c_Groups_Ozero__class_Ozero(_1142168)), _1142170) = c_Groups_Ozero__class_Ozero(_1142168))], (41470 ^ _775828) ^ [_1578172, _1578174, _1578176, _1578178] : [-(hAPP(c_Set_OCollect(tc_prod(_1578172, _1578174)), hAPP(c_Product__Type_Oprod_Oprod__case(_1578172, _1578174, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1578172, tc_fun(_1578174, tc_HOL_Obool), tc_fun(_1578174, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578174, tc_HOL_Obool), tc_fun(_1578174, tc_HOL_Obool)), _1578172), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578174)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578172), c_fconj), _1578176))), _1578178))) = hAPP(hAPP(c_Product__Type_OSigma(_1578172, _1578174), hAPP(c_Set_OCollect(_1578172), _1578176)), hAPP(hAPP(c_COMBB(tc_fun(_1578174, tc_HOL_Obool), tc_fun(_1578174, tc_HOL_Obool), _1578172), c_Set_OCollect(_1578174)), _1578178)))], (32321 ^ _775828) ^ [_1372941, _1372943, _1372945, _1372947] : [class_Orderings_Olinorder(_1372941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372941), _1372943), _1372945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372941), _1372945), _1372947)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372941, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1372941, _1372943, _1372945)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1372941, _1372945, _1372947)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1372941, _1372943, _1372947))], (40297 ^ _775828) ^ [_1548215, _1548217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548215), hAPP(c_Set_OCollect(_1548215), _1548217))), 40300 ^ _775828 : [(40307 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548215), c_Orderings_Otop__class_Otop(tc_fun(_1548215, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548215), hAPP(c_Set_OCollect(_1548215), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1548215), c_fNot), _1548217)))))], (40301 ^ _775828) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548215), hAPP(c_Set_OCollect(_1548215), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1548215), c_fNot), _1548217)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548215), c_Orderings_Otop__class_Otop(tc_fun(_1548215, tc_HOL_Obool)))))]]], (15804 ^ _775828) ^ [_1042418, _1042420, _1042422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042418), _1042420)), 15807 ^ _775828 : [(15814 ^ _775828) ^ [] : [_1042420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042422), _1042418), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042420), _1042418) = _1042422)], (15808 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042420), _1042418) = _1042422, -(_1042420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042422), _1042418))]]], (31605 ^ _775828) ^ [_1357714, _1357716] : [-(c_Transitive__Closure_Ortrancl(_1357714, c_Transitive__Closure_Otrancl(_1357714, _1357716)) = c_Transitive__Closure_Ortrancl(_1357714, _1357716))], (30651 ^ _775828) ^ [_1336000, _1336002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1336000, _1336000)), _1336002)), 30654 ^ _775828 : [(30661 ^ _775828) ^ [] : [c_Wellfounded_Oacyclic(_1336000, _1336002), -(c_Wellfounded_Owf(_1336000, _1336002))], (30655 ^ _775828) ^ [] : [c_Wellfounded_Owf(_1336000, _1336002), -(c_Wellfounded_Oacyclic(_1336000, _1336002))]]], (28675 ^ _775828) ^ [_1291117, _1291119, _1291121, _1291123] : [hBOOL(hAPP(hAPP(c_member(_1291117), _1291123), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291117, tc_HOL_Obool)), _1291119), _1291121))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291117, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1291117, tc_fun(_1291117, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291117)), _1291119)), hAPP(hAPP(c_COMBC(_1291117, tc_fun(_1291117, tc_HOL_Obool), tc_HOL_Obool), c_member(_1291117)), _1291121)), _1291123)))], (25399 ^ _775828) ^ [_1223864, _1223866] : [hAPP(c_Code__Numeral_Onat__of, _1223864) = hAPP(c_Code__Numeral_Onat__of, _1223866), -(_1223864 = _1223866)], (15940 ^ _775828) ^ [_1045286, _1045288, _1045290, _1045292, _1045294, _1045296] : [class_Rings_Oordered__ring(_1045286), 15943 ^ _775828 : [(15950 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045286), _1045292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045286), _1045294), _1045288)), _1045290)), _1045296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045286), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), _1045288), _1045290)), _1045292)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), _1045294), _1045290)), _1045296))))], (15944 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045286), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), _1045288), _1045290)), _1045292)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), _1045294), _1045290)), _1045296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045286), _1045292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045286), _1045294), _1045288)), _1045290)), _1045296))))]]], (30641 ^ _775828) ^ [_1335857, _1335859] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1335857, _1335857)), _1335859)), c_Wellfounded_Oacyclic(_1335857, _1335859), -(c_Wellfounded_Owf(_1335857, _1335859))], (49740 ^ _775828) ^ [_1775752, _1775754, _1775756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1775752), _1775754)), _1775756)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1775754), c_List_Oupt(_1775752, _1775756)) = c_List_Oupt(_1775752, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1775752), _1775754)))], (51256 ^ _775828) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (19952 ^ _775828) ^ [_1118415] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118415) = 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(_1118415)))))], (32813 ^ _775828) ^ [_1382703, _1382705, _1382707, _1382709, _1382711, _1382713] : [hBOOL(hAPP(hAPP(c_member(_1382703), _1382705), _1382707)), -(hAPP(c_Set_Oimage(_1382703, _1382709, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1382703, _1382709), _1382711), _1382705), _1382713)), _1382707) = hAPP(hAPP(c_Set_Oinsert(_1382709), _1382713), hAPP(c_Set_Oimage(_1382703, _1382709, _1382711), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1382703, tc_HOL_Obool)), _1382707), hAPP(hAPP(c_Set_Oinsert(_1382703), _1382705), c_Orderings_Obot__class_Obot(tc_fun(_1382703, tc_HOL_Obool)))))))], (15374 ^ _775828) ^ [_1034203, _1034205] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034203), _1034205))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1034203, _1034205) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034203), _1034205), _1034205))], (31679 ^ _775828) ^ [_1359548, _1359550] : [-(c_Transitive__Closure_Otrancl(_1359548, _1359550) = hAPP(hAPP(c_Relation_Orel__comp(_1359548, _1359548, _1359548), _1359550), c_Transitive__Closure_Ortrancl(_1359548, _1359550)))], (40479 ^ _775828) ^ [_1552138, _1552140, _1552142, _1552144, _1552146] : [c_Fun_Oinj__on(_1552138, _1552140, _1552142, c_Orderings_Otop__class_Otop(tc_fun(_1552138, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1552138, _1552140, _1552142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1552138, tc_HOL_Obool)), _1552144), _1552146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1552140, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1552138, _1552140, _1552142), _1552144)), hAPP(c_Set_Oimage(_1552138, _1552140, _1552142), _1552146)))], (47944 ^ _775828) ^ [_1733916, _1733918, _1733920] : [-(hAPP(c_List_Oset(_1733916), hAPP(hAPP(c_List_Oappend(_1733916), _1733918), _1733920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1733916, tc_HOL_Obool)), hAPP(c_List_Oset(_1733916), _1733918)), hAPP(c_List_Oset(_1733916), _1733920)))], (48417 ^ _775828) ^ [_1746364, _1746366] : [-(hAPP(hAPP(c_List_Odrop(_1746364), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1746366) = _1746366)], (43980 ^ _775828) ^ [_1635847, _1635849, _1635851, _1635853, _1635855, _1635857] : [c_Finite__Set_Ofun__left__comm(_1635847, _1635849, _1635851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1635847), _1635853)), -(hAPP(hAPP(_1635851, _1635855), hAPP(hAPP(c_Finite__Set_Ofold(_1635847, _1635849, _1635851), _1635857), _1635853)) = hAPP(hAPP(c_Finite__Set_Ofold(_1635847, _1635849, _1635851), hAPP(hAPP(_1635851, _1635855), _1635857)), _1635853))], (40887 ^ _775828) ^ [_1562674, _1562676, _1562678, _1562680, _1562682] : [hAPP(c_Set_Oimage(_1562674, _1562676, _1562678), c_Orderings_Otop__class_Otop(tc_fun(_1562674, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1562676, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562674, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1562674, _1562676, _1562678), _1562680)), _1562682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562676, tc_HOL_Obool)), _1562680), hAPP(c_Set_Oimage(_1562674, _1562676, _1562678), _1562682))))], (25639 ^ _775828) ^ [_1229115, _1229117] : [class_Rings_Ocomm__semiring__1(_1229115), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229115), c_Groups_Oone__class_Oone(_1229115)), _1229117)))], (18559 ^ _775828) ^ [_1094924, _1094926] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094924), _1094926) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18564 ^ _775828 : [(18567 ^ _775828) ^ [] : [-(_1094926 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18565 ^ _775828) ^ [] : [-(_1094924 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18568 ^ _775828 : [(18571 ^ _775828) ^ [] : [-(_1094926 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18569 ^ _775828) ^ [] : [-(_1094924 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (21156 ^ _775828) ^ [_1142069, _1142071] : [class_Rings_Odivision__ring__inverse__zero(_1142069), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142069), _1142071), c_Groups_Ozero__class_Ozero(_1142069)) = c_Groups_Ozero__class_Ozero(_1142069))], (42760 ^ _775828) ^ [_1608298, _1608300, _1608302, _1608304, _1608306, _1608308, _1608310] : [-(hAPP(c_Fun_Ocomp(_1608298, _1608300, _1608302, _1608304), hAPP(c_Fun_Ocomp(_1608306, _1608298, _1608302, _1608308), _1608310)) = hAPP(c_Fun_Ocomp(_1608306, _1608300, _1608302, hAPP(c_Fun_Ocomp(_1608298, _1608300, _1608306, _1608304), _1608308)), _1608310))], (6047 ^ _775828) ^ [_871888, _871890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871888), _871890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871888), hAPP(c_Nat_OSuc, _871890))))], (50347 ^ _775828) ^ [_1787713, _1787715, _1787717, _1787719] : [_1787715 = hAPP(hAPP(c_List_Oappend(_1787713), hAPP(c_List_Orev(_1787713), _1787719)), hAPP(hAPP(c_List_Olist_OCons(_1787713), _1787717), c_List_Olist_ONil(_1787713))), -(hAPP(c_List_Orev(_1787713), _1787715) = hAPP(hAPP(c_List_Olist_OCons(_1787713), _1787717), _1787719))], (38204 ^ _775828) ^ [_1501058, _1501060, _1501062, _1501064] : [-(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), _1501058), _1501060)), 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), _1501062), _1501064)), 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), _1501058), _1501062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1501060), _1501064))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (47477 ^ _775828) ^ [_1722832, _1722834, _1722836, _1722838, _1722840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722832), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722834)), _1722836))), 47480 ^ _775828 : [(47487 ^ _775828) ^ [] : [-(_1722832 = _1722838), -(hAPP(hAPP(c_List_Onth(_1722834), hAPP(hAPP(c_List_Olist__update(_1722834, _1722836), _1722832), _1722840)), _1722838) = hAPP(hAPP(c_List_Onth(_1722834), _1722836), _1722838))], (47481 ^ _775828) ^ [] : [_1722832 = _1722838, -(hAPP(hAPP(c_List_Onth(_1722834), hAPP(hAPP(c_List_Olist__update(_1722834, _1722836), _1722832), _1722840)), _1722838) = _1722840)]]], (10064 ^ _775828) ^ [_938679, _938681] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938679), _938681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938681), _938679)))], (44920 ^ _775828) ^ [_1659533, _1659535, _1659537] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659533, tc_HOL_Obool)), _1659535), _1659537) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659533, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1659533, tc_HOL_Obool)), _1659535), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1659533, tc_HOL_Obool)), _1659537), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1659533, tc_HOL_Obool), tc_HOL_Obool))))))], (32775 ^ _775828) ^ [_1381862, _1381864, _1381866, _1381868] : [c_Sum__Type_OPlus(_1381862, _1381864, _1381866, _1381868) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1381862, _1381864), tc_HOL_Obool)), 32778 ^ _775828 : [(32781 ^ _775828) ^ [] : [-(_1381868 = c_Orderings_Obot__class_Obot(tc_fun(_1381864, tc_HOL_Obool)))], (32779 ^ _775828) ^ [] : [-(_1381866 = c_Orderings_Obot__class_Obot(tc_fun(_1381862, tc_HOL_Obool)))]]], (32335 ^ _775828) ^ [_1373206, _1373208, _1373210] : [class_Orderings_Olinorder(_1373206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373206), _1373208)), -(hBOOL(hAPP(hAPP(c_member(_1373206), _1373210), _1373208))), -(_1373208 = c_Orderings_Obot__class_Obot(tc_fun(_1373206, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1373206, hAPP(hAPP(c_Set_Oinsert(_1373206), _1373210), _1373208)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1373206), _1373210), c_Big__Operators_Olinorder__class_OMin(_1373206, _1373208)))], (40365 ^ _775828) ^ [_1549770] : [class_Lattices_Oboolean__algebra(_1549770), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1549770), c_Orderings_Obot__class_Obot(_1549770)) = c_Orderings_Otop__class_Otop(_1549770))], (7373 ^ _775828) ^ [_893393, _893395] : [class_Rings_Oring__1(_893393), -(hAPP(c_Int_Oring__1__class_Oof__int(_893393), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _893395)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_893393), _893395))], (51514 ^ _775828) ^ [_1808218, _1808220] : [-(hAPP(c_COMBI(_1808218), _1808220) = _1808220)], (50806 ^ _775828) ^ [_1798498, _1798500] : [c_List_Oremdups(_1798498, _1798500) = _1798500, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798498)), c_List_Oremdups(_1798498, _1798500)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798498)), _1798500))], (49819 ^ _775828) ^ [_1777074] : [class_Orderings_Olinorder(_1777074), -(c_List_Olinorder__class_Osorted(_1777074, c_List_Olist_ONil(_1777074)))], (44639 ^ _775828) ^ [_1653301, _1653303, _1653305, _1653307] : [-(hAPP(c_Set_Ovimage(_1653301, _1653303, _1653305), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1653303, tc_HOL_Obool), _1653307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1653303, tc_HOL_Obool), tc_fun(_1653301, tc_HOL_Obool)), _1653307), c_Set_Ovimage(_1653301, _1653303, _1653305)))], (3352 ^ _775828) ^ [_826557, _826559, _826561, _826563] : [-(c_Predicate_OPowp(_826563, _826559) = c_Predicate_OPowp(_826561, _826557)), _826563 = _826561, _826559 = _826557], (13660 ^ _775828) ^ [_1003066, _1003068, _1003070, _1003072, _1003074] : [c_Com_Ocom_OAss(_1003066, _1003068) = c_Com_Ocom_OCond(_1003070, _1003072, _1003074)], (6620 ^ _775828) ^ [_880988, _880990, _880992] : [class_Orderings_Olinorder(_880988), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880988), _880990), _880992))), 6627 ^ _775828 : [(6634 ^ _775828) ^ [] : [_880992 = _880990, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880988), _880992), _880990))], (6628 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880988), _880992), _880990))), -(_880992 = _880990)]]], (50241 ^ _775828) ^ [_1785366, _1785368] : [-(c_List_Oconcat(_1785366, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785366), tc_List_Olist(_1785366)), c_List_Olist_Olist__case(tc_List_Olist(_1785366), _1785366, c_List_Olist_ONil(_1785366), hAPP(hAPP(c_COMBB(tc_List_Olist(_1785366), tc_fun(tc_List_Olist(_1785366), tc_List_Olist(_1785366)), _1785366), c_COMBK(tc_List_Olist(_1785366), tc_List_Olist(_1785366))), hAPP(hAPP(c_COMBC(_1785366, tc_List_Olist(_1785366), tc_List_Olist(_1785366)), c_List_Olist_OCons(_1785366)), c_List_Olist_ONil(_1785366))))), _1785368)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785366), _1785366), c_List_Ohd(_1785366)), hAPP(c_List_Ofilter(tc_List_Olist(_1785366), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1785366)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1785366), tc_List_Olist(_1785366), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1785366)))), _1785368)))], (9667 ^ _775828) ^ [_931307, _931309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _931307)), 9670 ^ _775828 : [(9677 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _931309), _931307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _931309)), hAPP(c_Int_Onat, _931307))))], (9671 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _931309)), hAPP(c_Int_Onat, _931307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _931309), _931307)))]]], (44303 ^ _775828) ^ [_1644487, _1644489, _1644491, _1644493, _1644495] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644487, tc_HOL_Obool)), _1644489), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644491, tc_fun(_1644487, tc_HOL_Obool)), _1644493), _1644495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644491, tc_fun(_1644487, tc_HOL_Obool)), _1644493), hAPP(hAPP(c_COMBB(tc_fun(_1644487, tc_HOL_Obool), tc_fun(_1644487, tc_HOL_Obool), _1644491), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1644487, tc_HOL_Obool)), _1644489)), _1644495)))], (2162 ^ _775828) ^ [_807402, _807404] : [_807404 = _807402, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_807404) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_807402))], (17841 ^ _775828) ^ [_1081348, _1081350] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1081348), c_Groups_Ozero__class_Ozero(_1081348)), hAPP(c_Nat_OSuc, _1081350)) = c_Groups_Ozero__class_Ozero(_1081348)), class_Power_Opower(_1081348), class_Rings_Osemiring__0(_1081348)], (45836 ^ _775828) ^ [_1680676, _1680678, _1680680, _1680682] : [hBOOL(hAPP(c_List_Odistinct(_1680676), hAPP(hAPP(c_List_Omap(_1680678, _1680676), _1680680), _1680682))), 45839 ^ _775828 : [(45842 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1680678, _1680676, _1680680, hAPP(c_List_Oset(_1680678), _1680682)))], (45840 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680678), _1680682)))]]], (1620 ^ _775828) ^ [_798696, _798698] : [-(class_Orderings_Olinorder(_798696)), _798698 = _798696, class_Orderings_Olinorder(_798698)], (918 ^ _775828) ^ [_789859, _789861] : [-(c_List_Onat__list(_789859)), _789861 = _789859, c_List_Onat__list(_789861)], (3808 ^ _775828) ^ [_833725, _833727, _833729, _833731] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_833731, _833727) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_833729, _833725)), _833731 = _833729, _833727 = _833725], (48471 ^ _775828) ^ [_1747666, _1747668, _1747670, _1747672] : [-(hAPP(hAPP(c_List_Oappend(_1747666), _1747668), _1747670) = _1747672), _1747668 = hAPP(hAPP(c_List_Otake(_1747666), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747666)), _1747668)), _1747672), _1747670 = hAPP(hAPP(c_List_Odrop(_1747666), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747666)), _1747668)), _1747672)], (28405 ^ _775828) ^ [_1285884, _1285886] : [class_Lattices_Olattice(_1285884), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285884), _1285886), _1285886) = _1285886)], (30896 ^ _775828) ^ [_1340978, _1340980, _1340982] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340978), _1340980)), hBOOL(hAPP(hAPP(c_member(_1340978), _1340982), _1340980)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1340978), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340978, tc_HOL_Obool)), _1340980), hAPP(hAPP(c_Set_Oinsert(_1340978), _1340982), c_Orderings_Obot__class_Obot(tc_fun(_1340978, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1340978), _1340980))], (7463 ^ _775828) ^ [_894958, _894960, _894962] : [class_Groups_Ogroup__add(_894958), 7466 ^ _775828 : [(7473 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_894958), _894962) = _894960, -(hAPP(c_Groups_Ouminus__class_Ouminus(_894958), _894960) = _894962)], (7467 ^ _775828) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_894958), _894960) = _894962, -(hAPP(c_Groups_Ouminus__class_Ouminus(_894958), _894962) = _894960)]]], (14676 ^ _775828) ^ [_1021384, _1021386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021384)), 14679 ^ _775828 : [(14688 ^ _775828) ^ [] : [-(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), _1021384), _1021386)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021386), _1021384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021386))], (14680 ^ _775828) ^ [] : [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), _1021384), _1021386))), 14683 ^ _775828 : [(14686 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021386)))], (14684 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021386), _1021384)))]]]]], (12183 ^ _775828) ^ [_976563, _976565] : [12184 ^ _775828 : [(12187 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976565))], (12185 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976563))]], 12188 ^ _775828 : [(12195 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _976563), _976565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _976563)), hAPP(c_Int_Onat, _976565))))], (12189 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _976563)), hAPP(c_Int_Onat, _976565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _976563), _976565)))]]], (50864 ^ _775828) ^ [_1799892, _1799894, _1799896] : [hBOOL(hAPP(c_List_Odistinct(_1799892), _1799894)), -(hBOOL(hAPP(c_List_Odistinct(_1799892), c_List_OdropWhile(_1799892, _1799896, _1799894))))], (2238 ^ _775828) ^ [_808554, _808556, _808558, _808560] : [-(c_Nitpick_Onumber__of__frac(_808560, _808556) = c_Nitpick_Onumber__of__frac(_808558, _808554)), _808560 = _808558, _808556 = _808554], (3734 ^ _775828) ^ [_832562, _832564, _832566, _832568, _832570, _832572] : [-(c_Set_Ovimage(_832572, _832568, _832564) = c_Set_Ovimage(_832570, _832566, _832562)), _832572 = _832570, _832568 = _832566, _832564 = _832562], (2472 ^ _775828) ^ [_812225, _812227] : [_812227 = _812225, -(c_DSequence_Ounion(_812227) = c_DSequence_Ounion(_812225))], (27787 ^ _775828) ^ [_1270806, _1270808, _1270810] : [-(hAPP(c_Set_Oimage(tc_prod(_1270806, _1270808), _1270806, c_Product__Type_Ofst(_1270806, _1270808)), _1270810) = hAPP(c_Relation_ODomain(_1270806, _1270808), _1270810))], (14990 ^ _775828) ^ [_1027183, _1027185] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027183))), -(c_SMT_Oz3div(_1027185, _1027183) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027185), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1027183))))], (5210 ^ _775828) ^ [_855500, _855502, _855504, _855506] : [-(c_List_Oconcat(_855506, _855502) = c_List_Oconcat(_855504, _855500)), _855506 = _855504, _855502 = _855500], (1360 ^ _775828) ^ [_795446, _795448] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_795446)), _795448 = _795446, class_Groups_Oordered__cancel__ab__semigroup__add(_795448)], (39750 ^ _775828) ^ [_1536792, _1536794, _1536796, _1536798, _1536800] : [_1536792 = c_Orderings_Obot__class_Obot(tc_fun(_1536794, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536794, tc_fun(_1536796, tc_HOL_Obool)), _1536792), hAPP(hAPP(c_COMBB(tc_fun(_1536796, tc_HOL_Obool), tc_fun(_1536796, tc_HOL_Obool), _1536794), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536796, tc_HOL_Obool)), _1536798)), _1536800)) = c_Orderings_Obot__class_Obot(tc_fun(_1536796, tc_HOL_Obool)))], (35003 ^ _775828) ^ [_1430142, _1430144] : [class_Lattices_Olattice(_1430142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430142), _1430144)), -(_1430144 = c_Orderings_Obot__class_Obot(tc_fun(_1430142, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1430142), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1430142), 35016 ^ [_1430142, _1430144]), 35017 ^ [_1430142, _1430144])), hAPP(hAPP(c_Set_Oinsert(_1430142), 35016 ^ [_1430142, _1430144]), hAPP(hAPP(c_Set_Oinsert(_1430142), 35017 ^ [_1430142, _1430144]), c_Orderings_Obot__class_Obot(tc_fun(_1430142, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1430142), c_Big__Operators_Olattice__class_OInf__fin(_1430142, _1430144)), _1430144)))], (21630 ^ _775828) ^ [_1150284, _1150286] : [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(_1150286))), 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), _1150284)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150284)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150286))))], (50393 ^ _775828) ^ [_1788814, _1788816, _1788818] : [hAPP(c_List_Orev(_1788814), _1788816) = hAPP(c_List_Orev(_1788814), _1788818), -(_1788816 = _1788818)], (48813 ^ _775828) ^ [_1755090, _1755092] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1755090), _1755092) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48816 ^ _775828 : [(48819 ^ _775828) ^ [_1755204] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1755204), hAPP(c_List_Oset(tc_Nat_Onat), _1755092))), -(_1755204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48817 ^ _775828) ^ [] : [-(_1755090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25567 ^ _775828) ^ [_1227879, _1227881] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227879), _1227881)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227881), _1227879))))], (24457 ^ _775828) ^ [_1205300, _1205302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1205302, _1205300) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205302), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205300)))], (50369 ^ _775828) ^ [_1788318, _1788320, _1788322] : [-(c_List_Oconcat(_1788318, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1788318)), _1788320), _1788322)) = hAPP(hAPP(c_List_Oappend(_1788318), c_List_Oconcat(_1788318, _1788320)), c_List_Oconcat(_1788318, _1788322)))], (49927 ^ _775828) ^ [_1778694, _1778696] : [class_Orderings_Olinorder(_1778694), c_List_Olinorder__class_Osorted(_1778694, _1778696), -(c_List_Olinorder__class_Osorted(_1778694, hAPP(c_List_Otl(_1778694), _1778696)))], (38702 ^ _775828) ^ [_1512270, _1512272, _1512274, _1512276, _1512278] : [c_Equiv__Relations_Oequiv(_1512270, _1512272, _1512274), hBOOL(hAPP(hAPP(c_member(tc_fun(_1512270, tc_HOL_Obool)), _1512276), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512270), _1512272), _1512274))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1512270, tc_HOL_Obool)), _1512278), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1512270), _1512272), _1512274))), -(_1512276 = _1512278), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512270, tc_HOL_Obool)), _1512276), _1512278) = c_Orderings_Obot__class_Obot(tc_fun(_1512270, tc_HOL_Obool)))], (41270 ^ _775828) ^ [_1572601, _1572603, _1572605, _1572607] : [_1572601 = c_Finite__Set_Ofold1(_1572603, _1572605), -(hAPP(_1572601, hAPP(hAPP(c_Set_Oinsert(_1572603), _1572607), c_Orderings_Obot__class_Obot(tc_fun(_1572603, tc_HOL_Obool)))) = _1572607)], (36245 ^ _775828) ^ [_1456452] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1456452), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23632 ^ _775828) ^ [] : [-(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))], (19612 ^ _775828) ^ [_1112835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1112835)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112835), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39108 ^ _775828) ^ [_1520396, _1520398, _1520400, _1520402, _1520404] : [c_Fun_Oinj__on(_1520396, _1520398, _1520400, hAPP(hAPP(c_Set_Oinsert(_1520396), _1520402), _1520404)), 39111 ^ _775828 : [(39114 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1520398), hAPP(_1520400, _1520402)), hAPP(c_Set_Oimage(_1520396, _1520398, _1520400), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520396, tc_HOL_Obool)), _1520404), hAPP(hAPP(c_Set_Oinsert(_1520396), _1520402), c_Orderings_Obot__class_Obot(tc_fun(_1520396, tc_HOL_Obool)))))))], (39112 ^ _775828) ^ [] : [-(c_Fun_Oinj__on(_1520396, _1520398, _1520400, _1520404))]]], (28251 ^ _775828) ^ [_1282396, _1282398, _1282400] : [class_Lattices_Olattice(_1282396), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282396), _1282398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282396), _1282398), _1282400)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282396), _1282398), _1282400))], (4202 ^ _775828) ^ [_840032, _840034, _840036, _840038] : [-(c_Transitive__Closure_Ortrancl(_840038, _840034) = c_Transitive__Closure_Ortrancl(_840036, _840032)), _840038 = _840036, _840034 = _840032], (46057 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hAPP(hAPP(c_Power_Opower__class_Opower(_1242227), _1242229), _1242233)), hAPP(hAPP(c_Power_Opower__class_Opower(_1242227), _1242231), _1242235))))], (20084 ^ _775828) ^ [_1120841] : [_1120841 = c_Int_OPls, -(c_Int_OBit0(_1120841) = c_Int_OPls)], (28239 ^ _775828) ^ [_1282162, _1282164, _1282166] : [class_Lattices_Osemilattice__sup(_1282162), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282162), _1282164), _1282166) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282162), _1282166), _1282164))], (26677 ^ _775828) ^ [_1247351, _1247353, _1247355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247351)), 26680 ^ _775828 : [(26687 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247353), _1247355)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247351), _1247353)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247351), _1247355))))], (26681 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247351), _1247353)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247351), _1247355))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247353), _1247355)))]]], (10224 ^ _775828) ^ [_941435, _941437, _941439, _941441] : [class_Groups_Oab__semigroup__add(_941435), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941435), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941435), _941437), _941439)), _941441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941435), _941437), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941435), _941439), _941441)))], (11721 ^ _775828) ^ [_968447, _968449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968447), _968449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968447), hAPP(c_Nat_OSuc, _968449))))], (10858 ^ _775828) ^ [_953449, _953451, _953453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953449), _953451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953449), _953453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953451), _953453))))], (28763 ^ _775828) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (30371 ^ _775828) ^ [_1330738, _1330740, _1330742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330738), _1330740)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330738), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330738, tc_HOL_Obool)), _1330740), _1330742))))], (49088 ^ _775828) ^ [_1761629, _1761631, _1761633] : [_1761629 = c_List_Olist_ONil(_1761631), -(c_List_Olast(_1761631, hAPP(hAPP(c_List_Olist_OCons(_1761631), _1761633), _1761629)) = _1761633)], (49027 ^ _775828) ^ [_1760130] : [-(c_List_Olists(_1760130, c_Orderings_Obot__class_Obot(tc_fun(_1760130, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1760130)), c_List_Olist_ONil(_1760130)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1760130), tc_HOL_Obool))))], (3626 ^ _775828) ^ [_830958, _830960, _830962, _830964] : [-(c_New__DSequence_Opos__single(_830964, _830960) = c_New__DSequence_Opos__single(_830962, _830958)), _830964 = _830962, _830960 = _830958], (46516 ^ _775828) ^ [_1698977, _1698979, _1698981, _1698983] : [-(_1698977 = _1698979), -(c_List_Oremove1(_1698981, _1698977, hAPP(hAPP(c_List_Olist_OCons(_1698981), _1698979), _1698983)) = hAPP(hAPP(c_List_Olist_OCons(_1698981), _1698979), c_List_Oremove1(_1698981, _1698977, _1698983)))], (25473 ^ _775828) ^ [_1225270, _1225272, _1225274, _1225276, _1225278] : [_1225270 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1225272, _1225274, _1225276, _1225278), _1225270) = c_Lazy__Sequence_Ohit__bound(_1225274))], (11336 ^ _775828) ^ [_961922, _961924, _961926, _961928, _961930] : [class_Groups_Oordered__cancel__ab__semigroup__add(_961922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961922), _961924), _961926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961922), _961928), _961930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961922), _961924), _961928)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961922), _961926), _961930))))], (45657 ^ _775828) ^ [_1676337, _1676339, _1676341, _1676343, _1676345] : [hAPP(hAPP(c_List_Omap(_1676337, _1676339), _1676341), _1676343) = hAPP(hAPP(c_List_Omap(_1676337, _1676339), _1676345), _1676343), 45660 ^ _775828 : [(45661 ^ _775828) ^ [_1676460] : [hBOOL(hAPP(hAPP(c_member(_1676337), _1676460), hAPP(c_List_Oset(_1676337), _1676343))), -(hAPP(_1676341, _1676460) = hAPP(_1676345, _1676460))]]], (35308 ^ _775828) ^ [_1437943, _1437945, _1437947, _1437949, _1437951, _1437953, _1437955] : [c_Big__Operators_Ocomm__monoid__big(_1437943, _1437945, _1437947, _1437949, _1437951), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1437945), _1437953))), -(hAPP(hAPP(_1437951, _1437955), _1437953) = _1437949)], (50694 ^ _775828) ^ [_1796409, _1796411, _1796413, _1796415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796411)), c_List_OtakeWhile(_1796411, _1796413, _1796415)))), -(hAPP(hAPP(c_List_Onth(_1796411), c_List_OtakeWhile(_1796411, _1796413, _1796415)), _1796409) = hAPP(hAPP(c_List_Onth(_1796411), _1796415), _1796409))], (40263 ^ _775828) ^ [_1547621, _1547623] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547621, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547621, tc_HOL_Obool)), _1547623)), _1547623) = c_Orderings_Otop__class_Otop(tc_fun(_1547621, tc_HOL_Obool)))], (50249 ^ _775828) ^ [_1785650] : [-(hAPP(c_List_Orev(_1785650), c_List_Olist_ONil(_1785650)) = c_List_Olist_ONil(_1785650))], (2356 ^ _775828) ^ [_810345, _810347, _810349, _810351, _810353, _810355] : [-(c_Random_Ominus__shift(_810355, _810351, _810347) = c_Random_Ominus__shift(_810353, _810349, _810345)), _810355 = _810353, _810351 = _810349, _810347 = _810345], (30049 ^ _775828) ^ [_1323492, _1323494] : [30050 ^ _775828 : [(30053 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323494), _1323492))], (30051 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1323492), _1323494)))]], -(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), 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408027), _1408029), _1408031)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408027), _1408029), _1408031) = _1408029)]]], (40875 ^ _775828) ^ [_1562389, _1562391, _1562393, _1562395, _1562397] : [-(hAPP(c_Set_Ovimage(_1562389, _1562391, _1562393), hAPP(hAPP(c_Set_Oinsert(_1562391), _1562395), _1562397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562389, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1562389, _1562391, _1562393), hAPP(hAPP(c_Set_Oinsert(_1562391), _1562395), c_Orderings_Obot__class_Obot(tc_fun(_1562391, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1562389, _1562391, _1562393), _1562397)))], (20504 ^ _775828) ^ [_1128193] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128193), _1128193)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1128193)], (7741 ^ _775828) ^ [_899399, _899401, _899403] : 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[_1525404, _1525406, _1525408, _1525410] : [-(hAPP(c_Relation_OImage(_1525404, _1525406, _1525408), _1525410) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1525404, tc_fun(_1525406, tc_HOL_Obool)), _1525410), hAPP(hAPP(c_COMBB(tc_fun(_1525404, tc_HOL_Obool), tc_fun(_1525406, tc_HOL_Obool), _1525404), c_Relation_OImage(_1525404, _1525406, _1525408)), hAPP(hAPP(c_COMBC(_1525404, tc_fun(_1525404, tc_HOL_Obool), tc_fun(_1525404, tc_HOL_Obool)), c_Set_Oinsert(_1525404)), c_Orderings_Obot__class_Obot(tc_fun(_1525404, tc_HOL_Obool))))))], (6536 ^ _775828) ^ [_879775, _879777, _879779] : [class_Orderings_Oorder(_879775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879775), _879777), _879779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879775), _879779), _879777))], (18843 ^ _775828) ^ [_1099824, _1099826, _1099828, _1099830, _1099832] : [hBOOL(hAPP(hAPP(_1099824, _1099826), _1099828)), -(hBOOL(hAPP(hAPP(_1099824, hAPP(c_Product__Type_Osnd(_1099830, _1099832), hAPP(hAPP(c_Product__Type_OPair(_1099830, _1099832), _1099828), _1099826))), hAPP(c_Product__Type_Ofst(_1099830, _1099832), hAPP(hAPP(c_Product__Type_OPair(_1099830, _1099832), _1099828), _1099826)))))], (19630 ^ _775828) ^ [_1113126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1113126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1113126))))], (33779 ^ _775828) ^ [_1403304, _1403306, _1403308] : [class_Lattices_Osemilattice__inf(_1403304), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403304), _1403306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403304), _1403306), _1403308)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403304), _1403306), _1403308))], (8771 ^ _775828) ^ [_916354, _916356, _916358] : [class_Orderings_Oorder(_916354), -(_916356 = _916358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916354), _916358), _916356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916354), _916358), _916356)))], (34285 ^ _775828) ^ [_1414270, _1414272, _1414274] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414270, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414270, tc_HOL_Obool)), _1414272), _1414274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414270, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414270, tc_HOL_Obool)), _1414272)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414270, tc_HOL_Obool)), _1414274)))], (11166 ^ _775828) ^ [_958811, _958813, _958815, _958817, _958819, _958821] : [class_Rings_Olinordered__semiring__1(_958811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958811), _958813), _958815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958811), _958817), _958815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958811), c_Groups_Ozero__class_Ozero(_958811)), _958819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958811), c_Groups_Ozero__class_Ozero(_958811)), _958821)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958811), _958819), _958821) = c_Groups_Oone__class_Oone(_958811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958811), _958819), _958813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958811), _958821), _958817))), _958815)))], (46460 ^ _775828) ^ [_1697848, _1697850, _1697852] : [hAPP(hAPP(c_List_Olist_OCons(_1697848), _1697850), _1697852) = _1697852], (2432 ^ _775828) ^ [_811535, _811537, _811539, _811541, _811543, _811545, _811547, _811549, _811551, _811553] : [-(c_Nitpick_Opair__box_Opair__box__size(_811553, _811549, _811545, _811541, _811537) = c_Nitpick_Opair__box_Opair__box__size(_811551, _811547, _811543, _811539, _811535)), _811553 = _811551, _811549 = _811547, _811545 = _811543, _811541 = _811539, _811537 = _811535], (19544 ^ _775828) ^ [_1111720, _1111722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111720)), c_Int_OBit1(_1111722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111720), _1111722)))], (6274 ^ _775828) ^ [_875773, _875775, _875777] : [class_Orderings_Olinorder(_875773), 6277 ^ _775828 : [(6278 ^ _775828) ^ [] : [-(_875775 = _875777), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875773), _875775), _875777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875773), _875777), _875775)))], (6288 ^ _775828) ^ [] : [6289 ^ _775828 : [(6292 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875773), _875777), _875775))], (6290 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875773), _875775), _875777))]], _875775 = _875777]]], (25257 ^ _775828) ^ [_1221308, _1221310] : [-(c_HOL_OThe(_1221308, hAPP(c_fequal, _1221310)) = _1221310)], (28874 ^ _775828) ^ [_1296465, _1296467, _1296469, _1296471] : [-(c_Hilbert__Choice_OEps(tc_prod(_1296465, _1296467), hAPP(c_Product__Type_Oprod_Oprod__case(_1296465, _1296467, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1296465, tc_fun(_1296467, tc_HOL_Obool), tc_fun(_1296467, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1296467, tc_HOL_Obool), tc_fun(_1296467, tc_HOL_Obool)), _1296465), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1296467)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1296465), c_fconj), hAPP(c_fequal, _1296469)))), hAPP(c_fequal, _1296471)))) = hAPP(hAPP(c_Product__Type_OPair(_1296465, _1296467), _1296469), _1296471))], (41478 ^ _775828) ^ [_1578469, _1578471, _1578473, _1578475] : [-(_1578469 = c_Orderings_Obot__class_Obot(tc_fun(_1578471, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1578473, _1578471), _1578473, c_Product__Type_Ofst(_1578473, _1578471)), hAPP(hAPP(c_Product__Type_OSigma(_1578473, _1578471), _1578475), hAPP(c_COMBK(tc_fun(_1578471, tc_HOL_Obool), _1578473), _1578469))) = _1578475)], (50321 ^ _775828) ^ [_1787087, _1787089, _1787091] : [_1787089 = hAPP(hAPP(c_List_Olist_OCons(_1787087), _1787091), c_List_Olist_ONil(_1787087)), -(hAPP(c_List_Orev(_1787087), _1787089) = hAPP(hAPP(c_List_Olist_OCons(_1787087), _1787091), c_List_Olist_ONil(_1787087)))], (50900 ^ _775828) ^ [_1800480, _1800482, _1800484] : [c_List_OdropWhile(_1800480, _1800482, _1800484) = c_List_Olist_ONil(_1800480), 50903 ^ _775828 : [(50904 ^ _775828) ^ [_1800571] : [hBOOL(hAPP(hAPP(c_member(_1800480), _1800571), hAPP(c_List_Oset(_1800480), _1800484))), -(hBOOL(hAPP(_1800482, _1800571)))]]], (48319 ^ _775828) ^ [_1743806, _1743808, _1743810, _1743812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743806), tc_List_Olist(_1743806))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743806), tc_List_Olist(_1743806)), _1743808), _1743810)), c_List_Olistrel1(_1743806, _1743812))), 48324 ^ _775828 : [(48329 ^ _775828) ^ [] : [-(_1743810 = hAPP(hAPP(c_List_Olist__update(_1743806, _1743808), 48323 ^ [_1743806, _1743808, _1743810, _1743812]), 48322 ^ [_1743806, _1743808, _1743810, _1743812]))], (48327 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48323 ^ [_1743806, _1743808, _1743810, _1743812]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743806)), _1743808))))], (48325 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743806, _1743806)), hAPP(hAPP(c_Product__Type_OPair(_1743806, _1743806), hAPP(hAPP(c_List_Onth(_1743806), _1743808), 48323 ^ [_1743806, _1743808, _1743810, _1743812])), 48322 ^ [_1743806, _1743808, _1743810, _1743812])), _1743812)))]]], (46957 ^ _775828) ^ [_1710612, _1710614, _1710616] : [_1710612 = _1710614, 46960 ^ _775828 : [(46963 ^ _775828) ^ [_1710760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710616)), _1710612))), -(hAPP(hAPP(c_List_Onth(_1710616), _1710612), _1710760) = hAPP(hAPP(c_List_Onth(_1710616), _1710614), _1710760))], (46961 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710616)), _1710612) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710616)), _1710614))]]], (19722 ^ _775828) ^ [_1114622, _1114624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114622), _1114624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1114622)), _1114624)))], (41414 ^ _775828) ^ [_1576882, _1576884, _1576886, _1576888] : [c_Finite__Set_Ofolding__one(_1576882, _1576884, _1576886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576882), _1576888)), -(hAPP(_1576886, _1576888) = hAPP(c_Finite__Set_Ofold1(_1576882, _1576884), _1576888))], (50509 ^ _775828) ^ [_1792045, _1792047, _1792049, _1792051] : [class_Orderings_Olinorder(_1792045), c_List_Olinorder__class_Osorted(_1792045, hAPP(c_List_Orev(_1792045), _1792047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1792049), _1792051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1792051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792045)), _1792047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792045), hAPP(hAPP(c_List_Onth(_1792045), _1792047), _1792051)), hAPP(hAPP(c_List_Onth(_1792045), _1792047), _1792049))))], (40592 ^ _775828) ^ [_1556235, _1556237, _1556239, _1556241, _1556243] : [c_Equiv__Relations_Oequivp(_1556235, _1556237), hBOOL(hAPP(hAPP(_1556237, _1556239), _1556241)), hBOOL(hAPP(hAPP(_1556237, _1556241), _1556243)), -(hBOOL(hAPP(hAPP(_1556237, _1556239), _1556243)))], (8299 ^ _775828) ^ [_909142, _909144, _909146, _909148] : [class_Orderings_Oorder(_909142), _909144 = _909146, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909142), _909148), _909146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909142), _909148), _909144)))], (9207 ^ _775828) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41040 ^ _775828) ^ [_1566659, _1566661, _1566663, _1566665, _1566667] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566659, _1566659)), hAPP(hAPP(c_Product__Type_OPair(_1566659, _1566659), _1566661), _1566663)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566659, _1566659), tc_HOL_Obool), _1566665), _1566667))), 41045 ^ _775828 : [(41048 ^ _775828) ^ [] : [-(_1566661 = _1566663)], (41046 ^ _775828) ^ [] : [-(_1566665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41051 ^ _775828 : [(41056 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566659, _1566659)), hAPP(hAPP(c_Product__Type_OPair(_1566659, _1566659), 41049 ^ [_1566659, _1566661, _1566663, _1566665, _1566667]), _1566663)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1566659, _1566659), tc_HOL_Obool), 41050 ^ [_1566659, _1566661, _1566663, _1566665, _1566667]), _1566667))))], (41054 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566659, _1566659)), hAPP(hAPP(c_Product__Type_OPair(_1566659, _1566659), _1566661), 41049 ^ [_1566659, _1566661, _1566663, _1566665, _1566667])), _1566667)))], (41052 ^ _775828) ^ [] : [-(_1566665 = hAPP(c_Nat_OSuc, 41050 ^ [_1566659, _1566661, _1566663, _1566665, _1566667]))]]], (51062 ^ _775828) ^ [_1803773, _1803775] : [class_Orderings_Opreorder(_1803773), -(class_Orderings_Opreorder(tc_fun(_1803775, _1803773)))], (9869 ^ _775828) ^ [_935135, _935137, _935139, _935141] : [class_Rings_Olinordered__ring__strict(_935135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935135), _935137), c_Groups_Ozero__class_Ozero(_935135))), 9876 ^ _775828 : [(9883 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935135), _935141), _935139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935135), _935137), _935139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935135), _935137), _935141))))], (9877 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935135), _935137), _935139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935135), _935137), _935141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935135), _935141), _935139)))]]], (9987 ^ _775828) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9657 ^ _775828) ^ [_931140, _931142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _931140)), hAPP(c_Int_Onat, _931142)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _931142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _931140), _931142))], (13074 ^ _775828) ^ [_991974, _991976, _991978, _991980, _991982, _991984] : [hBOOL(hAPP(_991974, _991976)), c_Natural_Oevaln(_991978, _991976, _991980, _991982), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_991974, _991978, _991984), _991976, _991980, _991982))], (34319 ^ _775828) ^ [_1415141, _1415143, _1415145] : [class_Lattices_Olattice(_1415141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415141), _1415143)), hBOOL(hAPP(hAPP(c_member(_1415141), _1415145), _1415143)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415141), _1415145), c_Big__Operators_Olattice__class_OInf__fin(_1415141, _1415143)) = c_Big__Operators_Olattice__class_OInf__fin(_1415141, _1415143))], (1490 ^ _775828) ^ [_797071, _797073] : [-(class_Groups_Oab__semigroup__mult(_797071)), _797073 = _797071, class_Groups_Oab__semigroup__mult(_797073)], (44856 ^ _775828) ^ [_1658299] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1658299, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1658299, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1658299, tc_HOL_Obool)))], (18986 ^ _775828) ^ [_1102597, _1102599, _1102601, _1102603] : [-(hAPP(c_Product__Type_Ofst(_1102597, _1102599), hAPP(hAPP(c_Product__Type_OPair(_1102597, _1102599), _1102601), _1102603)) = _1102601)], (20100 ^ _775828) ^ [_1121119, _1121121] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1121119)), c_Int_OBit0(_1121121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121119), _1121121)))], (12367 ^ _775828) ^ [_979835] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _979835), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _979835)], (10972 ^ _775828) ^ [_955400, _955402] : [10973 ^ _775828 : [(10976 ^ _775828) ^ [] : [_955400 = _955402], (10974 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955400), _955402))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955400), _955402)))], (25036 ^ _775828) ^ [_1217270, _1217272, _1217274, _1217276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1217270), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1217272, _1217274, _1217270, _1217276) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1217272, 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(_1217272)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1217274, _1217276)), 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(_1217272)))), 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(_1217272)))), 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(_1217272)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1217272, 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(_1217272)))), 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(_1217272)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1217272, _1217274, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1217270), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1217276))), 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(_1217272)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272)))), 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(_1217272)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1217272, 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(_1217272)))), 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(_1217272)))), 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(_1217272))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272)))), 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(_1217272)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272))))), tc_prod(_1217272, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1217272)), hAPP(hAPP(c_COMBB(_1217272, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1217272)))), tc_prod(_1217272, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1217272)), c_Product__Type_Ofst(_1217272, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (5813 ^ _775828) ^ [_868475] : [-(_868475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_868475 = hAPP(c_Nat_OSuc, 5816 ^ [_868475]))], (18501 ^ _775828) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47349 ^ _775828) ^ [_1720375, _1720377, _1720379, _1720381, _1720383] : [-(hAPP(hAPP(c_List_Olist__update(_1720375, hAPP(hAPP(c_List_Olist_OCons(_1720375), _1720377), _1720379)), _1720381), _1720383) = c_Nat_Onat_Onat__case(tc_List_Olist(_1720375), hAPP(hAPP(c_List_Olist_OCons(_1720375), _1720383), _1720379), hAPP(hAPP(c_COMBB(tc_List_Olist(_1720375), tc_List_Olist(_1720375), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1720375), _1720377)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1720375, tc_List_Olist(_1720375)), c_List_Olist__update(_1720375, _1720379)), _1720383)), _1720381))], (16649 ^ _775828) ^ [_1059263] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059263)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059263))], (32717 ^ _775828) ^ [_1380784, _1380786, _1380788, _1380790] : [32718 ^ _775828 : [(32721 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380788), _1380790)))], (32719 ^ _775828) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380784), _1380786)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1380784, _1380788)), c_Sum__Type_OPlus(_1380784, _1380788, _1380786, _1380790)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18849 ^ _775828) ^ [_1099987, _1099989, _1099991, _1099993, _1099995, _1099997] : [hBOOL(hAPP(_1099987, _1099989)), hBOOL(hAPP(_1099991, _1099993)), 18856 ^ _775828 : [(18859 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1099991, hAPP(c_Product__Type_Osnd(_1099995, _1099997), hAPP(hAPP(c_Product__Type_OPair(_1099995, _1099997), _1099989), _1099993)))))], (18857 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1099987, hAPP(c_Product__Type_Ofst(_1099995, _1099997), hAPP(hAPP(c_Product__Type_OPair(_1099995, _1099997), _1099989), _1099993)))))]]], (17125 ^ _775828) ^ [_1068463, _1068465] : [class_Int_Onumber__ring(_1068463), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1068463), hAPP(c_Int_Onumber__class_Onumber__of(_1068463), _1068465)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068463), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068465)))], (7425 ^ _775828) ^ [_894365, _894367] : [c_Option_Ois__none(_894365, _894367), -(_894367 = c_Option_Ooption_ONone(_894365))], (23822 ^ _775828) ^ [_1192994, _1192996, _1192998] : [class_Orderings_Olinorder(_1192994), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192994), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192994), _1192996), _1192998)), _1192998)))], (20198 ^ _775828) ^ [_1122817, _1122819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122817), _1122819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1122817)), c_Int_OBit0(_1122819))))], (23782 ^ _775828) ^ [_1192315, _1192317, _1192319, _1192321] : [class_Orderings_Olinorder(_1192315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192315), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192315), _1192317), _1192319)), _1192321)), 23789 ^ _775828 : [(23792 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192315), _1192319), _1192321)))], (23790 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192315), _1192317), _1192321)))]]], (33140 ^ _775828) ^ [_1389223, _1389225, _1389227, _1389229, _1389231] : [class_Groups_Ocomm__monoid__mult(_1389223), class_Rings_Odvd(_1389223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389225), _1389227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1389225, tc_HOL_Obool)), _1389229), _1389227)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1389223), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389225, _1389223), _1389231), _1389229)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389225, _1389223), _1389231), _1389227))))], (1010 ^ _775828) ^ [_791071, _791073] : [-(class_Rings_Olinordered__ring__strict(_791071)), _791073 = _791071, class_Rings_Olinordered__ring__strict(_791073)], (44667 ^ _775828) ^ [_1654238, _1654240, _1654242] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654238, tc_HOL_Obool)), _1654240), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1654238, tc_HOL_Obool), _1654242)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1654238, tc_HOL_Obool), tc_fun(_1654238, tc_HOL_Obool)), _1654242), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654238, tc_HOL_Obool)), _1654240)))], (20382 ^ _775828) ^ [_1126068, _1126070] : [class_Int_Onumber__ring(_1126068), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126068), c_Groups_Oone__class_Oone(_1126068)), c_Groups_Oone__class_Oone(_1126068))), hAPP(c_Int_Onumber__class_Onumber__of(_1126068), _1126070)) = hAPP(c_Int_Onumber__class_Onumber__of(_1126068), c_Int_OBit0(_1126070)))], (33905 ^ _775828) ^ [_1406081, _1406083, _1406085, _1406087] : [class_Lattices_Odistrib__lattice(_1406081), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1406081), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1406081), _1406083), _1406085)), _1406087) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1406081), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1406081), _1406083), _1406087)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1406081), _1406085), _1406087)))], (10366 ^ _775828) ^ [_944337, _944339, _944341, _944343] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_944337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944337), _944339), _944341)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944337), _944339), _944343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944337), _944341), _944343)))], (19490 ^ _775828) ^ [_1110751, _1110753] : [class_Int_Onumber__ring(_1110751), 19493 ^ _775828 : [(19500 ^ _775828) ^ [] : [c_Int_Oiszero(_1110751, hAPP(c_Int_Onumber__class_Onumber__of(_1110751), 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), _1110753)))), -(c_Groups_Oone__class_Oone(_1110751) = hAPP(c_Int_Onumber__class_Onumber__of(_1110751), _1110753))], (19494 ^ _775828) ^ [] : [c_Groups_Oone__class_Oone(_1110751) = hAPP(c_Int_Onumber__class_Onumber__of(_1110751), _1110753), -(c_Int_Oiszero(_1110751, hAPP(c_Int_Onumber__class_Onumber__of(_1110751), 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), _1110753)))))]]], (24158 ^ _775828) ^ [_1198868, _1198870, _1198872] : [class_Orderings_Olinorder(_1198868), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198868), _1198870), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198868), _1198870), _1198872)) = _1198870)], (48423 ^ _775828) ^ [_1746538, _1746540] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746538)), hAPP(c_List_Orotate1(_1746538), _1746540)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746538)), _1746540))], (12257 ^ _775828) ^ [_977899, _977901] : [class_Rings_Olinordered__idom(_977899), 12260 ^ _775828 : [(12267 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977899), _977901), c_Groups_Ozero__class_Ozero(_977899))), -(c_Groups_Osgn__class_Osgn(_977899, _977901) = hAPP(c_Groups_Ouminus__class_Ouminus(_977899), c_Groups_Oone__class_Oone(_977899)))], (12261 ^ _775828) ^ [] : [c_Groups_Osgn__class_Osgn(_977899, _977901) = hAPP(c_Groups_Ouminus__class_Ouminus(_977899), c_Groups_Oone__class_Oone(_977899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977899), _977901), c_Groups_Ozero__class_Ozero(_977899))))]]], (25441 ^ _775828) ^ [_1224549] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1224549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1224549))], (9007 ^ _775828) ^ [_919917, _919919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _919917), _919919)), 9010 ^ _775828 : [(9013 ^ _775828) ^ [] : [_919917 = _919919], (9011 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _919917), _919919)))]]], (48623 ^ _775828) ^ [_1751367, _1751369, _1751371, _1751373] : [-(_1751367 = c_List_Olist_ONil(_1751369)), -(hAPP(c_List_Ohd(_1751371), hAPP(hAPP(c_List_Omap(_1751369, _1751371), _1751373), _1751367)) = hAPP(_1751373, hAPP(c_List_Ohd(_1751369), _1751367)))], (8905 ^ _775828) ^ [_918320, _918322, _918324] : [class_Orderings_Olinorder(_918320), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918320), _918322), _918324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918320), _918324), _918322)))], (24286 ^ _775828) ^ [_1201791] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1201791) = _1201791)], (23630 ^ _775828) ^ [_1189457, _1189459] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1189457)), hAPP(c_Nat_OSuc, _1189459)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1189457))), 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)), _1189459)))))], (17763 ^ _775828) ^ [_1080038, _1080040, _1080042] : [class_Rings_Olinordered__semidom(_1080038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080038), c_Groups_Ozero__class_Ozero(_1080038)), _1080040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080038), c_Groups_Ozero__class_Ozero(_1080038)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080038), _1080040), _1080042))))], (2736 ^ _775828) ^ [_816573, _816575] : [_816575 = _816573, -(c_Lazy__Sequence_Oempty(_816575) = c_Lazy__Sequence_Oempty(_816573))], (51482 ^ _775828) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (41372 ^ _775828) ^ [_1575724, _1575726, _1575728, _1575730, _1575732] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1575724, _1575726), _1575728), hAPP(hAPP(c_COMBS(_1575724, tc_fun(_1575726, tc_HOL_Obool), tc_fun(_1575726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575726, tc_HOL_Obool), tc_fun(tc_fun(_1575726, tc_HOL_Obool), tc_fun(_1575726, tc_HOL_Obool)), _1575724), c_Groups_Ominus__class_Ominus(tc_fun(_1575726, tc_HOL_Obool))), _1575730)), _1575732)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575724, _1575726), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575724, _1575726), _1575728), _1575730)), hAPP(hAPP(c_Product__Type_OSigma(_1575724, _1575726), _1575728), _1575732)))], (28189 ^ _775828) ^ [_1281145, _1281147, _1281149, _1281151] : [-(hAPP(c_Relation_ODomain(_1281145, _1281147), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1281145, _1281147), tc_HOL_Obool)), _1281149), _1281151)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281145, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1281145, _1281147), _1281149)), hAPP(c_Relation_ODomain(_1281145, _1281147), _1281151)))], (48763 ^ _775828) ^ [_1753952, _1753954, _1753956, _1753958, _1753960, _1753962] : [-(hAPP(c_List_Ofoldl(_1753952, _1753954, _1753956, _1753958), hAPP(hAPP(c_List_Olist_OCons(_1753954), _1753960), _1753962)) = hAPP(c_List_Ofoldl(_1753952, _1753954, _1753956, hAPP(hAPP(_1753956, _1753958), _1753960)), _1753962))], (13178 ^ _775828) ^ [_993806, _993808, _993810, _993812, _993814] : [c_Com_Ocom_OSemi(_993806, _993808) = c_Com_Ocom_OLocal(_993810, _993812, _993814)], (19568 ^ _775828) ^ [_1112166, _1112168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1112166)), c_Int_OBit1(_1112168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112166), _1112168)))], (38007 ^ _775828) ^ [_1496395, _1496397, _1496399] : [-(hAPP(c_Relation_OImage(_1496395, _1496397, _1496399), c_Orderings_Obot__class_Obot(tc_fun(_1496395, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1496397, tc_HOL_Obool)))], (16218 ^ _775828) ^ [_1051200, _1051202] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051200), _1051202))), -(c_Nat__Transfer_Otsub(_1051202, _1051200) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46107 ^ _775828) ^ [_1687354, _1687356, _1687358, _1687360, _1687362] : [class_Orderings_Olinorder(_1687354), -(hAPP(c_List_Oset(_1687356), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687356, _1687354, _1687358), _1687360), _1687362)) = hAPP(hAPP(c_Set_Oinsert(_1687356), _1687360), hAPP(c_List_Oset(_1687356), _1687362)))], (1600 ^ _775828) ^ [_798446, _798448] : [-(class_Rings_Ozero__neq__one(_798446)), _798448 = _798446, class_Rings_Ozero__neq__one(_798448)], (27112 ^ _775828) ^ [_1254780, _1254782] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254780)), _1254782)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1254780), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254782)))))], (29008 ^ _775828) ^ [_1300692, _1300694, _1300696, _1300698, _1300700] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1300692, _1300692)), hAPP(hAPP(c_Product__Type_OPair(_1300692, _1300692), _1300694), _1300696)), _1300698)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1300692, _1300692)), hAPP(hAPP(c_Product__Type_OPair(_1300692, _1300692), _1300696), _1300700)), c_Transitive__Closure_Otrancl(_1300692, _1300698))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1300692, _1300692)), hAPP(hAPP(c_Product__Type_OPair(_1300692, _1300692), _1300694), _1300700)), c_Transitive__Closure_Otrancl(_1300692, _1300698))))], (30906 ^ _775828) ^ [_1341207, _1341209, _1341211, _1341213] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1341207), _1341209)), hBOOL(hAPP(hAPP(c_member(_1341207), _1341211), _1341209)), hBOOL(hAPP(hAPP(c_member(_1341207), _1341213), _1341209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1341207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341207, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341207, tc_HOL_Obool)), _1341209), hAPP(hAPP(c_Set_Oinsert(_1341207), _1341211), c_Orderings_Obot__class_Obot(tc_fun(_1341207, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1341207), _1341213), c_Orderings_Obot__class_Obot(tc_fun(_1341207, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1341207), _1341209))))], (11634 ^ _775828) ^ [_967020, _967022] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967020), _967022) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11639 ^ _775828 : [(11642 ^ _775828) ^ [] : [-(_967022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11640 ^ _775828) ^ [] : [-(_967020 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11643 ^ _775828 : [(11646 ^ _775828) ^ [] : [-(_967022 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11644 ^ _775828) ^ [] : [-(_967020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41580 ^ _775828) ^ [_1580874, _1580876, _1580878] : [class_Lattices_Osemilattice__inf(_1580874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580874), _1580876)), hBOOL(hAPP(hAPP(c_member(_1580874), _1580878), _1580876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1580874), hAPP(c_Finite__Set_Ofold1(_1580874, c_Lattices_Osemilattice__inf__class_Oinf(_1580874)), _1580876)), _1580878)))], (28263 ^ _775828) ^ [_1282646, _1282648, _1282650, _1282652] : [class_Lattices_Osemilattice__sup(_1282646), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282646), _1282648), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282646), _1282650), _1282652)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282646), _1282650), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282646), _1282648), _1282652)))], (19074 ^ _775828) ^ [_1104388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104388), 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), _1104388)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (39628 ^ _775828) ^ [_1533284, _1533286, _1533288, _1533290, _1533292] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533284, tc_fun(_1533286, tc_HOL_Obool)), _1533288), hAPP(hAPP(c_COMBB(tc_fun(_1533286, tc_HOL_Obool), tc_fun(_1533286, tc_HOL_Obool), _1533284), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533286, tc_HOL_Obool)), _1533290)), _1533292)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533286, tc_HOL_Obool)), _1533290), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533284, tc_fun(_1533286, tc_HOL_Obool)), _1533288), _1533292)))], (51484 ^ _775828) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (47323 ^ _775828) ^ [_1719791, _1719793, _1719795, _1719797] : [hAPP(hAPP(c_List_Omap(_1719791, _1719793), _1719795), _1719797) = c_List_Olist_ONil(_1719793), -(_1719797 = c_List_Olist_ONil(_1719791))], (5310 ^ _775828) ^ [_856984, _856986] : [_856986 = _856984, -(tc_List_Olist(_856986) = tc_List_Olist(_856984))], (42230 ^ _775828) ^ [_1595827, _1595829] : [-(c_Relation_Orefl__on(_1595827, c_Orderings_Otop__class_Otop(tc_fun(_1595827, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595827, _1595827), tc_HOL_Obool)), _1595829), c_Relation_OId(_1595827))))], (51194 ^ _775828) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (6380 ^ _775828) ^ [_877271, _877273, _877275] : [class_Rings_Olinordered__semidom(_877271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _877273), _877275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877271), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877271), _877273)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877271), _877275))))], (4888 ^ _775828) ^ [_850551, _850553, _850555, _850557] : [-(c_Product__Type_Osnd(_850557, _850553) = c_Product__Type_Osnd(_850555, _850551)), _850557 = _850555, _850553 = _850551], (7305 ^ _775828) ^ [_892322, _892324] : [class_Int_Oring__char__0(_892322), 7308 ^ _775828 : [(7315 ^ _775828) ^ [] : [_892324 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_892322), _892324) = c_Groups_Ozero__class_Ozero(_892322))], (7309 ^ _775828) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_892322), _892324) = c_Groups_Ozero__class_Ozero(_892322), -(_892324 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (15586 ^ _775828) ^ [_1038122, _1038124, _1038126, _1038128, _1038130, _1038132] : [class_Rings_Oring(_1038122), 15589 ^ _775828 : [(15596 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038122), _1038124), _1038130)), _1038126)), _1038128) = _1038132, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), _1038124), _1038126)), _1038128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), _1038130), _1038126)), _1038132))], (15590 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), _1038124), _1038126)), _1038128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), _1038130), _1038126)), _1038132), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038122), _1038124), _1038130)), _1038126)), _1038128) = _1038132)]]], (7531 ^ _775828) ^ [_895998, _896000] : [class_Groups_Olinordered__ab__group__add(_895998), 7534 ^ _775828 : [(7541 ^ _775828) ^ [] : [_896000 = c_Groups_Ozero__class_Ozero(_895998), -(_896000 = hAPP(c_Groups_Ouminus__class_Ouminus(_895998), _896000))], (7535 ^ _775828) ^ [] : [_896000 = hAPP(c_Groups_Ouminus__class_Ouminus(_895998), _896000), -(_896000 = c_Groups_Ozero__class_Ozero(_895998))]]], (8717 ^ _775828) ^ [_915607, _915609, _915611] : [class_Orderings_Oorder(_915607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915607), _915609), _915611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915607), _915609), _915611))), -(_915609 = _915611)], (45383 ^ _775828) ^ [_1669721, _1669723, _1669725, _1669727, _1669729] : [-(hBOOL(hAPP(hAPP(c_member(_1669721), _1669723), c_Map_Odom(_1669721, _1669725, _1669727)))), -(hAPP(c_Map_Omap__add(_1669721, _1669725, _1669729, _1669727), _1669723) = hAPP(_1669729, _1669723))], (30613 ^ _775828) ^ [_1335292, _1335294, _1335296, _1335298, _1335300] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335292), _1335294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335296, tc_HOL_Obool)), _1335298), hAPP(c_Set_Oimage(_1335292, _1335296, _1335300), _1335294))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335296), _1335298)))], (38009 ^ _775828) ^ [_1496439, _1496441, _1496443, _1496445, _1496447] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496439, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496441, _1496439, _1496443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496441, tc_HOL_Obool)), _1496445), _1496447))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496439, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496441, _1496439, _1496443), _1496445)), hAPP(c_Relation_OImage(_1496441, _1496439, _1496443), _1496447)))))], (4816 ^ _775828) ^ [_849393, _849395, _849397, _849399, _849401, _849403, _849405, _849407, _849409, _849411] : [-(c_List_Ofoldr(_849411, _849407, _849403, _849399, _849395) = c_List_Ofoldr(_849409, _849405, _849401, _849397, _849393)), _849411 = _849409, _849407 = _849405, _849403 = _849401, _849399 = _849397, _849395 = _849393], (35239 ^ _775828) ^ [_1436555, _1436557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436555), _1436557)), -(hAPP(c_Finite__Set_Ocard(_1436555), _1436557) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1436555, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1436555), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436557))], (7697 ^ _775828) ^ [_898699, _898701, _898703] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898699), _898701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898699), _898703), -(_898701 = _898703), -(_898699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1060 ^ _775828) ^ [_791696, _791698] : [-(class_Rings_Olinordered__ring(_791696)), _791698 = _791696, class_Rings_Olinordered__ring(_791698)], (11699 ^ _775828) ^ [_968022, _968024] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968022), hAPP(c_Nat_OSuc, _968024)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968022), _968024)))], (20252 ^ _775828) ^ [_1123809] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123809)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123809))))], (658 ^ _775828) ^ [_785845, _785847, _785849, _785851, _785853, _785855, _785857, _785859] : [-(c_Finite__Set_Ofolding__idem(_785857, _785853, _785849, _785845)), c_Finite__Set_Ofolding__idem(_785859, _785855, _785851, _785847), _785859 = _785857, _785855 = _785853, _785851 = _785849, _785847 = _785845], (3116 ^ _775828) ^ [_822777, _822779, _822781, _822783, _822785, _822787, _822789, _822791, _822793, _822795] : [-(c_SetInterval_Oord_OatLeastLessThan(_822795, _822791, _822787, _822783, _822779) = c_SetInterval_Oord_OatLeastLessThan(_822793, _822789, _822785, _822781, _822777)), _822795 = _822793, _822791 = _822789, _822787 = _822785, _822783 = _822781, _822779 = _822777], (26453 ^ _775828) ^ [_1243083] : [_1243083 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243083), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (25048 ^ _775828) ^ [_1217769, _1217771] : [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)), _1217769)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1217771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1217769), _1217771)))], (8689 ^ _775828) ^ [_915259, _915261, _915263] : [class_Orderings_Oorder(_915259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915259), _915261), _915263)), -(_915263 = _915261), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915259), _915261), _915263)))], (34847 ^ _775828) ^ [_1426073, _1426075, _1426077] : [class_Orderings_Olinorder(_1426073), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426073), _1426075)), -(_1426075 = c_Orderings_Obot__class_Obot(tc_fun(_1426073, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426073), _1426077)), -(_1426077 = c_Orderings_Obot__class_Obot(tc_fun(_1426073, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426073, tc_HOL_Obool)), _1426075), _1426077) = c_Orderings_Obot__class_Obot(tc_fun(_1426073, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1426073, c_Orderings_Oord__class_Omax(_1426073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426073, tc_HOL_Obool)), _1426075), _1426077)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1426073), c_Big__Operators_Olattice_OSup__fin(_1426073, c_Orderings_Oord__class_Omax(_1426073), _1426075)), c_Big__Operators_Olattice_OSup__fin(_1426073, c_Orderings_Oord__class_Omax(_1426073), _1426077)))], (16248 ^ _775828) ^ [_1051701, _1051703, _1051705] : [-(hBOOL(hAPP(_1051701, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051703), _1051705)))), 16251 ^ _775828 : [(16254 ^ _775828) ^ [] : [hBOOL(hAPP(_1051701, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16252 ^ _775828) ^ [] : [-(_1051705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 16255 ^ _775828 : [(16260 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16258 ^ [_1051701, _1051703, _1051705]), _1051705)))], (16262 ^ _775828) ^ [] : [-(_1051703 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051705), 16257 ^ [_1051701, _1051703, _1051705])), 16258 ^ [_1051701, _1051703, _1051705]))], (16264 ^ _775828) ^ [] : [hBOOL(hAPP(_1051701, 16257 ^ [_1051701, _1051703, _1051705]))], (16256 ^ _775828) ^ [] : [_1051705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (17037 ^ _775828) ^ [_1066598, _1066600, _1066602, _1066604] : [class_Rings_Ocomm__semiring__1(_1066598), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066598), hAPP(hAPP(c_Power_Opower__class_Opower(_1066598), _1066600), _1066602)), hAPP(hAPP(c_Power_Opower__class_Opower(_1066598), _1066600), _1066604)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1066598), _1066600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1066602), _1066604)))], (2620 ^ _775828) ^ [_814613, _814615, _814617, _814619] : [-(c_Quickcheck_Obeyond(_814619, _814615) = c_Quickcheck_Obeyond(_814617, _814613)), _814619 = _814617, _814615 = _814613], (48393 ^ _775828) ^ [_1745880, _1745882] : [-(hAPP(c_List_Oset(_1745880), hAPP(c_List_Orotate1(_1745880), _1745882)) = hAPP(c_List_Oset(_1745880), _1745882))], (48858 ^ _775828) ^ [_1755933, _1755935, _1755937] : [class_Lattices_Olattice(_1755933), -(c_Big__Operators_Olattice__class_OSup__fin(_1755933, hAPP(c_List_Oset(_1755933), hAPP(hAPP(c_List_Olist_OCons(_1755933), _1755935), _1755937))) = hAPP(c_List_Ofoldl(_1755933, _1755933, c_Lattices_Osemilattice__sup__class_Osup(_1755933), _1755935), _1755937))], (32239 ^ _775828) ^ [_1371574, _1371576] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1371574, _1371576)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1371576), _1371574)))], (23754 ^ _775828) ^ [_1191795, _1191797, _1191799, _1191801] : [class_Orderings_Olinorder(_1191795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191795), _1191797), _1191799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191795), _1191801), _1191799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191795), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191795), _1191797), _1191801)), _1191799)))], (41500 ^ _775828) ^ [_1578906, _1578908] : [class_Lattices_Olattice(_1578906), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578906), _1578908)), -(c_Big__Operators_Olattice__class_OSup__fin(_1578906, _1578908) = hAPP(c_Finite__Set_Ofold1(_1578906, c_Lattices_Osemilattice__sup__class_Osup(_1578906)), _1578908))], (20258 ^ _775828) ^ [_1123904] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123904))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123904)))))], (50037 ^ _775828) ^ [_1780722, _1780724, _1780726, _1780728] : [class_Groups_Ocomm__monoid__add(_1780722), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1780722), _1780724), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1780726, _1780728))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1780722), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1780722), _1780724), c_List_Oupt(_1780726, _1780728))))], (33410 ^ _775828) ^ [_1395462, _1395464, _1395466] : [33412 ^ _775828 : [(33415 ^ _775828) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1395466, 33411 ^ [_1395462, _1395464, _1395466]))], (33413 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395462), 33411 ^ [_1395462, _1395464, _1395466]), _1395464)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395462, tc_Int_Oint), _1395466), _1395464) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395462, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1395462), c_Int_Onat), _1395466)), _1395464)))], (8731 ^ _775828) ^ [_915779, _915781, _915783] : [class_Orderings_Olinorder(_915779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915779), _915781), _915783)), 8738 ^ _775828 : [(8745 ^ _775828) ^ [] : [_915781 = _915783, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915779), _915781), _915783))], (8739 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915779), _915781), _915783))), -(_915781 = _915783)]]], (39217 ^ _775828) ^ [_1523209, _1523211, _1523213, _1523215, _1523217] : [class_Groups_Oab__semigroup__mult(_1523209), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1523209, _1523209, c_Groups_Otimes__class_Otimes(_1523209), _1523211, _1523213), _1523215)), hBOOL(hAPP(hAPP(c_member(_1523209), _1523217), _1523213)), -(hBOOL(hAPP(hAPP(c_member(_1523209), _1523211), _1523213))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1523209, _1523209, c_Groups_Otimes__class_Otimes(_1523209), _1523217, hAPP(hAPP(c_Set_Oinsert(_1523209), _1523211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523209, tc_HOL_Obool)), _1523213), hAPP(hAPP(c_Set_Oinsert(_1523209), _1523217), c_Orderings_Obot__class_Obot(tc_fun(_1523209, tc_HOL_Obool)))))), _1523215)))], (16679 ^ _775828) ^ [_1059948, _1059950, _1059952] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059948), _1059950)), _1059952) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059950), _1059952)))], (51402 ^ _775828) ^ [_1807111] : [class_Finite__Set_Ofinite(_1807111), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1807111)))], (21186 ^ _775828) ^ [_1142728, _1142730] : [class_Rings_Odivision__ring(_1142728), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142728), _1142730), c_Groups_Oone__class_Oone(_1142728)) = _1142730)], (17901 ^ _775828) ^ [_1082493, _1082495, _1082497, _1082499] : [class_Rings_Olinordered__semidom(_1082493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), hAPP(hAPP(c_Power_Opower__class_Opower(_1082493), _1082495), _1082497)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082493), _1082499), _1082497))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082493), c_Groups_Ozero__class_Ozero(_1082493)), _1082499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), _1082495), _1082499)))], (44914 ^ _775828) ^ [_1659412, _1659414, _1659416] : [class_Complete__Lattice_Ocomplete__lattice(_1659412), -(c_Complete__Lattice_OInf__class_OInf(_1659412, hAPP(hAPP(c_Set_Oinsert(_1659412), _1659414), _1659416)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1659412), _1659414), c_Complete__Lattice_OInf__class_OInf(_1659412, _1659416)))], (16687 ^ _775828) ^ [_1060090, _1060092, _1060094] : [-(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, _1060090, _1060092)), _1060094), _1060092) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1060090), _1060094), _1060092))], (15544 ^ _775828) ^ [_1037371, _1037373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1037371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037371), _1037373)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1037373), _1037371) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037373), _1037371)), _1037371)))], (51162 ^ _775828) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (12409 ^ _775828) ^ [_980609, _980611] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980609), _980611), 12412 ^ _775828 : [(12415 ^ _775828) ^ [] : [-(_980611 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12413 ^ _775828) ^ [] : [-(_980609 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (40243 ^ _775828) ^ [_1547261] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547261, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1547261, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1547261, tc_HOL_Obool)))], (25521 ^ _775828) ^ [_1226516, _1226518, _1226520, _1226522, _1226524, _1226526, _1226528] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1226516, _1226518, _1226520, _1226522), _1226524), _1226526), _1226528) = c_New__DSequence_Oneg__bind(_1226516, _1226518, hAPP(hAPP(hAPP(_1226520, _1226524), _1226526), _1226528), hAPP(hAPP(c_COMBC(_1226516, 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(_1226518)))), hAPP(hAPP(c_COMBC(_1226516, 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(_1226518))))), hAPP(hAPP(c_COMBC(_1226516, 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(_1226518)))))), _1226522), _1226524)), _1226526)), _1226528)))], (19260 ^ _775828) ^ [_1107038, _1107040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107038)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107040))), 19263 ^ _775828 : [(19264 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107038), _1107040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1107040)))], (19270 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107038), _1107040)))]]], (7867 ^ _775828) ^ [_901512, _901514, _901516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _901512), _901514)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _901512), _901516))), 7870 ^ _775828 : [(7873 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _901514), _901516)))], (7871 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901512)))]]], (24485 ^ _775828) ^ [_1205722, _1205724, _1205726] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1205722, hAPP(hAPP(c_COMBC(_1205722, tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_fun(_1205722, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205722, tc_fun(tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_fun(_1205722, tc_HOL_Obool)), _1205722), c_COMBC(_1205722, tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205722, tc_prod(_1205722, _1205722)), tc_fun(_1205722, tc_fun(tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_HOL_Obool)), _1205722), hAPP(c_COMBB(tc_prod(_1205722, _1205722), tc_fun(tc_fun(tc_prod(_1205722, _1205722), tc_HOL_Obool), tc_HOL_Obool), _1205722), c_member(tc_prod(_1205722, _1205722)))), c_Product__Type_OPair(_1205722, _1205722)))), _1205724)), _1205726)), -(hBOOL(hAPP(hAPP(c_member(_1205722), _1205726), c_Wellfounded_Oacc(_1205722, _1205724))))], (39732 ^ _775828) ^ [_1536314, _1536316, _1536318, _1536320, _1536322] : [-(_1536314 = c_Orderings_Obot__class_Obot(tc_fun(_1536316, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536318, tc_HOL_Obool)), _1536320), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536316, tc_fun(_1536318, tc_HOL_Obool)), _1536314), _1536322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536316, tc_fun(_1536318, tc_HOL_Obool)), _1536314), hAPP(hAPP(c_COMBB(tc_fun(_1536318, tc_HOL_Obool), tc_fun(_1536318, tc_HOL_Obool), _1536316), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536318, tc_HOL_Obool)), _1536320)), _1536322)))], (8341 ^ _775828) ^ [_909799, _909801, _909803] : [class_Orderings_Oorder(_909799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909799), _909801), _909803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909799), _909803), _909801)), -(_909801 = _909803)], (43038 ^ _775828) ^ [_1615048, _1615050, _1615052, _1615054, _1615056, _1615058] : [c_Finite__Set_Ofolding(_1615048, _1615050, _1615052, _1615054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615048), _1615056)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615048), _1615058)), -(hAPP(c_Fun_Ocomp(_1615050, _1615050, _1615050, hAPP(_1615054, _1615058)), hAPP(_1615054, _1615056)) = hAPP(c_Fun_Ocomp(_1615050, _1615050, _1615050, hAPP(_1615054, _1615056)), hAPP(_1615054, _1615058)))], (18523 ^ _775828) ^ [_1094415] : [class_Int_Onumber__ring(_1094415), -(hAPP(c_Int_Onumber__class_Onumber__of(_1094415), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1094415), c_Groups_Oone__class_Oone(_1094415)))], (47415 ^ _775828) ^ [_1721704, _1721706] : [-(c_List_Olistrelp(_1721704, _1721706, c_List_Olist_ONil(_1721704), c_List_Olist_ONil(_1721704)))], (35603 ^ _775828) ^ [_1444387, _1444389] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1444387), _1444389) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1444387, _1444389))], (17437 ^ _775828) ^ [_1074488, _1074490] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074488)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074490)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1074488), _1074490)))], (40215 ^ _775828) ^ [_1546747, _1546749] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1546747), c_Orderings_Otop__class_Otop(tc_fun(_1546747, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1546747), _1546749) = hAPP(c_Finite__Set_Ocard(_1546747), c_Orderings_Otop__class_Otop(tc_fun(_1546747, tc_HOL_Obool))), -(_1546749 = c_Orderings_Otop__class_Otop(tc_fun(_1546747, tc_HOL_Obool)))], (45844 ^ _775828) ^ [_1680827, _1680829, _1680831, _1680833] : [-(hBOOL(hAPP(c_List_Odistinct(_1680827), hAPP(hAPP(c_List_Omap(_1680829, _1680827), _1680831), _1680833)))), hBOOL(hAPP(c_List_Odistinct(_1680829), _1680833)), c_Fun_Oinj__on(_1680829, _1680827, _1680831, hAPP(c_List_Oset(_1680829), _1680833))], (29775 ^ _775828) ^ [_1316717, _1316719, _1316721, _1316723] : [-(c_Predicate_Oconversep(_1316717, _1316719, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316717, tc_fun(_1316719, tc_HOL_Obool))), _1316721), _1316723)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316719, tc_fun(_1316717, tc_HOL_Obool))), c_Predicate_Oconversep(_1316717, _1316719, _1316721)), c_Predicate_Oconversep(_1316717, _1316719, _1316723)))], (48084 ^ _775828) ^ [_1736740, _1736742, _1736744, _1736746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736742)), _1736744)))), -(hAPP(hAPP(c_List_Onth(_1736742), hAPP(hAPP(c_List_Oappend(_1736742), _1736744), _1736746)), _1736740) = hAPP(hAPP(c_List_Onth(_1736742), _1736746), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1736740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736742)), _1736744))))], (35899 ^ _775828) ^ [_1449959, _1449961, _1449963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449959)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1449961), _1449963)), 35906 ^ _775828 : [(35907 ^ _775828) ^ [_1450155] : [35909 ^ _775828 : [(35915 ^ _775828) ^ [] : [-(_1450155 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35911 ^ [_1449959, _1449961, _1449963, _1450155]), 35908 ^ [_1449959, _1449961, _1449963, _1450155]))], (35913 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35911 ^ [_1449959, _1449961, _1449963, _1450155]), _1449963)))], (35910 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35908 ^ [_1449959, _1449961, _1449963, _1450155]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449959))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1450155), _1449961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450155), _1449959)), _1449961)))]]], (15468 ^ _775828) ^ [_1035929, _1035931, _1035933] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1035929), _1035931)), _1035933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035929), _1035933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035931), _1035933)))], (40521 ^ _775828) ^ [_1553273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553273), c_Orderings_Otop__class_Otop(tc_fun(_1553273, 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(_1553273), c_Orderings_Otop__class_Otop(tc_fun(_1553273, tc_HOL_Obool))))))], (35923 ^ _775828) ^ [_1450431, _1450433, _1450435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450431)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1450433), _1450435)), 35930 ^ _775828 : [(35931 ^ _775828) ^ [_1450627] : [35933 ^ _775828 : [(35939 ^ _775828) ^ [] : [-(_1450627 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35935 ^ [_1450431, _1450433, _1450435, _1450627]), 35932 ^ [_1450431, _1450433, _1450435, _1450627]))], (35937 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35935 ^ [_1450431, _1450433, _1450435, _1450627]), _1450435)))], (35934 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35932 ^ [_1450431, _1450433, _1450435, _1450627]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450431))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1450433), _1450627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1450433), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450627), _1450431))))]]], (45509 ^ _775828) ^ [_1672786, _1672788, _1672790, _1672792, _1672794, _1672796, _1672798] : [c_Fun_Oinj__on(_1672786, _1672788, _1672790, c_Orderings_Otop__class_Otop(tc_fun(_1672786, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1672786, _1672792, _1672794), _1672796) = hAPP(c_Option_Ooption_OSome(_1672792), _1672798), -(hAPP(c_Map_Omap__of(_1672788, _1672792, hAPP(hAPP(c_List_Omap(tc_prod(_1672786, _1672792), tc_prod(_1672788, _1672792)), hAPP(c_Product__Type_Oprod_Oprod__case(_1672786, _1672792, tc_prod(_1672788, _1672792)), hAPP(hAPP(c_COMBB(_1672788, tc_fun(_1672792, tc_prod(_1672788, _1672792)), _1672786), c_Product__Type_OPair(_1672788, _1672792)), _1672790))), _1672794)), hAPP(_1672790, _1672796)) = hAPP(c_Option_Ooption_OSome(_1672792), _1672798))], (15144 ^ _775828) ^ [_1030070, _1030072, _1030074, _1030076, _1030078] : [class_Groups_Oab__group__add(_1030070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030070), _1030072), _1030074) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030070), _1030076), _1030078), 15151 ^ _775828 : [(15158 ^ _775828) ^ [] : [_1030076 = _1030078, -(_1030072 = _1030074)], (15152 ^ _775828) ^ [] : [_1030072 = _1030074, -(_1030076 = _1030078)]]], (48759 ^ _775828) ^ [_1753827, _1753829, _1753831, _1753833] : [-(c_List_Olist_Olist__size(_1753827, _1753829, hAPP(hAPP(c_List_Olist_OCons(_1753827), _1753831), _1753833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1753829, _1753831)), c_List_Olist_Olist__size(_1753827, _1753829, _1753833))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13582 ^ _775828) ^ [_1001524, _1001526, _1001528, _1001530, _1001532] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_1001524, _1001526), _1001528, _1001530, _1001532), 13586 ^ _775828 : [(13589 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_1001526, 13585 ^ [_1001524, _1001526, _1001528, _1001530, _1001532], _1001530, _1001532))], (13587 ^ _775828) ^ [] : [-(c_Natural_Oevaln(_1001524, _1001528, _1001530, 13585 ^ [_1001524, _1001526, _1001528, _1001530, _1001532]))]]], (16395 ^ _775828) ^ [_1054597, _1054599, _1054601] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1054597, _1054599) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1054601, _1054599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054601), _1054597)), -(_1054597 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1054599), 16402 ^ [_1054597, _1054599, _1054601])))], (33370 ^ _775828) ^ [_1394386, _1394388, _1394390, _1394392, _1394394] : [-(hBOOL(hAPP(hAPP(c_member(_1394386), _1394388), _1394390))), -(hAPP(c_Map_Orestrict__map(_1394386, _1394392, _1394394, _1394390), _1394388) = c_Option_Ooption_ONone(_1394392))], (46480 ^ _775828) ^ [_1698246, _1698248, _1698250, _1698252, _1698254, _1698256] : [c_List_Olistrelp(_1698246, _1698248, hAPP(hAPP(c_List_Olist_OCons(_1698246), _1698250), _1698252), hAPP(hAPP(c_List_Olist_OCons(_1698246), _1698254), _1698256)), 46483 ^ _775828 : [(46486 ^ _775828) ^ [] : [-(c_List_Olistrelp(_1698246, _1698248, _1698252, _1698256))], (46484 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(_1698248, _1698250), _1698254)))]]], (15894 ^ _775828) ^ [_1044142, _1044144] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044142), _1044144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044142), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044144)))], (27461 ^ _775828) ^ [_1263562, _1263564] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1263562), 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)))), _1263564)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263564), _1263562)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263562), _1263564)))], (26479 ^ _775828) ^ [_1243474, _1243476, _1243478] : [26480 ^ _775828 : [(26483 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243476), _1243478))], (26481 ^ _775828) ^ [] : [_1243474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243474), _1243476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243474), _1243478))))], (48846 ^ _775828) ^ [_1755703, _1755705] : [class_Complete__Lattice_Ocomplete__lattice(_1755703), -(c_Complete__Lattice_OSup__class_OSup(_1755703, hAPP(c_List_Oset(_1755703), _1755705)) = hAPP(c_List_Ofoldl(_1755703, _1755703, c_Lattices_Osemilattice__sup__class_Osup(_1755703), c_Orderings_Obot__class_Obot(_1755703)), _1755705))], (42023 ^ _775828) ^ [_1590888, _1590890, _1590892] : [class_Lattices_Oab__semigroup__idem__mult(_1590888), hAPP(_1590890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1590888), 42028 ^ [_1590888, _1590890, _1590892]), 42029 ^ [_1590888, _1590890, _1590892])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1590888), hAPP(_1590890, 42028 ^ [_1590888, _1590890, _1590892])), hAPP(_1590890, 42029 ^ [_1590888, _1590890, _1590892])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590888), _1590892)), -(_1590892 = c_Orderings_Obot__class_Obot(tc_fun(_1590888, tc_HOL_Obool))), -(hAPP(_1590890, hAPP(c_Finite__Set_Ofold1(_1590888, c_Groups_Otimes__class_Otimes(_1590888)), _1590892)) = hAPP(c_Finite__Set_Ofold1(_1590888, c_Groups_Otimes__class_Otimes(_1590888)), hAPP(c_Set_Oimage(_1590888, _1590888, _1590890), _1590892)))], (1470 ^ _775828) ^ [_796821, _796823] : [-(class_Rings_Olinordered__semiring(_796821)), _796823 = _796821, class_Rings_Olinordered__semiring(_796823)], (31823 ^ _775828) ^ [_1363042, _1363044, _1363046, _1363048] : [c_Wellfounded_Owf(_1363042, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1363042, _1363042)), hAPP(hAPP(c_Product__Type_OPair(_1363042, _1363042), _1363044), _1363046)), _1363048)), 31826 ^ _775828 : [(31829 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1363042, _1363042)), hAPP(hAPP(c_Product__Type_OPair(_1363042, _1363042), _1363046), _1363044)), c_Transitive__Closure_Ortrancl(_1363042, _1363048)))], (31827 ^ _775828) ^ [] : [-(c_Wellfounded_Owf(_1363042, _1363048))]]], (15956 ^ _775828) ^ [_1045725, _1045727, _1045729, _1045731, _1045733, _1045735] : [class_Rings_Oordered__ring(_1045725), 15959 ^ _775828 : [(15966 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045725), _1045727), _1045733)), _1045729)), _1045731)), _1045735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), _1045727), _1045729)), _1045731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), _1045733), _1045729)), _1045735))))], (15960 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), _1045727), _1045729)), _1045731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), _1045733), _1045729)), _1045735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045725), _1045727), _1045733)), _1045729)), _1045731)), _1045735)))]]], (5820 ^ _775828) ^ [_868517, _868519] : [hBOOL(hAPP(_868517, _868519)), 5826 ^ _775828 : [(5829 ^ _775828) ^ [] : [hBOOL(hAPP(_868517, 5825 ^ [_868517, _868519]))], (5827 ^ _775828) ^ [] : [-(hBOOL(hAPP(_868517, hAPP(c_Nat_OSuc, 5825 ^ [_868517, _868519]))))]], -(hBOOL(hAPP(_868517, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50547 ^ _775828) ^ [_1792696, _1792698, _1792700, _1792702] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1792696)), c_List_Otranspose__rel(_1792696)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1792696)), hAPP(hAPP(c_List_Olist_OCons(_1792696), _1792698), _1792700)), _1792702))), -(c_List_Otranspose(_1792696, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1792696)), hAPP(hAPP(c_List_Olist_OCons(_1792696), _1792698), _1792700)), _1792702)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1792696)), hAPP(hAPP(c_List_Olist_OCons(_1792696), _1792698), c_List_Oconcat(_1792696, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1792696), tc_List_Olist(_1792696)), c_List_Olist_Olist__case(tc_List_Olist(_1792696), _1792696, c_List_Olist_ONil(_1792696), hAPP(hAPP(c_COMBB(tc_List_Olist(_1792696), tc_fun(tc_List_Olist(_1792696), tc_List_Olist(_1792696)), _1792696), c_COMBK(tc_List_Olist(_1792696), tc_List_Olist(_1792696))), hAPP(hAPP(c_COMBC(_1792696, tc_List_Olist(_1792696), tc_List_Olist(_1792696)), c_List_Olist_OCons(_1792696)), c_List_Olist_ONil(_1792696))))), _1792702)))), c_List_Otranspose(_1792696, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1792696)), _1792700), c_List_Oconcat(tc_List_Olist(_1792696), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1792696), tc_List_Olist(tc_List_Olist(_1792696))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1792696)), _1792696, c_List_Olist_ONil(tc_List_Olist(_1792696)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1792696), tc_List_Olist(tc_List_Olist(_1792696))), _1792696), hAPP(hAPP(c_COMBC(tc_List_Olist(_1792696), tc_List_Olist(tc_List_Olist(_1792696)), tc_List_Olist(tc_List_Olist(_1792696))), c_List_Olist_OCons(tc_List_Olist(_1792696))), c_List_Olist_ONil(tc_List_Olist(_1792696)))))), _1792702))))))], (12957 ^ _775828) ^ [_989867, _989869, _989871] : [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), _989867), _989869)), _989871)), 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)), _989871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989869), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8131 ^ _775828) ^ [_906528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _906528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _906528))))], (36891 ^ _775828) ^ [_1469251, _1469253, _1469255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469251), _1469253)), 36894 ^ _775828 : [(36895 ^ _775828) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469251, tc_Nat_Onat), _1469255), _1469253) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 36898 ^ _775828 : [(36899 ^ _775828) ^ [_1469413] : [hBOOL(hAPP(hAPP(c_member(_1469251), _1469413), _1469253)), -(hAPP(_1469255, _1469413) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36905 ^ _775828) ^ [] : [36907 ^ _775828 : [(36910 ^ _775828) ^ [] : [hAPP(_1469255, 36906 ^ [_1469251, _1469253, _1469255]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36908 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469251), 36906 ^ [_1469251, _1469253, _1469255]), _1469253)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469251, tc_Nat_Onat), _1469255), _1469253) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25735 ^ _775828) ^ [_1230740, _1230742] : [class_Rings_Ocomm__semiring__1(_1230740), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230740), _1230742), _1230742)))], (3192 ^ _775828) ^ [_824077, _824079, _824081, _824083] : [-(c_Wellfounded_Omin__ext(_824083, _824079) = c_Wellfounded_Omin__ext(_824081, _824077)), _824083 = _824081, _824079 = _824077], (36507 ^ _775828) ^ [_1461672, _1461674] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1461672), _1461674))))], (9929 ^ _775828) ^ [_936231, _936233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936231)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936233))))), _936231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _936233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24360 ^ _775828) ^ [_1203321] : [class_Orderings_Oord(_1203321), -(c_Orderings_Oord__class_Omin(_1203321) = c_Orderings_Oord_Omin(_1203321, c_Orderings_Oord__class_Oless__eq(_1203321)))], (37046 ^ _775828) ^ [_1473205, _1473207, _1473209, _1473211] : [class_Groups_Ocomm__monoid__add(_1473205), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473205), _1473207), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1473209), hAPP(c_Nat_OSuc, _1473211))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1473205), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1473205, tc_Nat_Onat), _1473207), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1473209, _1473211)))], (13188 ^ _775828) ^ [_994113, _994115, _994117, _994119] : [c_Com_Ocom_OSemi(_994113, _994115) = c_Com_Ocom_OSemi(_994117, _994119), 13191 ^ _775828 : [(13194 ^ _775828) ^ [] : [-(_994115 = _994119)], (13192 ^ _775828) ^ [] : [-(_994113 = _994117)]]], (15530 ^ _775828) ^ [_1037096, _1037098, _1037100] : [-(hBOOL(hAPP(_1037096, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037098), _1037100))))), 15533 ^ _775828 : [(15536 ^ _775828) ^ [] : [hBOOL(hAPP(_1037096, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037098)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037100))))], (15534 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037100), _1037098)))]], 15537 ^ _775828 : [(15540 ^ _775828) ^ [] : [hBOOL(hAPP(_1037096, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15538 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037098), _1037100)))]]], (36621 ^ _775828) ^ [] : [-(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))))], (27453 ^ _775828) ^ [_1263417, _1263419] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1263417), 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)))), _1263419))), 27456 ^ _775828 : [(27459 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263417), _1263419))], (27457 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1263419), _1263417)))]]], (18473 ^ _775828) ^ [_1093650, _1093652] : [-(_1093650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1093652, _1093650) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1093652), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1093650)))], (3874 ^ _775828) ^ [_834758, _834760] : [_834760 = _834758, -(c_Smallcheck_Osmall__class_Osmall(_834760) = c_Smallcheck_Osmall__class_Osmall(_834758))], (13504 ^ _775828) ^ [_1000077, _1000079, _1000081, _1000083, _1000085] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1000077, _1000079, _1000081)), _1000083), _1000085))), 13505 ^ _775828 : [(13512 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1000077, _1000083))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000081), _1000083), _1000085))], (13506 ^ _775828) ^ [] : [hBOOL(hAPP(_1000077, _1000083)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1000079), _1000083), _1000085))]]], (47115 ^ _775828) ^ [_1714533, _1714535, _1714537, _1714539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714533), tc_List_Olist(_1714533))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714533), tc_List_Olist(_1714533)), _1714535), _1714537)), c_List_Olistrel(_1714533, _1714539))), 47118 ^ _775828 : [(47121 ^ _775828) ^ [_1714762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714762), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714533)), _1714535))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714533, _1714533)), hAPP(hAPP(c_Product__Type_OPair(_1714533, _1714533), hAPP(hAPP(c_List_Onth(_1714533), _1714535), _1714762)), hAPP(hAPP(c_List_Onth(_1714533), _1714537), _1714762))), _1714539)))], (47119 ^ _775828) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714533)), _1714535) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714533)), _1714537))]]], (50219 ^ _775828) ^ [_1784753, _1784755] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1784753)), c_List_Otranspose__rel(_1784753)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1784753)), c_List_Olist_ONil(_1784753)), _1784755))), -(c_List_Otranspose(_1784753, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1784753)), c_List_Olist_ONil(_1784753)), _1784755)) = c_List_Otranspose(_1784753, _1784755))], (27822 ^ _775828) ^ [_1272178, _1272180, _1272182, _1272184] : [hBOOL(hAPP(hAPP(c_member(_1272178), _1272180), hAPP(c_Relation_ODomain(_1272178, _1272182), _1272184))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1272178, _1272182)), hAPP(hAPP(c_Product__Type_OPair(_1272178, _1272182), _1272180), 27825 ^ [_1272178, _1272180, _1272182, _1272184])), _1272184)))], (4756 ^ _775828) ^ [_848483, _848485, _848487, _848489] : [-(c_List_Orotate(_848489, _848485) = c_List_Orotate(_848487, _848483)), _848489 = _848487, _848485 = _848483], (4504 ^ _775828) ^ [_844579, _844581] : [_844581 = _844579, -(c_Set_OCollect(_844581) = c_Set_OCollect(_844579))], (44010 ^ _775828) ^ [_1636436, _1636438, _1636440, _1636442, _1636444, _1636446] : [c_Finite__Set_Ofun__left__comm(_1636436, _1636438, _1636440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636436), _1636442)), -(hBOOL(hAPP(hAPP(c_member(_1636436), _1636444), _1636442))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1636436, _1636438, _1636440), _1636446), hAPP(hAPP(c_Set_Oinsert(_1636436), _1636444), _1636442)) = hAPP(hAPP(_1636440, _1636444), hAPP(hAPP(c_Finite__Set_Ofold(_1636436, _1636438, _1636440), _1636446), _1636442)))], (49594 ^ _775828) ^ [_1773023, _1773025] : [class_Orderings_Olinorder(_1773023), -(c_List_Olinorder__class_Osorted(_1773023, hAPP(hAPP(c_List_Olist_OCons(_1773023), _1773025), c_List_Olist_ONil(_1773023))))], (28221 ^ _775828) ^ [_1281853, _1281855] : [class_Lattices_Osemilattice__sup(_1281853), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281853), _1281855), _1281855) = _1281855)], (44160 ^ _775828) ^ [_1639741, _1639743, _1639745, _1639747, _1639749] : [hBOOL(hAPP(hAPP(c_member(_1639741), _1639743), _1639745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1639747, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639741, tc_fun(_1639747, tc_HOL_Obool)), _1639745), _1639749)), hAPP(_1639749, _1639743))))], (47377 ^ _775828) ^ [_1721007, _1721009, _1721011] : [-(hAPP(c_Map_Omap__of(_1721007, _1721009, c_List_Olist_ONil(tc_prod(_1721007, _1721009))), _1721011) = c_Option_Ooption_ONone(_1721009))], (14431 ^ _775828) ^ [_1017551] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017551, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40543 ^ _775828) ^ [_1554111, _1554113, _1554115, _1554117, _1554119, _1554121] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554113, _1554115)), hAPP(hAPP(c_Product__Type_OPair(_1554113, _1554115), _1554119), _1554121)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554111, tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1554111, tc_HOL_Obool))), _1554117))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554111, tc_fun(_1554113, tc_fun(_1554115, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1554111, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_fun(_1554113, tc_fun(_1554115, tc_HOL_Obool)), _1554111), hAPP(c_COMBC(_1554113, tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_fun(_1554115, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554115, tc_fun(tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_fun(_1554115, tc_HOL_Obool)), _1554113), c_COMBC(_1554115, tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554115, tc_prod(_1554113, _1554115)), tc_fun(_1554115, tc_fun(tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_HOL_Obool)), _1554113), hAPP(c_COMBB(tc_prod(_1554113, _1554115), tc_fun(tc_fun(tc_prod(_1554113, _1554115), tc_HOL_Obool), tc_HOL_Obool), _1554115), c_member(tc_prod(_1554113, _1554115)))), c_Product__Type_OPair(_1554113, _1554115))))), _1554117)), _1554119), _1554121)))], (30099 ^ _775828) ^ [_1324385, _1324387] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1324385), _1324387)), -(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)))), _1324387, _1324385) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (45286 ^ _775828) ^ [_1667765, _1667767, _1667769, _1667771, _1667773, _1667775] : [-(hBOOL(hAPP(hAPP(c_member(_1667765), _1667767), c_Map_Odom(_1667765, _1667769, _1667771)))), -(c_Map_Omap__add(_1667765, _1667769, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1667765, tc_Option_Ooption(_1667769)), _1667773), _1667767), hAPP(c_Option_Ooption_OSome(_1667769), _1667775)), _1667771) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1667765, tc_Option_Ooption(_1667769)), c_Map_Omap__add(_1667765, _1667769, _1667773, _1667771)), _1667767), hAPP(c_Option_Ooption_OSome(_1667769), _1667775)))], (16677 ^ _775828) ^ [_1059900, _1059902, _1059904] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059900, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059900, tc_HOL_Obool)), _1059902), _1059904)), _1059902)))], (44624 ^ _775828) ^ [_1652799, _1652801, _1652803, _1652805, _1652807, _1652809, _1652811] : [44626 ^ _775828 : [(44629 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1652807, 44625 ^ [_1652799, _1652801, _1652803, _1652805, _1652807, _1652809, _1652811]), _1652809), _1652811))], (44627 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652799), 44625 ^ [_1652799, _1652801, _1652803, _1652805, _1652807, _1652809, _1652811]), _1652805)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652799, tc_fun(_1652801, tc_fun(_1652803, tc_HOL_Obool))), _1652805), _1652807), _1652809), _1652811)))], (51438 ^ _775828) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (44569 ^ _775828) ^ [_1651416, _1651418, _1651420, _1651422] : [hBOOL(hAPP(hAPP(c_member(_1651416), _1651418), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651416, tc_HOL_Obool), _1651420))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1651416, tc_HOL_Obool)), _1651422), _1651420)), -(hBOOL(hAPP(hAPP(c_member(_1651416), _1651418), _1651422)))], (47960 ^ _775828) ^ [_1734299, _1734301, _1734303] : [hAPP(hAPP(c_List_Oappend(_1734299), _1734301), _1734303) = _1734303, -(_1734301 = c_List_Olist_ONil(_1734299))], (40197 ^ _775828) ^ [_1546371] : [-(hAPP(c_Set_OPow(_1546371), c_Orderings_Otop__class_Otop(tc_fun(_1546371, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1546371, tc_HOL_Obool), tc_HOL_Obool)))], (21064 ^ _775828) ^ [_1138260, _1138262, _1138264, _1138266] : [hAPP(hAPP(c_COMBC(_1138260, tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_fun(_1138262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138262, tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_fun(_1138262, tc_HOL_Obool)), _1138260), c_COMBC(_1138262, tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138262, tc_prod(_1138260, _1138262)), tc_fun(_1138262, tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), _1138260), hAPP(c_COMBB(tc_prod(_1138260, _1138262), tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool), _1138262), c_member(tc_prod(_1138260, _1138262)))), c_Product__Type_OPair(_1138260, _1138262)))), _1138264) = hAPP(hAPP(c_COMBC(_1138260, tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_fun(_1138262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138262, tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_fun(_1138262, tc_HOL_Obool)), _1138260), c_COMBC(_1138262, tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1138262, tc_prod(_1138260, _1138262)), tc_fun(_1138262, tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool)), _1138260), hAPP(c_COMBB(tc_prod(_1138260, _1138262), tc_fun(tc_fun(tc_prod(_1138260, _1138262), tc_HOL_Obool), tc_HOL_Obool), _1138262), c_member(tc_prod(_1138260, _1138262)))), c_Product__Type_OPair(_1138260, _1138262)))), _1138266), -(_1138264 = _1138266)], (6127 ^ _775828) ^ [_873200, _873202, _873204, _873206] : [hAPP(c_Com_Ocom_OBODY, _873200) = c_Com_Ocom_OCall(_873202, _873204, _873206)], (5721 ^ _775828) ^ [_867017] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _867017)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19936 ^ _775828) ^ [_1118069, _1118071] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118069))), _1118071) = 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)))), _1118069), _1118071))], (23604 ^ _775828) ^ [_1188988, _1188990, _1188992, _1188994] : [-(hAPP(c_Nat_Onat_Onat__rec(_1188988, _1188990, _1188992), hAPP(c_Nat_OSuc, _1188994)) = hAPP(hAPP(_1188992, _1188994), hAPP(c_Nat_Onat_Onat__rec(_1188988, _1188990, _1188992), _1188994)))], (49505 ^ _775828) ^ [_1770143, _1770145, _1770147, _1770149] : [-(c_List_Opartition(_1770143, _1770145, hAPP(hAPP(c_List_Olist_OCons(_1770143), _1770147), _1770149)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1770143), tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1770143), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1770143), tc_fun(tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), tc_fun(tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), tc_List_Olist(_1770143)), c_COMBS(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_fun(tc_List_Olist(_1770143), tc_fun(tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), tc_List_Olist(_1770143)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_fun(tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_List_Olist(_1770143)), hAPP(c_If(tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), hAPP(_1770145, _1770147)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1770143), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_List_Olist(_1770143)), c_Product__Type_OPair(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), hAPP(c_List_Olist_OCons(_1770143), _1770147))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1770143), tc_fun(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143))), tc_fun(tc_fun(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_fun(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), tc_List_Olist(_1770143)), c_COMBB(tc_List_Olist(_1770143), tc_prod(tc_List_Olist(_1770143), tc_List_Olist(_1770143)), tc_List_Olist(_1770143))), c_Product__Type_OPair(tc_List_Olist(_1770143), tc_List_Olist(_1770143)))), hAPP(c_List_Olist_OCons(_1770143), _1770147)))), c_List_Opartition(_1770143, _1770145, _1770149)))], (18607 ^ _775828) ^ [_1095624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095624)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1095624) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (38180 ^ _775828) ^ [_1500350, _1500352, _1500354, _1500356, _1500358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500354, _1500350)), hAPP(hAPP(c_Product__Type_OPair(_1500354, _1500350), _1500358), _1500352)), _1500356)), -(hBOOL(hAPP(hAPP(c_member(_1500350), _1500352), hAPP(c_Relation_OImage(_1500354, _1500350, _1500356), hAPP(hAPP(c_Set_Oinsert(_1500354), _1500358), c_Orderings_Obot__class_Obot(tc_fun(_1500354, tc_HOL_Obool)))))))], (14516 ^ _775828) ^ [_1018833, _1018835] : [14517 ^ _775828 : [(14518 ^ _775828) ^ [_1018882] : [_1018833 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018835), _1018882)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018833, _1018835) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47695 ^ _775828) ^ [_1727860, _1727862, _1727864, _1727866, _1727868, _1727870, _1727872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727860)), _1727862)), _1727864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727864), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727866)), _1727868))), -(c_Map_Omap__upds(_1727860, _1727866, _1727870, _1727862, hAPP(hAPP(c_List_Olist__update(_1727866, _1727868), _1727864), _1727872)) = c_Map_Omap__upds(_1727860, _1727866, _1727870, _1727862, _1727868))], (30429 ^ _775828) ^ [_1331933, _1331935, _1331937] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331933), _1331935)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331933), _1331937)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331933, tc_HOL_Obool)), _1331935), _1331937))))], (29306 ^ _775828) ^ [_1307327, _1307329] : [_1307329 = c_Orderings_Obot__class_Obot(tc_fun(_1307327, tc_HOL_Obool)), 29309 ^ _775828 : [(29310 ^ _775828) ^ [_1307407] : [hBOOL(hAPP(hAPP(c_member(_1307327), _1307407), _1307329))]]], (35027 ^ _775828) ^ [_1430673, _1430675] : [c_Nat__Transfer_Onat__set(_1430673), c_Nat__Transfer_Onat__set(_1430675), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1430673), _1430675)))], (21198 ^ _775828) ^ [_1142952, _1142954, _1142956, _1142958] : [class_Fields_Ofield__inverse__zero(_1142952), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142952), _1142954), _1142956)), _1142958) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142952), hAPP(hAPP(c_Power_Opower__class_Opower(_1142952), _1142954), _1142958)), hAPP(hAPP(c_Power_Opower__class_Opower(_1142952), _1142956), _1142958)))], (1210 ^ _775828) ^ [_793571, _793573] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_793571)), _793573 = _793571, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_793573)], (49124 ^ _775828) ^ [_1762108, _1762110, _1762112] : [-(_1762108 = c_List_Olist_ONil(_1762110)), -(c_List_Olast(_1762110, hAPP(hAPP(c_List_Oappend(_1762110), _1762112), _1762108)) = c_List_Olast(_1762110, _1762108))], (28705 ^ _775828) ^ [_1291731, _1291733] : [c_Wellfounded_Oacyclic(_1291731, _1291733), -(c_Wellfounded_Oacyclic(_1291731, hAPP(c_Relation_Oconverse(_1291731, _1291731), _1291733)))], (2820 ^ _775828) ^ [_818019, _818021, _818023, _818025, _818027, _818029, _818031, _818033] : [-(c_New__DSequence_Oneg__decr__bind(_818033, _818029, _818025, _818021) = c_New__DSequence_Oneg__decr__bind(_818031, _818027, _818023, _818019)), _818033 = _818031, _818029 = _818027, _818025 = _818023, _818021 = _818019], (51552 ^ _775828) ^ [_1808776, _1808778] : [hBOOL(_1808776), hBOOL(_1808778), -(hBOOL(hAPP(hAPP(c_fconj, _1808776), _1808778)))], (3078 ^ _775828) ^ [_822178, _822180, _822182, _822184] : [-(c_Com_Ocom_OAss(_822184, _822180) = c_Com_Ocom_OAss(_822182, _822178)), _822184 = _822182, _822180 = _822178], (29663 ^ _775828) ^ [_1314296, _1314298, _1314300, _1314302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314296, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314296, tc_HOL_Obool)), _1314298), hAPP(hAPP(c_Set_Oinsert(_1314296), _1314300), c_Orderings_Obot__class_Obot(tc_fun(_1314296, tc_HOL_Obool))))), _1314302)), hBOOL(hAPP(hAPP(c_member(_1314296), _1314300), _1314298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314296, tc_HOL_Obool)), _1314298), hAPP(hAPP(c_Set_Oinsert(_1314296), _1314300), _1314302))))], (19232 ^ _775828) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (45053 ^ _775828) ^ [_1662597, _1662599, _1662601] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1662597, tc_HOL_Obool)), _1662599), _1662601))), 45059 ^ _775828 : [(45063 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1662597, tc_HOL_Obool)), 45061 ^ [_1662597, _1662599, _1662601]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1662597, tc_HOL_Obool)), _1662599), _1662601))))], (45065 ^ _775828) ^ [] : [45058 ^ [_1662597, _1662599, _1662601] = 45061 ^ [_1662597, _1662599, _1662601]], (45067 ^ _775828) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1662597, tc_HOL_Obool)), 45058 ^ [_1662597, _1662599, _1662601]), 45061 ^ [_1662597, _1662599, _1662601]) = c_Orderings_Obot__class_Obot(tc_fun(_1662597, tc_HOL_Obool))], (45060 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1662597, tc_HOL_Obool)), 45058 ^ [_1662597, _1662599, _1662601]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1662597, tc_HOL_Obool)), _1662599), _1662601))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1662597, tc_HOL_Obool)), _1662599), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662597, tc_HOL_Obool), _1662601)) = c_Orderings_Obot__class_Obot(tc_fun(_1662597, tc_HOL_Obool)))], (41663 ^ _775828) ^ [_1582429, _1582431, _1582433] : [class_Orderings_Olinorder(_1582429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582429), _1582431)), -(_1582431 = c_Orderings_Obot__class_Obot(tc_fun(_1582429, tc_HOL_Obool))), 41674 ^ _775828 : [(41684 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582429), hAPP(c_Finite__Set_Ofold1(_1582429, c_Orderings_Oord__class_Omin(_1582429)), _1582431)), _1582433))), 41685 ^ _775828 : [(41686 ^ _775828) ^ [_1582818] : [hBOOL(hAPP(hAPP(c_member(_1582429), _1582818), _1582431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582429), _1582818), _1582433))]]], (41675 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582429), hAPP(c_Finite__Set_Ofold1(_1582429, c_Orderings_Oord__class_Omin(_1582429)), _1582431)), _1582433)), 41679 ^ _775828 : [(41682 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1582429), 41678 ^ [_1582429, _1582431, _1582433]), _1582433)))], (41680 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582429), 41678 ^ [_1582429, _1582431, _1582433]), _1582431)))]]]]], (38440 ^ _775828) ^ [_1506199, _1506201, _1506203, _1506205, _1506207] : [hAPP(_1506199, _1506201) = c_Option_Ooption_ONone(_1506203), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506205, tc_HOL_Obool)), c_Map_Odom(_1506205, _1506203, _1506199)), hAPP(hAPP(c_Set_Oinsert(_1506205), _1506201), _1506207)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506205, tc_HOL_Obool)), c_Map_Odom(_1506205, _1506203, _1506199)), _1506207))], (20454 ^ _775828) ^ [_1127293] : [-(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)))), _1127293) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1127293)))], (26747 ^ _775828) ^ [_1248525, _1248527] : [c_Relation_Oirrefl(_1248525, _1248527), 26750 ^ _775828 : [(26751 ^ _775828) ^ [_1248607] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1248525, _1248525)), hAPP(hAPP(c_Product__Type_OPair(_1248525, _1248525), _1248607), _1248607)), _1248527))]]], (51184 ^ _775828) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (39971 ^ _775828) ^ [_1542276, _1542278, _1542280, _1542282, _1542284, _1542286, _1542288] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542276, tc_fun(_1542278, tc_fun(_1542280, tc_HOL_Obool))), _1542282), _1542284), _1542286), _1542288)), 39975 ^ _775828 : [(39978 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1542284, 39974 ^ [_1542276, _1542278, _1542280, _1542282, _1542284, _1542286, _1542288]), _1542286), _1542288)))], (39976 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542276), 39974 ^ [_1542276, _1542278, _1542280, _1542282, _1542284, _1542286, _1542288]), _1542282)))]]], (19194 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (16268 ^ _775828) ^ [_1052123, _1052125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052123)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1052123), _1052125)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1052123)), hAPP(c_Int_Onat, _1052125)))], (27354 ^ _775828) ^ [_1260864, _1260866, _1260868, _1260870] : [hBOOL(hAPP(hAPP(c_member(_1260864), _1260866), hAPP(c_Relation_ORange(_1260868, _1260864), _1260870))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1260868, _1260864)), hAPP(hAPP(c_Product__Type_OPair(_1260868, _1260864), 27357 ^ [_1260864, _1260866, _1260868, _1260870]), _1260866)), _1260870)))], (51134 ^ _775828) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (29781 ^ _775828) ^ [_1316958, _1316960, _1316962, _1316964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316958, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1316958), _1316960), _1316962)), _1316964)), 29784 ^ _775828 : [(29787 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316958, tc_HOL_Obool)), _1316962), _1316964)))], (29785 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316958), _1316960), _1316964)))]]], (19192 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (17209 ^ _775828) ^ [_1070209, _1070211] : [class_Groups_Oordered__ab__group__add__abs(_1070209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070209), hAPP(c_Groups_Ouminus__class_Ouminus(_1070209), hAPP(c_Groups_Oabs__class_Oabs(_1070209), _1070211))), c_Groups_Ozero__class_Ozero(_1070209))))], (47641 ^ _775828) ^ [_1726379, _1726381, _1726383, _1726385, _1726387, _1726389] : [-(hAPP(c_List_Olist_Olist__case(_1726379, _1726381, _1726383, _1726385), hAPP(hAPP(c_List_Olist_OCons(_1726381), _1726387), _1726389)) = hAPP(hAPP(_1726385, _1726387), _1726389))], (21966 ^ _775828) ^ [_1157121, _1157123, _1157125, _1157127] : [class_Fields_Olinordered__field__inverse__zero(_1157121), class_Int_Onumber(_1157121), 21973 ^ _775828 : [(21974 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157121), _1157125), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)))), 21977 ^ _775828 : [(21984 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), c_Groups_Ozero__class_Ozero(_1157121)), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)))), 21987 ^ _775828 : [(21994 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)), c_Groups_Ozero__class_Ozero(_1157121)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157123), c_Groups_Ozero__class_Ozero(_1157121))))], (21988 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)), c_Groups_Ozero__class_Ozero(_1157121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157121), _1157123), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)))))]]], (21978 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), c_Groups_Ozero__class_Ozero(_1157121)), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157121), _1157123), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))), _1157125)))]]], (22000 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157121), _1157125), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))))), 22003 ^ _775828 : [(22006 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157121), _1157123), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))), _1157125))], (22004 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), c_Groups_Ozero__class_Ozero(_1157121)), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))))]], 22007 ^ _775828 : [(22010 ^ _775828) ^ [] : [22011 ^ _775828 : [(22014 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157121), _1157123), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127))))], (22012 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)), c_Groups_Ozero__class_Ozero(_1157121))))]], 22015 ^ _775828 : [(22018 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157121), _1157123), c_Groups_Ozero__class_Ozero(_1157121)))], (22016 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)), c_Groups_Ozero__class_Ozero(_1157121)))]]], (22008 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157121), c_Groups_Ozero__class_Ozero(_1157121)), hAPP(c_Int_Onumber__class_Onumber__of(_1157121), _1157127)))]]]]], (5382 ^ _775828) ^ [_858056, _858058, _858060, _858062, _858064, _858066] : [-(c_COMBC(_858066, _858062, _858058) = c_COMBC(_858064, _858060, _858056)), _858066 = _858064, _858062 = _858060, _858058 = _858056], (39066 ^ _775828) ^ [_1519585, _1519587, _1519589, _1519591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1519585), hAPP(c_Set_Oimage(_1519587, _1519585, _1519589), _1519591))), hAPP(c_Finite__Set_Ocard(_1519587), _1519591))), c_Fun_Oinj__on(_1519587, _1519585, _1519589, _1519591)], (5977 ^ _775828) ^ [_870960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870960), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47105 ^ _775828) ^ [_1714225, _1714227, _1714229, _1714231] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714225), tc_List_Olist(_1714225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714225), tc_List_Olist(_1714225)), _1714227), _1714229)), c_List_Olex(_1714225, _1714231)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714225), tc_List_Olist(_1714225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714225), tc_List_Olist(_1714225)), _1714227), _1714229)), c_List_Olexord(_1714225, _1714231))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714225)), _1714227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714225)), _1714229)], (20610 ^ _775828) ^ [_1129919, _1129921] : [class_Rings_Oring__1__no__zero__divisors(_1129919), 20613 ^ _775828 : [(20614 ^ _775828) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1129919), _1129921), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1129919), -(_1129921 = c_Groups_Oone__class_Oone(_1129919)), -(_1129921 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129919), c_Groups_Oone__class_Oone(_1129919)))], (20624 ^ _775828) ^ [] : [20625 ^ _775828 : [(20628 ^ _775828) ^ [] : [_1129921 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129919), c_Groups_Oone__class_Oone(_1129919))], (20626 ^ _775828) ^ [] : [_1129921 = c_Groups_Oone__class_Oone(_1129919)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1129919), _1129921), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1129919))]]], (46546 ^ _775828) ^ [_1699610, _1699612, _1699614] : [-(hBOOL(hAPP(c_List_Odistinct(_1699610), hAPP(hAPP(c_List_Olist_OCons(_1699610), _1699612), _1699614)))), -(hBOOL(hAPP(hAPP(c_member(_1699610), _1699612), hAPP(c_List_Oset(_1699610), _1699614)))), hBOOL(hAPP(c_List_Odistinct(_1699610), _1699614))], (48603 ^ _775828) ^ [_1751088, _1751090, _1751092] : [-(_1751088 = c_List_Olist_ONil(_1751090)), -(hAPP(c_List_Ohd(_1751090), hAPP(hAPP(c_List_Oappend(_1751090), _1751088), _1751092)) = hAPP(c_List_Ohd(_1751090), _1751088))], (38838 ^ _775828) ^ [_1515223, _1515225, _1515227, _1515229] : [38840 ^ _775828 : [(38844 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515223), 38842 ^ [_1515223, _1515225, _1515227, _1515229]), _1515229)))], (38846 ^ _775828) ^ [] : [-(hAPP(_1515227, 38839 ^ [_1515223, _1515225, _1515227, _1515229]) = hAPP(_1515227, 38842 ^ [_1515223, _1515225, _1515227, _1515229]))], (38848 ^ _775828) ^ [] : [38839 ^ [_1515223, _1515225, _1515227, _1515229] = 38842 ^ [_1515223, _1515225, _1515227, _1515229]], (38841 