TSTP Solution File: SWW361+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW361+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:26:02 EDT 2023

% Result   : Theorem 94.92s 91.69s
% Output   : Proof 95.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWW361+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.14  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 22:06:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 94.92/91.69  
% 94.92/91.69  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 94.92/91.69  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.92/91.69  %-----------------------------------------------------
% 94.92/91.69  ncf(matrix, plain, [(52793 ^ _2085008) ^ [] : [v_P(hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))], !, (52765 ^ _779142) ^ [_1837706, _1837708] : [-(hBOOL(_1837706)), -(hBOOL(hAPP(hAPP(c_fimplies, _1837706), _1837708)))], (21750 ^ _779142) ^ [_1161147, _1161149] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1161147)), _1161149) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161147), _1161149)))], (17631 ^ _779142) ^ [_1089738] : [-(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), _1089738))))], (47799 ^ _779142) ^ [_1742341, _1742343] : [-(c_List_Olist__all(_1742341, _1742343, c_List_Olist_ONil(_1742341)))], (43251 ^ _779142) ^ [_1641976, _1641978, _1641980] : [_1641976 = c_List_Olist_ONil(_1641978), -(c_List_Obutlast(_1641978, hAPP(hAPP(c_List_Oappend(_1641978), _1641980), _1641976)) = c_List_Obutlast(_1641978, _1641980))], (40245 ^ _779142) ^ [_1565121, _1565123, _1565125, _1565127, _1565129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565121, _1565121)), hAPP(hAPP(c_Product__Type_OPair(_1565121, _1565121), _1565123), _1565125)), c_Transitive__Closure_Otrancl(_1565121, _1565127))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565121, _1565121)), hAPP(hAPP(c_Product__Type_OPair(_1565121, _1565121), _1565125), _1565129)), _1565127)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565121, _1565121)), hAPP(hAPP(c_Product__Type_OPair(_1565121, _1565121), _1565123), _1565129)), c_Transitive__Closure_Otrancl(_1565121, _1565127))))], (10617 ^ _779142) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13523 ^ _779142) ^ [_1014443, _1014445] : [class_Rings_Odivision__ring(_1014443), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014443), _1014445), c_Groups_Oone__class_Oone(_1014443)) = _1014445)], (52395 ^ _779142) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (1896 ^ _779142) ^ [_805784, _805786] : [-(class_Groups_Ozero(_805784)), _805786 = _805784, class_Groups_Ozero(_805786)], (48408 ^ _779142) ^ [_1755156, _1755158] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755156), _1755158))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755156, _1755158) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755158), c_Lazy__Sequence_Osmall__lazy_H(_1755156, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755158), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (716 ^ _779142) ^ [_789912, _789914, _789916, _789918] : [-(c_Predicate_Oreflp(_789916, _789912)), c_Predicate_Oreflp(_789918, _789914), _789918 = _789916, _789914 = _789912], (49352 ^ _779142) ^ [_1776775, _1776777, _1776779, _1776781] : [c_Relation_Osym(_1776775, _1776777), -(c_Relation_Osym(_1776779, hAPP(hAPP(c_Relation_Oinv__image(_1776775, _1776779), _1776777), _1776781)))], (22520 ^ _779142) ^ [_1175529, _1175531, _1175533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175529)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1175531), _1175533)), 22527 ^ _779142 : [(22528 ^ _779142) ^ [_1175725] : [22530 ^ _779142 : [(22536 ^ _779142) ^ [] : [-(_1175725 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22532 ^ [_1175529, _1175531, _1175533, _1175725]), 22529 ^ [_1175529, _1175531, _1175533, _1175725]))], (22534 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22532 ^ [_1175529, _1175531, _1175533, _1175725]), _1175533)))], (22531 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22529 ^ [_1175529, _1175531, _1175533, _1175725]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1175529))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175531), _1175725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175531), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175725), _1175529))))]]], (41543 ^ _779142) ^ [_1600481, _1600483, _1600485, _1600487, _1600489, _1600491] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600481), tc_List_Olist(_1600481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600481), tc_List_Olist(_1600481)), hAPP(hAPP(c_List_Olist_OCons(_1600481), _1600483), _1600485)), hAPP(hAPP(c_List_Olist_OCons(_1600481), _1600487), _1600489))), c_List_Olistrel1(_1600481, _1600491)))), 41544 ^ _779142 : [(41551 ^ _779142) ^ [] : [_1600483 = _1600487, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600481), tc_List_Olist(_1600481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600481), tc_List_Olist(_1600481)), _1600485), _1600489)), c_List_Olistrel1(_1600481, _1600491)))], (41545 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600481, _1600481)), hAPP(hAPP(c_Product__Type_OPair(_1600481, _1600481), _1600483), _1600487)), _1600491)), _1600485 = _1600489]]], (29405 ^ _779142) ^ [_1301471, _1301473, _1301475, _1301477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301471, tc_HOL_Obool)), _1301477), _1301473)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301471, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301471, tc_HOL_Obool)), _1301473), _1301475)), _1301477) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301471, tc_HOL_Obool)), _1301473), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301471, tc_HOL_Obool)), _1301475), _1301477)))], (1166 ^ _779142) ^ [_796659, _796661] : [-(class_Rings_Olinordered__ring__strict(_796659)), _796661 = _796659, class_Rings_Olinordered__ring__strict(_796661)], (32855 ^ _779142) ^ [_1379322, _1379324] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1379322), hAPP(c_Nat_OSuc, _1379324)) = 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)), _1379324)), _1379322))], (41953 ^ _779142) ^ [_1611968, _1611970, _1611972, _1611974] : [-(hAPP(hAPP(c_List_Otake(_1611968), _1611970), hAPP(hAPP(c_List_Otake(_1611968), _1611972), _1611974)) = hAPP(hAPP(c_List_Otake(_1611968), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1611970), _1611972)), _1611974))], (33411 ^ _779142) ^ [_1390461, _1390463, _1390465, _1390467] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1390461, _1390463), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390465), _1390467))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1390461, _1390463) = _1390467)], (23221 ^ _779142) ^ [_1188092] : [-(hAPP(c_Set_OPow(_1188092), c_Orderings_Obot__class_Obot(tc_fun(_1188092, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1188092, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1188092, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1188092, tc_HOL_Obool), tc_HOL_Obool))))], (48080 ^ _779142) ^ [_1748213, _1748215, _1748217, _1748219] : [-(c_Predicate_Oconversep(_1748213, _1748215, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748213, tc_fun(_1748215, tc_HOL_Obool))), _1748217), _1748219)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748215, tc_fun(_1748213, tc_HOL_Obool))), c_Predicate_Oconversep(_1748213, _1748215, _1748217)), c_Predicate_Oconversep(_1748213, _1748215, _1748219)))], (4942 ^ _779142) ^ [_854439, _854441, _854443, _854445, _854447, _854449, _854451, _854453] : [-(c_Product__Type_Ocurry(_854453, _854449, _854445, _854441) = c_Product__Type_Ocurry(_854451, _854447, _854443, _854439)), _854453 = _854451, _854449 = _854447, _854445 = _854443, _854441 = _854439], (25524 ^ _779142) ^ [_1227717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227717), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1227717)), c_Int_OPls)))], (22628 ^ _779142) ^ [_1177604, _1177606, _1177608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177604)), 22631 ^ _779142 : [(22632 ^ _779142) ^ [_1177738] : [22634 ^ _779142 : [(22640 ^ _779142) ^ [] : [-(_1177738 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22636 ^ [_1177604, _1177606, _1177608, _1177738]), 22633 ^ [_1177604, _1177606, _1177608, _1177738]))], (22638 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22636 ^ [_1177604, _1177606, _1177608, _1177738]), _1177606)))], (22635 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22633 ^ [_1177604, _1177606, _1177608, _1177738]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1177604))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177608), _1177738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177608), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177738), _1177604))))]]], (24886 ^ _779142) ^ [_1216685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1216685)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216685), c_Int_OMin)))], (16655 ^ _779142) ^ [_1072353] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072353) = _1072353)], (39375 ^ _779142) ^ [_1544736, _1544738, _1544740, _1544742, _1544744, _1544746] : [hBOOL(hAPP(hAPP(c_member(_1544736), _1544738), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1544740, _1544742, tc_fun(_1544736, tc_HOL_Obool)), _1544744), _1544746))), 39380 ^ _779142 : [(39383 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544736), _1544738), hAPP(hAPP(_1544744, 39378 ^ [_1544736, _1544738, _1544740, _1544742, _1544744, _1544746]), 39379 ^ [_1544736, _1544738, _1544740, _1544742, _1544744, _1544746]))))], (39381 ^ _779142) ^ [] : [-(_1544746 = hAPP(hAPP(c_Product__Type_OPair(_1544740, _1544742), 39378 ^ [_1544736, _1544738, _1544740, _1544742, _1544744, _1544746]), 39379 ^ [_1544736, _1544738, _1544740, _1544742, _1544744, _1544746]))]]], (48511 ^ _779142) ^ [_1757433, _1757435, _1757437] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757433), _1757437), _1757435)), -(hBOOL(hAPP(hAPP(c_member(_1757433), _1757435), hAPP(c_List_Oset(_1757433), _1757437))))], (47921 ^ _779142) ^ [_1744563, _1744565, _1744567] : [47923 ^ _779142 : [(47926 ^ _779142) ^ [] : [hBOOL(hAPP(_1744565, 47922 ^ [_1744563, _1744565, _1744567]))], (47924 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744563), 47922 ^ [_1744563, _1744565, _1744567]), hAPP(c_List_Oset(_1744563), _1744567))))]], -(c_List_Olist__all(_1744563, _1744565, _1744567))], (31074 ^ _779142) ^ [_1335966, _1335968, _1335970] : [class_Orderings_Oorder(_1335966), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335966, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1335966, _1335968), _1335970)), hAPP(c_SetInterval_Oord__class_OatLeast(_1335966), _1335970)) = c_Orderings_Obot__class_Obot(tc_fun(_1335966, tc_HOL_Obool)))], (20937 ^ _779142) ^ [_1147317, _1147319, _1147321] : [-(hBOOL(hAPP(_1147317, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1147319), _1147321)))), 20938 ^ _779142 : [(20945 ^ _779142) ^ [_1147485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147321), _1147485)), _1147319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147321), hAPP(c_Nat_OSuc, _1147485)))), hBOOL(hAPP(_1147317, _1147485))], (20939 ^ _779142) ^ [] : [_1147321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1147317, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (34490 ^ _779142) ^ [_1415022, _1415024, _1415026, _1415028] : [34492 ^ _779142 : [(34495 ^ _779142) ^ [] : [hAPP(_1415028, 34491 ^ [_1415022, _1415024, _1415026, _1415028]) = c_Orderings_Obot__class_Obot(tc_fun(_1415024, tc_HOL_Obool))], (34493 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415022), 34491 ^ [_1415022, _1415024, _1415026, _1415028]), _1415026)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415022, tc_fun(_1415024, tc_HOL_Obool)), _1415026), _1415028) = c_Orderings_Obot__class_Obot(tc_fun(_1415024, tc_HOL_Obool)))], (35318 ^ _779142) ^ [] : [-(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)))))], (22757 ^ _779142) ^ [_1180099, _1180101, _1180103] : [class_Lattices_Oboolean__algebra(_1180099), 22760 ^ _779142 : [(22767 ^ _779142) ^ [] : [_1180101 = _1180103, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1180099), _1180101) = hAPP(c_Groups_Ouminus__class_Ouminus(_1180099), _1180103))], (22761 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1180099), _1180101) = hAPP(c_Groups_Ouminus__class_Ouminus(_1180099), _1180103), -(_1180101 = _1180103)]]], (51869 ^ _779142) ^ [_1826381, _1826383, _1826385, _1826387] : [-(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), _1826381, _1826383)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826385, _1826387)))), 51870 ^ _779142 : [(51873 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826385), _1826381)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826383), _1826387))], (51871 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826381), _1826383)))]]], (34579 ^ _779142) ^ [_1417713, _1417715, _1417717, _1417719, _1417721] : [hBOOL(hAPP(hAPP(c_member(_1417713), _1417715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417717, tc_fun(_1417713, tc_HOL_Obool)), _1417719), _1417721))), 34582 ^ _779142 : [(34583 ^ _779142) ^ [_1417837] : [hBOOL(hAPP(hAPP(c_member(_1417717), _1417837), _1417719)), -(hBOOL(hAPP(hAPP(c_member(_1417713), _1417715), hAPP(_1417721, _1417837))))]]], (46720 ^ _779142) ^ [_1718479, _1718481, _1718483] : [-(hAPP(c_List_Orev(_1718479), hAPP(hAPP(c_List_Otake(_1718479), _1718481), _1718483)) = hAPP(hAPP(c_List_Odrop(_1718479), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718479)), _1718483)), _1718481)), hAPP(c_List_Orev(_1718479), _1718483)))], (7284 ^ _779142) ^ [_900253, _900255] : [class_Orderings_Opreorder(_900253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900253), _900255), _900255))], (21682 ^ _779142) ^ [_1160045, _1160047] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1160045, _1160047)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1160045), hAPP(c_Nat_OSuc, _1160047)))], (22032 ^ _779142) ^ [_1166399, _1166401] : [class_Power_Opower(_1166399), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1166399), _1166401), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1166399))], (52289 ^ _779142) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (17593 ^ _779142) ^ [_1089167] : [_1089167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1089167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12186 ^ _779142) ^ [_989583, _989585, _989587] : [class_Groups_Oordered__ab__group__add(_989583), 12189 ^ _779142 : [(12196 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989583), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_989583), _989585), _989587)), c_Groups_Ozero__class_Ozero(_989583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989583), _989585), _989587)))], (12190 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989583), _989585), _989587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989583), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_989583), _989585), _989587)), c_Groups_Ozero__class_Ozero(_989583))))]]], (35415 ^ _779142) ^ [_1440712, _1440714, _1440716, _1440718, _1440720, _1440722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1440718, _1440718)), hAPP(hAPP(c_Product__Type_OPair(_1440718, _1440718), hAPP(_1440722, _1440714)), hAPP(_1440722, _1440716))), _1440720)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440712, _1440712)), hAPP(hAPP(c_Product__Type_OPair(_1440712, _1440712), _1440714), _1440716)), hAPP(hAPP(c_Relation_Oinv__image(_1440718, _1440712), _1440720), _1440722))))], (43371 ^ _779142) ^ [_1644941, _1644943, _1644945, _1644947, _1644949, _1644951, _1644953, _1644955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644941, _1644941)), hAPP(hAPP(c_Product__Type_OPair(_1644941, _1644941), _1644943), _1644945)), _1644947)), _1644949 = hAPP(hAPP(c_List_Oappend(_1644941), _1644951), hAPP(hAPP(c_List_Olist_OCons(_1644941), _1644943), _1644953)), _1644955 = hAPP(hAPP(c_List_Oappend(_1644941), _1644951), hAPP(hAPP(c_List_Olist_OCons(_1644941), _1644945), _1644953)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644941), tc_List_Olist(_1644941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644941), tc_List_Olist(_1644941)), _1644949), _1644955)), c_List_Olistrel1(_1644941, _1644947))))], (3468 ^ _779142) ^ [_830908, _830910, _830912, _830914, _830916, _830918] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_830918, _830914, _830910) = c_SetInterval_Oord__class_OgreaterThanLessThan(_830916, _830912, _830908)), _830918 = _830916, _830914 = _830912, _830910 = _830908], (14481 ^ _779142) ^ [_1031571, _1031573, _1031575, _1031577] : [class_Fields_Olinordered__field(_1031571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031571), c_Groups_Ozero__class_Ozero(_1031571)), _1031573)), 14488 ^ _779142 : [(14495 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031571), _1031575), _1031573)), _1031577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031571), _1031575), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031571), _1031577), _1031573))))], (14489 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031571), _1031575), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031571), _1031577), _1031573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031571), _1031575), _1031573)), _1031577)))]]], (3030 ^ _779142) ^ [_824121, _824123, _824125, _824127] : [-(c_List_Olistset(_824127, _824123) = c_List_Olistset(_824125, _824121)), _824127 = _824125, _824123 = _824121], (6001 ^ _779142) ^ [_874723, _874725, _874727] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_874723), hAPP(hAPP(c_Set_Oinsert(_874723), _874725), _874727))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_874723), _874727)))], (11746 ^ _779142) ^ [_981442, _981444, _981446, _981448, _981450] : [class_Rings_Oordered__semiring(_981442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981442), _981444), _981446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981442), _981448), _981450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981442), c_Groups_Ozero__class_Ozero(_981442)), _981444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981442), c_Groups_Ozero__class_Ozero(_981442)), _981448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981442), _981444), _981448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981442), _981446), _981450))))], (35349 ^ _779142) ^ [_1438301, _1438303, _1438305, _1438307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1438301, tc_HOL_Obool), tc_fun(_1438301, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1438301, tc_HOL_Obool), tc_fun(_1438301, tc_HOL_Obool)), _1438305), _1438307)), c_Wellfounded_Omax__ext(_1438301, _1438303))), -(c_Wellfounded_Omax__extp(_1438301, hAPP(hAPP(c_COMBC(_1438301, tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_fun(_1438301, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438301, tc_fun(tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_fun(_1438301, tc_HOL_Obool)), _1438301), c_COMBC(_1438301, tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438301, tc_prod(_1438301, _1438301)), tc_fun(_1438301, tc_fun(tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_HOL_Obool)), _1438301), hAPP(c_COMBB(tc_prod(_1438301, _1438301), tc_fun(tc_fun(tc_prod(_1438301, _1438301), tc_HOL_Obool), tc_HOL_Obool), _1438301), c_member(tc_prod(_1438301, _1438301)))), c_Product__Type_OPair(_1438301, _1438301)))), _1438303), _1438305, _1438307))], (46582 ^ _779142) ^ [_1715578, _1715580] : [_1715580 = c_List_Olist_ONil(_1715578), -(hAPP(c_List_Orev(_1715578), _1715580) = c_List_Olist_ONil(_1715578))], (13597 ^ _779142) ^ [_1015654, _1015656, _1015658, _1015660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1015654, _1015656)), c_Sum__Type_OPlus(_1015654, _1015656, _1015658, _1015660))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1015656), _1015660)))], (24101 ^ _779142) ^ [_1203486, _1203488, _1203490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203486, tc_HOL_Obool)), _1203490), _1203488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203486, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203486, tc_HOL_Obool)), _1203488)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203486, tc_HOL_Obool)), _1203490))))], (37541 ^ _779142) ^ [_1490040, _1490042, _1490044, _1490046, _1490048, _1490050] : [class_Groups_Ocomm__monoid__mult(_1490040), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490042, _1490040), hAPP(hAPP(c_COMBC(_1490042, tc_fun(_1490044, tc_HOL_Obool), _1490040), hAPP(hAPP(c_COMBB(tc_fun(_1490044, _1490040), tc_fun(tc_fun(_1490044, tc_HOL_Obool), _1490040), _1490042), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490044, _1490040)), _1490046)), _1490048)), _1490050) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1490042, _1490044), _1490040), hAPP(c_Product__Type_Oprod_Oprod__case(_1490042, _1490044, _1490040), _1490046)), hAPP(hAPP(c_Product__Type_OSigma(_1490042, _1490044), _1490050), hAPP(c_COMBK(tc_fun(_1490044, tc_HOL_Obool), _1490042), _1490048))))], (41941 ^ _779142) ^ [_1611755, _1611757, _1611759, _1611761] : [hBOOL(hAPP(hAPP(c_member(_1611755), _1611757), hAPP(c_List_Oset(_1611755), hAPP(hAPP(c_List_Olist_OCons(_1611755), _1611759), _1611761)))), -(_1611757 = _1611759), -(hBOOL(hAPP(hAPP(c_member(_1611755), _1611757), hAPP(c_List_Oset(_1611755), _1611761))))], (5616 ^ _779142) ^ [_864984, _864986] : [_864986 = _864984, -(c_Set_Oinsert(_864986) = c_Set_Oinsert(_864984))], (17929 ^ _779142) ^ [_1094968, _1094970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094968), 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, _1094970, _1094968)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52269 ^ _779142) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (42169 ^ _779142) ^ [_1618835, _1618837, _1618839, _1618841, _1618843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618835), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618837)), _1618839))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618835), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618841)), _1618843))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1618837, _1618841)), hAPP(hAPP(c_List_Ozip(_1618837, _1618841), _1618839), _1618843)), _1618835) = hAPP(hAPP(c_Product__Type_OPair(_1618837, _1618841), hAPP(hAPP(c_List_Onth(_1618837), _1618839), _1618835)), hAPP(hAPP(c_List_Onth(_1618841), _1618843), _1618835)))], (24095 ^ _779142) ^ [_1203339, _1203341, _1203343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203339, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203339, tc_HOL_Obool)), _1203341)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203339, tc_HOL_Obool)), _1203343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203339, tc_HOL_Obool)), _1203343), _1203341)))], (11932 ^ _779142) ^ [_984907, _984909, _984911, _984913] : [class_Rings_Olinordered__comm__semiring__strict(_984907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984907), _984909), _984911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984907), c_Groups_Ozero__class_Ozero(_984907)), _984913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984907), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984907), _984913), _984909)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984907), _984913), _984911))))], (52459 ^ _779142) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (31725 ^ _779142) ^ [_1348588, _1348590, _1348592, _1348594] : [class_Groups_Oordered__ab__group__add__abs(_1348588), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348588), hAPP(c_Groups_Oabs__class_Oabs(_1348588), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348590, _1348588), _1348592), _1348594))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348590, _1348588), hAPP(hAPP(c_COMBB(_1348588, _1348588, _1348590), c_Groups_Oabs__class_Oabs(_1348588)), _1348592)), _1348594))))], (35970 ^ _779142) ^ [_1454412, _1454414] : [c_Equiv__Relations_Oequivp(_1454412, hAPP(hAPP(c_COMBC(_1454412, tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_fun(_1454412, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454412, tc_fun(tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_fun(_1454412, tc_HOL_Obool)), _1454412), c_COMBC(_1454412, tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454412, tc_prod(_1454412, _1454412)), tc_fun(_1454412, tc_fun(tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_HOL_Obool)), _1454412), hAPP(c_COMBB(tc_prod(_1454412, _1454412), tc_fun(tc_fun(tc_prod(_1454412, _1454412), tc_HOL_Obool), tc_HOL_Obool), _1454412), c_member(tc_prod(_1454412, _1454412)))), c_Product__Type_OPair(_1454412, _1454412)))), _1454414)), -(c_Equiv__Relations_Oequiv(_1454412, c_Orderings_Otop__class_Otop(tc_fun(_1454412, tc_HOL_Obool)), _1454414))], (45470 ^ _779142) ^ [_1691560, _1691562] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691560)), c_List_Oremdups(_1691560, c_List_Oconcat(_1691560, _1691562))) = hAPP(c_Finite__Set_Ocard(_1691560), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1691560), tc_fun(_1691560, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1691560)), _1691562)), c_List_Oset(_1691560))))], (25028 ^ _779142) ^ [_1219207, _1219209] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219207), _1219209), hAPP(c_Int_Onumber__class_Onumber__of(_1219207), c_Int_OBit1(c_Int_OPls))) = _1219209), class_Fields_Ofield(_1219207), class_Int_Onumber__ring(_1219207)], (20057 ^ _779142) ^ [_1131171, _1131173] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1131171) = _1131173), _1131171 = hAPP(c_Int_Onat, _1131173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131173))], (5924 ^ _779142) ^ [_873080, _873082, _873084, _873086, _873088, _873090] : [hBOOL(hAPP(hAPP(c_member(_873080), _873082), _873084)), _873086 = hAPP(_873088, _873082), -(hBOOL(hAPP(hAPP(c_member(_873090), _873086), hAPP(c_Set_Oimage(_873080, _873090, _873088), _873084))))], (25476 ^ _779142) ^ [_1226889, _1226891] : [c_Int_OBit0(_1226889) = c_Int_OBit1(_1226891)], (8861 ^ _779142) ^ [_928550, _928552, _928554, _928556, _928558] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928550), _928552), _928554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928550), _928556), _928558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928550), _928552), _928556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928550), _928554), _928558))))], (19131 ^ _779142) ^ [_1115405] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115405))), -(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), _1115405)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34550 ^ _779142) ^ [_1416976, _1416978, _1416980, _1416982, _1416984, _1416986] : [-(hAPP(c_Set_Oimage(_1416976, _1416978, _1416980), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416982, tc_fun(_1416976, tc_HOL_Obool)), _1416984), _1416986)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416982, tc_fun(_1416978, tc_HOL_Obool)), _1416984), hAPP(hAPP(c_COMBB(tc_fun(_1416976, tc_HOL_Obool), tc_fun(_1416978, tc_HOL_Obool), _1416982), c_Set_Oimage(_1416976, _1416978, _1416980)), _1416986)))], (23847 ^ _779142) ^ [_1199186] : [-(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), _1199186))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23423 ^ _779142) ^ [_1191742, _1191744] : [class_Groups_Oab__group__add(_1191742), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191742), hAPP(c_Groups_Ouminus__class_Ouminus(_1191742), _1191744)), _1191744) = c_Groups_Ozero__class_Ozero(_1191742))], (52613 ^ _779142) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (35061 ^ _779142) ^ [_1431017, _1431019, _1431021, _1431023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1431017), _1431019)), -(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), _1431017), _1431021)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1431019), _1431023))), c_FunDef_Opair__less)))], (47730 ^ _779142) ^ [_1740637, _1740639, _1740641, _1740643] : [47731 ^ _779142 : [(47734 ^ _779142) ^ [] : [c_List_Olist__ex(_1740637, _1740639, _1740643)], (47732 ^ _779142) ^ [] : [hBOOL(hAPP(_1740639, _1740641))]], -(c_List_Olist__ex(_1740637, _1740639, hAPP(hAPP(c_List_Olist_OCons(_1740637), _1740641), _1740643)))], (40436 ^ _779142) ^ [_1570618, _1570620] : [-(hAPP(c_Relation_ORange(_1570618, _1570618), c_Transitive__Closure_Ortrancl(_1570618, _1570620)) = c_Orderings_Otop__class_Otop(tc_fun(_1570618, tc_HOL_Obool)))], (42007 ^ _779142) ^ [_1613233, _1613235, _1613237] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613233)), _1613235), c_List_Olists(_1613233, _1613237))), 42010 ^ _779142 : [(42011 ^ _779142) ^ [_1613341] : [hBOOL(hAPP(hAPP(c_member(_1613233), _1613341), hAPP(c_List_Oset(_1613233), _1613235))), -(hBOOL(hAPP(hAPP(c_member(_1613233), _1613341), _1613237)))]]], (49825 ^ _779142) ^ [_1786737, _1786739] : [49827 ^ _779142 : [(49830 ^ _779142) ^ [] : [hBOOL(hAPP(_1786737, hAPP(c_Code__Numeral_Oof__nat, 49826 ^ [_1786737, _1786739])))], (49828 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49826 ^ [_1786737, _1786739]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1786737, _1786739)))], (51891 ^ _779142) ^ [_1826804, _1826806, _1826808, _1826810, _1826812] : [class_Rings_Ocomm__semiring__1(_1826804), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826804), _1826806), _1826808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826810), _1826812)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826804), hAPP(hAPP(c_Power_Opower__class_Opower(_1826804), _1826806), _1826810)), hAPP(hAPP(c_Power_Opower__class_Opower(_1826804), _1826808), _1826812))))], (28146 ^ _779142) ^ [_1276640, _1276642, _1276644] : [class_Orderings_Olinorder(_1276640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276640), _1276642)), hBOOL(hAPP(hAPP(c_member(_1276640), _1276644), _1276642)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1276640), _1276644), c_Big__Operators_Olinorder__class_OMax(_1276640, _1276642)) = c_Big__Operators_Olinorder__class_OMax(_1276640, _1276642))], (1776 ^ _779142) ^ [_804284, _804286] : [-(class_Orderings_Opreorder(_804284)), _804286 = _804284, class_Orderings_Opreorder(_804286)], (31551 ^ _779142) ^ [_1345238, _1345240, _1345242] : [31553 ^ _779142 : [(31556 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1345238), _1345242), 31552 ^ [_1345238, _1345240, _1345242]))], (31554 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1345238, tc_HOL_Obool)), 31552 ^ [_1345238, _1345240, _1345242]), _1345240)))]], -(hBOOL(hAPP(hAPP(c_member(_1345238), _1345242), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1345238, tc_HOL_Obool), _1345240))))], (17469 ^ _779142) ^ [_1086700, _1086702, _1086704, _1086706] : [class_Divides_Osemiring__div(_1086700), -(c_Divides_Odiv__class_Omod(_1086700, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086700), _1086702), _1086704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086700), _1086706), _1086704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086700), c_Divides_Odiv__class_Omod(_1086700, _1086702, _1086706)), _1086704))], (12924 ^ _779142) ^ [_1002792, _1002794, _1002796] : [hBOOL(hAPP(_1002792, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002794), _1002796))), 12927 ^ _779142 : [(12934 ^ _779142) ^ [_1002977] : [_1002794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002796), _1002977), -(hBOOL(hAPP(_1002792, _1002977)))], (12928 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002794), _1002796)), -(hBOOL(hAPP(_1002792, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (29705 ^ _779142) ^ [_1308387, _1308389, _1308391, _1308393, _1308395] : [class_Groups_Ocomm__monoid__mult(_1308387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308389), _1308391)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308389), _1308393)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308387), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308389, _1308387), _1308395), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308389, tc_HOL_Obool)), _1308391), _1308393))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308389, _1308387), _1308395), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308389, tc_HOL_Obool)), _1308391), _1308393))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308387), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308389, _1308387), _1308395), _1308391)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308389, _1308387), _1308395), _1308393)))], (18613 ^ _779142) ^ [_1106856, _1106858] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106856, _1106858) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1106856 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106858), 18616 ^ [_1106856, _1106858]))], (29121 ^ _779142) ^ [_1295515, _1295517, _1295519] : [class_Lattices_Olattice(_1295515), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295515), _1295517), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295515), _1295517), _1295519)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295515), _1295517), _1295519))], (49196 ^ _779142) ^ [_1773559, _1773561] : [c_Relation_Oantisym(_1773559, _1773561), 49199 ^ _779142 : [(49200 ^ _779142) ^ [_1773671, _1773673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773559, _1773559)), hAPP(hAPP(c_Product__Type_OPair(_1773559, _1773559), _1773673), _1773671)), _1773561)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773559, _1773559)), hAPP(hAPP(c_Product__Type_OPair(_1773559, _1773559), _1773671), _1773673)), _1773561)), -(_1773673 = _1773671)]]], (4742 ^ _779142) ^ [_851269, _851271, _851273, _851275] : [-(c_Complete__Lattice_OInf__class_OInf(_851275, _851271) = c_Complete__Lattice_OInf__class_OInf(_851273, _851269)), _851275 = _851273, _851271 = _851269], (34873 ^ _779142) ^ [_1426121, _1426123] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426121, tc_fun(_1426121, tc_HOL_Obool)), _1426123), hAPP(hAPP(c_COMBC(_1426121, tc_fun(_1426121, tc_HOL_Obool), tc_fun(_1426121, tc_HOL_Obool)), c_Set_Oinsert(_1426121)), c_Orderings_Obot__class_Obot(tc_fun(_1426121, tc_HOL_Obool)))) = _1426123)], (34446 ^ _779142) ^ [_1413504, _1413506, _1413508, _1413510, _1413512] : [-(_1413504 = c_Orderings_Obot__class_Obot(tc_fun(_1413506, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413506, tc_fun(_1413508, tc_HOL_Obool)), _1413504), hAPP(hAPP(c_COMBB(tc_fun(_1413508, tc_HOL_Obool), tc_fun(_1413508, tc_HOL_Obool), _1413506), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413508, tc_HOL_Obool)), _1413510)), _1413512)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413508, tc_HOL_Obool)), _1413510), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413506, tc_fun(_1413508, tc_HOL_Obool)), _1413504), _1413512)))], (44091 ^ _779142) ^ [_1661480, _1661482, _1661484, _1661486, _1661488] : [class_Orderings_Olinorder(_1661480), -(hBOOL(hAPP(hAPP(c_member(_1661480), hAPP(_1661482, _1661484)), hAPP(c_Set_Oimage(_1661486, _1661480, _1661482), hAPP(c_List_Oset(_1661486), _1661488))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661486, _1661480, _1661482, _1661484, _1661488) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661486, _1661480, _1661482), _1661484), _1661488))], (1094 ^ _779142) ^ [_795681, _795683, _795685, _795687, _795689, _795691, _795693, _795695] : [-(c_Orderings_Oorder_Ostrict__mono(_795693, _795689, _795685, _795681)), c_Orderings_Oorder_Ostrict__mono(_795695, _795691, _795687, _795683), _795695 = _795693, _795691 = _795689, _795687 = _795685, _795683 = _795681], (43638 ^ _779142) ^ [_1651901, _1651903, _1651905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651901), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651903)), _1651905))), -(hAPP(hAPP(c_List_Olist_OCons(_1651903), hAPP(hAPP(c_List_Onth(_1651903), _1651905), _1651901)), hAPP(hAPP(c_List_Odrop(_1651903), hAPP(c_Nat_OSuc, _1651901)), _1651905)) = hAPP(hAPP(c_List_Odrop(_1651903), _1651901), _1651905))], (6962 ^ _779142) ^ [_893266, _893268, _893270, _893272] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_893266, _893268, _893270), _893272), c_Orderings_Obot__class_Obot(tc_fun(_893266, tc_HOL_Obool))) = _893272)], (40719 ^ _779142) ^ [_1577369, _1577371, _1577373, _1577375, _1577377] : [-(hAPP(c_Relation_Oconverse(_1577369, _1577371), hAPP(hAPP(c_Relation_Orel__comp(_1577369, _1577373, _1577371), _1577375), _1577377)) = hAPP(hAPP(c_Relation_Orel__comp(_1577371, _1577373, _1577369), hAPP(c_Relation_Oconverse(_1577373, _1577371), _1577377)), hAPP(c_Relation_Oconverse(_1577369, _1577373), _1577375)))], (11768 ^ _779142) ^ [_981865, _981867, _981869, _981871, _981873] : [class_Rings_Oordered__semiring(_981865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981865), _981867), _981869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981865), _981871), _981873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981865), c_Groups_Ozero__class_Ozero(_981865)), _981869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981865), c_Groups_Ozero__class_Ozero(_981865)), _981871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981865), _981867), _981871)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981865), _981869), _981873))))], (38770 ^ _779142) ^ [_1529773, _1529775, _1529777] : [hAPP(c_Relation_ODomain(_1529773, _1529775), _1529777) = c_Orderings_Obot__class_Obot(tc_fun(_1529773, tc_HOL_Obool)), -(_1529777 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529773, _1529775), tc_HOL_Obool)))], (26434 ^ _779142) ^ [_1244103, _1244105, _1244107] : [class_Lattices_Osemilattice__sup(_1244103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244103), _1244105), _1244107)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1244103), _1244105), _1244107) = _1244107)], (2102 ^ _779142) ^ [_809691, _809693, _809695, _809697] : [-(c_Nitpick_Onat__lcm(_809697, _809693) = c_Nitpick_Onat__lcm(_809695, _809691)), _809697 = _809695, _809693 = _809691], (23215 ^ _779142) ^ [_1187961, _1187963] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187961)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187963)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187961), _1187963))], (25110 ^ _779142) ^ [_1220466] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220466), hAPP(c_Nat_OSuc, _1220466)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1220466), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31248 ^ _779142) ^ [_1339293] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1339293)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1339293)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1339293)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (41008 ^ _779142) ^ [_1584588, _1584590, _1584592] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584588, _1584588), hAPP(c_Nat_OSuc, _1584590)), _1584592) = hAPP(c_Fun_Ocomp(_1584588, _1584588, _1584588, _1584592), hAPP(hAPP(c_Nat_Ocompow(_1584588, _1584588), _1584590), _1584592)))], (21061 ^ _779142) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (8346 ^ _779142) ^ [_918124, _918126, _918128, _918130] : [hBOOL(hAPP(hAPP(c_member(_918124), _918126), _918128)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918124, tc_Nat_Onat), _918130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918124, tc_HOL_Obool)), _918128), hAPP(hAPP(c_Set_Oinsert(_918124), _918126), c_Orderings_Obot__class_Obot(tc_fun(_918124, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918124, tc_Nat_Onat), _918130), _918128)), hAPP(_918130, _918126)))], (32275 ^ _779142) ^ [_1366637, _1366639, _1366641] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1366637), _1366639), _1366641) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1366637), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1366637, tc_Int_Oint), _1366639), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1366641))), class_Groups_Ocomm__monoid__add(_1366637), class_Groups_Ocomm__monoid__mult(_1366637)], (33929 ^ _779142) ^ [_1400691, _1400693, _1400695, _1400697, _1400699, _1400701] : [hBOOL(hAPP(_1400691, _1400693)), hBOOL(hAPP(_1400695, _1400697)), 33936 ^ _779142 : [(33939 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1400695, hAPP(c_Product__Type_Osnd(_1400699, _1400701), hAPP(hAPP(c_Product__Type_OPair(_1400699, _1400701), _1400693), _1400697)))))], (33937 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1400691, hAPP(c_Product__Type_Ofst(_1400699, _1400701), hAPP(hAPP(c_Product__Type_OPair(_1400699, _1400701), _1400693), _1400697)))))]]], (43127 ^ _779142) ^ [_1639539, _1639541, _1639543, _1639545, _1639547, _1639549] : [hAPP(hAPP(c_List_Oappend(_1639539), _1639541), _1639543) = _1639545, _1639547 = hAPP(hAPP(c_List_Oappend(_1639539), _1639543), _1639549), -(hAPP(hAPP(c_List_Oappend(_1639539), _1639541), _1639547) = hAPP(hAPP(c_List_Oappend(_1639539), _1639545), _1639549))], (34476 ^ _779142) ^ [_1414460, _1414462, _1414464, _1414466, _1414468] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414460, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414462, tc_fun(_1414460, tc_HOL_Obool)), _1414464), _1414466)), _1414468) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414462, tc_fun(_1414460, tc_HOL_Obool)), _1414464), hAPP(hAPP(c_COMBC(_1414462, tc_fun(_1414460, tc_HOL_Obool), tc_fun(_1414460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414460, tc_HOL_Obool), tc_fun(tc_fun(_1414460, tc_HOL_Obool), tc_fun(_1414460, tc_HOL_Obool)), _1414462), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414460, tc_HOL_Obool))), _1414466)), _1414468)))], (41055 ^ _779142) ^ [_1585813, _1585815, _1585817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585813, _1585813)), _1585815), c_Transitive__Closure_Otrancl(_1585813, _1585817))), 41059 ^ _779142 : [(41062 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585813, _1585813)), _1585815), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585813, _1585813), tc_HOL_Obool), 41058 ^ [_1585813, _1585815, _1585817]), _1585817))))], (41060 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41058 ^ [_1585813, _1585815, _1585817])))]]], (37307 ^ _779142) ^ [_1483969, _1483971, _1483973, _1483975] : [-(hAPP(c_Set_Ovimage(_1483969, _1483971, _1483973), _1483975) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483971, tc_fun(_1483969, tc_HOL_Obool)), _1483975), hAPP(hAPP(c_COMBB(tc_fun(_1483971, tc_HOL_Obool), tc_fun(_1483969, tc_HOL_Obool), _1483971), c_Set_Ovimage(_1483969, _1483971, _1483973)), hAPP(hAPP(c_COMBC(_1483971, tc_fun(_1483971, tc_HOL_Obool), tc_fun(_1483971, tc_HOL_Obool)), c_Set_Oinsert(_1483971)), c_Orderings_Obot__class_Obot(tc_fun(_1483971, tc_HOL_Obool))))))], (47187 ^ _779142) ^ [_1728364, _1728366, _1728368] : [hBOOL(hAPP(c_List_Odistinct(_1728364), _1728366)), -(hBOOL(hAPP(c_List_Odistinct(_1728364), c_List_Oinsert(_1728364, _1728368, _1728366))))], (26874 ^ _779142) ^ [_1252947, _1252949, _1252951] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252947, tc_HOL_Obool)), _1252949), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252947, tc_HOL_Obool)), _1252951), _1252949)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252947, tc_HOL_Obool)), _1252949), _1252951))], (17531 ^ _779142) ^ [_1088095] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1088095, _1088095) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18066 ^ _779142) ^ [_1097328, _1097330] : [18067 ^ _779142 : [(18070 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097328), c_Int_OPls))], (18068 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097328), _1097330))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097328)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097330))))], (19977 ^ _779142) ^ [_1129876, _1129878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129876)), 19980 ^ _779142 : [(19987 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129878), _1129876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1129878)), hAPP(c_Int_Onat, _1129876))))], (19981 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1129878)), hAPP(c_Int_Onat, _1129876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129878), _1129876)))]]], (51399 ^ _779142) ^ [_1818215, _1818217, _1818219] : [_1818215 = _1818217, 51410 ^ _779142 : [(51413 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818219), _1818215))], (51411 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818215), _1818219)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818217), _1818219)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818219), _1818217)))], (19305 ^ _779142) ^ [_1118647] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1118647)) = _1118647)], (35053 ^ _779142) ^ [_1430659, _1430661, _1430663, _1430665, _1430667] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430659, tc_fun(_1430661, tc_HOL_Obool)), _1430663), hAPP(hAPP(c_COMBS(_1430659, tc_fun(_1430661, tc_HOL_Obool), tc_fun(_1430661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430661, tc_HOL_Obool), tc_fun(tc_fun(_1430661, tc_HOL_Obool), tc_fun(_1430661, tc_HOL_Obool)), _1430659), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430661, tc_HOL_Obool))), _1430665)), _1430667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430661, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1430661, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430659, tc_fun(_1430661, tc_HOL_Obool), _1430665), _1430663))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1430661, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430659, tc_fun(_1430661, tc_HOL_Obool), _1430667), _1430663))))], (34278 ^ _779142) ^ [_1408504, _1408506, _1408508, _1408510, _1408512, _1408514, _1408516, _1408518] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408504, tc_fun(_1408506, tc_fun(_1408508, tc_HOL_Obool))), _1408510), _1408512), _1408514), _1408516)), hBOOL(hAPP(hAPP(c_member(_1408504), _1408518), _1408510)), -(hBOOL(hAPP(hAPP(hAPP(_1408512, _1408518), _1408514), _1408516)))], (5632 ^ _779142) ^ [_865218, _865220] : [_865220 = _865218, -(c_Orderings_Obot__class_Obot(_865220) = c_Orderings_Obot__class_Obot(_865218))], (40414 ^ _779142) ^ [_1570037, _1570039, _1570041, _1570043, _1570045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570037, _1570037)), hAPP(hAPP(c_Product__Type_OPair(_1570037, _1570037), _1570039), _1570041)), c_Transitive__Closure_Ortrancl(_1570037, _1570043))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570037, _1570037)), hAPP(hAPP(c_Product__Type_OPair(_1570037, _1570037), _1570041), _1570045)), _1570043)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570037, _1570037)), hAPP(hAPP(c_Product__Type_OPair(_1570037, _1570037), _1570039), _1570045)), c_Transitive__Closure_Ortrancl(_1570037, _1570043))))], (28819 ^ _779142) ^ [_1289337, _1289339, _1289341, _1289343] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289337, tc_HOL_Obool)), _1289339), _1289341)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289337, tc_HOL_Obool)), _1289341), _1289343))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289337, tc_HOL_Obool)), _1289343), _1289339)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289337, tc_HOL_Obool)), _1289339), _1289341)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289337, tc_HOL_Obool)), _1289341), _1289343))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289337, tc_HOL_Obool)), _1289343), _1289339)))], (23681 ^ _779142) ^ [_1196271, _1196273] : [class_Groups_Oordered__ab__group__add__abs(_1196271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196271), _1196273), c_Groups_Ozero__class_Ozero(_1196271))), -(hAPP(c_Groups_Oabs__class_Oabs(_1196271), _1196273) = hAPP(c_Groups_Ouminus__class_Ouminus(_1196271), _1196273))], (49705 ^ _779142) ^ [_1783679, _1783681, _1783683, _1783685, _1783687, _1783689] : [hAPP(c_Set_Oimage(_1783679, _1783681, _1783683), _1783685) = _1783687, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783681, tc_HOL_Obool)), _1783689), _1783687)), -(hAPP(c_Set_Oimage(_1783679, _1783681, _1783683), hAPP(c_Set_Oimage(_1783681, _1783679, c_Hilbert__Choice_Oinv__into(_1783679, _1783681, _1783685, _1783683)), _1783689)) = _1783689)], (45264 ^ _779142) ^ [_1687311, _1687313, _1687315] : [-(c_Enum_Osublists(_1687311, hAPP(hAPP(c_List_Olist_OCons(_1687311), _1687313), _1687315)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1687311)), tc_List_Olist(tc_List_Olist(_1687311))), c_Enum_Osublists(_1687311, _1687315)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1687311)), tc_List_Olist(tc_List_Olist(_1687311)), tc_List_Olist(tc_List_Olist(_1687311))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1687311)), tc_fun(tc_List_Olist(tc_List_Olist(_1687311)), tc_List_Olist(tc_List_Olist(_1687311))), tc_List_Olist(tc_List_Olist(_1687311))), c_List_Oappend(tc_List_Olist(_1687311))), hAPP(c_List_Omap(tc_List_Olist(_1687311), tc_List_Olist(_1687311)), hAPP(c_List_Olist_OCons(_1687311), _1687313)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1687311))))))], (1126 ^ _779142) ^ [_796159, _796161] : [-(class_Rings_Olinordered__semiring__1__strict(_796159)), _796161 = _796159, class_Rings_Olinordered__semiring__1__strict(_796161)], (13895 ^ _779142) ^ [_1021159, _1021161, _1021163] : [class_Fields_Olinordered__field__inverse__zero(_1021159), 13898 ^ _779142 : [(13913 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021159), _1021161), _1021163)))), 13914 ^ _779142 : [(13921 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), _1021161), c_Groups_Ozero__class_Ozero(_1021159))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), _1021163), c_Groups_Ozero__class_Ozero(_1021159)))], (13915 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), _1021161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), _1021163))]]], (13899 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021159), _1021161), _1021163))), 13904 ^ _779142 : [(13907 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), _1021163)))], (13905 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), c_Groups_Ozero__class_Ozero(_1021159)), _1021161)))]], 13908 ^ _779142 : [(13911 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), _1021163), c_Groups_Ozero__class_Ozero(_1021159))))], (13909 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021159), _1021161), c_Groups_Ozero__class_Ozero(_1021159))))]]]]], (17708 ^ _779142) ^ [_1091107, _1091109] : [17709 ^ _779142 : [(17710 ^ _779142) ^ [_1091156] : [_1091107 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1091109), _1091156)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1091107, _1091109) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19389 ^ _779142) ^ [_1119954, _1119956, _1119958] : [class_Groups_Oordered__ab__group__add__abs(_1119954), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119954), hAPP(c_Groups_Oabs__class_Oabs(_1119954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119954), _1119956), _1119958))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119954), hAPP(c_Groups_Oabs__class_Oabs(_1119954), _1119956)), hAPP(c_Groups_Oabs__class_Oabs(_1119954), _1119958)))))], (10553 ^ _779142) ^ [_961738, _961740] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961738), _961740)), 10554 ^ _779142 : [(10561 ^ _779142) ^ [] : [_961738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _961740 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10555 ^ _779142) ^ [] : [_961738 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (41828 ^ _779142) ^ [_1608784, _1608786, _1608788, _1608790] : [-(hAPP(hAPP(c_List_Onth(_1608784), hAPP(hAPP(c_List_Olist_OCons(_1608784), _1608786), _1608788)), hAPP(c_Nat_OSuc, _1608790)) = hAPP(hAPP(c_List_Onth(_1608784), _1608788), _1608790))], (2250 ^ _779142) ^ [_811969, _811971, _811973, _811975] : [-(c_Orderings_Oord_Omin(_811975, _811971) = c_Orderings_Oord_Omin(_811973, _811969)), _811975 = _811973, _811971 = _811969], (3050 ^ _779142) ^ [_824419, _824421, _824423, _824425, _824427, _824429, _824431, _824433] : [-(c_Nat_Onat_Onat__case(_824433, _824429, _824425, _824421) = c_Nat_Onat_Onat__case(_824431, _824427, _824423, _824419)), _824433 = _824431, _824429 = _824427, _824425 = _824423, _824421 = _824419], (35489 ^ _779142) ^ [_1442587, _1442589, _1442591, _1442593, _1442595] : [-(hBOOL(hAPP(hAPP(c_member(_1442587), _1442589), hAPP(c_Relation_OImage(_1442591, _1442587, _1442593), _1442595)))), 35490 ^ _779142 : [(35491 ^ _779142) ^ [_1442673] : [hBOOL(hAPP(hAPP(c_member(_1442591), _1442673), _1442595)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1442591, _1442587)), hAPP(hAPP(c_Product__Type_OPair(_1442591, _1442587), _1442673), _1442589)), _1442593))]]], (35499 ^ _779142) ^ [_1442853, _1442855, _1442857, _1442859, _1442861, _1442863] : [hBOOL(hAPP(hAPP(c_member(_1442853), _1442855), _1442857)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1442853, _1442859)), hAPP(hAPP(c_Product__Type_OPair(_1442853, _1442859), _1442855), _1442861)), _1442863)), -(hBOOL(hAPP(hAPP(c_member(_1442859), _1442861), hAPP(c_Relation_OImage(_1442853, _1442859, _1442863), _1442857))))], (1416 ^ _779142) ^ [_799784, _799786] : [-(class_Lattices_Osemilattice__sup(_799784)), _799786 = _799784, class_Lattices_Osemilattice__sup(_799786)], (32547 ^ _779142) ^ [_1372995, _1372997, _1372999, _1373001, _1373003, _1373005] : [class_Groups_Ocomm__monoid__mult(_1372995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372997), _1372999)), 32554 ^ _779142 : [(32561 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372997), _1373001), _1372999))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372997, _1372995), hAPP(hAPP(c_COMBC(_1372997, _1372995, _1372995), hAPP(hAPP(c_COMBS(_1372997, _1372995, tc_fun(_1372995, _1372995)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1372995, tc_fun(_1372995, _1372995)), _1372997), c_If(_1372995)), hAPP(hAPP(c_COMBC(_1372997, _1372997, tc_HOL_Obool), c_fequal), _1373001))), _1373003)), _1373005)), _1372999) = hAPP(hAPP(c_Power_Opower__class_Opower(_1372995), _1373005), hAPP(c_Finite__Set_Ocard(_1372997), _1372999)))], (32555 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1372997), _1373001), _1372999)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372997, _1372995), hAPP(hAPP(c_COMBC(_1372997, _1372995, _1372995), hAPP(hAPP(c_COMBS(_1372997, _1372995, tc_fun(_1372995, _1372995)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1372995, tc_fun(_1372995, _1372995)), _1372997), c_If(_1372995)), hAPP(hAPP(c_COMBC(_1372997, _1372997, tc_HOL_Obool), c_fequal), _1373001))), _1373003)), _1373005)), _1372999) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1372995), hAPP(_1373003, _1373001)), hAPP(hAPP(c_Power_Opower__class_Opower(_1372995), _1373005), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1372997), _1372999)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (22843 ^ _779142) ^ [_1181431, _1181433, _1181435] : [class_Orderings_Olinorder(_1181431), 22846 ^ _779142 : [(22853 ^ _779142) ^ [] : [_1181433 = _1181435, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1181431), _1181433) = hAPP(c_SetInterval_Oord__class_OlessThan(_1181431), _1181435))], (22847 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1181431), _1181433) = hAPP(c_SetInterval_Oord__class_OlessThan(_1181431), _1181435), -(_1181433 = _1181435)]]], (39995 ^ _779142) ^ [_1559042, _1559044, _1559046] : [39997 ^ _779142 : [(40000 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1559042), 39996 ^ [_1559042, _1559044, _1559046]), c_Wellfounded_Oacc(_1559042, _1559046)))], (39998 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559042, _1559042)), hAPP(hAPP(c_Product__Type_OPair(_1559042, _1559042), 39996 ^ [_1559042, _1559044, _1559046]), _1559044)), _1559046)))]], -(hBOOL(hAPP(hAPP(c_member(_1559042), _1559044), c_Wellfounded_Oacc(_1559042, _1559046))))], (38524 ^ _779142) ^ [_1524790, _1524792, _1524794, _1524796] : [hBOOL(hAPP(c_Predicate_ORangeP(_1524790, _1524792, _1524794), _1524796)), -(hBOOL(hAPP(hAPP(_1524794, 38527 ^ [_1524790, _1524792, _1524794, _1524796]), _1524796)))], (30664 ^ _779142) ^ [_1328053, _1328055, _1328057, _1328059] : [class_Groups_Ocomm__monoid__add(_1328053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328055), _1328057)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328055, _1328053), _1328059), _1328057) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328053, _1328055, c_Groups_Oplus__class_Oplus(_1328053)), _1328059), c_Groups_Ozero__class_Ozero(_1328053)), _1328057))], (12505 ^ _779142) ^ [_994990, _994992] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994990), _994992) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994990), _994992)))], (48006 ^ _779142) ^ [_1746342, _1746344, _1746346, _1746348, _1746350] : [_1746342 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746344, _1746346, _1746348, _1746350), _1746342) = c_Lazy__Sequence_Ohit__bound(_1746346))], (45067 ^ _779142) ^ [_1683145, _1683147, _1683149, _1683151, _1683153, _1683155] : [c_List_Olist__all2(_1683145, _1683147, _1683149, _1683151, _1683153), -(c_List_Olist__all2(_1683145, _1683147, _1683149, hAPP(hAPP(c_List_Odrop(_1683145), _1683155), _1683151), hAPP(hAPP(c_List_Odrop(_1683147), _1683155), _1683153)))], (43977 ^ _779142) ^ [_1659006, _1659008, _1659010] : [class_Orderings_Olinorder(_1659006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1659006), _1659008)), -(c_List_Olinorder__class_Osorted__list__of__set(_1659006, hAPP(hAPP(c_Set_Oinsert(_1659006), _1659010), _1659008)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659006, _1659006, c_COMBI(_1659006)), _1659010), c_List_Olinorder__class_Osorted__list__of__set(_1659006, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659006, tc_HOL_Obool)), _1659008), hAPP(hAPP(c_Set_Oinsert(_1659006), _1659010), c_Orderings_Obot__class_Obot(tc_fun(_1659006, tc_HOL_Obool)))))))], (20796 ^ _779142) ^ [_1144704, _1144706] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144704), _1144706)), _1144706) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144704), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144704, _1144706)))], (37813 ^ _779142) ^ [_1497973, _1497975, _1497977, _1497979] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497973), _1497975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497973, _1497973), tc_HOL_Obool)), _1497977), hAPP(hAPP(c_Product__Type_OSigma(_1497973, _1497973), _1497975), hAPP(c_COMBK(tc_fun(_1497973, tc_HOL_Obool), _1497973), _1497975)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1497973, tc_HOL_Obool)), _1497979), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1497973), _1497975), _1497977))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497973), _1497979)))], (41895 ^ _779142) ^ [_1610670, _1610672] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610670), hAPP(c_List_Oset(_1610670), _1610672))))], (30982 ^ _779142) ^ [_1334263, _1334265, _1334267] : [class_Orderings_Oord(_1334263), 30985 ^ _779142 : [(30992 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334263), _1334267), _1334265)), -(hBOOL(hAPP(hAPP(c_member(_1334263), _1334265), hAPP(c_SetInterval_Oord__class_OatLeast(_1334263), _1334267))))], (30986 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1334263), _1334265), hAPP(c_SetInterval_Oord__class_OatLeast(_1334263), _1334267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334263), _1334267), _1334265)))]]], (52505 ^ _779142) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (17541 ^ _779142) ^ [_1088302, _1088304, _1088306] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088302), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1088304, _1088306)), _1088306) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088302), _1088304), _1088306))], (44980 ^ _779142) ^ [_1680862, _1680864, _1680866, _1680868] : [hBOOL(hAPP(c_List_Olistsp(_1680862, _1680864), hAPP(hAPP(c_List_Oappend(_1680862), _1680866), _1680868))), 44983 ^ _779142 : [(44986 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680862, _1680864), _1680868)))], (44984 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680862, _1680864), _1680866)))]]], (42226 ^ _779142) ^ [_1620046] : [c_List_Onat__list(_1620046), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1620046)))], (17877 ^ _779142) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (29251 ^ _779142) ^ [_1298156, _1298158] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298156, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1298156, tc_HOL_Obool))), _1298158) = c_Orderings_Obot__class_Obot(tc_fun(_1298156, tc_HOL_Obool)))], (38812 ^ _779142) ^ [_1530665, _1530667, _1530669, _1530671, _1530673] : [c_Relation_Orefl__on(_1530665, _1530667, _1530669), c_Relation_Orefl__on(_1530665, _1530671, _1530673), -(c_Relation_Orefl__on(_1530665, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530665, tc_HOL_Obool)), _1530667), _1530671), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1530665, _1530665), tc_HOL_Obool)), _1530669), _1530673)))], (21912 ^ _779142) ^ [_1164333, _1164335, _1164337, _1164339] : [class_Rings_Olinordered__semidom(_1164333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164333), _1164335), _1164337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164333), c_Groups_Ozero__class_Ozero(_1164333)), _1164335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164333), hAPP(hAPP(c_Power_Opower__class_Opower(_1164333), _1164335), _1164339)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164333), _1164337), _1164339))))], (17961 ^ _779142) ^ [_1095487, _1095489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095487), _1095489)), -(_1095489 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095487), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 17964 ^ [_1095487, _1095489]))))], (10919 ^ _779142) ^ [_967648, _967650, _967652] : [_967650 = _967652, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967648)), _967650) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967648)), _967652))], (22418 ^ _779142) ^ [_1173570, _1173572] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1173570), _1173572) = 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), _1173570)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1173572)))))], (22260 ^ _779142) ^ [_1170675, _1170677, _1170679] : [class_Rings_Olinordered__semidom(_1170675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170675), c_Groups_Ozero__class_Ozero(_1170675)), _1170677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170675), _1170677), c_Groups_Oone__class_Oone(_1170675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170675), hAPP(hAPP(c_Power_Opower__class_Opower(_1170675), _1170677), hAPP(c_Nat_OSuc, _1170679))), c_Groups_Oone__class_Oone(_1170675))))], (40741 ^ _779142) ^ [_1577890, _1577892, _1577894] : [-(hAPP(c_Relation_Oconverse(_1577890, _1577892), hAPP(c_Relation_Oconverse(_1577892, _1577890), _1577894)) = _1577894)], (23169 ^ _779142) ^ [_1187061, _1187063, _1187065] : [class_Divides_Oring__div(_1187061), -(c_Divides_Odiv__class_Omod(_1187061, hAPP(c_Groups_Ouminus__class_Ouminus(_1187061), _1187063), _1187065) = c_Divides_Odiv__class_Omod(_1187061, hAPP(c_Groups_Ouminus__class_Ouminus(_1187061), c_Divides_Odiv__class_Omod(_1187061, _1187063, _1187065)), _1187065))], (52183 ^ _779142) ^ [_1831575, _1831577] : [class_Orderings_Oorder(_1831575), -(class_Orderings_Oorder(tc_fun(_1831577, _1831575)))], (25610 ^ _779142) ^ [_1229264, _1229266] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1229264)), c_Int_OBit1(_1229266)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229264), _1229266)))], (34556 ^ _779142) ^ [_1417214, _1417216, _1417218, _1417220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417214), _1417216)), 34559 ^ _779142 : [(34560 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417218), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417214, tc_fun(_1417218, tc_HOL_Obool)), _1417216), _1417220))), 34563 ^ _779142 : [(34564 ^ _779142) ^ [_1417398] : [hBOOL(hAPP(hAPP(c_member(_1417214), _1417398), _1417216)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417218), hAPP(_1417220, _1417398))))]]], (34570 ^ _779142) ^ [] : [34572 ^ _779142 : [(34575 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417218), hAPP(_1417220, 34571 ^ [_1417214, _1417216, _1417218, _1417220])))], (34573 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417214), 34571 ^ [_1417214, _1417216, _1417218, _1417220]), _1417216)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417218), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417214, tc_fun(_1417218, tc_HOL_Obool)), _1417216), _1417220))))]]], (26766 ^ _779142) ^ [_1250588, _1250590, _1250592] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250588, tc_HOL_Obool)), _1250590), _1250592) = c_Orderings_Obot__class_Obot(tc_fun(_1250588, tc_HOL_Obool)), 26769 ^ _779142 : [(26772 ^ _779142) ^ [] : [-(_1250592 = c_Orderings_Obot__class_Obot(tc_fun(_1250588, tc_HOL_Obool)))], (26770 ^ _779142) ^ [] : [-(_1250590 = c_Orderings_Obot__class_Obot(tc_fun(_1250588, tc_HOL_Obool)))]]], (23929 ^ _779142) ^ [_1200474, _1200476, _1200478, _1200480] : [class_Int_Onumber__ring(_1200474), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200474), hAPP(c_Int_Onumber__class_Onumber__of(_1200474), _1200476)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200474), _1200478), hAPP(c_Int_Onumber__class_Onumber__of(_1200474), _1200480))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200474), hAPP(c_Int_Onumber__class_Onumber__of(_1200474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200476), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200480)))), _1200478))], (4392 ^ _779142) ^ [_845808, _845810] : [_845810 = _845808, -(c_Lazy__Sequence_Oyieldn(_845810) = c_Lazy__Sequence_Oyieldn(_845808))], (10599 ^ _779142) ^ [_962404, _962406] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962404), _962406) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10602 ^ _779142 : [(10605 ^ _779142) ^ [] : [-(_962406 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10603 ^ _779142) ^ [] : [-(_962404 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (52319 ^ _779142) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (29079 ^ _779142) ^ [_1294532, _1294534, _1294536, _1294538] : [class_Lattices_Osemilattice__inf(_1294532), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294532), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294532), _1294534), _1294536)), _1294538) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294532), _1294534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294532), _1294536), _1294538)))], (26816 ^ _779142) ^ [_1251535, _1251537, _1251539, _1251541] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251535, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1251535), _1251537), _1251539)), _1251541) = hAPP(hAPP(c_Set_Oinsert(_1251535), _1251537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251535, tc_HOL_Obool)), _1251539), _1251541)))], (50893 ^ _779142) ^ [_1809726, _1809728] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809726, _1809728) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809726), _1809728))], (44382 ^ _779142) ^ [_1667410, _1667412, _1667414, _1667416] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667410)), hAPP(hAPP(c_List_Omap(_1667412, _1667410), _1667414), _1667416)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667412)), _1667416))], (9501 ^ _779142) ^ [_941022, _941024, _941026] : [class_Rings_Olinordered__idom(_941022), -(_941024 = _941026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941022), _941024), _941026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941022), _941026), _941024)))], (31695 ^ _779142) ^ [_1348069] : [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), _1348069))), 31698 ^ _779142 : [(31705 ^ _779142) ^ [] : [-(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), _1348069))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348069)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348069)), 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), _1348069)))))], (31699 ^ _779142) ^ [] : [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), _1348069)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348069)) = 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), _1348069))))]]], (49947 ^ _779142) ^ [_1789218, _1789220, _1789222, _1789224, _1789226, _1789228, _1789230, _1789232] : [c_Fun_Obij__betw(_1789218, _1789220, _1789222, _1789224, _1789226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789218, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1789228, _1789218, _1789230), _1789232)), _1789224)), 49954 ^ _779142 : [(49961 ^ _779142) ^ [] : [c_Fun_Obij__betw(_1789228, _1789220, hAPP(c_Fun_Ocomp(_1789218, _1789220, _1789228, _1789222), _1789230), _1789232, _1789226), -(c_Fun_Obij__betw(_1789228, _1789218, _1789230, _1789232, _1789224))], (49955 ^ _779142) ^ [] : [c_Fun_Obij__betw(_1789228, _1789218, _1789230, _1789232, _1789224), -(c_Fun_Obij__betw(_1789228, _1789220, hAPP(c_Fun_Ocomp(_1789218, _1789220, _1789228, _1789222), _1789230), _1789232, _1789226))]]], (23653 ^ _779142) ^ [_1195683] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1195683) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195683))], (24728 ^ _779142) ^ [_1213995] : [c_Int_OMin = c_Int_OBit1(_1213995), -(c_Int_OMin = _1213995)], (46256 ^ _779142) ^ [_1708996, _1708998, _1709000, _1709002, _1709004] : [class_Orderings_Olinorder(_1708996), c_List_Olinorder__class_Osorted(_1708996, hAPP(hAPP(c_List_Omap(_1708998, _1708996), _1709000), _1709002)), -(c_List_Olinorder__class_Osorted(_1708996, hAPP(hAPP(c_List_Omap(_1708998, _1708996), _1709000), c_List_Oremove1(_1708998, _1709004, _1709002))))], (42323 ^ _779142) ^ [_1622239, _1622241, _1622243, _1622245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622239), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622241)), _1622243))), -(hAPP(hAPP(c_List_Onth(_1622241), hAPP(hAPP(c_List_Olist__update(_1622241, _1622243), _1622239), _1622245)), _1622239) = _1622245)], (10925 ^ _779142) ^ [_967765, _967767] : [class_Groups_Ocomm__monoid__add(_967765), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967765), _967767), c_Groups_Ozero__class_Ozero(_967765)) = _967767)], (4350 ^ _779142) ^ [_845121, _845123, _845125, _845127] : [-(c_Lazy__Sequence_Osmall__lazy_H(_845127, _845123) = c_Lazy__Sequence_Osmall__lazy_H(_845125, _845121)), _845127 = _845125, _845123 = _845121], (52479 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (48024 ^ _779142) ^ [_1746634, _1746636, _1746638, _1746640, _1746642] : [-(_1746634 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746636, _1746638, _1746640, _1746642), _1746634) = hAPP(c_Lazy__Sequence_Obind(_1746636, _1746638, hAPP(_1746640, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746634), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1746636, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746638)), _1746642), _1746634)))], (19325 ^ _779142) ^ [_1118969, _1118971] : [class_Groups_Oordered__ab__group__add__abs(_1118969), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118969), c_Groups_Ozero__class_Ozero(_1118969)), hAPP(c_Groups_Oabs__class_Oabs(_1118969), _1118971))))], (17075 ^ _779142) ^ [_1079566, _1079568, _1079570] : [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), _1079566), _1079568)), _1079570))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079570), _1079566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079568)))], (28048 ^ _779142) ^ [_1274532, _1274534, _1274536, _1274538] : [class_Orderings_Olinorder(_1274532), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274532), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274532), _1274534), _1274536)), _1274538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274532), _1274534), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274532), _1274536), _1274538)))], (50915 ^ _779142) ^ [_1810028, _1810030] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810028), _1810030)), -(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)))), _1810030, _1810028) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (17921 ^ _779142) ^ [_1094819, _1094821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094819), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 17924 ^ _779142 : [(17927 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094819), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1094821, _1094819))))], (17925 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1094821, _1094819)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (48965 ^ _779142) ^ [_1768033, _1768035, _1768037, _1768039] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768033, tc_fun(_1768035, tc_HOL_Obool)), _1768037), _1768039) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1768035, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1768035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768033, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1768035, tc_HOL_Obool)), c_HOL_OEx(_1768033)), hAPP(hAPP(c_COMBB(tc_fun(_1768033, tc_HOL_Obool), tc_fun(_1768033, tc_HOL_Obool), tc_fun(_1768035, tc_HOL_Obool)), hAPP(c_COMBS(_1768033, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768033), c_fconj), hAPP(hAPP(c_COMBC(_1768033, tc_fun(_1768033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1768033)), _1768037)))), hAPP(hAPP(c_COMBC(tc_fun(_1768035, tc_HOL_Obool), tc_fun(_1768033, tc_fun(_1768035, tc_HOL_Obool)), tc_fun(_1768033, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768035, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1768033, tc_fun(_1768035, tc_HOL_Obool)), tc_fun(_1768033, tc_HOL_Obool)), tc_fun(_1768035, tc_HOL_Obool)), c_COMBB(tc_fun(_1768035, tc_HOL_Obool), tc_HOL_Obool, _1768033)), c_fequal)), _1768039))))))], (45274 ^ _779142) ^ [_1687727, _1687729] : [-(c_Enum_Oenum__the(_1687727, _1687729) = c_HOL_OThe(_1687727, _1687729))], (31220 ^ _779142) ^ [_1338725, _1338727, _1338729] : [class_Orderings_Olinorder(_1338725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338725), _1338727), _1338729)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338725, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1338725, _1338727, _1338729)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338725), _1338729)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338725), _1338727))], (12284 ^ _779142) ^ [_991243, _991245, _991247, _991249] : [class_Groups_Ocomm__monoid__add(_991243), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_991245), _991247))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991245, _991243), _991249), _991247) = c_Groups_Ozero__class_Ozero(_991243))], (48497 ^ _779142) ^ [_1757137, _1757139, _1757141, _1757143] : [48498 ^ _779142 : [(48501 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757137), _1757141), _1757143))], (48499 ^ _779142) ^ [] : [_1757139 = _1757143]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1757137), hAPP(hAPP(c_List_Olist_OCons(_1757137), _1757139), _1757141)), _1757143)))], (15601 ^ _779142) ^ [_1052603, _1052605, _1052607, _1052609] : [class_Int_Onumber__ring(_1052603), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052603), hAPP(c_Int_Onumber__class_Onumber__of(_1052603), _1052605)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052603), hAPP(c_Int_Onumber__class_Onumber__of(_1052603), _1052607)), _1052609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052603), hAPP(c_Int_Onumber__class_Onumber__of(_1052603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052605), _1052607))), _1052609))], (17569 ^ _779142) ^ [_1088733, _1088735, _1088737, _1088739] : [class_Divides_Osemiring__div(_1088733), -(c_Divides_Odiv__class_Omod(_1088733, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088733), _1088735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088733), _1088737), _1088739)), _1088737) = c_Divides_Odiv__class_Omod(_1088733, _1088735, _1088737))], (17103 ^ _779142) ^ [_1080028, _1080030, _1080032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080028)), _1080028 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1080030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1080028), _1080032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1080032), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19573 ^ _779142) ^ [_1123177] : [-(_1123177 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1123177), _1123177) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40925 ^ _779142) ^ [_1582556, _1582558, _1582560, _1582562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582556, _1582558), tc_HOL_Obool)), _1582560), _1582562)), c_Relation_Osingle__valued(_1582556, _1582558, _1582562), -(c_Relation_Osingle__valued(_1582556, _1582558, _1582560))], (18527 ^ _779142) ^ [_1105345, _1105347] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105345)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105347))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1105345), _1105347)))], (22913 ^ _779142) ^ [_1182624, _1182626, _1182628] : [class_Groups_Oordered__ab__group__add(_1182624), 22916 ^ _779142 : [(22923 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182624), _1182628), _1182626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182624), hAPP(c_Groups_Ouminus__class_Ouminus(_1182624), _1182626)), hAPP(c_Groups_Ouminus__class_Ouminus(_1182624), _1182628))))], (22917 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182624), hAPP(c_Groups_Ouminus__class_Ouminus(_1182624), _1182626)), hAPP(c_Groups_Ouminus__class_Ouminus(_1182624), _1182628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182624), _1182628), _1182626)))]]], (47698 ^ _779142) ^ [_1740104, _1740106, _1740108] : [-(c_List_Olist__ex(_1740104, _1740106, _1740108)), 47699 ^ _779142 : [(47700 ^ _779142) ^ [_1740161] : [hBOOL(hAPP(hAPP(c_member(_1740104), _1740161), hAPP(c_List_Oset(_1740104), _1740108))), hBOOL(hAPP(_1740106, _1740161))]]], (52789 ^ _779142) ^ [] : [-(v_G = hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))], (40121 ^ _779142) ^ [_1562229, _1562231] : [c_Wellfounded_Owf(_1562229, _1562231), 40124 ^ _779142 : [(40125 ^ _779142) ^ [_1562361] : [40126 ^ _779142 : [(40127 ^ _779142) ^ [_1562466] : [hBOOL(hAPP(hAPP(c_member(_1562229), _1562466), _1562361))]], 40129 ^ _779142 : [(40132 ^ _779142) ^ [_1562588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562229, _1562229)), hAPP(hAPP(c_Product__Type_OPair(_1562229, _1562229), _1562588), 40128 ^ [_1562229, _1562231, _1562361])), _1562231)), hBOOL(hAPP(hAPP(c_member(_1562229), _1562588), _1562361))], (40130 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562229), 40128 ^ [_1562229, _1562231, _1562361]), _1562361)))]]]]], (26486 ^ _779142) ^ [_1245002, _1245004, _1245006] : [class_Lattices_Osemilattice__sup(_1245002), 26489 ^ _779142 : [(26496 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245002), _1245004), _1245006) = _1245006, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245002), _1245004), _1245006)))], (26490 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245002), _1245004), _1245006)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245002), _1245004), _1245006) = _1245006)]]], (42457 ^ _779142) ^ [_1625238, _1625240] : [hBOOL(hAPP(c_List_Odistinct(_1625238), _1625240)), -(hAPP(c_Finite__Set_Ocard(_1625238), hAPP(c_List_Oset(_1625238), _1625240)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625238)), _1625240))], (48458 ^ _779142) ^ [_1756309] : [-(c_Lazy__Sequence_Oyieldn(_1756309) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1756309), _1756309, c_Lazy__Sequence_Oyield(_1756309)))], (22672 ^ _779142) ^ [_1178519] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1178519) = 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), _1178519))))], (27518 ^ _779142) ^ [_1264802] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1264802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1264802)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29526 ^ _779142) ^ [_1304495, _1304497, _1304499] : [class_Orderings_Oorder(_1304495), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304495, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1304495), _1304497)), c_SetInterval_Oord__class_OatLeastAtMost(_1304495, _1304497, _1304499)) = c_Orderings_Obot__class_Obot(tc_fun(_1304495, tc_HOL_Obool)))], (38390 ^ _779142) ^ [_1519461, _1519463, _1519465, _1519467] : [hAPP(hAPP(c_Relation_Orel__comp(_1519461, _1519461, _1519461), _1519463), _1519465) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519461, _1519461), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519461, _1519461, _1519461), _1519463), _1519467) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519461, _1519461), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1519461, _1519461, _1519461), _1519463), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519461, _1519461), tc_HOL_Obool)), _1519465), _1519467)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519461, _1519461), tc_HOL_Obool)))], (34328 ^ _779142) ^ [_1409966, _1409968, _1409970, _1409972, _1409974, _1409976] : [class_Complete__Lattice_Ocomplete__lattice(_1409966), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409968, _1409966), _1409970), hAPP(hAPP(c_COMBB(tc_fun(_1409972, _1409966), _1409966, _1409968), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409972, _1409966), _1409974)), _1409976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409972, _1409966), _1409974), hAPP(hAPP(c_COMBB(tc_fun(_1409968, _1409966), _1409966, _1409972), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409968, _1409966), _1409970)), hAPP(c_COMBC(_1409968, _1409972, _1409966), _1409976))))], (39800 ^ _779142) ^ [_1554596, _1554598, _1554600, _1554602] : [c_Finite__Set_Ofolding(_1554596, _1554598, _1554600, _1554602), -(hAPP(_1554602, c_Orderings_Obot__class_Obot(tc_fun(_1554596, tc_HOL_Obool))) = c_Fun_Oid(_1554598))], (52647 ^ _779142) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (37353 ^ _779142) ^ [_1485493, _1485495] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485493))), -(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)), _1485493))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1485495)))) = 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)), _1485493))), 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, _1485495))))))], (5286 ^ _779142) ^ [_859945, _859947, _859949, _859951, _859953, _859955, _859957, _859959, _859961, _859963] : [-(c_SetInterval_Oord_OatLeastLessThan(_859963, _859959, _859955, _859951, _859947) = c_SetInterval_Oord_OatLeastLessThan(_859961, _859957, _859953, _859949, _859945)), _859963 = _859961, _859959 = _859957, _859955 = _859953, _859951 = _859949, _859947 = _859945], (23975 ^ _779142) ^ [_1201459, _1201461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201459))), -(c_SMT_Oz3div(_1201461, _1201459) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201461), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201459))))], (21680 ^ _779142) ^ [_1160014, _1160016] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1160014, _1160016))))], (45016 ^ _779142) ^ [_1681633, _1681635, _1681637, _1681639, _1681641] : [-(c_Enum_Oproduct(_1681633, _1681635, hAPP(hAPP(c_List_Olist_OCons(_1681633), _1681637), _1681639), _1681641) = hAPP(hAPP(c_List_Oappend(tc_prod(_1681633, _1681635)), hAPP(hAPP(c_List_Omap(_1681635, tc_prod(_1681633, _1681635)), hAPP(c_Product__Type_OPair(_1681633, _1681635), _1681637)), _1681641)), c_Enum_Oproduct(_1681633, _1681635, _1681639, _1681641)))], (39287 ^ _779142) ^ [_1541937, _1541939, _1541941, _1541943] : [-(hAPP(c_Set_OCollect(_1541937), hAPP(hAPP(c_COMBB(tc_fun(_1541939, tc_HOL_Obool), tc_HOL_Obool, _1541937), c_HOL_OAll(_1541939)), hAPP(hAPP(c_COMBB(tc_fun(_1541939, tc_HOL_Obool), tc_fun(_1541939, tc_HOL_Obool), _1541937), hAPP(c_COMBS(_1541939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541939), c_fimplies), hAPP(hAPP(c_COMBC(_1541939, tc_fun(_1541939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541939)), _1541941)))), _1541943))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1541939, tc_fun(_1541937, tc_HOL_Obool)), _1541941), hAPP(hAPP(c_COMBB(tc_fun(_1541937, tc_HOL_Obool), tc_fun(_1541937, tc_HOL_Obool), _1541939), c_Set_OCollect(_1541937)), hAPP(c_COMBC(_1541937, _1541939, tc_HOL_Obool), _1541943))))], (10841 ^ _779142) ^ [_966333, _966335] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966333)), _966335) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966333), hAPP(c_Nat_OSuc, _966335)))], (44542 ^ _779142) ^ [_1671251, _1671253, _1671255, _1671257] : [c_Fun_Oinj__on(_1671251, _1671253, _1671255, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671251, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1671251), tc_fun(_1671251, tc_HOL_Obool), c_List_Oset(_1671251)), _1671257))), -(c_Fun_Oinj__on(tc_List_Olist(_1671251), tc_List_Olist(_1671253), hAPP(c_List_Omap(_1671251, _1671253), _1671255), _1671257))], (52161 ^ _779142) ^ [_1831288, _1831290] : [class_Orderings_Opreorder(_1831288), -(class_Orderings_Opreorder(tc_fun(_1831290, _1831288)))], (43590 ^ _779142) ^ [_1650599, _1650601, _1650603, _1650605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650599), _1650601)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650603)), _1650605))), -(hAPP(hAPP(c_List_Onth(_1650603), hAPP(hAPP(c_List_Odrop(_1650603), _1650599), _1650605)), _1650601) = hAPP(hAPP(c_List_Onth(_1650603), _1650605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650599), _1650601)))], (52709 ^ _779142) ^ [_1837014] : [hBOOL(hAPP(c_fNot, _1837014)), hBOOL(_1837014)], (5406 ^ _779142) ^ [_861859, _861861] : [_861861 = _861859, -(c_Divides_Odiv__class_Odiv(_861861) = c_Divides_Odiv__class_Odiv(_861859))], (36834 ^ _779142) ^ [_1473136, _1473138, _1473140, _1473142] : [c_Fun_Oinj__on(_1473136, _1473138, _1473140, c_Orderings_Otop__class_Otop(tc_fun(_1473136, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1473136, _1473138, c_Orderings_Otop__class_Otop(tc_fun(_1473136, tc_HOL_Obool)), _1473140), hAPP(_1473140, _1473142)) = _1473142)], (46937 ^ _779142) ^ [_1723064, _1723066, _1723068] : [hBOOL(hAPP(c_List_Odistinct(_1723064), _1723066)), hBOOL(hAPP(hAPP(c_member(_1723064), _1723068), hAPP(c_List_Oset(_1723064), _1723066))), -(c_List_OtakeWhile(_1723064, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723064), c_fNot), hAPP(hAPP(c_COMBC(_1723064, _1723064, tc_HOL_Obool), c_fequal), _1723068)), hAPP(c_List_Orev(_1723064), _1723066)) = hAPP(c_List_Orev(_1723064), hAPP(c_List_Otl(_1723064), c_List_OdropWhile(_1723064, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723064), c_fNot), hAPP(hAPP(c_COMBC(_1723064, _1723064, tc_HOL_Obool), c_fequal), _1723068)), _1723066))))], (28432 ^ _779142) ^ [_1281661, _1281663, _1281665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1281661, tc_HOL_Obool), tc_HOL_Obool)), _1281663), _1281665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281661, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281661, tc_HOL_Obool), _1281663)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281661, tc_HOL_Obool), _1281665))))], (49574 ^ _779142) ^ [_1780741, _1780743, _1780745] : [hAPP(c_Fun_Ocomp(_1780743, _1780741, _1780741, c_Hilbert__Choice_Oinv__into(_1780741, _1780743, c_Orderings_Otop__class_Otop(tc_fun(_1780741, tc_HOL_Obool)), _1780745)), _1780745) = c_Fun_Oid(_1780741), -(c_Fun_Oinj__on(_1780741, _1780743, _1780745, c_Orderings_Otop__class_Otop(tc_fun(_1780741, tc_HOL_Obool))))], (17982 ^ _779142) ^ [_1095896, _1095898] : [class_Rings_Osemiring__1(_1095896), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1095896), hAPP(c_Nat_OSuc, _1095898)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095896), c_Groups_Oone__class_Oone(_1095896)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1095896), _1095898)))], (20634 ^ _779142) ^ [_1141556, _1141558, _1141560, _1141562, _1141564, _1141566] : [hBOOL(hAPP(hAPP(c_member(_1141556), _1141558), c_SetInterval_Oord_OgreaterThanAtMost(_1141556, _1141560, _1141562, _1141564, _1141566))), 20637 ^ _779142 : [(20640 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1141560, _1141558), _1141566)))], (20638 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1141562, _1141564), _1141558)))]]], (35523 ^ _779142) ^ [_1443541] : [-(c_Wellfounded_Omeasure(_1443541) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1443541), c_Wellfounded_Oless__than))], (22146 ^ _779142) ^ [_1168537, _1168539, _1168541] : [class_Rings_Olinordered__semidom(_1168537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168537), c_Groups_Oone__class_Oone(_1168537)), _1168539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168537), c_Groups_Oone__class_Oone(_1168537)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168537), _1168539), hAPP(c_Nat_OSuc, _1168541)))))], (4040 ^ _779142) ^ [_840248, _840250, _840252, _840254] : [-(c_Lazy__Sequence_Ohb__single(_840254, _840250) = c_Lazy__Sequence_Ohb__single(_840252, _840248)), _840254 = _840252, _840250 = _840248], (18891 ^ _779142) ^ [] : [c_Int_OMin = c_Int_OPls], (3040 ^ _779142) ^ [_824270, _824272, _824274, _824276] : [-(c_List_Olistrel1(_824276, _824272) = c_List_Olistrel1(_824274, _824270)), _824276 = _824274, _824272 = _824270], (38228 ^ _779142) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (4248 ^ _779142) ^ [_843406, _843408, _843410, _843412, _843414, _843416, _843418, _843420, _843422, _843424] : [-(c_Predicate_Opred__comp(_843424, _843420, _843416, _843412, _843408) = c_Predicate_Opred__comp(_843422, _843418, _843414, _843410, _843406)), _843424 = _843422, _843420 = _843418, _843416 = _843414, _843412 = _843410, _843408 = _843406], (41745 ^ _779142) ^ [_1606526, _1606528, _1606530, _1606532] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606526)), hAPP(hAPP(c_List_Olist_OCons(_1606526), _1606528), _1606530)), c_List_Olists(_1606526, _1606532)))), hBOOL(hAPP(hAPP(c_member(_1606526), _1606528), _1606532)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606526)), _1606530), c_List_Olists(_1606526, _1606532)))], (44566 ^ _779142) ^ [_1671809, _1671811, _1671813, _1671815] : [class_Groups_Ocomm__monoid__add(_1671809), hBOOL(hAPP(c_List_Odistinct(_1671811), _1671813)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671809), hAPP(hAPP(c_List_Omap(_1671811, _1671809), _1671815), _1671813)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671811, _1671809), _1671815), hAPP(c_List_Oset(_1671811), _1671813)))], (25486 ^ _779142) ^ [_1227074, _1227076] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1227074)), c_Int_OBit0(_1227076)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227074), _1227076)))], (26657 ^ _779142) ^ [_1248511, _1248513, _1248515, _1248517] : [26658 ^ _779142 : [(26659 ^ _779142) ^ [_1248621] : [hBOOL(hAPP(hAPP(c_member(_1248511), _1248621), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248511, tc_HOL_Obool)), _1248513), _1248515))), hBOOL(hAPP(_1248517, _1248621))]], 26667 ^ _779142 : [(26670 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1248517, 26666 ^ [_1248511, _1248513, _1248515, _1248517])))], (26668 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248511), 26666 ^ [_1248511, _1248513, _1248515, _1248517]), _1248513)))]], 26672 ^ _779142 : [(26675 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1248517, 26671 ^ [_1248511, _1248513, _1248515, _1248517])))], (26673 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248511), 26671 ^ [_1248511, _1248513, _1248515, _1248517]), _1248515)))]]], (25154 ^ _779142) ^ [] : [-(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)))))], (46849 ^ _779142) ^ [_1721299, _1721301, _1721303, _1721305, _1721307] : [-(hAPP(hAPP(c_List_Ozip(_1721299, _1721301), _1721303), c_List_OtakeWhile(_1721301, _1721305, _1721307)) = c_List_OtakeWhile(tc_prod(_1721299, _1721301), hAPP(c_Fun_Ocomp(_1721301, tc_HOL_Obool, tc_prod(_1721299, _1721301), _1721305), c_Product__Type_Osnd(_1721299, _1721301)), hAPP(hAPP(c_List_Ozip(_1721299, _1721301), _1721303), _1721307)))], (52603 ^ _779142) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (30461 ^ _779142) ^ [_1323878, _1323880, _1323882] : [class_Lattices_Olattice(_1323878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323878), _1323880)), -(_1323880 = c_Orderings_Obot__class_Obot(tc_fun(_1323878, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323878), _1323882)), -(_1323882 = c_Orderings_Obot__class_Obot(tc_fun(_1323878, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323878, tc_HOL_Obool)), _1323880), _1323882) = c_Orderings_Obot__class_Obot(tc_fun(_1323878, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1323878, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323878, tc_HOL_Obool)), _1323880), _1323882)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323878), c_Big__Operators_Olattice__class_OInf__fin(_1323878, _1323880)), c_Big__Operators_Olattice__class_OInf__fin(_1323878, _1323882)))], (52471 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (23637 ^ _779142) ^ [_1195412, _1195414] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1195412), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195412), _1195414))], (38453 ^ _779142) ^ [_1521132, _1521134, _1521136, _1521138] : [38454 ^ _779142 : [(38455 ^ _779142) ^ [_1521207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521136, _1521132)), hAPP(hAPP(c_Product__Type_OPair(_1521136, _1521132), _1521207), _1521134)), _1521138))]], -(hBOOL(hAPP(hAPP(c_member(_1521132), _1521134), hAPP(c_Relation_ORange(_1521136, _1521132), _1521138))))], (5689 ^ _779142) ^ [_868935, _868937, _868939, _868941] : [5690 ^ _779142 : [(5693 ^ _779142) ^ [] : [_868937 = _868941], (5691 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_868935), _868937), _868939))]], -(hBOOL(hAPP(hAPP(c_member(_868935), _868937), hAPP(hAPP(c_Set_Oinsert(_868935), _868941), _868939))))], (46716 ^ _779142) ^ [_1718378, _1718380] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718378), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1718378))), c_List_Otranspose(_1718378, _1718380)))))], (32307 ^ _779142) ^ [_1367286, _1367288, _1367290] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1367286, tc_HOL_Obool)), _1367290), hAPP(c_Set_OPow(_1367286), _1367288))), -(hBOOL(hAPP(c_Predicate_OPowp(_1367286, hAPP(hAPP(c_COMBC(_1367286, tc_fun(_1367286, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367286)), _1367288)), _1367290)))], (9859 ^ _779142) ^ [_947156, _947158] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947156), _947158)), _947156)))], (7770 ^ _779142) ^ [_907385, _907387, _907389] : [class_Orderings_Oorder(_907385), -(_907387 = _907389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907385), _907387), _907389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907385), _907387), _907389)))], (43923 ^ _779142) ^ [_1657769, _1657771, _1657773] : [class_Lattices_Olattice(_1657769), -(c_Big__Operators_Olattice__class_OSup__fin(_1657769, hAPP(c_List_Oset(_1657769), hAPP(hAPP(c_List_Olist_OCons(_1657769), _1657771), _1657773))) = hAPP(c_List_Ofoldl(_1657769, _1657769, c_Lattices_Osemilattice__sup__class_Osup(_1657769), _1657771), _1657773))], (35427 ^ _779142) ^ [_1441051, _1441053] : [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)), _1441051), _1441053)), 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)), _1441051), 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)), _1441053), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (43959 ^ _779142) ^ [_1658555, _1658557, _1658559, _1658561] : [class_Complete__Lattice_Ocomplete__lattice(_1658555), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658557, _1658555), hAPP(c_List_Oset(_1658557), _1658559)), _1658561) = hAPP(c_List_Ofoldl(_1658555, _1658557, hAPP(c_COMBC(_1658557, _1658555, _1658555), hAPP(hAPP(c_COMBB(_1658555, tc_fun(_1658555, _1658555), _1658557), c_Lattices_Osemilattice__sup__class_Osup(_1658555)), _1658561)), c_Orderings_Obot__class_Obot(_1658555)), _1658559))], (36896 ^ _779142) ^ [_1474292, _1474294, _1474296, _1474298, _1474300, _1474302] : [c_Typedef_Otype__definition(_1474292, _1474294, _1474296, _1474298, _1474300), -(hAPP(_1474298, hAPP(_1474296, _1474302)) = _1474302)], (32323 ^ _779142) ^ [_1367758, _1367760, _1367762, _1367764] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1367758), _1367760)), -(hAPP(c_Set_Oimage(_1367758, _1367762, _1367764), _1367760) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1367762, tc_HOL_Obool), _1367758, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367762, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1367758, tc_fun(_1367762, tc_HOL_Obool), tc_fun(_1367762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1367762, tc_fun(tc_fun(_1367762, tc_HOL_Obool), tc_fun(_1367762, tc_HOL_Obool)), _1367758), c_Set_Oinsert(_1367762)), _1367764)), c_Orderings_Obot__class_Obot(tc_fun(_1367762, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1367762, tc_HOL_Obool))), _1367760))], (18915 ^ _779142) ^ [_1111929] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111929), c_Int_OMin) = c_Int_Opred(_1111929))], (3488 ^ _779142) ^ [_831214, _831216, _831218, _831220, _831222, _831224, _831226, _831228] : [-(c_List_Olinorder__class_Osort__key(_831228, _831224, _831220, _831216) = c_List_Olinorder__class_Osort__key(_831226, _831222, _831218, _831214)), _831228 = _831226, _831224 = _831222, _831220 = _831218, _831216 = _831214], (40440 ^ _779142) ^ [_1570691, _1570693] : [-(hAPP(c_Relation_ODomain(_1570691, _1570691), c_Transitive__Closure_Ortrancl(_1570691, _1570693)) = c_Orderings_Otop__class_Otop(tc_fun(_1570691, tc_HOL_Obool)))], (34943 ^ _779142) ^ [_1427932, _1427934, _1427936] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427932, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427932, tc_HOL_Obool), _1427934)), _1427936) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1427932, tc_HOL_Obool), tc_fun(_1427932, tc_HOL_Obool)), _1427934), hAPP(hAPP(c_COMBC(tc_fun(_1427932, tc_HOL_Obool), tc_fun(_1427932, tc_HOL_Obool), tc_fun(_1427932, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427932, tc_HOL_Obool))), _1427936)))], (1970 ^ _779142) ^ [_807521, _807523] : [_807523 = _807521, -(v_mgt(_807523) = v_mgt(_807521))], (9551 ^ _779142) ^ [_941744, _941746] : [-(_941744 = _941746), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941744), _941746))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941746), _941744)))], (8731 ^ _779142) ^ [_925999, _926001, _926003, _926005] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925999), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925999), _926001), _926003)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925999), _926005), _926003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925999), _926001), _926005)))], (30876 ^ _779142) ^ [_1332407, _1332409] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332407, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1332407, tc_HOL_Obool))), _1332409) = _1332409)], (52591 ^ _779142) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (17481 ^ _779142) ^ [_1086986, _1086988, _1086990, _1086992] : [class_Divides_Osemiring__div(_1086986), -(c_Divides_Odiv__class_Omod(_1086986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086986), _1086988), _1086990), _1086992) = c_Divides_Odiv__class_Omod(_1086986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086986), c_Divides_Odiv__class_Omod(_1086986, _1086988, _1086992)), c_Divides_Odiv__class_Omod(_1086986, _1086990, _1086992)), _1086992))], (47511 ^ _779142) ^ [_1736408, _1736410, _1736412, _1736414, _1736416] : [-(hAPP(hAPP(c_List_Olist_OCons(_1736408), _1736410), _1736412) = hAPP(c_List_Ofilter(_1736408, _1736414), _1736416)), 47512 ^ _779142 : [(47513 ^ _779142) ^ [_1736536, _1736538] : [_1736416 = hAPP(hAPP(c_List_Oappend(_1736408), _1736538), hAPP(hAPP(c_List_Olist_OCons(_1736408), _1736410), _1736536)), 47519 ^ _779142 : [(47522 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1736414, 47518 ^ [_1736408, _1736410, _1736412, _1736414, _1736416, _1736536, _1736538])))], (47520 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736408), 47518 ^ [_1736408, _1736410, _1736412, _1736414, _1736416, _1736536, _1736538]), hAPP(c_List_Oset(_1736408), _1736538))))]], hBOOL(hAPP(_1736414, _1736410)), _1736412 = hAPP(c_List_Ofilter(_1736408, _1736414), _1736536)]]], (42279 ^ _779142) ^ [_1621138, _1621140, _1621142, _1621144] : [-(_1621138 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621140)), _1621142)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1621140, hAPP(hAPP(c_List_Olist__update(_1621140, _1621142), _1621138), _1621144)) = hAPP(hAPP(c_List_Olist__update(_1621140, c_List_Obutlast(_1621140, _1621142)), _1621138), _1621144))], (35537 ^ _779142) ^ [_1443903, _1443905] : [-(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), _1443903), _1443905)), 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), _1443905), _1443903)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36536 ^ _779142) ^ [_1466429, _1466431, _1466433, _1466435, _1466437] : [c_Fun_Oinj__on(_1466429, _1466431, _1466433, c_Orderings_Otop__class_Otop(tc_fun(_1466429, tc_HOL_Obool))), 36539 ^ _779142 : [(36546 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466429, tc_HOL_Obool)), _1466435), _1466437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466431, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466429, _1466431, _1466433), _1466435)), hAPP(c_Set_Oimage(_1466429, _1466431, _1466433), _1466437))))], (36540 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466431, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466429, _1466431, _1466433), _1466435)), hAPP(c_Set_Oimage(_1466429, _1466431, _1466433), _1466437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466429, tc_HOL_Obool)), _1466435), _1466437)))]]], (37527 ^ _779142) ^ [_1489605, _1489607, _1489609, _1489611] : [37528 ^ _779142 : [(37531 ^ _779142) ^ [] : [_1489611 = c_Orderings_Obot__class_Obot(tc_fun(_1489607, tc_HOL_Obool))], (37529 ^ _779142) ^ [] : [_1489609 = c_Orderings_Obot__class_Obot(tc_fun(_1489605, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1489605, _1489607), _1489609), hAPP(c_COMBK(tc_fun(_1489607, tc_HOL_Obool), _1489605), _1489611)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489605, _1489607), tc_HOL_Obool)))], (41053 ^ _779142) ^ [_1585759, _1585761] : [-(hAPP(hAPP(c_Nat_Ocompow(_1585759, _1585759), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585761) = c_Fun_Oid(_1585759))], (26820 ^ _779142) ^ [_1251669, _1251671, _1251673, _1251675, _1251677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251669, tc_HOL_Obool)), _1251671), _1251673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251669, tc_HOL_Obool)), _1251675), _1251677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251669, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251669, tc_HOL_Obool)), _1251671), _1251675)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251669, tc_HOL_Obool)), _1251673), _1251677))))], (37941 ^ _779142) ^ [_1502659, _1502661, _1502663, _1502665, _1502667, _1502669] : [class_Groups_Ocomm__monoid__add(_1502659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502661), _1502663)), 37951 ^ _779142 : [(37954 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502665), hAPP(_1502667, 37950 ^ [_1502659, _1502661, _1502663, _1502665, _1502667, _1502669])))], (37952 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502661), 37950 ^ [_1502659, _1502661, _1502663, _1502665, _1502667, _1502669]), _1502663)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502661, _1502659), hAPP(hAPP(c_COMBS(_1502661, tc_fun(_1502665, tc_HOL_Obool), _1502659), hAPP(hAPP(c_COMBB(tc_fun(_1502665, _1502659), tc_fun(tc_fun(_1502665, tc_HOL_Obool), _1502659), _1502661), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502665, _1502659)), _1502669)), _1502667)), _1502663) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1502661, _1502665), _1502659), hAPP(c_Product__Type_Oprod_Oprod__case(_1502661, _1502665, _1502659), _1502669)), hAPP(hAPP(c_Product__Type_OSigma(_1502661, _1502665), _1502663), _1502667)))], (43538 ^ _779142) ^ [_1649449, _1649451, _1649453] : [hAPP(hAPP(c_List_Odrop(_1649449), _1649451), _1649453) = c_List_Olist_ONil(_1649449), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649449)), _1649453)), _1649451)))], (45691 ^ _779142) ^ [_1697131, _1697133, _1697135, _1697137, _1697139] : [-(hAPP(c_List_Ofilter(_1697131, _1697133), hAPP(hAPP(c_List_Omap(_1697135, _1697131), _1697137), _1697139)) = hAPP(hAPP(c_List_Omap(_1697135, _1697131), _1697137), hAPP(c_List_Ofilter(_1697135, hAPP(c_Fun_Ocomp(_1697131, tc_HOL_Obool, _1697135, _1697133), _1697137)), _1697139)))], (5760 ^ _779142) ^ [_870340, _870342, _870344, _870346] : [_870340 = _870342, 5763 ^ _779142 : [(5770 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870344), _870342), _870346)), -(hBOOL(hAPP(hAPP(c_member(_870344), _870340), _870346)))], (5764 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870344), _870340), _870346)), -(hBOOL(hAPP(hAPP(c_member(_870344), _870342), _870346)))]]], (42073 ^ _779142) ^ [_1615217, _1615219, _1615221, _1615223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615217), tc_List_Olist(_1615217))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615217), tc_List_Olist(_1615217)), _1615219), _1615221)), c_List_Olistrel(_1615217, _1615223))), 42076 ^ _779142 : [(42079 ^ _779142) ^ [_1615553] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615217, _1615217)), _1615553), hAPP(c_List_Oset(tc_prod(_1615217, _1615217)), hAPP(hAPP(c_List_Ozip(_1615217, _1615217), _1615219), _1615221)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615217, _1615217, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615217, tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_fun(_1615217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615217, tc_fun(tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_fun(_1615217, tc_HOL_Obool)), _1615217), c_COMBC(_1615217, tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615217, tc_prod(_1615217, _1615217)), tc_fun(_1615217, tc_fun(tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_HOL_Obool)), _1615217), hAPP(c_COMBB(tc_prod(_1615217, _1615217), tc_fun(tc_fun(tc_prod(_1615217, _1615217), tc_HOL_Obool), tc_HOL_Obool), _1615217), c_member(tc_prod(_1615217, _1615217)))), c_Product__Type_OPair(_1615217, _1615217)))), _1615223)), _1615553)))], (42077 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615217)), _1615219) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615217)), _1615221))]]], (12497 ^ _779142) ^ [_994839, _994841] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994839), _994841)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9887 ^ _779142) ^ [_947742, _947744, _947746] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947742), _947744)), -(hAPP(c_Finite__Set_Ocard(_947742), hAPP(hAPP(c_Set_Oinsert(_947742), _947746), _947744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_947742), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947742, tc_HOL_Obool)), _947744), hAPP(hAPP(c_Set_Oinsert(_947742), _947746), c_Orderings_Obot__class_Obot(tc_fun(_947742, tc_HOL_Obool)))))))], (37509 ^ _779142) ^ [_1489106, _1489108, _1489110, _1489112] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1489106, _1489108)), hAPP(hAPP(c_Product__Type_OSigma(_1489106, _1489108), _1489110), hAPP(c_COMBK(tc_fun(_1489108, tc_HOL_Obool), _1489106), _1489112))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1489106), _1489110)), hAPP(c_Finite__Set_Ocard(_1489108), _1489112)))], (16531 ^ _779142) ^ [_1069995, _1069997, _1069999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069995), _1069997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069995), _1069999)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069997), _1069999))))], (38386 ^ _779142) ^ [_1519225, _1519227, _1519229, _1519231, _1519233, _1519235, _1519237] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519225, _1519227, _1519229), _1519231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519233, tc_fun(tc_prod(_1519227, _1519229), tc_HOL_Obool)), _1519235), _1519237)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519233, tc_fun(tc_prod(_1519225, _1519229), tc_HOL_Obool)), _1519235), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519227, _1519229), tc_HOL_Obool), tc_fun(tc_prod(_1519225, _1519229), tc_HOL_Obool), _1519233), hAPP(c_Relation_Orel__comp(_1519225, _1519227, _1519229), _1519231)), _1519237)))], (35185 ^ _779142) ^ [_1434226, _1434228, _1434230, _1434232, _1434234, _1434236, _1434238] : [35187 ^ _779142 : [(35190 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1434234, 35186 ^ [_1434226, _1434228, _1434230, _1434232, _1434234, _1434236, _1434238]), _1434236), _1434238))], (35188 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434226), 35186 ^ [_1434226, _1434228, _1434230, _1434232, _1434234, _1434236, _1434238]), _1434232)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1434226, tc_fun(_1434228, tc_fun(_1434230, tc_HOL_Obool))), _1434232), _1434234), _1434236), _1434238)))], (2960 ^ _779142) ^ [_822968, _822970, _822972, _822974, _822976, _822978, _822980, _822982, _822984, _822986, _822988, _822990] : [-(c_Product__Type_Omap__pair(_822990, _822986, _822982, _822978, _822974, _822970) = c_Product__Type_Omap__pair(_822988, _822984, _822980, _822976, _822972, _822968)), _822990 = _822988, _822986 = _822984, _822982 = _822980, _822978 = _822976, _822974 = _822972, _822970 = _822968], (25802 ^ _779142) ^ [_1232660] : [class_Rings_Osemiring__1(_1232660), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1232660), c_Groups_Ozero__class_Ozero(_1232660)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1232660))], (39385 ^ _779142) ^ [_1545005, _1545007, _1545009, _1545011, _1545013, _1545015] : [39388 ^ _779142 : [(39391 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1545011), _1545013), hAPP(hAPP(_1545015, 39386 ^ [_1545005, _1545007, _1545009, _1545011, _1545013, _1545015]), 39387 ^ [_1545005, _1545007, _1545009, _1545011, _1545013, _1545015])))], (39389 ^ _779142) ^ [] : [-(_1545005 = hAPP(hAPP(c_Product__Type_OPair(_1545007, _1545009), 39386 ^ [_1545005, _1545007, _1545009, _1545011, _1545013, _1545015]), 39387 ^ [_1545005, _1545007, _1545009, _1545011, _1545013, _1545015]))]], -(hBOOL(hAPP(hAPP(c_member(_1545011), _1545013), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545007, _1545009, tc_fun(_1545011, tc_HOL_Obool)), _1545015), _1545005))))], (25162 ^ _779142) ^ [_1221453, _1221455] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221453), _1221455))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221453), hAPP(c_Nat_OSuc, _1221455)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (39550 ^ _779142) ^ [_1548735, _1548737, _1548739] : [hBOOL(hAPP(_1548735, _1548737)), -(hBOOL(hAPP(_1548735, c_Hilbert__Choice_OEps(_1548739, _1548735))))], (34797 ^ _779142) ^ [_1424170, _1424172, _1424174] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424170, tc_fun(_1424172, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1424170, tc_HOL_Obool))), _1424174) = c_Orderings_Otop__class_Otop(tc_fun(_1424172, tc_HOL_Obool)))], (26184 ^ _779142) ^ [_1239484] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1239484, 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, _1239484, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (2530 ^ _779142) ^ [_816339, _816341, _816343, _816345] : [-(c_Divides_Odivmod__nat__rel(_816345, _816341) = c_Divides_Odivmod__nat__rel(_816343, _816339)), _816345 = _816343, _816341 = _816339], (18022 ^ _779142) ^ [_1096571, _1096573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096571)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096573))), 18025 ^ _779142 : [(18026 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096571), _1096573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1096573)))], (18032 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096571), _1096573)))]]], (45572 ^ _779142) ^ [_1693680, _1693682] : [class_Orderings_Olinorder(_1693680), -(c_List_Olinorder__class_Osort__key(_1693680, _1693680, c_COMBI(_1693680), _1693682) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693680), _1693680, hAPP(c_COMBC(_1693680, tc_List_Olist(_1693680), tc_List_Olist(_1693680)), c_List_Olinorder__class_Oinsort__key(_1693680, _1693680, c_COMBI(_1693680))), c_List_Olist_ONil(_1693680)), _1693682))], (24884 ^ _779142) ^ [_1216635, _1216637] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1216635), hAPP(c_Nat_OSuc, _1216637)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1216635, _1216637))], (5836 ^ _779142) ^ [_871579, _871581, _871583] : [-(hAPP(hAPP(c_Set_Oinsert(_871579), _871581), hAPP(hAPP(c_Set_Oinsert(_871579), _871581), _871583)) = hAPP(hAPP(c_Set_Oinsert(_871579), _871581), _871583))], (29091 ^ _779142) ^ [_1294818, _1294820, _1294822, _1294824] : [class_Lattices_Osemilattice__inf(_1294818), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294818), _1294820), _1294822)), _1294824) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294818), _1294820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294818), _1294822), _1294824)))], (19253 ^ _779142) ^ [_1117609] : [class_Groups_Oordered__ab__group__add__abs(_1117609), -(hAPP(c_Groups_Oabs__class_Oabs(_1117609), c_Groups_Ozero__class_Ozero(_1117609)) = c_Groups_Ozero__class_Ozero(_1117609))], (38784 ^ _779142) ^ [_1530049, _1530051, _1530053, _1530055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530049, _1530051), tc_HOL_Obool)), _1530053), _1530055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530049, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530049, _1530051), _1530053)), hAPP(c_Relation_ODomain(_1530049, _1530051), _1530055))))], (2716 ^ _779142) ^ [_819224, _819226, _819228, _819230, _819232, _819234, _819236, _819238] : [-(c_Product__Type_Oapfst(_819238, _819234, _819230, _819226) = c_Product__Type_Oapfst(_819236, _819232, _819228, _819224)), _819238 = _819236, _819234 = _819232, _819230 = _819228, _819226 = _819224], (6924 ^ _779142) ^ [_892424, _892426, _892428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892424), _892426)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_892424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892424, tc_HOL_Obool)), _892426), _892428))))], (34069 ^ _779142) ^ [_1403675, _1403677, _1403679, _1403681, _1403683, _1403685, _1403687] : [hBOOL(hAPP(_1403675, _1403677)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1403679, _1403679)), hAPP(hAPP(c_Product__Type_OPair(_1403679, _1403679), _1403681), _1403683)), hAPP(_1403685, _1403677))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1403687, _1403679), tc_prod(_1403687, _1403679))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1403687, _1403679), tc_prod(_1403687, _1403679)), hAPP(hAPP(c_Product__Type_OPair(_1403687, _1403679), _1403677), _1403681)), hAPP(hAPP(c_Product__Type_OPair(_1403687, _1403679), _1403677), _1403683))), c_Recdef_Osame__fst(_1403687, _1403679, _1403675, _1403685))))], (42247 ^ _779142) ^ [_1620448, _1620450, _1620452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620448), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1620450))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1620450), _1620448), _1620452)) = 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), _1620450)), _1620452)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1620450), _1620448)))], (48012 ^ _779142) ^ [_1746439, _1746441, _1746443, _1746445, _1746447] : [-(_1746439 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746441, _1746443, _1746445, _1746447), _1746439) = c_Lazy__Sequence_Ohb__bind(_1746441, _1746443, hAPP(_1746445, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746439), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1746441, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746443))), _1746447), _1746439)))], (28438 ^ _779142) ^ [_1281810, _1281812, _1281814] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281810, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1281810, tc_HOL_Obool)), _1281812), _1281814)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281810, tc_HOL_Obool)), _1281812), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281810, tc_HOL_Obool), _1281814)))], (42908 ^ _779142) ^ [_1634252, _1634254, _1634256, _1634258, _1634260] : [-(hAPP(hAPP(c_List_Ozip(_1634252, _1634254), _1634256), hAPP(hAPP(c_List_Olist_OCons(_1634254), _1634258), _1634260)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1634252, _1634254)), _1634252, c_List_Olist_ONil(tc_prod(_1634252, _1634254)), hAPP(hAPP(c_COMBC(_1634252, tc_fun(tc_List_Olist(_1634252), tc_List_Olist(tc_prod(_1634252, _1634254))), tc_fun(tc_List_Olist(_1634252), tc_List_Olist(tc_prod(_1634252, _1634254)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1634252, _1634254)), tc_List_Olist(tc_prod(_1634252, _1634254))), tc_fun(tc_fun(tc_List_Olist(_1634252), tc_List_Olist(tc_prod(_1634252, _1634254))), tc_fun(tc_List_Olist(_1634252), tc_List_Olist(tc_prod(_1634252, _1634254)))), _1634252), c_COMBB(tc_List_Olist(tc_prod(_1634252, _1634254)), tc_List_Olist(tc_prod(_1634252, _1634254)), tc_List_Olist(_1634252))), hAPP(hAPP(c_COMBB(tc_prod(_1634252, _1634254), tc_fun(tc_List_Olist(tc_prod(_1634252, _1634254)), tc_List_Olist(tc_prod(_1634252, _1634254))), _1634252), c_List_Olist_OCons(tc_prod(_1634252, _1634254))), hAPP(hAPP(c_COMBC(_1634252, _1634254, tc_prod(_1634252, _1634254)), c_Product__Type_OPair(_1634252, _1634254)), _1634258)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634252), tc_List_Olist(_1634254), tc_List_Olist(tc_prod(_1634252, _1634254))), c_List_Ozip(_1634252, _1634254)), _1634260))), _1634256))], (23969 ^ _779142) ^ [_1201366, _1201368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201366)), -(c_SMT_Oz3div(_1201368, _1201366) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201368), _1201366))], (44137 ^ _779142) ^ [_1662275, _1662277, _1662279, _1662281, _1662283] : [class_Orderings_Olinorder(_1662275), hBOOL(hAPP(hAPP(c_member(_1662275), hAPP(_1662277, _1662279)), hAPP(c_Set_Oimage(_1662281, _1662275, _1662277), hAPP(c_List_Oset(_1662281), _1662283)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1662281, _1662275, _1662277, _1662279, _1662283) = _1662283)], (17367 ^ _779142) ^ [_1084689, _1084691, _1084693] : [class_Divides_Osemiring__div(_1084689), -(c_Divides_Odiv__class_Omod(_1084689, c_Divides_Odiv__class_Omod(_1084689, _1084691, _1084693), _1084693) = c_Divides_Odiv__class_Omod(_1084689, _1084691, _1084693))], (45262 ^ _779142) ^ [_1687267] : [-(c_Enum_Osublists(_1687267, c_List_Olist_ONil(_1687267)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687267)), c_List_Olist_ONil(_1687267)), c_List_Olist_ONil(tc_List_Olist(_1687267))))], (43249 ^ _779142) ^ [_1641929, _1641931] : [-(hAPP(hAPP(c_List_Oappend(_1641929), c_List_Olist_ONil(_1641929)), _1641931) = _1641931)], (6039 ^ _779142) ^ [_875485, _875487, _875489, _875491, _875493] : [-(hAPP(c_Set_Oimage(_875485, _875487, _875489), hAPP(hAPP(c_Set_Oinsert(_875485), _875491), _875493)) = hAPP(hAPP(c_Set_Oinsert(_875487), hAPP(_875489, _875491)), hAPP(c_Set_Oimage(_875485, _875487, _875489), _875493)))], (44684 ^ _779142) ^ [_1674255, _1674257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674255)), hAPP(c_Code__Numeral_Oof__nat, _1674257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674255), _1674257)))], (18236 ^ _779142) ^ [_1100118, _1100120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1100118, _1100120))))], (44779 ^ _779142) ^ [_1676411] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1676411)) = _1676411)], (4086 ^ _779142) ^ [_840999, _841001] : [_841001 = _840999, -(c_New__Random__Sequence_Opos__single(_841001) = c_New__Random__Sequence_Opos__single(_840999))], (4560 ^ _779142) ^ [_848432, _848434] : [_848434 = _848432, -(c_DSequence_Ounion(_848434) = c_DSequence_Ounion(_848432))], (35547 ^ _779142) ^ [_1444182] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444182) = 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, _1444182)), 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))))))))], (45895 ^ _779142) ^ [_1702618, _1702620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702618), _1702620)), -(c_List_Oupt(_1702618, _1702620) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702618), c_List_Oupt(hAPP(c_Nat_OSuc, _1702618), _1702620)))], (12050 ^ _779142) ^ [_987115, _987117, _987119] : [class_Rings_Olinordered__semiring__strict(_987115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987115), c_Groups_Ozero__class_Ozero(_987115)), _987117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987115), _987119), c_Groups_Ozero__class_Ozero(_987115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987115), _987119), _987117)), c_Groups_Ozero__class_Ozero(_987115))))], (51335 ^ _779142) ^ [_1817215, _1817217, _1817219] : [_1817215 = _1817217, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817217), _1817219)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817215), _1817219)))], (36992 ^ _779142) ^ [_1476575, _1476577, _1476579, _1476581] : [-(c_Wellfounded_Omax__extp(_1476575, _1476577, _1476579, _1476581)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476575), _1476579)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476575), _1476581)), -(_1476581 = c_Orderings_Obot__class_Obot(tc_fun(_1476575, tc_HOL_Obool))), 37006 ^ _779142 : [(37009 ^ _779142) ^ [_1476920] : [hBOOL(hAPP(hAPP(c_member(_1476575), _1476920), _1476581)), hBOOL(hAPP(hAPP(_1476577, 37005 ^ [_1476575, _1476577, _1476579, _1476581]), _1476920))], (37007 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476575), 37005 ^ [_1476575, _1476577, _1476579, _1476581]), _1476579)))]]], (49640 ^ _779142) ^ [_1782189, _1782191, _1782193, _1782195, _1782197, _1782199] : [c_Fun_Oinj__on(_1782189, _1782191, _1782193, _1782195), hBOOL(hAPP(hAPP(c_member(_1782189), _1782197), _1782195)), hAPP(_1782193, _1782197) = _1782199, -(hAPP(c_Hilbert__Choice_Oinv__into(_1782189, _1782191, _1782195, _1782193), _1782199) = _1782197)], (3814 ^ _779142) ^ [_836343, _836345, _836347, _836349, _836351, _836353, _836355, _836357, _836359, _836361, _836363, _836365, _836367, _836369] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836369, _836365, _836361, _836357, _836353, _836349, _836345) = c_New__Random__Sequence_Oneg__decr__bind(_836367, _836363, _836359, _836355, _836351, _836347, _836343)), _836369 = _836367, _836365 = _836363, _836361 = _836359, _836357 = _836355, _836353 = _836351, _836349 = _836347, _836345 = _836343], (26410 ^ _779142) ^ [_1243693, _1243695, _1243697, _1243699] : [class_Lattices_Osemilattice__sup(_1243693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243693), _1243695), _1243697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243693), _1243699), _1243697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1243693), _1243695), _1243699)), _1243697)))], (28513 ^ _779142) ^ [_1283236, _1283238, _1283240] : [class_Orderings_Olinorder(_1283236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283236), _1283238)), hBOOL(hAPP(hAPP(c_member(_1283236), _1283240), _1283238)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1283236), _1283240), c_Big__Operators_Olattice_OSup__fin(_1283236, c_Orderings_Oord__class_Omax(_1283236), _1283238)) = c_Big__Operators_Olattice_OSup__fin(_1283236, c_Orderings_Oord__class_Omax(_1283236), _1283238))], (41419 ^ _779142) ^ [_1596586, _1596588, _1596590, _1596592, _1596594, _1596596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596586), tc_List_Olist(_1596586))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596586), tc_List_Olist(_1596586)), hAPP(hAPP(c_List_Olist_OCons(_1596586), _1596588), _1596590)), hAPP(hAPP(c_List_Olist_OCons(_1596586), _1596592), _1596594))), c_List_Olexord(_1596586, _1596596))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596586, _1596586)), hAPP(hAPP(c_Product__Type_OPair(_1596586, _1596586), _1596588), _1596592)), _1596596))), 41426 ^ _779142 : [(41429 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596586), tc_List_Olist(_1596586))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596586), tc_List_Olist(_1596586)), _1596590), _1596594)), c_List_Olexord(_1596586, _1596596))))], (41427 ^ _779142) ^ [] : [-(_1596588 = _1596592)]]], (21864 ^ _779142) ^ [_1163291, _1163293, _1163295] : [class_Groups_Omonoid__mult(_1163291), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163291), hAPP(hAPP(c_Power_Opower__class_Opower(_1163291), _1163293), _1163295)), _1163293) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163291), _1163293), hAPP(hAPP(c_Power_Opower__class_Opower(_1163291), _1163293), _1163295)))], (45622 ^ _779142) ^ [_1695402, _1695404, _1695406, _1695408] : [-(c_List_Otranspose(_1695402, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695402)), hAPP(hAPP(c_List_Olist_OCons(_1695402), _1695404), _1695406)), _1695408)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695402)), hAPP(hAPP(c_List_Olist_OCons(_1695402), _1695404), c_List_Oconcat(_1695402, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695402), tc_List_Olist(_1695402)), c_List_Olist_Olist__case(tc_List_Olist(_1695402), _1695402, c_List_Olist_ONil(_1695402), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695402), tc_fun(tc_List_Olist(_1695402), tc_List_Olist(_1695402)), _1695402), c_COMBK(tc_List_Olist(_1695402), tc_List_Olist(_1695402))), hAPP(hAPP(c_COMBC(_1695402, tc_List_Olist(_1695402), tc_List_Olist(_1695402)), c_List_Olist_OCons(_1695402)), c_List_Olist_ONil(_1695402))))), _1695408)))), c_List_Otranspose(_1695402, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695402)), _1695406), c_List_Oconcat(tc_List_Olist(_1695402), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695402), tc_List_Olist(tc_List_Olist(_1695402))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1695402)), _1695402, c_List_Olist_ONil(tc_List_Olist(_1695402)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1695402), tc_List_Olist(tc_List_Olist(_1695402))), _1695402), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695402), tc_List_Olist(tc_List_Olist(_1695402)), tc_List_Olist(tc_List_Olist(_1695402))), c_List_Olist_OCons(tc_List_Olist(_1695402))), c_List_Olist_ONil(tc_List_Olist(_1695402)))))), _1695408))))))], (37719 ^ _779142) ^ [_1495035, _1495037, _1495039, _1495041, _1495043, _1495045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495035, _1495037), tc_HOL_Obool)), _1495039), hAPP(hAPP(c_Product__Type_OSigma(_1495035, _1495037), _1495041), hAPP(c_COMBK(tc_fun(_1495037, tc_HOL_Obool), _1495035), _1495043)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495037, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1495035, _1495037, _1495039), _1495045)), _1495043)))], (38949 ^ _779142) ^ [_1533824, _1533826, _1533828, _1533830] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533824, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533824, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533824, _1533826), _1533828)), hAPP(c_Relation_ODomain(_1533824, _1533826), _1533830))), hAPP(c_Relation_ODomain(_1533824, _1533826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1533824, _1533826), tc_HOL_Obool)), _1533828), _1533830)))))], (25650 ^ _779142) ^ [_1229960] : [-(c_Int_Opred(c_Int_OBit0(_1229960)) = c_Int_OBit1(c_Int_Opred(_1229960)))], (29133 ^ _779142) ^ [_1295765, _1295767, _1295769] : [class_Lattices_Osemilattice__inf(_1295765), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295765), _1295767), _1295769) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295765), _1295769), _1295767))], (28873 ^ _779142) ^ [_1290709, _1290711, _1290713, _1290715] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290709, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290709, tc_HOL_Obool)), _1290711), _1290713)), _1290715) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290709, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290709, tc_HOL_Obool)), _1290711), _1290715)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290709, tc_HOL_Obool)), _1290713), _1290715)))], (2592 ^ _779142) ^ [_817316, _817318] : [_817318 = _817316, -(c_Wellfounded_Omeasure(_817318) = c_Wellfounded_Omeasure(_817316))], (934 ^ _779142) ^ [_793145, _793147, _793149, _793151] : [-(c_Equiv__Relations_Oequivp(_793149, _793145)), c_Equiv__Relations_Oequivp(_793151, _793147), _793151 = _793149, _793147 = _793145], (18644 ^ _779142) ^ [_1107279, _1107281, _1107283] : [-(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), _1107279), _1107281)), _1107283), _1107281) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107283, _1107281))], (41215 ^ _779142) ^ [_1590387, _1590389] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590387, _1590387)), _1590389), c_Relation_OId(_1590387))), -(_1590389 = hAPP(hAPP(c_Product__Type_OPair(_1590387, _1590387), 41218 ^ [_1590387, _1590389]), 41218 ^ [_1590387, _1590389]))], (34607 ^ _779142) ^ [_1418436, _1418438, _1418440, _1418442, _1418444] : [-(hBOOL(hAPP(hAPP(c_member(_1418436), _1418438), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418440, tc_fun(_1418436, tc_HOL_Obool)), _1418442), _1418444)))), 34608 ^ _779142 : [(34609 ^ _779142) ^ [_1418518] : [hBOOL(hAPP(hAPP(c_member(_1418440), _1418518), _1418442)), hBOOL(hAPP(hAPP(c_member(_1418436), _1418438), hAPP(_1418444, _1418518)))]]], (13271 ^ _779142) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32988 ^ _779142) ^ [_1382673, _1382675, _1382677, _1382679, _1382681, _1382683, _1382685] : [hBOOL(hAPP(hAPP(c_member(_1382673), _1382675), hAPP(hAPP(_1382677, _1382679), _1382681))), -(hBOOL(hAPP(hAPP(c_member(_1382673), _1382675), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382683, _1382685, tc_fun(_1382673, tc_HOL_Obool)), _1382677), hAPP(hAPP(c_Product__Type_OPair(_1382683, _1382685), _1382679), _1382681)))))], (17321 ^ _779142) ^ [_1083983, _1083985, _1083987, _1083989] : [_1083983 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083985), _1083987)), _1083989), -(_1083985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1083983, _1083985) = _1083989), 17328 ^ _779142 : [(17331 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083989), _1083985))], (17329 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083985)))]], 17336 ^ _779142 : [(17339 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083985), _1083989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083989), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17337 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083985))]]], (8256 ^ _779142) ^ [_916605, _916607, _916609] : [class_Lattices_Oab__semigroup__idem__mult(_916605), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916605), _916607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916605), _916607), _916609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916605), _916607), _916609))], (18202 ^ _779142) ^ [_1099548] : [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), _1099548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1099548)))], (5478 ^ _779142) ^ [_862909, _862911] : [_862911 = _862909, -(c_Orderings_Oord__class_Oless(_862911) = c_Orderings_Oord__class_Oless(_862909))], (29311 ^ _779142) ^ [_1299381, _1299383] : [class_Lattices_Oboolean__algebra(_1299381), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299381), _1299383), hAPP(c_Groups_Ouminus__class_Ouminus(_1299381), _1299383)) = c_Orderings_Obot__class_Obot(_1299381))], (34472 ^ _779142) ^ [_1414281, _1414283, _1414285, _1414287, _1414289] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414281, tc_HOL_Obool)), _1414283), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414285, tc_fun(_1414281, tc_HOL_Obool)), _1414287), _1414289)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414285, tc_fun(_1414281, tc_HOL_Obool)), _1414287), hAPP(hAPP(c_COMBB(tc_fun(_1414281, tc_HOL_Obool), tc_fun(_1414281, tc_HOL_Obool), _1414285), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414281, tc_HOL_Obool)), _1414283)), _1414289)))], (48818 ^ _779142) ^ [_1764881] : [-(c_Relation_Otrans(_1764881, c_Relation_OId(_1764881)))], (33173 ^ _779142) ^ [_1386303, _1386305, _1386307] : [class_Rings_Osemiring__1(_1386303), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1386303, _1386305, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1386307) = _1386307)], (8705 ^ _779142) ^ [_925497, _925499, _925501, _925503] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925497), 8708 ^ _779142 : [(8715 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925497), _925499), _925503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925497), _925499), _925501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925497), _925503), _925501))))], (8709 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925497), _925499), _925501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925497), _925503), _925501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925497), _925499), _925503)))]]], (51355 ^ _779142) ^ [_1817521, _1817523, _1817525, _1817527] : [class_Rings_Ocomm__semiring__1(_1817521), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817521), _1817523), _1817525)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817521), _1817525), _1817527)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817521), _1817523), _1817527)))], (30924 ^ _779142) ^ [_1333155, _1333157] : [class_Lattices_Obounded__lattice__top(_1333155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1333155), _1333157), c_Orderings_Otop__class_Otop(_1333155)) = _1333157)], (11790 ^ _779142) ^ [_982288, _982290, _982292] : [class_Rings_Oordered__ring(_982288), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982288), c_Groups_Ozero__class_Ozero(_982288)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982288), _982290), _982292)))), 11795 ^ _779142 : [(11802 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982288), _982290), c_Groups_Ozero__class_Ozero(_982288))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982288), _982292), c_Groups_Ozero__class_Ozero(_982288)))], (11796 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982288), c_Groups_Ozero__class_Ozero(_982288)), _982290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982288), c_Groups_Ozero__class_Ozero(_982288)), _982292))]]], (22176 ^ _779142) ^ [_1169101, _1169103, _1169105, _1169107] : [class_Rings_Olinordered__semidom(_1169101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), c_Groups_Oone__class_Oone(_1169101)), _1169103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), hAPP(hAPP(c_Power_Opower__class_Opower(_1169101), _1169103), _1169105)), hAPP(hAPP(c_Power_Opower__class_Opower(_1169101), _1169103), _1169107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169105), _1169107)))], (11295 ^ _779142) ^ [_973214, _973216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973214), _973216)), -(_973216 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973214), 11298 ^ [_973214, _973216])))], (16491 ^ _779142) ^ [_1069474, _1069476] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069474), _1069476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069476), _1069474)))], (35133 ^ _779142) ^ [_1432810, _1432812, _1432814, _1432816, _1432818, _1432820] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432810, tc_fun(_1432812, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432814, tc_fun(_1432810, tc_HOL_Obool)), _1432816), _1432818)), _1432820) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432814, tc_fun(_1432812, tc_HOL_Obool)), _1432816), hAPP(hAPP(c_COMBC(_1432814, tc_fun(_1432810, tc_fun(_1432812, tc_HOL_Obool)), tc_fun(_1432812, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432810, tc_HOL_Obool), tc_fun(tc_fun(_1432810, tc_fun(_1432812, tc_HOL_Obool)), tc_fun(_1432812, tc_HOL_Obool)), _1432814), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432810, tc_fun(_1432812, tc_HOL_Obool))), _1432818)), _1432820)))], (3068 ^ _779142) ^ [_824720, _824722, _824724, _824726] : [-(c_Nat_Ocompow(_824726, _824722) = c_Nat_Ocompow(_824724, _824720)), _824726 = _824724, _824722 = _824720], (49865 ^ _779142) ^ [_1787467, _1787469, _1787471, _1787473, _1787475] : [hBOOL(hAPP(_1787467, hAPP(hAPP(c_Product__Type_OPair(_1787469, _1787471), _1787473), _1787475))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787469, _1787471, tc_HOL_Obool, _1787467), _1787473), _1787475)))], (30307 ^ _779142) ^ [_1321308, _1321310, _1321312] : [class_Lattices_Olattice(_1321308), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321308), _1321310)), hBOOL(hAPP(hAPP(c_member(_1321308), _1321312), _1321310)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321308), _1321312), c_Big__Operators_Olattice__class_OInf__fin(_1321308, _1321310)) = _1321312)], (5176 ^ _779142) ^ [_858110, _858112, _858114, _858116] : [-(c_Lazy__Sequence_Oflat(_858116, _858112) = c_Lazy__Sequence_Oflat(_858114, _858110)), _858116 = _858114, _858112 = _858110], (46867 ^ _779142) ^ [_1721718, _1721720, _1721722, _1721724] : [-(hBOOL(hAPP(_1721718, _1721720))), -(c_List_OtakeWhile(_1721722, _1721718, hAPP(hAPP(c_List_Olist_OCons(_1721722), _1721720), _1721724)) = c_List_Olist_ONil(_1721722))], (27172 ^ _779142) ^ [_1258639, _1258641, _1258643] : [class_Orderings_Olinorder(_1258639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258639), _1258641), _1258643)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258639, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1258639), _1258641)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1258639, _1258641, _1258643)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1258639), _1258643))], (25150 ^ _779142) ^ [_1221250] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1221250))) = 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)))), _1221250))], (40358 ^ _779142) ^ [_1568639, _1568641, _1568643, _1568645] : [40359 ^ _779142 : [(40362 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568639, _1568639)), _1568641), c_Transitive__Closure_Ortrancl(_1568639, _1568645)))], (40360 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568639, _1568639)), _1568641), c_Transitive__Closure_Ortrancl(_1568639, _1568643)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568639, _1568639)), _1568641), c_Transitive__Closure_Ortrancl(_1568639, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568639, _1568639), tc_HOL_Obool)), _1568643), _1568645)))))], (25946 ^ _779142) ^ [_1235099, _1235101, _1235103] : [class_Rings_Olinordered__semidom(_1235099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235099), hAPP(hAPP(c_Power_Opower__class_Opower(_1235099), _1235101), 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(_1235099), _1235103), 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(_1235099), c_Groups_Ozero__class_Ozero(_1235099)), _1235103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235099), _1235101), _1235103)))], (48178 ^ _779142) ^ [_1750770, _1750772, _1750774] : [-(_1750770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750772, c_List_Oreplicate(_1750772, _1750770, _1750774)) = _1750774)], (42287 ^ _779142) ^ [_1621269, _1621271, _1621273, _1621275, _1621277, _1621279, _1621281] : [-(hAPP(hAPP(c_List_Ozip(_1621269, _1621271), hAPP(hAPP(c_List_Olist__update(_1621269, _1621273), _1621275), _1621277)), hAPP(hAPP(c_List_Olist__update(_1621271, _1621279), _1621275), _1621281)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1621269, _1621271), hAPP(hAPP(c_List_Ozip(_1621269, _1621271), _1621273), _1621279)), _1621275), hAPP(hAPP(c_Product__Type_OPair(_1621269, _1621271), _1621277), _1621281)))], (31014 ^ _779142) ^ [_1334823] : [class_Lattices_Oboolean__algebra(_1334823), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334823), c_Orderings_Obot__class_Obot(_1334823)) = c_Orderings_Otop__class_Otop(_1334823))], (39656 ^ _779142) ^ [_1551194, _1551196, _1551198, _1551200, _1551202, _1551204, _1551206] : [class_Groups_Oab__semigroup__mult(_1551194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551196), _1551198)), c_Fun_Oinj__on(_1551196, _1551200, _1551202, _1551198), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1551194, _1551200, c_Groups_Otimes__class_Otimes(_1551194)), _1551204), _1551206), hAPP(c_Set_Oimage(_1551196, _1551200, _1551202), _1551198)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1551194, _1551196, c_Groups_Otimes__class_Otimes(_1551194)), hAPP(c_Fun_Ocomp(_1551200, _1551194, _1551196, _1551204), _1551202)), _1551206), _1551198))], (52585 ^ _779142) ^ [_1835670, _1835672] : [-(class_Nat_Osize(tc_prod(_1835670, _1835672)))], (35770 ^ _779142) ^ [_1449695, _1449697, _1449699, _1449701, _1449703, _1449705, _1449707] : [c_Equiv__Relations_Oequiv(_1449695, _1449697, _1449699), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449695, tc_HOL_Obool)), _1449701), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449695), _1449697), _1449699))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449695, tc_HOL_Obool)), _1449703), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449695), _1449697), _1449699))), hBOOL(hAPP(hAPP(c_member(_1449695), _1449705), _1449701)), hBOOL(hAPP(hAPP(c_member(_1449695), _1449707), _1449703)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449695, _1449695)), hAPP(hAPP(c_Product__Type_OPair(_1449695, _1449695), _1449705), _1449707)), _1449699)), -(_1449701 = _1449703)], (52493 ^ _779142) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (39270 ^ _779142) ^ [_1541622, _1541624, _1541626] : [39272 ^ _779142 : [(39275 ^ _779142) ^ [] : [hBOOL(hAPP(_1541624, 39271 ^ [_1541622, _1541624, _1541626]))], (39273 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541622), 39271 ^ [_1541622, _1541624, _1541626]), _1541626)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1541622, _1541624), _1541626)))], (18074 ^ _779142) ^ [_1097501] : [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), _1097501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1097501)))], (52229 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (50152 ^ _779142) ^ [_1793122, _1793124, _1793126, _1793128, _1793130, _1793132, _1793134] : [c_Fun_Obij__betw(_1793122, _1793124, _1793126, _1793128, _1793130), c_Fun_Obij__betw(_1793122, _1793124, _1793126, _1793132, _1793134), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793124, tc_HOL_Obool)), _1793130), _1793134) = c_Orderings_Obot__class_Obot(tc_fun(_1793124, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1793122, _1793124, _1793126, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793122, tc_HOL_Obool)), _1793128), _1793132), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793124, tc_HOL_Obool)), _1793130), _1793134)))], (46132 ^ _779142) ^ [_1707031, _1707033, _1707035] : [class_Orderings_Olinorder(_1707031), 46135 ^ _779142 : [(46142 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1707031, _1707035), -(c_List_Olinorder__class_Osorted(_1707031, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707031, _1707031, c_COMBI(_1707031)), _1707033), _1707035)))], (46136 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1707031, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707031, _1707031, c_COMBI(_1707031)), _1707033), _1707035)), -(c_List_Olinorder__class_Osorted(_1707031, _1707035))]]], (45364 ^ _779142) ^ [_1689616, _1689618] : [hBOOL(hAPP(c_List_Odistinct(_1689616), _1689618)), -(c_List_Oremdups(_1689616, _1689618) = _1689618)], (32679 ^ _779142) ^ [_1376043, _1376045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376043), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1376045, _1376043) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376045), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376043)))], (5466 ^ _779142) ^ [_862739, _862741] : [_862741 = _862739, -(c_Groups_Oone__class_Oone(_862741) = c_Groups_Oone__class_Oone(_862739))], (24652 ^ _779142) ^ [_1212687, _1212689] : [c_Int_OBit1(_1212687) = c_Int_OBit1(_1212689), -(_1212687 = _1212689)], (4436 ^ _779142) ^ [_846454, _846456, _846458, _846460] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846460, _846456) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846458, _846454)), _846460 = _846458, _846456 = _846454], (38537 ^ _779142) ^ [_1525053, _1525055, _1525057, _1525059, _1525061, _1525063, _1525065] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1525053, _1525055, _1525057, _1525059, _1525061), _1525063), _1525065)), 38541 ^ _779142 : [(38544 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1525061, 38540 ^ [_1525053, _1525055, _1525057, _1525059, _1525061, _1525063, _1525065]), _1525065)))], (38542 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1525059, _1525063), 38540 ^ [_1525053, _1525055, _1525057, _1525059, _1525061, _1525063, _1525065])))]]], (2608 ^ _779142) ^ [_817550, _817552, _817554, _817556, _817558, _817560] : [-(c_Wellfounded_Omlex__prod(_817560, _817556, _817552) = c_Wellfounded_Omlex__prod(_817558, _817554, _817550)), _817560 = _817558, _817556 = _817554, _817552 = _817550], (42834 ^ _779142) ^ [_1632684] : [-(c_List_Olists(_1632684, c_Orderings_Obot__class_Obot(tc_fun(_1632684, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632684)), c_List_Olist_ONil(_1632684)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632684), tc_HOL_Obool))))], (37601 ^ _779142) ^ [_1491870, _1491872, _1491874] : [-(hBOOL(hAPP(_1491870, _1491872))), -(hAPP(c_Set_OCollect(_1491874), hAPP(hAPP(c_COMBS(_1491874, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491874), c_fconj), hAPP(hAPP(c_COMBC(_1491874, _1491874, tc_HOL_Obool), c_fequal), _1491872))), _1491870)) = c_Orderings_Obot__class_Obot(tc_fun(_1491874, tc_HOL_Obool)))], (2200 ^ _779142) ^ [_811216, _811218, _811220, _811222] : [-(c_Random_Olog(_811222, _811218) = c_Random_Olog(_811220, _811216)), _811222 = _811220, _811218 = _811216], (24878 ^ _779142) ^ [_1216546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1216546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1216546))))], (32447 ^ _779142) ^ [_1370486, _1370488, _1370490] : [class_Fields_Ofield(_1370486), -(_1370488 = c_Groups_Oone__class_Oone(_1370486)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370486), hAPP(c_Power_Opower__class_Opower(_1370486), _1370488)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1370490)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1370486), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1370486), hAPP(hAPP(c_Power_Opower__class_Opower(_1370486), _1370488), _1370490)), c_Groups_Oone__class_Oone(_1370486))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1370486), _1370488), c_Groups_Oone__class_Oone(_1370486))))], (7232 ^ _779142) ^ [_899137, _899139, _899141, _899143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899137, tc_HOL_Obool)), _899139), hAPP(hAPP(c_Set_Oinsert(_899137), _899141), _899143)))), 7235 ^ _779142 : [(7238 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899137, tc_HOL_Obool)), _899139), _899143))], (7236 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899137), _899141), _899143)))]], 7239 ^ _779142 : [(7242 ^ _779142) ^ [] : [7243 ^ _779142 : [(7246 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899137, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899137, tc_HOL_Obool)), _899139), hAPP(hAPP(c_Set_Oinsert(_899137), _899141), c_Orderings_Obot__class_Obot(tc_fun(_899137, tc_HOL_Obool))))), _899143))], (7244 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899137), _899141), _899139)))]], 7247 ^ _779142 : [(7250 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899137, tc_HOL_Obool)), _899139), _899143))], (7248 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899137), _899141), _899139))]]], (7240 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899137), _899141), _899143))]]], (45732 ^ _779142) ^ [_1697956, _1697958, _1697960, _1697962] : [-(hBOOL(hAPP(_1697956, _1697958))), -(hAPP(c_List_OremoveAll(_1697960, _1697958), hAPP(c_List_Ofilter(_1697960, _1697956), _1697962)) = hAPP(c_List_Ofilter(_1697960, _1697956), _1697962))], (28430 ^ _779142) ^ [_1281619] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281619, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1281619, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1281619, tc_HOL_Obool)))], (28466 ^ _779142) ^ [_1282335, _1282337] : [class_Orderings_Olinorder(_1282335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282335), _1282337)), -(_1282337 = c_Orderings_Obot__class_Obot(tc_fun(_1282335, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1282335), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282335), 28479 ^ [_1282335, _1282337]), 28480 ^ [_1282335, _1282337])), hAPP(hAPP(c_Set_Oinsert(_1282335), 28479 ^ [_1282335, _1282337]), hAPP(hAPP(c_Set_Oinsert(_1282335), 28480 ^ [_1282335, _1282337]), c_Orderings_Obot__class_Obot(tc_fun(_1282335, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1282335), c_Big__Operators_Olinorder__class_OMax(_1282335, _1282337)), _1282337)))], (32625 ^ _779142) ^ [_1374823, _1374825] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1374823)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374825)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1374825))), 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), _1374823)), c_Int_Onat)))))], (24822 ^ _779142) ^ [_1215621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1215621)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215621), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6524 ^ _779142) ^ [_883779, _883781, _883783, _883785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883779, tc_HOL_Obool)), _883781), _883783)), hBOOL(hAPP(hAPP(c_member(_883779), _883785), _883781)), -(hBOOL(hAPP(hAPP(c_member(_883779), _883785), _883783)))], (41262 ^ _779142) ^ [_1591691, _1591693, _1591695] : [-(c_Product__Type_Ointernal__split(_1591691, _1591693, _1591695) = c_Product__Type_Oprod_Oprod__case(_1591691, _1591693, _1591695))], (28136 ^ _779142) ^ [_1276417, _1276419, _1276421, _1276423] : [class_Orderings_Olinorder(_1276417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276417), _1276419)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1276417, _1276417, c_Orderings_Oord__class_Omax(_1276417)), _1276421), hAPP(hAPP(c_Set_Oinsert(_1276417), _1276423), _1276419)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1276417), _1276423), hAPP(hAPP(c_Finite__Set_Ofold(_1276417, _1276417, c_Orderings_Oord__class_Omax(_1276417)), _1276421), _1276419)))], (41589 ^ _779142) ^ [_1601852, _1601854, _1601856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601852, _1601852), tc_HOL_Obool)), _1601854), _1601856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601852), tc_List_Olist(_1601852)), tc_HOL_Obool)), c_List_Olistrel(_1601852, _1601854)), c_List_Olistrel(_1601852, _1601856))))], (19102 ^ _779142) ^ [_1114842] : [19104 ^ _779142 : [(19107 ^ _779142) ^ [_1114952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19103 ^ [_1114842, _1114952]), _1114952))], (19105 ^ _779142) ^ [_1114918] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19103 ^ [_1114842, _1114918]), _1114842)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1114842)))], (40101 ^ _779142) ^ [_1561751, _1561753, _1561755, _1561757] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561751, _1561753, _1561755, tc_prod(_1561753, _1561755)), _1561757), c_Product__Type_OPair(_1561753, _1561755)) = _1561757)], (41329 ^ _779142) ^ [_1593101, _1593103, _1593105, _1593107, _1593109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593101), tc_List_Olist(_1593101))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593101), tc_List_Olist(_1593101)), _1593103), _1593105)), hAPP(c_List_Olexn(_1593101, _1593107), _1593109))), 41332 ^ _779142 : [(41335 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593101)), _1593105) = _1593109)], (41333 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593101)), _1593103) = _1593109)]]], (9209 ^ _779142) ^ [_936123, _936125, _936127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936123), _936125)), _936127)), 9212 ^ _779142 : [(9215 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936125), _936127)))], (9213 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936123), _936127)))]]], (35602 ^ _779142) ^ [_1445645, _1445647, _1445649] : [-(hAPP(c_Relation_OField(_1445645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445645, _1445645), tc_HOL_Obool)), _1445647), _1445649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445645, tc_HOL_Obool)), hAPP(c_Relation_OField(_1445645), _1445647)), hAPP(c_Relation_OField(_1445645), _1445649)))], (35055 ^ _779142) ^ [_1430788, _1430790, _1430792, _1430794, _1430796] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430788, tc_fun(_1430790, tc_HOL_Obool)), _1430792), hAPP(hAPP(c_COMBS(_1430788, tc_fun(_1430790, tc_HOL_Obool), tc_fun(_1430790, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430790, tc_HOL_Obool), tc_fun(tc_fun(_1430790, tc_HOL_Obool), tc_fun(_1430790, tc_HOL_Obool)), _1430788), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430790, tc_HOL_Obool))), _1430794)), _1430796)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430790, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1430790, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430788, tc_fun(_1430790, tc_HOL_Obool), _1430794), _1430792))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1430790, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430788, tc_fun(_1430790, tc_HOL_Obool), _1430796), _1430792))))], (44329 ^ _779142) ^ [_1666177, _1666179, _1666181, _1666183] : [c_List_Olist_ONil(_1666177) = hAPP(hAPP(c_List_Omap(_1666179, _1666177), _1666181), _1666183), -(_1666183 = c_List_Olist_ONil(_1666179))], (34466 ^ _779142) ^ [_1413961, _1413963, _1413965, _1413967, _1413969] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413961, tc_fun(_1413963, tc_HOL_Obool)), _1413965), hAPP(hAPP(c_COMBC(_1413961, tc_fun(_1413963, tc_HOL_Obool), tc_fun(_1413963, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413963, tc_HOL_Obool), tc_fun(tc_fun(_1413963, tc_HOL_Obool), tc_fun(_1413963, tc_HOL_Obool)), _1413961), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413963, tc_HOL_Obool))), _1413967)), _1413969)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413963, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413961, tc_fun(_1413963, tc_HOL_Obool)), _1413965), _1413967)), _1413969))], (18515 ^ _779142) ^ [_1105134, _1105136] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105134) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105136), -(_1105134 = _1105136)], (40935 ^ _779142) ^ [_1582723, _1582725, _1582727] : [c_Wellfounded_Owf(_1582723, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582723, _1582723), tc_HOL_Obool), _1582725), _1582727)), -(c_Wellfounded_Owf(_1582723, _1582727))], (37096 ^ _779142) ^ [_1478935, _1478937, _1478939] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1478935), _1478937), _1478939) = c_Nitpick_OAbs__Frac(_1478935, c_Nitpick_Onorm__frac(_1478937, _1478939)))], (48292 ^ _779142) ^ [_1752827, _1752829, _1752831] : [_1752829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1752827, _1752829, _1752831) = c_List_Olist_ONil(_1752827))], (50502 ^ _779142) ^ [_1802351] : [-(c_Lazy__Sequence_Oflat(_1802351, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1802351))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802351))], (42778 ^ _779142) ^ [_1631506, _1631508] : [-(c_List_Osublist(_1631506, _1631508, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1631506))], (40314 ^ _779142) ^ [_1567579, _1567581, _1567583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567579, _1567579)), _1567581), _1567583)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567579, _1567579)), _1567581), c_Transitive__Closure_Ortrancl(_1567579, _1567583))))], (29229 ^ _779142) ^ [_1297617, _1297619, _1297621, _1297623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297617, tc_HOL_Obool)), _1297619), _1297621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297617, tc_HOL_Obool)), _1297619), _1297623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297617, tc_HOL_Obool)), _1297619), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297617, tc_HOL_Obool)), _1297621), _1297623))))], (29454 ^ _779142) ^ [_1302921, _1302923, _1302925] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302921, tc_HOL_Obool)), _1302923), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302921, tc_HOL_Obool)), _1302925)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302921, tc_HOL_Obool)), _1302923), _1302925))], (8989 ^ _779142) ^ [_931018, _931020, _931022, _931024, _931026] : [class_Groups_Ocomm__monoid__add(_931018), hBOOL(hAPP(c_Finite__Set_Ofinite(_931020), _931022)), -(hBOOL(hAPP(hAPP(c_member(_931020), _931024), _931022))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931020, _931018), _931026), hAPP(hAPP(c_Set_Oinsert(_931020), _931024), _931022)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931018), hAPP(_931026, _931024)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931020, _931018), _931026), _931022)))], (32053 ^ _779142) ^ [_1359937, _1359939, _1359941, _1359943, _1359945] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359937), hAPP(c_Set_Oimage(_1359939, _1359937, _1359941), c_Orderings_Otop__class_Otop(tc_fun(_1359939, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359943), hAPP(c_Set_Oimage(_1359939, _1359943, hAPP(hAPP(c_COMBB(_1359937, _1359943, _1359939), _1359945), _1359941)), c_Orderings_Otop__class_Otop(tc_fun(_1359939, tc_HOL_Obool))))))], (26806 ^ _779142) ^ [_1251354, _1251356, _1251358] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1251354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251354, tc_HOL_Obool)), _1251356), _1251358)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251354), _1251356)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251354), _1251358))], (25736 ^ _779142) ^ [_1231487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1231487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1231487)))], (39514 ^ _779142) ^ [_1547843, _1547845, _1547847, _1547849, _1547851] : [c_Finite__Set_Ofun__left__comm(_1547843, _1547845, _1547847), -(hAPP(c_Fun_Ocomp(_1547845, _1547845, _1547845, hAPP(_1547847, _1547849)), hAPP(_1547847, _1547851)) = hAPP(c_Fun_Ocomp(_1547845, _1547845, _1547845, hAPP(_1547847, _1547851)), hAPP(_1547847, _1547849)))], (3248 ^ _779142) ^ [_827520, _827522] : [_827522 = _827520, -(c_Int_OBit1(_827522) = c_Int_OBit1(_827520))], (21270 ^ _779142) ^ [_1153130, _1153132] : [c_Nat__Transfer_Ois__nat(_1153130), c_Nat__Transfer_Ois__nat(_1153132), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1153130), _1153132)))], (23545 ^ _779142) ^ [_1193794, _1193796, _1193798] : [class_Groups_Oordered__ab__group__add__abs(_1193794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193794), _1193796), _1193798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193794), hAPP(c_Groups_Ouminus__class_Ouminus(_1193794), _1193796)), _1193798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193794), hAPP(c_Groups_Oabs__class_Oabs(_1193794), _1193796)), _1193798)))], (33907 ^ _779142) ^ [_1400248, _1400250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1400248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400250), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1400248), _1400250) = 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), _1400248), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1400250)))))], (25784 ^ _779142) ^ [_1232319, _1232321] : [class_Int_Onumber__ring(_1232319), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232319), hAPP(c_Int_Onumber__class_Onumber__of(_1232319), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1232321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232319), _1232321), _1232321))], (46548 ^ _779142) ^ [_1714985, _1714987] : [-(c_Fun_Oinj__on(tc_List_Olist(_1714985), tc_List_Olist(_1714985), c_List_Orev(_1714985), _1714987))], (25554 ^ _779142) ^ [_1228276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1228276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1228276)))], (40705 ^ _779142) ^ [_1577101, _1577103] : [c_Wellfounded_Oacyclic(_1577101, hAPP(c_Relation_Oconverse(_1577101, _1577101), _1577103)), -(c_Wellfounded_Oacyclic(_1577101, _1577103))], (16941 ^ _779142) ^ [_1077162, _1077164, _1077166] : [class_Orderings_Olinorder(_1077162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077162), _1077164)), -(hBOOL(hAPP(hAPP(c_member(_1077162), _1077166), _1077164))), -(c_Big__Operators_Olattice_OInf__fin(_1077162, c_Orderings_Oord__class_Omin(_1077162), hAPP(hAPP(c_Set_Oinsert(_1077162), _1077166), _1077164)) = hAPP(hAPP(c_Finite__Set_Ofold(_1077162, _1077162, c_Orderings_Oord__class_Omin(_1077162)), _1077166), _1077164))], (51137 ^ _779142) ^ [_1813966, _1813968, _1813970, _1813972] : [class_Divides_Osemiring__div(_1813966), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813966), _1813968), _1813970)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813966), _1813968), _1813972)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813966), _1813968), c_Divides_Odiv__class_Omod(_1813966, _1813970, _1813972))))], (47167 ^ _779142) ^ [_1728096, _1728098, _1728100] : [hBOOL(hAPP(hAPP(c_member(_1728096), _1728098), hAPP(c_List_Oset(_1728096), _1728100))), -(c_List_Oinsert(_1728096, _1728098, _1728100) = _1728100)], (40103 ^ _779142) ^ [_1561797, _1561799, _1561801, _1561803, _1561805] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561797, _1561799, _1561797, _1561801), hAPP(c_Product__Type_OPair(_1561799, _1561797), _1561803)), _1561805) = hAPP(_1561805, _1561803))], (52271 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (1836 ^ _779142) ^ [_805034, _805036] : [-(class_Rings_Omult__zero(_805034)), _805036 = _805034, class_Rings_Omult__zero(_805036)], (42159 ^ _779142) ^ [_1618600, _1618602, _1618604, _1618606] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618600, _1618600)), hAPP(hAPP(c_Product__Type_OPair(_1618600, _1618600), _1618602), _1618604)), hAPP(c_List_Oset(tc_prod(_1618600, _1618600)), hAPP(hAPP(c_List_Ozip(_1618600, _1618600), _1618606), _1618606))))), hBOOL(hAPP(hAPP(c_member(_1618600), _1618602), hAPP(c_List_Oset(_1618600), _1618606))), _1618602 = _1618604], (42634 ^ _779142) ^ [_1629031, _1629033, _1629035, _1629037] : [-(_1629031 = _1629033), -(c_List_Oremove1(_1629035, _1629031, hAPP(hAPP(c_List_Olist_OCons(_1629035), _1629033), _1629037)) = hAPP(hAPP(c_List_Olist_OCons(_1629035), _1629033), c_List_Oremove1(_1629035, _1629031, _1629037)))], (19753 ^ _779142) ^ [_1126265] : [hAPP(c_Int_Onat, _1126265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126265), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23883 ^ _779142) ^ [_1199720] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199720), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1199720) = _1199720)], (11518 ^ _779142) ^ [_977278, _977280, _977282] : [class_Groups_Oordered__comm__monoid__add(_977278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977278), _977280), c_Groups_Ozero__class_Ozero(_977278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977278), _977282), c_Groups_Ozero__class_Ozero(_977278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977278), _977280), _977282)), c_Groups_Ozero__class_Ozero(_977278))))], (38867 ^ _779142) ^ [_1531797, _1531799, _1531801, _1531803] : [38868 ^ _779142 : [(38869 ^ _779142) ^ [_1531872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531797, _1531801)), hAPP(hAPP(c_Product__Type_OPair(_1531797, _1531801), _1531799), _1531872)), _1531803))]], -(hBOOL(hAPP(hAPP(c_member(_1531797), _1531799), hAPP(c_Relation_ODomain(_1531797, _1531801), _1531803))))], (16465 ^ _779142) ^ [_1069043, _1069045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069043), _1069045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1069043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1069045))))], (15607 ^ _779142) ^ [_1052772, _1052774, _1052776] : [class_Int_Onumber__ring(_1052772), -(hAPP(c_Int_Onumber__class_Onumber__of(_1052772), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052774), _1052776)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1052772), hAPP(c_Int_Onumber__class_Onumber__of(_1052772), _1052774)), hAPP(c_Int_Onumber__class_Onumber__of(_1052772), _1052776)))], (42800 ^ _779142) ^ [_1631947, _1631949] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631947), tc_List_Olist(_1631947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631947), tc_List_Olist(_1631947)), c_List_Olist_ONil(_1631947)), c_List_Olist_ONil(_1631947))), c_List_Olistrel(_1631947, _1631949))))], (48646 ^ _779142) ^ [_1760716, _1760718] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760716, _1760718), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760716)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7508 ^ _779142) ^ [_903330, _903332, _903334, _903336] : [class_Orderings_Opreorder(_903330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903330), _903332), _903334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903330), _903334), _903336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903330), _903332), _903336)))], (37785 ^ _779142) ^ [_1496885, _1496887, _1496889, _1496891] : [_1496885 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1496887, _1496889), 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)), _1496891))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496887), _1496885)))], (7432 ^ _779142) ^ [_902134, _902136, _902138] : [class_Orderings_Opreorder(_902134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902134), _902136), _902138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902134), _902138), _902136))], (44225 ^ _779142) ^ [_1663570, _1663572, _1663574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663570), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663572)), _1663574))), -(c_List_Olast(_1663572, hAPP(hAPP(c_List_Odrop(_1663572), _1663570), _1663574)) = c_List_Olast(_1663572, _1663574))], (41905 ^ _779142) ^ [_1610878, _1610880, _1610882, _1610884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1610878), _1610880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610882, tc_HOL_Obool)), hAPP(c_List_Oset(_1610882), hAPP(hAPP(c_List_Otake(_1610882), _1610878), _1610884))), hAPP(c_List_Oset(_1610882), hAPP(hAPP(c_List_Otake(_1610882), _1610880), _1610884)))))], (42684 ^ _779142) ^ [_1629855, _1629857, _1629859] : [-(hAPP(hAPP(c_List_Ozip(_1629855, _1629857), c_List_Olist_ONil(_1629855)), _1629859) = c_List_Olist_ONil(tc_prod(_1629855, _1629857)))], (48808 ^ _779142) ^ [_1764742, _1764744] : [-(c_Relation_Otrans(_1764742, c_Relation_OId__on(_1764742, _1764744)))], (17121 ^ _779142) ^ [_1080307, _1080309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1080307), _1080309))))], (14625 ^ _779142) ^ [_1034351, _1034353, _1034355, _1034357] : [class_Fields_Ofield__inverse__zero(_1034351), -(_1034353 = c_Groups_Ozero__class_Ozero(_1034351)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034351), _1034355), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034351), _1034357), _1034353)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034351), _1034357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034351), _1034355), _1034353))), _1034353))], (7952 ^ _779142) ^ [_910075, _910077, _910079] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910075, tc_HOL_Obool)), _910077), _910079))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910075, tc_HOL_Obool)), _910077), _910079)), -(_910077 = _910079)], (34412 ^ _779142) ^ [_1412509, _1412511, _1412513, _1412515, _1412517] : [34414 ^ _779142 : [(34417 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412509, tc_HOL_Obool)), _1412511), hAPP(_1412517, 34413 ^ [_1412509, _1412511, _1412513, _1412515, _1412517])))], (34415 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412513), 34413 ^ [_1412509, _1412511, _1412513, _1412515, _1412517]), _1412515)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412509, tc_HOL_Obool)), _1412511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412513, tc_fun(_1412509, tc_HOL_Obool)), _1412515), _1412517))))], (12752 ^ _779142) ^ [_999563, _999565, _999567, _999569, _999571] : [class_Rings_Olinordered__semiring__strict(_999563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999563), _999565), _999567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999563), _999569), _999571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999563), c_Groups_Ozero__class_Ozero(_999563)), _999565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999563), c_Groups_Ozero__class_Ozero(_999563)), _999569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999563), _999565), _999569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999563), _999567), _999571))))], (45953 ^ _779142) ^ [_1703651, _1703653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703651)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703653)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703653)) = c_List_Olist_ONil(tc_Nat_Onat))], (23963 ^ _779142) ^ [_1201216, _1201218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201216), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201216), _1201218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201216))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201218))))], (28042 ^ _779142) ^ [_1274389, _1274391, _1274393, _1274395] : [class_Orderings_Olinorder(_1274389), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274389), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274389), _1274391), _1274393)), _1274395) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274389), _1274391), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274389), _1274393), _1274395)))], (40324 ^ _779142) ^ [_1567799, _1567801, _1567803, _1567805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567799, _1567799)), hAPP(hAPP(c_Product__Type_OPair(_1567799, _1567799), _1567801), _1567803)), c_Transitive__Closure_Otrancl(_1567799, _1567805))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567799, _1567799)), hAPP(hAPP(c_Product__Type_OPair(_1567799, _1567799), _1567801), _1567803)), c_Transitive__Closure_Ortrancl(_1567799, _1567805))))], (22116 ^ _779142) ^ [_1168064, _1168066, _1168068] : [class_Rings_Olinordered__semidom(_1168064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168064), c_Groups_Oone__class_Oone(_1168064)), _1168066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168064), c_Groups_Oone__class_Oone(_1168064)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168064), _1168066), hAPP(hAPP(c_Power_Opower__class_Opower(_1168064), _1168066), _1168068)))))], (44831 ^ _779142) ^ [_1677271, _1677273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677271), _1677273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677271)), hAPP(c_Code__Numeral_Onat__of, _1677273))))], (27876 ^ _779142) ^ [_1271374, _1271376, _1271378, _1271380] : [class_Orderings_Olinorder(_1271374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271374), _1271376), _1271378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271374), _1271380), _1271378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271374), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271374), _1271376), _1271380)), _1271378)))], (5798 ^ _779142) ^ [_870973, _870975, _870977] : [hBOOL(hAPP(_870977, _870975)), -(hBOOL(hAPP(hAPP(c_member(_870973), _870975), _870977)))], (23853 ^ _779142) ^ [_1199310, _1199312] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199310, _1199312) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199310, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199312)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42285 ^ _779142) ^ [_1621217, _1621219, _1621221, _1621223] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621217)), hAPP(hAPP(c_List_Olist__update(_1621217, _1621219), _1621221), _1621223)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621217)), _1621219))], (5454 ^ _779142) ^ [_862569, _862571] : [_862571 = _862569, -(c_Groups_Ozero__class_Ozero(_862571) = c_Groups_Ozero__class_Ozero(_862569))], (11718 ^ _779142) ^ [_980904, _980906, _980908, _980910] : [class_Rings_Oordered__ring(_980904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980904), _980906), _980908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980904), _980910), c_Groups_Ozero__class_Ozero(_980904))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980904), _980908), _980910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980904), _980906), _980910))))], (21496 ^ _779142) ^ [_1156784, _1156786, _1156788, _1156790, _1156792] : [class_Orderings_Oorder(_1156784), 21499 ^ _779142 : [(21520 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1156784, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1156784, _1156786, _1156788)), c_SetInterval_Oord__class_OatLeastAtMost(_1156784, _1156790, _1156792)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156790), _1156792)), 21523 ^ _779142 : [(21526 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156790), _1156786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156788), _1156792)), 21533 ^ _779142 : [(21536 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156784), _1156788), _1156792))], (21534 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156784), _1156790), _1156786))]]], (21524 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156786), _1156788)))]]], (21500 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1156784, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1156784, _1156786, _1156788)), c_SetInterval_Oord__class_OatLeastAtMost(_1156784, _1156790, _1156792))), 21503 ^ _779142 : [(21504 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156786), _1156788)), 21507 ^ _779142 : [(21512 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156784), _1156790), _1156786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156784), _1156788), _1156792)))], (21510 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156788), _1156792)))], (21508 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156790), _1156786)))]]], (21518 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156784), _1156790), _1156792)))]]]]], (868 ^ _779142) ^ [_792078, _792080, _792082, _792084, _792086, _792088, _792090, _792092] : [-(c_Fun_Oinj__on(_792090, _792086, _792082, _792078)), c_Fun_Oinj__on(_792092, _792088, _792084, _792080), _792092 = _792090, _792088 = _792086, _792084 = _792082, _792080 = _792078], (36798 ^ _779142) ^ [_1472528] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1472528))], (46933 ^ _779142) ^ [_1722993, _1722995] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1722993), _1722995) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1722993)), c_List_Oembed__list(_1722995))))], (37841 ^ _779142) ^ [_1499067, _1499069, _1499071, _1499073] : [-(hAPP(c_Relation_OImage(_1499067, _1499069, _1499071), hAPP(hAPP(c_Set_Oinsert(_1499067), _1499073), c_Orderings_Obot__class_Obot(tc_fun(_1499067, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1499069), hAPP(hAPP(c_COMBC(_1499069, tc_fun(tc_prod(_1499067, _1499069), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1499067, _1499069), tc_fun(tc_fun(tc_prod(_1499067, _1499069), tc_HOL_Obool), tc_HOL_Obool), _1499069), c_member(tc_prod(_1499067, _1499069))), hAPP(c_Product__Type_OPair(_1499067, _1499069), _1499073))), _1499071)))], (1446 ^ _779142) ^ [_800159, _800161] : [-(class_Lattices_Oboolean__algebra(_800159)), _800161 = _800159, class_Lattices_Oboolean__algebra(_800161)], (36212 ^ _779142) ^ [_1460259, _1460261, _1460263, _1460265, _1460267, _1460269] : [c_Fun_Oinj__on(_1460259, _1460261, _1460263, _1460265), -(_1460267 = _1460269), hBOOL(hAPP(hAPP(c_member(_1460259), _1460267), _1460265)), hBOOL(hAPP(hAPP(c_member(_1460259), _1460269), _1460265)), hAPP(_1460263, _1460267) = hAPP(_1460263, _1460269)], (43806 ^ _779142) ^ [_1655299, _1655301, _1655303] : [-(hAPP(c_List_Orotate(_1655299, hAPP(c_Nat_OSuc, _1655301)), _1655303) = hAPP(c_List_Orotate1(_1655299), hAPP(c_List_Orotate(_1655299, _1655301), _1655303)))], (46690 ^ _779142) ^ [_1717896, _1717898, _1717900] : [-(hAPP(c_List_Orev(_1717896), hAPP(hAPP(c_List_Olist_OCons(_1717896), _1717898), _1717900)) = hAPP(hAPP(c_List_Oappend(_1717896), hAPP(c_List_Orev(_1717896), _1717900)), hAPP(hAPP(c_List_Olist_OCons(_1717896), _1717898), c_List_Olist_ONil(_1717896))))], (51905 ^ _779142) ^ [_1827071, _1827073, _1827075, _1827077, _1827079] : [class_Rings_Ocomm__semiring__1(_1827071), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827071), hAPP(hAPP(c_Power_Opower__class_Opower(_1827071), _1827073), _1827075)), _1827077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827079), _1827075)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827071), hAPP(hAPP(c_Power_Opower__class_Opower(_1827071), _1827073), _1827079)), _1827077)))], (34511 ^ _779142) ^ [_1415472, _1415474, _1415476] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415472, tc_fun(_1415474, tc_HOL_Obool)), _1415476), hAPP(c_COMBK(tc_fun(_1415474, tc_HOL_Obool), _1415472), c_Orderings_Obot__class_Obot(tc_fun(_1415474, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1415474, tc_HOL_Obool)))], (13889 ^ _779142) ^ [_1020982, _1020984, _1020986, _1020988, _1020990] : [class_Fields_Ofield__inverse__zero(_1020982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020982), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020982), _1020984), _1020986)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020982), _1020988), _1020990)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020982), _1020984), _1020988)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020982), _1020986), _1020990)))], (15619 ^ _779142) ^ [_1053008, _1053010, _1053012] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053008), _1053010)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053012), _1053010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1053008), _1053012)), _1053010))], (25326 ^ _779142) ^ [_1224222] : [-(_1224222 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25329 ^ _779142 : [(25336 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224222))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1224222) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25330 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224222)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1224222) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (41260 ^ _779142) ^ [_1591560, _1591562, _1591564] : [-(c_Nitpick_Oplus__frac(_1591560, _1591562, _1591564) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1591560), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1591560), _1591562), hAPP(c_Nitpick_Odenom(_1591560), _1591564))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1591560), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1591560), tc_Int_Oint), c_Nitpick_Ofrac(_1591560)), 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(_1591560), _1591562))), 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(_1591560), _1591562))))), 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(_1591560), _1591564))), 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(_1591560), _1591564)))))), c_COMBI(tc_Int_Oint))))], (42201 ^ _779142) ^ [_1619544] : [42203 ^ _779142 : [(42206 ^ _779142) ^ [] : [42202 ^ [_1619544] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42204 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42202 ^ [_1619544]), hAPP(c_List_Oset(tc_Nat_Onat), _1619544))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27984 ^ _779142) ^ [_1273274, _1273276, _1273278, _1273280] : [class_Orderings_Olinorder(_1273274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273274), _1273276), _1273278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273274), _1273276), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273274), _1273280), _1273278))))], (35588 ^ _779142) ^ [_1445254] : [-(_1445254 = 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), 35585 ^ [_1445254]), 35586 ^ [_1445254])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31020 ^ _779142) ^ [_1334914] : [class_Lattices_Oboolean__algebra(_1334914), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334914), c_Orderings_Otop__class_Otop(_1334914)) = c_Orderings_Obot__class_Obot(_1334914))], (48238 ^ _779142) ^ [_1751940, _1751942, _1751944, _1751946, _1751948] : [c_List_Oreplicate(_1751940, _1751942, _1751944) = c_List_Oreplicate(_1751940, _1751946, _1751948), 48241 ^ _779142 : [(48244 ^ _779142) ^ [] : [-(_1751942 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1751944 = _1751948)], (48242 ^ _779142) ^ [] : [-(_1751942 = _1751946)]]], (6123 ^ _779142) ^ [_876926, _876928, _876930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876926), _876928)), hBOOL(hAPP(_876930, c_Orderings_Obot__class_Obot(tc_fun(_876926, tc_HOL_Obool)))), 6134 ^ _779142 : [(6137 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876926), 6132 ^ [_876926, _876928, _876930]), 6133 ^ [_876926, _876928, _876930]))], (6139 ^ _779142) ^ [] : [-(hBOOL(hAPP(_876930, 6133 ^ [_876926, _876928, _876930])))], (6141 ^ _779142) ^ [] : [hBOOL(hAPP(_876930, hAPP(hAPP(c_Set_Oinsert(_876926), 6132 ^ [_876926, _876928, _876930]), 6133 ^ [_876926, _876928, _876930])))], (6135 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_876926), 6133 ^ [_876926, _876928, _876930])))]], -(hBOOL(hAPP(_876930, _876928)))], (12481 ^ _779142) ^ [_994556, _994558, _994560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _994556)), 12484 ^ _779142 : [(12491 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994558), _994560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994556), _994558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994556), _994560))))], (12485 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994556), _994558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994556), _994560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994558), _994560)))]]], (49753 ^ _779142) ^ [_1784860, _1784862, _1784864] : [hAPP(c_Set_Oimage(_1784860, _1784862, _1784864), c_Orderings_Otop__class_Otop(tc_fun(_1784860, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784862, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1784860, _1784862, _1784862, _1784864), c_Hilbert__Choice_Oinv__into(_1784860, _1784862, c_Orderings_Otop__class_Otop(tc_fun(_1784860, tc_HOL_Obool)), _1784864)) = c_Fun_Oid(_1784862))], (25450 ^ _779142) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (31483 ^ _779142) ^ [_1343835, _1343837, _1343839, _1343841, _1343843, _1343845] : [class_Groups_Oab__semigroup__mult(_1343835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343837), _1343839)), 31493 ^ _779142 : [(31496 ^ _779142) ^ [] : [hAPP(_1343841, 31492 ^ [_1343835, _1343837, _1343839, _1343841, _1343843, _1343845]) = hAPP(_1343843, 31492 ^ [_1343835, _1343837, _1343839, _1343841, _1343843, _1343845])], (31494 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1343837), 31492 ^ [_1343835, _1343837, _1343839, _1343841, _1343843, _1343845]), _1343839)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1343835, _1343837, c_Groups_Otimes__class_Otimes(_1343835)), _1343841), _1343845), _1343839) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1343835, _1343837, c_Groups_Otimes__class_Otimes(_1343835)), _1343843), _1343845), _1343839))], (11648 ^ _779142) ^ [_979587, _979589, _979591] : [class_Rings_Oordered__cancel__semiring(_979587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979587), _979589), c_Groups_Ozero__class_Ozero(_979587))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979587), c_Groups_Ozero__class_Ozero(_979587)), _979591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979587), _979589), _979591)), c_Groups_Ozero__class_Ozero(_979587))))], (43137 ^ _779142) ^ [_1639748, _1639750, _1639752] : [class_Groups_Omonoid__add(_1639748), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639748), hAPP(hAPP(c_List_Oappend(_1639748), _1639750), _1639752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639748), hAPP(c_List_Omonoid__add__class_Olistsum(_1639748), _1639750)), hAPP(c_List_Omonoid__add__class_Olistsum(_1639748), _1639752)))], (10937 ^ _779142) ^ [_967955, _967957] : [class_Groups_Olinordered__ab__group__add(_967955), 10940 ^ _779142 : [(10947 ^ _779142) ^ [] : [_967957 = c_Groups_Ozero__class_Ozero(_967955), -(c_Groups_Ozero__class_Ozero(_967955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967955), _967957), _967957))], (10941 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_967955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967955), _967957), _967957), -(_967957 = c_Groups_Ozero__class_Ozero(_967955))]]], (35320 ^ _779142) ^ [] : [-(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)))))], (6599 ^ _779142) ^ [_885357, _885359, _885361, _885363, _885365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885357, tc_HOL_Obool)), _885359), _885361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885363, tc_HOL_Obool)), hAPP(c_Set_Oimage(_885357, _885363, _885365), _885359)), hAPP(c_Set_Oimage(_885357, _885363, _885365), _885361))))], (12910 ^ _779142) ^ [_1002531, _1002533] : [12911 ^ _779142 : [(12914 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002531), _1002533)))], (12912 ^ _779142) ^ [] : [_1002533 = c_Orderings_Obot__class_Obot(tc_fun(_1002531, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1002531), _1002533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25742 ^ _779142) ^ [_1231570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1231570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1231570))))], (43494 ^ _779142) ^ [_1648387, _1648389, _1648391, _1648393] : [-(hAPP(hAPP(c_List_Odrop(_1648387), _1648389), hAPP(hAPP(c_List_Otake(_1648387), _1648391), _1648393)) = hAPP(hAPP(c_List_Otake(_1648387), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1648391), _1648389)), hAPP(hAPP(c_List_Odrop(_1648387), _1648389), _1648393)))], (2702 ^ _779142) ^ [_819003, _819005, _819007, _819009, _819011, _819013] : [-(c_Predicate_ORangeP(_819013, _819009, _819005) = c_Predicate_ORangeP(_819011, _819007, _819003)), _819013 = _819011, _819009 = _819007, _819005 = _819003], (48130 ^ _779142) ^ [_1749240, _1749242, _1749244, _1749246, _1749248] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749240, _1749242, _1749244), _1749246), _1749248)), -(hBOOL(hAPP(hAPP(_1749244, _1749248), _1749246)))], (10909 ^ _779142) ^ [_967419, _967421] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967419)), hAPP(c_Nat_OSuc, _967421)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967419), _967421))], (6285 ^ _779142) ^ [_879875, _879877, _879879] : [class_Orderings_Oorder(_879875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879875), _879877), _879879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879875), _879879), _879877)), -(_879879 = _879877)], (37399 ^ _779142) ^ [_1486570, _1486572, _1486574, _1486576, _1486578] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486570, _1486572), _1486574), hAPP(hAPP(c_COMBS(_1486570, tc_fun(_1486572, tc_HOL_Obool), tc_fun(_1486572, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1486572, tc_HOL_Obool), tc_fun(tc_fun(_1486572, tc_HOL_Obool), tc_fun(_1486572, tc_HOL_Obool)), _1486570), c_Groups_Ominus__class_Ominus(tc_fun(_1486572, tc_HOL_Obool))), _1486576)), _1486578)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486570, _1486572), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486570, _1486572), _1486574), _1486576)), hAPP(hAPP(c_Product__Type_OSigma(_1486570, _1486572), _1486574), _1486578)))], (49310 ^ _779142) ^ [_1776115, _1776117] : [c_Relation_Osym(_1776115, hAPP(c_Relation_Oconverse(_1776115, _1776115), _1776117)), -(c_Relation_Osym(_1776115, _1776117))], (37443 ^ _779142) ^ [_1487527, _1487529, _1487531] : [-(hAPP(hAPP(c_Set_Oinsert(_1487527), _1487529), hAPP(c_Set_OCollect(_1487527), _1487531)) = hAPP(c_Set_OCollect(_1487527), hAPP(hAPP(c_COMBS(_1487527, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487527), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1487527), c_fNot), hAPP(hAPP(c_COMBC(_1487527, _1487527, tc_HOL_Obool), c_fequal), _1487529)))), _1487531)))], (17425 ^ _779142) ^ [_1085794, _1085796, _1085798, _1085800] : [class_Divides_Osemiring__div(_1085794), -(c_Divides_Odiv__class_Omod(_1085794, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085794), _1085796), _1085798), _1085800) = c_Divides_Odiv__class_Omod(_1085794, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085794), c_Divides_Odiv__class_Omod(_1085794, _1085796, _1085800)), _1085798), _1085800))], (48624 ^ _779142) ^ [_1760186, _1760188, _1760190, _1760192, _1760194, _1760196, _1760198] : [48626 ^ _779142 : [(48629 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1760190, 48625 ^ [_1760186, _1760188, _1760190, _1760192, _1760194, _1760196, _1760198]), _1760192), _1760194))], (48627 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760186), 48625 ^ [_1760186, _1760188, _1760190, _1760192, _1760194, _1760196, _1760198]), _1760188)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1760186, tc_fun(_1760196, tc_fun(_1760198, tc_HOL_Obool))), _1760188), _1760190), _1760192), _1760194)))], (2916 ^ _779142) ^ [_822330, _822332, _822334, _822336] : [-(c_Nitpick_Ouminus__frac(_822336, _822332) = c_Nitpick_Ouminus__frac(_822334, _822330)), _822336 = _822334, _822332 = _822330], (44512 ^ _779142) ^ [_1670607, _1670609, _1670611, _1670613] : [hBOOL(hAPP(c_List_Odistinct(_1670607), hAPP(hAPP(c_List_Omap(_1670609, _1670607), _1670611), _1670613))), 44515 ^ _779142 : [(44518 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1670609, _1670607, _1670611, hAPP(c_List_Oset(_1670609), _1670613)))], (44516 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670609), _1670613)))]]], (472 ^ _779142) ^ [_786210, _786212, _786214, _786216, _786218, _786220] : [-(c_Nitpick_Oless__eq__frac(_786218, _786214, _786210)), c_Nitpick_Oless__eq__frac(_786220, _786216, _786212), _786220 = _786218, _786216 = _786214, _786212 = _786210], (17633 ^ _779142) ^ [_1089778] : [17635 ^ _779142 : [(17638 ^ _779142) ^ [] : [hBOOL(hAPP(_1089778, 17634 ^ [_1089778]))], (17636 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17634 ^ [_1089778])))]], 17639 ^ _779142 : [(17640 ^ _779142) ^ [_1089905] : [-(hBOOL(hAPP(_1089778, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1089905))))]]], (16489 ^ _779142) ^ [_1069450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069450), _1069450)))], (25652 ^ _779142) ^ [_1229991] : [-(c_Int_Opred(c_Int_OBit1(_1229991)) = c_Int_OBit0(_1229991))], (7646 ^ _779142) ^ [_905608, _905610, _905612, _905614] : [class_Orderings_Oorder(_905608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905608), _905610), _905612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905608), _905614), _905610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905608), _905614), _905612)))], (43397 ^ _779142) ^ [_1645789, _1645791, _1645793, _1645795, _1645797, _1645799] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645789), tc_List_Olist(_1645789))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645789), tc_List_Olist(_1645789)), hAPP(hAPP(c_List_Oappend(_1645789), _1645791), hAPP(hAPP(c_List_Olist_OCons(_1645789), _1645793), c_List_Olist_ONil(_1645789)))), hAPP(hAPP(c_List_Oappend(_1645789), _1645795), hAPP(hAPP(c_List_Olist_OCons(_1645789), _1645797), c_List_Olist_ONil(_1645789))))), c_List_Olistrel1(_1645789, _1645799))), 43402 ^ _779142 : [(43405 ^ _779142) ^ [] : [-(_1645793 = _1645797)], (43403 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645789), tc_List_Olist(_1645789))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645789), tc_List_Olist(_1645789)), _1645791), _1645795)), c_List_Olistrel1(_1645789, _1645799))))]], 43406 ^ _779142 : [(43409 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645789, _1645789)), hAPP(hAPP(c_Product__Type_OPair(_1645789, _1645789), _1645793), _1645797)), _1645799)))], (43407 ^ _779142) ^ [] : [-(_1645791 = _1645795)]]], (13929 ^ _779142) ^ [_1021749, _1021751, _1021753] : [class_Fields_Olinordered__field__inverse__zero(_1021749), 13932 ^ _779142 : [(13947 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021749), _1021751), _1021753)), c_Groups_Ozero__class_Ozero(_1021749)))), 13948 ^ _779142 : [(13955 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), _1021751), c_Groups_Ozero__class_Ozero(_1021749))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), c_Groups_Ozero__class_Ozero(_1021749)), _1021753))], (13949 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), c_Groups_Ozero__class_Ozero(_1021749)), _1021751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), _1021753), c_Groups_Ozero__class_Ozero(_1021749)))]]], (13933 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021749), _1021751), _1021753)), c_Groups_Ozero__class_Ozero(_1021749))), 13938 ^ _779142 : [(13941 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), _1021753), c_Groups_Ozero__class_Ozero(_1021749))))], (13939 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), c_Groups_Ozero__class_Ozero(_1021749)), _1021751)))]], 13942 ^ _779142 : [(13945 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), c_Groups_Ozero__class_Ozero(_1021749)), _1021753)))], (13943 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021749), _1021751), c_Groups_Ozero__class_Ozero(_1021749))))]]]]], (43782 ^ _779142) ^ [_1654855, _1654857, _1654859] : [_1654859 = c_List_Olist_ONil(_1654855), -(hAPP(c_List_Orotate(_1654855, _1654857), _1654859) = c_List_Olist_ONil(_1654855))], (49853 ^ _779142) ^ [_1787146] : [-(c_Quickcheck_Obeyond(_1787146, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (52477 ^ _779142) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (28012 ^ _779142) ^ [_1273744, _1273746, _1273748] : [class_Orderings_Olinorder(_1273744), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273744), _1273746), _1273748) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273744), _1273748), _1273746))], (48298 ^ _779142) ^ [_1752938, _1752940, _1752942] : [c_List_Olist_ONil(_1752938) = c_List_Oreplicate(_1752938, _1752940, _1752942), -(_1752940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13350 ^ _779142) ^ [_1010876, _1010878, _1010880] : [-(hAPP(c_Finite__Set_Ocard(_1010876), _1010878) = hAPP(c_Nat_OSuc, _1010880)), 13351 ^ _779142 : [(13352 ^ _779142) ^ [_1010976, _1010978] : [_1010878 = hAPP(hAPP(c_Set_Oinsert(_1010876), _1010978), _1010976), -(hBOOL(hAPP(hAPP(c_member(_1010876), _1010978), _1010976))), hAPP(c_Finite__Set_Ocard(_1010876), _1010976) = _1010880, 13363 ^ _779142 : [(13366 ^ _779142) ^ [] : [_1010976 = c_Orderings_Obot__class_Obot(tc_fun(_1010876, tc_HOL_Obool))], (13364 ^ _779142) ^ [] : [-(_1010880 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (27038 ^ _779142) ^ [_1256223, _1256225, _1256227, _1256229, _1256231] : [c_Finite__Set_Ofolding__one__idem(_1256223, _1256225, _1256227), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256223), _1256229)), -(_1256229 = c_Orderings_Obot__class_Obot(tc_fun(_1256223, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256223), _1256231)), -(_1256231 = c_Orderings_Obot__class_Obot(tc_fun(_1256223, tc_HOL_Obool))), -(hAPP(_1256227, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256223, tc_HOL_Obool)), _1256229), _1256231)) = hAPP(hAPP(_1256225, hAPP(_1256227, _1256229)), hAPP(_1256227, _1256231)))], (6073 ^ _779142) ^ [_876067, _876069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _876067), _876069)), -(v_P(_876069, _876067))], (21796 ^ _779142) ^ [_1162032, _1162034, _1162036, _1162038, _1162040] : [class_Groups_Ocomm__monoid__add(_1162032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1162036), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162032), _1162038), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1162034, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1162036), _1162040))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162032), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162032), _1162038), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1162034, _1162036))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162032), _1162038), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1162036), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1162036), _1162040)))))], (32329 ^ _779142) ^ [_1367997, _1367999, _1368001] : [class_Int_Onumber__ring(_1367997), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1367997), hAPP(c_Int_Onumber__class_Onumber__of(_1367997), _1367999)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1368001))) = hAPP(hAPP(c_HOL_OLet(_1367997, _1367997), hAPP(hAPP(c_Power_Opower__class_Opower(_1367997), hAPP(c_Int_Onumber__class_Onumber__of(_1367997), _1367999)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368001))), hAPP(hAPP(c_COMBS(_1367997, _1367997, _1367997), c_Groups_Otimes__class_Otimes(_1367997)), c_COMBI(_1367997))))], (45823 ^ _779142) ^ [_1700969, _1700971, _1700973, _1700975] : [-(c_List_Ofoldr(_1700969, _1700971, _1700973, c_List_Olist_ONil(_1700969), _1700975) = _1700975)], (19259 ^ _779142) ^ [_1117700, _1117702, _1117704] : [class_Groups_Oordered__ab__group__add__abs(_1117700), -(hAPP(c_Groups_Oabs__class_Oabs(_1117700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117700), hAPP(c_Groups_Oabs__class_Oabs(_1117700), _1117702)), hAPP(c_Groups_Oabs__class_Oabs(_1117700), _1117704))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117700), hAPP(c_Groups_Oabs__class_Oabs(_1117700), _1117702)), hAPP(c_Groups_Oabs__class_Oabs(_1117700), _1117704)))], (52111 ^ _779142) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (22648 ^ _779142) ^ [_1178012, _1178014, _1178016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178012)), 22651 ^ _779142 : [(22652 ^ _779142) ^ [_1178146] : [22654 ^ _779142 : [(22660 ^ _779142) ^ [] : [-(_1178146 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22656 ^ [_1178012, _1178014, _1178016, _1178146]), 22653 ^ [_1178012, _1178014, _1178016, _1178146]))], (22658 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22656 ^ [_1178012, _1178014, _1178016, _1178146]), _1178014)))], (22655 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22653 ^ [_1178012, _1178014, _1178016, _1178146]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1178012))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178146), _1178016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178146), _1178012)), _1178016)))]]], (30818 ^ _779142) ^ [_1331406] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1331406)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1331406), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331406), c_Orderings_Otop__class_Otop(tc_fun(_1331406, tc_HOL_Obool)))))], (27142 ^ _779142) ^ [_1258032, _1258034, _1258036, _1258038] : [class_Orderings_Olinorder(_1258032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258032), _1258034), _1258036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258032), _1258036), _1258038)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258032, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1258032, _1258034, _1258036)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1258032, _1258036), _1258038)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1258032, _1258034, _1258038))], (45560 ^ _779142) ^ [_1693380, _1693382] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693380)), c_List_Oconcat(_1693380, _1693382)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693380), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1693380))), _1693382)))], (44614 ^ _779142) ^ [_1672992, _1672994] : [hAPP(c_Code__Numeral_Oof__nat, _1672992) = hAPP(c_Code__Numeral_Oof__nat, _1672994), -(_1672992 = _1672994)], (24415 ^ _779142) ^ [_1208772, _1208774, _1208776] : [class_Rings_Oring__1(_1208772), -(hAPP(c_Int_Oring__1__class_Oof__int(_1208772), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1208774), _1208776)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1208772), hAPP(c_Int_Oring__1__class_Oof__int(_1208772), _1208774)), _1208776))], (43321 ^ _779142) ^ [_1643821, _1643823, _1643825] : [hBOOL(hAPP(c_List_Odistinct(_1643821), hAPP(hAPP(c_List_Oappend(_1643821), _1643823), _1643825))), 43324 ^ _779142 : [(43329 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643821, tc_HOL_Obool)), hAPP(c_List_Oset(_1643821), _1643823)), hAPP(c_List_Oset(_1643821), _1643825)) = c_Orderings_Obot__class_Obot(tc_fun(_1643821, tc_HOL_Obool)))], (43327 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643821), _1643825)))], (43325 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643821), _1643823)))]]], (37191 ^ _779142) ^ [_1481208, _1481210, _1481212, _1481214, _1481216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481208, tc_HOL_Obool)), _1481210), _1481212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481214, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481214, _1481208, _1481216), _1481210)), hAPP(c_Set_Ovimage(_1481214, _1481208, _1481216), _1481212))))], (39473 ^ _779142) ^ [_1547045, _1547047, _1547049, _1547051, _1547053, _1547055] : [-(hAPP(hAPP(c_Fun_Ocomp(_1547045, _1547047, _1547049, hAPP(c_COMBK(_1547047, _1547045), _1547051)), _1547053), _1547055) = _1547051)], (51787 ^ _779142) ^ [_1824890, _1824892] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824892), _1824890)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824890), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824892))))], (44384 ^ _779142) ^ [_1667462, _1667464, _1667466, _1667468, _1667470] : [class_Groups_Ocomm__monoid__add(_1667462), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667462), hAPP(hAPP(c_List_Omap(_1667464, _1667462), hAPP(hAPP(c_COMBS(_1667464, _1667462, _1667462), hAPP(hAPP(c_COMBB(_1667462, tc_fun(_1667462, _1667462), _1667464), c_Groups_Oplus__class_Oplus(_1667462)), _1667466)), _1667468)), _1667470)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667462), hAPP(c_List_Omonoid__add__class_Olistsum(_1667462), hAPP(hAPP(c_List_Omap(_1667464, _1667462), _1667466), _1667470))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667462), hAPP(hAPP(c_List_Omap(_1667464, _1667462), _1667468), _1667470))))], (17653 ^ _779142) ^ [_1090138] : [-(hBOOL(hAPP(_1090138, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 17660 ^ [_1090138])))), 17654 ^ _779142 : [(17655 ^ _779142) ^ [_1090190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1090190)), hBOOL(hAPP(_1090138, _1090190))]]], (23953 ^ _779142) ^ [_1201002] : [-(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, _1201002)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26234 ^ _779142) ^ [_1240523, _1240525] : [class_Int_Onumber__ring(_1240523), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240523), hAPP(c_Int_Onumber__class_Onumber__of(_1240523), 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)))), _1240525))) = hAPP(c_Int_Onumber__class_Onumber__of(_1240523), c_Int_OMin))], (5162 ^ _779142) ^ [_857889, _857891, _857893, _857895, _857897, _857899] : [-(c_Lazy__Sequence_Obind(_857899, _857895, _857891) = c_Lazy__Sequence_Obind(_857897, _857893, _857889)), _857899 = _857897, _857895 = _857893, _857891 = _857889], (8280 ^ _779142) ^ [_917033, _917035, _917037, _917039, _917041] : [hAPP(_917037, _917039) = _917041, -(c_Fun_Ofun__upd(_917033, _917035, _917037, _917039, _917041) = _917037)], (40725 ^ _779142) ^ [_1577550, _1577552, _1577554, _1577556] : [-(hAPP(c_Relation_Oconverse(_1577550, _1577550), hAPP(hAPP(c_Relation_Oinv__image(_1577552, _1577550), _1577554), _1577556)) = hAPP(hAPP(c_Relation_Oinv__image(_1577552, _1577550), hAPP(c_Relation_Oconverse(_1577552, _1577552), _1577554)), _1577556))], (21818 ^ _779142) ^ [_1162557, _1162559] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1162557, _1162559) = 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), _1162557), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1162559))))], (40201 ^ _779142) ^ [_1564095, _1564097, _1564099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564095, _1564095), tc_HOL_Obool)), _1564097), _1564099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564095, _1564095), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564095, _1564095, _1564095), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1564095, _1564095), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564095, _1564097)), _1564099)), _1564097)), _1564099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564095, _1564095), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564095, _1564097)), _1564099)))], (29359 ^ _779142) ^ [_1300399, _1300401, _1300403, _1300405] : [-(hBOOL(hAPP(hAPP(c_member(_1300399), _1300401), _1300403))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300399, tc_HOL_Obool)), _1300403), hAPP(hAPP(c_Set_Oinsert(_1300399), _1300401), _1300405)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300399, tc_HOL_Obool)), _1300403), _1300405))], (17885 ^ _779142) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (12202 ^ _779142) ^ [_989866, _989868, _989870] : [class_Groups_Oordered__ab__group__add(_989866), 12205 ^ _779142 : [(12212 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_989866), _989868), _989870)), c_Groups_Ozero__class_Ozero(_989866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989866), _989868), _989870)))], (12206 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989866), _989868), _989870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_989866), _989868), _989870)), c_Groups_Ozero__class_Ozero(_989866))))]]], (44809 ^ _779142) ^ [_1676880, _1676882] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1676880), _1676882) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676880)), hAPP(c_Code__Numeral_Onat__of, _1676882))))], (51389 ^ _779142) ^ [_1818052, _1818054, _1818056] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818052), _1818054)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818054), _1818056)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818052), _1818056)))], (8006 ^ _779142) ^ [_911071, _911073, _911075, _911077] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911071, _911073, _911075, _911077, c_Orderings_Obot__class_Obot(tc_fun(_911071, tc_HOL_Obool))), _911077)))], (21812 ^ _779142) ^ [_1162440, _1162442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162440)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1162440), _1162442)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1162440)), _1162442))], (51295 ^ _779142) ^ [_1816593, _1816595] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816593), _1816595)), 51298 ^ _779142 : [(51305 ^ _779142) ^ [] : [_1816595 = _1816593, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816595), _1816593)))], (51299 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816595), _1816593)), -(_1816595 = _1816593)]]], (36342 ^ _779142) ^ [_1462733, _1462735, _1462737, _1462739, _1462741] : [c_Fun_Oinj__on(_1462733, _1462735, _1462737, c_Orderings_Otop__class_Otop(tc_fun(_1462733, tc_HOL_Obool))), 36345 ^ _779142 : [(36352 ^ _779142) ^ [] : [_1462739 = _1462741, -(hAPP(_1462737, _1462739) = hAPP(_1462737, _1462741))], (36346 ^ _779142) ^ [] : [hAPP(_1462737, _1462739) = hAPP(_1462737, _1462741), -(_1462739 = _1462741)]]], (47472 ^ _779142) ^ [_1735340, _1735342, _1735344, _1735346, _1735348] : [-(hAPP(c_List_Ofilter(_1735340, _1735342), _1735344) = hAPP(hAPP(c_List_Olist_OCons(_1735340), _1735346), _1735348)), 47473 ^ _779142 : [(47474 ^ _779142) ^ [_1735468, _1735470] : [_1735344 = hAPP(hAPP(c_List_Oappend(_1735340), _1735470), hAPP(hAPP(c_List_Olist_OCons(_1735340), _1735346), _1735468)), 47480 ^ _779142 : [(47483 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1735342, 47479 ^ [_1735340, _1735342, _1735344, _1735346, _1735348, _1735468, _1735470])))], (47481 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735340), 47479 ^ [_1735340, _1735342, _1735344, _1735346, _1735348, _1735468, _1735470]), hAPP(c_List_Oset(_1735340), _1735470))))]], hBOOL(hAPP(_1735342, _1735346)), _1735348 = hAPP(c_List_Ofilter(_1735340, _1735342), _1735468)]]], (43672 ^ _779142) ^ [_1652720, _1652722, _1652724, _1652726, _1652728] : [-(hAPP(hAPP(c_List_Ozip(_1652720, _1652722), _1652724), hAPP(hAPP(c_List_Oappend(_1652722), _1652726), _1652728)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652720, _1652722)), hAPP(hAPP(c_List_Ozip(_1652720, _1652722), hAPP(hAPP(c_List_Otake(_1652720), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652722)), _1652726)), _1652724)), _1652726)), hAPP(hAPP(c_List_Ozip(_1652720, _1652722), hAPP(hAPP(c_List_Odrop(_1652720), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652722)), _1652726)), _1652724)), _1652728)))], (25152 ^ _779142) ^ [] : [-(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)))))], (35268 ^ _779142) ^ [_1436180, _1436182, _1436184, _1436186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436180), _1436182)), 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)), _1436180), _1436184)), 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)), _1436182), _1436186)), 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)), _1436182), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436184), _1436186))), c_FunDef_Omin__weak)))], (28813 ^ _779142) ^ [_1289085, _1289087, _1289089, _1289091] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289085, tc_HOL_Obool)), _1289087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289085, tc_HOL_Obool)), _1289089), _1289091)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289085, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289085, tc_HOL_Obool)), _1289087), _1289089)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289085, tc_HOL_Obool)), _1289087), _1289091)))], (30741 ^ _779142) ^ [_1329826, _1329828, _1329830] : [class_Lattices_Oboolean__algebra(_1329826), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1329826), _1329828), _1329830) = c_Orderings_Obot__class_Obot(_1329826), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1329826), _1329828), _1329830) = c_Orderings_Otop__class_Otop(_1329826), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1329826), _1329828) = _1329830)], (25846 ^ _779142) ^ [_1233333] : [class_Rings_Osemiring__1(_1233333), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233333), c_Groups_Oone__class_Oone(_1233333)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1233333))], (46658 ^ _779142) ^ [_1717283, _1717285, _1717287] : [_1717285 = _1717287, -(hAPP(c_List_Orev(_1717283), _1717285) = hAPP(c_List_Orev(_1717283), _1717287))], (42131 ^ _779142) ^ [_1617783, _1617785, _1617787, _1617789, _1617791, _1617793] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617783, _1617785)), hAPP(hAPP(c_Product__Type_OPair(_1617783, _1617785), _1617787), _1617789)), hAPP(c_List_Oset(tc_prod(_1617783, _1617785)), hAPP(hAPP(c_List_Ozip(_1617783, _1617785), _1617791), _1617793)))), 42134 ^ _779142 : [(42137 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617785), _1617789), hAPP(c_List_Oset(_1617785), _1617793))))], (42135 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617783), _1617787), hAPP(c_List_Oset(_1617783), _1617791))))]]], (40572 ^ _779142) ^ [_1573660, _1573662, _1573664, _1573666] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573660, _1573660)), hAPP(hAPP(c_Product__Type_OPair(_1573660, _1573660), _1573662), _1573664)), c_Transitive__Closure_Ortrancl(_1573660, _1573666))), hBOOL(hAPP(hAPP(c_member(_1573660), _1573664), c_Wellfounded_Oacc(_1573660, _1573666))), -(hBOOL(hAPP(hAPP(c_member(_1573660), _1573662), c_Wellfounded_Oacc(_1573660, _1573666))))], (48432 ^ _779142) ^ [_1755506, _1755508, _1755510] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755506), _1755508))), -(hBOOL(hAPP(hAPP(_1755510, _1755506), _1755508))), 48439 ^ _779142 : [(48442 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48437 ^ [_1755506, _1755508, _1755510]), 48438 ^ [_1755506, _1755508, _1755510]))), -(hBOOL(hAPP(hAPP(_1755510, 48437 ^ [_1755506, _1755508, _1755510]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48438 ^ [_1755506, _1755508, _1755510]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48448 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1755510, 48437 ^ [_1755506, _1755508, _1755510]), 48438 ^ [_1755506, _1755508, _1755510]))], (48440 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 48437 ^ [_1755506, _1755508, _1755510]), 48438 ^ [_1755506, _1755508, _1755510]))))]]], (50905 ^ _779142) ^ [_1809866, _1809868] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809868, _1809866) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809866), _1809868)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809868), _1809866)))], (51605 ^ _779142) ^ [_1821612, _1821614, _1821616] : [class_Rings_Olinordered__idom(_1821612), 51608 ^ _779142 : [(51615 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821612), _1821614), _1821616)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821612), _1821614), hAPP(c_Groups_Oabs__class_Oabs(_1821612), _1821616))))], (51609 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821612), _1821614), hAPP(c_Groups_Oabs__class_Oabs(_1821612), _1821616))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821612), _1821614), _1821616)))]]], (31382 ^ _779142) ^ [_1341878, _1341880, _1341882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1341878, tc_HOL_Obool), tc_HOL_Obool)), _1341880), _1341882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341878, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341878, tc_HOL_Obool), _1341882)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341878, tc_HOL_Obool), _1341880))))], (1506 ^ _779142) ^ [_800909, _800911] : [-(class_Finite__Set_Ofinite(_800909)), _800911 = _800909, class_Finite__Set_Ofinite(_800911)], (23871 ^ _779142) ^ [_1199564, _1199566] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199564, _1199566) = 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), _1199564), _1199566) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199566), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199564, _1199566)))], (13783 ^ _779142) ^ [_1018998, _1019000, _1019002, _1019004] : [class_Fields_Olinordered__field(_1018998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018998), c_Groups_Ozero__class_Ozero(_1018998)), _1019000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018998), _1019002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018998), _1019004), _1019000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018998), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018998), _1019002), _1019000)), _1019004)))], (18585 ^ _779142) ^ [_1106358, _1106360, _1106362] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106358, _1106360)), _1106362) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106358), _1106362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106360), _1106362)))], (50625 ^ _779142) ^ [_1804553, _1804555, _1804557] : [50626 ^ _779142 : [(50629 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1804555), _1804557))], (50627 ^ _779142) ^ [] : [_1804553 = 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), _1804553), _1804555)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804553), _1804557))))], (46957 ^ _779142) ^ [_1723652, _1723654, _1723656] : [-(hAPP(hAPP(c_List_Oappend(_1723652), c_List_OtakeWhile(_1723652, _1723654, _1723656)), c_List_OdropWhile(_1723652, _1723654, _1723656)) = _1723656)], (25692 ^ _779142) ^ [_1230652, _1230654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230652), _1230654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1230652)), c_Int_OBit1(_1230654))))], (16657 ^ _779142) ^ [_1072388] : [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)), _1072388)), _1072388) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (45857 ^ _779142) ^ [_1701962, _1701964] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701962), _1701964) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701962, _1701964)))], (45642 ^ _779142) ^ [_1696134, _1696136, _1696138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696134, tc_HOL_Obool)), hAPP(c_List_Oset(_1696134), hAPP(c_List_Ofilter(_1696134, _1696136), _1696138))), hAPP(c_List_Oset(_1696134), _1696138))))], (2276 ^ _779142) ^ [_812352, _812354, _812356, _812358, _812360, _812362] : [-(c_Nat_Onat_Onat__rec(_812362, _812358, _812354) = c_Nat_Onat_Onat__rec(_812360, _812356, _812352)), _812362 = _812360, _812358 = _812356, _812354 = _812352], (28877 ^ _779142) ^ [_1290898, _1290900, _1290902, _1290904] : [hBOOL(hAPP(hAPP(c_member(_1290898), _1290900), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290898, tc_HOL_Obool)), _1290902), _1290904))), 28880 ^ _779142 : [(28883 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290898), _1290900), _1290904)))], (28881 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290898), _1290900), _1290902)))]]], (16537 ^ _779142) ^ [_1070118, _1070120, _1070122] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070120), _1070122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070118), _1070120)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070118), _1070122)))], (38314 ^ _779142) ^ [_1516739, _1516741, _1516743, _1516745, _1516747, _1516749, _1516751, _1516753, _1516755, _1516757] : [hAPP(c_Set_Oimage(_1516739, _1516741, _1516743), _1516745) = _1516747, hAPP(c_Set_Oimage(_1516749, _1516751, _1516753), _1516755) = _1516757, -(hAPP(c_Set_Oimage(tc_prod(_1516739, _1516749), tc_prod(_1516741, _1516751), c_Product__Type_Omap__pair(_1516739, _1516741, _1516749, _1516751, _1516743, _1516753)), hAPP(hAPP(c_Product__Type_OSigma(_1516739, _1516749), _1516745), hAPP(c_COMBK(tc_fun(_1516749, tc_HOL_Obool), _1516739), _1516755))) = hAPP(hAPP(c_Product__Type_OSigma(_1516741, _1516751), _1516747), hAPP(c_COMBK(tc_fun(_1516751, tc_HOL_Obool), _1516741), _1516757)))], (40687 ^ _779142) ^ [_1576571, _1576573, _1576575, _1576577, _1576579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576573, _1576571)), hAPP(hAPP(c_Product__Type_OPair(_1576573, _1576571), _1576577), _1576575)), _1576579)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576571, _1576573)), hAPP(hAPP(c_Product__Type_OPair(_1576571, _1576573), _1576575), _1576577)), hAPP(c_Relation_Oconverse(_1576573, _1576571), _1576579))))], (16553 ^ _779142) ^ [_1070485] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070485), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1070485)], (22929 ^ _779142) ^ [_1182907, _1182909, _1182911] : [class_Lattices_Oboolean__algebra(_1182907), 22932 ^ _779142 : [(22939 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182907), _1182911), _1182909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182907), hAPP(c_Groups_Ouminus__class_Ouminus(_1182907), _1182909)), hAPP(c_Groups_Ouminus__class_Ouminus(_1182907), _1182911))))], (22933 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182907), hAPP(c_Groups_Ouminus__class_Ouminus(_1182907), _1182909)), hAPP(c_Groups_Ouminus__class_Ouminus(_1182907), _1182911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182907), _1182911), _1182909)))]]], (17945 ^ _779142) ^ [_1095224, _1095226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095224)), 17948 ^ _779142 : [(17951 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1095226, _1095224)), _1095224)))], (17949 ^ _779142) ^ [] : [-(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, _1095226, _1095224))))]]], (35165 ^ _779142) ^ [_1433725, _1433727, _1433729, _1433731, _1433733] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433725, tc_fun(_1433727, tc_HOL_Obool)), _1433729), _1433731), _1433733))), 35166 ^ _779142 : [(35167 ^ _779142) ^ [_1433797] : [hBOOL(hAPP(hAPP(c_member(_1433725), _1433797), _1433729)), hBOOL(hAPP(hAPP(_1433731, _1433797), _1433733))]]], (47946 ^ _779142) ^ [_1745042, _1745044, _1745046, _1745048] : [-(c_List_Olist__ex1(_1745042, _1745044, hAPP(hAPP(c_List_Olist_OCons(_1745042), _1745046), _1745048))), 47949 ^ _779142 : [(47952 ^ _779142) ^ [] : [c_List_Olist__all(_1745042, hAPP(hAPP(c_COMBS(_1745042, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1745042), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1745042), c_fNot), _1745044))), hAPP(c_fequal, _1745046)), _1745048)], (47950 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1745044, _1745046)))]], 47953 ^ _779142 : [(47956 ^ _779142) ^ [] : [c_List_Olist__ex1(_1745042, _1745044, _1745048)], (47954 ^ _779142) ^ [] : [hBOOL(hAPP(_1745044, _1745046))]]], (49298 ^ _779142) ^ [_1775914, _1775916, _1775918] : [c_Relation_Osym(_1775914, _1775916), c_Relation_Osym(_1775914, _1775918), -(c_Relation_Osym(_1775914, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775914, _1775914), tc_HOL_Obool)), _1775916), _1775918)))], (42692 ^ _779142) ^ [_1629989] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629989)), c_List_Olist_ONil(_1629989)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40223 ^ _779142) ^ [_1564628, _1564630] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564628, _1564628)), c_Transitive__Closure_Otrancl(_1564628, _1564630))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564628, _1564628)), _1564630)))], (43566 ^ _779142) ^ [_1650098, _1650100, _1650102, _1650104] : [-(hAPP(hAPP(c_List_Oappend(_1650098), _1650100), _1650102) = _1650104), _1650100 = hAPP(hAPP(c_List_Otake(_1650098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650098)), _1650100)), _1650104), _1650102 = hAPP(hAPP(c_List_Odrop(_1650098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650098)), _1650100)), _1650104)], (29448 ^ _779142) ^ [_1302718, _1302720, _1302722] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302718, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302718, tc_HOL_Obool)), _1302720), _1302722)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302718, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302718, tc_HOL_Obool)), _1302720)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302718, tc_HOL_Obool)), _1302722)))], (2986 ^ _779142) ^ [_823453, _823455, _823457, _823459] : [-(c_List_Olexn(_823459, _823455) = c_List_Olexn(_823457, _823453)), _823459 = _823457, _823455 = _823453], (10845 ^ _779142) ^ [_966425, _966427] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966425), _966427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966427)), _966425)))], (2876 ^ _779142) ^ [_821726, _821728, _821730, _821732] : [-(c_Nitpick_Oinverse__frac(_821732, _821728) = c_Nitpick_Oinverse__frac(_821730, _821726)), _821732 = _821730, _821728 = _821726], (28350 ^ _779142) ^ [_1280097, _1280099, _1280101] : [class_Complete__Lattice_Ocomplete__lattice(_1280097), -(c_Complete__Lattice_OSup__class_OSup(_1280097, hAPP(hAPP(c_Set_Oinsert(_1280097), _1280099), hAPP(hAPP(c_Set_Oinsert(_1280097), _1280101), c_Orderings_Obot__class_Obot(tc_fun(_1280097, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280097), _1280099), _1280101))], (45782 ^ _779142) ^ [_1699188, _1699190] : [45784 ^ _779142 : [(45787 ^ _779142) ^ [] : [45783 ^ [_1699188, _1699190] = c_List_Olist_ONil(_1699188)], (45785 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699188)), 45783 ^ [_1699188, _1699190]), hAPP(c_List_Oset(tc_List_Olist(_1699188)), _1699190))))]], -(c_List_Otranspose(_1699188, _1699190) = c_List_Olist_ONil(tc_List_Olist(_1699188)))], (37677 ^ _779142) ^ [_1493924, _1493926, _1493928, _1493930, _1493932, _1493934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493924, _1493926)), hAPP(hAPP(c_Product__Type_OPair(_1493924, _1493926), _1493928), _1493930)), hAPP(hAPP(c_Product__Type_OSigma(_1493924, _1493926), _1493932), _1493934))), -(hBOOL(hAPP(hAPP(c_member(_1493924), _1493928), _1493932)))], (52267 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51515 ^ _779142) ^ [_1820100, _1820102, _1820104] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820100), _1820102)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820102), _1820100))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820102), _1820104)), 51526 ^ _779142 : [(51529 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820104), _1820100))], (51527 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820100), _1820104)))]]], (46620 ^ _779142) ^ [_1716445, _1716447, _1716449, _1716451] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716445)), _1716447) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716449)), _1716451), -(hAPP(hAPP(c_List_Ozip(_1716445, _1716449), hAPP(c_List_Orev(_1716445), _1716447)), hAPP(c_List_Orev(_1716449), _1716451)) = hAPP(c_List_Orev(tc_prod(_1716445, _1716449)), hAPP(hAPP(c_List_Ozip(_1716445, _1716449), _1716447), _1716451)))], (40287 ^ _779142) ^ [_1566186, _1566188, _1566190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566186, _1566186), tc_HOL_Obool)), _1566188), hAPP(hAPP(c_Product__Type_OSigma(_1566186, _1566186), _1566190), hAPP(c_COMBK(tc_fun(_1566186, tc_HOL_Obool), _1566186), _1566190)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566186, _1566186), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1566186, _1566188)), hAPP(hAPP(c_Product__Type_OSigma(_1566186, _1566186), _1566190), hAPP(c_COMBK(tc_fun(_1566186, tc_HOL_Obool), _1566186), _1566190)))))], (18672 ^ _779142) ^ [_1107786, _1107788, _1107790] : [-(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), _1107786), _1107788)), _1107790)), _1107788) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1107790), _1107788))], (30606 ^ _779142) ^ [_1326989, _1326991, _1326993, _1326995, _1326997] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1326989, _1326991, _1326993), _1326995), _1326997), c_Orderings_Obot__class_Obot(tc_fun(_1326991, tc_HOL_Obool))) = _1326997)], (5736 ^ _779142) ^ [_869912, _869914, _869916, _869918] : [_869912 = _869914, 5741 ^ _779142 : [(5744 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_869916), _869918), _869914)))], (5742 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_869916), _869918), _869912)))]], 5745 ^ _779142 : [(5748 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869916), _869918), _869914))], (5746 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869916), _869918), _869912))]]], (7060 ^ _779142) ^ [_895596, _895598, _895600] : [-(hBOOL(hAPP(hAPP(c_member(_895596), _895598), _895600))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895596, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_895596), _895598), _895600)), hAPP(hAPP(c_Set_Oinsert(_895596), _895598), c_Orderings_Obot__class_Obot(tc_fun(_895596, tc_HOL_Obool)))) = _895600)], (48719 ^ _779142) ^ [_1762352, _1762354, _1762356, _1762358] : [-(c_Random__Sequence_Omap(_1762352, _1762354, _1762356, _1762358) = c_Random__Sequence_Obind(_1762352, _1762354, _1762358, hAPP(c_Fun_Ocomp(_1762354, 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(_1762354)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1762352, c_Random__Sequence_Osingle(_1762354)), _1762356)))], (37864 ^ _779142) ^ [_1499868, _1499870, _1499872, _1499874, _1499876, _1499878] : [class_Groups_Ocomm__monoid__mult(_1499868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499870), _1499872)), 37874 ^ _779142 : [(37877 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499874), hAPP(_1499876, 37873 ^ [_1499868, _1499870, _1499872, _1499874, _1499876, _1499878])))], (37875 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499870), 37873 ^ [_1499868, _1499870, _1499872, _1499874, _1499876, _1499878]), _1499872)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1499868, _1499870, c_Groups_Otimes__class_Otimes(_1499868)), hAPP(hAPP(c_COMBS(_1499870, tc_fun(_1499874, tc_HOL_Obool), _1499868), hAPP(hAPP(c_COMBC(_1499870, _1499868, tc_fun(tc_fun(_1499874, tc_HOL_Obool), _1499868)), hAPP(hAPP(c_COMBB(tc_fun(_1499874, _1499868), tc_fun(_1499868, tc_fun(tc_fun(_1499874, tc_HOL_Obool), _1499868)), _1499870), c_Finite__Set_Ofold__image(_1499868, _1499874, c_Groups_Otimes__class_Otimes(_1499868))), _1499878)), c_Groups_Oone__class_Oone(_1499868))), _1499876)), c_Groups_Oone__class_Oone(_1499868)), _1499872) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1499868, tc_prod(_1499870, _1499874), c_Groups_Otimes__class_Otimes(_1499868)), hAPP(c_Product__Type_Oprod_Oprod__case(_1499870, _1499874, _1499868), _1499878)), c_Groups_Oone__class_Oone(_1499868)), hAPP(hAPP(c_Product__Type_OSigma(_1499870, _1499874), _1499872), _1499876)))], (18384 ^ _779142) ^ [_1102932, _1102934, _1102936] : [hBOOL(hAPP(_1102932, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102934), _1102936)))), 18387 ^ _779142 : [(18394 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102934), _1102936)), -(hBOOL(hAPP(_1102932, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18388 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102936), _1102934)), -(hBOOL(hAPP(_1102932, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102934)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102936)))))]]], (5724 ^ _779142) ^ [_869672, _869674, _869676] : [_869674 = _869676, -(hBOOL(hAPP(hAPP(c_member(_869672), _869674), hAPP(hAPP(c_Set_Oinsert(_869672), _869676), c_Orderings_Obot__class_Obot(tc_fun(_869672, tc_HOL_Obool))))))], (49240 ^ _779142) ^ [_1774519, _1774521, _1774523, _1774525, _1774527, _1774529] : [-(c_Partial__Function_Ofun__lub(_1774519, _1774521, _1774523, _1774525, _1774527, _1774529) = hAPP(_1774525, hAPP(c_Set_OCollect(_1774519), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool), tc_HOL_Obool, _1774519), c_HOL_OEx(tc_fun(_1774523, _1774519))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool), tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool), _1774519), hAPP(c_COMBS(tc_fun(_1774523, _1774519), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774523, _1774519)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774523, _1774519), tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774523, _1774519))), _1774527)))), hAPP(hAPP(c_COMBC(_1774519, tc_fun(tc_fun(_1774523, _1774519), _1774519), tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774519, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774523, _1774519), _1774519), tc_fun(tc_fun(_1774523, _1774519), tc_HOL_Obool)), _1774519), c_COMBB(_1774519, tc_HOL_Obool, tc_fun(_1774523, _1774519))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774523, _1774519), _1774523, _1774519), c_COMBI(tc_fun(_1774523, _1774519))), _1774529)))))))], (40442 ^ _779142) ^ [_1570730] : [-(c_Transitive__Closure_Ortrancl(_1570730, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570730, _1570730), tc_HOL_Obool))) = c_Relation_OId(_1570730))], (32733 ^ _779142) ^ [_1376975, _1376977] : [-(c_Divides_OposDivAlg(_1376975, _1376977) = hAPP(c_Divides_Oadjust(_1376977), c_Divides_OposDivAlg(_1376975, 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)))), _1376977)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376975), _1376977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1376977), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28907 ^ _779142) ^ [_1291530] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1291530) = c_Orderings_Oord__class_Omin(_1291530)), class_Lattices_Osemilattice__inf(_1291530), class_Orderings_Olinorder(_1291530)], (7900 ^ _779142) ^ [_909253, _909255, _909257] : [class_Orderings_Olinorder(_909253), 7903 ^ _779142 : [(7910 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909253), _909257), _909255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909253), _909255), _909257))], (7904 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909253), _909255), _909257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909253), _909257), _909255)))]]], (45927 ^ _779142) ^ [_1703104, _1703106, _1703108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703104), _1703106)), _1703108)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1703106), c_List_Oupt(_1703104, _1703108)) = c_List_Oupt(_1703104, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703104), _1703106)))], (44343 ^ _779142) ^ [_1666450, _1666452, _1666454, _1666456] : [hAPP(hAPP(c_List_Omap(_1666450, _1666452), _1666454), _1666456) = c_List_Olist_ONil(_1666452), -(_1666456 = c_List_Olist_ONil(_1666450))], (33463 ^ _779142) ^ [_1391218, _1391220] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1391218, _1391220), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1391218), _1391220)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1391218, _1391220)))))], (20400 ^ _779142) ^ [_1137146, _1137148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137148)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1137146), hAPP(c_Int_Onat, _1137148)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1137146, _1137148)))], (52599 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (29415 ^ _779142) ^ [_1301806, _1301808, _1301810, _1301812] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301806, tc_HOL_Obool)), _1301808), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301806, tc_HOL_Obool)), _1301810), _1301812)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301806, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301806, tc_HOL_Obool)), _1301808), _1301810)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301806, tc_HOL_Obool)), _1301808), _1301812)))], (48304 ^ _779142) ^ [_1753025, _1753027, _1753029] : [_1753027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1753025) = c_List_Oreplicate(_1753025, _1753027, _1753029))], (24421 ^ _779142) ^ [_1208897] : [-(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)), _1208897))))], (16529 ^ _779142) ^ [_1069938, _1069940, _1069942] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1069938), _1069940)), _1069942) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069938), _1069942)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069940), _1069942)))], (14255 ^ _779142) ^ [_1027376, _1027378, _1027380] : [class_Fields_Olinordered__field(_1027376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027376), _1027378), c_Groups_Ozero__class_Ozero(_1027376))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027376), _1027380), c_Groups_Ozero__class_Ozero(_1027376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027376), c_Groups_Ozero__class_Ozero(_1027376)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027376), _1027378), _1027380))))], (25484 ^ _779142) ^ [_1227033, _1227035] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1227033)), _1227035) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227033), _1227035)))], (6261 ^ _779142) ^ [_879457, _879459, _879461, _879463, _879465] : [class_Orderings_Oord(_879457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879459, _879457)), _879461), _879463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879457), hAPP(_879461, _879465)), hAPP(_879463, _879465))))], (9545 ^ _779142) ^ [_941623, _941625, _941627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941625), _941627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941623), _941625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941623), _941627))))], (47211 ^ _779142) ^ [_1728860, _1728862] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1728860)), _1728862)), 47217 ^ _779142 : [(47220 ^ _779142) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1728860), 47216 ^ [_1728860, _1728862]))], (47218 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728860)), 47216 ^ [_1728860, _1728862]), hAPP(c_List_Oset(tc_List_Olist(_1728860)), _1728862))))]], 47224 ^ _779142 : [(47228 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728860)), 47226 ^ [_1728860, _1728862]), hAPP(c_List_Oset(tc_List_Olist(_1728860)), _1728862))))], (47230 ^ _779142) ^ [] : [47223 ^ [_1728860, _1728862] = 47226 ^ [_1728860, _1728862]], (47232 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728860, tc_HOL_Obool)), hAPP(c_List_Oset(_1728860), 47223 ^ [_1728860, _1728862])), hAPP(c_List_Oset(_1728860), 47226 ^ [_1728860, _1728862])) = c_Orderings_Obot__class_Obot(tc_fun(_1728860, tc_HOL_Obool))], (47225 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728860)), 47223 ^ [_1728860, _1728862]), hAPP(c_List_Oset(tc_List_Olist(_1728860)), _1728862))))]], -(hBOOL(hAPP(c_List_Odistinct(_1728860), c_List_Oconcat(_1728860, _1728862))))], (44187 ^ _779142) ^ [_1663083, _1663085, _1663087] : [-(_1663083 = c_List_Olist_ONil(_1663085)), -(c_List_Olast(_1663085, hAPP(hAPP(c_List_Olist_OCons(_1663085), _1663087), _1663083)) = c_List_Olast(_1663085, _1663083))], (40757 ^ _779142) ^ [_1578242, _1578244, _1578246] : [c_Relation_Orefl__on(_1578242, _1578244, hAPP(c_Relation_Oconverse(_1578242, _1578242), _1578246)), -(c_Relation_Orefl__on(_1578242, _1578244, _1578246))], (51087 ^ _779142) ^ [_1813058, _1813060, _1813062] : [class_Divides_Oring__div(_1813058), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813058), _1813060), _1813062)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813058), _1813062), hAPP(c_Groups_Ouminus__class_Ouminus(_1813058), _1813060)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1813058), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813058), _1813062), _1813060)))], (10867 ^ _779142) ^ [_966709, _966711] : [10868 ^ _779142 : [(10871 ^ _779142) ^ [] : [_966709 = hAPP(c_Nat_OSuc, _966711)], (10869 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966709), _966711))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966709), hAPP(c_Nat_OSuc, _966711))))], (27330 ^ _779142) ^ [_1261293, _1261295, _1261297] : [hBOOL(hAPP(hAPP(c_member(_1261293), _1261295), hAPP(c_fequal, _1261297))), -(_1261295 = _1261297)], (30866 ^ _779142) ^ [] : [-(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))], (47987 ^ _779142) ^ [_1745895, _1745897, _1745899] : [-(c_List_Olist__ex1(_1745895, _1745897, _1745899)), 47988 ^ _779142 : [(47989 ^ _779142) ^ [_1745989] : [hBOOL(hAPP(hAPP(c_member(_1745895), _1745989), hAPP(c_List_Oset(_1745895), _1745899))), hBOOL(hAPP(_1745897, _1745989)), 47997 ^ _779142 : [(48002 ^ _779142) ^ [] : [47996 ^ [_1745895, _1745897, _1745899, _1745989] = _1745989], (48000 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1745897, 47996 ^ [_1745895, _1745897, _1745899, _1745989])))], (47998 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745895), 47996 ^ [_1745895, _1745897, _1745899, _1745989]), hAPP(c_List_Oset(_1745895), _1745899))))]]]]], (27362 ^ _779142) ^ [_1261819, _1261821, _1261823, _1261825] : [hBOOL(hAPP(_1261819, _1261821)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261823, tc_HOL_Obool)), _1261825), _1261819), _1261821)))], (41403 ^ _779142) ^ [_1595725, _1595727, _1595729] : [-(c_List_Oset__Cons(_1595725, _1595727, _1595729) = hAPP(c_Set_OCollect(tc_List_Olist(_1595725)), hAPP(hAPP(c_COMBB(tc_fun(_1595725, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1595725)), c_HOL_OEx(_1595725)), hAPP(hAPP(c_COMBB(tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_fun(_1595725, tc_HOL_Obool), tc_List_Olist(_1595725)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_HOL_Obool, _1595725), c_HOL_OEx(tc_List_Olist(_1595725)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595725), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595725, tc_fun(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), tc_fun(tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), tc_List_Olist(_1595725)), c_COMBS(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1595725, tc_fun(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), tc_List_Olist(_1595725)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595725), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), _1595725), c_COMBS(tc_List_Olist(_1595725), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1595725)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1595725), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1595725)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595725), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_List_Olist(_1595725))), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1595725), tc_List_Olist(_1595725)), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_fun(tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_List_Olist(_1595725))), tc_fun(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool))), tc_List_Olist(_1595725)), c_COMBB(tc_fun(tc_List_Olist(_1595725), tc_List_Olist(_1595725)), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), _1595725)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595725), tc_List_Olist(_1595725)), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), tc_List_Olist(_1595725)), c_COMBB(tc_List_Olist(_1595725), tc_HOL_Obool, tc_List_Olist(_1595725))), c_fequal))), c_List_Olist_OCons(_1595725)))))), hAPP(hAPP(c_COMBC(_1595725, tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool)), _1595725), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1595725))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595725), c_fconj), hAPP(hAPP(c_COMBC(_1595725, tc_fun(_1595725, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595725)), _1595727)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595725), tc_fun(tc_List_Olist(_1595725), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1595725))), _1595729)))))))], (50551 ^ _779142) ^ [_1803272, _1803274, _1803276, _1803278, _1803280] : [-(c_New__DSequence_Opos__map(_1803272, _1803274, _1803276, _1803278, _1803280) = c_Lazy__Sequence_Omap(_1803272, _1803274, _1803276, hAPP(_1803278, _1803280)))], (26540 ^ _779142) ^ [_1245984, _1245986, _1245988, _1245990] : [class_Lattices_Olattice(_1245984), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245984), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245984), _1245986), _1245988)), _1245990) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245984), _1245986), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245984), _1245988), _1245990)))], (15519 ^ _779142) ^ [_1050914, _1050916, _1050918] : [class_Int_Onumber__ring(_1050914), class_Rings_Olinordered__idom(_1050914), 15526 ^ _779142 : [(15533 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050916), _1050918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050914), hAPP(c_Int_Onumber__class_Onumber__of(_1050914), _1050916)), hAPP(c_Int_Onumber__class_Onumber__of(_1050914), _1050918))))], (15527 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050914), hAPP(c_Int_Onumber__class_Onumber__of(_1050914), _1050916)), hAPP(c_Int_Onumber__class_Onumber__of(_1050914), _1050918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050916), _1050918)))]]], (24267 ^ _779142) ^ [_1206205, _1206207, _1206209] : [class_Rings_Olinordered__idom(_1206205), 24270 ^ _779142 : [(24277 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206207), _1206209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206205), hAPP(c_Int_Oring__1__class_Oof__int(_1206205), _1206207)), hAPP(c_Int_Oring__1__class_Oof__int(_1206205), _1206209))))], (24271 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206205), hAPP(c_Int_Oring__1__class_Oof__int(_1206205), _1206207)), hAPP(c_Int_Oring__1__class_Oof__int(_1206205), _1206209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1206207), _1206209)))]]], (52375 ^ _779142) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (46001 ^ _779142) ^ [_1704496, _1704498] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1704496, _1704498) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704496), hAPP(c_Nat_OSuc, _1704498))))], (45991 ^ _779142) ^ [_1704295, _1704297] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1704295, _1704297) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704295, hAPP(c_Nat_OSuc, _1704297))))], (17277 ^ _779142) ^ [_1083142, _1083144, _1083146, _1083148] : [class_Orderings_Olinorder(_1083142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083142), _1083144)), 17287 ^ _779142 : [(17290 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083142), _1083146), 17286 ^ [_1083142, _1083144, _1083146, _1083148]))], (17288 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083142), 17286 ^ [_1083142, _1083144, _1083146, _1083148]), _1083144)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083142), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1083142), _1083146), _1083148)), hAPP(hAPP(c_Finite__Set_Ofold(_1083142, _1083142, c_Orderings_Oord__class_Omin(_1083142)), _1083148), _1083144))))], (23107 ^ _779142) ^ [_1185920, _1185922, _1185924] : [class_Rings_Oring(_1185920), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1185920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185920), _1185922), _1185924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185920), _1185922), hAPP(c_Groups_Ouminus__class_Ouminus(_1185920), _1185924)))], (11055 ^ _779142) ^ [_969705, _969707] : [class_Rings_Ocomm__semiring__1(_969705), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969705), c_Groups_Ozero__class_Ozero(_969705)), _969707) = c_Groups_Ozero__class_Ozero(_969705))], (31859 ^ _779142) ^ [_1352725, _1352727, _1352729, _1352731] : [class_Fields_Olinordered__field(_1352725), -(hAPP(c_Groups_Oabs__class_Oabs(_1352725), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352727, _1352725), _1352729), _1352731)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352727, _1352725), hAPP(hAPP(c_COMBB(_1352725, _1352725, _1352727), c_Groups_Oabs__class_Oabs(_1352725)), _1352729)), _1352731))], (7028 ^ _779142) ^ [_894703, _894705, _894707, _894709] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894703, tc_HOL_Obool)), _894705), hAPP(hAPP(c_Set_Oinsert(_894703), _894707), _894709)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894703, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894703, tc_HOL_Obool)), _894705), hAPP(hAPP(c_Set_Oinsert(_894703), _894707), c_Orderings_Obot__class_Obot(tc_fun(_894703, tc_HOL_Obool))))), _894709))], (31781 ^ _779142) ^ [_1351079, _1351081, _1351083, _1351085, _1351087] : [class_Lattices_Olattice(_1351079), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351081, _1351079)), _1351083), _1351085), _1351087) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1351079), hAPP(_1351083, _1351087)), hAPP(_1351085, _1351087)))], (20299 ^ _779142) ^ [_1135377, _1135379] : [hBOOL(hAPP(_1135377, hAPP(c_Int_Onat, _1135379))), 20302 ^ _779142 : [(20309 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135379), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1135377, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20303 ^ _779142) ^ [_1135477] : [_1135379 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1135477), -(hBOOL(hAPP(_1135377, _1135477)))]]], (24339 ^ _779142) ^ [_1207519, _1207521] : [class_Rings_Oring__1(_1207519), -(hAPP(c_Int_Oring__1__class_Oof__int(_1207519), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207521)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1207519), _1207521))], (25982 ^ _779142) ^ [_1235695, _1235697] : [class_Rings_Olinordered__idom(_1235695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235695), hAPP(hAPP(c_Power_Opower__class_Opower(_1235695), _1235697), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1235695)))], (23283 ^ _779142) ^ [_1189376, _1189378] : [class_Groups_Oordered__ab__group__add(_1189376), 23286 ^ _779142 : [(23293 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189376), c_Groups_Ozero__class_Ozero(_1189376)), _1189378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189376), hAPP(c_Groups_Ouminus__class_Ouminus(_1189376), _1189378)), c_Groups_Ozero__class_Ozero(_1189376))))], (23287 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189376), hAPP(c_Groups_Ouminus__class_Ouminus(_1189376), _1189378)), c_Groups_Ozero__class_Ozero(_1189376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189376), c_Groups_Ozero__class_Ozero(_1189376)), _1189378)))]]], (29514 ^ _779142) ^ [_1304165, _1304167, _1304169, _1304171, _1304173] : [class_Orderings_Olinorder(_1304165), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304165, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1304165, _1304167, _1304169)), c_SetInterval_Oord__class_OatLeastAtMost(_1304165, _1304171, _1304173)) = c_SetInterval_Oord__class_OatLeastAtMost(_1304165, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1304165), _1304167), _1304171), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1304165), _1304169), _1304173)))], (27098 ^ _779142) ^ [_1257316, _1257318, _1257320] : [class_Orderings_Olinorder(_1257316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257316), _1257318)), -(_1257318 = c_Orderings_Obot__class_Obot(tc_fun(_1257316, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257316), _1257320)), -(_1257320 = c_Orderings_Obot__class_Obot(tc_fun(_1257316, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1257316, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257316, tc_HOL_Obool)), _1257318), _1257320)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1257316), c_Big__Operators_Olinorder__class_OMin(_1257316, _1257318)), c_Big__Operators_Olinorder__class_OMin(_1257316, _1257320)))], (47246 ^ _779142) ^ [_1729850, _1729852] : [-(c_Wellfounded_Owf(_1729850, c_List_Omeasures(_1729850, _1729852)))], (28324 ^ _779142) ^ [_1279654, _1279656, _1279658] : [class_Orderings_Olinorder(_1279654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279654), _1279656)), -(hBOOL(hAPP(hAPP(c_member(_1279654), _1279658), _1279656))), -(c_Big__Operators_Olinorder__class_OMax(_1279654, hAPP(hAPP(c_Set_Oinsert(_1279654), _1279658), _1279656)) = hAPP(hAPP(c_Finite__Set_Ofold(_1279654, _1279654, c_Orderings_Oord__class_Omax(_1279654)), _1279658), _1279656))], (31763 ^ _779142) ^ [_1349991, _1349993, _1349995, _1349997, _1349999, _1350001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1349991, _1349993)), hAPP(hAPP(c_Product__Type_OPair(_1349991, _1349993), _1349999), _1350001)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool)), _1349995), _1349997))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349991, tc_fun(_1349993, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1349991, tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_fun(_1349993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349993, tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_fun(_1349993, tc_HOL_Obool)), _1349991), c_COMBC(_1349993, tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349993, tc_prod(_1349991, _1349993)), tc_fun(_1349993, tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), _1349991), hAPP(c_COMBB(tc_prod(_1349991, _1349993), tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool), _1349993), c_member(tc_prod(_1349991, _1349993)))), c_Product__Type_OPair(_1349991, _1349993)))), _1349995)), hAPP(hAPP(c_COMBC(_1349991, tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_fun(_1349993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349993, tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_fun(_1349993, tc_HOL_Obool)), _1349991), c_COMBC(_1349993, tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349993, tc_prod(_1349991, _1349993)), tc_fun(_1349993, tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool)), _1349991), hAPP(c_COMBB(tc_prod(_1349991, _1349993), tc_fun(tc_fun(tc_prod(_1349991, _1349993), tc_HOL_Obool), tc_HOL_Obool), _1349993), c_member(tc_prod(_1349991, _1349993)))), c_Product__Type_OPair(_1349991, _1349993)))), _1349997)), _1349999), _1350001)))], (45358 ^ _779142) ^ [_1689509, _1689511, _1689513] : [hBOOL(hAPP(c_List_Odistinct(_1689509), _1689511)), -(hBOOL(hAPP(c_List_Odistinct(_1689509), hAPP(c_List_OremoveAll(_1689509, _1689513), _1689511))))], (44069 ^ _779142) ^ [_1661078, _1661080, _1661082, _1661084, _1661086] : [class_Orderings_Olinorder(_1661078), 44072 ^ _779142 : [(44081 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661080), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661080, _1661078, _1661082), _1661084), _1661086)))), -(hBOOL(hAPP(hAPP(c_member(_1661080), _1661084), hAPP(c_List_Oset(_1661080), _1661086)))), hBOOL(hAPP(c_List_Odistinct(_1661080), _1661086))], (44073 ^ _779142) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1661080), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661080, _1661078, _1661082), _1661084), _1661086))), 44076 ^ _779142 : [(44079 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661080), _1661086)))], (44077 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1661080), _1661084), hAPP(c_List_Oset(_1661080), _1661086)))]]]]], (41268 ^ _779142) ^ [_1591855, _1591857, _1591859] : [-(c_Nitpick_Oof__frac(_1591857, _1591855, _1591859) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1591855), hAPP(c_Int_Oring__1__class_Oof__int(_1591855), hAPP(c_Nitpick_Onum(_1591857), _1591859))), hAPP(c_Int_Oring__1__class_Oof__int(_1591855), hAPP(c_Nitpick_Odenom(_1591857), _1591859)))), class_Rings_Oinverse(_1591855), class_Rings_Oring__1(_1591855)], (46122 ^ _779142) ^ [_1706894, _1706896] : [class_Orderings_Olinorder(_1706894), c_List_Olinorder__class_Osorted(_1706894, _1706896), -(c_List_Olinorder__class_Osorted(_1706894, hAPP(c_List_Otl(_1706894), _1706896)))], (24783 ^ _779142) ^ [_1214875, _1214877] : [24785 ^ _779142 : [(24788 ^ _779142) ^ [] : [hBOOL(hAPP(_1214877, 24784 ^ [_1214875, _1214877]))], (24786 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24784 ^ [_1214875, _1214877]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214875))))]], 24789 ^ _779142 : [(24790 ^ _779142) ^ [_1215028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1215028), _1214875)), -(hBOOL(hAPP(_1214877, _1215028)))]]], (3254 ^ _779142) ^ [_827605, _827607, _827609, _827611] : [-(c_List_Olistsp(_827611, _827607) = c_List_Olistsp(_827609, _827605)), _827611 = _827609, _827607 = _827605], (50687 ^ _779142) ^ [_1805611, _1805613, _1805615, _1805617] : [class_Rings_Ocomm__semiring__1(_1805611), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805611), _1805613), _1805615)), _1805617)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805611), _1805613), _1805617)))], (46005 ^ _779142) ^ [_1704575] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1704575) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1704575))))], (19227 ^ _779142) ^ [_1117208, _1117210, _1117212] : [class_Groups_Oordered__ab__group__add__abs(_1117208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117208), hAPP(c_Groups_Oabs__class_Oabs(_1117208), _1117210)), _1117212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117208), _1117210), _1117212)))], (24539 ^ _779142) ^ [_1210812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210812), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1210812 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 24542 ^ [_1210812]))))], (26868 ^ _779142) ^ [_1252729, _1252731, _1252733, _1252735, _1252737] : [-(hAPP(c_Set_Oimage(_1252729, _1252731, _1252733), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252729, tc_HOL_Obool)), _1252735), _1252737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252731, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1252729, _1252731, _1252733), _1252735)), hAPP(c_Set_Oimage(_1252729, _1252731, _1252733), _1252737)))], (33692 ^ _779142) ^ [_1395714, _1395716, _1395718, _1395720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1395720, _1395716)), hAPP(_1395720, _1395718))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395714, _1395714)), hAPP(hAPP(c_Product__Type_OPair(_1395714, _1395714), _1395716), _1395718)), hAPP(c_Wellfounded_Omeasure(_1395714), _1395720))))], (8156 ^ _779142) ^ [_914468, _914470, _914472, _914474, _914476] : [class_Groups_Oab__semigroup__mult(_914468), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914468, _914468, c_Groups_Otimes__class_Otimes(_914468), _914470, _914472), _914474)), hBOOL(hAPP(hAPP(c_member(_914468), _914476), _914472)), -(hBOOL(hAPP(hAPP(c_member(_914468), _914470), _914472))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914468, _914468, c_Groups_Otimes__class_Otimes(_914468), _914476, hAPP(hAPP(c_Set_Oinsert(_914468), _914470), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914468, tc_HOL_Obool)), _914472), hAPP(hAPP(c_Set_Oinsert(_914468), _914476), c_Orderings_Obot__class_Obot(tc_fun(_914468, tc_HOL_Obool)))))), _914474)))], (11392 ^ _779142) ^ [_974979, _974981] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974979)), _974981) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974979), _974981)))], (29377 ^ _779142) ^ [_1300750, _1300752, _1300754, _1300756] : [hBOOL(hAPP(hAPP(c_member(_1300750), _1300752), _1300754)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300750, tc_HOL_Obool)), _1300754), hAPP(hAPP(c_Set_Oinsert(_1300750), _1300752), _1300756)) = hAPP(hAPP(c_Set_Oinsert(_1300750), _1300752), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300750, tc_HOL_Obool)), _1300754), _1300756)))], (9691 ^ _779142) ^ [_943947, _943949] : [9692 ^ _779142 : [(9695 ^ _779142) ^ [] : [_943947 = _943949], (9693 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943947), _943949))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943947), _943949)))], (31390 ^ _779142) ^ [_1342069, _1342071, _1342073] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342069, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1342069, tc_HOL_Obool)), _1342071), _1342073)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342069, tc_HOL_Obool)), _1342071), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342069, tc_HOL_Obool), _1342073)))], (8074 ^ _779142) ^ [_912334, _912336, _912338, _912340, _912342, _912344, _912346] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912334, _912336, _912338, _912340, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912334, tc_HOL_Obool)), _912342), hAPP(hAPP(c_Set_Oinsert(_912334), _912344), c_Orderings_Obot__class_Obot(tc_fun(_912334, tc_HOL_Obool))))), _912346)), hBOOL(hAPP(hAPP(c_member(_912334), _912344), _912342)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912334, _912336, _912338, _912340, _912342), hAPP(hAPP(_912338, _912344), _912346))))], (34021 ^ _779142) ^ [_1402408, _1402410, _1402412, _1402414, _1402416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1402408, _1402410)), hAPP(_1402408, _1402412))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1402414, _1402414)), hAPP(hAPP(c_Product__Type_OPair(_1402414, _1402414), _1402410), _1402412)), _1402416)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402414, _1402414)), hAPP(hAPP(c_Product__Type_OPair(_1402414, _1402414), _1402410), _1402412)), c_Wellfounded_Omlex__prod(_1402414, _1402408, _1402416))))], (44313 ^ _779142) ^ [_1665233, _1665235, _1665237, _1665239] : [-(hAPP(hAPP(c_List_Omap(_1665233, _1665235), _1665237), hAPP(c_List_Otl(_1665233), _1665239)) = hAPP(c_List_Otl(_1665235), hAPP(hAPP(c_List_Omap(_1665233, _1665235), _1665237), _1665239)))], (31823 ^ _779142) ^ [_1351973, _1351975, _1351977, _1351979] : [class_Rings_Oring__1(_1351973), -(hAPP(c_Int_Oring__1__class_Oof__int(_1351973), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351975, tc_Int_Oint), _1351977), _1351979)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351975, _1351973), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1351973, _1351975), c_Int_Oring__1__class_Oof__int(_1351973)), _1351977)), _1351979))], (2434 ^ _779142) ^ [_814865, _814867] : [_814867 = _814865, -(c_SetInterval_Oord__class_OatLeast(_814867) = c_SetInterval_Oord__class_OatLeast(_814865))], (36566 ^ _779142) ^ [_1467105, _1467107, _1467109, _1467111, _1467113] : [c_Fun_Oinj__on(_1467105, _1467107, _1467109, c_Orderings_Otop__class_Otop(tc_fun(_1467105, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1467105, _1467107, _1467109), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467105, tc_HOL_Obool)), _1467111), _1467113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467107, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467105, _1467107, _1467109), _1467111)), hAPP(c_Set_Oimage(_1467105, _1467107, _1467109), _1467113)))], (40370 ^ _779142) ^ [_1568978, _1568980] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568978, _1568978), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568978, _1568980)), c_Relation_OId(_1568978)) = c_Transitive__Closure_Ortrancl(_1568978, _1568980))], (43744 ^ _779142) ^ [_1654087, _1654089, _1654091] : [-(hAPP(hAPP(c_List_Odrop(_1654087), _1654089), hAPP(c_List_Otl(_1654087), _1654091)) = hAPP(c_List_Otl(_1654087), hAPP(hAPP(c_List_Odrop(_1654087), _1654089), _1654091)))], (43824 ^ _779142) ^ [_1655710, _1655712, _1655714] : [-(hAPP(c_List_Otl(_1655710), hAPP(hAPP(c_List_Otake(_1655710), _1655712), _1655714)) = hAPP(hAPP(c_List_Otake(_1655710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655712), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1655710), _1655714)))], (18842 ^ _779142) ^ [_1110980] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110980))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110980)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29502 ^ _779142) ^ [_1303885, _1303887, _1303889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303885, tc_HOL_Obool)), _1303887), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1303885, tc_HOL_Obool)), _1303889))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1303885, tc_HOL_Obool)), _1303887), _1303889) = c_Orderings_Obot__class_Obot(tc_fun(_1303885, tc_HOL_Obool)))], (46853 ^ _779142) ^ [_1721447, _1721449, _1721451, _1721453, _1721455] : [-(c_List_OtakeWhile(_1721447, _1721449, hAPP(hAPP(c_List_Omap(_1721451, _1721447), _1721453), _1721455)) = hAPP(hAPP(c_List_Omap(_1721451, _1721447), _1721453), c_List_OtakeWhile(_1721451, hAPP(c_Fun_Ocomp(_1721447, tc_HOL_Obool, _1721451, _1721449), _1721453), _1721455)))], (21686 ^ _779142) ^ [_1160128, _1160130] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1160128), _1160130) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1160130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1160128 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51455 ^ _779142) ^ [_1819136, _1819138] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819136), _1819138))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819136), _1819138)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819138), _1819136)))], (18949 ^ _779142) ^ [_1112375] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112375, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35612 ^ _779142) ^ [_1445945, _1445947, _1445949] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445945), _1445947), _1445949) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1445945, tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool)), _1445947), hAPP(hAPP(c_COMBC(_1445945, tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445945, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool)), _1445945), c_Set_Oinsert(tc_fun(_1445945, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1445945, tc_HOL_Obool), tc_fun(_1445945, tc_HOL_Obool), _1445945), c_Relation_OImage(_1445945, _1445945, _1445949)), hAPP(hAPP(c_COMBC(_1445945, tc_fun(_1445945, tc_HOL_Obool), tc_fun(_1445945, tc_HOL_Obool)), c_Set_Oinsert(_1445945)), c_Orderings_Obot__class_Obot(tc_fun(_1445945, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445945, tc_HOL_Obool), tc_HOL_Obool)))))], (44696 ^ _779142) ^ [_1674471, _1674473] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1674471)), hAPP(c_Code__Numeral_Oof__nat, _1674473)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1674471), _1674473)))], (25010 ^ _779142) ^ [_1218922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218922), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1218922)), c_Int_OPls)))], (4418 ^ _779142) ^ [_846199, _846201] : [_846201 = _846199, -(c_List_Olist_ONil(_846201) = c_List_Olist_ONil(_846199))], (7274 ^ _779142) ^ [_900056, _900058, _900060, _900062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_900056, tc_HOL_Obool)), _900058), _900060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_900056, tc_HOL_Obool)), _900060), _900062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_900056, tc_HOL_Obool)), _900058), _900062)))], (15427 ^ _779142) ^ [_1049371, _1049373, _1049375] : [class_Orderings_Olinorder(_1049371), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049371), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049371), _1049373), _1049375)), _1049373)))], (42303 ^ _779142) ^ [_1621739, _1621741, _1621743, _1621745, _1621747] : [-(hAPP(hAPP(c_List_Olist__update(_1621739, hAPP(hAPP(c_List_Olist_OCons(_1621739), _1621741), _1621743)), hAPP(c_Nat_OSuc, _1621745)), _1621747) = hAPP(hAPP(c_List_Olist_OCons(_1621739), _1621741), hAPP(hAPP(c_List_Olist__update(_1621739, _1621743), _1621745), _1621747)))], (14823 ^ _779142) ^ [_1038034, _1038036, _1038038, _1038040, _1038042] : [class_Groups_Ocomm__monoid__add(_1038034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038036), _1038038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038036, tc_HOL_Obool)), _1038040), _1038038)), 14837 ^ _779142 : [(14840 ^ _779142) ^ [] : [hAPP(_1038042, 14836 ^ [_1038034, _1038036, _1038038, _1038040, _1038042]) = c_Groups_Ozero__class_Ozero(_1038034)], (14838 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038036), 14836 ^ [_1038034, _1038036, _1038038, _1038040, _1038042]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038036, tc_HOL_Obool)), _1038038), _1038040))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038036, _1038034), _1038042), _1038040) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038036, _1038034), _1038042), _1038038))], (27846 ^ _779142) ^ [_1270873, _1270875, _1270877, _1270879] : [class_Orderings_Olinorder(_1270873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270873), _1270875), _1270877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270873), _1270875), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270873), _1270879), _1270877))))], (10 ^ _779142) ^ [_779265, _779267, _779269] : [-(_779269 = _779265), _779269 = _779267, _779267 = _779265], (15010 ^ _779142) ^ [_1041636, _1041638, _1041640] : [class_Orderings_Olinorder(_1041636), -(_1041638 = c_Orderings_Obot__class_Obot(tc_fun(_1041636, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1041636, tc_HOL_Obool)), _1041638), _1041640)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041636), _1041640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041636), hAPP(c_Finite__Set_Ofold1(_1041636, c_Orderings_Oord__class_Omin(_1041636)), _1041640)), hAPP(c_Finite__Set_Ofold1(_1041636, c_Orderings_Oord__class_Omin(_1041636)), _1041638))))], (27690 ^ _779142) ^ [_1267911, _1267913, _1267915] : [class_Orderings_Olinorder(_1267911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267911), _1267913)), hBOOL(hAPP(hAPP(c_member(_1267911), _1267915), _1267913)), 27701 ^ _779142 : [(27708 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267911, tc_HOL_Obool)), _1267913), hAPP(hAPP(c_Set_Oinsert(_1267911), _1267915), c_Orderings_Obot__class_Obot(tc_fun(_1267911, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1267911, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1267911, _1267913) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1267911), _1267915), c_Big__Operators_Olinorder__class_OMax(_1267911, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267911, tc_HOL_Obool)), _1267913), hAPP(hAPP(c_Set_Oinsert(_1267911), _1267915), c_Orderings_Obot__class_Obot(tc_fun(_1267911, tc_HOL_Obool)))))))], (27702 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267911, tc_HOL_Obool)), _1267913), hAPP(hAPP(c_Set_Oinsert(_1267911), _1267915), c_Orderings_Obot__class_Obot(tc_fun(_1267911, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1267911, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1267911, _1267913) = _1267915)]]], (25966 ^ _779142) ^ [_1235471, _1235473] : [class_Rings_Olinordered__idom(_1235471), 25969 ^ _779142 : [(25976 ^ _779142) ^ [] : [-(_1235473 = c_Groups_Ozero__class_Ozero(_1235471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235471), c_Groups_Ozero__class_Ozero(_1235471)), hAPP(hAPP(c_Power_Opower__class_Opower(_1235471), _1235473), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25970 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235471), c_Groups_Ozero__class_Ozero(_1235471)), hAPP(hAPP(c_Power_Opower__class_Opower(_1235471), _1235473), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1235473 = c_Groups_Ozero__class_Ozero(_1235471)]]], (52607 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (41647 ^ _779142) ^ [_1603594, _1603596, _1603598, _1603600] : [c_List_Olistrelp(_1603594, hAPP(hAPP(c_COMBC(_1603594, tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_fun(_1603594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603594, tc_fun(tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_fun(_1603594, tc_HOL_Obool)), _1603594), c_COMBC(_1603594, tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603594, tc_prod(_1603594, _1603594)), tc_fun(_1603594, tc_fun(tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_HOL_Obool)), _1603594), hAPP(c_COMBB(tc_prod(_1603594, _1603594), tc_fun(tc_fun(tc_prod(_1603594, _1603594), tc_HOL_Obool), tc_HOL_Obool), _1603594), c_member(tc_prod(_1603594, _1603594)))), c_Product__Type_OPair(_1603594, _1603594)))), _1603596), _1603598, _1603600), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603594), tc_List_Olist(_1603594))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603594), tc_List_Olist(_1603594)), _1603598), _1603600)), c_List_Olistrel(_1603594, _1603596))))], (23803 ^ _779142) ^ [_1198432, _1198434, _1198436] : [class_Orderings_Olinorder(_1198432), 23806 ^ _779142 : [(23813 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198432), _1198434), _1198436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198432, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1198432), _1198434)), hAPP(c_SetInterval_Oord__class_OlessThan(_1198432), _1198436))))], (23807 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198432, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1198432), _1198434)), hAPP(c_SetInterval_Oord__class_OlessThan(_1198432), _1198436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198432), _1198434), _1198436)))]]], (6964 ^ _779142) ^ [_893310, _893312] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893310, tc_HOL_Obool)), _893312), _893312) = c_Orderings_Obot__class_Obot(tc_fun(_893310, tc_HOL_Obool)))], (13209 ^ _779142) ^ [_1008113, _1008115, _1008117] : [class_Rings_Olinordered__ring__strict(_1008113), 13212 ^ _779142 : [(13213 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008113), c_Groups_Ozero__class_Ozero(_1008113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008113), _1008115), _1008115)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008113), _1008117), _1008117)))), _1008115 = c_Groups_Ozero__class_Ozero(_1008113), _1008117 = c_Groups_Ozero__class_Ozero(_1008113)], (13223 ^ _779142) ^ [] : [13224 ^ _779142 : [(13227 ^ _779142) ^ [] : [-(_1008117 = c_Groups_Ozero__class_Ozero(_1008113))], (13225 ^ _779142) ^ [] : [-(_1008115 = c_Groups_Ozero__class_Ozero(_1008113))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008113), c_Groups_Ozero__class_Ozero(_1008113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008113), _1008115), _1008115)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008113), _1008117), _1008117)))))]]], (5596 ^ _779142) ^ [_864678, _864680] : [_864680 = _864678, -(c_member(_864680) = c_member(_864678))], (44444 ^ _779142) ^ [_1669020, _1669022, _1669024, _1669026] : [-(hAPP(hAPP(c_List_Omap(_1669020, _1669022), _1669024), c_List_Obutlast(_1669020, _1669026)) = c_List_Obutlast(_1669022, hAPP(hAPP(c_List_Omap(_1669020, _1669022), _1669024), _1669026)))], (45113 ^ _779142) ^ [_1684088, _1684090, _1684092, _1684094, _1684096, _1684098, _1684100] : [-(c_List_Olist__all2(_1684088, _1684090, _1684092, hAPP(hAPP(c_List_Olist_OCons(_1684088), _1684094), _1684096), hAPP(hAPP(c_List_Olist_OCons(_1684090), _1684098), _1684100))), hBOOL(hAPP(hAPP(_1684092, _1684094), _1684098)), c_List_Olist__all2(_1684088, _1684090, _1684092, _1684096, _1684100)], (14693 ^ _779142) ^ [_1035557, _1035559, _1035561, _1035563] : [class_Fields_Ofield(_1035557), -(_1035559 = c_Groups_Ozero__class_Ozero(_1035557)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035557), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035557), _1035561), _1035559)), _1035563) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035557), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035557), _1035561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035557), _1035559), _1035563))), _1035559))], (28499 ^ _779142) ^ [_1283038, _1283040] : [class_Orderings_Olinorder(_1283038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283038), _1283040)), -(_1283040 = c_Orderings_Obot__class_Obot(tc_fun(_1283038, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283038), c_Big__Operators_Olattice_OInf__fin(_1283038, c_Orderings_Oord__class_Omin(_1283038), _1283040)), c_Big__Operators_Olattice_OSup__fin(_1283038, c_Orderings_Oord__class_Omax(_1283038), _1283040))))], (37916 ^ _779142) ^ [_1501921] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1501921) = 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), _1501921), c_Int_Onat)))))], (50875 ^ _779142) ^ [_1809457, _1809459] : [_1809457 = _1809459, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809457, _1809459) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809457), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (49290 ^ _779142) ^ [_1775803, _1775805] : [-(c_Relation_Osym(_1775803, c_Relation_OId__on(_1775803, _1775805)))], (48066 ^ _779142) ^ [_1747872, _1747874, _1747876] : [-(hAPP(c_New__DSequence_Opos__single(_1747872, _1747874), _1747876) = hAPP(c_Lazy__Sequence_Osingle(_1747872), _1747874))], (50547 ^ _779142) ^ [_1803184, _1803186, _1803188, _1803190, _1803192] : [-(c_Lazy__Sequence_Omap(_1803184, _1803186, _1803188, c_Lazy__Sequence_Olazy__sequence_OInsert(_1803184, _1803190, _1803192)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1803186, hAPP(_1803188, _1803190), c_Lazy__Sequence_Omap(_1803184, _1803186, _1803188, _1803192)))], (38052 ^ _779142) ^ [_1506875, _1506877, _1506879] : [class_Groups_Olinordered__ab__semigroup__add(_1506875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506875), _1506877)), -(_1506877 = c_Orderings_Obot__class_Obot(tc_fun(_1506875, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1506875), _1506879), c_Big__Operators_Olinorder__class_OMax(_1506875, _1506877)) = c_Big__Operators_Olinorder__class_OMax(_1506875, hAPP(c_Set_OCollect(_1506875), hAPP(hAPP(c_COMBB(tc_fun(_1506875, tc_HOL_Obool), tc_HOL_Obool, _1506875), c_HOL_OEx(_1506875)), hAPP(hAPP(c_COMBC(_1506875, tc_fun(_1506875, tc_HOL_Obool), tc_fun(_1506875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506875, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506875, tc_HOL_Obool), tc_fun(_1506875, tc_HOL_Obool)), _1506875), c_COMBS(_1506875, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506875, tc_HOL_Obool), tc_fun(_1506875, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506875), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506875), c_fconj)), hAPP(hAPP(c_COMBC(_1506875, tc_fun(_1506875, _1506875), tc_fun(_1506875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506875, tc_HOL_Obool), tc_fun(tc_fun(_1506875, _1506875), tc_fun(_1506875, tc_HOL_Obool)), _1506875), c_COMBB(_1506875, tc_HOL_Obool, _1506875)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1506875), _1506879))))), hAPP(hAPP(c_COMBC(_1506875, tc_fun(_1506875, tc_HOL_Obool), tc_HOL_Obool), c_member(_1506875)), _1506877))))))], (43052 ^ _779142) ^ [_1637827, _1637829, _1637831, _1637833] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637827)), hAPP(hAPP(c_List_Oappend(_1637827), _1637829), _1637831)), c_List_Olists(_1637827, _1637833))), 43055 ^ _779142 : [(43058 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637827)), _1637831), c_List_Olists(_1637827, _1637833))))], (43056 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637827)), _1637829), c_List_Olists(_1637827, _1637833))))]]], (15343 ^ _779142) ^ [_1047948, _1047950, _1047952] : [class_Orderings_Olinorder(_1047948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047948), _1047950), _1047952)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047948), _1047952), _1047950) = _1047950)], (27036 ^ _779142) ^ [] : [-(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))], (19737 ^ _779142) ^ [_1126017] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1126017), hAPP(c_Int_Onumber__class_Onumber__of(_1126017), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1126017)), class_Int_Onumber__ring(_1126017), class_Rings_Olinordered__idom(_1126017)], (19939 ^ _779142) ^ [_1129191, _1129193, _1129195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129191), _1129193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129191), _1129195)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129193), _1129195))))], (32069 ^ _779142) ^ [_1360371, _1360373, _1360375, _1360377, _1360379] : [class_Groups_Ocomm__monoid__add(_1360371), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360371), _1360373), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1360375), _1360377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1360379), _1360377))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360371), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1360371, tc_Nat_Onat), _1360373), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1360377))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1360375), _1360379)))], (14665 ^ _779142) ^ [_1035063, _1035065, _1035067, _1035069, _1035071] : [class_Fields_Ofield(_1035063), -(_1035065 = c_Groups_Ozero__class_Ozero(_1035063)), -(_1035067 = c_Groups_Ozero__class_Ozero(_1035063)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035063), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035063), _1035069), _1035065)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035063), _1035071), _1035067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035063), _1035069), _1035067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035063), _1035071), _1035065))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035063), _1035065), _1035067)))], (45740 ^ _779142) ^ [_1698061, _1698063] : [-(c_List_OremoveAll(_1698061, _1698063) = c_List_Ofilter(_1698061, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698061), c_fNot), hAPP(c_fequal, _1698063))))], (18776 ^ _779142) ^ [_1109738, _1109740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1109738)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109738), _1109740)), _1109738) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37255 ^ _779142) ^ [_1482864, _1482866, _1482868, _1482870, _1482872] : [-(hAPP(c_Set_Ovimage(_1482864, _1482866, _1482868), hAPP(hAPP(c_Set_Oinsert(_1482866), _1482870), _1482872)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482864, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1482864, _1482866, _1482868), hAPP(hAPP(c_Set_Oinsert(_1482866), _1482870), c_Orderings_Obot__class_Obot(tc_fun(_1482866, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1482864, _1482866, _1482868), _1482872)))], (26866 ^ _779142) ^ [_1252681, _1252683, _1252685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252681, tc_HOL_Obool)), _1252683), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252681, tc_HOL_Obool)), _1252683), _1252685))))], (41405 ^ _779142) ^ [_1596275, _1596277, _1596279, _1596281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596275), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596277), _1596279))), -(hAPP(c_Random_Opick(_1596277, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596277)), _1596279), _1596281)), _1596275) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1596277), _1596279))], (46021 ^ _779142) ^ [_1704945, _1704947, _1704949, _1704951, _1704953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704947), _1704949))), -(hAPP(hAPP(c_List_Onth(_1704951), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704951), _1704953), c_List_Oupt(_1704949, _1704947))), _1704945) = hAPP(_1704953, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704949), _1704945)))], (25762 ^ _779142) ^ [_1231900] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1231900)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1231900)))], (38677 ^ _779142) ^ [_1527799, _1527801, _1527803] : [c_Wellfounded_Owf(_1527799, _1527801), -(c_Wellfounded_Owf(_1527799, c_Wellfounded_Omlex__prod(_1527799, _1527803, _1527801)))], (25828 ^ _779142) ^ [_1233034, _1233036] : [class_Rings_Ocomm__semiring__1(_1233034), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233034), _1233036), _1233036) = hAPP(hAPP(c_Power_Opower__class_Opower(_1233034), _1233036), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (46692 ^ _779142) ^ [_1717980, _1717982, _1717984, _1717986] : [hAPP(c_List_Orev(_1717980), _1717982) = hAPP(hAPP(c_List_Olist_OCons(_1717980), _1717984), _1717986), -(_1717982 = hAPP(hAPP(c_List_Oappend(_1717980), hAPP(c_List_Orev(_1717980), _1717986)), hAPP(hAPP(c_List_Olist_OCons(_1717980), _1717984), c_List_Olist_ONil(_1717980))))], (32994 ^ _779142) ^ [_1382844, _1382846, _1382848, _1382850, _1382852, _1382854, _1382856] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382844, _1382846, tc_fun(_1382848, tc_HOL_Obool)), _1382850), hAPP(hAPP(c_Product__Type_OPair(_1382844, _1382846), _1382852), _1382854)), _1382856)), -(hBOOL(hAPP(hAPP(hAPP(_1382850, _1382852), _1382854), _1382856)))], (27328 ^ _779142) ^ [_1261237, _1261239] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1261237, _1261239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1261239), _1261237))], (48884 ^ _779142) ^ [_1766296, _1766298] : [48885 ^ _779142 : [(48886 ^ _779142) ^ [_1766362] : [hBOOL(hAPP(_1766298, _1766362))]], 48888 ^ _779142 : [(48891 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1766298, 48887 ^ [_1766296, _1766298])))], (48889 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766296), 48887 ^ [_1766296, _1766298]), c_Orderings_Otop__class_Otop(tc_fun(_1766296, tc_HOL_Obool)))))]]], (21059 ^ _779142) ^ [_1149523, _1149525] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1149523, _1149525))))], (48270 ^ _779142) ^ [_1752451, _1752453, _1752455, _1752457] : [-(c_List_Oreplicate(_1752451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752453), _1752455), _1752457) = hAPP(hAPP(c_List_Oappend(_1752451), c_List_Oreplicate(_1752451, _1752453, _1752457)), c_List_Oreplicate(_1752451, _1752455, _1752457)))], (29959 ^ _779142) ^ [_1313880, _1313882, _1313884] : [class_Orderings_Olinorder(_1313880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313880), _1313882)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313880), _1313884)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313880, tc_HOL_Obool)), _1313882), _1313884) = c_Orderings_Obot__class_Obot(tc_fun(_1313880, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313880), c_Big__Operators_Olinorder__class_OMin(_1313880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313880, tc_HOL_Obool)), _1313882), _1313884))), c_Big__Operators_Olinorder__class_OMin(_1313880, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313880, tc_HOL_Obool)), _1313882), _1313884))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313880), c_Big__Operators_Olinorder__class_OMin(_1313880, _1313882)), c_Big__Operators_Olinorder__class_OMin(_1313880, _1313884)))], (48038 ^ _779142) ^ [_1747035, _1747037, _1747039, _1747041] : [-(c_New__Random__Sequence_Opos__empty(_1747035, _1747037, _1747039, _1747041) = c_New__DSequence_Opos__empty(_1747035))], (48430 ^ _779142) ^ [_1755474] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1755474) = c_Lazy__Sequence_Osmall__lazy_H(_1755474, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1755474)))], (24523 ^ _779142) ^ [_1210529, _1210531, _1210533] : [class_Int_Onumber__ring(_1210529), 24526 ^ _779142 : [(24533 ^ _779142) ^ [] : [c_Int_Oiszero(_1210529, hAPP(c_Int_Onumber__class_Onumber__of(_1210529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1210531), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1210533)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1210529), _1210531) = hAPP(c_Int_Onumber__class_Onumber__of(_1210529), _1210533))], (24527 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1210529), _1210531) = hAPP(c_Int_Onumber__class_Onumber__of(_1210529), _1210533), -(c_Int_Oiszero(_1210529, hAPP(c_Int_Onumber__class_Onumber__of(_1210529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1210531), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1210533)))))]]], (44728 ^ _779142) ^ [_1675218] : [-(_1675218 = 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)), _1675218)))], (2870 ^ _779142) ^ [_821641, _821643] : [_821643 = _821641, -(c_Int_Oring__1__class_Oof__int(_821643) = c_Int_Oring__1__class_Oof__int(_821641))], (42788 ^ _779142) ^ [_1631697, _1631699] : [-(_1631699 = c_List_Olist_ONil(_1631697)), -(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(_1631697)), _1631699))))], (42726 ^ _779142) ^ [_1630586, _1630588] : [_1630588 = c_List_Olist_ONil(_1630586), -(hAPP(c_List_Oset(_1630586), _1630588) = c_Orderings_Obot__class_Obot(tc_fun(_1630586, tc_HOL_Obool)))], (33712 ^ _779142) ^ [_1396200, _1396202, _1396204, _1396206, _1396208, _1396210] : [hAPP(_1396206, hAPP(c_Product__Type_Osnd(_1396204, _1396200), _1396208)) = hAPP(_1396210, hAPP(c_Product__Type_Osnd(_1396204, _1396200), _1396208)), -(hAPP(c_Product__Type_Oapsnd(_1396200, _1396202, _1396204, _1396206), _1396208) = hAPP(c_Product__Type_Oapsnd(_1396200, _1396202, _1396204, _1396210), _1396208))], (19533 ^ _779142) ^ [_1122611, _1122613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122613)), 19540 ^ _779142 : [(19547 ^ _779142) ^ [] : [_1122611 = _1122613, -(hAPP(c_Int_Onat, _1122611) = hAPP(c_Int_Onat, _1122613))], (19541 ^ _779142) ^ [] : [hAPP(c_Int_Onat, _1122611) = hAPP(c_Int_Onat, _1122613), -(_1122611 = _1122613)]]], (13657 ^ _779142) ^ [_1016702, _1016704] : [class_Rings_Odivision__ring(_1016702), -(_1016704 = c_Groups_Ozero__class_Ozero(_1016702)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016702), _1016704), _1016704) = c_Groups_Oone__class_Oone(_1016702))], (44690 ^ _779142) ^ [_1674360, _1674362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674360), _1674362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674360)), hAPP(c_Code__Numeral_Oof__nat, _1674362))))], (34513 ^ _779142) ^ [_1415551, _1415553, _1415555, _1415557] : [c_Orderings_Obot__class_Obot(tc_fun(_1415551, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415553, tc_fun(_1415551, tc_HOL_Obool)), _1415555), _1415557), 34516 ^ _779142 : [(34517 ^ _779142) ^ [_1415667] : [hBOOL(hAPP(hAPP(c_member(_1415553), _1415667), _1415555)), -(hAPP(_1415557, _1415667) = c_Orderings_Obot__class_Obot(tc_fun(_1415551, tc_HOL_Obool)))]]], (98 ^ _779142) ^ [_780591, _780593, _780595, _780597] : [-(c_Int_Oiszero(_780595, _780591)), c_Int_Oiszero(_780597, _780593), _780597 = _780595, _780593 = _780591], (40322 ^ _779142) ^ [_1567753, _1567755] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567753, _1567753)), hAPP(hAPP(c_Product__Type_OPair(_1567753, _1567753), _1567755), _1567755)), c_Relation_OId(_1567753))))], (1526 ^ _779142) ^ [_801159, _801161] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801159)), _801161 = _801159, class_Groups_Oordered__cancel__ab__semigroup__add(_801161)], (8268 ^ _779142) ^ [_916821, _916823] : [class_Lattices_Oab__semigroup__idem__mult(_916821), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916821), _916823), _916823) = _916823)], (25378 ^ _779142) ^ [_1225180, _1225182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225180), 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)))), _1225182))), 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)))), _1225180)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225182), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1225180))], (45795 ^ _779142) ^ [_1699615, _1699617, _1699619, _1699621] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699615)), c_List_Otranspose__rel(_1699615)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699615)), hAPP(hAPP(c_List_Olist_OCons(_1699615), _1699617), _1699619)), _1699621))), -(c_List_Otranspose(_1699615, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699615)), hAPP(hAPP(c_List_Olist_OCons(_1699615), _1699617), _1699619)), _1699621)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699615)), hAPP(hAPP(c_List_Olist_OCons(_1699615), _1699617), c_List_Oconcat(_1699615, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699615), tc_List_Olist(_1699615)), c_List_Olist_Olist__case(tc_List_Olist(_1699615), _1699615, c_List_Olist_ONil(_1699615), hAPP(hAPP(c_COMBB(tc_List_Olist(_1699615), tc_fun(tc_List_Olist(_1699615), tc_List_Olist(_1699615)), _1699615), c_COMBK(tc_List_Olist(_1699615), tc_List_Olist(_1699615))), hAPP(hAPP(c_COMBC(_1699615, tc_List_Olist(_1699615), tc_List_Olist(_1699615)), c_List_Olist_OCons(_1699615)), c_List_Olist_ONil(_1699615))))), _1699621)))), c_List_Otranspose(_1699615, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699615)), _1699619), c_List_Oconcat(tc_List_Olist(_1699615), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699615), tc_List_Olist(tc_List_Olist(_1699615))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699615)), _1699615, c_List_Olist_ONil(tc_List_Olist(_1699615)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699615), tc_List_Olist(tc_List_Olist(_1699615))), _1699615), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699615), tc_List_Olist(tc_List_Olist(_1699615)), tc_List_Olist(tc_List_Olist(_1699615))), c_List_Olist_OCons(tc_List_Olist(_1699615))), c_List_Olist_ONil(tc_List_Olist(_1699615)))))), _1699621))))))], (35732 ^ _779142) ^ [_1448909, _1448911, _1448913, _1448915] : [c_Equiv__Relations_Oequiv(_1448909, _1448911, _1448913), hBOOL(hAPP(hAPP(c_member(_1448909), _1448915), _1448911)), -(hBOOL(hAPP(hAPP(c_member(_1448909), _1448915), hAPP(c_Relation_OImage(_1448909, _1448909, _1448913), hAPP(hAPP(c_Set_Oinsert(_1448909), _1448915), c_Orderings_Obot__class_Obot(tc_fun(_1448909, tc_HOL_Obool)))))))], (24578 ^ _779142) ^ [_1211443, _1211445] : [class_Groups_Osgn__if(_1211443), 24581 ^ _779142 : [(24588 ^ _779142) ^ [] : [-(_1211445 = c_Groups_Ozero__class_Ozero(_1211443)), 24591 ^ _779142 : [(24598 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211443), c_Groups_Ozero__class_Ozero(_1211443)), _1211445))), -(c_Groups_Osgn__class_Osgn(_1211443, _1211445) = hAPP(c_Groups_Ouminus__class_Ouminus(_1211443), c_Groups_Oone__class_Oone(_1211443)))], (24592 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211443), c_Groups_Ozero__class_Ozero(_1211443)), _1211445)), -(c_Groups_Osgn__class_Osgn(_1211443, _1211445) = c_Groups_Oone__class_Oone(_1211443))]]], (24582 ^ _779142) ^ [] : [_1211445 = c_Groups_Ozero__class_Ozero(_1211443), -(c_Groups_Osgn__class_Osgn(_1211443, _1211445) = c_Groups_Ozero__class_Ozero(_1211443))]]], (17740 ^ _779142) ^ [_1091741, _1091743] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091741)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091743)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091741), _1091743)))], (12576 ^ _779142) ^ [_996261, _996263, _996265] : [class_Groups_Oordered__comm__monoid__add(_996261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996261), c_Groups_Ozero__class_Ozero(_996261)), _996263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996261), c_Groups_Ozero__class_Ozero(_996261)), _996265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996261), c_Groups_Ozero__class_Ozero(_996261)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996261), _996263), _996265))))], (31895 ^ _779142) ^ [_1354005, _1354007, _1354009, _1354011, _1354013] : [class_Fields_Ofield(_1354005), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354005), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354007, _1354005), _1354009), _1354011)), _1354013) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354007, _1354005), hAPP(hAPP(c_COMBC(_1354007, _1354005, _1354005), hAPP(hAPP(c_COMBB(_1354005, tc_fun(_1354005, _1354005), _1354007), c_Rings_Oinverse__class_Odivide(_1354005)), _1354009)), _1354013)), _1354011))], (32707 ^ _779142) ^ [_1376447, _1376449, _1376451, _1376453, _1376455] : [-(c_Nat_Onat_Onat__case(_1376447, _1376449, _1376451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376453)), _1376455)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1376447), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1376453))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1376447, _1376447), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1376447, tc_fun(_1376447, _1376447)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1376447, tc_fun(_1376447, _1376447)), tc_Int_Oint), c_If(_1376447)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1376447, _1376449, _1376451, _1376455))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1376447, tc_Int_Oint), _1376451), 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)), _1376455)))))], (20792 ^ _779142) ^ [_1144568, _1144570, _1144572] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144568), _1144570)), _1144572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144568), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144570), _1144572))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144568), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144570, _1144572))), _1144572)))], (32269 ^ _779142) ^ [_1366478, _1366480, _1366482] : [class_Groups_Ocomm__monoid__add(_1366478), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1366478), _1366480), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1366482))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366478), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1366478), _1366480), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1366482))), hAPP(_1366480, hAPP(c_Nat_OSuc, _1366482))))], (40482 ^ _779142) ^ [_1571682, _1571684, _1571686, _1571688, _1571690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571682, _1571682)), hAPP(hAPP(c_Product__Type_OPair(_1571682, _1571682), _1571684), _1571686)), c_Transitive__Closure_Ortrancl(_1571682, _1571688))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571682, _1571682)), hAPP(hAPP(c_Product__Type_OPair(_1571682, _1571682), _1571686), _1571690)), _1571688)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571682, _1571682)), hAPP(hAPP(c_Product__Type_OPair(_1571682, _1571682), _1571684), _1571690)), c_Transitive__Closure_Otrancl(_1571682, _1571688))))], (37365 ^ _779142) ^ [_1485706, _1485708, _1485710] : [hBOOL(hAPP(_1485706, _1485708)), -(hBOOL(hAPP(hAPP(c_member(_1485710), _1485708), hAPP(c_Set_OCollect(_1485710), _1485706))))], (35964 ^ _779142) ^ [_1454091, _1454093] : [c_Equiv__Relations_Oequiv(_1454091, c_Orderings_Otop__class_Otop(tc_fun(_1454091, tc_HOL_Obool)), _1454093), -(c_Equiv__Relations_Oequivp(_1454091, hAPP(hAPP(c_COMBC(_1454091, tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_fun(_1454091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454091, tc_fun(tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_fun(_1454091, tc_HOL_Obool)), _1454091), c_COMBC(_1454091, tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454091, tc_prod(_1454091, _1454091)), tc_fun(_1454091, tc_fun(tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_HOL_Obool)), _1454091), hAPP(c_COMBB(tc_prod(_1454091, _1454091), tc_fun(tc_fun(tc_prod(_1454091, _1454091), tc_HOL_Obool), tc_HOL_Obool), _1454091), c_member(tc_prod(_1454091, _1454091)))), c_Product__Type_OPair(_1454091, _1454091)))), _1454093)))], (44548 ^ _779142) ^ [_1671400, _1671402, _1671404] : [c_Fun_Oinj__on(tc_List_Olist(_1671400), tc_List_Olist(_1671402), hAPP(c_List_Omap(_1671400, _1671402), _1671404), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671400), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671400, _1671402, _1671404, c_Orderings_Otop__class_Otop(tc_fun(_1671400, tc_HOL_Obool))))], (13749 ^ _779142) ^ [_1018348, _1018350, _1018352, _1018354] : [class_Fields_Olinordered__field(_1018348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018348), _1018350), c_Groups_Ozero__class_Ozero(_1018348))), 13756 ^ _779142 : [(13763 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018348), _1018354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018348), _1018352), _1018350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018348), _1018352), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018348), _1018354), _1018350))))], (13757 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018348), _1018352), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018348), _1018354), _1018350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018348), _1018354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018348), _1018352), _1018350))))]]], (15329 ^ _779142) ^ [_1047699, _1047701, _1047703, _1047705] : [class_Orderings_Olinorder(_1047699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047699), _1047701), _1047703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047699), _1047701), _1047705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047699), _1047701), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047699), _1047703), _1047705))))], (21820 ^ _779142) ^ [_1162599, _1162601] : [c_Nat__Transfer_Ois__nat(_1162599), c_Nat__Transfer_Ois__nat(_1162601), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1162599, _1162601) = 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, _1162599), hAPP(c_Int_Onat, _1162601))))], (43121 ^ _779142) ^ [_1639424, _1639426, _1639428, _1639430] : [_1639426 = _1639430, -(hAPP(hAPP(c_List_Oappend(_1639424), _1639426), _1639428) = hAPP(hAPP(c_List_Oappend(_1639424), _1639430), _1639428))], (44193 ^ _779142) ^ [_1663139, _1663141, _1663143] : [_1663139 = c_List_Olist_ONil(_1663141), -(c_List_Olast(_1663141, hAPP(hAPP(c_List_Oappend(_1663141), _1663143), _1663139)) = c_List_Olast(_1663141, _1663143))], (39111 ^ _779142) ^ [_1537708, _1537710, _1537712] : [c_Wellfounded_OwfP(_1537708, _1537710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537708, tc_fun(_1537708, tc_HOL_Obool))), _1537712), _1537710)), -(c_Wellfounded_OwfP(_1537708, _1537712))], (52023 ^ _779142) ^ [_1829207, _1829209, _1829211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829207)), 52026 ^ _779142 : [(52033 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829209), _1829211)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829207), _1829209)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829207), _1829211))))], (52027 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829207), _1829209)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829207), _1829211))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829209), _1829211)))]]], (19747 ^ _779142) ^ [_1126162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1126162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18356 ^ _779142) ^ [_1102384, _1102386, _1102388, _1102390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102386), _1102388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102388), 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), _1102386), _1102384)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102386), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1102390, _1102384))), _1102388))))], (41461 ^ _779142) ^ [_1597845, _1597847, _1597849, _1597851, _1597853, _1597855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597845, _1597845)), hAPP(hAPP(c_Product__Type_OPair(_1597845, _1597845), _1597847), _1597849)), c_Transitive__Closure_Ortrancl(_1597845, _1597851))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597845), tc_List_Olist(_1597845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597845), tc_List_Olist(_1597845)), _1597853), _1597855)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597845), c_List_Olistrel1(_1597845, _1597851)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597845), tc_List_Olist(_1597845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597845), tc_List_Olist(_1597845)), hAPP(hAPP(c_List_Olist_OCons(_1597845), _1597847), _1597853)), hAPP(hAPP(c_List_Olist_OCons(_1597845), _1597849), _1597855))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597845), c_List_Olistrel1(_1597845, _1597851)))))], (6970 ^ _779142) ^ [_893438, _893440, _893442] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893438), _893440)), 6973 ^ _779142 : [(6980 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893438), _893442)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893438, tc_HOL_Obool)), _893442), _893440))))], (6974 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893438, tc_HOL_Obool)), _893442), _893440))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893438), _893442)))]]], (45947 ^ _779142) ^ [_1703498, _1703500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703498)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703500))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703498), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703500)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703498)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703498)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703500))))], (52407 ^ _779142) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (8302 ^ _779142) ^ [_917399, _917401, _917403, _917405, _917407, _917409, _917411] : [-(_917399 = _917401), -(c_Fun_Ofun__upd(_917403, _917405, c_Fun_Ofun__upd(_917403, _917405, _917407, _917399, _917409), _917401, _917411) = c_Fun_Ofun__upd(_917403, _917405, c_Fun_Ofun__upd(_917403, _917405, _917407, _917401, _917411), _917399, _917409))], (4092 ^ _779142) ^ [_841084, _841086, _841088, _841090, _841092, _841094] : [-(c_List_Osplice(_841094, _841090, _841086) = c_List_Osplice(_841092, _841088, _841084)), _841094 = _841092, _841090 = _841088, _841086 = _841084], (26202 ^ _779142) ^ [_1239891, _1239893, _1239895] : [class_Rings_Olinordered__idom(_1239891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239891), c_Groups_Ozero__class_Ozero(_1239891)), hAPP(hAPP(c_Power_Opower__class_Opower(_1239891), _1239893), 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)))), _1239895))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239891), c_Groups_Ozero__class_Ozero(_1239891)), _1239893)))], (46600 ^ _779142) ^ [_1715967, _1715969, _1715971] : [hAPP(hAPP(c_List_Olist_OCons(_1715967), _1715969), c_List_Olist_ONil(_1715967)) = hAPP(c_List_Orev(_1715967), _1715971), -(_1715971 = hAPP(hAPP(c_List_Olist_OCons(_1715967), _1715969), c_List_Olist_ONil(_1715967)))], (18593 ^ _779142) ^ [_1106548] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106548, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43676 ^ _779142) ^ [_1652934, _1652936, _1652938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652934), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652936)), _1652938))), -(_1652938 = hAPP(hAPP(c_List_Oappend(_1652936), hAPP(hAPP(c_List_Otake(_1652936), _1652934), _1652938)), hAPP(hAPP(c_List_Olist_OCons(_1652936), hAPP(hAPP(c_List_Onth(_1652936), _1652938), _1652934)), hAPP(hAPP(c_List_Odrop(_1652936), hAPP(c_Nat_OSuc, _1652934)), _1652938))))], (28981 ^ _779142) ^ [_1292812, _1292814, _1292816] : [class_Lattices_Osemilattice__inf(_1292812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292812), _1292814), _1292816)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1292812), _1292814), _1292816) = _1292814)], (48991 ^ _779142) ^ [_1769989, _1769991, _1769993, _1769995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1769989), _1769991)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1769989), _1769993)), -(_1769993 = c_Orderings_Obot__class_Obot(tc_fun(_1769989, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1769989, _1769995, _1769991, _1769993)), 49005 ^ _779142 : [(49008 ^ _779142) ^ [_1770334] : [hBOOL(hAPP(hAPP(c_member(_1769989), _1770334), _1769993)), hBOOL(hAPP(hAPP(_1769995, 49004 ^ [_1769989, _1769991, _1769993, _1769995]), _1770334))], (49006 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769989), 49004 ^ [_1769989, _1769991, _1769993, _1769995]), _1769991)))]]], (9111 ^ _779142) ^ [_933923, _933925, _933927, _933929, _933931, _933933] : [class_Rings_Oring(_933923), 9114 ^ _779142 : [(9121 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933923), _933925), _933931)), _933927)), _933929) = _933933, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), _933925), _933927)), _933929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), _933931), _933927)), _933933))], (9115 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), _933925), _933927)), _933929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), _933931), _933927)), _933933), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933923), _933925), _933931)), _933927)), _933929) = _933933)]]], (11259 ^ _779142) ^ [_972608, _972610, _972612] : [11260 ^ _779142 : [(11263 ^ _779142) ^ [] : [_972608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11261 ^ _779142) ^ [] : [_972610 = _972612]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972608), _972610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972608), _972612))], (11372 ^ _779142) ^ [_974551, _974553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974551)), _974553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974551), _974553)))], (48668 ^ _779142) ^ [_1761125, _1761127, _1761129] : [c_List_Olist__ex(tc_Int_Oint, _1761125, c_List_Oupto(_1761127, _1761129)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761125), _1761127, _1761129)], (47004 ^ _779142) ^ [_1724517, _1724519, _1724521] : [hBOOL(hAPP(c_List_Odistinct(_1724517), _1724519)), -(hBOOL(hAPP(c_List_Odistinct(_1724517), c_List_OdropWhile(_1724517, _1724521, _1724519))))], (18782 ^ _779142) ^ [_1109845, _1109847] : [class_Int_Onumber__ring(_1109845), -(hAPP(c_Int_Onumber__class_Onumber__of(_1109845), c_Int_Osucc(_1109847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109845), c_Groups_Oone__class_Oone(_1109845)), hAPP(c_Int_Onumber__class_Onumber__of(_1109845), _1109847)))], (30648 ^ _779142) ^ [_1327781, _1327783, _1327785, _1327787] : [class_Groups_Ocomm__monoid__add(_1327781), 30651 ^ _779142 : [(30658 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1327783), _1327785))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327783, _1327781), _1327787), _1327785) = c_Groups_Ozero__class_Ozero(_1327781))], (30652 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327783), _1327785)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327783, _1327781), _1327787), _1327785) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1327781, _1327783, c_Groups_Oplus__class_Oplus(_1327781)), _1327787), c_Groups_Ozero__class_Ozero(_1327781)), _1327785))]]], (16615 ^ _779142) ^ [_1071612, _1071614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071612), _1071614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071612), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1071614)))], (29139 ^ _779142) ^ [_1295874, _1295876, _1295878] : [class_Lattices_Olattice(_1295874), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295874), _1295876), _1295878) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295874), _1295878), _1295876))], (29598 ^ _779142) ^ [_1306123, _1306125, _1306127, _1306129] : [class_Orderings_Oorder(_1306123), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306123, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1306123, _1306125, _1306127)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1306123, _1306127, _1306129)) = c_Orderings_Obot__class_Obot(tc_fun(_1306123, tc_HOL_Obool)))], (42139 ^ _779142) ^ [_1618018, _1618020, _1618022, _1618024, _1618026, _1618028] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618018, _1618020)), hAPP(hAPP(c_Product__Type_OPair(_1618018, _1618020), _1618022), _1618024)), hAPP(c_List_Oset(tc_prod(_1618018, _1618020)), hAPP(hAPP(c_List_Ozip(_1618018, _1618020), _1618026), _1618028)))), -(hBOOL(hAPP(hAPP(c_member(_1618020), _1618024), hAPP(c_List_Oset(_1618020), _1618028))))], (41799 ^ _779142) ^ [_1608085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1608085)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1608085), tc_HOL_Obool))))], (14958 ^ _779142) ^ [_1040618, _1040620] : [class_Int_Oring__char__0(_1040618), hBOOL(hAPP(hAPP(c_member(_1040618), _1040620), c_Int_Oring__1__class_OInts(_1040618))), 14965 ^ _779142 : [(14972 ^ _779142) ^ [] : [_1040620 = c_Groups_Ozero__class_Ozero(_1040618), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040618), _1040620), _1040620) = c_Groups_Ozero__class_Ozero(_1040618))], (14966 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040618), _1040620), _1040620) = c_Groups_Ozero__class_Ozero(_1040618), -(_1040620 = c_Groups_Ozero__class_Ozero(_1040618))]]], (44367 ^ _779142) ^ [_1667002, _1667004, _1667006, _1667008, _1667010] : [44369 ^ _779142 : [(44372 ^ _779142) ^ [] : [hAPP(_1667006, 44368 ^ [_1667002, _1667004, _1667006, _1667008, _1667010]) = hAPP(_1667010, 44368 ^ [_1667002, _1667004, _1667006, _1667008, _1667010])], (44370 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667002), 44368 ^ [_1667002, _1667004, _1667006, _1667008, _1667010]), hAPP(c_List_Oset(_1667002), _1667008))))]], -(hAPP(hAPP(c_List_Omap(_1667002, _1667004), _1667006), _1667008) = hAPP(hAPP(c_List_Omap(_1667002, _1667004), _1667010), _1667008))], (1956 ^ _779142) ^ [_806530, _806532, _806534, _806536] : [-(v_P(_806534, _806530)), v_P(_806536, _806532), _806536 = _806534, _806532 = _806530], (47317 ^ _779142) ^ [_1731730, _1731732, _1731734] : [class_Enum_Oenum(_1731730), class_Enum_Oenum(_1731732), 47324 ^ _779142 : [(47331 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731732), hAPP(hAPP(c_COMBB(tc_fun(_1731730, tc_HOL_Obool), tc_HOL_Obool, _1731732), c_Enum_Oenum__class_Oenum__ex(_1731730)), hAPP(hAPP(c_COMBB(tc_fun(_1731730, tc_prod(_1731732, _1731730)), tc_fun(_1731730, tc_HOL_Obool), _1731732), hAPP(c_COMBB(tc_prod(_1731732, _1731730), tc_HOL_Obool, _1731730), _1731734)), c_Product__Type_OPair(_1731732, _1731730))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731732, _1731730)), _1731734)))], (47325 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731732, _1731730)), _1731734)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731732), hAPP(hAPP(c_COMBB(tc_fun(_1731730, tc_HOL_Obool), tc_HOL_Obool, _1731732), c_Enum_Oenum__class_Oenum__ex(_1731730)), hAPP(hAPP(c_COMBB(tc_fun(_1731730, tc_prod(_1731732, _1731730)), tc_fun(_1731730, tc_HOL_Obool), _1731732), hAPP(c_COMBB(tc_prod(_1731732, _1731730), tc_HOL_Obool, _1731730), _1731734)), c_Product__Type_OPair(_1731732, _1731730))))))]]], (52421 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (40608 ^ _779142) ^ [_1574539, _1574541, _1574543, _1574545] : [-(c_Wellfounded_Oacyclic(_1574539, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574539, _1574539)), hAPP(hAPP(c_Product__Type_OPair(_1574539, _1574539), _1574541), _1574543)), _1574545))), c_Wellfounded_Oacyclic(_1574539, _1574545), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574539, _1574539)), hAPP(hAPP(c_Product__Type_OPair(_1574539, _1574539), _1574543), _1574541)), c_Transitive__Closure_Ortrancl(_1574539, _1574545))))], (47966 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52239 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (32841 ^ _779142) ^ [_1379065, _1379067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379065)), _1379067)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379065), _1379067)))], (29550 ^ _779142) ^ [_1305007, _1305009, _1305011, _1305013] : [class_Orderings_Oorder(_1305007), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305007, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1305007, _1305009, _1305011)), c_SetInterval_Oord__class_OatLeastAtMost(_1305007, _1305011, _1305013)) = c_Orderings_Obot__class_Obot(tc_fun(_1305007, tc_HOL_Obool)))], (17205 ^ _779142) ^ [_1081958, _1081960, _1081962] : [class_Orderings_Olinorder(_1081958), hAPP(_1081960, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081958), 17210 ^ [_1081958, _1081960, _1081962]), 17211 ^ [_1081958, _1081960, _1081962])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081958), hAPP(_1081960, 17210 ^ [_1081958, _1081960, _1081962])), hAPP(_1081960, 17211 ^ [_1081958, _1081960, _1081962])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081958), _1081962)), -(_1081962 = c_Orderings_Obot__class_Obot(tc_fun(_1081958, tc_HOL_Obool))), -(hAPP(_1081960, c_Big__Operators_Olinorder__class_OMin(_1081958, _1081962)) = c_Big__Operators_Olinorder__class_OMin(_1081958, hAPP(c_Set_Oimage(_1081958, _1081958, _1081960), _1081962)))], (41339 ^ _779142) ^ [_1593860, _1593862, _1593864] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593860)), c_List_Osublist(_1593860, _1593862, _1593864)) = 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(_1593860)), _1593862)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1593864)))))], (39684 ^ _779142) ^ [_1551818, _1551820, _1551822, _1551824, _1551826, _1551828, _1551830, _1551832] : [c_Finite__Set_Ofolding__image(_1551818, _1551820, _1551822, _1551824, _1551826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551820), _1551828)), c_Fun_Oinj__on(_1551820, _1551820, _1551830, _1551828), -(hAPP(hAPP(_1551826, _1551832), hAPP(c_Set_Oimage(_1551820, _1551820, _1551830), _1551828)) = hAPP(hAPP(_1551826, hAPP(c_Fun_Ocomp(_1551820, _1551818, _1551820, _1551832), _1551830)), _1551828))], (51819 ^ _779142) ^ [_1825489, _1825491] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825489), 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)))), _1825491)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825491), _1825489)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825489), _1825491)))], (35655 ^ _779142) ^ [_1447068, _1447070, _1447072, _1447074] : [hBOOL(hAPP(hAPP(c_member(_1447068), _1447070), _1447072)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1447068, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447068, _1447068, _1447074), hAPP(hAPP(c_Set_Oinsert(_1447068), _1447070), c_Orderings_Obot__class_Obot(tc_fun(_1447068, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447068), _1447072), _1447074))))], (31038 ^ _779142) ^ [_1335215, _1335217, _1335219, _1335221] : [hAPP(c_Set_Oimage(_1335215, _1335217, _1335219), c_Orderings_Otop__class_Otop(tc_fun(_1335215, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1335217, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335217, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1335217, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1335215, _1335217, _1335219), _1335221))), hAPP(c_Set_Oimage(_1335215, _1335217, _1335219), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1335215, tc_HOL_Obool)), _1335221)))))], (22841 ^ _779142) ^ [_1181399] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1181399)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1181399))], (30838 ^ _779142) ^ [_1331787, _1331789, _1331791] : [class_Orderings_Olinorder(_1331787), 30841 ^ _779142 : [(30848 ^ _779142) ^ [] : [_1331789 = _1331791, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1331787), _1331789) = hAPP(c_SetInterval_Oord__class_OatLeast(_1331787), _1331791))], (30842 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1331787), _1331789) = hAPP(c_SetInterval_Oord__class_OatLeast(_1331787), _1331791), -(_1331789 = _1331791)]]], (51311 ^ _779142) ^ [_1816825, _1816827] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816825), _1816827)), 51316 ^ _779142 : [(51319 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816827), _1816825))], (51317 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816825), _1816827)))]], -(_1816825 = _1816827)], (18034 ^ _779142) ^ [_1096774, _1096776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096774)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096776)))), 18037 ^ _779142 : [(18040 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1096776))], (18038 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096774), _1096776)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096774), _1096776))], (42564 ^ _779142) ^ [_1627703, _1627705, _1627707] : [hBOOL(hAPP(c_List_Odistinct(_1627703), _1627705)), -(hAPP(c_List_Oset(_1627703), c_List_Oremove1(_1627703, _1627707, _1627705)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627703, tc_HOL_Obool)), hAPP(c_List_Oset(_1627703), _1627705)), hAPP(hAPP(c_Set_Oinsert(_1627703), _1627707), c_Orderings_Obot__class_Obot(tc_fun(_1627703, tc_HOL_Obool)))))], (37100 ^ _779142) ^ [_1479046, _1479048] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1479046), c_Int_OInteg)), hBOOL(hAPP(_1479048, hAPP(c_Int_ORep__Integ, 37105 ^ [_1479046, _1479048]))), -(hBOOL(hAPP(_1479048, _1479046)))], (16695 ^ _779142) ^ [_1072987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1072987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072987)))], (34041 ^ _779142) ^ [_1402931, _1402933, _1402935, _1402937, _1402939, _1402941, _1402943, _1402945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1402931, _1402933), tc_prod(_1402931, _1402933))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1402931, _1402933), tc_prod(_1402931, _1402933)), hAPP(hAPP(c_Product__Type_OPair(_1402931, _1402933), _1402935), _1402937)), hAPP(hAPP(c_Product__Type_OPair(_1402931, _1402933), _1402939), _1402941))), c_Wellfounded_Olex__prod(_1402931, _1402933, _1402943, _1402945))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402931, _1402931)), hAPP(hAPP(c_Product__Type_OPair(_1402931, _1402931), _1402935), _1402939)), _1402943))), 34048 ^ _779142 : [(34051 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402933, _1402933)), hAPP(hAPP(c_Product__Type_OPair(_1402933, _1402933), _1402937), _1402941)), _1402945)))], (34049 ^ _779142) ^ [] : [-(_1402935 = _1402939)]]], (35567 ^ _779142) ^ [_1444847, _1444849, _1444851, _1444853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444847), _1444853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444851), _1444849))), -(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), _1444847), _1444849)), 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), _1444851), _1444853)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (19122 ^ _779142) ^ [_1115220] : [19124 ^ _779142 : [(19127 ^ _779142) ^ [_1115330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19123 ^ [_1115220, _1115330]), _1115330))], (19125 ^ _779142) ^ [_1115296] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19123 ^ [_1115220, _1115296]), _1115220)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1115220)))], (8314 ^ _779142) ^ [_917521, _917523, _917525, _917527, _917529] : [hAPP(_917521, _917523) = _917525, -(c_Fun_Ofun__upd(_917527, _917529, _917521, _917523, _917525) = _917521)], (4924 ^ _779142) ^ [_854184, _854186] : [_854186 = _854184, -(c_Fun_Oid(_854186) = c_Fun_Oid(_854184))], (49759 ^ _779142) ^ [_1785009, _1785011, _1785013] : [hAPP(c_Fun_Ocomp(_1785009, _1785011, _1785011, _1785013), c_Hilbert__Choice_Oinv__into(_1785009, _1785011, c_Orderings_Otop__class_Otop(tc_fun(_1785009, tc_HOL_Obool)), _1785013)) = c_Fun_Oid(_1785011), -(hAPP(c_Set_Oimage(_1785009, _1785011, _1785013), c_Orderings_Otop__class_Otop(tc_fun(_1785009, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785011, tc_HOL_Obool)))], (17911 ^ _779142) ^ [_1094662, _1094664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094662), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094664), _1094662)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1094662, _1094664) = _1094662)], (37130 ^ _779142) ^ [_1479741, _1479743, _1479745] : [-(c_HOL_OThe(tc_prod(_1479741, _1479743), hAPP(c_Product__Type_Oprod_Oprod__case(_1479741, _1479743, tc_HOL_Obool), _1479745)) = c_HOL_OThe(tc_prod(_1479741, _1479743), hAPP(hAPP(c_COMBS(tc_prod(_1479741, _1479743), _1479743, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1479741, tc_fun(_1479743, tc_HOL_Obool), tc_prod(_1479741, _1479743)), _1479745), c_Product__Type_Ofst(_1479741, _1479743))), c_Product__Type_Osnd(_1479741, _1479743))))], (16851 ^ _779142) ^ [_1075527, _1075529, _1075531] : [class_Orderings_Olinorder(_1075527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075527), _1075529)), -(c_Big__Operators_Olattice_OInf__fin(_1075527, c_Orderings_Oord__class_Omin(_1075527), hAPP(hAPP(c_Set_Oinsert(_1075527), _1075531), _1075529)) = hAPP(hAPP(c_Finite__Set_Ofold(_1075527, _1075527, c_Orderings_Oord__class_Omin(_1075527)), _1075531), _1075529))], (1536 ^ _779142) ^ [_801284, _801286] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801284)), _801286 = _801284, class_Groups_Oordered__ab__semigroup__add__imp__le(_801286)], (35385 ^ _779142) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (52611 ^ _779142) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (46298 ^ _779142) ^ [_1709836, _1709838, _1709840] : [class_Orderings_Olinorder(_1709836), -(c_List_Olinorder__class_Osorted(_1709836, hAPP(c_List_Ofilter(_1709836, hAPP(hAPP(c_COMBC(_1709836, _1709836, tc_HOL_Obool), c_fequal), hAPP(_1709838, _1709840))), _1709840)))], (19502 ^ _779142) ^ [_1122069] : [-(hBOOL(hAPP(_1122069, 19509 ^ [_1122069]))), 19503 ^ _779142 : [(19504 ^ _779142) ^ [_1122121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122121)), hBOOL(hAPP(_1122069, hAPP(c_Int_Onat, _1122121)))]]], (9829 ^ _779142) ^ [_946511, _946513, _946515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946511), _946513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946515), _946513)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946515), _946511))))], (17563 ^ _779142) ^ [_1088628, _1088630, _1088632] : [class_Divides_Osemiring__div(_1088628), -(c_Divides_Odiv__class_Omod(_1088628, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088628), _1088630), _1088632), _1088632) = c_Groups_Ozero__class_Ozero(_1088628))], (24688 ^ _779142) ^ [_1213316, _1213318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1213316)), c_Int_OBit1(_1213318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213316), _1213318)))], (38810 ^ _779142) ^ [_1530619, _1530621, _1530623] : [-(hAPP(c_Set_Oimage(tc_prod(_1530619, _1530621), _1530619, c_Product__Type_Ofst(_1530619, _1530621)), _1530623) = hAPP(c_Relation_ODomain(_1530619, _1530621), _1530623))], (25890 ^ _779142) ^ [_1234114, _1234116] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1234114)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1234116))) = 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), _1234114), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234116))))], (22362 ^ _779142) ^ [_1172625, _1172627, _1172629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172625)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1172627), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1172629)), 22372 ^ _779142 : [(22378 ^ _779142) ^ [] : [-(_1172627 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22374 ^ [_1172625, _1172627, _1172629]), 22371 ^ [_1172625, _1172627, _1172629]))], (22376 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22374 ^ [_1172625, _1172627, _1172629]), _1172629)))], (22373 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22371 ^ [_1172625, _1172627, _1172629]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1172625))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1172627), _1172625) = _1172627)], (36390 ^ _779142) ^ [_1463589, _1463591, _1463593, _1463595, _1463597] : [c_Fun_Oinj__on(_1463589, _1463591, _1463593, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463589, tc_HOL_Obool)), _1463595), _1463597)), 36393 ^ _779142 : [(36400 ^ _779142) ^ [] : [_1463595 = _1463597, -(hAPP(c_Set_Oimage(_1463589, _1463591, _1463593), _1463595) = hAPP(c_Set_Oimage(_1463589, _1463591, _1463593), _1463597))], (36394 ^ _779142) ^ [] : [hAPP(c_Set_Oimage(_1463589, _1463591, _1463593), _1463595) = hAPP(c_Set_Oimage(_1463589, _1463591, _1463593), _1463597), -(_1463595 = _1463597)]]], (22074 ^ _779142) ^ [_1167245, _1167247, _1167249, _1167251] : [class_Rings_Olinordered__semidom(_1167245), hAPP(hAPP(c_Power_Opower__class_Opower(_1167245), _1167247), hAPP(c_Nat_OSuc, _1167249)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1167245), _1167251), hAPP(c_Nat_OSuc, _1167249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167245), c_Groups_Ozero__class_Ozero(_1167245)), _1167247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167245), c_Groups_Ozero__class_Ozero(_1167245)), _1167251)), -(_1167247 = _1167251)], (12417 ^ _779142) ^ [_993408, _993410, _993412] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993408), _993410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993408), _993412)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993410), _993412))], (31907 ^ _779142) ^ [_1354344, _1354346, _1354348] : [class_Orderings_Obot(_1354344), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1354346, _1354344)), _1354348) = c_Orderings_Obot__class_Obot(_1354344))], (19177 ^ _779142) ^ [_1116234, _1116236, _1116238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116234)), 19180 ^ _779142 : [(19181 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1116236, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1116238), _1116234)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116238, _1116234))), 19184 ^ _779142 : [(19185 ^ _779142) ^ [_1116435, _1116437] : [-(hBOOL(hAPP(hAPP(_1116236, _1116437), _1116435))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116435), _1116234)), _1116238 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116234), _1116437)), _1116435)]]], (19199 ^ _779142) ^ [] : [19202 ^ _779142 : [(19205 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19201 ^ [_1116234, _1116236, _1116238]), _1116234)))], (19207 ^ _779142) ^ [] : [-(_1116238 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116234), 19200 ^ [_1116234, _1116236, _1116238])), 19201 ^ [_1116234, _1116236, _1116238]))], (19209 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1116236, 19200 ^ [_1116234, _1116236, _1116238]), 19201 ^ [_1116234, _1116236, _1116238]))], (19203 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19201 ^ [_1116234, _1116236, _1116238])))]], -(hBOOL(hAPP(hAPP(_1116236, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1116238), _1116234)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116238, _1116234))))]]], (36040 ^ _779142) ^ [_1455879, _1455881, _1455883, _1455885, _1455887, _1455889, _1455891, _1455893] : [c_Equiv__Relations_Oequiv(_1455879, _1455881, _1455883), c_Equiv__Relations_Ocongruent2(_1455879, _1455885, _1455887, _1455883, _1455889, _1455891), hBOOL(hAPP(hAPP(c_member(_1455879), _1455893), _1455881)), -(c_Equiv__Relations_Ocongruent(_1455885, _1455887, _1455889, hAPP(_1455891, _1455893)))], (3162 ^ _779142) ^ [_826141, _826143, _826145, _826147, _826149, _826151, _826153, _826155, _826157, _826159] : [-(c_Fun_Ofun__upd(_826159, _826155, _826151, _826147, _826143) = c_Fun_Ofun__upd(_826157, _826153, _826149, _826145, _826141)), _826159 = _826157, _826155 = _826153, _826151 = _826149, _826147 = _826145, _826143 = _826141], (45829 ^ _779142) ^ [_1701124, _1701126, _1701128] : [class_Groups_Oab__semigroup__add(_1701124), -(c_List_Ofoldr(_1701124, _1701124, c_Groups_Oplus__class_Oplus(_1701124), _1701126, _1701128) = hAPP(c_List_Ofoldl(_1701124, _1701124, c_Groups_Oplus__class_Oplus(_1701124), _1701128), _1701126))], (52207 ^ _779142) ^ [_1831891, _1831893] : [class_Groups_Ouminus(_1831891), -(class_Groups_Ouminus(tc_fun(_1831893, _1831891)))], (43616 ^ _779142) ^ [_1651313, _1651315, _1651317, _1651319, _1651321] : [-(hAPP(hAPP(c_List_Oappend(_1651313), _1651315), _1651317) = hAPP(hAPP(c_List_Oappend(_1651313), _1651319), _1651321)), 43619 ^ _779142 : [(43622 ^ _779142) ^ [] : [_1651315 = hAPP(hAPP(c_List_Otake(_1651313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651315)), _1651319), _1651317 = hAPP(hAPP(c_List_Oappend(_1651313), hAPP(hAPP(c_List_Odrop(_1651313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651315)), _1651319)), _1651321)], (43620 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651315)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651319))))]], 43627 ^ _779142 : [(43630 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Otake(_1651313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651319)), _1651315) = _1651319, hAPP(hAPP(c_List_Oappend(_1651313), hAPP(hAPP(c_List_Odrop(_1651313), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651319)), _1651315)), _1651317) = _1651321], (43628 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651315)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651313)), _1651319)))]]], (44376 ^ _779142) ^ [_1667259, _1667261, _1667263, _1667265, _1667267, _1667269, _1667271] : [hAPP(hAPP(c_List_Omap(_1667259, _1667261), _1667263), _1667265) = hAPP(hAPP(c_List_Omap(_1667267, _1667261), _1667269), _1667271), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667259)), _1667265) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667267)), _1667271))], (20744 ^ _779142) ^ [_1143724, _1143726, _1143728] : [class_Orderings_Oorder(_1143724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143724), _1143726), _1143728)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1143724, _1143728, _1143726) = c_Orderings_Obot__class_Obot(tc_fun(_1143724, tc_HOL_Obool)))], (37663 ^ _779142) ^ [_1493558, _1493560, _1493562, _1493564, _1493566, _1493568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493558, _1493560)), hAPP(hAPP(c_Product__Type_OPair(_1493558, _1493560), _1493562), _1493564)), hAPP(hAPP(c_Product__Type_OSigma(_1493558, _1493560), _1493566), _1493568))), 37666 ^ _779142 : [(37669 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493560), _1493564), hAPP(_1493568, _1493562))))], (37667 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493558), _1493562), _1493566)))]]], (34356 ^ _779142) ^ [_1410922, _1410924, _1410926, _1410928, _1410930] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410922, tc_HOL_Obool)), _1410924), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410926, tc_fun(_1410922, tc_HOL_Obool)), _1410928), _1410930)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410926, tc_fun(_1410922, tc_HOL_Obool)), _1410928), hAPP(hAPP(c_COMBB(tc_fun(_1410922, tc_HOL_Obool), tc_fun(_1410922, tc_HOL_Obool), _1410926), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410922, tc_HOL_Obool)), _1410924)), _1410930)))], (20971 ^ _779142) ^ [_1147937, _1147939] : [c_Nat__Transfer_Onat__set(_1147937), c_Nat__Transfer_Onat__set(_1147939), 20978 ^ _779142 : [(20985 ^ _779142) ^ [] : [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), _1147937)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1147937), _1147939)))], (20979 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1147937), _1147939)), -(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), _1147937)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147939))))]]], (21122 ^ _779142) ^ [_1150454] : [c_Nat__Transfer_Onat__set(_1150454), 21125 ^ _779142 : [(21132 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1150454))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1150454)))], (21126 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1150454)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1150454))))]]], (25048 ^ _779142) ^ [_1219509, _1219511] : [class_Rings_Olinordered__idom(_1219509), 25051 ^ _779142 : [(25058 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219509), _1219511), c_Groups_Ozero__class_Ozero(_1219509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219509), c_Groups_Osgn__class_Osgn(_1219509, _1219511)), c_Groups_Ozero__class_Ozero(_1219509))))], (25052 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219509), c_Groups_Osgn__class_Osgn(_1219509, _1219511)), c_Groups_Ozero__class_Ozero(_1219509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219509), _1219511), c_Groups_Ozero__class_Ozero(_1219509))))]]], (50471 ^ _779142) ^ [_1801665, _1801667, _1801669, _1801671] : [50474 ^ _779142 : [(50477 ^ _779142) ^ [] : [hAPP(_1801669, 50472 ^ [_1801665, _1801667, _1801669, _1801671]) = hAPP(_1801669, 50473 ^ [_1801665, _1801667, _1801669, _1801671])], (50475 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801665, _1801665)), hAPP(hAPP(c_Product__Type_OPair(_1801665, _1801665), 50472 ^ [_1801665, _1801667, _1801669, _1801671]), 50473 ^ [_1801665, _1801667, _1801669, _1801671])), _1801667)))]], -(c_Equiv__Relations_Ocongruent(_1801665, _1801671, _1801667, _1801669))], (25566 ^ _779142) ^ [_1228460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1228460)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228460), c_Int_OPls)))], (47337 ^ _779142) ^ [_1732169, _1732171] : [class_Enum_Oenum(_1732169), 47340 ^ _779142 : [(47347 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732169), _1732171)), -(hBOOL(hAPP(_1732171, 47350 ^ [_1732169, _1732171])))], (47341 ^ _779142) ^ [] : [47342 ^ _779142 : [(47343 ^ _779142) ^ [_1732271] : [hBOOL(hAPP(_1732171, _1732271))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732169), _1732171)))]]], (43231 ^ _779142) ^ [_1641637, _1641639, _1641641] : [c_List_Olist_ONil(_1641637) = hAPP(hAPP(c_List_Oappend(_1641637), _1641639), _1641641), 43234 ^ _779142 : [(43237 ^ _779142) ^ [] : [-(_1641641 = c_List_Olist_ONil(_1641637))], (43235 ^ _779142) ^ [] : [-(_1641639 = c_List_Olist_ONil(_1641637))]]], (49937 ^ _779142) ^ [_1788983, _1788985, _1788987, _1788989, _1788991] : [c_Fun_Obij__betw(_1788983, _1788985, _1788987, c_Orderings_Otop__class_Otop(tc_fun(_1788983, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788985, tc_HOL_Obool))), c_Fun_Obij__betw(_1788985, _1788989, _1788991, c_Orderings_Otop__class_Otop(tc_fun(_1788985, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788989, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1788983, _1788989, hAPP(c_Fun_Ocomp(_1788985, _1788989, _1788983, _1788991), _1788987), c_Orderings_Otop__class_Otop(tc_fun(_1788983, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788989, tc_HOL_Obool))))], (18607 ^ _779142) ^ [_1106742, _1106744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1106742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106744, _1106742)), _1106742)))], (1976 ^ _779142) ^ [_807606, _807608, _807610, _807612] : [-(c_Option_Othe(_807612, _807608) = c_Option_Othe(_807610, _807606)), _807612 = _807610, _807608 = _807606], (20221 ^ _779142) ^ [_1134214, _1134216] : [_1134214 = hAPP(c_Int_Onat, _1134216), 20224 ^ _779142 : [(20231 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134216))), -(_1134214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20225 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134216)), -(_1134216 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134214))]]], (26706 ^ _779142) ^ [_1249604, _1249606] : [class_Lattices_Olattice(_1249604), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1249604), _1249606), _1249606) = _1249606)], (29283 ^ _779142) ^ [_1298821, _1298823] : [c_Nat__Transfer_Onat__set(_1298821), c_Nat__Transfer_Onat__set(_1298823), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298821), _1298823)))], (2158 ^ _779142) ^ [_810529, _810531] : [_810531 = _810529, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810531) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810529))], (38418 ^ _779142) ^ [_1520201, _1520203, _1520205] : [_1520205 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520201, _1520203), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1520201, _1520203), _1520205) = c_Orderings_Obot__class_Obot(tc_fun(_1520203, tc_HOL_Obool)))], (45742 ^ _779142) ^ [_1698105, _1698107] : [-(c_List_Otranspose(_1698105, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698105)), c_List_Olist_ONil(_1698105)), _1698107)) = c_List_Otranspose(_1698105, _1698107))], (5997 ^ _779142) ^ [_874610, _874612, _874614] : [hAPP(hAPP(c_Set_Oinsert(_874610), _874612), _874614) = c_Orderings_Obot__class_Obot(tc_fun(_874610, tc_HOL_Obool))], (31799 ^ _779142) ^ [_1351446, _1351448, _1351450] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351446, tc_Nat_Onat), _1351448), _1351450)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351446, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1351446), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1351448)), _1351450))], (28370 ^ _779142) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (47619 ^ _779142) ^ [_1738555, _1738557, _1738559] : [class_Orderings_Olinorder(_1738555), 47625 ^ _779142 : [(47628 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738555), _1738559), 47624 ^ [_1738555, _1738557, _1738559]))], (47626 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738555), 47624 ^ [_1738555, _1738557, _1738559]), hAPP(c_List_Oset(_1738555), _1738557))))]], c_List_Olinorder__class_Osorted(_1738555, _1738557), -(c_List_Olinorder__class_Osorted(_1738555, hAPP(hAPP(c_List_Olist_OCons(_1738555), _1738559), _1738557)))], (47850 ^ _779142) ^ [_1743218, _1743220, _1743222] : [c_FunDef_Ois__measure(_1743218, _1743220), -(c_FunDef_Ois__measure(tc_prod(_1743218, _1743222), hAPP(hAPP(c_COMBB(_1743218, tc_Nat_Onat, tc_prod(_1743218, _1743222)), _1743220), c_Product__Type_Ofst(_1743218, _1743222))))], (33012 ^ _779142) ^ [_1383248, _1383250] : [33013 ^ _779142 : [(33016 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1383250), _1383248))], (33014 ^ _779142) ^ [] : [_1383248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1383250, _1383248) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1383250))], (36846 ^ _779142) ^ [_1473386, _1473388, _1473390, _1473392] : [c_Fun_Oinj__on(_1473386, _1473388, _1473390, _1473392), -(c_Fun_Oinj__on(_1473388, _1473386, c_Fun_Othe__inv__into(_1473386, _1473388, _1473392, _1473390), hAPP(c_Set_Oimage(_1473386, _1473388, _1473390), _1473392)))], (22739 ^ _779142) ^ [_1179745, _1179747, _1179749] : [hAPP(c_Set_Oimage(_1179747, tc_fun(_1179747, tc_HOL_Obool), _1179745), _1179749) = hAPP(c_Set_OPow(_1179747), _1179749)], (40235 ^ _779142) ^ [_1564848, _1564850, _1564852, _1564854, _1564856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564848, _1564848)), hAPP(hAPP(c_Product__Type_OPair(_1564848, _1564848), _1564850), _1564852)), c_Transitive__Closure_Otrancl(_1564848, _1564854))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1564848, _1564848)), hAPP(hAPP(c_Product__Type_OPair(_1564848, _1564848), _1564852), _1564856)), c_Transitive__Closure_Otrancl(_1564848, _1564854))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564848, _1564848)), hAPP(hAPP(c_Product__Type_OPair(_1564848, _1564848), _1564850), _1564856)), c_Transitive__Closure_Otrancl(_1564848, _1564854))))], (13627 ^ _779142) ^ [_1016221, _1016223, _1016225, _1016227] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1016221, _1016223)), c_Sum__Type_OPlus(_1016221, _1016223, _1016225, _1016227)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016221), _1016225)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016223), _1016227))], (10511 ^ _779142) ^ [_961077] : [hAPP(c_Nat_OSuc, _961077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46981 ^ _779142) ^ [_1724102, _1724104, _1724106] : [46983 ^ _779142 : [(46986 ^ _779142) ^ [] : [hBOOL(hAPP(_1724104, 46982 ^ [_1724102, _1724104, _1724106]))], (46984 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724102), 46982 ^ [_1724102, _1724104, _1724106]), hAPP(c_List_Oset(_1724102), _1724106))))]], -(c_List_OdropWhile(_1724102, _1724104, _1724106) = c_List_Olist_ONil(_1724102))], (37649 ^ _779142) ^ [_1493007, _1493009, _1493011, _1493013, _1493015] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493007, _1493009), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493007, tc_HOL_Obool)), _1493011), _1493013)), _1493015) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493007, _1493009), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493007, _1493009), _1493011), _1493015)), hAPP(hAPP(c_Product__Type_OSigma(_1493007, _1493009), _1493013), _1493015)))], (38989 ^ _779142) ^ [_1535193, _1535195] : [c_Wellfounded_Owf(_1535193, _1535195), -(c_Wellfounded_Owf(tc_List_Olist(_1535193), c_List_Olenlex(_1535193, _1535195)))], (15973 ^ _779142) ^ [_1059531, _1059533, _1059535, _1059537] : [class_Fields_Olinordered__field__inverse__zero(_1059531), class_Int_Onumber(_1059531), 15980 ^ _779142 : [(15981 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1059531), _1059535), _1059537))), 15984 ^ _779142 : [(15991 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), c_Groups_Ozero__class_Ozero(_1059531)), _1059537))), 15994 ^ _779142 : [(16001 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059537), c_Groups_Ozero__class_Ozero(_1059531)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), c_Groups_Ozero__class_Ozero(_1059531))))], (15995 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059537), c_Groups_Ozero__class_Ozero(_1059531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), _1059537))))]]], (15985 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), c_Groups_Ozero__class_Ozero(_1059531)), _1059537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), _1059537)), _1059535)))]]], (16007 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1059531), _1059535), _1059537)))), 16010 ^ _779142 : [(16013 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), _1059537)), _1059535))], (16011 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), c_Groups_Ozero__class_Ozero(_1059531)), _1059537)))]], 16014 ^ _779142 : [(16017 ^ _779142) ^ [] : [16018 ^ _779142 : [(16021 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), _1059537)))], (16019 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059537), c_Groups_Ozero__class_Ozero(_1059531))))]], 16022 ^ _779142 : [(16025 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)), c_Groups_Ozero__class_Ozero(_1059531)))], (16023 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), _1059537), c_Groups_Ozero__class_Ozero(_1059531)))]]], (16015 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059531), c_Groups_Ozero__class_Ozero(_1059531)), _1059537))]]]]], (38881 ^ _779142) ^ [_1532150, _1532152] : [c_FunDef_Oreduction__pair(_1532150, _1532152), 38884 ^ _779142 : [(38887 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532150, _1532150, _1532150), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool), tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool)), _1532152)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool), tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool)), _1532152))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool), tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool)), _1532152))))], (38885 ^ _779142) ^ [] : [-(c_Wellfounded_Owf(_1532150, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool), tc_fun(tc_prod(_1532150, _1532150), tc_HOL_Obool)), _1532152)))]]], (17998 ^ _779142) ^ [_1096184] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096184), c_Int_OPls)))], (43504 ^ _779142) ^ [_1648689, _1648691] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648689)), hAPP(c_List_Orotate1(_1648689), _1648691)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648689)), _1648691))], (10857 ^ _779142) ^ [_966591, _966593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966591), hAPP(c_Nat_OSuc, _966593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966591), _966593))), -(_966591 = hAPP(c_Nat_OSuc, _966593))], (26066 ^ _779142) ^ [_1237068, _1237070, _1237072] : [class_Rings_Olinordered__semidom(_1237068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237068), hAPP(hAPP(c_Power_Opower__class_Opower(_1237068), _1237070), 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(_1237068), _1237072), 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(_1237068), c_Groups_Ozero__class_Ozero(_1237068)), _1237072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237068), _1237070), _1237072)))], (38308 ^ _779142) ^ [_1516530, _1516532, _1516534, _1516536] : [-(c_Product__Type_Oapfst(_1516530, _1516532, _1516534, _1516536) = c_Product__Type_Omap__pair(_1516530, _1516532, _1516534, _1516534, _1516536, c_Fun_Oid(_1516534)))], (4854 ^ _779142) ^ [_853039, _853041, _853043, _853045, _853047, _853049] : [-(c_Finite__Set_Ofold__image(_853049, _853045, _853041) = c_Finite__Set_Ofold__image(_853047, _853043, _853039)), _853049 = _853047, _853045 = _853043, _853041 = _853039], (45135 ^ _779142) ^ [_1684521, _1684523, _1684525] : [c_List_Olist__all2(_1684525, _1684525, c_fequal, _1684521, _1684523), -(_1684521 = _1684523)], (28659 ^ _779142) ^ [_1285841, _1285843, _1285845] : [class_Orderings_Olinorder(_1285841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285841), _1285843)), -(hBOOL(hAPP(hAPP(c_member(_1285841), _1285845), _1285843))), -(c_Big__Operators_Olattice_OSup__fin(_1285841, c_Orderings_Oord__class_Omax(_1285841), hAPP(hAPP(c_Set_Oinsert(_1285841), _1285845), _1285843)) = hAPP(hAPP(c_Finite__Set_Ofold(_1285841, _1285841, c_Orderings_Oord__class_Omax(_1285841)), _1285845), _1285843))], (27752 ^ _779142) ^ [_1269277, _1269279, _1269281] : [class_Orderings_Olinorder(_1269277), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269277), _1269279), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269277), _1269279), _1269281)) = _1269279)], (20330 ^ _779142) ^ [_1135903, _1135905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135905)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1135903)), hAPP(c_Int_Onat, _1135905)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1135903), _1135905)))], (32313 ^ _779142) ^ [_1367437, _1367439, _1367441, _1367443, _1367445] : [class_Groups_Ocomm__monoid__add(_1367437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367439), _1367441)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367439, _1367437), _1367443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367439, tc_HOL_Obool)), _1367441), _1367445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367439, _1367437), hAPP(hAPP(c_COMBC(_1367439, _1367437, _1367437), hAPP(hAPP(c_COMBS(_1367439, _1367437, tc_fun(_1367437, _1367437)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1367437, tc_fun(_1367437, _1367437)), _1367439), c_If(_1367437)), hAPP(hAPP(c_COMBC(_1367439, tc_fun(_1367439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367439)), _1367445))), _1367443)), c_Groups_Ozero__class_Ozero(_1367437))), _1367441))], (40396 ^ _779142) ^ [_1569597, _1569599, _1569601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1569597, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1569597, _1569597, _1569599), _1569601)), _1569601)), -(hAPP(c_Relation_OImage(_1569597, _1569597, c_Transitive__Closure_Ortrancl(_1569597, _1569599)), _1569601) = _1569601)], (24846 ^ _779142) ^ [_1216013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1216013)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216013), c_Int_OPls)))], (36130 ^ _779142) ^ [_1458063, _1458065, _1458067, _1458069, _1458071, _1458073, _1458075, _1458077, _1458079, _1458081, _1458083] : [c_Equiv__Relations_Oequiv(_1458063, _1458065, _1458067), c_Equiv__Relations_Oequiv(_1458069, _1458071, _1458073), c_Equiv__Relations_Ocongruent2(_1458063, _1458069, tc_fun(_1458075, tc_HOL_Obool), _1458067, _1458073, _1458077), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458063, tc_HOL_Obool)), _1458079), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458063), _1458065), _1458067))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458069, tc_HOL_Obool)), _1458081), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458069), _1458071), _1458073))), 36152 ^ _779142 : [(36158 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1458075, tc_HOL_Obool)), hAPP(hAPP(_1458077, 36151 ^ [_1458063, _1458065, _1458067, _1458069, _1458071, _1458073, _1458075, _1458077, _1458079, _1458081, _1458083]), 36154 ^ [_1458063, _1458065, _1458067, _1458069, _1458071, _1458073, _1458075, _1458077, _1458079, _1458081, _1458083])), _1458083))], (36156 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458069), 36154 ^ [_1458063, _1458065, _1458067, _1458069, _1458071, _1458073, _1458075, _1458077, _1458079, _1458081, _1458083]), _1458071)))], (36153 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458063), 36151 ^ [_1458063, _1458065, _1458067, _1458069, _1458071, _1458073, _1458075, _1458077, _1458079, _1458081, _1458083]), _1458065)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1458075, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458063, tc_fun(_1458075, tc_HOL_Obool)), _1458079), hAPP(hAPP(c_COMBB(tc_fun(_1458069, tc_fun(_1458075, tc_HOL_Obool)), tc_fun(_1458075, tc_HOL_Obool), _1458063), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458069, tc_fun(_1458075, tc_HOL_Obool)), _1458081)), _1458077))), _1458083)))], (11732 ^ _779142) ^ [_981173, _981175, _981177, _981179] : [class_Rings_Oordered__ring(_981173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981173), _981175), _981177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981173), _981179), c_Groups_Ozero__class_Ozero(_981173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981173), _981179), _981177)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981173), _981179), _981175))))], (44678 ^ _779142) ^ [] : [-(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))], (1936 ^ _779142) ^ [_806284, _806286] : [-(class_Nat_Osize(_806284)), _806286 = _806284, class_Nat_Osize(_806286)], (38370 ^ _779142) ^ [_1518701, _1518703, _1518705, _1518707, _1518709, _1518711] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518701, _1518703, _1518705), _1518707), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518703, _1518705), tc_HOL_Obool)), _1518709), _1518711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518701, _1518705), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518701, _1518703, _1518705), _1518707), _1518709)), hAPP(hAPP(c_Relation_Orel__comp(_1518701, _1518703, _1518705), _1518707), _1518711)))], (38746 ^ _779142) ^ [_1529121, _1529123, _1529125] : [c_Wellfounded_Owf(_1529121, _1529123), -(hBOOL(hAPP(hAPP(c_member(_1529121), _1529125), c_Wellfounded_Oacc(_1529121, _1529123))))], (11380 ^ _779142) ^ [_974711, _974713, _974715] : [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, _974711)), _974713)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974711)), _974715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974713), _974715)))], (18905 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (50943 ^ _779142) ^ [_1810499, _1810501] : [50944 ^ _779142 : [(50947 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810501), _1810499))], (50945 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810499), _1810501)))]], -(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)))), _1810499, _1810501) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (36618 ^ _779142) ^ [_1468273, _1468275, _1468277, _1468279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1468273), hAPP(c_Set_Oimage(_1468275, _1468273, _1468277), _1468279))), hAPP(c_Finite__Set_Ocard(_1468275), _1468279))), c_Fun_Oinj__on(_1468275, _1468273, _1468277, _1468279)], (29452 ^ _779142) ^ [_1302864, _1302866, _1302868] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302864, tc_HOL_Obool)), _1302866), _1302868) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302864, tc_HOL_Obool)), _1302866), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302864, tc_HOL_Obool)), _1302868)))], (8509 ^ _779142) ^ [_921655, _921657, _921659, _921661, _921663] : [class_Groups_Ocomm__monoid__mult(_921655), hBOOL(hAPP(c_Finite__Set_Ofinite(_921657), _921659)), hBOOL(hAPP(hAPP(c_member(_921657), _921661), _921659)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_921657, _921655), _921663), _921659) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921655), hAPP(_921663, _921661)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_921657, _921655), _921663), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921657, tc_HOL_Obool)), _921659), hAPP(hAPP(c_Set_Oinsert(_921657), _921661), c_Orderings_Obot__class_Obot(tc_fun(_921657, tc_HOL_Obool)))))))], (43187 ^ _779142) ^ [_1640864, _1640866, _1640868] : [hAPP(hAPP(c_List_Oappend(_1640864), _1640866), _1640868) = c_List_Olist_ONil(_1640864), 43190 ^ _779142 : [(43193 ^ _779142) ^ [] : [-(_1640868 = c_List_Olist_ONil(_1640864))], (43191 ^ _779142) ^ [] : [-(_1640866 = c_List_Olist_ONil(_1640864))]]], (22590 ^ _779142) ^ [_1176910, _1176912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176910)), 22599 ^ _779142 : [(22602 ^ _779142) ^ [] : [hBOOL(hAPP(_1176912, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22595 ^ [_1176910, _1176912]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 22596 ^ [_1176910, _1176912]), _1176910))))], (22600 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1176912, 22595 ^ [_1176910, _1176912])))]], 22603 ^ _779142 : [(22606 ^ _779142) ^ [] : [hBOOL(hAPP(_1176912, 22595 ^ [_1176910, _1176912]))], (22604 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1176912, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22595 ^ [_1176910, _1176912]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 22596 ^ [_1176910, _1176912]), _1176910)))))]], 22607 ^ _779142 : [(22617 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1176912, 22624 ^ [_1176910, _1176912]))), 22618 ^ _779142 : [(22619 ^ _779142) ^ [_1177457] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1177457), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1176910))), hBOOL(hAPP(_1176912, _1177457))]]], (22608 ^ _779142) ^ [] : [22609 ^ _779142 : [(22610 ^ _779142) ^ [_1177342] : [hBOOL(hAPP(_1176912, _1177342))]], 22612 ^ _779142 : [(22615 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1176912, 22611 ^ [_1176910, _1176912])))], (22613 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22611 ^ [_1176910, _1176912]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1176910))))]]]]], (32245 ^ _779142) ^ [_1365974] : [class_Orderings_Olinorder(_1365974), -(c_Orderings_Oord_Omin(_1365974, hAPP(c_COMBC(_1365974, _1365974, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1365974))) = c_Orderings_Oord__class_Omax(_1365974))], (46556 ^ _779142) ^ [_1715132, _1715134] : [hBOOL(hAPP(c_List_Odistinct(_1715132), _1715134)), -(hBOOL(hAPP(c_List_Odistinct(_1715132), hAPP(c_List_Orev(_1715132), _1715134))))], (17726 ^ _779142) ^ [_1091465, _1091467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091465)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091465), _1091467)))], (7368 ^ _779142) ^ [_901241, _901243, _901245] : [class_Orderings_Olinorder(_901241), -(_901243 = _901245), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901241), _901243), _901245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901241), _901245), _901243)))], (12274 ^ _779142) ^ [_991119, _991121, _991123, _991125] : [class_Groups_Ocomm__monoid__add(_991119), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_991121), _991123))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991121, _991119), _991125), _991123) = c_Groups_Ozero__class_Ozero(_991119))], (48652 ^ _779142) ^ [_1760843, _1760845, _1760847] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760843) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760843, _1760845, _1760847)], (50697 ^ _779142) ^ [_1805790, _1805792, _1805794, _1805796] : [class_Rings_Odvd(_1805790), _1805792 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805790), _1805794), _1805796), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805790), _1805794), _1805792)))], (7674 ^ _779142) ^ [_906074, _906076, _906078] : [class_Orderings_Oorder(_906074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906074), _906076), _906078)), -(_906078 = _906076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906074), _906076), _906078)))], (30884 ^ _779142) ^ [_1332537, _1332539] : [class_Orderings_Otop(_1332537), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332537), _1332539), c_Orderings_Otop__class_Otop(_1332537))))], (17499 ^ _779142) ^ [_1087399, _1087401, _1087403, _1087405, _1087407, _1087409] : [class_Divides_Oring__div(_1087399), c_Divides_Odiv__class_Omod(_1087399, _1087401, _1087403) = c_Divides_Odiv__class_Omod(_1087399, _1087405, _1087403), c_Divides_Odiv__class_Omod(_1087399, _1087407, _1087403) = c_Divides_Odiv__class_Omod(_1087399, _1087409, _1087403), -(c_Divides_Odiv__class_Omod(_1087399, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087399), _1087401), _1087407), _1087403) = c_Divides_Odiv__class_Omod(_1087399, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087399), _1087405), _1087409), _1087403))], (38790 ^ _779142) ^ [_1530200, _1530202, _1530204, _1530206] : [-(hAPP(c_Relation_ODomain(_1530200, _1530202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530200, _1530202), tc_HOL_Obool)), _1530204), _1530206)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530200, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530200, _1530202), _1530204)), hAPP(c_Relation_ODomain(_1530200, _1530202), _1530206)))], (49604 ^ _779142) ^ [_1781442, _1781444, _1781446] : [c_Fun_Oinj__on(_1781442, _1781444, _1781446, c_Orderings_Otop__class_Otop(tc_fun(_1781442, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781444, _1781442, c_Hilbert__Choice_Oinv__into(_1781442, _1781444, c_Orderings_Otop__class_Otop(tc_fun(_1781442, tc_HOL_Obool)), _1781446)), c_Orderings_Otop__class_Otop(tc_fun(_1781444, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781442, tc_HOL_Obool)))], (9699 ^ _779142) ^ [_944082, _944084, _944086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944082), _944084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944082), _944086)), 9706 ^ _779142 : [(9713 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944084), _944086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944084), _944082)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944086), _944082))))], (9707 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944084), _944082)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944086), _944082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944084), _944086)))]]], (41371 ^ _779142) ^ [_1594789, _1594791, _1594793] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594789)), hAPP(hAPP(c_List_Olist_OCons(_1594789), _1594791), _1594793)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594789)), _1594793)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31230 ^ _779142) ^ [_1338920, _1338922] : [class_Groups_Oordered__ab__group__add(_1338920), -(hAPP(c_Set_Oimage(_1338920, _1338920, c_Groups_Ouminus__class_Ouminus(_1338920)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338920), _1338922)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338920), hAPP(c_Groups_Ouminus__class_Ouminus(_1338920), _1338922)))], (28380 ^ _779142) ^ [_1280725, _1280727, _1280729] : [class_Complete__Lattice_Ocomplete__lattice(_1280725), 28383 ^ _779142 : [(28384 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280725), c_Complete__Lattice_OSup__class_OSup(_1280725, _1280727)), _1280729)), 28387 ^ _779142 : [(28388 ^ _779142) ^ [_1280883] : [hBOOL(hAPP(hAPP(c_member(_1280725), _1280883), _1280727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280725), _1280883), _1280729)))]]], (28394 ^ _779142) ^ [] : [28396 ^ _779142 : [(28399 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280725), 28395 ^ [_1280725, _1280727, _1280729]), _1280729))], (28397 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280725), 28395 ^ [_1280725, _1280727, _1280729]), _1280727)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280725), c_Complete__Lattice_OSup__class_OSup(_1280725, _1280727)), _1280729)))]]], (44057 ^ _779142) ^ [_1660863, _1660865, _1660867] : [class_Orderings_Olinorder(_1660863), -(c_List_Oremove1(_1660863, _1660865, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660863, _1660863, c_COMBI(_1660863)), _1660865), _1660867)) = _1660867)], (42796 ^ _779142) ^ [_1631814, _1631816, _1631818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631814), tc_List_Olist(_1631814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631814), tc_List_Olist(_1631814)), _1631816), c_List_Olist_ONil(_1631814))), c_List_Olistrel1(_1631814, _1631818)))], (2338 ^ _779142) ^ [_813321, _813323] : [_813323 = _813321, -(c_Divides_Oadjust(_813323) = c_Divides_Oadjust(_813321))], (16921 ^ _779142) ^ [_1076674, _1076676, _1076678] : [class_Orderings_Olinorder(_1076674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076674), _1076676)), 16928 ^ _779142 : [(16935 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1076674, tc_HOL_Obool)), _1076676), hAPP(hAPP(c_Set_Oinsert(_1076674), _1076678), c_Orderings_Obot__class_Obot(tc_fun(_1076674, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1076674, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1076674, c_Orderings_Oord__class_Omin(_1076674), hAPP(hAPP(c_Set_Oinsert(_1076674), _1076678), _1076676)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1076674), _1076678), c_Big__Operators_Olattice_OInf__fin(_1076674, c_Orderings_Oord__class_Omin(_1076674), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1076674, tc_HOL_Obool)), _1076676), hAPP(hAPP(c_Set_Oinsert(_1076674), _1076678), c_Orderings_Obot__class_Obot(tc_fun(_1076674, tc_HOL_Obool)))))))], (16929 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1076674, tc_HOL_Obool)), _1076676), hAPP(hAPP(c_Set_Oinsert(_1076674), _1076678), c_Orderings_Obot__class_Obot(tc_fun(_1076674, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1076674, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1076674, c_Orderings_Oord__class_Omin(_1076674), hAPP(hAPP(c_Set_Oinsert(_1076674), _1076678), _1076676)) = _1076678)]]], (8907 ^ _779142) ^ [_929448, _929450, _929452, _929454] : [c_Finite__Set_Ofolding__one(_929448, _929450, _929452), hBOOL(hAPP(c_Finite__Set_Ofinite(_929448), _929454)), -(hAPP(_929452, _929454) = hAPP(c_Finite__Set_Ofold1(_929448, _929450), _929454))], (29739 ^ _779142) ^ [_1309262, _1309264, _1309266] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309262), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309262, tc_HOL_Obool)), _1309264), _1309266))), -(hAPP(c_Finite__Set_Ocard(_1309262), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309262, tc_HOL_Obool)), _1309264), _1309266)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1309262), _1309264)), hAPP(c_Finite__Set_Ocard(_1309262), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309262, tc_HOL_Obool)), _1309264), _1309266))))], (9783 ^ _779142) ^ [_945629, _945631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945629), _945631)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945631), _945629)), _945629) = _945631)], (32527 ^ _779142) ^ [_1372499, _1372501] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372499)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372501)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1372501))), 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, _1372499))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1372499)), c_Int_Onat)))))], (45901 ^ _779142) ^ [_1702750, _1702752] : [c_List_Oupt(_1702750, _1702752) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702752), _1702750)))], (47552 ^ _779142) ^ [_1737324, _1737326] : [class_Enum_Oenum(_1737324), 47555 ^ _779142 : [(47562 ^ _779142) ^ [] : [hBOOL(hAPP(_1737326, 47563 ^ [_1737324, _1737326])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737324), _1737326)))], (47556 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737324), _1737326)), 47559 ^ _779142 : [(47560 ^ _779142) ^ [_1737450] : [-(hBOOL(hAPP(_1737326, _1737450)))]]]]], (49334 ^ _779142) ^ [_1776482, _1776484] : [c_Relation_Osym(_1776482, _1776484), -(c_Relation_Osym(tc_List_Olist(_1776482), c_List_Olistrel(_1776482, _1776484)))], (52305 ^ _779142) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (48336 ^ _779142) ^ [_1753660, _1753662, _1753664] : [_1753660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1753662), c_List_Oreplicate(_1753662, _1753660, _1753664)) = c_Orderings_Obot__class_Obot(tc_fun(_1753662, tc_HOL_Obool)))], (2328 ^ _779142) ^ [_813172, _813174, _813176, _813178] : [-(c_Divides_Odivmod__int__rel(_813178, _813174) = c_Divides_Odivmod__int__rel(_813176, _813172)), _813178 = _813176, _813174 = _813172], (46614 ^ _779142) ^ [_1716281, _1716283] : [-(hAPP(c_List_Orev(_1716281), c_List_Oconcat(_1716281, _1716283)) = c_List_Oconcat(_1716281, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1716281), tc_List_Olist(_1716281)), c_List_Orev(_1716281)), hAPP(c_List_Orev(tc_List_Olist(_1716281)), _1716283))))], (8290 ^ _779142) ^ [_917248, _917250, _917252, _917254, _917256, _917258] : [_917248 = _917250, -(hAPP(c_Fun_Ofun__upd(_917252, _917254, _917256, _917250, _917258), _917248) = _917258)], (3796 ^ _779142) ^ [_836088, _836090] : [_836090 = _836088, -(c_Enum_Oenum__class_Oenum__all(_836090) = c_Enum_Oenum__class_Oenum__all(_836088))], (21144 ^ _779142) ^ [_1150765, _1150767] : [c_Nat__Transfer_Ois__nat(_1150765), c_Nat__Transfer_Onat__set(_1150767), 21151 ^ _779142 : [(21158 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1150765)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1150767))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1150765), _1150767)))], (21152 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1150765), _1150767)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1150765)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1150767))))]]], (32761 ^ _779142) ^ [_1377385, _1377387, _1377389, _1377391, _1377393, _1377395] : [hBOOL(hAPP(hAPP(_1377385, _1377387), _1377389)), hBOOL(hAPP(hAPP(_1377391, _1377387), _1377389)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377393, tc_fun(_1377395, tc_HOL_Obool))), _1377385), _1377391), _1377387), _1377389)))], (40462 ^ _779142) ^ [_1571136, _1571138, _1571140, _1571142, _1571144] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571136, _1571136)), hAPP(hAPP(c_Product__Type_OPair(_1571136, _1571136), _1571138), _1571140)), c_Transitive__Closure_Ortrancl(_1571136, _1571142))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571136, _1571136)), hAPP(hAPP(c_Product__Type_OPair(_1571136, _1571136), _1571140), _1571144)), c_Transitive__Closure_Otrancl(_1571136, _1571142))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571136, _1571136)), hAPP(hAPP(c_Product__Type_OPair(_1571136, _1571136), _1571138), _1571144)), c_Transitive__Closure_Otrancl(_1571136, _1571142))))], (34470 ^ _779142) ^ [_1414191, _1414193, _1414195, _1414197, _1414199] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414191, tc_HOL_Obool)), _1414193), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414195, tc_fun(_1414191, tc_HOL_Obool)), _1414197), _1414199)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414195, tc_fun(_1414191, tc_HOL_Obool)), _1414197), hAPP(hAPP(c_COMBB(tc_fun(_1414191, tc_HOL_Obool), tc_fun(_1414191, tc_HOL_Obool), _1414195), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414191, tc_HOL_Obool)), _1414193)), _1414199)))], (48054 ^ _779142) ^ [_1747584, _1747586, _1747588, _1747590, _1747592] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1747584), _1747586), _1747588), _1747590), _1747592) = c_New__DSequence_Opos__single(_1747584, _1747586))], (1050 ^ _779142) ^ [_794967, _794969, _794971, _794973, _794975, _794977] : [-(c_List_Oall__interval__nat(_794975, _794971, _794967)), c_List_Oall__interval__nat(_794977, _794973, _794969), _794977 = _794975, _794973 = _794971, _794969 = _794967], (8543 ^ _779142) ^ [_922377, _922379, _922381, _922383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922377), _922379)), hBOOL(hAPP(hAPP(c_member(_922377), _922381), _922379)), hBOOL(hAPP(hAPP(c_member(_922377), _922383), _922379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_922377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922377, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922377, tc_HOL_Obool)), _922379), hAPP(hAPP(c_Set_Oinsert(_922377), _922381), c_Orderings_Obot__class_Obot(tc_fun(_922377, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_922377), _922383), c_Orderings_Obot__class_Obot(tc_fun(_922377, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_922377), _922379))))], (34623 ^ _779142) ^ [_1419195, _1419197, _1419199, _1419201, _1419203, _1419205] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419197, _1419199)), hAPP(hAPP(c_Product__Type_OPair(_1419197, _1419199), _1419203), _1419205)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419195, tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1419195, tc_HOL_Obool))), _1419201))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419195, tc_fun(_1419197, tc_fun(_1419199, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1419195, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_fun(_1419197, tc_fun(_1419199, tc_HOL_Obool)), _1419195), hAPP(c_COMBC(_1419197, tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_fun(_1419199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419199, tc_fun(tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_fun(_1419199, tc_HOL_Obool)), _1419197), c_COMBC(_1419199, tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419199, tc_prod(_1419197, _1419199)), tc_fun(_1419199, tc_fun(tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_HOL_Obool)), _1419197), hAPP(c_COMBB(tc_prod(_1419197, _1419199), tc_fun(tc_fun(tc_prod(_1419197, _1419199), tc_HOL_Obool), tc_HOL_Obool), _1419199), c_member(tc_prod(_1419197, _1419199)))), c_Product__Type_OPair(_1419197, _1419199))))), _1419201)), _1419203), _1419205)))], (49855 ^ _779142) ^ [_1787172, _1787174, _1787176, _1787178, _1787180, _1787182] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787172, _1787174, _1787176, _1787178, c_Lazy__Sequence_Olazy__sequence_OInsert(_1787174, _1787180, _1787182)) = hAPP(hAPP(hAPP(_1787178, _1787180), _1787182), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787172, _1787174, _1787176, _1787178, _1787182)))], (12918 ^ _779142) ^ [_1002675, _1002677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1002675), _1002677))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002675), _1002677)))], (10931 ^ _779142) ^ [_967860, _967862] : [class_Groups_Omonoid__add(_967860), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967860), _967862), c_Groups_Ozero__class_Ozero(_967860)) = _967862)], (680 ^ _779142) ^ [_789374, _789376, _789378, _789380, _789382, _789384] : [-(c_List_Olist__ex1(_789382, _789378, _789374)), c_List_Olist__ex1(_789384, _789380, _789376), _789384 = _789382, _789380 = _789378, _789376 = _789374], (43072 ^ _779142) ^ [_1638330, _1638332, _1638334, _1638336, _1638338] : [hAPP(hAPP(c_List_Oappend(_1638330), _1638332), _1638334) = hAPP(hAPP(c_List_Oappend(_1638330), _1638336), _1638338), 43078 ^ _779142 : [(43081 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638330), 43075 ^ [_1638330, _1638332, _1638334, _1638336, _1638338]), _1638334) = _1638338)], (43079 ^ _779142) ^ [] : [-(_1638332 = hAPP(hAPP(c_List_Oappend(_1638330), _1638336), 43075 ^ [_1638330, _1638332, _1638334, _1638336, _1638338]))]], 43082 ^ _779142 : [(43085 ^ _779142) ^ [] : [-(_1638334 = hAPP(hAPP(c_List_Oappend(_1638330), 43075 ^ [_1638330, _1638332, _1638334, _1638336, _1638338]), _1638338))], (43083 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638330), _1638332), 43075 ^ [_1638330, _1638332, _1638334, _1638336, _1638338]) = _1638336)]]], (27374 ^ _779142) ^ [_1262041, _1262043, _1262045, _1262047] : [class_Orderings_Olinorder(_1262041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262041), _1262043), _1262045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262041), _1262045), _1262047)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262041, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1262041, _1262043, _1262045)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262041, _1262045, _1262047)) = c_SetInterval_Oord__class_OatLeastAtMost(_1262041, _1262043, _1262047))], (18583 ^ _779142) ^ [_1106324, _1106326] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106324, _1106326)), _1106324)))], (11946 ^ _779142) ^ [_985176, _985178, _985180, _985182] : [class_Rings_Olinordered__semiring__strict(_985176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985176), _985178), _985180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985176), c_Groups_Ozero__class_Ozero(_985176)), _985182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985176), _985182), _985178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985176), _985182), _985180))))], (46820 ^ _779142) ^ [_1720680, _1720682, _1720684] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720680)), c_List_OtakeWhile(_1720680, _1720682, _1720684))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720680)), _1720684))))], (26992 ^ _779142) ^ [_1255438, _1255440, _1255442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1255438), _1255440)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1255440), _1255442)) = 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, _1255438), _1255440)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255440), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1255440), _1255442))))], (45969 ^ _779142) ^ [_1703903, _1703905, _1703907, _1703909] : [-(c_List_Oupt(_1703903, _1703905) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703907), _1703909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703903), _1703905)), _1703903 = _1703907, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703903), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703905) = _1703909], (42253 ^ _779142) ^ [_1620609, _1620611, _1620613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620609), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620611)), _1620613))), -(c_List_Obutlast(_1620611, hAPP(hAPP(c_List_Otake(_1620611), _1620609), _1620613)) = hAPP(hAPP(c_List_Otake(_1620611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620609), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620613))], (38798 ^ _779142) ^ [_1530385] : [-(c_Relation_Orefl__on(_1530385, c_Orderings_Obot__class_Obot(tc_fun(_1530385, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530385, _1530385), tc_HOL_Obool))))], (33083 ^ _779142) ^ [_1384515, _1384517] : [-(c_Divides_Odivmod__nat(_1384515, _1384517) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1384515), _1384517)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1384515, _1384517)))], (32395 ^ _779142) ^ [_1369316, _1369318, _1369320, _1369322] : [class_Groups_Ocomm__monoid__add(_1369316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1369318), _1369320)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369316), _1369322), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1369318, _1369320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369316), hAPP(_1369322, _1369318)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369316), _1369322), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1369318, _1369320))))], (16801 ^ _779142) ^ [_1074669, _1074671, _1074673] : [class_Orderings_Olinorder(_1074669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074669), _1074671)), -(_1074671 = c_Orderings_Obot__class_Obot(tc_fun(_1074669, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1074669, c_Orderings_Oord__class_Omin(_1074669), hAPP(hAPP(c_Set_Oinsert(_1074669), _1074673), _1074671)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074669), _1074673), c_Big__Operators_Olattice_OInf__fin(_1074669, c_Orderings_Oord__class_Omin(_1074669), _1074671)))], (27210 ^ _779142) ^ [_1259353, _1259355, _1259357] : [class_Orderings_Olinorder(_1259353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259353), _1259355), _1259357)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259353, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1259353), _1259355), c_Orderings_Obot__class_Obot(tc_fun(_1259353, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1259353, _1259355, _1259357)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259353, _1259355), _1259357))], (46640 ^ _779142) ^ [_1716942, _1716944, _1716946, _1716948, _1716950] : [c_List_Olist__all2(_1716942, _1716944, _1716946, hAPP(c_List_Orev(_1716942), _1716948), hAPP(c_List_Orev(_1716944), _1716950)), -(c_List_Olist__all2(_1716942, _1716944, _1716946, _1716948, _1716950))], (5124 ^ _779142) ^ [_857290, _857292, _857294, _857296] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_857296, _857292) = c_SetInterval_Oord__class_OatLeastLessThan(_857294, _857290)), _857296 = _857294, _857292 = _857290], (18010 ^ _779142) ^ [_1096376] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096376) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096376), c_Int_OPls)))], (11117 ^ _779142) ^ [_970657] : [class_Rings_Ozero__neq__one(_970657), c_Groups_Ozero__class_Ozero(_970657) = c_Groups_Oone__class_Oone(_970657)], (37393 ^ _779142) ^ [_1486321, _1486323, _1486325, _1486327] : [-(hAPP(c_Set_Ovimage(_1486321, _1486323, _1486325), hAPP(c_Set_OCollect(_1486323), _1486327)) = hAPP(c_Set_OCollect(_1486321), hAPP(hAPP(c_COMBB(_1486323, tc_HOL_Obool, _1486321), _1486327), _1486325)))], (4752 ^ _779142) ^ [_851418, _851420, _851422, _851424, _851426, _851428, _851430, _851432, _851434, _851436, _851438, _851440] : [-(c_Partial__Function_Ofun__lub(_851440, _851436, _851432, _851428, _851424, _851420) = c_Partial__Function_Ofun__lub(_851438, _851434, _851430, _851426, _851422, _851418)), _851440 = _851438, _851436 = _851434, _851432 = _851430, _851428 = _851426, _851424 = _851422, _851420 = _851418], (17603 ^ _779142) ^ [_1089286, _1089288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089288)), -(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, _1089286, _1089288))))], (32685 ^ _779142) ^ [_1376149, _1376151] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376149), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 32688 ^ _779142 : [(32697 ^ _779142) ^ [] : [-(c_Nitpick_Onorm__frac(_1376151, _1376149) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1376151), _1376149)), 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), _1376151))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376149)))), -(_1376151 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1376149 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32689 ^ _779142) ^ [] : [32690 ^ _779142 : [(32693 ^ _779142) ^ [] : [_1376149 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32691 ^ _779142) ^ [] : [_1376151 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1376151, _1376149) = 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)))]]], (1556 ^ _779142) ^ [_801534, _801536] : [-(class_Groups_Olinordered__ab__semigroup__add(_801534)), _801536 = _801534, class_Groups_Olinordered__ab__semigroup__add(_801536)], (24604 ^ _779142) ^ [_1211840, _1211842] : [class_Rings_Olinordered__idom(_1211840), 24607 ^ _779142 : [(24614 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211840), _1211842), c_Groups_Ozero__class_Ozero(_1211840))), -(c_Groups_Osgn__class_Osgn(_1211840, _1211842) = hAPP(c_Groups_Ouminus__class_Ouminus(_1211840), c_Groups_Oone__class_Oone(_1211840)))], (24608 ^ _779142) ^ [] : [c_Groups_Osgn__class_Osgn(_1211840, _1211842) = hAPP(c_Groups_Ouminus__class_Ouminus(_1211840), c_Groups_Oone__class_Oone(_1211840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211840), _1211842), c_Groups_Ozero__class_Ozero(_1211840))))]]], (3748 ^ _779142) ^ [_835340, _835342, _835344, _835346, _835348, _835350] : [-(c_List_OdropWhile(_835350, _835346, _835342) = c_List_OdropWhile(_835348, _835344, _835340)), _835350 = _835348, _835346 = _835344, _835342 = _835340], (20133 ^ _779142) ^ [_1132540, _1132542, _1132544] : [class_Divides_Osemiring__div(_1132540), -(_1132542 = c_Groups_Ozero__class_Ozero(_1132540)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132540), _1132544), _1132542)), _1132542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132540), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132540), _1132544), _1132542)), c_Groups_Oone__class_Oone(_1132540)))], (45983 ^ _779142) ^ [_1704144, _1704146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704144), _1704146)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1704144, _1704146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704146), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16673 ^ _779142) ^ [_1072674, _1072676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072674)), 16676 ^ _779142 : [(16685 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072674), _1072676) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1072674 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1072676 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (16677 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072674), _1072676) = c_Groups_Oone__class_Oone(tc_Int_Oint), 16680 ^ _779142 : [(16683 ^ _779142) ^ [] : [-(_1072676 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (16681 ^ _779142) ^ [] : [-(_1072674 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (43834 ^ _779142) ^ [_1655921, _1655923] : [class_Lattices_Oab__semigroup__idem__mult(_1655921), -(_1655923 = c_List_Olist_ONil(_1655921)), -(hAPP(c_Finite__Set_Ofold1(_1655921, c_Groups_Otimes__class_Otimes(_1655921)), hAPP(c_List_Oset(_1655921), _1655923)) = hAPP(c_List_Ofoldl(_1655921, _1655921, c_Groups_Otimes__class_Otimes(_1655921), hAPP(c_List_Ohd(_1655921), _1655923)), hAPP(c_List_Otl(_1655921), _1655923)))], (33453 ^ _779142) ^ [_1391059, _1391061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391059), 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)), _1391061)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391059, _1391061), c_Divides_OnegDivAlg(_1391059, _1391061))))], (14521 ^ _779142) ^ [_1032333, _1032335, _1032337, _1032339] : [class_Fields_Olinordered__field(_1032333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032333), c_Groups_Ozero__class_Ozero(_1032333)), _1032335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032333), _1032337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032333), _1032339), _1032335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032333), _1032337), _1032335)), _1032339)))], (47291 ^ _779142) ^ [_1731210, _1731212, _1731214, _1731216] : [class_Orderings_Oorder(_1731210), class_Enum_Oenum(_1731212), 47298 ^ _779142 : [(47307 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731212, _1731210)), _1731214), _1731216))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731212, _1731210)), _1731214), _1731216)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731212), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731212), c_fNot), hAPP(hAPP(c_COMBS(_1731212, _1731210, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731210, tc_fun(_1731210, tc_HOL_Obool), _1731212), c_fequal), _1731214)), _1731216))))], (47299 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731212, _1731210)), _1731214), _1731216)), 47302 ^ _779142 : [(47305 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731212), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731212), c_fNot), hAPP(hAPP(c_COMBS(_1731212, _1731210, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731210, tc_fun(_1731210, tc_HOL_Obool), _1731212), c_fequal), _1731214)), _1731216)))))], (47303 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731212, _1731210)), _1731214), _1731216)))]]]]], (25414 ^ _779142) ^ [_1225869, _1225871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1225869)), c_Int_OBit0(_1225871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225869), _1225871)))], (29163 ^ _779142) ^ [_1296274, _1296276, _1296278, _1296280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296274, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296274, tc_HOL_Obool)), _1296276), _1296278)), _1296280) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296274, tc_HOL_Obool)), _1296276), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296274, tc_HOL_Obool)), _1296278), _1296280)))], (15171 ^ _779142) ^ [_1044726, _1044728, _1044730] : [class_Int_Onumber__ring(_1044726), class_Int_Oring__char__0(_1044726), 15178 ^ _779142 : [(15185 ^ _779142) ^ [] : [_1044728 = _1044730, -(hAPP(c_Int_Onumber__class_Onumber__of(_1044726), _1044728) = hAPP(c_Int_Onumber__class_Onumber__of(_1044726), _1044730))], (15179 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1044726), _1044728) = hAPP(c_Int_Onumber__class_Onumber__of(_1044726), _1044730), -(_1044728 = _1044730)]]], (48701 ^ _779142) ^ [_1761700, _1761702, _1761704, _1761706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761700), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761702, _1761704, _1761700, _1761706) = 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(_1761702)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761702)))], (38220 ^ _779142) ^ [_1514504, _1514506] : [-(hAPP(c_Fun_Oid(_1514504), _1514506) = _1514506)], (49654 ^ _779142) ^ [_1782434, _1782436, _1782438, _1782440, _1782442] : [hBOOL(hAPP(hAPP(c_member(_1782434), _1782436), hAPP(c_Set_Oimage(_1782438, _1782434, _1782440), _1782442))), -(hAPP(_1782440, hAPP(c_Hilbert__Choice_Oinv__into(_1782438, _1782434, _1782442, _1782440), _1782436)) = _1782436)], (49660 ^ _779142) ^ [_1782567, _1782569, _1782571, _1782573, _1782575] : [hBOOL(hAPP(hAPP(c_member(_1782567), _1782569), hAPP(c_Set_Oimage(_1782571, _1782567, _1782573), _1782575))), -(hBOOL(hAPP(hAPP(c_member(_1782571), hAPP(c_Hilbert__Choice_Oinv__into(_1782571, _1782567, _1782575, _1782573), _1782569)), _1782575)))], (42902 ^ _779142) ^ [_1634110, _1634112, _1634114, _1634116, _1634118, _1634120] : [-(hAPP(c_List_Olist_Olist__case(_1634110, _1634112, _1634114, _1634116), hAPP(hAPP(c_List_Olist_OCons(_1634112), _1634118), _1634120)) = hAPP(hAPP(_1634116, _1634118), _1634120))], (10269 ^ _779142) ^ [_956527, _956529] : [class_Rings_Ocomm__semiring__1(_956527), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956527), _956529), c_Groups_Oone__class_Oone(_956527)) = _956529)], (12618 ^ _779142) ^ [_997022, _997024, _997026] : [class_Groups_Oordered__comm__monoid__add(_997022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997022), _997024), c_Groups_Ozero__class_Ozero(_997022))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997022), _997026), c_Groups_Ozero__class_Ozero(_997022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997022), _997024), _997026)), c_Groups_Ozero__class_Ozero(_997022))))], (21842 ^ _779142) ^ [_1162945, _1162947] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162945))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162945)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162947)) = 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), _1162947)))], (8016 ^ _779142) ^ [_911264, _911266, _911268, _911270, _911272, _911274] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911264, _911266, _911268, _911270, _911272), _911274)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_911264), _911272)))], (24930 ^ _779142) ^ [_1217406, _1217408] : [c_Int_Oiszero(_1217406, hAPP(c_Int_Onumber__class_Onumber__of(_1217406), c_Int_OBit1(_1217408))), class_Int_Onumber__ring(_1217406), class_Int_Oring__char__0(_1217406)], (27388 ^ _779142) ^ [_1262306, _1262308] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262306), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1262308) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1262306, _1262308))], (42810 ^ _779142) ^ [_1632326, _1632328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632326), _1632328)), -(c_List_Oupto(_1632326, _1632328) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1632326), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1632326), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1632328)))], (48985 ^ _779142) ^ [_1769546, _1769548, _1769550, _1769552] : [class_Complete__Lattice_Ocomplete__lattice(_1769546), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769548, _1769546), _1769550), _1769552) = c_Complete__Lattice_OInf__class_OInf(_1769546, hAPP(c_Set_OCollect(_1769546), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool), tc_HOL_Obool, _1769546), c_HOL_OEx(tc_fun(_1769548, _1769546))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool), tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool), _1769546), hAPP(c_COMBS(tc_fun(_1769548, _1769546), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769548, _1769546)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769548, _1769546), tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769548, _1769546))), _1769550)))), hAPP(hAPP(c_COMBC(_1769546, tc_fun(tc_fun(_1769548, _1769546), _1769546), tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769546, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769548, _1769546), _1769546), tc_fun(tc_fun(_1769548, _1769546), tc_HOL_Obool)), _1769546), c_COMBB(_1769546, tc_HOL_Obool, tc_fun(_1769548, _1769546))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769548, _1769546), _1769548, _1769546), c_COMBI(tc_fun(_1769548, _1769546))), _1769552)))))))], (50528 ^ _779142) ^ [_1802733, _1802735, _1802737, _1802739] : [-(hAPP(c_Lazy__Sequence_Obind(_1802733, _1802735, _1802737), _1802739) = c_Lazy__Sequence_Oflat(_1802735, c_Lazy__Sequence_Omap(_1802733, tc_Lazy__Sequence_Olazy__sequence(_1802735), _1802739, _1802737)))], (20969 ^ _779142) ^ [_1147899] : [-(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), _1147899)) = 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), _1147899))))], (4906 ^ _779142) ^ [_853883, _853885, _853887, _853889, _853891, _853893, _853895, _853897] : [-(c_Fun_Othe__inv__into(_853897, _853893, _853889, _853885) = c_Fun_Othe__inv__into(_853895, _853891, _853887, _853883)), _853897 = _853895, _853893 = _853891, _853889 = _853887, _853885 = _853883], (18638 ^ _779142) ^ [_1107222, _1107224] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107222), _1107224))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107222, _1107224) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1107222), _1107224), _1107224))], (41913 ^ _779142) ^ [_1611096, _1611098, _1611100] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611096, tc_HOL_Obool)), hAPP(c_List_Oset(_1611096), c_List_Osublist(_1611096, _1611098, _1611100))), hAPP(c_List_Oset(_1611096), _1611098))))], (4180 ^ _779142) ^ [_842398, _842400] : [_842400 = _842398, -(c_Orderings_Oord__class_Omin(_842400) = c_Orderings_Oord__class_Omin(_842398))], (41312 ^ _779142) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29215 ^ _779142) ^ [_1297327, _1297329, _1297331] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297327, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297327, tc_HOL_Obool)), _1297329), _1297331)), _1297331)))], (40217 ^ _779142) ^ [_1564491] : [-(c_Transitive__Closure_Otrancl(_1564491, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564491, _1564491), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564491, _1564491), tc_HOL_Obool)))], (9269 ^ _779142) ^ [_937309, _937311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937309), _937311)), -(_937311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937309), 9272 ^ [_937309, _937311]))], (15271 ^ _779142) ^ [_1046662, _1046664, _1046666, _1046668, _1046670, _1046672] : [c_Nitpick_Opair__box_OPairBox(_1046662, _1046664, _1046666, _1046668) = c_Nitpick_Opair__box_OPairBox(_1046662, _1046664, _1046670, _1046672), 15274 ^ _779142 : [(15277 ^ _779142) ^ [] : [-(_1046668 = _1046672)], (15275 ^ _779142) ^ [] : [-(_1046666 = _1046670)]]], (39854 ^ _779142) ^ [_1555652, _1555654, _1555656, _1555658, _1555660, _1555662] : [c_Finite__Set_Ofolding(_1555652, _1555654, _1555656, _1555658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555652), _1555660)), -(hAPP(_1555658, hAPP(hAPP(c_Set_Oinsert(_1555652), _1555662), _1555660)) = hAPP(c_Fun_Ocomp(_1555654, _1555654, _1555654, hAPP(_1555658, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1555652, tc_HOL_Obool)), _1555660), hAPP(hAPP(c_Set_Oinsert(_1555652), _1555662), c_Orderings_Obot__class_Obot(tc_fun(_1555652, tc_HOL_Obool)))))), hAPP(_1555656, _1555662)))], (23669 ^ _779142) ^ [_1196058] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1196058) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1196058))], (39041 ^ _779142) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (10721 ^ _779142) ^ [_964489, _964491] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964489), _964491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964491), hAPP(c_Nat_OSuc, _964489))))], (29383 ^ _779142) ^ [_1300915, _1300917, _1300919, _1300921] : [-(hBOOL(hAPP(hAPP(c_member(_1300915), _1300917), _1300919))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300915, tc_HOL_Obool)), _1300919), hAPP(hAPP(c_Set_Oinsert(_1300915), _1300917), _1300921)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300915, tc_HOL_Obool)), _1300919), _1300921))], (13243 ^ _779142) ^ [_1008775, _1008777, _1008779] : [class_Rings_Olinordered__ring__strict(_1008775), 13246 ^ _779142 : [(13255 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008775), _1008777), _1008777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008775), _1008779), _1008779))), c_Groups_Ozero__class_Ozero(_1008775)))), _1008777 = c_Groups_Ozero__class_Ozero(_1008775), _1008779 = c_Groups_Ozero__class_Ozero(_1008775)], (13247 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008775), _1008777), _1008777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008775), _1008779), _1008779))), c_Groups_Ozero__class_Ozero(_1008775))), 13250 ^ _779142 : [(13253 ^ _779142) ^ [] : [-(_1008779 = c_Groups_Ozero__class_Ozero(_1008775))], (13251 ^ _779142) ^ [] : [-(_1008777 = c_Groups_Ozero__class_Ozero(_1008775))]]]]], (29249 ^ _779142) ^ [_1298081, _1298083, _1298085, _1298087] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298081, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1298081), _1298083), _1298085)), hAPP(hAPP(c_Set_Oinsert(_1298081), _1298083), _1298087)) = hAPP(hAPP(c_Set_Oinsert(_1298081), _1298083), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298081, tc_HOL_Obool)), _1298085), _1298087)))], (52643 ^ _779142) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (51369 ^ _779142) ^ [_1817754, _1817756] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817754), _1817756)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817756), _1817754)), -(_1817754 = _1817756)], (42525 ^ _779142) ^ [_1626818, _1626820] : [class_Groups_Ocomm__monoid__add(_1626818), hBOOL(hAPP(c_List_Odistinct(_1626818), _1626820)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626818), _1626820) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626818, _1626818), c_COMBI(_1626818)), hAPP(c_List_Oset(_1626818), _1626820)))], (31577 ^ _779142) ^ [_1345818, _1345820, _1345822, _1345824, _1345826, _1345828, _1345830, _1345832] : [class_Groups_Ocomm__monoid__add(_1345818), class_Orderings_Oord(_1345820), _1345822 = _1345824, _1345826 = _1345828, 31595 ^ _779142 : [(31600 ^ _779142) ^ [] : [hAPP(_1345830, 31594 ^ [_1345818, _1345820, _1345822, _1345824, _1345826, _1345828, _1345830, _1345832]) = hAPP(_1345832, 31594 ^ [_1345818, _1345820, _1345822, _1345824, _1345826, _1345828, _1345830, _1345832])], (31598 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345820), 31594 ^ [_1345818, _1345820, _1345822, _1345824, _1345826, _1345828, _1345830, _1345832]), _1345828)))], (31596 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345820), _1345824), 31594 ^ [_1345818, _1345820, _1345822, _1345824, _1345826, _1345828, _1345830, _1345832])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345820, _1345818), _1345830), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1345820, _1345822), _1345826)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345820, _1345818), _1345832), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1345820, _1345824), _1345828)))], (25088 ^ _779142) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (45989 ^ _779142) ^ [_1704255, _1704257] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1704255, _1704257)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1704255), hAPP(c_Nat_OSuc, _1704257)))], (24445 ^ _779142) ^ [_1209258, _1209260] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1209258), _1209260)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1209260), _1209258)))], (36406 ^ _779142) ^ [_1463882, _1463884, _1463886, _1463888] : [c_Fun_Oinj__on(_1463882, _1463884, _1463886, _1463888), -(hAPP(c_Finite__Set_Ocard(_1463884), hAPP(c_Set_Oimage(_1463882, _1463884, _1463886), _1463888)) = hAPP(c_Finite__Set_Ocard(_1463882), _1463888))], (3928 ^ _779142) ^ [_838424, _838426, _838428, _838430, _838432, _838434, _838436, _838438] : [-(c_New__Random__Sequence_Opos__empty(_838438, _838434, _838430, _838426) = c_New__Random__Sequence_Opos__empty(_838436, _838432, _838428, _838424)), _838438 = _838436, _838434 = _838432, _838430 = _838428, _838426 = _838424], (21936 ^ _779142) ^ [_1164785, _1164787, _1164789] : [class_Rings_Olinordered__semidom(_1164785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164785), c_Groups_Ozero__class_Ozero(_1164785)), _1164787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164785), c_Groups_Ozero__class_Ozero(_1164785)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164785), _1164787), _1164789))))], (51749 ^ _779142) ^ [_1824168, _1824170, _1824172, _1824174] : [class_Divides_Osemiring__div(_1824168), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824168), _1824170), _1824172)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1824168), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824168), _1824172), _1824170)), _1824174) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824168), hAPP(hAPP(c_Power_Opower__class_Opower(_1824168), _1824172), _1824174)), hAPP(hAPP(c_Power_Opower__class_Opower(_1824168), _1824170), _1824174)))], (7996 ^ _779142) ^ [_910874, _910876, _910878, _910880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910874, tc_HOL_Obool)), _910876), _910878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910874, tc_HOL_Obool)), _910878), _910880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910874, tc_HOL_Obool)), _910876), _910880)))], (34346 ^ _779142) ^ [_1410477, _1410479, _1410481, _1410483] : [-(hAPP(c_Set_OPow(_1410477), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410479, tc_fun(_1410477, tc_HOL_Obool)), _1410481), _1410483)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410479, tc_fun(tc_fun(_1410477, tc_HOL_Obool), tc_HOL_Obool)), _1410481), hAPP(hAPP(c_COMBB(tc_fun(_1410477, tc_HOL_Obool), tc_fun(tc_fun(_1410477, tc_HOL_Obool), tc_HOL_Obool), _1410479), c_Set_OPow(_1410477)), _1410483)))], (19949 ^ _779142) ^ [_1129372, _1129374, _1129376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129372), _1129374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129376), 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), _1129374), _1129376)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129372), _1129376))))], (16707 ^ _779142) ^ [_1073151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1073151)), -(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)), _1073151))))], (3892 ^ _779142) ^ [_837822, _837824, _837826, _837828, _837830, _837832, _837834, _837836] : [-(c_New__DSequence_Opos__decr__bind(_837836, _837832, _837828, _837824) = c_New__DSequence_Opos__decr__bind(_837834, _837830, _837826, _837822)), _837836 = _837834, _837832 = _837830, _837828 = _837826, _837824 = _837822], (29213 ^ _779142) ^ [_1297279, _1297281, _1297283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297279, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297279, tc_HOL_Obool)), _1297281), _1297283)), _1297281)))], (36824 ^ _779142) ^ [_1472955, _1472957, _1472959, _1472961, _1472963] : [c_Fun_Oinj__on(_1472955, _1472957, _1472959, _1472961), hBOOL(hAPP(hAPP(c_member(_1472955), _1472963), _1472961)), -(hAPP(c_Fun_Othe__inv__into(_1472955, _1472957, _1472961, _1472959), hAPP(_1472959, _1472963)) = _1472963)], (38368 ^ _779142) ^ [_1518646, _1518648, _1518650, _1518652] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518646, _1518648, _1518650), _1518652), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518648, _1518650), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518646, _1518650), tc_HOL_Obool)))], (47403 ^ _779142) ^ [_1733688, _1733690] : [class_Orderings_Olinorder(_1733688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1733688), _1733690)), 47411 ^ _779142 : [(47414 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1733688, 47410 ^ [_1733688, _1733690]))], (47416 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1733688), 47410 ^ [_1733688, _1733690])))], (47418 ^ _779142) ^ [_1734014] : [-(_1734014 = 47410 ^ [_1733688, _1733690]), hAPP(c_List_Oset(_1733688), _1734014) = _1733690, c_List_Olinorder__class_Osorted(_1733688, _1734014), hBOOL(hAPP(c_List_Odistinct(_1733688), _1734014))], (47412 ^ _779142) ^ [] : [-(hAPP(c_List_Oset(_1733688), 47410 ^ [_1733688, _1733690]) = _1733690)]]], (45644 ^ _779142) ^ [_1696205, _1696207, _1696209] : [hAPP(c_List_Ofilter(_1696205, _1696207), _1696209) = _1696209, 45647 ^ _779142 : [(45648 ^ _779142) ^ [_1696296] : [hBOOL(hAPP(hAPP(c_member(_1696205), _1696296), hAPP(c_List_Oset(_1696205), _1696209))), -(hBOOL(hAPP(_1696207, _1696296)))]]], (41671 ^ _779142) ^ [_1604770, _1604772, _1604774, _1604776, _1604778, _1604780] : [c_List_Olistrelp(_1604770, _1604772, hAPP(hAPP(c_List_Olist_OCons(_1604770), _1604774), _1604776), hAPP(hAPP(c_List_Olist_OCons(_1604770), _1604778), _1604780)), 41674 ^ _779142 : [(41677 ^ _779142) ^ [] : [-(c_List_Olistrelp(_1604770, _1604772, _1604776, _1604780))], (41675 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1604772, _1604774), _1604778)))]]], (20726 ^ _779142) ^ [_1143376, _1143378, _1143380] : [_1143376 = 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), _1143376), _1143378)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143376), _1143380)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30634 ^ _779142) ^ [_1327503, _1327505, _1327507, _1327509, _1327511, _1327513] : [class_Groups_Oab__semigroup__mult(_1327503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327505), _1327507)), -(hBOOL(hAPP(hAPP(c_member(_1327505), _1327509), _1327507))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1327503, _1327505, c_Groups_Otimes__class_Otimes(_1327503)), _1327511), _1327513), hAPP(hAPP(c_Set_Oinsert(_1327505), _1327509), _1327507)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327503), hAPP(_1327511, _1327509)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1327503, _1327505, c_Groups_Otimes__class_Otimes(_1327503)), _1327511), _1327513), _1327507)))], (22731 ^ _779142) ^ [_1179592] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1179592))))], (52481 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (33195 ^ _779142) ^ [_1386698, _1386700] : [-(_1386698 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1386700, _1386698) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1386700), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1386698)))], (19765 ^ _779142) ^ [_1126460, _1126462] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126460), _1126462) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1126462 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19774 ^ _779142 : [(19777 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126460), _1126462)))], (19775 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126460)))]], 19778 ^ _779142 : [(19781 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126462), _1126460)))], (19779 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126460), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (44907 ^ _779142) ^ [_1679244, _1679246, _1679248] : [-(c_List_Olistsp(_1679244, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1679244, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1679244, tc_fun(_1679244, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679244)), _1679246)), hAPP(hAPP(c_COMBC(_1679244, tc_fun(_1679244, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679244)), _1679248))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1679244), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679244), tc_fun(tc_List_Olist(_1679244), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679244))), c_List_Olists(_1679244, _1679246))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679244), tc_fun(tc_List_Olist(_1679244), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679244))), c_List_Olists(_1679244, _1679248))))], (41431 ^ _779142) ^ [_1596913, _1596915, _1596917, _1596919, _1596921, _1596923] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596913), tc_List_Olist(_1596913))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596913), tc_List_Olist(_1596913)), hAPP(hAPP(c_List_Olist_OCons(_1596913), _1596915), _1596917)), hAPP(hAPP(c_List_Olist_OCons(_1596913), _1596919), _1596921))), c_List_Olexord(_1596913, _1596923)))), 41432 ^ _779142 : [(41435 ^ _779142) ^ [] : [_1596915 = _1596919, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596913), tc_List_Olist(_1596913))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596913), tc_List_Olist(_1596913)), _1596917), _1596921)), c_List_Olexord(_1596913, _1596923)))], (41433 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596913, _1596913)), hAPP(hAPP(c_Product__Type_OPair(_1596913, _1596913), _1596915), _1596919)), _1596923))]]], (8825 ^ _779142) ^ [_927820, _927822, _927824] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927820), _927822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927820, tc_HOL_Obool)), _927824), _927822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_927820), _927824)), hAPP(c_Finite__Set_Ocard(_927820), _927822))))], (31150 ^ _779142) ^ [_1337525, _1337527, _1337529] : [class_Orderings_Olinorder(_1337525), 31153 ^ _779142 : [(31160 ^ _779142) ^ [] : [_1337527 = _1337529, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337525), _1337527) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337525), _1337529))], (31154 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337525), _1337527) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337525), _1337529), -(_1337527 = _1337529)]]], (9917 ^ _779142) ^ [_948428, _948430, _948432, _948434] : [class_Rings_Ocomm__semiring(_948428), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948428), _948430), _948432)), _948434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948428), _948430), _948434)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948428), _948432), _948434)))], (37725 ^ _779142) ^ [_1495216, _1495218, _1495220, _1495222, _1495224, _1495226, _1495228] : [class_Groups_Ocomm__monoid__add(_1495216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495218), _1495220)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495222), _1495224)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495218, _1495216), hAPP(hAPP(c_COMBS(_1495218, tc_fun(_1495222, tc_HOL_Obool), _1495216), hAPP(hAPP(c_COMBB(tc_fun(_1495222, _1495216), tc_fun(tc_fun(_1495222, tc_HOL_Obool), _1495216), _1495218), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495222, _1495216)), _1495226)), hAPP(hAPP(c_COMBB(tc_fun(_1495222, tc_HOL_Obool), tc_fun(_1495222, tc_HOL_Obool), _1495218), c_Set_OCollect(_1495222)), hAPP(hAPP(c_COMBB(tc_fun(_1495222, tc_HOL_Obool), tc_fun(_1495222, tc_HOL_Obool), _1495218), hAPP(c_COMBS(_1495222, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495222), c_fconj), hAPP(hAPP(c_COMBC(_1495222, tc_fun(_1495222, tc_HOL_Obool), tc_HOL_Obool), c_member(_1495222)), _1495224)))), _1495228)))), _1495220) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495222, _1495216), hAPP(hAPP(c_COMBS(_1495222, tc_fun(_1495218, tc_HOL_Obool), _1495216), hAPP(hAPP(c_COMBB(tc_fun(_1495218, _1495216), tc_fun(tc_fun(_1495218, tc_HOL_Obool), _1495216), _1495222), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495218, _1495216)), hAPP(c_COMBC(_1495218, _1495222, _1495216), _1495226))), hAPP(hAPP(c_COMBB(tc_fun(_1495218, tc_HOL_Obool), tc_fun(_1495218, tc_HOL_Obool), _1495222), c_Set_OCollect(_1495218)), hAPP(hAPP(c_COMBB(tc_fun(_1495218, tc_HOL_Obool), tc_fun(_1495218, tc_HOL_Obool), _1495222), hAPP(c_COMBS(_1495218, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495218), c_fconj), hAPP(hAPP(c_COMBC(_1495218, tc_fun(_1495218, tc_HOL_Obool), tc_HOL_Obool), c_member(_1495218)), _1495220)))), hAPP(c_COMBC(_1495218, _1495222, tc_HOL_Obool), _1495228))))), _1495224))], (20161 ^ _779142) ^ [_1133171, _1133173, _1133175] : [class_Divides_Osemiring__div(_1133171), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133171), _1133173), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133171), _1133175), _1133173))), c_Divides_Odiv__class_Omod(_1133171, _1133175, _1133173)) = _1133175)], (40138 ^ _779142) ^ [_1562748, _1562750] : [-(c_Wellfounded_Owf(_1562748, _1562750)), 40141 ^ _779142 : [(40144 ^ _779142) ^ [_1562968] : [hBOOL(hAPP(hAPP(c_member(_1562748), _1562968), 40139 ^ [_1562748, _1562750])), 40148 ^ _779142 : [(40151 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562748), 40147 ^ [_1562748, _1562750, _1562968]), 40139 ^ [_1562748, _1562750])))], (40149 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562748, _1562748)), hAPP(hAPP(c_Product__Type_OPair(_1562748, _1562748), 40147 ^ [_1562748, _1562750, _1562968]), _1562968)), _1562750)))]]], (40142 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562748), 40140 ^ [_1562748, _1562750]), 40139 ^ [_1562748, _1562750])))]]], (4778 ^ _779142) ^ [_851903, _851905, _851907, _851909, _851911, _851913] : [-(c_Relation_Orel__comp(_851913, _851909, _851905) = c_Relation_Orel__comp(_851911, _851907, _851903)), _851913 = _851911, _851909 = _851907, _851905 = _851903], (44634 ^ _779142) ^ [_1673283, _1673285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673283)), hAPP(c_Code__Numeral_Oof__nat, _1673285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673283), _1673285)))], (854 ^ _779142) ^ [_791885, _791887, _791889, _791891] : [-(c_Equiv__Relations_Opart__equivp(_791889, _791885)), c_Equiv__Relations_Opart__equivp(_791891, _791887), _791891 = _791889, _791887 = _791885], (26148 ^ _779142) ^ [_1238721, _1238723, _1238725] : [class_Rings_Ocomm__semiring__1(_1238721), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1238721), _1238723), 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)))), _1238725))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238721), _1238723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238721), hAPP(hAPP(c_Power_Opower__class_Opower(_1238721), _1238723), _1238725)), hAPP(hAPP(c_Power_Opower__class_Opower(_1238721), _1238723), _1238725))))], (26704 ^ _779142) ^ [_1249568, _1249570] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249568, tc_HOL_Obool)), _1249570), _1249570) = _1249570)], (6455 ^ _779142) ^ [_882485, _882487, _882489, _882491] : [class_Orderings_Oord(_882485), 6458 ^ _779142 : [(6465 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882485), hAPP(_882489, 6466 ^ [_882485, _882487, _882489, _882491])), hAPP(_882491, 6466 ^ [_882485, _882487, _882489, _882491]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882487, _882485)), _882489), _882491)))], (6459 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882487, _882485)), _882489), _882491)), 6462 ^ _779142 : [(6463 ^ _779142) ^ [_882642] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882485), hAPP(_882489, _882642)), hAPP(_882491, _882642))))]]]]], (16144 ^ _779142) ^ [_1062796, _1062798, _1062800] : [class_Orderings_Olinorder(_1062796), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062796), _1062798)), -(_1062798 = c_Orderings_Obot__class_Obot(tc_fun(_1062796, tc_HOL_Obool))), 16155 ^ _779142 : [(16165 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062796), hAPP(c_Finite__Set_Ofold1(_1062796, c_Orderings_Oord__class_Omin(_1062796)), _1062798)), _1062800))), 16166 ^ _779142 : [(16167 ^ _779142) ^ [_1063185] : [hBOOL(hAPP(hAPP(c_member(_1062796), _1063185), _1062798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062796), _1063185), _1062800))]]], (16156 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062796), hAPP(c_Finite__Set_Ofold1(_1062796, c_Orderings_Oord__class_Omin(_1062796)), _1062798)), _1062800)), 16160 ^ _779142 : [(16163 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062796), 16159 ^ [_1062796, _1062798, _1062800]), _1062800)))], (16161 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062796), 16159 ^ [_1062796, _1062798, _1062800]), _1062798)))]]]]], (51637 ^ _779142) ^ [_1822168] : [_1822168 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822168), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45624 ^ _779142) ^ [_1695628, _1695630] : [-(c_List_Oconcat(_1695628, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695628), tc_List_Olist(_1695628)), c_List_Olist_Olist__case(tc_List_Olist(_1695628), _1695628, c_List_Olist_ONil(_1695628), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695628), tc_fun(tc_List_Olist(_1695628), tc_List_Olist(_1695628)), _1695628), c_COMBK(tc_List_Olist(_1695628), tc_List_Olist(_1695628))), hAPP(hAPP(c_COMBC(_1695628, tc_List_Olist(_1695628), tc_List_Olist(_1695628)), c_List_Olist_OCons(_1695628)), c_List_Olist_ONil(_1695628))))), _1695630)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695628), _1695628), c_List_Ohd(_1695628)), hAPP(c_List_Ofilter(tc_List_Olist(_1695628), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695628)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695628), tc_List_Olist(_1695628), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695628)))), _1695630)))], (43788 ^ _779142) ^ [_1654956] : [-(hAPP(c_List_Otl(_1654956), c_List_Olist_ONil(_1654956)) = c_List_Olist_ONil(_1654956))], (29915 ^ _779142) ^ [_1313055, _1313057, _1313059] : [class_Lattices_Olattice(_1313055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313055), _1313057)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313055), _1313059)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313055, tc_HOL_Obool)), _1313057), _1313059) = c_Orderings_Obot__class_Obot(tc_fun(_1313055, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1313055), c_Big__Operators_Olattice__class_OSup__fin(_1313055, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313055, tc_HOL_Obool)), _1313057), _1313059))), c_Big__Operators_Olattice__class_OSup__fin(_1313055, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313055, tc_HOL_Obool)), _1313057), _1313059))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1313055), c_Big__Operators_Olattice__class_OSup__fin(_1313055, _1313057)), c_Big__Operators_Olattice__class_OSup__fin(_1313055, _1313059)))], (52425 ^ _779142) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52371 ^ _779142) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (25722 ^ _779142) ^ [_1231220, _1231222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1231220)), c_Int_OBit0(_1231222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231220), _1231222)))], (44781 ^ _779142) ^ [_1676440] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676440)) = _1676440)], (25710 ^ _779142) ^ [_1230997, _1230999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1230997)), c_Int_OBit0(_1230999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230997), _1230999)))], (44869 ^ _779142) ^ [_1677911, _1677913] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1677911), _1677913) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1677911, 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)))), _1677913))))], (20782 ^ _779142) ^ [_1144409, _1144411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1144409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144411), _1144409)), _1144411)))], (3762 ^ _779142) ^ [_835561, _835563] : [_835563 = _835561, -(c_List_Odistinct(_835563) = c_List_Odistinct(_835561))], (1916 ^ _779142) ^ [_806034, _806036] : [-(class_Groups_Oone(_806034)), _806036 = _806034, class_Groups_Oone(_806036)], (2126 ^ _779142) ^ [_810061, _810063, _810065, _810067] : [-(c_SMT_Oz3div(_810067, _810063) = c_SMT_Oz3div(_810065, _810061)), _810067 = _810065, _810063 = _810061], (9455 ^ _779142) ^ [_940301, _940303, _940305] : [class_Rings_Olinordered__semidom(_940301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940301), c_Groups_Oone__class_Oone(_940301)), _940303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940301), c_Groups_Oone__class_Oone(_940301)), _940305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940301), c_Groups_Oone__class_Oone(_940301)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940301), _940303), _940305))))], (52653 ^ _779142) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (36712 ^ _779142) ^ [_1470435, _1470437, _1470439, _1470441, _1470443] : [c_Fun_Oinj__on(_1470435, _1470437, _1470439, _1470441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470437, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470435, _1470437, _1470439), _1470441)), _1470443)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470437), _1470443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470435), _1470441)), hAPP(c_Finite__Set_Ocard(_1470437), _1470443))))], (18885 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (23491 ^ _779142) ^ [_1192896, _1192898] : [class_Rings_Ocomm__ring__1(_1192896), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1192896), _1192898) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192896), hAPP(c_Groups_Ouminus__class_Ouminus(_1192896), c_Groups_Oone__class_Oone(_1192896))), _1192898))], (28793 ^ _779142) ^ [_1288637, _1288639, _1288641, _1288643] : [hBOOL(hAPP(hAPP(c_member(_1288637), _1288639), _1288641)), hBOOL(hAPP(hAPP(c_member(_1288637), _1288639), _1288643)), -(hBOOL(hAPP(hAPP(c_member(_1288637), _1288639), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288637, tc_HOL_Obool)), _1288641), _1288643))))], (34147 ^ _779142) ^ [_1405440, _1405442, _1405444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1405440, 34148 ^ [_1405440, _1405442, _1405444])), hAPP(_1405442, 34148 ^ [_1405440, _1405442, _1405444]))), -(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), _1405442), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405444))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1405440), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405444))) = 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)), _1405442)), _1405440)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405444)))], (17373 ^ _779142) ^ [_1084790, _1084792] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1084790), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1084792)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1084790), _1084792)))], (26322 ^ _779142) ^ [_1241983, _1241985, _1241987, _1241989] : [26323 ^ _779142 : [(26326 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1241983), _1241985), _1241989))], (26324 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1241983), _1241985), _1241987))]], -(hBOOL(hAPP(hAPP(c_member(_1241983), _1241985), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241983, tc_HOL_Obool)), _1241989), _1241987))))], (51431 ^ _779142) ^ [_1818753, _1818755] : [_1818753 = _1818755, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818753), _1818755)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818755), _1818753)))], (10489 ^ _779142) ^ [_960762, _960764] : [class_Groups_Ozero(_960762), 10492 ^ _779142 : [(10499 ^ _779142) ^ [] : [_960764 = c_Groups_Ozero__class_Ozero(_960762), -(c_Groups_Ozero__class_Ozero(_960762) = _960764)], (10493 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_960762) = _960764, -(_960764 = c_Groups_Ozero__class_Ozero(_960762))]]], (25360 ^ _779142) ^ [_1224824, _1224826] : [-(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), _1224824)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1224826)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1224824))) = 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), _1224826)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1224824)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52699 ^ _779142) ^ [_1836883, _1836885] : [_1836883 = _1836885, -(hBOOL(hAPP(hAPP(c_fequal, _1836883), _1836885)))], (11179 ^ _779142) ^ [_971466] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971466)))], (27076 ^ _779142) ^ [_1256937, _1256939, _1256941] : [class_Lattices_Oab__semigroup__idem__mult(_1256937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256937), _1256939)), -(_1256939 = c_Orderings_Obot__class_Obot(tc_fun(_1256937, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256937), _1256941)), -(_1256941 = c_Orderings_Obot__class_Obot(tc_fun(_1256937, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1256937, c_Groups_Otimes__class_Otimes(_1256937)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256937, tc_HOL_Obool)), _1256939), _1256941)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256937), hAPP(c_Finite__Set_Ofold1(_1256937, c_Groups_Otimes__class_Otimes(_1256937)), _1256939)), hAPP(c_Finite__Set_Ofold1(_1256937, c_Groups_Otimes__class_Otimes(_1256937)), _1256941)))], (35480 ^ _779142) ^ [_1442371, _1442373, _1442375, _1442377, _1442379] : [hBOOL(hAPP(hAPP(c_member(_1442371), _1442373), hAPP(c_Relation_OImage(_1442375, _1442371, _1442377), _1442379))), 35484 ^ _779142 : [(35487 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442375, _1442371)), hAPP(hAPP(c_Product__Type_OPair(_1442375, _1442371), 35483 ^ [_1442371, _1442373, _1442375, _1442377, _1442379]), _1442373)), _1442377)))], (35485 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442375), 35483 ^ [_1442371, _1442373, _1442375, _1442377, _1442379]), _1442379)))]]], (13269 ^ _779142) ^ [_1009249] : [-(hAPP(c_Nat_OSuc, _1009249) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1009249))], (44837 ^ _779142) ^ [_1677376, _1677378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677376)), hAPP(c_Code__Numeral_Onat__of, _1677378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677376), _1677378)))], (51211 ^ _779142) ^ [_1815241, _1815243] : [_1815241 = _1815243, 51214 ^ _779142 : [(51217 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815243), _1815241)))], (51215 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815241), _1815243)))]]], (39508 ^ _779142) ^ [_1547726, _1547728, _1547730, _1547732] : [c_Finite__Set_Ofun__left__comm__idem(_1547726, _1547728, _1547730), -(hAPP(c_Fun_Ocomp(_1547728, _1547728, _1547728, hAPP(_1547730, _1547732)), hAPP(_1547730, _1547732)) = hAPP(_1547730, _1547732))], (19595 ^ _779142) ^ [_1123470, _1123472, _1123474] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123470), _1123472)), _1123474) = 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), _1123470), _1123474)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1123472), _1123474))), 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, _1123470, _1123474)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1123472, _1123474))), _1123474)))], (52429 ^ _779142) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (33171 ^ _779142) ^ [_1386241, _1386243, _1386245, _1386247, _1386249, _1386251] : [-(hAPP(c_Product__Type_Oapsnd(_1386241, _1386243, _1386245, _1386247), hAPP(hAPP(c_Product__Type_OPair(_1386245, _1386241), _1386249), _1386251)) = hAPP(hAPP(c_Product__Type_OPair(_1386245, _1386243), _1386249), hAPP(_1386247, _1386251)))], (28767 ^ _779142) ^ [_1288146, _1288148, _1288150, _1288152] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288146, tc_HOL_Obool)), _1288148), _1288150), _1288152)), 28770 ^ _779142 : [(28773 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1288150, _1288152)))], (28771 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1288148, _1288152)))]]], (9302 ^ _779142) ^ [_937819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937819), _937819)))], (44871 ^ _779142) ^ [_1677949, _1677951, _1677953, _1677955, _1677957] : [c_List_Opartition(_1677949, _1677951, _1677953) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677949), tc_List_Olist(_1677949)), _1677955), _1677957), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1677949, tc_HOL_Obool)), hAPP(c_List_Oset(_1677949), _1677955)), hAPP(c_List_Oset(_1677949), _1677957)) = hAPP(c_List_Oset(_1677949), _1677953))], (9276 ^ _779142) ^ [_937416, _937418] : [9277 ^ _779142 : [(9278 ^ _779142) ^ [_937466] : [_937418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937416), _937466)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937416), _937418)))], (40336 ^ _779142) ^ [_1568083, _1568085] : [-(c_Transitive__Closure_Otrancl(_1568083, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568083, _1568083), tc_HOL_Obool)), _1568085), c_Relation_OId(_1568083))) = c_Transitive__Closure_Ortrancl(_1568083, _1568085))], (37277 ^ _779142) ^ [_1483392, _1483394, _1483396, _1483398] : [-(hAPP(c_Set_Oimage(_1483392, _1483394, _1483396), hAPP(c_Set_Ovimage(_1483392, _1483394, _1483396), _1483398)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483394, tc_HOL_Obool)), _1483398), hAPP(c_Set_Oimage(_1483392, _1483394, _1483396), c_Orderings_Otop__class_Otop(tc_fun(_1483392, tc_HOL_Obool)))))], (41357 ^ _779142) ^ [_1594514, _1594516, _1594518, _1594520, _1594522] : [-(hAPP(hAPP(c_List_Olist_OCons(_1594514), _1594516), _1594518) = hAPP(hAPP(c_List_Olist_OCons(_1594514), _1594520), _1594522)), _1594516 = _1594520, _1594518 = _1594522], (26968 ^ _779142) ^ [_1254946, _1254948, _1254950, _1254952] : [class_Lattices_Osemilattice__sup(_1254946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254946), _1254948)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1254946, _1254946, c_Lattices_Osemilattice__sup__class_Osup(_1254946)), _1254950), hAPP(hAPP(c_Set_Oinsert(_1254946), _1254952), _1254948)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254946), _1254952), hAPP(hAPP(c_Finite__Set_Ofold(_1254946, _1254946, c_Lattices_Osemilattice__sup__class_Osup(_1254946)), _1254950), _1254948)))], (48973 ^ _779142) ^ [_1768660, _1768662, _1768664, _1768666] : [class_Complete__Lattice_Ocomplete__lattice(_1768660), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768662, _1768660), _1768664), _1768666) = c_Complete__Lattice_OSup__class_OSup(_1768660, hAPP(c_Set_OCollect(_1768660), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool), tc_HOL_Obool, _1768660), c_HOL_OEx(tc_fun(_1768662, _1768660))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool), tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool), _1768660), hAPP(c_COMBS(tc_fun(_1768662, _1768660), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768662, _1768660)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768662, _1768660), tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768662, _1768660))), _1768664)))), hAPP(hAPP(c_COMBC(_1768660, tc_fun(tc_fun(_1768662, _1768660), _1768660), tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768660, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768662, _1768660), _1768660), tc_fun(tc_fun(_1768662, _1768660), tc_HOL_Obool)), _1768660), c_COMBB(_1768660, tc_HOL_Obool, tc_fun(_1768662, _1768660))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768662, _1768660), _1768662, _1768660), c_COMBI(tc_fun(_1768662, _1768660))), _1768666)))))))], (28717 ^ _779142) ^ [_1287035, _1287037, _1287039] : [class_Orderings_Olinorder(_1287035), hAPP(_1287037, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287035), 28722 ^ [_1287035, _1287037, _1287039]), 28723 ^ [_1287035, _1287037, _1287039])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287035), hAPP(_1287037, 28722 ^ [_1287035, _1287037, _1287039])), hAPP(_1287037, 28723 ^ [_1287035, _1287037, _1287039])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287035), _1287039)), -(_1287039 = c_Orderings_Obot__class_Obot(tc_fun(_1287035, tc_HOL_Obool))), -(hAPP(_1287037, c_Big__Operators_Olattice_OSup__fin(_1287035, c_Orderings_Oord__class_Omax(_1287035), _1287039)) = c_Big__Operators_Olattice_OSup__fin(_1287035, c_Orderings_Oord__class_Omax(_1287035), hAPP(c_Set_Oimage(_1287035, _1287035, _1287037), _1287039)))], (18901 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30776 ^ _779142) ^ [_1330562, _1330564] : [-(hBOOL(hAPP(hAPP(c_member(_1330562), _1330564), c_Orderings_Otop__class_Otop(tc_fun(_1330562, tc_HOL_Obool)))))], (35011 ^ _779142) ^ [_1429612, _1429614, _1429616, _1429618, _1429620] : [-(_1429612 = c_Orderings_Obot__class_Obot(tc_fun(_1429614, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429616, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429614, tc_fun(_1429616, tc_HOL_Obool)), _1429612), _1429618)), _1429620) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429614, tc_fun(_1429616, tc_HOL_Obool)), _1429612), hAPP(hAPP(c_COMBC(_1429614, tc_fun(_1429616, tc_HOL_Obool), tc_fun(_1429616, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429616, tc_HOL_Obool), tc_fun(tc_fun(_1429616, tc_HOL_Obool), tc_fun(_1429616, tc_HOL_Obool)), _1429614), c_Groups_Ominus__class_Ominus(tc_fun(_1429616, tc_HOL_Obool))), _1429618)), _1429620)))], (39556 ^ _779142) ^ [_1548828, _1548830, _1548832, _1548834, _1548836, _1548838, _1548840, _1548842, _1548844, _1548846, _1548848] : [-(hAPP(c_Product__Type_Omap__pair(_1548828, _1548830, _1548832, _1548834, _1548836, _1548838), hAPP(c_Product__Type_Omap__pair(_1548840, _1548828, _1548842, _1548832, _1548844, _1548846), _1548848)) = hAPP(c_Product__Type_Omap__pair(_1548840, _1548830, _1548842, _1548834, hAPP(c_Fun_Ocomp(_1548828, _1548830, _1548840, _1548836), _1548844), hAPP(c_Fun_Ocomp(_1548832, _1548834, _1548842, _1548838), _1548846)), _1548848))], (37295 ^ _779142) ^ [_1483777, _1483779, _1483781, _1483783] : [hBOOL(hAPP(hAPP(c_member(_1483777), _1483779), _1483781)), -(hAPP(c_Set_Ovimage(_1483783, _1483777, hAPP(c_COMBK(_1483777, _1483783), _1483779)), _1483781) = c_Orderings_Otop__class_Otop(tc_fun(_1483783, tc_HOL_Obool)))], (21756 ^ _779142) ^ [_1161276, _1161278, _1161280, _1161282] : [class_Groups_Ocomm__monoid__add(_1161276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161278), _1161280)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1161276), _1161282), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161278, _1161280)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161276), hAPP(_1161282, _1161278)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1161276), _1161282), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1161278), _1161280))))], (48925 ^ _779142) ^ [_1767131, _1767133, _1767135] : [-(c_List_Olist__ex(_1767131, _1767135, _1767133)), 48926 ^ _779142 : [(48927 ^ _779142) ^ [_1767188] : [hBOOL(hAPP(hAPP(c_member(_1767131), _1767188), hAPP(c_List_Oset(_1767131), _1767133))), hBOOL(hAPP(_1767135, _1767188))]]], (13472 ^ _779142) ^ [_1013333, _1013335, _1013337, _1013339, _1013341] : [class_Groups_Ocomm__monoid__add(_1013333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013335), _1013337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013335, tc_HOL_Obool)), _1013339), _1013337)), 13486 ^ _779142 : [(13489 ^ _779142) ^ [] : [hAPP(_1013341, 13485 ^ [_1013333, _1013335, _1013337, _1013339, _1013341]) = c_Groups_Ozero__class_Ozero(_1013333)], (13487 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013335), 13485 ^ [_1013333, _1013335, _1013337, _1013339, _1013341]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013335, tc_HOL_Obool)), _1013337), _1013339))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013335, _1013333), _1013341), _1013337) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013335, _1013333), _1013341), _1013339))], (50349 ^ _779142) ^ [_1797131, _1797133, _1797135, _1797137] : [c_Equiv__Relations_Oequivp(_1797131, _1797133), -(c_Quotient_OBabs(_1797131, _1797135, c_Quotient_ORespects(_1797131, _1797133), _1797137) = _1797137)], (45484 ^ _779142) ^ [_1691832, _1691834, _1691836] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1691832), tc_List_Olist(_1691832), c_List_Oappend(_1691832), _1691834), _1691836) = hAPP(hAPP(c_List_Oappend(_1691832), _1691834), c_List_Oconcat(_1691832, _1691836)))], (30868 ^ _779142) ^ [_1332272] : [class_Complete__Lattice_Ocomplete__lattice(_1332272), -(c_Complete__Lattice_OSup__class_OSup(_1332272, c_Orderings_Otop__class_Otop(tc_fun(_1332272, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1332272))], (41951 ^ _779142) ^ [_1611913, _1611915, _1611917] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611913)), hAPP(hAPP(c_List_Otake(_1611913), _1611915), _1611917)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611913)), _1611917)), _1611915))], (4936 ^ _779142) ^ [_854354, _854356] : [_854356 = _854354, -(c_Lattices_Osemilattice__sup__class_Osup(_854356) = c_Lattices_Osemilattice__sup__class_Osup(_854354))], (52453 ^ _779142) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (17545 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (29427 ^ _779142) ^ [_1302120, _1302122] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302120, tc_HOL_Obool)), _1302122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302120, tc_HOL_Obool)), _1302122)) = c_Orderings_Obot__class_Obot(tc_fun(_1302120, tc_HOL_Obool)))], (25492 ^ _779142) ^ [_1227193] : [c_Int_OBit0(_1227193) = c_Int_OMin], (52721 ^ _779142) ^ [_1837125, _1837127] : [hBOOL(_1837125), hBOOL(_1837127), -(hBOOL(hAPP(hAPP(c_fconj, _1837125), _1837127)))], (42674 ^ _779142) ^ [_1629672, _1629674] : [-(c_List_Oremove1(_1629672, _1629674, c_List_Olist_ONil(_1629672)) = c_List_Olist_ONil(_1629672))], (49119 ^ _779142) ^ [_1772167, _1772169, _1772171, _1772173] : [-(c_Wellfounded_Omax__extp(_1772167, _1772169, _1772171, _1772173)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772167), _1772171)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772167), _1772173)), -(_1772173 = c_Orderings_Obot__class_Obot(tc_fun(_1772167, tc_HOL_Obool))), 49133 ^ _779142 : [(49136 ^ _779142) ^ [_1772512] : [hBOOL(hAPP(hAPP(c_member(_1772167), _1772512), _1772173)), hBOOL(hAPP(hAPP(_1772169, 49132 ^ [_1772167, _1772169, _1772171, _1772173]), _1772512))], (49134 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772167), 49132 ^ [_1772167, _1772169, _1772171, _1772173]), _1772171)))]]], (10141 ^ _779142) ^ [_953613, _953615, _953617, _953619] : [class_Rings_Ocomm__semiring__1(_953613), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953613), _953615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953613), _953617), _953619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953613), _953615), _953617)), _953619))], (38995 ^ _779142) ^ [_1535280, _1535282, _1535284, _1535286, _1535288] : [hBOOL(hAPP(hAPP(_1535280, _1535282), _1535284)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1535286, _1535288, _1535280), _1535282)))], (40265 ^ _779142) ^ [_1565655, _1565657, _1565659, _1565661, _1565663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565655, _1565655)), hAPP(hAPP(c_Product__Type_OPair(_1565655, _1565655), _1565657), _1565659)), _1565661)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565655, _1565655)), hAPP(hAPP(c_Product__Type_OPair(_1565655, _1565655), _1565659), _1565663)), _1565661)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565655, _1565655)), hAPP(hAPP(c_Product__Type_OPair(_1565655, _1565655), _1565657), _1565663)), c_Transitive__Closure_Otrancl(_1565655, _1565661))))], (50150 ^ _779142) ^ [_1793084] : [-(c_Fun_Obij__betw(_1793084, _1793084, c_Fun_Oid(_1793084), c_Orderings_Otop__class_Otop(tc_fun(_1793084, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793084, tc_HOL_Obool))))], (33269 ^ _779142) ^ [_1388070, _1388072, _1388074, _1388076, _1388078] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1388070, _1388072), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1388074), _1388076))), -(_1388072 = 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)), _1388078)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1388070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388072), _1388078)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1388074), _1388078)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388072), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1388074, _1388078))), _1388076)))))], (52377 ^ _779142) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (34158 ^ _779142) ^ [_1405840, _1405842, _1405844, _1405846, _1405848, _1405850] : [hAPP(c_Product__Type_Oapfst(_1405840, _1405842, _1405844, _1405846), _1405848) = hAPP(c_Product__Type_Oapfst(_1405840, _1405842, _1405844, _1405850), _1405848), -(hAPP(_1405846, hAPP(c_Product__Type_Ofst(_1405840, _1405844), _1405848)) = hAPP(_1405850, hAPP(c_Product__Type_Ofst(_1405840, _1405844), _1405848)))], (32301 ^ _779142) ^ [_1367141, _1367143, _1367145] : [hBOOL(hAPP(c_Predicate_OPowp(_1367141, hAPP(hAPP(c_COMBC(_1367141, tc_fun(_1367141, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367141)), _1367143)), _1367145)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1367141, tc_HOL_Obool)), _1367145), hAPP(c_Set_OPow(_1367141), _1367143))))], (20378 ^ _779142) ^ [_1136753, _1136755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136753)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136753), _1136755)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1136753)), hAPP(c_Int_Onat, _1136755)))], (47831 ^ _779142) ^ [_1742846, _1742848, _1742850] : [c_List_Olist__all(_1742846, _1742848, _1742850), 47834 ^ _779142 : [(47835 ^ _779142) ^ [_1742927] : [hBOOL(hAPP(hAPP(c_member(_1742846), _1742927), hAPP(c_List_Oset(_1742846), _1742850))), -(hBOOL(hAPP(_1742848, _1742927)))]]], (40630 ^ _779142) ^ [_1575102, _1575104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1575102), _1575104)), -(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), _1575102), _1575104)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (44819 ^ _779142) ^ [_1677064, _1677066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677064)), hAPP(c_Code__Numeral_Onat__of, _1677066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1677064), _1677066)))], (23067 ^ _779142) ^ [_1185121, _1185123, _1185125] : [class_Groups_Oordered__ab__group__add(_1185121), 23070 ^ _779142 : [(23077 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185121), _1185125), _1185123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185121), hAPP(c_Groups_Ouminus__class_Ouminus(_1185121), _1185123)), hAPP(c_Groups_Ouminus__class_Ouminus(_1185121), _1185125))))], (23071 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185121), hAPP(c_Groups_Ouminus__class_Ouminus(_1185121), _1185123)), hAPP(c_Groups_Ouminus__class_Ouminus(_1185121), _1185125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185121), _1185125), _1185123)))]]], (48213 ^ _779142) ^ [_1751439, _1751441, _1751443, _1751445] : [48220 ^ _779142 : [(48223 ^ _779142) ^ [] : [_1751441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48221 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1751445, _1751443)))]], 48214 ^ _779142 : [(48215 ^ _779142) ^ [_1751511] : [hBOOL(hAPP(hAPP(c_member(_1751439), _1751511), hAPP(c_List_Oset(_1751439), c_List_Oreplicate(_1751439, _1751441, _1751443)))), hBOOL(hAPP(_1751445, _1751511))]]], (6825 ^ _779142) ^ [_890315, _890317, _890319, _890321, _890323] : [c_Finite__Set_Ofolding__one(_890315, _890317, _890319), hBOOL(hAPP(c_Finite__Set_Ofinite(_890315), _890321)), -(hBOOL(hAPP(hAPP(c_member(_890315), _890323), _890321))), -(hAPP(_890319, hAPP(hAPP(c_Set_Oinsert(_890315), _890323), _890321)) = hAPP(hAPP(c_Finite__Set_Ofold(_890315, _890315, _890317), _890323), _890321))], (32503 ^ _779142) ^ [_1371928, _1371930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371928)), hAPP(c_Nat_OSuc, _1371930))), -(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(_1371928))), 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)), _1371930)))))], (29618 ^ _779142) ^ [_1306583, _1306585, _1306587, _1306589] : [class_Lattices_Osemilattice__inf(_1306583), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306583), _1306585)), hBOOL(hAPP(hAPP(c_member(_1306583), _1306587), _1306585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306583), hAPP(hAPP(c_Finite__Set_Ofold(_1306583, _1306583, c_Lattices_Osemilattice__inf__class_Oinf(_1306583)), _1306589), _1306585)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1306583), _1306587), _1306589))))], (25290 ^ _779142) ^ [_1223475, _1223477] : [class_Int_Onumber__ring(_1223475), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223475), c_Groups_Oone__class_Oone(_1223475)), hAPP(c_Int_Onumber__class_Onumber__of(_1223475), _1223477)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1223477)))], (46418 ^ _779142) ^ [_1712139, _1712141] : [class_Orderings_Olinorder(_1712139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1712139), _1712141)), 46425 ^ _779142 : [(46430 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1712139), c_List_Olinorder__class_Osorted__list__of__set(_1712139, _1712141))))], (46428 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712139, c_List_Olinorder__class_Osorted__list__of__set(_1712139, _1712141)))], (46426 ^ _779142) ^ [] : [-(hAPP(c_List_Oset(_1712139), c_List_Olinorder__class_Osorted__list__of__set(_1712139, _1712141)) = _1712141)]]], (16781 ^ _779142) ^ [_1074349, _1074351] : [class_Orderings_Olinorder(_1074349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074349), _1074351)), -(c_Big__Operators_Olattice_OInf__fin(_1074349, c_Orderings_Oord__class_Omin(_1074349), _1074351) = hAPP(c_Finite__Set_Ofold1(_1074349, c_Orderings_Oord__class_Omin(_1074349)), _1074351))], (36492 ^ _779142) ^ [_1465613, _1465615, _1465617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465613), _1465615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465613, tc_HOL_Obool)), _1465615), hAPP(c_Set_Oimage(_1465613, _1465613, _1465617), _1465615))), -(c_Fun_Oinj__on(_1465613, _1465613, _1465617, _1465615))], (34859 ^ _779142) ^ [_1425761, _1425763, _1425765, _1425767, _1425769] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425761, tc_fun(_1425763, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1425761), _1425765), _1425767)), _1425769) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425763, tc_HOL_Obool)), hAPP(_1425769, _1425765)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425761, tc_fun(_1425763, tc_HOL_Obool)), _1425767), _1425769)))], (27252 ^ _779142) ^ [_1260008, _1260010, _1260012, _1260014] : [class_Orderings_Olinorder(_1260008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260008), _1260010), _1260012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260008), _1260012), _1260014)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260008, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1260008, _1260010, _1260012)), c_SetInterval_Oord__class_OatLeastAtMost(_1260008, _1260012, _1260014)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1260008, _1260010, _1260014))], (2440 ^ _779142) ^ [_814950, _814952] : [_814952 = _814950, -(c_SetInterval_Oord__class_OgreaterThan(_814952) = c_SetInterval_Oord__class_OgreaterThan(_814950))], (52213 ^ _779142) ^ [_1831970, _1831972] : [class_Groups_Ominus(_1831970), -(class_Groups_Ominus(tc_fun(_1831972, _1831970)))], (5382 ^ _779142) ^ [_861473, _861475] : [_861475 = _861473, -(c_Groups_Ominus__class_Ominus(_861475) = c_Groups_Ominus__class_Ominus(_861473))], (40921 ^ _779142) ^ [_1582435, _1582437, _1582439, _1582441] : [-(hAPP(_1582435, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582437, _1582437), _1582439), _1582435), _1582441)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582437, _1582437), _1582439), _1582435), hAPP(_1582435, _1582441)))], (20716 ^ _779142) ^ [_1143185, _1143187, _1143189] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143187), _1143189)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143185), _1143187)), _1143189))], (38909 ^ _779142) ^ [_1532955, _1532957, _1532959, _1532961, _1532963] : [c_Relation_Orefl__on(_1532955, _1532957, _1532959), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532955, _1532955)), hAPP(hAPP(c_Product__Type_OPair(_1532955, _1532955), _1532961), _1532963)), _1532959)), -(hBOOL(hAPP(hAPP(c_member(_1532955), _1532961), _1532957)))], (48806 ^ _779142) ^ [_1764714] : [-(c_Relation_Otrans(tc_fun(_1764714, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1764714)))], (32485 ^ _779142) ^ [_1371469, _1371471] : [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(_1371469))), 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)), _1371471)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371469)), hAPP(c_Nat_OSuc, _1371471))))], (40514 ^ _779142) ^ [_1572499, _1572501, _1572503, _1572505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572499, _1572499)), hAPP(hAPP(c_Product__Type_OPair(_1572499, _1572499), _1572501), _1572503)), c_Transitive__Closure_Ortrancl(_1572499, _1572505))), -(_1572501 = _1572503), 40521 ^ _779142 : [(40524 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572499, _1572499)), hAPP(hAPP(c_Product__Type_OPair(_1572499, _1572499), _1572501), _1572503)), c_Transitive__Closure_Otrancl(_1572499, _1572505))))], (40522 ^ _779142) ^ [] : [_1572501 = _1572503]]], (37477 ^ _779142) ^ [_1488257, _1488259, _1488261] : [-(hAPP(c_Set_OCollect(_1488257), hAPP(hAPP(c_COMBS(_1488257, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488257), c_fdisj), _1488259)), _1488261)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488257, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488257), _1488259)), hAPP(c_Set_OCollect(_1488257), _1488261)))], (21784 ^ _779142) ^ [_1161887, _1161889] : [_1161887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161889), _1161887) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11490 ^ _779142) ^ [_976772, _976774, _976776, _976778] : [class_Groups_Oordered__comm__monoid__add(_976772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976772), c_Groups_Ozero__class_Ozero(_976772)), _976774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976772), _976776), _976778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976772), _976776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976772), _976774), _976778))))], (21854 ^ _779142) ^ [_1163132, _1163134, _1163136] : [class_Rings_Oring__1__no__zero__divisors(_1163132), -(_1163134 = c_Groups_Ozero__class_Ozero(_1163132)), hAPP(hAPP(c_Power_Opower__class_Opower(_1163132), _1163134), _1163136) = c_Groups_Ozero__class_Ozero(_1163132)], (41897 ^ _779142) ^ [_1610704, _1610706, _1610708] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610704, tc_HOL_Obool)), hAPP(c_List_Oset(_1610704), _1610706)), hAPP(c_List_Oset(_1610704), hAPP(hAPP(c_List_Olist_OCons(_1610704), _1610708), _1610706)))))], (40853 ^ _779142) ^ [_1580510, _1580512, _1580514] : [c_Relation_Ototal__on(_1580510, _1580512, _1580514), 40856 ^ _779142 : [(40857 ^ _779142) ^ [_1580654] : [hBOOL(hAPP(hAPP(c_member(_1580510), _1580654), _1580512)), 40860 ^ _779142 : [(40861 ^ _779142) ^ [_1580794] : [hBOOL(hAPP(hAPP(c_member(_1580510), _1580794), _1580512)), -(_1580654 = _1580794), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580510, _1580510)), hAPP(hAPP(c_Product__Type_OPair(_1580510, _1580510), _1580654), _1580794)), _1580514))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580510, _1580510)), hAPP(hAPP(c_Product__Type_OPair(_1580510, _1580510), _1580794), _1580654)), _1580514)))]]]]], (43315 ^ _779142) ^ [_1643568, _1643570, _1643572, _1643574, _1643576] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643568), tc_List_Olist(_1643568))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643568), tc_List_Olist(_1643568)), _1643570), _1643572)), c_List_Olexord(_1643568, _1643574))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643568), tc_List_Olist(_1643568))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643568), tc_List_Olist(_1643568)), hAPP(hAPP(c_List_Oappend(_1643568), _1643576), _1643570)), hAPP(hAPP(c_List_Oappend(_1643568), _1643576), _1643572))), c_List_Olexord(_1643568, _1643574))))], (10039 ^ _779142) ^ [_951140, _951142, _951144, _951146, _951148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951140), _951142)), -(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), _951140), _951144)), _951146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951142), _951144)), _951148)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951146), 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), _951142), _951140)), _951144)), _951148)))], (16543 ^ _779142) ^ [_1070283, _1070285, _1070287] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070283), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070285), _1070287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070285), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070283), _1070287)))], (22106 ^ _779142) ^ [_1167853, _1167855, _1167857] : [class_Rings_Olinordered__semidom(_1167853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167853), c_Groups_Oone__class_Oone(_1167853)), _1167855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167853), hAPP(hAPP(c_Power_Opower__class_Opower(_1167853), _1167855), _1167857)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167853), _1167855), hAPP(hAPP(c_Power_Opower__class_Opower(_1167853), _1167855), _1167857)))))], (21484 ^ _779142) ^ [_1156613, _1156615] : [-(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), _1156613)), _1156615))))], (39888 ^ _779142) ^ [_1556644, _1556646, _1556648, _1556650, _1556652, _1556654] : [c_Finite__Set_Ofolding__idem(_1556644, _1556646, _1556648, _1556650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556644), _1556652)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556644), _1556654)), -(hAPP(_1556650, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556644, tc_HOL_Obool)), _1556652), _1556654)) = hAPP(c_Fun_Ocomp(_1556646, _1556646, _1556646, hAPP(_1556650, _1556652)), hAPP(_1556650, _1556654)))], (7916 ^ _779142) ^ [_909462, _909464, _909466] : [class_Orderings_Olinorder(_909462), 7919 ^ _779142 : [(7926 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909462), _909466), _909464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909462), _909464), _909466))], (7920 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909462), _909464), _909466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909462), _909466), _909464)))]]], (1666 ^ _779142) ^ [_802909, _802911] : [-(class_Groups_Ocomm__monoid__mult(_802909)), _802911 = _802909, class_Groups_Ocomm__monoid__mult(_802911)], (41120 ^ _779142) ^ [_1587375, _1587377, _1587379, _1587381, _1587383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587375, _1587375)), hAPP(hAPP(c_Product__Type_OPair(_1587375, _1587375), _1587377), _1587379)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587375, _1587375), tc_HOL_Obool), _1587381), _1587383))), 41125 ^ _779142 : [(41128 ^ _779142) ^ [] : [-(_1587377 = _1587379)], (41126 ^ _779142) ^ [] : [-(_1587381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41131 ^ _779142 : [(41136 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587375, _1587375)), hAPP(hAPP(c_Product__Type_OPair(_1587375, _1587375), 41129 ^ [_1587375, _1587377, _1587379, _1587381, _1587383]), _1587379)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587375, _1587375), tc_HOL_Obool), 41130 ^ [_1587375, _1587377, _1587379, _1587381, _1587383]), _1587383))))], (41134 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587375, _1587375)), hAPP(hAPP(c_Product__Type_OPair(_1587375, _1587375), _1587377), 41129 ^ [_1587375, _1587377, _1587379, _1587381, _1587383])), _1587383)))], (41132 ^ _779142) ^ [] : [-(_1587381 = hAPP(c_Nat_OSuc, 41130 ^ [_1587375, _1587377, _1587379, _1587381, _1587383]))]]], (47645 ^ _779142) ^ [_1739059, _1739061, _1739063] : [-(c_List_Olist__ex(_1739059, _1739061, _1739063)), 47646 ^ _779142 : [(47647 ^ _779142) ^ [_1739124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739124), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739059)), _1739063))), hBOOL(hAPP(_1739061, hAPP(hAPP(c_List_Onth(_1739059), _1739063), _1739124)))]]], (50707 ^ _779142) ^ [_1805955, _1805957, _1805959, _1805961, _1805963] : [class_Rings_Ocomm__semiring__1(_1805955), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805955), _1805957), _1805959)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805955), _1805961), _1805963)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805955), _1805957), _1805961)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805955), _1805959), _1805963))))], (50969 ^ _779142) ^ [_1810986, _1810988] : [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)))), _1810986, _1810988), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810986), _1810988)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810988), _1810986)))], (39572 ^ _779142) ^ [_1549322, _1549324, _1549326, _1549328, _1549330, _1549332] : [class_Groups_Ocomm__monoid__add(_1549322), c_Fun_Oinj__on(_1549324, _1549326, _1549328, _1549330), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549326, _1549322), _1549332), hAPP(c_Set_Oimage(_1549324, _1549326, _1549328), _1549330)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549324, _1549322), hAPP(c_Fun_Ocomp(_1549326, _1549322, _1549324, _1549332), _1549328)), _1549330))], (29423 ^ _779142) ^ [_1302025, _1302027] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1302025), _1302027) = 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)), _1302025)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1302027))))], (44909 ^ _779142) ^ [_1679376, _1679378] : [-(hBOOL(hAPP(c_List_Olistsp(_1679376, _1679378), c_List_Olist_ONil(_1679376))))], (26240 ^ _779142) ^ [_1240646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1240646)), -(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), _1240646), 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)))))))], (32417 ^ _779142) ^ [_1369940, _1369942] : [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(_1369940))), 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)), _1369942))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369940) = hAPP(c_Nat_OSuc, _1369942))], (52119 ^ _779142) ^ [_1830735, _1830737] : [class_Complete__Lattice_Ocomplete__lattice(_1830735), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1830737, _1830735)))], (6894 ^ _779142) ^ [_891849, _891851, _891853, _891855] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_891849, _891851, hAPP(hAPP(c_Set_Oinsert(_891849), _891853), c_Orderings_Obot__class_Obot(tc_fun(_891849, tc_HOL_Obool)))), _891855)), -(_891853 = _891855)], (3134 ^ _779142) ^ [_825699, _825701, _825703, _825705, _825707, _825709] : [-(c_Big__Operators_Olattice_OInf__fin(_825709, _825705, _825701) = c_Big__Operators_Olattice_OInf__fin(_825707, _825703, _825699)), _825709 = _825707, _825705 = _825703, _825701 = _825699], (38776 ^ _779142) ^ [_1529886, _1529888, _1529890] : [_1529890 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529886, _1529888), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1529886, _1529888), _1529890) = c_Orderings_Obot__class_Obot(tc_fun(_1529886, tc_HOL_Obool)))], (24914 ^ _779142) ^ [_1217135] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1217135)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1217135))))], (33030 ^ _779142) ^ [_1383462, _1383464, _1383466] : [hBOOL(hAPP(_1383462, 33031 ^ [_1383462, _1383464, _1383466])), 33034 ^ _779142 : [(33035 ^ _779142) ^ [_1383573, _1383575] : [-(hBOOL(hAPP(_1383462, hAPP(hAPP(c_Product__Type_OPair(_1383464, _1383466), _1383575), _1383573))))]]], (11219 ^ _779142) ^ [_972038, _972040, _972042] : [11220 ^ _779142 : [(11223 ^ _779142) ^ [] : [_972040 = _972042], (11221 ^ _779142) ^ [] : [_972038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972038), _972040) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972038), _972042))], (52413 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (28885 ^ _779142) ^ [_1291065, _1291067, _1291069, _1291071] : [-(hBOOL(hAPP(hAPP(c_member(_1291065), _1291067), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291065, tc_HOL_Obool)), _1291069), _1291071)))), hBOOL(hAPP(hAPP(c_member(_1291065), _1291067), _1291069)), hBOOL(hAPP(hAPP(c_member(_1291065), _1291067), _1291071))], (32909 ^ _779142) ^ [_1380406, _1380408, _1380410, _1380412, _1380414] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1380406, _1380408)), hAPP(hAPP(c_Product__Type_OPair(_1380406, _1380408), _1380412), _1380414)), _1380410)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1380406, _1380408, _1380410), _1380412), _1380414)))], (31813 ^ _779142) ^ [_1351770, _1351772, _1351774, _1351776] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1351770), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351772, tc_Int_Oint), _1351774), _1351776)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351772, _1351770), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1351770, _1351772), c_Int_Oring__1__class_Oof__int(_1351770)), _1351774)), _1351776)), class_Groups_Ocomm__monoid__mult(_1351770), class_Rings_Oring__1(_1351770)], (33037 ^ _779142) ^ [_1383609, _1383611, _1383613] : [hBOOL(hAPP(_1383609, hAPP(hAPP(c_Product__Type_OPair(_1383611, _1383613), 33038 ^ [_1383609, _1383611, _1383613]), 33039 ^ [_1383609, _1383611, _1383613]))), 33042 ^ _779142 : [(33043 ^ _779142) ^ [_1383756] : [-(hBOOL(hAPP(_1383609, _1383756)))]]], (40875 ^ _779142) ^ [_1580999, _1581001, _1581003] : [40877 ^ _779142 : [(40878 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580999), 40876 ^ [_1580999, _1581001, _1581003]), _1581001)))], (40883 ^ _779142) ^ [] : [40876 ^ [_1580999, _1581001, _1581003] = 40879 ^ [_1580999, _1581001, _1581003]], (40887 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580999, _1580999)), hAPP(hAPP(c_Product__Type_OPair(_1580999, _1580999), 40879 ^ [_1580999, _1581001, _1581003]), 40876 ^ [_1580999, _1581001, _1581003])), _1581003))], (40885 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580999, _1580999)), hAPP(hAPP(c_Product__Type_OPair(_1580999, _1580999), 40876 ^ [_1580999, _1581001, _1581003]), 40879 ^ [_1580999, _1581001, _1581003])), _1581003))], (40881 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580999), 40879 ^ [_1580999, _1581001, _1581003]), _1581001)))]], -(c_Relation_Ototal__on(_1580999, _1581001, _1581003))], (40755 ^ _779142) ^ [_1578183, _1578185] : [-(hAPP(c_Relation_OField(_1578183), hAPP(c_Relation_Oconverse(_1578183, _1578183), _1578185)) = hAPP(c_Relation_OField(_1578183), _1578185))], (24113 ^ _779142) ^ [_1203790, _1203792] : [class_Int_Onumber__ring(_1203790), -(hAPP(c_Int_Onumber__class_Onumber__of(_1203790), _1203792) = hAPP(c_Int_Oring__1__class_Oof__int(_1203790), _1203792))], (36438 ^ _779142) ^ [_1464525, _1464527, _1464529, _1464531] : [c_Fun_Oinj__on(_1464525, _1464527, _1464529, c_Orderings_Otop__class_Otop(tc_fun(_1464525, tc_HOL_Obool))), 36441 ^ _779142 : [(36455 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464527), _1464531), hAPP(c_Set_Oimage(_1464525, _1464527, _1464529), c_Orderings_Otop__class_Otop(tc_fun(_1464525, tc_HOL_Obool)))))), 36456 ^ _779142 : [(36457 ^ _779142) ^ [_1464928] : [_1464531 = hAPP(_1464529, _1464928), 36461 ^ _779142 : [(36464 ^ _779142) ^ [] : [36460 ^ [_1464525, _1464527, _1464529, _1464531, _1464928] = _1464928], (36462 ^ _779142) ^ [] : [-(_1464531 = hAPP(_1464529, 36460 ^ [_1464525, _1464527, _1464529, _1464531, _1464928]))]]]]], (36442 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464527), _1464531), hAPP(c_Set_Oimage(_1464525, _1464527, _1464529), c_Orderings_Otop__class_Otop(tc_fun(_1464525, tc_HOL_Obool))))), 36446 ^ _779142 : [(36449 ^ _779142) ^ [_1464790] : [_1464531 = hAPP(_1464529, _1464790), -(_1464790 = 36445 ^ [_1464525, _1464527, _1464529, _1464531])], (36447 ^ _779142) ^ [] : [-(_1464531 = hAPP(_1464529, 36445 ^ [_1464525, _1464527, _1464529, _1464531]))]]]]], (46883 ^ _779142) ^ [_1721962] : [-(c_List_Oreturn__list(_1721962) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1721962))], (18682 ^ _779142) ^ [_1107965, _1107967, _1107969] : [class_Rings_Osemiring__1(_1107965), hBOOL(hAPP(hAPP(c_member(_1107965), _1107967), c_Nat_Osemiring__1__class_ONats(_1107965))), hBOOL(hAPP(hAPP(c_member(_1107965), _1107969), c_Nat_Osemiring__1__class_ONats(_1107965))), -(hBOOL(hAPP(hAPP(c_member(_1107965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107965), _1107967), _1107969)), c_Nat_Osemiring__1__class_ONats(_1107965))))], (13411 ^ _779142) ^ [_1012098, _1012100, _1012102, _1012104] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1012098, _1012102)), c_Sum__Type_OPlus(_1012098, _1012102, _1012100, _1012104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1012098), _1012100)), hAPP(c_Finite__Set_Ocard(_1012102), _1012104))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012098), _1012100)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012102), _1012104))], (17493 ^ _779142) ^ [_1087264, _1087266, _1087268, _1087270] : [class_Divides_Osemiring__div(_1087264), -(c_Divides_Odiv__class_Omod(_1087264, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087264), _1087266), _1087268), _1087270) = c_Divides_Odiv__class_Omod(_1087264, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087264), _1087266), c_Divides_Odiv__class_Omod(_1087264, _1087268, _1087270)), _1087270))], (35147 ^ _779142) ^ [_1433290, _1433292, _1433294, _1433296, _1433298] : [35149 ^ _779142 : [(35152 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1433296, 35148 ^ [_1433290, _1433292, _1433294, _1433296, _1433298]), _1433298))], (35150 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433290), 35148 ^ [_1433290, _1433292, _1433294, _1433296, _1433298]), _1433294)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1433290, tc_fun(_1433292, tc_HOL_Obool)), _1433294), _1433296), _1433298)))], (8901 ^ _779142) ^ [_929329, _929331, _929333, _929335] : [_929329 = c_Finite__Set_Ofold1(_929331, _929333), -(hAPP(_929329, hAPP(hAPP(c_Set_Oinsert(_929331), _929335), c_Orderings_Obot__class_Obot(tc_fun(_929331, tc_HOL_Obool)))) = _929335)], (31560 ^ _779142) ^ [_1345454, _1345456, _1345458, _1345460] : [class_Lattices_Osemilattice__sup(_1345454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345454), _1345456)), 31570 ^ _779142 : [(31573 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345454), 31569 ^ [_1345454, _1345456, _1345458, _1345460]), _1345458))], (31571 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345454), 31569 ^ [_1345454, _1345456, _1345458, _1345460]), _1345456)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345454), hAPP(hAPP(c_Finite__Set_Ofold(_1345454, _1345454, c_Lattices_Osemilattice__sup__class_Osup(_1345454)), _1345460), _1345456)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1345454), _1345458), _1345460))))], (52125 ^ _779142) ^ [_1830814, _1830816] : [class_Lattices_Obounded__lattice(_1830814), -(class_Lattices_Obounded__lattice__top(tc_fun(_1830816, _1830814)))], (36726 ^ _779142) ^ [_1470710, _1470712, _1470714, _1470716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470710), _1470712)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470714), _1470716)), 36733 ^ _779142 : [(36734 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470710), _1470712)), hAPP(c_Finite__Set_Ocard(_1470714), _1470716)))), 36735 ^ _779142 : [(36736 ^ _779142) ^ [_1470921] : [c_Fun_Oinj__on(_1470710, _1470714, _1470921, _1470712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470714, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470710, _1470714, _1470921), _1470712)), _1470716))]]], (36744 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470710), _1470712)), hAPP(c_Finite__Set_Ocard(_1470714), _1470716))), 36748 ^ _779142 : [(36751 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470714, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470710, _1470714, 36747 ^ [_1470710, _1470712, _1470714, _1470716]), _1470712)), _1470716)))], (36749 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1470710, _1470714, 36747 ^ [_1470710, _1470712, _1470714, _1470716], _1470712))]]]]], (16517 ^ _779142) ^ [_1069828, _1069830] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069828), _1069830))), -(_1069828 = _1069830), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069830), _1069828)))], (12353 ^ _779142) ^ [_992355, _992357] : [12354 ^ _779142 : [(12357 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992357))], (12355 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992355))]], -(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), _992355), _992357))))], (40338 ^ _779142) ^ [_1568130, _1568132] : [-(c_Transitive__Closure_Otrancl(_1568130, _1568132) = hAPP(hAPP(c_Relation_Orel__comp(_1568130, _1568130, _1568130), c_Transitive__Closure_Ortrancl(_1568130, _1568132)), _1568132))], (52369 ^ _779142) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (45290 ^ _779142) ^ [_1688034, _1688036] : [-(_1688034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1688036, _1688034, c_List_Olist_ONil(_1688036)) = c_List_Olist_ONil(tc_List_Olist(_1688036)))], (25080 ^ _779142) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (11396 ^ _779142) ^ [_975071, _975073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975071), _975073)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _975073)), _975071) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _975073), _975071)))], (25082 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9761 ^ _779142) ^ [_945233, _945235, _945237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945233), _945235)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945237), _945235)), _945233) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945235), _945233)))], (46446 ^ _779142) ^ [_1712601, _1712603, _1712605, _1712607] : [class_Orderings_Olinorder(_1712601), c_List_Olinorder__class_Osorted(_1712601, _1712603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712605), _1712607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712607), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712601)), _1712603))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712601), hAPP(hAPP(c_List_Onth(_1712601), _1712603), _1712605)), hAPP(hAPP(c_List_Onth(_1712601), _1712603), _1712607))))], (18997 ^ _779142) ^ [_1113035, _1113037] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113037), 19000 ^ _779142 : [(19007 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113035)))), 19010 ^ _779142 : [(19017 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113037)))), -(_1113035 = _1113037)], (19011 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113037))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113035) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (19001 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113037)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24283 ^ _779142) ^ [_1206482, _1206484, _1206486] : [class_Rings_Olinordered__idom(_1206482), 24286 ^ _779142 : [(24293 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206484), _1206486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206482), hAPP(c_Int_Oring__1__class_Oof__int(_1206482), _1206484)), hAPP(c_Int_Oring__1__class_Oof__int(_1206482), _1206486))))], (24287 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206482), hAPP(c_Int_Oring__1__class_Oof__int(_1206482), _1206484)), hAPP(c_Int_Oring__1__class_Oof__int(_1206482), _1206486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206484), _1206486)))]]], (37449 ^ _779142) ^ [_1487858] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1487858, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1487858), hAPP(c_COMBK(tc_HOL_Obool, _1487858), c_fFalse)))], (78 ^ _779142) ^ [_780341, _780343] : [-(class_Rings_Odivision__ring__inverse__zero(_780341)), _780343 = _780341, class_Rings_Odivision__ring__inverse__zero(_780343)], (42439 ^ _779142) ^ [_1624877, _1624879, _1624881] : [hBOOL(hAPP(c_List_Odistinct(_1624877), hAPP(hAPP(c_List_Olist_OCons(_1624877), _1624879), _1624881))), 42442 ^ _779142 : [(42445 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1624877), _1624881)))], (42443 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624877), _1624879), hAPP(c_List_Oset(_1624877), _1624881)))]]], (41369 ^ _779142) ^ [_1594754, _1594756, _1594758] : [_1594754 = hAPP(hAPP(c_List_Olist_OCons(_1594756), _1594758), _1594754)], (4136 ^ _779142) ^ [_841760, _841762] : [_841762 = _841760, -(c_List_Orev(_841762) = c_List_Orev(_841760))], (15211 ^ _779142) ^ [_1045413, _1045415] : [class_Orderings_Olinorder(_1045413), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045413), _1045415), _1045415) = _1045415)], (39001 ^ _779142) ^ [_1535385, _1535387, _1535389] : [c_Predicate_Oreflp(_1535385, _1535387), -(hBOOL(hAPP(hAPP(_1535387, _1535389), _1535389)))], (5026 ^ _779142) ^ [_855789, _855791] : [_855791 = _855789, -(c_Finite__Set_Ocard(_855791) = c_Finite__Set_Ocard(_855789))], (44640 ^ _779142) ^ [_1673388, _1673390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673388), _1673390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673388)), hAPP(c_Code__Numeral_Oof__nat, _1673390))))], (27758 ^ _779142) ^ [_1269386, _1269388, _1269390] : [class_Orderings_Olinorder(_1269386), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269386), _1269388), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269386), _1269388), _1269390)) = _1269388)], (36698 ^ _779142) ^ [_1470096, _1470098, _1470100, _1470102, _1470104] : [-(c_Fun_Oinj__on(_1470096, _1470098, _1470100, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470096, tc_HOL_Obool)), _1470102), _1470104))), c_Fun_Oinj__on(_1470096, _1470098, _1470100, _1470102), c_Fun_Oinj__on(_1470096, _1470098, _1470100, _1470104), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470098, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470096, _1470098, _1470100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470096, tc_HOL_Obool)), _1470102), _1470104))), hAPP(c_Set_Oimage(_1470096, _1470098, _1470100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470096, tc_HOL_Obool)), _1470104), _1470102))) = c_Orderings_Obot__class_Obot(tc_fun(_1470098, tc_HOL_Obool))], (37470 ^ _779142) ^ [_1488200, _1488202] : [-(hBOOL(hAPP(_1488202, 37471 ^ [_1488200, _1488202]))), -(hAPP(c_Set_OCollect(_1488200), _1488202) = c_Orderings_Obot__class_Obot(tc_fun(_1488200, tc_HOL_Obool)))], (24435 ^ _779142) ^ [_1209101, _1209103] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1209101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1209103), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1209101, _1209103))], (34945 ^ _779142) ^ [_1428015, _1428017, _1428019] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428015, tc_HOL_Obool)), _1428017), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428015, tc_HOL_Obool), _1428019)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1428015, tc_HOL_Obool), tc_fun(_1428015, tc_HOL_Obool)), _1428019), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428015, tc_HOL_Obool)), _1428017)))], (40255 ^ _779142) ^ [_1565388, _1565390, _1565392, _1565394, _1565396] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565388, _1565388)), hAPP(hAPP(c_Product__Type_OPair(_1565388, _1565388), _1565390), _1565392)), _1565394)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565388, _1565388)), hAPP(hAPP(c_Product__Type_OPair(_1565388, _1565388), _1565392), _1565396)), c_Transitive__Closure_Otrancl(_1565388, _1565394))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565388, _1565388)), hAPP(hAPP(c_Product__Type_OPair(_1565388, _1565388), _1565390), _1565396)), c_Transitive__Closure_Otrancl(_1565388, _1565394))))], (3600 ^ _779142) ^ [_833046, _833048, _833050, _833052] : [-(c_List_Otranspose(_833052, _833048) = c_List_Otranspose(_833050, _833046)), _833052 = _833050, _833048 = _833046], (48979 ^ _779142) ^ [_1769103, _1769105, _1769107, _1769109] : [class_Complete__Lattice_Ocomplete__lattice(_1769103), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769105, _1769103), _1769107), _1769109) = c_Complete__Lattice_OInf__class_OInf(_1769103, hAPP(c_Set_OCollect(_1769103), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool), tc_HOL_Obool, _1769103), c_HOL_OEx(tc_fun(_1769105, _1769103))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool), tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool), _1769103), hAPP(c_COMBS(tc_fun(_1769105, _1769103), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769105, _1769103)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769105, _1769103), tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769105, _1769103))), _1769107)))), hAPP(hAPP(c_COMBC(_1769103, tc_fun(tc_fun(_1769105, _1769103), _1769103), tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769103, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769105, _1769103), _1769103), tc_fun(tc_fun(_1769105, _1769103), tc_HOL_Obool)), _1769103), c_COMBB(_1769103, tc_HOL_Obool, tc_fun(_1769105, _1769103))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769105, _1769103), _1769105, _1769103), c_COMBI(tc_fun(_1769105, _1769103))), _1769109)))))))], (37749 ^ _779142) ^ [_1496073, _1496075, _1496077, _1496079] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1496073, _1496075)), hAPP(hAPP(c_Product__Type_OSigma(_1496073, _1496075), _1496077), hAPP(c_COMBK(tc_fun(_1496075, tc_HOL_Obool), _1496073), _1496079)))), -(_1496079 = c_Orderings_Obot__class_Obot(tc_fun(_1496075, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496073), _1496077)))], (17413 ^ _779142) ^ [_1085516, _1085518, _1085520, _1085522] : [class_Divides_Osemiring__div(_1085516), -(c_Divides_Odiv__class_Omod(_1085516, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085516), _1085518), c_Divides_Odiv__class_Omod(_1085516, _1085520, _1085522)), _1085522) = c_Divides_Odiv__class_Omod(_1085516, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085516), _1085518), _1085520), _1085522))], (36374 ^ _779142) ^ [_1463308, _1463310, _1463312, _1463314, _1463316] : [c_Fun_Oinj__on(_1463308, _1463310, _1463312, c_Orderings_Otop__class_Otop(tc_fun(_1463308, tc_HOL_Obool))), 36377 ^ _779142 : [(36384 ^ _779142) ^ [] : [_1463314 = _1463316, -(hAPP(c_Set_Oimage(_1463308, _1463310, _1463312), _1463314) = hAPP(c_Set_Oimage(_1463308, _1463310, _1463312), _1463316))], (36378 ^ _779142) ^ [] : [hAPP(c_Set_Oimage(_1463308, _1463310, _1463312), _1463314) = hAPP(c_Set_Oimage(_1463308, _1463310, _1463312), _1463316), -(_1463314 = _1463316)]]], (45711 ^ _779142) ^ [_1697564, _1697566, _1697568] : [hAPP(c_List_Ofilter(_1697564, _1697566), _1697568) = c_List_Olist_ONil(_1697564), 45714 ^ _779142 : [(45715 ^ _779142) ^ [_1697661] : [hBOOL(hAPP(hAPP(c_member(_1697564), _1697661), hAPP(c_List_Oset(_1697564), _1697568))), hBOOL(hAPP(_1697566, _1697661))]]], (39145 ^ _779142) ^ [_1538698, _1538700] : [-(c_HOL_OThe(_1538698, hAPP(c_fequal, _1538700)) = _1538700)], (9402 ^ _779142) ^ [_939392, _939394] : [class_Groups_Ocomm__monoid__mult(_939392), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939392), _939394), c_Groups_Oone__class_Oone(_939392)) = _939394)], (25402 ^ _779142) ^ [_1225646, _1225648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1225646)), c_Int_OBit0(_1225648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225646), _1225648)))], (51801 ^ _779142) ^ [_1825157, _1825159] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825157), 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)))), _1825159)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825157), _1825159)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825159), _1825157)))], (49222 ^ _779142) ^ [_1774220, _1774222] : [c_Relation_Oantisym(_1774220, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774220, _1774220), tc_HOL_Obool)), _1774222), c_Relation_OId(_1774220))), -(c_Relation_Oantisym(_1774220, _1774222))], (52381 ^ _779142) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (22210 ^ _779142) ^ [_1169752, _1169754, _1169756, _1169758] : [class_Rings_Olinordered__semidom(_1169752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169754), _1169756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169752), c_Groups_Oone__class_Oone(_1169752)), _1169758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169752), hAPP(hAPP(c_Power_Opower__class_Opower(_1169752), _1169758), _1169754)), hAPP(hAPP(c_Power_Opower__class_Opower(_1169752), _1169758), _1169756))))], (9951 ^ _779142) ^ [_949145, _949147, _949149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949147), _949149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949145), _949149)), _949147)))], (44041 ^ _779142) ^ [_1660498, _1660500, _1660502, _1660504] : [class_Orderings_Olinorder(_1660498), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660498, _1660498, c_COMBI(_1660498)), _1660500), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660498, _1660498, c_COMBI(_1660498)), _1660502), _1660504)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660498, _1660498, c_COMBI(_1660498)), _1660502), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660498, _1660498, c_COMBI(_1660498)), _1660500), _1660504)))], (6566 ^ _779142) ^ [_884549, _884551, _884553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884549, tc_HOL_Obool)), _884551), hAPP(hAPP(c_Set_Oinsert(_884549), _884553), _884551))))], (46802 ^ _779142) ^ [_1720330, _1720332] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1720330), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1720330))), _1720332))), -(c_List_Otranspose(_1720330, c_List_Otranspose(_1720330, _1720332)) = c_List_OtakeWhile(tc_List_Olist(_1720330), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1720330)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720330), tc_List_Olist(_1720330), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1720330))), _1720332))], (46664 ^ _779142) ^ [_1717402, _1717404, _1717406] : [hAPP(c_List_Orev(_1717402), _1717404) = _1717406, -(_1717404 = hAPP(c_List_Orev(_1717402), _1717406))], (5622 ^ _779142) ^ [_865069, _865071, _865073, _865075] : [-(hAPP(_865075, _865071) = hAPP(_865073, _865069)), _865075 = _865073, _865071 = _865069], (8190 ^ _779142) ^ [_915269, _915271, _915273, _915275, _915277, _915279] : [-(hBOOL(hAPP(hAPP(c_member(_915269), _915271), _915273))), -(hAPP(c_Set_Oimage(_915269, _915275, c_Fun_Ofun__upd(_915269, _915275, _915277, _915271, _915279)), _915273) = hAPP(c_Set_Oimage(_915269, _915275, _915277), _915273))], (1336 ^ _779142) ^ [_798784, _798786] : [-(class_Rings_Oring__1(_798784)), _798786 = _798784, class_Rings_Oring__1(_798786)], (52771 ^ _779142) ^ [_1837746, _1837748] : [hBOOL(_1837746), -(hBOOL(hAPP(hAPP(c_fimplies, _1837748), _1837746)))], (23175 ^ _779142) ^ [] : [-(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))], (39670 ^ _779142) ^ [_1551505, _1551507, _1551509, _1551511, _1551513, _1551515] : [c_Finite__Set_Ofolding(_1551505, _1551507, _1551509, _1551511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551505), _1551513)), hBOOL(hAPP(hAPP(c_member(_1551505), _1551515), _1551513)), -(hAPP(_1551511, _1551513) = hAPP(c_Fun_Ocomp(_1551507, _1551507, _1551507, hAPP(_1551511, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1551505, tc_HOL_Obool)), _1551513), hAPP(hAPP(c_Set_Oinsert(_1551505), _1551515), c_Orderings_Obot__class_Obot(tc_fun(_1551505, tc_HOL_Obool)))))), hAPP(_1551509, _1551515)))], (41188 ^ _779142) ^ [_1589555, _1589557, _1589559, _1589561, _1589563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589555, _1589555)), hAPP(hAPP(c_Product__Type_OPair(_1589555, _1589555), _1589557), _1589559)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589555, _1589555), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589561)), _1589563))), 41192 ^ _779142 : [(41195 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589555, _1589555)), hAPP(hAPP(c_Product__Type_OPair(_1589555, _1589555), 41191 ^ [_1589555, _1589557, _1589559, _1589561, _1589563]), _1589559)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589555, _1589555), tc_HOL_Obool), _1589561), _1589563))))], (41193 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589555, _1589555)), hAPP(hAPP(c_Product__Type_OPair(_1589555, _1589555), _1589557), 41191 ^ [_1589555, _1589557, _1589559, _1589561, _1589563])), _1589563)))]]], (9767 ^ _779142) ^ [_945370, _945372, _945374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945370), _945372)), 9770 ^ _779142 : [(9777 ^ _779142) ^ [] : [_945372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945374), _945370), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945372), _945370) = _945374)], (9771 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945372), _945370) = _945374, -(_945372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945374), _945370))]]], (30618 ^ _779142) ^ [_1327235, _1327237, _1327239, _1327241, _1327243, _1327245, _1327247] : [c_Big__Operators_Ocomm__monoid__big(_1327235, _1327237, _1327239, _1327241, _1327243), 30621 ^ _779142 : [(30628 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1327237), _1327245))), -(hAPP(hAPP(_1327243, _1327247), _1327245) = _1327241)], (30622 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327237), _1327245)), -(hAPP(hAPP(_1327243, _1327247), _1327245) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1327235, _1327237, _1327239), _1327247), _1327241), _1327245))]]], (49382 ^ _779142) ^ [_1777220, _1777222, _1777224] : [c_Equiv__Relations_Oequiv(_1777220, _1777222, _1777224), 49385 ^ _779142 : [(49390 ^ _779142) ^ [] : [-(c_Relation_Otrans(_1777220, _1777224))], (49388 ^ _779142) ^ [] : [-(c_Relation_Osym(_1777220, _1777224))], (49386 ^ _779142) ^ [] : [-(c_Relation_Orefl__on(_1777220, _1777222, _1777224))]]], (47708 ^ _779142) ^ [_1740318, _1740320, _1740322] : [c_List_Olist__ex(_1740318, _1740320, hAPP(c_List_Orev(_1740318), _1740322)), -(c_List_Olist__ex(_1740318, _1740320, _1740322))], (1436 ^ _779142) ^ [_800034, _800036] : [-(class_Lattices_Odistrib__lattice(_800034)), _800036 = _800034, class_Lattices_Odistrib__lattice(_800036)], (34172 ^ _779142) ^ [_1406198, _1406200, _1406202, _1406204, _1406206] : [-(hAPP(c_Product__Type_Osnd(_1406198, _1406200), hAPP(c_Product__Type_Oapfst(_1406202, _1406198, _1406200, _1406204), _1406206)) = hAPP(c_Product__Type_Osnd(_1406202, _1406200), _1406206))], (48903 ^ _779142) ^ [_1766626] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1766626, tc_HOL_Obool) = c_Set_OBex(_1766626))], (1946 ^ _779142) ^ [_806409, _806411] : [-(hBOOL(_806409)), _806411 = _806409, hBOOL(_806411)], (51289 ^ _779142) ^ [_1816506, _1816508] : [_1816506 = _1816508, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816506), _1816508)))], (21306 ^ _779142) ^ [_1153662, _1153664, _1153666] : [class_Rings_Ocomm__semiring__1(_1153662), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153662), _1153664), hAPP(hAPP(c_Power_Opower__class_Opower(_1153662), _1153664), _1153666)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1153662), _1153664), hAPP(c_Nat_OSuc, _1153666)))], (30755 ^ _779142) ^ [_1330061, _1330063, _1330065, _1330067, _1330069, _1330071, _1330073, _1330075] : [c_Finite__Set_Ofolding__image__simple(_1330061, _1330063, _1330065, _1330067, _1330069, _1330071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330063), _1330073)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330063), _1330075)), 30769 ^ _779142 : [(30772 ^ _779142) ^ [] : [hAPP(_1330069, 30768 ^ [_1330061, _1330063, _1330065, _1330067, _1330069, _1330071, _1330073, _1330075]) = _1330067], (30770 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330063), 30768 ^ [_1330061, _1330063, _1330065, _1330067, _1330069, _1330071, _1330073, _1330075]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330063, tc_HOL_Obool)), _1330073), _1330075))))]], -(hAPP(_1330071, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330063, tc_HOL_Obool)), _1330073), _1330075)) = hAPP(hAPP(_1330065, hAPP(_1330071, _1330073)), hAPP(_1330071, _1330075)))], (20368 ^ _779142) ^ [_1136574, _1136576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136576)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1136574)), hAPP(c_Int_Onat, _1136576)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136574), _1136576)))], (24658 ^ _779142) ^ [_1212768, _1212770] : [_1212768 = _1212770, -(c_Int_OBit1(_1212768) = c_Int_OBit1(_1212770))], (22156 ^ _779142) ^ [_1168726, _1168728, _1168730, _1168732] : [class_Rings_Olinordered__semidom(_1168726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168726), c_Groups_Oone__class_Oone(_1168726)), _1168728)), 22163 ^ _779142 : [(22170 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168730), _1168732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168726), hAPP(hAPP(c_Power_Opower__class_Opower(_1168726), _1168728), _1168730)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168726), _1168728), _1168732))))], (22164 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168726), hAPP(hAPP(c_Power_Opower__class_Opower(_1168726), _1168728), _1168730)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168726), _1168728), _1168732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168730), _1168732)))]]], (32361 ^ _779142) ^ [_1368711, _1368713] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1368711))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1368713)), hAPP(c_Int_Onat, _1368711)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1368713), _1368711)), 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)))], (37132 ^ _779142) ^ [_1479834, _1479836, _1479838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479834, tc_HOL_Obool)), _1479836), hAPP(hAPP(c_Set_Oinsert(_1479834), _1479838), c_Orderings_Obot__class_Obot(tc_fun(_1479834, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1479834, _1479838, _1479836) = _1479838)], (45183 ^ _779142) ^ [_1685399, _1685401, _1685403, _1685405, _1685407, _1685409] : [c_List_Olist__all2(_1685399, _1685401, _1685403, _1685405, _1685407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685399)), _1685405))), -(hBOOL(hAPP(hAPP(_1685403, hAPP(hAPP(c_List_Onth(_1685399), _1685405), _1685409)), hAPP(hAPP(c_List_Onth(_1685401), _1685407), _1685409))))], (45344 ^ _779142) ^ [_1689267, _1689269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689267)), c_List_Oremdups(_1689267, _1689269))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689267)), _1689269))))], (18497 ^ _779142) ^ [_1104858, _1104860] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1104858) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1104860), -(_1104858 = _1104860)], (6546 ^ _779142) ^ [_884211, _884213, _884215] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_884211), _884213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884211, tc_HOL_Obool)), _884215), _884213)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_884211), _884215)))], (10099 ^ _779142) ^ [_952648, _952650, _952652] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952648), _952650) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952648), _952652), -(_952650 = _952652)], (27714 ^ _779142) ^ [_1268417, _1268419] : [class_Complete__Lattice_Ocomplete__lattice(_1268417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268417), _1268419)), -(c_Complete__Lattice_OSup__class_OSup(_1268417, _1268419) = hAPP(hAPP(c_Finite__Set_Ofold(_1268417, _1268417, c_Lattices_Osemilattice__sup__class_Osup(_1268417)), c_Orderings_Obot__class_Obot(_1268417)), _1268419))], (43357 ^ _779142) ^ [_1644590, _1644592, _1644594, _1644596, _1644598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644590), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644592)), _1644594))), -(hAPP(hAPP(c_List_Olist__update(_1644592, hAPP(hAPP(c_List_Oappend(_1644592), _1644594), _1644596)), _1644590), _1644598) = hAPP(hAPP(c_List_Oappend(_1644592), hAPP(hAPP(c_List_Olist__update(_1644592, _1644594), _1644590), _1644598)), _1644596))], (40099 ^ _779142) ^ [_1561624, _1561626, _1561628, _1561630, _1561632, _1561634, _1561636, _1561638, _1561640] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561624, _1561626, _1561628, _1561630), hAPP(hAPP(c_Product__Type_Oscomp(_1561624, _1561632, _1561634, tc_prod(_1561626, _1561628)), _1561636), _1561638)), _1561640) = hAPP(hAPP(c_Product__Type_Oscomp(_1561624, _1561632, _1561634, _1561630), _1561636), hAPP(hAPP(c_COMBC(_1561632, tc_fun(_1561626, tc_fun(_1561628, _1561630)), tc_fun(_1561634, _1561630)), hAPP(hAPP(c_COMBB(tc_fun(_1561634, tc_prod(_1561626, _1561628)), tc_fun(tc_fun(_1561626, tc_fun(_1561628, _1561630)), tc_fun(_1561634, _1561630)), _1561632), c_Product__Type_Oscomp(_1561634, _1561626, _1561628, _1561630)), _1561638)), _1561640)))], (36412 ^ _779142) ^ [_1464001, _1464003, _1464005, _1464007, _1464009] : [c_Fun_Oinj__on(_1464001, _1464003, _1464005, _1464007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464001, tc_HOL_Obool)), _1464009), _1464007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464003, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464001, _1464003, _1464005), _1464009)), hAPP(c_Set_Oimage(_1464001, _1464003, _1464005), _1464007))))], (35057 ^ _779142) ^ [_1430917, _1430919, _1430921, _1430923] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430917, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1430919)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1430917, tc_HOL_Obool), tc_Nat_Onat), _1430921), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1430923))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430917, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1430923, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430919), _1430923))), _1430921))], (47354 ^ _779142) ^ [_1732412, _1732414] : [class_Enum_Oenum(_1732412), 47357 ^ _779142 : [(47365 ^ _779142) ^ [] : [47366 ^ _779142 : [(47367 ^ _779142) ^ [_1732592] : [hBOOL(hAPP(_1732414, _1732592))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732412), _1732414)))], (47358 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732412), _1732414)), -(hBOOL(hAPP(_1732414, 47361 ^ [_1732412, _1732414])))]]], (7442 ^ _779142) ^ [_902294, _902296, _902298] : [class_Orderings_Oorder(_902294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902294), _902296), _902298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902294), _902298), _902296))], (24481 ^ _779142) ^ [_1209857, _1209859] : [class_Rings_Olinordered__idom(_1209857), 24484 ^ _779142 : [(24491 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209857), c_Groups_Ozero__class_Ozero(_1209857)), hAPP(c_Int_Oring__1__class_Oof__int(_1209857), _1209859))))], (24485 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209857), c_Groups_Ozero__class_Ozero(_1209857)), hAPP(c_Int_Oring__1__class_Oof__int(_1209857), _1209859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209859)))]]], (35371 ^ _779142) ^ [] : [-(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)))], (26902 ^ _779142) ^ [_1253499, _1253501, _1253503, _1253505] : [class_Orderings_Olinorder(_1253499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253499), _1253501), _1253503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253499), _1253503), _1253505)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253499, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1253499, _1253501), _1253503)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1253499, _1253503), _1253505)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1253499, _1253501), _1253505))], (36358 ^ _779142) ^ [_1462990, _1462992, _1462994, _1462996] : [c_Fun_Oinj__on(_1462990, _1462992, _1462994, c_Orderings_Otop__class_Otop(tc_fun(_1462990, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1462990, tc_fun(_1462996, _1462992), hAPP(hAPP(c_COMBB(_1462992, tc_fun(_1462996, _1462992), _1462990), c_COMBK(_1462992, _1462996)), _1462994), c_Orderings_Otop__class_Otop(tc_fun(_1462990, tc_HOL_Obool))))], (26870 ^ _779142) ^ [_1252803, _1252805, _1252807, _1252809] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252803, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252803, tc_HOL_Obool)), _1252805), _1252807)), _1252809) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252803, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252803, tc_HOL_Obool)), _1252805), _1252809)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252803, tc_HOL_Obool)), _1252807), _1252809)))], (17253 ^ _779142) ^ [_1082767, _1082769, _1082771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082767), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082769)), _1082771)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32007 ^ _779142) ^ [_1358673, _1358675, _1358677, _1358679] : [class_Groups_Ocomm__monoid__add(_1358673), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358673), _1358675), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1358677)), hAPP(c_Nat_OSuc, _1358679))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358673), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1358673, tc_Nat_Onat), _1358675), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1358677), _1358679)))], (17533 ^ _779142) ^ [_1088122] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1088122) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34811 ^ _779142) ^ [_1424457, _1424459, _1424461, _1424463, _1424465] : [_1424457 = c_Orderings_Obot__class_Obot(tc_fun(_1424459, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424461, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424459, tc_fun(_1424461, tc_HOL_Obool)), _1424457), _1424463)), _1424465) = _1424465)], (47882 ^ _779142) ^ [_1743802, _1743804, _1743806, _1743808] : [-(c_List_Olist__all(_1743802, _1743804, hAPP(hAPP(c_List_Olist_OCons(_1743802), _1743806), _1743808))), hBOOL(hAPP(_1743804, _1743806)), c_List_Olist__all(_1743802, _1743804, _1743808)], (5354 ^ _779142) ^ [_861031, _861033, _861035, _861037, _861039, _861041] : [-(c_SetInterval_Oord_OlessThan(_861041, _861037, _861033) = c_SetInterval_Oord_OlessThan(_861039, _861035, _861031)), _861041 = _861039, _861037 = _861035, _861033 = _861031], (42794 ^ _779142) ^ [_1631746, _1631748, _1631750] : [-(hAPP(hAPP(c_List_Otake(_1631746), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1631746), _1631748), _1631750)) = hAPP(hAPP(c_List_Olist_OCons(_1631746), _1631748), c_List_Olist_ONil(_1631746)))], (500 ^ _779142) ^ [_786604, _786606, _786608, _786610, _786612, _786614, _786616, _786618] : [-(c_List_Olistrelp(_786616, _786612, _786608, _786604)), c_List_Olistrelp(_786618, _786614, _786610, _786606), _786618 = _786616, _786614 = _786612, _786610 = _786608, _786606 = _786604], (39165 ^ _779142) ^ [_1539003, _1539005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539003, _1539003)), _1539005)), 39168 ^ _779142 : [(39175 ^ _779142) ^ [] : [c_Wellfounded_Oacyclic(_1539003, _1539005), -(c_Wellfounded_Owf(_1539003, _1539005))], (39169 ^ _779142) ^ [] : [c_Wellfounded_Owf(_1539003, _1539005), -(c_Wellfounded_Oacyclic(_1539003, _1539005))]]], (21724 ^ _779142) ^ [_1160657, _1160659] : [21725 ^ _779142 : [(21728 ^ _779142) ^ [] : [_1160659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21726 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160657))]], -(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), _1160657), _1160659))))], (8835 ^ _779142) ^ [_928011, _928013, _928015] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_928011), _928013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928011, tc_HOL_Obool)), _928015), _928013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_928011), _928013)), hAPP(c_Finite__Set_Ocard(_928011), _928015))), -(_928015 = _928013)], (21542 ^ _779142) ^ [_1157555, _1157557] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1157555), hAPP(hAPP(c_Power_Opower__class_Opower(_1157555), hAPP(c_Int_Onumber__class_Onumber__of(_1157555), c_Int_OMin)), _1157557)) = c_Groups_Oone__class_Oone(_1157555)), class_Int_Onumber__ring(_1157555), class_Rings_Olinordered__idom(_1157555)], (5697 ^ _779142) ^ [_869112, _869114] : [hBOOL(hAPP(hAPP(c_member(_869112), _869114), c_Orderings_Obot__class_Obot(tc_fun(_869112, tc_HOL_Obool))))], (34887 ^ _779142) ^ [_1426454, _1426456, _1426458, _1426460, _1426462] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426454, tc_fun(_1426456, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426454, tc_HOL_Obool)), _1426458), _1426460)), _1426462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426456, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426454, tc_fun(_1426456, tc_HOL_Obool)), _1426458), _1426462)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426454, tc_fun(_1426456, tc_HOL_Obool)), _1426460), _1426462)))], (16701 ^ _779142) ^ [_1073066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1073066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1073066)))], (49292 ^ _779142) ^ [_1775831, _1775833] : [c_Relation_Osym(_1775831, _1775833), -(c_Relation_Osym(_1775831, c_Transitive__Closure_Otrancl(_1775831, _1775833)))], (36026 ^ _779142) ^ [_1455650, _1455652, _1455654, _1455656, _1455658] : [c_Equiv__Relations_Oequivp(_1455650, _1455652), hBOOL(hAPP(hAPP(_1455652, _1455654), _1455656)), hBOOL(hAPP(hAPP(_1455652, _1455656), _1455658)), -(hBOOL(hAPP(hAPP(_1455652, _1455654), _1455658)))], (6673 ^ _779142) ^ [_886831, _886833, _886835, _886837, _886839] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_886831), _886833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886835, tc_HOL_Obool)), _886837), hAPP(c_Set_Oimage(_886831, _886835, _886839), _886833))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_886835), _886837)))], (13185 ^ _779142) ^ [_1007803, _1007805] : [-(_1007803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007803), _1007805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1007803), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1007805)))], (20143 ^ _779142) ^ [_1132704, _1132706, _1132708, _1132710] : [class_Divides_Osemiring__div(_1132704), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132704), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132704), _1132706), _1132708)), _1132708)), c_Divides_Odiv__class_Omod(_1132704, _1132706, _1132708))), _1132710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132704), _1132706), _1132710))], (32825 ^ _779142) ^ [_1378723, _1378725, _1378727, _1378729, _1378731, _1378733] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378723, tc_fun(_1378725, tc_HOL_Obool))), _1378727), _1378729), _1378731), _1378733)), -(hBOOL(hAPP(hAPP(_1378729, _1378731), _1378733)))], (21472 ^ _779142) ^ [_1156447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156447)), -(c_Nat__Transfer_Ois__nat(_1156447))], (12435 ^ _779142) ^ [_993758, _993760, _993762] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993758), _993760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993762), _993760)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993758), _993762))], (13129 ^ _779142) ^ [_1006683, _1006685, _1006687, _1006689, _1006691, _1006693] : [class_Rings_Olinordered__semiring__1(_1006683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006683), _1006685), _1006687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006683), _1006689), _1006687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006683), c_Groups_Ozero__class_Ozero(_1006683)), _1006691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006683), c_Groups_Ozero__class_Ozero(_1006683)), _1006693)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006683), _1006691), _1006693) = c_Groups_Oone__class_Oone(_1006683), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006683), _1006691), _1006685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006683), _1006693), _1006689))), _1006687)))], (14713 ^ _779142) ^ [_1035913, _1035915, _1035917] : [class_Fields_Olinordered__field(_1035913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035913), _1035915), _1035917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035913), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035913), _1035915), _1035917)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035913), c_Groups_Oone__class_Oone(_1035913)), c_Groups_Oone__class_Oone(_1035913)))), _1035917)))], (42584 ^ _779142) ^ [_1628132, _1628134, _1628136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628132), tc_List_Olist(_1628132))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628132), tc_List_Olist(_1628132)), _1628134), c_List_Olist_ONil(_1628132))), c_List_Olistrel(_1628132, _1628136))), -(_1628134 = c_List_Olist_ONil(_1628132))], (50117 ^ _779142) ^ [_1792536, _1792538, _1792540, _1792542] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792536), _1792538)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792540), _1792542)), 50124 ^ _779142 : [(50131 ^ _779142) ^ [] : [hAPP(c_Finite__Set_Ocard(_1792536), _1792538) = hAPP(c_Finite__Set_Ocard(_1792540), _1792542), -(c_Fun_Obij__betw(_1792536, _1792540, 50134 ^ [_1792536, _1792538, _1792540, _1792542], _1792538, _1792542))], (50125 ^ _779142) ^ [] : [50126 ^ _779142 : [(50127 ^ _779142) ^ [_1792725] : [c_Fun_Obij__betw(_1792536, _1792540, _1792725, _1792538, _1792542)]], -(hAPP(c_Finite__Set_Ocard(_1792536), _1792538) = hAPP(c_Finite__Set_Ocard(_1792540), _1792542))]]], (17043 ^ _779142) ^ [_1078978, _1078980, _1078982, _1078984, _1078986] : [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), _1078978), _1078980)), _1078982)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078978), _1078984)), _1078986))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078982), _1078978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078986), _1078978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078980), _1078984)))], (17642 ^ _779142) ^ [_1089935] : [hBOOL(hAPP(_1089935, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 17643 ^ [_1089935]))), 17646 ^ _779142 : [(17647 ^ _779142) ^ [_1090035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1090035)), -(hBOOL(hAPP(_1089935, _1090035)))]]], (43858 ^ _779142) ^ [_1656431, _1656433, _1656435] : [class_Groups_Omonoid__add(_1656431), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656431), _1656433), hAPP(c_List_Ofoldl(_1656431, _1656431, c_Groups_Oplus__class_Oplus(_1656431), c_Groups_Ozero__class_Ozero(_1656431)), _1656435)) = hAPP(c_List_Ofoldl(_1656431, _1656431, c_Groups_Oplus__class_Oplus(_1656431), _1656433), _1656435))], (33331 ^ _779142) ^ [_1389323, _1389325, _1389327, _1389329] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389323, _1389325), _1389327)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389323, _1389325), _1389329)), -(_1389327 = _1389329)], (6179 ^ _779142) ^ [_878026, _878028, _878030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878026, tc_HOL_Obool)), _878028), _878030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878026, tc_HOL_Obool)), _878030), _878028)), -(_878028 = _878030)], (20770 ^ _779142) ^ [_1144173, _1144175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144173)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144173), _1144175)), _1144173) = _1144175)], (25754 ^ _779142) ^ [_1231766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231766), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1231766)), c_Int_OMin)))], (8064 ^ _779142) ^ [_912115, _912117, _912119, _912121, _912123, _912125] : [c_Finite__Set_Ofun__left__comm(_912115, _912117, _912119), hBOOL(hAPP(c_Finite__Set_Ofinite(_912115), _912121)), -(hAPP(hAPP(_912119, _912123), hAPP(hAPP(c_Finite__Set_Ofold(_912115, _912117, _912119), _912125), _912121)) = hAPP(hAPP(c_Finite__Set_Ofold(_912115, _912117, _912119), hAPP(hAPP(_912119, _912123), _912125)), _912121))], (50987 ^ _779142) ^ [_1811310, _1811312] : [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)))), _1811310, _1811312), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811310), _1811312)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811312), _1811310)))], (25612 ^ _779142) ^ [_1229319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1229319)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229319), c_Int_OMin)))], (52677 ^ _779142) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (35458 ^ _779142) ^ [_1441651, _1441653, _1441655, _1441657, _1441659, _1441661] : [-(hAPP(c_Relation_OImage(_1441651, _1441653, _1441655), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1441657, tc_fun(_1441651, tc_HOL_Obool)), _1441659), _1441661)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1441657, tc_fun(_1441653, tc_HOL_Obool)), _1441659), hAPP(hAPP(c_COMBB(tc_fun(_1441651, tc_HOL_Obool), tc_fun(_1441653, tc_HOL_Obool), _1441657), c_Relation_OImage(_1441651, _1441653, _1441655)), _1441661)))], (52233 ^ _779142) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (21318 ^ _779142) ^ [_1153924, _1153926] : [class_Rings_Ocomm__semiring__1(_1153924), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1153924), _1153926), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1153924))], (41792 ^ _779142) ^ [_1607901, _1607903, _1607905] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607901, _1607901)), hAPP(hAPP(c_Product__Type_OPair(_1607901, _1607901), 41793 ^ [_1607901, _1607903, _1607905]), 41793 ^ [_1607901, _1607903, _1607905])), _1607903))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607901), tc_List_Olist(_1607901))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607901), tc_List_Olist(_1607901)), _1607905), _1607905)), c_List_Olexord(_1607901, _1607903)))], (44001 ^ _779142) ^ [_1659630, _1659632, _1659634, _1659636] : [class_Orderings_Olinorder(_1659630), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659632, _1659630, _1659634), _1659636), c_List_Olist_ONil(_1659632)) = hAPP(hAPP(c_List_Olist_OCons(_1659632), _1659636), c_List_Olist_ONil(_1659632)))], (28403 ^ _779142) ^ [_1281159, _1281161, _1281163] : [class_Complete__Lattice_Ocomplete__lattice(_1281159), class_Orderings_Olinorder(_1281159), 28410 ^ _779142 : [(28420 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281159), _1281161), c_Complete__Lattice_OSup__class_OSup(_1281159, _1281163)))), 28421 ^ _779142 : [(28422 ^ _779142) ^ [_1281465] : [hBOOL(hAPP(hAPP(c_member(_1281159), _1281465), _1281163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281159), _1281161), _1281465))]]], (28411 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281159), _1281161), c_Complete__Lattice_OSup__class_OSup(_1281159, _1281163))), 28415 ^ _779142 : [(28418 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281159), _1281161), 28414 ^ [_1281159, _1281161, _1281163])))], (28416 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281159), 28414 ^ [_1281159, _1281161, _1281163]), _1281163)))]]]]], (5904 ^ _779142) ^ [_872739, _872741, _872743, _872745] : [hBOOL(hAPP(hAPP(c_member(_872739), _872741), hAPP(hAPP(c_Set_Oinsert(_872739), _872743), _872745))), -(_872741 = _872743), -(hBOOL(hAPP(hAPP(c_member(_872739), _872741), _872745)))], (40785 ^ _779142) ^ [_1578738, _1578740, _1578742] : [-(hAPP(c_Relation_ODomain(_1578738, _1578740), hAPP(c_Relation_Oconverse(_1578740, _1578738), _1578742)) = hAPP(c_Relation_ORange(_1578740, _1578738), _1578742))], (20630 ^ _779142) ^ [] : [-(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))))], (26552 ^ _779142) ^ [_1246270, _1246272, _1246274, _1246276] : [class_Lattices_Osemilattice__sup(_1246270), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246270), _1246272), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246270), _1246274), _1246276)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246270), _1246274), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246270), _1246272), _1246276)))], (41921 ^ _779142) ^ [_1611286, _1611288, _1611290, _1611292] : [-(hAPP(hAPP(c_List_Otake(_1611286), hAPP(c_Nat_OSuc, _1611288)), hAPP(hAPP(c_List_Olist_OCons(_1611286), _1611290), _1611292)) = hAPP(hAPP(c_List_Olist_OCons(_1611286), _1611290), hAPP(hAPP(c_List_Otake(_1611286), _1611288), _1611292)))], (31450 ^ _779142) ^ [_1343301, _1343303] : [class_Complete__Lattice_Ocomplete__lattice(_1343301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343301), _1343303)), -(_1343303 = c_Orderings_Obot__class_Obot(tc_fun(_1343301, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1343301, _1343303) = c_Complete__Lattice_OInf__class_OInf(_1343301, _1343303))], (31104 ^ _779142) ^ [_1336633, _1336635] : [class_Groups_Oordered__ab__group__add(_1336633), -(hAPP(c_Set_Oimage(_1336633, _1336633, c_Groups_Ouminus__class_Ouminus(_1336633)), hAPP(c_SetInterval_Oord__class_OatMost(_1336633), _1336635)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1336633), hAPP(c_Groups_Ouminus__class_Ouminus(_1336633), _1336635)))], (23757 ^ _779142) ^ [_1197583, _1197585] : [class_Int_Onumber__ring(_1197583), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197583), hAPP(c_Int_Onumber__class_Onumber__of(_1197583), c_Int_OMin)), _1197585) = hAPP(c_Groups_Ouminus__class_Ouminus(_1197583), _1197585))], (1296 ^ _779142) ^ [_798284, _798286] : [-(class_Int_Oring__char__0(_798284)), _798286 = _798284, class_Int_Oring__char__0(_798286)], (11293 ^ _779142) ^ [_973160, _973162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973160), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973162), _973160)))))], (40538 ^ _779142) ^ [_1573023] : [-(hAPP(c_Relation_ODomain(_1573023, _1573023), c_Relation_OId(_1573023)) = c_Orderings_Otop__class_Otop(tc_fun(_1573023, tc_HOL_Obool)))], (31080 ^ _779142) ^ [_1336097, _1336099, _1336101, _1336103] : [class_Orderings_Olinorder(_1336097), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336097, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1336097), _1336099)), c_SetInterval_Oord__class_OatLeastAtMost(_1336097, _1336101, _1336103)) = c_SetInterval_Oord__class_OatLeastAtMost(_1336097, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336097), _1336099), _1336101), _1336103))], (33857 ^ _779142) ^ [_1399202, _1399204, _1399206, _1399208, _1399210] : [hAPP(c_Product__Type_Ofst(_1399202, _1399204), hAPP(hAPP(c_Product__Type_OPair(_1399202, _1399204), _1399206), _1399208)) = _1399210, -(_1399206 = _1399210)], (29413 ^ _779142) ^ [_1301722, _1301724, _1301726, _1301728] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301722, tc_HOL_Obool)), _1301724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301722, tc_HOL_Obool)), _1301726), _1301728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301722, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301722, tc_HOL_Obool)), _1301724), _1301726)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301722, tc_HOL_Obool)), _1301724), _1301728)))], (6986 ^ _779142) ^ [_893716, _893718, _893720, _893722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893716, tc_HOL_Obool)), _893718), _893720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893716, tc_HOL_Obool)), _893720), _893722)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893716, tc_HOL_Obool)), _893720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893716, tc_HOL_Obool)), _893722), _893718)) = _893718)], (49624 ^ _779142) ^ [_1781881, _1781883, _1781885, _1781887] : [c_Fun_Oinj__on(_1781881, _1781883, _1781885, c_Orderings_Otop__class_Otop(tc_fun(_1781881, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1781881, _1781883, c_Orderings_Otop__class_Otop(tc_fun(_1781881, tc_HOL_Obool)), _1781885), hAPP(_1781885, _1781887)) = _1781887)], (37231 ^ _779142) ^ [_1482225, _1482227, _1482229, _1482231, _1482233] : [-(hAPP(c_Set_Ovimage(_1482225, _1482227, _1482229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482227, tc_HOL_Obool)), _1482231), _1482233)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482225, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1482225, _1482227, _1482229), _1482231)), hAPP(c_Set_Ovimage(_1482225, _1482227, _1482229), _1482233)))], (45386 ^ _779142) ^ [_1690026] : [-(c_List_Oremdups(_1690026, c_List_Olist_ONil(_1690026)) = c_List_Olist_ONil(_1690026))], (25488 ^ _779142) ^ [_1227117] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1227117)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1227117)))], (52663 ^ _779142) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (26934 ^ _779142) ^ [_1254268, _1254270] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254268), _1254270) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254268)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254270))))], (25774 ^ _779142) ^ [_1232162] : [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), _1232162))), 25777 ^ _779142 : [(25780 ^ _779142) ^ [] : [-(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(_1232162)))))], (25778 ^ _779142) ^ [] : [-(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(_1232162)))))]]], (40172 ^ _779142) ^ [_1563545, _1563547] : [c_Wellfounded_Owf(_1563545, _1563547), -(c_Wellfounded_Owf(_1563545, c_Transitive__Closure_Otrancl(_1563545, _1563547)))], (38226 ^ _779142) ^ [_1514605, _1514607] : [-(hAPP(c_Set_Oimage(_1514605, _1514605, c_Fun_Oid(_1514605)), _1514607) = _1514607)], (25178 ^ _779142) ^ [_1221660, _1221662] : [class_Rings_Olinordered__idom(_1221660), 25181 ^ _779142 : [(25188 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221660), c_Groups_Ozero__class_Ozero(_1221660)), _1221662)), -(c_Groups_Osgn__class_Osgn(_1221660, _1221662) = c_Groups_Oone__class_Oone(_1221660))], (25182 ^ _779142) ^ [] : [c_Groups_Osgn__class_Osgn(_1221660, _1221662) = c_Groups_Oone__class_Oone(_1221660), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221660), c_Groups_Ozero__class_Ozero(_1221660)), _1221662)))]]], (3380 ^ _779142) ^ [_829548, _829550, _829552, _829554] : [-(c_List_OremoveAll(_829554, _829550) = c_List_OremoveAll(_829552, _829548)), _829554 = _829552, _829550 = _829548], (33379 ^ _779142) ^ [_1389963, _1389965, _1389967, _1389969, _1389971, _1389973] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389963, _1389965), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389967), _1389969))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389963, _1389965), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389971), _1389973))), -(_1389965 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389969 = _1389973)], (29293 ^ _779142) ^ [_1298956] : [class_Lattices_Osemilattice__inf(_1298956), -(c_Finite__Set_Ofun__left__comm__idem(_1298956, _1298956, c_Lattices_Osemilattice__inf__class_Oinf(_1298956)))], (31913 ^ _779142) ^ [_1354459, _1354461, _1354463] : [hAPP(hAPP(c_COMBC(_1354459, tc_fun(_1354459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354459)), _1354461) = hAPP(hAPP(c_COMBC(_1354459, tc_fun(_1354459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354459)), _1354463), -(_1354461 = _1354463)], (30301 ^ _779142) ^ [_1321201, _1321203] : [class_Lattices_Olattice(_1321201), -(c_Big__Operators_Olattice__class_OInf__fin(_1321201, hAPP(hAPP(c_Set_Oinsert(_1321201), _1321203), c_Orderings_Obot__class_Obot(tc_fun(_1321201, tc_HOL_Obool)))) = _1321203)], (9358 ^ _779142) ^ [_938725] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938725), _938725)))))], (41411 ^ _779142) ^ [_1596418, _1596420, _1596422, _1596424] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596418), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596420), _1596422)))), -(hAPP(c_Random_Opick(_1596420, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596420)), _1596422), _1596424)), _1596418) = hAPP(c_Random_Opick(_1596420, _1596424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1596418), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596420), _1596422))))], (42746 ^ _779142) ^ [_1630962, _1630964, _1630966] : [-(hAPP(hAPP(c_List_Olist__update(_1630962, c_List_Olist_ONil(_1630962)), _1630964), _1630966) = c_List_Olist_ONil(_1630962))], (44390 ^ _779142) ^ [_1667693, _1667695, _1667697, _1667699, _1667701] : [class_Rings_Osemiring__0(_1667693), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667693), hAPP(hAPP(c_List_Omap(_1667695, _1667693), hAPP(hAPP(c_COMBB(_1667693, _1667693, _1667695), hAPP(c_Groups_Otimes__class_Otimes(_1667693), _1667697)), _1667699)), _1667701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667693), _1667697), hAPP(c_List_Omonoid__add__class_Olistsum(_1667693), hAPP(hAPP(c_List_Omap(_1667695, _1667693), _1667699), _1667701))))], (43953 ^ _779142) ^ [_1658420, _1658422, _1658424] : [class_Orderings_Olinorder(_1658420), -(c_Big__Operators_Olattice_OSup__fin(_1658420, c_Orderings_Oord__class_Omax(_1658420), hAPP(c_List_Oset(_1658420), hAPP(hAPP(c_List_Olist_OCons(_1658420), _1658422), _1658424))) = hAPP(c_List_Ofoldl(_1658420, _1658420, c_Orderings_Oord__class_Omax(_1658420), _1658422), _1658424))], (20714 ^ _779142) ^ [_1143149, _1143151] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143149), _1143151)), _1143149)))], (35355 ^ _779142) ^ [_1438692, _1438694, _1438696, _1438698] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438692, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35356 ^ [_1438692, _1438694, _1438696, _1438698])), _1438694) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438692, 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), 35356 ^ [_1438692, _1438694, _1438696, _1438698]), _1438696))), _1438698), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438692, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1438694) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438692, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1438698))], (29353 ^ _779142) ^ [_1300326, _1300328, _1300330, _1300332] : [-(hBOOL(hAPP(hAPP(c_member(_1300326), _1300328), _1300330))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300326, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1300326), _1300328), _1300332)), _1300330) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300326, tc_HOL_Obool)), _1300332), _1300330))], (37199 ^ _779142) ^ [_1481393, _1481395, _1481397, _1481399, _1481401, _1481403] : [-(hAPP(c_Set_Ovimage(_1481393, _1481395, _1481397), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481399, tc_fun(_1481395, tc_HOL_Obool)), _1481401), _1481403)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481399, tc_fun(_1481393, tc_HOL_Obool)), _1481401), hAPP(hAPP(c_COMBB(tc_fun(_1481395, tc_HOL_Obool), tc_fun(_1481393, tc_HOL_Obool), _1481399), c_Set_Ovimage(_1481393, _1481395, _1481397)), _1481403)))], (31326 ^ _779142) ^ [_1340853, _1340855, _1340857] : [class_Complete__Lattice_Ocomplete__lattice(_1340853), 31329 ^ _779142 : [(31330 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340853), _1340855), c_Complete__Lattice_OInf__class_OInf(_1340853, _1340857))), 31333 ^ _779142 : [(31334 ^ _779142) ^ [_1341011] : [hBOOL(hAPP(hAPP(c_member(_1340853), _1341011), _1340857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340853), _1340855), _1341011)))]]], (31340 ^ _779142) ^ [] : [31342 ^ _779142 : [(31345 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340853), _1340855), 31341 ^ [_1340853, _1340855, _1340857]))], (31343 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340853), 31341 ^ [_1340853, _1340855, _1340857]), _1340857)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340853), _1340855), c_Complete__Lattice_OInf__class_OInf(_1340853, _1340857))))]]], (22945 ^ _779142) ^ [_1183190, _1183192, _1183194] : [class_Groups_Oordered__ab__group__add(_1183190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183190), _1183192), _1183194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183190), hAPP(c_Groups_Ouminus__class_Ouminus(_1183190), _1183194)), hAPP(c_Groups_Ouminus__class_Ouminus(_1183190), _1183192))))], (38593 ^ _779142) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (45754 ^ _779142) ^ [_1698547, _1698549, _1698551, _1698553] : [hBOOL(hAPP(hAPP(c_member(_1698547), _1698549), hAPP(c_List_Oset(_1698547), _1698551))), -(hBOOL(hAPP(_1698553, _1698549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698547)), hAPP(c_List_Ofilter(_1698547, _1698553), _1698551))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698547)), _1698551))))], (31877 ^ _779142) ^ [_1353486, _1353488, _1353490, _1353492, _1353494] : [class_Rings_Osemiring__0(_1353486), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353486), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353488, _1353486), _1353490), _1353492)), _1353494) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353488, _1353486), hAPP(hAPP(c_COMBC(_1353488, _1353486, _1353486), hAPP(hAPP(c_COMBB(_1353486, tc_fun(_1353486, _1353486), _1353488), c_Groups_Otimes__class_Otimes(_1353486)), _1353490)), _1353494)), _1353492))], (39457 ^ _779142) ^ [_1546595, _1546597, _1546599, _1546601, _1546603, _1546605] : [-(hAPP(c_Set_Oimage(_1546595, _1546597, hAPP(c_Fun_Ocomp(_1546599, _1546597, _1546595, _1546601), _1546603)), _1546605) = hAPP(c_Set_Oimage(_1546599, _1546597, _1546601), hAPP(c_Set_Oimage(_1546595, _1546599, _1546603), _1546605)))], (11241 ^ _779142) ^ [_972349, _972351] : [11242 ^ _779142 : [(11245 ^ _779142) ^ [] : [_972351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11243 ^ _779142) ^ [] : [_972349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972349), _972351) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41987 ^ _779142) ^ [_1612817, _1612819, _1612821, _1612823, _1612825] : [hBOOL(hAPP(hAPP(c_member(_1612817), _1612819), hAPP(c_List_Oset(_1612817), _1612821))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612823), hAPP(_1612825, _1612819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612823), c_List_Olist_Olist__size(_1612817, _1612825, _1612821))))], (26712 ^ _779142) ^ [_1249695, _1249697] : [class_Lattices_Obounded__lattice__bot(_1249695), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1249695), c_Orderings_Obot__class_Obot(_1249695)), _1249697) = _1249697)], (48310 ^ _779142) ^ [_1753118, _1753120] : [-(c_List_Oreplicate(_1753118, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753120) = c_List_Olist_ONil(_1753118))], (41278 ^ _779142) ^ [_1592048, _1592050] : [-(c_Nitpick_Oinverse__frac(_1592048, _1592050) = hAPP(hAPP(c_Nitpick_Ofrac(_1592048), hAPP(c_Nitpick_Odenom(_1592048), _1592050)), hAPP(c_Nitpick_Onum(_1592048), _1592050)))], (26756 ^ _779142) ^ [_1250391, _1250393, _1250395, _1250397] : [class_Lattices_Osemilattice__sup(_1250391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250391), _1250393), _1250395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250391), _1250393), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1250391), _1250395), _1250397))))], (45153 ^ _779142) ^ [_1684837, _1684839, _1684841, _1684843] : [_1684843 = c_List_Olist_ONil(_1684837), -(c_List_Olist__all2(_1684837, _1684839, _1684841, _1684843, c_List_Olist_ONil(_1684839)))], (4106 ^ _779142) ^ [_841305, _841307, _841309, _841311] : [-(c_New__DSequence_Opos__single(_841311, _841307) = c_New__DSequence_Opos__single(_841309, _841305)), _841311 = _841309, _841307 = _841305], (17959 ^ _779142) ^ [] : [-(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))], (37761 ^ _779142) ^ [_1496400, _1496402, _1496404, _1496406] : [_1496400 = c_Orderings_Obot__class_Obot(tc_fun(_1496402, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1496404, _1496402), _1496404, c_Product__Type_Ofst(_1496404, _1496402)), hAPP(hAPP(c_Product__Type_OSigma(_1496404, _1496402), _1496406), hAPP(c_COMBK(tc_fun(_1496402, tc_HOL_Obool), _1496404), _1496400))) = c_Orderings_Obot__class_Obot(tc_fun(_1496404, tc_HOL_Obool)))], (51781 ^ _779142) ^ [_1824789, _1824791] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824789), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824791))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824791), _1824789)))], (16293 ^ _779142) ^ [_1065588, _1065590, _1065592, _1065594] : [class_Fields_Olinordered__field__inverse__zero(_1065588), class_Int_Onumber(_1065588), 16300 ^ _779142 : [(16301 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1065588), _1065592), _1065594))), 16304 ^ _779142 : [(16311 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), c_Groups_Ozero__class_Ozero(_1065588)), _1065594))), 16314 ^ _779142 : [(16321 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), _1065594), c_Groups_Ozero__class_Ozero(_1065588)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), c_Groups_Ozero__class_Ozero(_1065588))))], (16315 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), _1065594), c_Groups_Ozero__class_Ozero(_1065588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), _1065592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), _1065594))))]]], (16305 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), c_Groups_Ozero__class_Ozero(_1065588)), _1065594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), _1065594)), _1065592)))]]], (16327 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1065588), _1065592), _1065594)))), 16330 ^ _779142 : [(16333 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), _1065594)), _1065592))], (16331 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), c_Groups_Ozero__class_Ozero(_1065588)), _1065594)))]], 16334 ^ _779142 : [(16337 ^ _779142) ^ [] : [16338 ^ _779142 : [(16341 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), _1065592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), _1065594)))], (16339 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), _1065594), c_Groups_Ozero__class_Ozero(_1065588))))]], 16342 ^ _779142 : [(16345 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065588), hAPP(c_Int_Onumber__class_Onumber__of(_1065588), _1065590)), c_Groups_Ozero__class_Ozero(_1065588)))], (16343 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), _1065594), c_Groups_Ozero__class_Ozero(_1065588)))]]], (16335 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065588), c_Groups_Ozero__class_Ozero(_1065588)), _1065594))]]]]], (23131 ^ _779142) ^ [_1186436, _1186438, _1186440] : [class_Rings_Oidom(_1186436), 23134 ^ _779142 : [(23135 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186436), _1186438), _1186438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186436), _1186440), _1186440), -(_1186438 = _1186440), -(_1186438 = hAPP(c_Groups_Ouminus__class_Ouminus(_1186436), _1186440))], (23145 ^ _779142) ^ [] : [23146 ^ _779142 : [(23149 ^ _779142) ^ [] : [_1186438 = hAPP(c_Groups_Ouminus__class_Ouminus(_1186436), _1186440)], (23147 ^ _779142) ^ [] : [_1186438 = _1186440]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186436), _1186438), _1186438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186436), _1186440), _1186440))]]], (6568 ^ _779142) ^ [_884594, _884596, _884598, _884600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884594, tc_HOL_Obool)), _884596), _884598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884594, tc_HOL_Obool)), _884596), hAPP(hAPP(c_Set_Oinsert(_884594), _884600), _884598))))], (20706 ^ _779142) ^ [_1142995, _1142997] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1142995, _1142997))))], (18666 ^ _779142) ^ [_1107687, _1107689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1107687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107689, _1107687)), _1107687)))], (40330 ^ _779142) ^ [_1567968, _1567970] : [-(c_Transitive__Closure_Ortrancl(_1567968, c_Transitive__Closure_Otrancl(_1567968, _1567970)) = c_Transitive__Closure_Ortrancl(_1567968, _1567970))], (42952 ^ _779142) ^ [_1635411, _1635413, _1635415, _1635417, _1635419] : [-(_1635411 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635413, _1635415, _1635417), _1635411), _1635419) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1635415), _1635413), tc_prod(_1635415, _1635413), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635415), _1635413), c_List_Olist_ONil(_1635415)), _1635419), hAPP(c_Product__Type_Oprod_Oprod__case(_1635415, _1635413, tc_prod(tc_List_Olist(_1635415), _1635413)), hAPP(hAPP(c_COMBC(_1635415, tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413)), tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1635415), _1635413), tc_prod(tc_List_Olist(_1635415), _1635413)), tc_fun(tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413)), tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413))), _1635415), c_COMBB(tc_prod(tc_List_Olist(_1635415), _1635413), tc_prod(tc_List_Olist(_1635415), _1635413), _1635413)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635415), tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413))), tc_fun(tc_prod(tc_List_Olist(_1635415), _1635413), tc_prod(tc_List_Olist(_1635415), _1635413)), _1635415), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1635415), _1635413, tc_prod(tc_List_Olist(_1635415), _1635413))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635415), tc_List_Olist(_1635415)), tc_fun(tc_List_Olist(_1635415), tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413))), _1635415), hAPP(c_COMBB(tc_List_Olist(_1635415), tc_fun(_1635413, tc_prod(tc_List_Olist(_1635415), _1635413)), tc_List_Olist(_1635415)), c_Product__Type_OPair(tc_List_Olist(_1635415), _1635413))), c_List_Olist_OCons(_1635415))))), hAPP(c_Lazy__Sequence_Oanamorph(_1635413, _1635415, _1635417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1635411), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1635417, _1635419)))], (25318 ^ _779142) ^ [_1224091, _1224093] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224091), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1224093)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1224091), 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)))), _1224093)))], (45402 ^ _779142) ^ [_1690301, _1690303] : [c_List_Oremdups(_1690301, _1690303) = c_List_Olist_ONil(_1690301), -(_1690303 = c_List_Olist_ONil(_1690301))], (6201 ^ _779142) ^ [_878424, _878426] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878424, tc_HOL_Obool)), _878426), _878426)))], (24858 ^ _779142) ^ [_1216209] : [-(c_Int_OBit1(_1216209) = 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)), _1216209)), _1216209))], (10631 ^ _779142) ^ [_962882, _962884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _962882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _962884)), -(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), _962884), _962882))))], (28272 ^ _779142) ^ [_1278775, _1278777] : [class_Complete__Lattice_Ocomplete__lattice(_1278775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278775), _1278777)), -(_1278777 = c_Orderings_Obot__class_Obot(tc_fun(_1278775, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1278775, _1278777) = c_Complete__Lattice_OSup__class_OSup(_1278775, _1278777))], (49210 ^ _779142) ^ [_1773884, _1773886] : [49213 ^ _779142 : [(49218 ^ _779142) ^ [] : [49211 ^ [_1773884, _1773886] = 49212 ^ [_1773884, _1773886]], (49216 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773884, _1773884)), hAPP(hAPP(c_Product__Type_OPair(_1773884, _1773884), 49212 ^ [_1773884, _1773886]), 49211 ^ [_1773884, _1773886])), _1773886)))], (49214 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773884, _1773884)), hAPP(hAPP(c_Product__Type_OPair(_1773884, _1773884), 49211 ^ [_1773884, _1773886]), 49212 ^ [_1773884, _1773886])), _1773886)))]], -(c_Relation_Oantisym(_1773884, _1773886))], (22737 ^ _779142) ^ [_1179687, _1179689] : [-(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, _1179687)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1179689))))], (33947 ^ _779142) ^ [_1401101, _1401103] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401101), _1401103) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1401101, _1401103)))], (41719 ^ _779142) ^ [_1605991, _1605993, _1605995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605991, tc_HOL_Obool)), _1605993), _1605995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1605991), tc_HOL_Obool)), c_List_Olists(_1605991, _1605993)), c_List_Olists(_1605991, _1605995))))], (29157 ^ _779142) ^ [_1296183, _1296185] : [class_Lattices_Osemilattice__inf(_1296183), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296183), _1296185), _1296185) = _1296185)], (44047 ^ _779142) ^ [_1660673, _1660675, _1660677, _1660679, _1660681, _1660683] : [class_Orderings_Olinorder(_1660673), -(hAPP(_1660675, _1660677) = hAPP(_1660675, _1660679)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660681, _1660673, _1660675), _1660679), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660681, _1660673, _1660675), _1660677), _1660683)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660681, _1660673, _1660675), _1660677), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660681, _1660673, _1660675), _1660679), _1660683)))], (37583 ^ _779142) ^ [_1491451, _1491453, _1491455] : [hBOOL(hAPP(_1491451, _1491453)), -(hAPP(c_Set_OCollect(_1491455), hAPP(hAPP(c_COMBS(_1491455, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491455), c_fconj), hAPP(c_fequal, _1491453))), _1491451)) = hAPP(hAPP(c_Set_Oinsert(_1491455), _1491453), c_Orderings_Obot__class_Obot(tc_fun(_1491455, tc_HOL_Obool))))], (44305 ^ _779142) ^ [_1665071, _1665073, _1665075, _1665077] : [-(_1665071 = c_List_Olist_ONil(_1665073)), -(c_List_Olast(_1665075, hAPP(hAPP(c_List_Omap(_1665073, _1665075), _1665077), _1665071)) = hAPP(_1665077, c_List_Olast(_1665073, _1665071)))], (21196 ^ _779142) ^ [_1151749, _1151751, _1151753] : [21198 ^ _779142 : [(21201 ^ _779142) ^ [] : [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(_1151751, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21197 ^ [_1151749, _1151751, _1151753]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1151751, 21197 ^ [_1151749, _1151751, _1151753])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21199 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21197 ^ [_1151749, _1151751, _1151753]), _1151749)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1151751, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1151753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151753), hAPP(_1151751, _1151749))), 21211 ^ _779142 : [(21214 ^ _779142) ^ [] : [-(hAPP(_1151751, 21210 ^ [_1151749, _1151751, _1151753]) = _1151753)], (21212 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21210 ^ [_1151749, _1151751, _1151753]), _1151749)))]]], (27336 ^ _779142) ^ [_1261388, _1261390, _1261392] : [_1261390 = _1261392, -(hBOOL(hAPP(hAPP(c_member(_1261388), _1261390), hAPP(c_fequal, _1261392))))], (35077 ^ _779142) ^ [_1431385, _1431387, _1431389, _1431391, _1431393] : [class_Complete__Lattice_Ocomplete__lattice(_1431385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431387), _1431389)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1431385), _1431391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1431387, _1431385), _1431389), _1431393)) = hAPP(hAPP(c_Finite__Set_Ofold(_1431387, _1431385, hAPP(hAPP(c_COMBB(_1431385, tc_fun(_1431385, _1431385), _1431387), c_Lattices_Osemilattice__inf__class_Oinf(_1431385)), _1431393)), _1431391), _1431389))], (5186 ^ _779142) ^ [_858259, _858261, _858263, _858265, _858267, _858269] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_858269, _858265, _858261) = c_Lazy__Sequence_Olazy__sequence_OInsert(_858267, _858263, _858259)), _858269 = _858267, _858265 = _858263, _858261 = _858259], (14978 ^ _779142) ^ [_1040929] : [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), _1040929))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040929) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040929)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42299 ^ _779142) ^ [_1621588, _1621590, _1621592, _1621594, _1621596] : [-(hAPP(hAPP(c_List_Olist__update(_1621588, hAPP(hAPP(c_List_Olist_OCons(_1621588), _1621590), _1621592)), _1621594), _1621596) = c_Nat_Onat_Onat__case(tc_List_Olist(_1621588), hAPP(hAPP(c_List_Olist_OCons(_1621588), _1621596), _1621592), hAPP(hAPP(c_COMBB(tc_List_Olist(_1621588), tc_List_Olist(_1621588), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1621588), _1621590)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1621588, tc_List_Olist(_1621588)), c_List_Olist__update(_1621588, _1621592)), _1621596)), _1621594))], (37971 ^ _779142) ^ [_1503473, _1503475, _1503477] : [class_Orderings_Olinorder(_1503473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503473), _1503475)), -(_1503475 = c_Orderings_Obot__class_Obot(tc_fun(_1503473, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503473), _1503477)), -(_1503477 = c_Orderings_Obot__class_Obot(tc_fun(_1503473, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1503473), c_Big__Operators_Olattice_OInf__fin(_1503473, c_Orderings_Oord__class_Omin(_1503473), _1503475)), c_Big__Operators_Olattice_OInf__fin(_1503473, c_Orderings_Oord__class_Omin(_1503473), _1503477)) = c_Big__Operators_Olattice_OInf__fin(_1503473, c_Orderings_Oord__class_Omin(_1503473), hAPP(c_Set_OCollect(_1503473), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_HOL_Obool), tc_HOL_Obool, _1503473), c_HOL_OEx(_1503473)), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool)), tc_fun(_1503473, tc_HOL_Obool), _1503473), hAPP(c_COMBB(tc_fun(_1503473, tc_HOL_Obool), tc_HOL_Obool, _1503473), c_HOL_OEx(_1503473))), hAPP(hAPP(c_COMBC(_1503473, tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool)), tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_fun(tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool))), tc_fun(tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool)), tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool))), _1503473), c_COMBS(_1503473, tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_fun(_1503473, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1503473, tc_fun(tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool))), _1503473), hAPP(c_COMBB(tc_fun(_1503473, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool)), _1503473), c_COMBS(_1503473, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool)), tc_fun(_1503473, tc_fun(_1503473, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1503473), hAPP(c_COMBB(tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1503473), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503473), c_fconj))), hAPP(hAPP(c_COMBC(_1503473, tc_fun(_1503473, tc_fun(_1503473, _1503473)), tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503473, _1503473), tc_fun(_1503473, tc_HOL_Obool)), tc_fun(tc_fun(_1503473, tc_fun(_1503473, _1503473)), tc_fun(_1503473, tc_fun(_1503473, tc_HOL_Obool))), _1503473), c_COMBB(tc_fun(_1503473, _1503473), tc_fun(_1503473, tc_HOL_Obool), _1503473)), hAPP(hAPP(c_COMBB(tc_fun(_1503473, tc_HOL_Obool), tc_fun(tc_fun(_1503473, _1503473), tc_fun(_1503473, tc_HOL_Obool)), _1503473), c_COMBB(_1503473, tc_HOL_Obool, _1503473)), c_fequal))), c_Orderings_Oord__class_Omax(_1503473)))))), hAPP(hAPP(c_COMBC(_1503473, tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1503473, tc_HOL_Obool), tc_fun(_1503473, tc_HOL_Obool)), _1503473), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1503473)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503473), c_fconj), hAPP(hAPP(c_COMBC(_1503473, tc_fun(_1503473, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503473)), _1503475)))), hAPP(hAPP(c_COMBC(_1503473, tc_fun(_1503473, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503473)), _1503477))))))))], (19213 ^ _779142) ^ [_1116949, _1116951] : [class_Groups_Oordered__ab__group__add__abs(_1116949), -(hAPP(c_Groups_Oabs__class_Oabs(_1116949), hAPP(c_Groups_Oabs__class_Oabs(_1116949), _1116951)) = hAPP(c_Groups_Oabs__class_Oabs(_1116949), _1116951))], (35561 ^ _779142) ^ [_1444654, _1444656, _1444658, _1444660] : [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), _1444654), _1444656)), 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), _1444658), _1444660)), 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), _1444654), _1444660)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444658), _1444656))))], (23523 ^ _779142) ^ [_1193416, _1193418, _1193420] : [class_Groups_Oordered__ab__group__add__abs(_1193416), 23526 ^ _779142 : [(23535 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), hAPP(c_Groups_Oabs__class_Oabs(_1193416), _1193418)), _1193420))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), _1193418), _1193420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), hAPP(c_Groups_Ouminus__class_Ouminus(_1193416), _1193418)), _1193420))], (23527 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), hAPP(c_Groups_Oabs__class_Oabs(_1193416), _1193418)), _1193420)), 23530 ^ _779142 : [(23533 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), hAPP(c_Groups_Ouminus__class_Ouminus(_1193416), _1193418)), _1193420)))], (23531 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193416), _1193418), _1193420)))]]]]], (11860 ^ _779142) ^ [_983576, _983578] : [class_Groups_Olinordered__ab__group__add(_983576), 11863 ^ _779142 : [(11870 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983576), _983578), c_Groups_Ozero__class_Ozero(_983576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983576), _983578), _983578)), c_Groups_Ozero__class_Ozero(_983576))))], (11864 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983576), _983578), _983578)), c_Groups_Ozero__class_Ozero(_983576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983576), _983578), c_Groups_Ozero__class_Ozero(_983576))))]]], (13619 ^ _779142) ^ [_1016078, _1016080, _1016082, _1016084] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1016078, _1016080)), c_Sum__Type_OPlus(_1016078, _1016080, _1016082, _1016084))), 13622 ^ _779142 : [(13625 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1016080), _1016084)))], (13623 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1016078), _1016082)))]]], (7044 ^ _779142) ^ [_895202, _895204, _895206, _895208, _895210] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895202, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895202, tc_HOL_Obool)), hAPP(c_Set_Oimage(_895204, _895202, _895206), _895208)), hAPP(c_Set_Oimage(_895204, _895202, _895206), _895210))), hAPP(c_Set_Oimage(_895204, _895202, _895206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895204, tc_HOL_Obool)), _895208), _895210)))))], (34015 ^ _779142) ^ [_1402301, _1402303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1402301)), -(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(_1402301), _1402303))), _1402301)))], (39740 ^ _779142) ^ [_1553186, _1553188, _1553190, _1553192, _1553194, _1553196, _1553198, _1553200] : [c_Finite__Set_Ofolding__image(_1553186, _1553188, _1553190, _1553192, _1553194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553188), _1553196)), -(hAPP(hAPP(_1553194, hAPP(hAPP(c_COMBS(_1553188, _1553186, _1553186), hAPP(hAPP(c_COMBB(_1553186, tc_fun(_1553186, _1553186), _1553188), _1553190), _1553198)), _1553200)), _1553196) = hAPP(hAPP(_1553190, hAPP(hAPP(_1553194, _1553198), _1553196)), hAPP(hAPP(_1553194, _1553200), _1553196)))], (52307 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (40307 ^ _779142) ^ [_1567507, _1567509] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567507, _1567507)), hAPP(hAPP(c_Product__Type_OPair(_1567507, _1567507), 40308 ^ [_1567507, _1567509]), 40308 ^ [_1567507, _1567509])), c_Transitive__Closure_Otrancl(_1567507, _1567509)))), -(c_Wellfounded_Oacyclic(_1567507, _1567509))], (15737 ^ _779142) ^ [_1055325, _1055327, _1055329, _1055331] : [class_Fields_Ofield__inverse__zero(_1055325), class_Int_Onumber(_1055325), 15744 ^ _779142 : [(15745 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1055325), _1055329), _1055331), 15748 ^ _779142 : [(15755 ^ _779142) ^ [] : [_1055331 = c_Groups_Ozero__class_Ozero(_1055325), -(hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327) = c_Groups_Ozero__class_Ozero(_1055325))], (15749 ^ _779142) ^ [] : [-(_1055331 = c_Groups_Ozero__class_Ozero(_1055325)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055325), hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327)), _1055331) = _1055329)]]], (15761 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1055325), _1055329), _1055331)), 15764 ^ _779142 : [(15767 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055325), hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327)), _1055331) = _1055329], (15765 ^ _779142) ^ [] : [_1055331 = c_Groups_Ozero__class_Ozero(_1055325)]], 15768 ^ _779142 : [(15771 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1055325), _1055327) = c_Groups_Ozero__class_Ozero(_1055325)], (15769 ^ _779142) ^ [] : [-(_1055331 = c_Groups_Ozero__class_Ozero(_1055325))]]]]], (14167 ^ _779142) ^ [_1026064, _1026066, _1026068, _1026070] : [class_Fields_Ofield__inverse__zero(_1026064), -(_1026066 = c_Groups_Ozero__class_Ozero(_1026064)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026064), _1026066), _1026068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026064), _1026066), _1026070)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026064), _1026068), _1026070))], (46792 ^ _779142) ^ [_1720021, _1720023, _1720025] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1720021), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1720021))), _1720023))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1720021))), _1720023))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1720021))), hAPP(c_List_Ofilter(tc_List_Olist(_1720021), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1720021)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720025)), c_Nat_Osize__class_Osize(tc_List_Olist(_1720021)))), c_List_Otranspose(_1720021, _1720023))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720021)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1720021)), _1720023), _1720025)))], (34478 ^ _779142) ^ [_1414569, _1414571, _1414573, _1414575, _1414577, _1414579, _1414581] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414569, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414571, tc_fun(_1414569, tc_HOL_Obool)), _1414573), _1414575)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414577, tc_fun(_1414569, tc_HOL_Obool)), _1414579), _1414581)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414571, tc_fun(_1414569, tc_HOL_Obool)), _1414573), hAPP(hAPP(c_COMBB(tc_fun(_1414577, tc_fun(_1414569, tc_HOL_Obool)), tc_fun(_1414569, tc_HOL_Obool), _1414571), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414577, tc_fun(_1414569, tc_HOL_Obool)), _1414579)), hAPP(hAPP(c_COMBC(_1414571, tc_fun(_1414577, tc_fun(_1414569, tc_HOL_Obool)), tc_fun(_1414577, tc_fun(_1414569, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1414569, tc_HOL_Obool), tc_fun(_1414569, tc_HOL_Obool)), tc_fun(tc_fun(_1414577, tc_fun(_1414569, tc_HOL_Obool)), tc_fun(_1414577, tc_fun(_1414569, tc_HOL_Obool))), _1414571), c_COMBB(tc_fun(_1414569, tc_HOL_Obool), tc_fun(_1414569, tc_HOL_Obool), _1414577)), hAPP(hAPP(c_COMBB(tc_fun(_1414569, tc_HOL_Obool), tc_fun(tc_fun(_1414569, tc_HOL_Obool), tc_fun(_1414569, tc_HOL_Obool)), _1414571), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414569, tc_HOL_Obool))), _1414575))), _1414581))))], (32097 ^ _779142) ^ [_1361627, _1361629, _1361631, _1361633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool)), _1361631), _1361633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1361627, tc_fun(_1361629, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1361627, tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_fun(_1361629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361629, tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_fun(_1361629, tc_HOL_Obool)), _1361627), c_COMBC(_1361629, tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361629, tc_prod(_1361627, _1361629)), tc_fun(_1361629, tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), _1361627), hAPP(c_COMBB(tc_prod(_1361627, _1361629), tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool), _1361629), c_member(tc_prod(_1361627, _1361629)))), c_Product__Type_OPair(_1361627, _1361629)))), _1361631)), hAPP(hAPP(c_COMBC(_1361627, tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_fun(_1361629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361629, tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_fun(_1361629, tc_HOL_Obool)), _1361627), c_COMBC(_1361629, tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361629, tc_prod(_1361627, _1361629)), tc_fun(_1361629, tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool)), _1361627), hAPP(c_COMBB(tc_prod(_1361627, _1361629), tc_fun(tc_fun(tc_prod(_1361627, _1361629), tc_HOL_Obool), tc_HOL_Obool), _1361629), c_member(tc_prod(_1361627, _1361629)))), c_Product__Type_OPair(_1361627, _1361629)))), _1361633))))], (10275 ^ _779142) ^ [_956622, _956624] : [class_Rings_Ocomm__semiring__1(_956622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956622), c_Groups_Oone__class_Oone(_956622)), _956624) = _956624)], (7746 ^ _779142) ^ [_907009, _907011, _907013] : [class_Orderings_Olinorder(_907009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907009), _907011), _907013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907009), _907013), _907011))], (8196 ^ _779142) ^ [_915342, _915344, _915346] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_915342), _915344)), -(_915344 = c_Orderings_Obot__class_Obot(tc_fun(_915342, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_915342, _915346, _915344), 8203 ^ [_915342, _915344, _915346])))], (2308 ^ _779142) ^ [_812874, _812876, _812878, _812880] : [-(c_Groups_Osgn__class_Osgn(_812880, _812876) = c_Groups_Osgn__class_Osgn(_812878, _812874)), _812880 = _812878, _812876 = _812874], (32531 ^ _779142) ^ [_1372637, _1372639, _1372641] : [class_Int_Onumber__ring(_1372637), 32534 ^ _779142 : [(32541 ^ _779142) ^ [] : [-(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), _1372639)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1372637), _1372641), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1372639))) = c_Groups_Oone__class_Oone(_1372637))], (32535 ^ _779142) ^ [] : [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), _1372639))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1372637), _1372641), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1372639))) = hAPP(hAPP(c_HOL_OLet(_1372637, _1372637), hAPP(hAPP(c_Power_Opower__class_Opower(_1372637), _1372641), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372639))), hAPP(hAPP(c_COMBS(_1372637, _1372637, _1372637), hAPP(hAPP(c_COMBB(_1372637, tc_fun(_1372637, _1372637), _1372637), c_Groups_Otimes__class_Otimes(_1372637)), hAPP(c_Groups_Otimes__class_Otimes(_1372637), _1372641))), c_COMBI(_1372637))))]]], (22827 ^ _779142) ^ [_1181180, _1181182] : [class_Lattices_Oboolean__algebra(_1181180), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181180), hAPP(c_Groups_Ouminus__class_Ouminus(_1181180), _1181182)) = _1181182)], (52509 ^ _779142) ^ [_1834698] : [class_Lazy__Sequence_Osmall__lazy(_1834698), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1834698)))], (11249 ^ _779142) ^ [_972496, _972498, _972500] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972496), _972498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972496), _972500), -(_972498 = _972500), -(_972496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48905 ^ _779142) ^ [_1766654, _1766656] : [c_Relation_Otrans(_1766654, _1766656), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1766654, _1766654), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1766654, _1766654, _1766654), _1766656), _1766656)), _1766656)))], (17791 ^ _779142) ^ [_1092657, _1092659] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092657)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092659)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1092657), _1092659)))], (47892 ^ _779142) ^ [_1743983, _1743985, _1743987] : [47894 ^ _779142 : [(47897 ^ _779142) ^ [] : [hBOOL(hAPP(_1743987, 47893 ^ [_1743983, _1743985, _1743987]))], (47895 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743983), 47893 ^ [_1743983, _1743985, _1743987]), hAPP(c_List_Oset(_1743983), _1743985))))]], -(c_List_Olist__all(_1743983, _1743987, _1743985))], (38348 ^ _779142) ^ [_1518123, _1518125, _1518127, _1518129, _1518131, _1518133, _1518135, _1518137] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518123, _1518125)), hAPP(hAPP(c_Product__Type_OPair(_1518123, _1518125), _1518127), _1518129)), _1518131)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1518125, _1518133)), hAPP(hAPP(c_Product__Type_OPair(_1518125, _1518133), _1518129), _1518135)), _1518137)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518123, _1518133)), hAPP(hAPP(c_Product__Type_OPair(_1518123, _1518133), _1518127), _1518135)), hAPP(hAPP(c_Relation_Orel__comp(_1518123, _1518125, _1518133), _1518131), _1518137))))], (36926 ^ _779142) ^ [_1474808, _1474810, _1474812, _1474814, _1474816, _1474818] : [c_Typedef_Otype__definition(_1474808, _1474810, _1474812, _1474814, _1474816), hBOOL(hAPP(hAPP(c_member(_1474810), _1474818), _1474816)), -(hAPP(_1474812, hAPP(_1474814, _1474818)) = _1474818)], (18246 ^ _779142) ^ [_1100283, _1100285, _1100287] : [hBOOL(hAPP(_1100283, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1100285, _1100287))), 18249 ^ _779142 : [(18274 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100287), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 18277 ^ _779142 : [(18278 ^ _779142) ^ [_1100905, _1100907] : [-(hBOOL(hAPP(_1100283, _1100905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100287), _1100905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100905), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1100285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1100287), _1100907)), _1100905)]]], (18256 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100287)), 18259 ^ _779142 : [(18260 ^ _779142) ^ [_1100613, _1100615] : [-(hBOOL(hAPP(_1100283, _1100613))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100613), _1100287)), _1100285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1100287), _1100615)), _1100613)]]], (18250 ^ _779142) ^ [] : [_1100287 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1100283, _1100285)))]]], (24796 ^ _779142) ^ [_1215144, _1215146] : [24804 ^ _779142 : [(24807 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1215146, 24803 ^ [_1215144, _1215146])))], (24805 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24803 ^ [_1215144, _1215146]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215144))))]], 24797 ^ _779142 : [(24798 ^ _779142) ^ [_1215212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1215212), _1215144)), hBOOL(hAPP(_1215146, _1215212))]]], (18106 ^ _779142) ^ [_1098045, _1098047] : [class_Int_Onumber__ring(_1098045), class_Rings_Olinordered__idom(_1098045), 18113 ^ _779142 : [(18120 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098045), c_Groups_Ozero__class_Ozero(_1098045)), hAPP(c_Int_Onumber__class_Onumber__of(_1098045), _1098047))))], (18114 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098045), c_Groups_Ozero__class_Ozero(_1098045)), hAPP(c_Int_Onumber__class_Onumber__of(_1098045), _1098047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098047)))]]], (11173 ^ _779142) ^ [_971377, _971379] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971377), _971379) = _971377, -(_971379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17849 ^ _779142) ^ [] : [-(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)))], (38951 ^ _779142) ^ [_1533906, _1533908] : [-(hAPP(c_Relation_OField(_1533906), _1533908) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533906, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533906, _1533906), _1533908)), hAPP(c_Relation_ORange(_1533906, _1533906), _1533908)))], (42968 ^ _779142) ^ [_1635993, _1635995, _1635997, _1635999, _1636001] : [-(hAPP(hAPP(c_List_Oappend(_1635993), _1635995), hAPP(hAPP(c_List_Olist_OCons(_1635993), _1635997), c_List_Olist_ONil(_1635993))) = hAPP(hAPP(c_List_Oappend(_1635993), _1635999), hAPP(hAPP(c_List_Olist_OCons(_1635993), _1636001), c_List_Olist_ONil(_1635993)))), _1635995 = _1635999, _1635997 = _1636001], (37579 ^ _779142) ^ [_1491340, _1491342] : [-(hAPP(c_Set_OCollect(_1491340), hAPP(c_fequal, _1491342)) = hAPP(hAPP(c_Set_Oinsert(_1491340), _1491342), c_Orderings_Obot__class_Obot(tc_fun(_1491340, tc_HOL_Obool))))], (40446 ^ _779142) ^ [_1570800, _1570802, _1570804] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570800, _1570800, _1570802), c_Relation_OId(_1570800)), _1570804) = _1570804)], (34354 ^ _779142) ^ [_1410813, _1410815, _1410817, _1410819, _1410821] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410813, tc_fun(_1410815, tc_HOL_Obool)), _1410817), hAPP(hAPP(c_COMBC(_1410813, tc_fun(_1410815, tc_HOL_Obool), tc_fun(_1410815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410815, tc_HOL_Obool), tc_fun(tc_fun(_1410815, tc_HOL_Obool), tc_fun(_1410815, tc_HOL_Obool)), _1410813), c_Groups_Ominus__class_Ominus(tc_fun(_1410815, tc_HOL_Obool))), _1410819)), _1410821)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410815, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410813, tc_fun(_1410815, tc_HOL_Obool)), _1410817), _1410819)), _1410821))], (43024 ^ _779142) ^ [_1637189, _1637191, _1637193, _1637195, _1637197] : [-(hAPP(hAPP(c_List_Oappend(_1637189), _1637191), _1637193) = hAPP(hAPP(c_List_Olist_OCons(_1637189), _1637195), _1637197)), 43025 ^ _779142 : [(43032 ^ _779142) ^ [_1637372] : [_1637191 = hAPP(hAPP(c_List_Olist_OCons(_1637189), _1637195), _1637372), hAPP(hAPP(c_List_Oappend(_1637189), _1637372), _1637193) = _1637197], (43026 ^ _779142) ^ [] : [_1637191 = c_List_Olist_ONil(_1637189), _1637193 = hAPP(hAPP(c_List_Olist_OCons(_1637189), _1637195), _1637197)]]], (28875 ^ _779142) ^ [_1290793, _1290795, _1290797, _1290799] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290793, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290793, tc_HOL_Obool)), _1290795), _1290797)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290793, tc_HOL_Obool)), _1290799), _1290797)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290793, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290793, tc_HOL_Obool)), _1290795), _1290797)), _1290799))], (49857 ^ _779142) ^ [_1787230, _1787232, _1787234, _1787236] : [c_Fun_Obij__betw(_1787230, _1787232, _1787234, c_Orderings_Otop__class_Otop(tc_fun(_1787230, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787232, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1787230, _1787232, _1787234), hAPP(c_Set_OCollect(_1787230), _1787236)) = hAPP(c_Set_OCollect(_1787232), hAPP(hAPP(c_COMBB(_1787230, tc_HOL_Obool, _1787232), _1787236), c_Hilbert__Choice_Oinv__into(_1787230, _1787232, c_Orderings_Otop__class_Otop(tc_fun(_1787230, tc_HOL_Obool)), _1787234))))], (51643 ^ _779142) ^ [_1822255, _1822257, _1822259, _1822261] : [class_Rings_Ocomm__semiring__1(_1822255), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822255), _1822257), _1822259)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822255), _1822257), _1822261)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822255), _1822257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1822255), _1822259), _1822261))))], (38334 ^ _779142) ^ [_1517267, _1517269, _1517271, _1517273, _1517275, _1517277, _1517279, _1517281] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517267, _1517269)), _1517271), hAPP(c_Set_Oimage(tc_prod(_1517273, _1517275), tc_prod(_1517267, _1517269), c_Product__Type_Omap__pair(_1517273, _1517267, _1517275, _1517269, _1517277, _1517279)), _1517281))), 38339 ^ _779142 : [(38342 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517