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515223), 38839 ^ [_1515223, _1515225, _1515227, _1515229]), _1515229)))]], -(c_Fun_Oinj__on(_1515223, _1515225, _1515227, _1515229))], (47475 ^ _775828) ^ [_1722766, _1722768, _1722770, _1722772] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722766, tc_HOL_Obool)), hAPP(c_List_Oset(_1722766), hAPP(hAPP(c_List_Olist__update(_1722766, _1722768), _1722770), _1722772))), hAPP(hAPP(c_Set_Oinsert(_1722766), _1722772), hAPP(c_List_Oset(_1722766), _1722768)))))], (29345 ^ _775828) ^ [_1307974, _1307976, _1307978, _1307980] : [29346 ^ _775828 : [(29349 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1307974), _1307976), _1307980))], (29347 ^ _775828) ^ [] : [_1307976 = _1307978]], -(hBOOL(hAPP(hAPP(c_member(_1307974), _1307976), hAPP(hAPP(c_Set_Oinsert(_1307974), _1307978), _1307980))))], (4936 ^ _775828) ^ [_851323, _851325, _851327, _851329, _851331, _851333, _851335, _851337] : [-(c_Map_Omap__add(_851337, _851333, _851329, _851325) = c_Map_Omap__add(_851335, _851331, _851327, _851323)), _851337 = _851335, _851333 = _851331, _851329 = _851327, _851325 = _851323], (8166 ^ _775828) ^ [_907081, _907083] : [-(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), _907081))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907083))))], (20102 ^ _775828) ^ [_1121162] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1121162)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1121162)))], (48795 ^ _775828) ^ [_1754728] : [class_Groups_Omonoid__add(_1754728), -(c_List_Omonoid__add__class_Olistsum(_1754728) = c_List_Ofoldl(_1754728, _1754728, c_Groups_Oplus__class_Oplus(_1754728), c_Groups_Ozero__class_Ozero(_1754728)))], (11991 ^ _775828) ^ [_973362, _973364, _973366] : [class_Rings_Olinordered__idom(_973362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973362), c_Groups_Ozero__class_Ozero(_973362)), _973364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973362), c_Groups_Ozero__class_Ozero(_973362)), _973366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973362), _973366), c_Groups_Oone__class_Oone(_973362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973362), _973364), _973366)), _973364)))], (34289 ^ _775828) ^ [_1414416, _1414418, _1414420] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414416, tc_HOL_Obool)), _1414418), _1414420) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414416, tc_HOL_Obool)), _1414418), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1414416, tc_HOL_Obool)), _1414420)))], (20692 ^ _775828) ^ [_1131450, _1131452, _1131454] : [class_Rings_Olinordered__idom(_1131450), 20695 ^ _775828 : [(20696 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131450), c_Groups_Ozero__class_Ozero(_1131450)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131450), hAPP(hAPP(c_Power_Opower__class_Opower(_1131450), _1131452), 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(_1131450), _1131454), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1131452 = c_Groups_Ozero__class_Ozero(_1131450), _1131454 = c_Groups_Ozero__class_Ozero(_1131450)], (20706 ^ _775828) ^ [] : [20707 ^ _775828 : [(20710 ^ _775828) ^ [] : [-(_1131454 = c_Groups_Ozero__class_Ozero(_1131450))], (20708 ^ _775828) ^ [] : [-(_1131452 = c_Groups_Ozero__class_Ozero(_1131450))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131450), c_Groups_Ozero__class_Ozero(_1131450)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131450), hAPP(hAPP(c_Power_Opower__class_Opower(_1131450), _1131452), 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(_1131450), _1131454), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (47351 ^ _775828) ^ [_1720472, _1720474, _1720476, _1720478, _1720480] : [-(hAPP(hAPP(c_List_Olist__update(_1720472, hAPP(hAPP(c_List_Olist_OCons(_1720472), _1720474), _1720476)), hAPP(c_Nat_OSuc, _1720478)), _1720480) = hAPP(hAPP(c_List_Olist_OCons(_1720472), _1720474), hAPP(hAPP(c_List_Olist__update(_1720472, _1720476), _1720478), _1720480)))], (28575 ^ _775828) ^ [_1289028, _1289030, _1289032, _1289034] : [class_Lattices_Osemilattice__sup(_1289028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289028), _1289030), _1289032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289028), _1289034), _1289032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289028), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289028), _1289030), _1289034)), _1289032)))], (13364 ^ _775828) ^ [_997456, _997458, _997460, _997462, _997464, _997466] : [class_Divides_Osemiring__div(_997456), c_Divides_Odiv__class_Omod(_997456, _997458, _997460) = c_Divides_Odiv__class_Omod(_997456, _997462, _997460), c_Divides_Odiv__class_Omod(_997456, _997464, _997460) = c_Divides_Odiv__class_Omod(_997456, _997466, _997460), -(c_Divides_Odiv__class_Omod(_997456, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997456), _997458), _997464), _997460) = c_Divides_Odiv__class_Omod(_997456, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997456), _997462), _997466), _997460))], (51208 ^ _775828) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (25467 ^ _775828) ^ [_1225050, _1225052, _1225054, _1225056, _1225058, _1225060, _1225062] : [-(c_New__Random__Sequence_Opos__decr__bind(_1225050, _1225052, _1225054, _1225056, _1225058, _1225060, _1225062) = c_New__DSequence_Opos__decr__bind(_1225050, _1225052, hAPP(hAPP(hAPP(_1225054, _1225058), _1225060), _1225062), hAPP(hAPP(c_COMBC(_1225050, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1225052))), hAPP(hAPP(c_COMBC(_1225050, 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(_1225052)))), hAPP(hAPP(c_COMBC(_1225050, 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(_1225052))))), _1225056), _1225058)), _1225060)), _1225062)))], (39460 ^ _775828) ^ [_1528997, _1528999, _1529001, _1529003, _1529005, _1529007] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528997, tc_fun(_1528999, tc_HOL_Obool)), _1529001), hAPP(hAPP(c_COMBC(_1528997, tc_fun(_1529003, tc_fun(_1528999, tc_HOL_Obool)), tc_fun(_1528999, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529003, tc_HOL_Obool), tc_fun(tc_fun(_1529003, tc_fun(_1528999, tc_HOL_Obool)), tc_fun(_1528999, tc_HOL_Obool)), _1528997), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529003, tc_fun(_1528999, tc_HOL_Obool))), _1529005)), _1529007)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529003, tc_fun(_1528999, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528997, tc_fun(_1529003, tc_HOL_Obool)), _1529001), _1529005)), _1529007))], (40177 ^ _775828) ^ [_1546030, _1546032] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1546030, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1546030, tc_HOL_Obool))), _1546032) = c_Orderings_Otop__class_Otop(tc_fun(_1546030, tc_HOL_Obool)))], (6660 ^ _775828) ^ [_881475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _881475)), -(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), _881475))))], (8223 ^ _775828) ^ [_907966, _907968, _907970] : [class_Orderings_Oorder(_907966), 8226 ^ _775828 : [(8235 ^ _775828) ^ [] : [-(_907968 = _907970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907966), _907968), _907970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907966), _907970), _907968))], (8227 ^ _775828) ^ [] : [_907968 = _907970, 8230 ^ _775828 : [(8233 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907966), _907970), _907968)))], (8231 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907966), _907968), _907970)))]]]]], (47837 ^ _775828) ^ [_1731294, _1731296, _1731298, _1731300] : [-(hAPP(hAPP(c_List_Oappend(_1731294), hAPP(hAPP(c_List_Olist_OCons(_1731294), _1731296), _1731298)), _1731300) = hAPP(hAPP(c_List_Olist_OCons(_1731294), _1731296), hAPP(hAPP(c_List_Oappend(_1731294), _1731298), _1731300)))], (25899 ^ _775828) ^ [_1233357, _1233359] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233357), _1233359)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233359), _1233357)), -(_1233357 = _1233359)], (48146 ^ _775828) ^ [_1738547, _1738549, _1738551, _1738553, _1738555] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1738547), tc_List_Olist(_1738547))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1738547), tc_List_Olist(_1738547)), hAPP(hAPP(c_List_Oappend(_1738547), _1738549), _1738551)), hAPP(hAPP(c_List_Oappend(_1738547), _1738549), _1738553))), c_List_Olexord(_1738547, _1738555))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738547, _1738547)), hAPP(hAPP(c_Product__Type_OPair(_1738547, _1738547), 48151 ^ [_1738547, _1738549, _1738551, _1738553, _1738555]), 48151 ^ [_1738547, _1738549, _1738551, _1738553, _1738555])), _1738555))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1738547), tc_List_Olist(_1738547))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1738547), tc_List_Olist(_1738547)), _1738551), _1738553)), c_List_Olexord(_1738547, _1738555))))], (2766 ^ _775828) ^ [_817044, _817046, _817048, _817050, _817052, _817054, _817056, _817058] : [-(c_New__Random__Sequence_Opos__empty(_817058, _817054, _817050, _817046) = c_New__Random__Sequence_Opos__empty(_817056, _817052, _817048, _817044)), _817058 = _817056, _817054 = _817052, _817050 = _817048, _817046 = _817044], (3056 ^ _775828) ^ [_821789, _821791, _821793, _821795, _821797, _821799, _821801, _821803, _821805, _821807] : [-(c_Predicate_Opred__comp(_821807, _821803, _821799, _821795, _821791) = c_Predicate_Opred__comp(_821805, _821801, _821797, _821793, _821789)), _821807 = _821805, _821803 = _821801, _821799 = _821797, _821795 = _821793, _821791 = _821789], (13676 ^ _775828) ^ [_1003499, _1003501, _1003503, _1003505] : [c_Com_Ocom_OAss(_1003499, _1003501) = c_Com_Ocom_OSemi(_1003503, _1003505)], (50341 ^ _775828) ^ [_1787564, _1787566, _1787568, _1787570] : [hAPP(c_List_Orev(_1787564), _1787566) = hAPP(hAPP(c_List_Olist_OCons(_1787564), _1787568), _1787570), -(_1787566 = hAPP(hAPP(c_List_Oappend(_1787564), hAPP(c_List_Orev(_1787564), _1787570)), hAPP(hAPP(c_List_Olist_OCons(_1787564), _1787568), c_List_Olist_ONil(_1787564))))], (25715 ^ _775828) ^ [_1230399, _1230401, _1230403, _1230405] : [class_Divides_Osemiring__div(_1230399), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230399), _1230401), _1230403)), 25722 ^ _775828 : [(25729 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230399), _1230401), _1230405)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230399), _1230401), c_Divides_Odiv__class_Omod(_1230399, _1230405, _1230403))))], (25723 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230399), _1230401), c_Divides_Odiv__class_Omod(_1230399, _1230405, _1230403))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230399), _1230401), _1230405)))]]], (17545 ^ _775828) ^ [_1076201, _1076203] : [-(_1076201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076203), _1076201) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076203), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1076203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076201), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (2630 ^ _775828) ^ [_814762, _814764, _814766, _814768, _814770, _814772, _814774, _814776] : [-(c_Product__Type_Ocurry(_814776, _814772, _814768, _814764) = c_Product__Type_Ocurry(_814774, _814770, _814766, _814762)), _814776 = _814774, _814772 = _814770, _814768 = _814766, _814764 = _814762], (51102 ^ _775828) ^ [_1804297, _1804299] : [class_Orderings_Obot(_1804297), -(class_Orderings_Obot(tc_fun(_1804299, _1804297)))], (6258 ^ _775828) ^ [_875471, _875473, _875475] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875471, _875473)), _875475), hAPP(hAPP(hAPP(c_Natural_Oupdate, _875475), _875471), hAPP(_875473, _875475)))))], (23650 ^ _775828) ^ [_1190016, _1190018, _1190020] : [class_Orderings_Olinorder(_1190016), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190016), _1190018), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190016), _1190018), _1190020))))], (50728 ^ _775828) ^ [_1797149, _1797151] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797149)), c_List_Oremdups(_1797149, c_List_Oconcat(_1797149, _1797151))) = hAPP(c_Finite__Set_Ocard(_1797149), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1797149), tc_fun(_1797149, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1797149)), _1797151)), c_List_Oset(_1797149))))], (12655 ^ _775828) ^ [_984689, _984691] : [class_Rings_Oring__1(_984689), -(hBOOL(hAPP(hAPP(c_member(_984689), hAPP(c_Int_Oring__1__class_Oof__int(_984689), _984691)), c_Int_Oring__1__class_OInts(_984689))))], (25206 ^ _775828) ^ [_1220586] : [25208 ^ _775828 : [(25211 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25207 ^ [_1220586]))], (25209 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 25207 ^ [_1220586]), _1220586)))]], -(c_Nat__Transfer_Onat__set(_1220586))], (48419 ^ _775828) ^ [_1746397, _1746399, _1746401, _1746403, _1746405] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1746397, _1746399)), _1746401), hAPP(hAPP(c_List_Ozip(_1746397, _1746399), _1746403), _1746405)) = hAPP(hAPP(c_List_Ozip(_1746397, _1746399), hAPP(hAPP(c_List_Odrop(_1746397), _1746401), _1746403)), hAPP(hAPP(c_List_Odrop(_1746399), _1746401), _1746405)))], (45552 ^ _775828) ^ [_1673874, _1673876, _1673878, _1673880, _1673882, _1673884] : [hAPP(_1673874, _1673876) = c_Option_Ooption_ONone(_1673878), -(c_Map_Omap__comp(_1673878, _1673880, _1673882, _1673884, _1673874, _1673876) = c_Option_Ooption_ONone(_1673880))], (40584 ^ _775828) ^ [_1555890, _1555892] : [c_Equiv__Relations_Oequivp(_1555890, hAPP(hAPP(c_COMBC(_1555890, tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_fun(_1555890, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555890, tc_fun(tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_fun(_1555890, tc_HOL_Obool)), _1555890), c_COMBC(_1555890, tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555890, tc_prod(_1555890, _1555890)), tc_fun(_1555890, tc_fun(tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_HOL_Obool)), _1555890), hAPP(c_COMBB(tc_prod(_1555890, _1555890), tc_fun(tc_fun(tc_prod(_1555890, _1555890), tc_HOL_Obool), tc_HOL_Obool), _1555890), c_member(tc_prod(_1555890, _1555890)))), c_Product__Type_OPair(_1555890, _1555890)))), _1555892)), -(c_Equiv__Relations_Oequiv(_1555890, c_Orderings_Otop__class_Otop(tc_fun(_1555890, tc_HOL_Obool)), _1555892))], (38338 ^ _775828) ^ [_1503953, _1503955, _1503957] : [class_Orderings_Oorder(_1503953), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503953, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1503953, _1503955, _1503957)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1503953), _1503957)) = c_Orderings_Obot__class_Obot(tc_fun(_1503953, tc_HOL_Obool)))], (24194 ^ _775828) ^ [_1199586, _1199588, _1199590, _1199592] : [class_Orderings_Olinorder(_1199586), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199586), _1199588), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199586), _1199590), _1199592)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199586), _1199590), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199586), _1199588), _1199592)))], (40859 ^ _775828) ^ [_1561961, _1561963, _1561965, _1561967] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561961, _1561961), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1561963), _1561965)), _1561967) = hAPP(hAPP(c_Relation_Orel__comp(_1561961, _1561961, _1561961), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561961, _1561961), tc_HOL_Obool), _1561963), _1561967)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1561961, _1561961), tc_HOL_Obool), _1561965), _1561967)))], (27204 ^ _775828) ^ [_1256974, _1256976, _1256978, _1256980] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1256974, _1256976), _1256978), _1256980) = hAPP(c_Set_OCollect(tc_prod(_1256976, _1256976)), hAPP(c_Product__Type_Oprod_Oprod__case(_1256976, _1256976, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1256976, tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_fun(_1256976, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256976, tc_fun(tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_fun(_1256976, tc_HOL_Obool)), _1256976), c_COMBC(_1256976, tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256976, tc_prod(_1256974, _1256974)), tc_fun(_1256976, tc_fun(tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_HOL_Obool)), _1256976), hAPP(c_COMBB(tc_prod(_1256974, _1256974), tc_fun(tc_fun(tc_prod(_1256974, _1256974), tc_HOL_Obool), tc_HOL_Obool), _1256976), c_member(tc_prod(_1256974, _1256974)))), hAPP(hAPP(c_COMBC(_1256976, tc_fun(_1256976, _1256974), tc_fun(_1256976, tc_prod(_1256974, _1256974))), hAPP(hAPP(c_COMBB(tc_fun(_1256974, tc_prod(_1256974, _1256974)), tc_fun(tc_fun(_1256976, _1256974), tc_fun(_1256976, tc_prod(_1256974, _1256974))), _1256976), c_COMBB(_1256974, tc_prod(_1256974, _1256974), _1256976)), hAPP(hAPP(c_COMBB(_1256974, tc_fun(_1256974, tc_prod(_1256974, _1256974)), _1256976), c_Product__Type_OPair(_1256974, _1256974)), _1256980))), _1256980)))), _1256978))))], (41576 ^ _775828) ^ [_1580320, _1580322, _1580324, _1580326, _1580328, _1580330, _1580332, _1580334] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1580320, _1580322), tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1580320, _1580322), _1580328), hAPP(c_COMBK(tc_fun(_1580322, tc_HOL_Obool), _1580320), _1580330))), hAPP(c_Product__Type_Oprod_Oprod__case(_1580320, _1580322, tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1580320, tc_fun(_1580322, tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool))), tc_fun(_1580322, tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool)), tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool)), tc_fun(tc_fun(_1580322, tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool))), tc_fun(_1580322, tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool))), _1580320), c_COMBB(tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool)), tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool), _1580322)), hAPP(hAPP(c_COMBB(tc_fun(_1580324, tc_HOL_Obool), tc_fun(tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool)), tc_fun(tc_prod(_1580324, _1580326), tc_HOL_Obool)), _1580320), c_Product__Type_OSigma(_1580324, _1580326)), _1580332))), hAPP(hAPP(c_COMBB(tc_fun(_1580326, tc_HOL_Obool), tc_fun(_1580324, tc_fun(_1580326, tc_HOL_Obool)), _1580322), c_COMBK(tc_fun(_1580326, tc_HOL_Obool), _1580324)), _1580334)))) = hAPP(hAPP(c_Product__Type_OSigma(_1580324, _1580326), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580320, tc_fun(_1580324, tc_HOL_Obool)), _1580328), _1580332)), hAPP(c_COMBK(tc_fun(_1580326, tc_HOL_Obool), _1580324), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580322, tc_fun(_1580326, tc_HOL_Obool)), _1580330), _1580334))))], (21950 ^ _775828) ^ [_1156723, _1156725, _1156727] : [class_Int_Onumber__ring(_1156723), 21953 ^ _775828 : [(21960 ^ _775828) ^ [] : [-(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), _1156725)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156723), hAPP(c_Int_Onumber__class_Onumber__of(_1156723), _1156727)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156725))) = c_Groups_Oone__class_Oone(_1156723))], (21954 ^ _775828) ^ [] : [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), _1156725))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156723), hAPP(c_Int_Onumber__class_Onumber__of(_1156723), _1156727)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156725))) = hAPP(hAPP(c_HOL_OLet(_1156723, _1156723), hAPP(hAPP(c_Power_Opower__class_Opower(_1156723), hAPP(c_Int_Onumber__class_Onumber__of(_1156723), _1156727)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156725))), hAPP(hAPP(c_COMBS(_1156723, _1156723, _1156723), hAPP(hAPP(c_COMBB(_1156723, tc_fun(_1156723, _1156723), _1156723), c_Groups_Otimes__class_Otimes(_1156723)), hAPP(c_Groups_Otimes__class_Otimes(_1156723), hAPP(c_Int_Onumber__class_Onumber__of(_1156723), _1156727)))), c_COMBI(_1156723))))]]], (7011 ^ _775828) ^ [_886895] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _886895)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _886895))], (51428 ^ _775828) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (44844 ^ _775828) ^ [_1658077, _1658079, _1658081, _1658083] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658077, tc_fun(_1658079, tc_HOL_Obool)), _1658081), _1658083) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1658079, tc_HOL_Obool), hAPP(c_Set_Oimage(_1658077, tc_fun(_1658079, tc_HOL_Obool), _1658083), _1658081)))], (21572 ^ _775828) ^ [_1149356, _1149358] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149356), _1149358), hAPP(c_Int_Onumber__class_Onumber__of(_1149356), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1149356)), class_Fields_Ofield__inverse__zero(_1149356), class_Int_Onumber__ring(_1149356)], (340 ^ _775828) ^ [_780828, _780830] : [-(class_Fields_Olinordered__field(_780828)), _780830 = _780828, class_Fields_Olinordered__field(_780830)], (18511 ^ _775828) ^ [_1094193, _1094195] : 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hAPP(hAPP(c_Orderings_Oord__class_Omax(_1664330), _1664334), _1664336))))], (45918 ^ _775828) ^ [_1682501, _1682503, _1682505, _1682507, _1682509] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1682501, _1682503)), hAPP(hAPP(c_Product__Type_OPair(_1682501, _1682503), _1682505), _1682507)), hAPP(c_List_Oset(tc_prod(_1682501, _1682503)), _1682509))), -(hAPP(c_Map_Omap__of(_1682501, _1682503, _1682509), _1682505) = hAPP(c_Option_Ooption_OSome(_1682503), 45921 ^ [_1682501, _1682503, _1682505, _1682507, _1682509]))], (49136 ^ _775828) ^ [_1762269, _1762271, _1762273, _1762275] : [-(_1762269 = c_List_Olist_ONil(_1762271)), -(c_List_Olast(_1762273, hAPP(hAPP(c_List_Omap(_1762271, _1762273), _1762275), _1762269)) = hAPP(_1762275, c_List_Olast(_1762271, _1762269)))], (51278 ^ _775828) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (24182 ^ _775828) ^ [_1199336, _1199338, _1199340] : [class_Orderings_Olinorder(_1199336), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199336), _1199338), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199336), _1199338), _1199340)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199336), _1199338), _1199340))], (12895 ^ _775828) ^ [_988664, _988666, _988668, _988670, _988672] : [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), _988664), _988666)), _988668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _988664), _988670)), _988672))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988672), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988664), _988672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988664), _988668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _988670), _988666)))], (28167 ^ _775828) ^ [_1280618, _1280620, _1280622, _1280624] : [28168 ^ 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hAPP(c_Relation_Oconverse(tc_List_Olist(_1739107), tc_List_Olist(_1739107)), c_List_Olistrel1(_1739107, _1739109)))], (19246 ^ _775828) ^ [_1106825] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106825) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106825), c_Int_OPls)))], (49297 ^ _775828) ^ [_1765549, _1765551, _1765553] : [-(c_List_Obutlast(_1765549, hAPP(hAPP(c_List_Odrop(_1765549), _1765551), _1765553)) = hAPP(hAPP(c_List_Odrop(_1765549), _1765551), c_List_Obutlast(_1765549, _1765553)))], (1180 ^ _775828) ^ [_793196, _793198] : [-(class_Rings_Oring__1(_793196)), _793198 = _793196, class_Rings_Oring__1(_793198)], (13358 ^ _775828) ^ [_997321, _997323, _997325, _997327] : [class_Divides_Osemiring__div(_997321), -(c_Divides_Odiv__class_Omod(_997321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997321), c_Divides_Odiv__class_Omod(_997321, _997323, _997325)), _997327), _997325) = c_Divides_Odiv__class_Omod(_997321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997321), _997323), _997327), _997325))], (25339 ^ _775828) ^ [_1222766, _1222768, _1222770, _1222772, _1222774, _1222776] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1222766, _1222768, _1222770, _1222772), _1222774), _1222776) = hAPP(_1222772, hAPP(hAPP(c_Product__Type_OPair(_1222766, _1222768), _1222774), _1222776)))], (10458 ^ _775828) ^ [_946097, _946099] : [class_Rings_Ocomm__semiring__1(_946097), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946097), _946099), c_Groups_Ozero__class_Ozero(_946097)) = _946099)], (48020 ^ _775828) ^ [_1735346, _1735348, _1735350] : [_1735350 = c_List_Olist_ONil(_1735348), -(_1735346 = hAPP(hAPP(c_List_Oappend(_1735348), _1735346), _1735350))], (50814 ^ _775828) ^ [_1798651, _1798653, _1798655] : [-(c_List_Oremdups(_1798651, hAPP(c_List_Ofilter(_1798651, _1798653), _1798655)) = hAPP(c_List_Ofilter(_1798651, _1798653), c_List_Oremdups(_1798651, _1798655)))], (28842 ^ _775828) ^ 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_956146)], (28393 ^ _775828) ^ [_1285662, _1285664, _1285666, _1285668] : [hBOOL(hAPP(_1285662, _1285664)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285666, tc_HOL_Obool)), _1285662), _1285668), _1285664)))], (11674 ^ _775828) ^ [_967555, _967557] : [11675 ^ _775828 : [(11678 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967557))], (11676 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967555))]], -(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), _967555), _967557))))], (28140 ^ _775828) ^ [_1280148, _1280150, _1280152, _1280154] : [28142 ^ _775828 : [(28145 ^ _775828) ^ [] : [c_Wellfounded_Owf(_1280150, hAPP(_1280152, 28141 ^ [_1280148, _1280150, _1280152, _1280154]))], (28143 ^ _775828) ^ [] : [-(hBOOL(hAPP(_1280148, 28141 ^ [_1280148, _1280150, _1280152, _1280154])))]], -(c_Wellfounded_Owf(tc_prod(_1280154, _1280150), c_Recdef_Osame__fst(_1280154, _1280150, _1280148, _1280152)))], (10726 ^ _775828) ^ [_951068, _951070] : [class_Groups_Omonoid__mult(_951068), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951068), _951070), c_Groups_Oone__class_Oone(_951068)) = _951070)], (42184 ^ _775828) ^ [_1594910, _1594912, _1594914, _1594916, _1594918] : [c_Relation_Orefl__on(_1594910, _1594912, _1594914), c_Relation_Orefl__on(_1594910, _1594916, _1594918), -(c_Relation_Orefl__on(_1594910, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1594910, tc_HOL_Obool)), _1594912), _1594916), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594910, _1594910), tc_HOL_Obool)), _1594914), _1594918)))], (25124 ^ _775828) ^ [_1219285, _1219287, _1219289, _1219291, _1219293, _1219295] : [-(c_Nitpick_Opair__box_Opair__box__case(_1219285, _1219287, _1219289, _1219291, c_Nitpick_Opair__box_OPairBox(_1219285, _1219287, _1219293, _1219295)) = hAPP(hAPP(_1219291, _1219293), _1219295))], (8995 ^ _775828) ^ [_919705, _919707, _919709] : [class_Groups_Oordered__ab__group__add(_919705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919705), _919707), _919709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919705), hAPP(c_Groups_Ouminus__class_Ouminus(_919705), _919709)), hAPP(c_Groups_Ouminus__class_Ouminus(_919705), _919707))))], (28443 ^ _775828) ^ [_1286699, _1286701, _1286703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286699, tc_HOL_Obool)), _1286701), _1286703)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286699, tc_HOL_Obool)), _1286701), _1286703) = _1286703)], (24304 ^ _775828) ^ [_1202221, _1202223, _1202225] : [class_Int_Onumber(_1202221), class_Orderings_Oord(_1202221), 24311 ^ _775828 : [(24318 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202221), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202223)), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202225)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202221), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202223)), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202225)) = hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202223))], (24312 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202221), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202223)), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202225))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202221), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202223)), hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202225)) = hAPP(c_Int_Onumber__class_Onumber__of(_1202221), _1202225))]]], (10058 ^ _775828) ^ [_938569, _938571] : [10059 ^ _775828 : [(10060 ^ _775828) ^ [_938619] : [_938571 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938569), _938619)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938569), _938571)))], (4898 ^ _775828) ^ [_850700, _850702, _850704, _850706] : [-(c_Product__Type_Ofst(_850706, _850702) = c_Product__Type_Ofst(_850704, _850700)), _850706 = _850704, _850702 = _850700], (5014 ^ _775828) ^ [_852526, _852528, _852530, _852532, _852534, _852536] : [-(c_List_Oremove1(_852536, _852532, _852528) = c_List_Oremove1(_852534, _852530, _852526)), _852536 = _852534, _852532 = _852530, _852528 = _852526], (29869 ^ _775828) ^ [_1318896, _1318898, _1318900, _1318902] : [hBOOL(hAPP(hAPP(c_member(_1318896), _1318898), _1318900)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318896, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1318896), _1318898), _1318902)), _1318900) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318896, tc_HOL_Obool)), _1318902), _1318900))], (12427 ^ _775828) ^ [_980863] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _980863) = _980863)], (15420 ^ _775828) ^ [_1035041, _1035043, _1035045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035041), _1035043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035041), _1035045)), 15427 ^ _775828 : [(15434 ^ _775828) ^ [] : [_1035043 = _1035045, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035043), _1035041) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035045), _1035041))], (15428 ^ _775828) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035043), _1035041) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035045), _1035041), -(_1035043 = _1035045)]]], (21150 ^ _775828) ^ [_1141932, _1141934, _1141936, _1141938, _1141940] : [class_Groups_Ominus(_1141932), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1141934, _1141932)), _1141936), _1141938), _1141940) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141932), hAPP(_1141936, _1141940)), hAPP(_1141938, _1141940)))], (16010 ^ _775828) ^ [_1046845, _1046847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046845), hAPP(c_Nat_OSuc, _1046847))), _1046845)))], (39818 ^ _775828) ^ [_1538391, _1538393] : [_1538391 = _1538393, -(hAPP(c_Int_ORep__Integ, _1538391) = hAPP(c_Int_ORep__Integ, _1538393))], (25889 ^ _775828) ^ [_1233204, _1233206, _1233208] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233204), _1233206)), _1233206 = _1233208, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233204), _1233208)))], (35489 ^ _775828) ^ [_1442534, _1442536, _1442538] : [class_Orderings_Oorder(_1442534), 35492 ^ _775828 : [(35499 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442534), _1442536), _1442538))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1442534, _1442536, _1442538) = c_Orderings_Obot__class_Obot(tc_fun(_1442534, tc_HOL_Obool)))], (35493 ^ _775828) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1442534, _1442536, _1442538) = c_Orderings_Obot__class_Obot(tc_fun(_1442534, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442534), _1442536), _1442538))]]], (44461 ^ _775828) ^ [_1649119, _1649121, _1649123, _1649125, _1649127] : [_1649119 = c_Orderings_Obot__class_Obot(tc_fun(_1649121, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649121, tc_fun(_1649123, tc_HOL_Obool)), _1649119), hAPP(hAPP(c_COMBC(_1649121, tc_fun(_1649123, tc_HOL_Obool), tc_fun(_1649123, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649123, tc_HOL_Obool), tc_fun(tc_fun(_1649123, tc_HOL_Obool), tc_fun(_1649123, tc_HOL_Obool)), _1649121), c_Groups_Ominus__class_Ominus(tc_fun(_1649123, tc_HOL_Obool))), _1649125)), _1649127)) = c_Orderings_Otop__class_Otop(tc_fun(_1649123, tc_HOL_Obool)))], (51026 ^ _775828) ^ [_1803299, _1803301] : [class_Lattices_Obounded__lattice(_1803299), -(class_Lattices_Obounded__lattice__top(tc_fun(_1803301, _1803299)))], (10270 ^ _775828) ^ [_942239, _942241, _942243] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942239), _942241)), _942243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942241), _942243)))], (9111 ^ _775828) ^ [_921471, _921473] : [-(hAPP(c_Int_Onat, _921471) = _921473), 9114 ^ _775828 : [(9117 ^ _775828) ^ [] : [_921471 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921473)], (9115 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921471)))]], 9118 ^ _775828 : [(9121 ^ _775828) ^ [] : [_921473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9119 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _921471))]]], (6681 ^ _775828) ^ [_881822, _881824] : [class_Rings_Osemiring__1(_881822), hBOOL(hAPP(hAPP(c_member(_881822), _881824), c_Nat_Osemiring__1__class_ONats(_881822))), -(_881824 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_881822), 6688 ^ [_881822, _881824]))], (34021 ^ _775828) ^ [_1408663, _1408665, _1408667, _1408669] : [class_Lattices_Osemilattice__inf(_1408663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408663), _1408665), _1408667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408663), _1408665), _1408669)), _1408667)))], (19112 ^ _775828) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (5282 ^ _775828) ^ [_856580, _856582] : [_856582 = _856580, -(c_Nat_Osize__class_Osize(_856582) = c_Nat_Osize__class_Osize(_856580))], (516 ^ _775828) ^ [_783578, _783580, _783582, _783584] : [-(c_Predicate_Oreflp(_783582, _783578)), c_Predicate_Oreflp(_783584, _783580), _783584 = _783582, _783580 = _783578], (13568 ^ _775828) ^ [_1001239, _1001241, _1001243] : [hBOOL(hAPP(c_Com_OWT, _1001239)), hBOOL(hAPP(c_Com_OWT, _1001241)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1001243, _1001239, _1001241))))], (51344 ^ _775828) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (1770 ^ _775828) ^ [_800571, _800573] : [-(hBOOL(_800571)), _800573 = _800571, hBOOL(_800573)], (28053 ^ _775828) ^ [_1278175, _1278177] : [c_Wellfounded_OwfP(_1278175, _1278177), -(c_Wellfounded_Owf(_1278175, hAPP(c_Set_OCollect(tc_prod(_1278175, _1278175)), hAPP(c_Product__Type_Oprod_Oprod__case(_1278175, _1278175, tc_HOL_Obool), _1278177))))], (6085 ^ _775828) ^ [_872491, _872493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872491), _872493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _872491)), hAPP(c_Nat_OSuc, _872493))))], (12205 ^ _775828) ^ [_976937] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _976937)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _976937)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19574 ^ _775828) ^ [_1112267, _1112269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112267), _1112269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1112267)), c_Int_OBit1(_1112269))))], (40371 ^ _775828) ^ [_1549861] : [class_Lattices_Oboolean__algebra(_1549861), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1549861), c_Orderings_Otop__class_Otop(_1549861)) = c_Orderings_Obot__class_Obot(_1549861))], (19580 ^ _775828) ^ [_1112383] : [c_Int_OBit1(_1112383) = c_Int_OPls], (16471 ^ _775828) ^ [_1056047, _1056049] : [class_Groups_Oordered__ab__group__add__abs(_1056047), -(hAPP(c_Groups_Oabs__class_Oabs(_1056047), hAPP(c_Groups_Oabs__class_Oabs(_1056047), _1056049)) = hAPP(c_Groups_Oabs__class_Oabs(_1056047), _1056049))], (46742 ^ _775828) ^ [_1705473, _1705475, _1705477, _1705479] : [class_Groups_Ocomm__monoid__add(_1705473), hBOOL(hAPP(c_List_Odistinct(_1705475), _1705477)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705473), hAPP(hAPP(c_List_Omap(_1705475, _1705473), _1705479), _1705477)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1705475, _1705473), _1705479), hAPP(c_List_Oset(_1705475), _1705477)))], (45635 ^ _775828) ^ [_1675684, _1675686, _1675688, _1675690, _1675692, _1675694] : [-(c_Map_Omap__comp(_1675684, _1675686, _1675688, _1675690, _1675692, _1675694) = c_Option_Ooption_ONone(_1675686)), 45636 ^ _775828 : [(45639 ^ _775828) ^ [_1675796] : [hAPP(_1675692, _1675694) = hAPP(c_Option_Ooption_OSome(_1675684), _1675796), hAPP(_1675690, _1675796) = c_Option_Ooption_ONone(_1675686)], (45637 ^ _775828) ^ [] : [hAPP(_1675692, _1675694) = c_Option_Ooption_ONone(_1675684)]]], (40273 ^ _775828) ^ [_1547846] : [-(hAPP(c_Relation_ODomain(_1547846, _1547846), c_Relation_OId(_1547846)) = c_Orderings_Otop__class_Otop(tc_fun(_1547846, tc_HOL_Obool)))], (45680 ^ _775828) ^ [_1676978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1676978)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676978), tc_HOL_Obool))))], (29028 ^ _775828) ^ [_1301226, _1301228, _1301230, _1301232, _1301234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1301226, _1301226)), hAPP(hAPP(c_Product__Type_OPair(_1301226, _1301226), _1301228), _1301230)), c_Transitive__Closure_Otrancl(_1301226, _1301232))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1301226, _1301226)), hAPP(hAPP(c_Product__Type_OPair(_1301226, _1301226), _1301230), _1301234)), c_Transitive__Closure_Otrancl(_1301226, _1301232))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1301226, _1301226)), hAPP(hAPP(c_Product__Type_OPair(_1301226, _1301226), _1301228), _1301234)), c_Transitive__Closure_Otrancl(_1301226, _1301232))))], (33627 ^ _775828) ^ [_1400063, _1400065, _1400067] : [33629 ^ _775828 : [(33635 ^ _775828) ^ [] : [-(33628 ^ [_1400063, _1400065, _1400067] = 33631 ^ [_1400063, _1400065, _1400067])], (33633 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400063), 33631 ^ [_1400063, _1400065, _1400067]), _1400067)))], (33630 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400063), 33628 ^ [_1400063, _1400065, _1400067]), _1400065)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400063, tc_HOL_Obool)), _1400065), _1400067) = c_Orderings_Obot__class_Obot(tc_fun(_1400063, tc_HOL_Obool)))], (6692 ^ _775828) ^ [_881989] : [-(hAPP(c_Com_Obody, _881989) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _881989))))], (9577 ^ _775828) ^ [_929799, _929801] : [class_Rings_Olinordered__semidom(_929799), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929799), c_Groups_Ozero__class_Ozero(_929799)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929799), _929801))))], (49457 ^ _775828) ^ [_1768889, _1768891, _1768893, _1768895] : [-(hAPP(c_List_Ofilter(_1768889, _1768891), hAPP(hAPP(c_List_Oappend(_1768889), _1768893), _1768895)) = hAPP(hAPP(c_List_Oappend(_1768889), hAPP(c_List_Ofilter(_1768889, _1768891), _1768893)), hAPP(c_List_Ofilter(_1768889, _1768891), _1768895)))], (1900 ^ _775828) ^ [_803333, _803335] : [_803335 = _803333, -(c_Nat_Onat_Onat__size(_803335) = c_Nat_Onat_Onat__size(_803333))], (20094 ^ _775828) ^ [_1121004, _1121006] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1121004)), c_Int_OBit0(_1121006)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1121004), _1121006)))], (6037 ^ _775828) ^ [_871764, _871766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871764), _871766)), -(hAPP(c_Nat_OSuc, _871764) = _871766), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _871764)), _871766)))], (29965 ^ _775828) ^ [] : [-(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))))], (40738 ^ _775828) ^ [_1558917, _1558919, _1558921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1558917, _1558917)), _1558919), c_Transitive__Closure_Ortrancl(_1558917, _1558921))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558917, _1558917)), _1558919), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1558917, _1558917), 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(_1558917, _1558917), tc_HOL_Obool), tc_fun(tc_prod(_1558917, _1558917), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1558917, _1558917), tc_HOL_Obool)), _1558921)))))], (8407 ^ _775828) ^ [_910876, _910878, _910880] : [class_Orderings_Olinorder(_910876), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910876), _910878), _910880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910876), _910880), _910878)))], (30573 ^ _775828) ^ [_1334517, _1334519] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334517, _1334517)), _1334519)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1334517, _1334517)), c_Transitive__Closure_Otrancl(_1334517, _1334519))))], (6546 ^ _775828) ^ [_879935, _879937, _879939] : [class_Orderings_Opreorder(_879935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879935), _879937), _879939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879935), _879939), _879937))], (13601 ^ _775828) ^ [_1001881, _1001883, _1001885, _1001887, _1001889] : [c_Com_Ocom_OAss(_1001881, _1001883) = c_Com_Ocom_OLocal(_1001885, _1001887, _1001889)], (27060 ^ _775828) ^ [_1253925, _1253927] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253927), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253925)) = 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), _1253925)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253927))))], (48345 ^ _775828) ^ [_1744587, _1744589, _1744591, _1744593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744587), tc_List_Olist(_1744587))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744587), tc_List_Olist(_1744587)), _1744589), _1744591)), c_List_Olistrel1(_1744587, _1744593))), 48350 ^ _775828 : [(48357 ^ _775828) ^ [] : [-(_1744591 = hAPP(hAPP(c_List_Oappend(_1744587), 48352 ^ [_1744587, _1744589, _1744591, _1744593]), hAPP(hAPP(c_List_Olist_OCons(_1744587), 48349 ^ [_1744587, _1744589, _1744591, _1744593]), 48353 ^ [_1744587, _1744589, _1744591, _1744593])))], (48355 ^ _775828) ^ [] : [-(_1744589 = hAPP(hAPP(c_List_Oappend(_1744587), 48352 ^ [_1744587, _1744589, _1744591, _1744593]), hAPP(hAPP(c_List_Olist_OCons(_1744587), 48348 ^ [_1744587, _1744589, _1744591, _1744593]), 48353 ^ [_1744587, _1744589, _1744591, _1744593])))], (48351 ^ _775828) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1744587, _1744587)), hAPP(hAPP(c_Product__Type_OPair(_1744587, _1744587), 48348 ^ [_1744587, _1744589, _1744591, _1744593]), 48349 ^ [_1744587, _1744589, _1744591, _1744593])), _1744593)))]]], (47839 ^ _775828) ^ [_1731355, _1731357, _1731359, _1731361] : [-(hAPP(hAPP(c_List_Otake(_1731355), _1731357), hAPP(hAPP(c_List_Oappend(_1731355), _1731359), _1731361)) = hAPP(hAPP(c_List_Oappend(_1731355), hAPP(hAPP(c_List_Otake(_1731355), _1731357), _1731359)), hAPP(hAPP(c_List_Otake(_1731355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1731357), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731355)), _1731359))), _1731361)))]], input).
% 45.15/44.01  ncf('1',plain,[c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_na), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(v_x)), hAPP(c_Com_Ocom_OBODY, v_x)), v_Q(v_x)))],start(51638 ^ 0)).
% 45.15/44.01  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_na), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(v_x)), hAPP(c_Com_Ocom_OBODY, v_x)), v_Q(v_x)))), c_Hoare__Mirabelle_Otriple__valid(t_a, v_na, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(v_x)), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_x))), v_Q(v_x)))],extension(5463 ^ 1,bind([[_862007, _862009, _862011, _862013, _862015], [t_a, v_na, v_P(v_x), v_x, v_Q(v_x)]]))).
% 45.15/44.01  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Otriple__valid(t_a, v_na, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P(v_x)), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_x))), v_Q(v_x)))), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_x), v_Procs))],extension(51632 ^ 2,bind([[_1809843], [v_x]]))).
% 45.15/44.01  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_x), v_Procs)))],extension(51618 ^ 3)).
% 45.15/44.01  %-----------------------------------------------------
% 45.15/44.01  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------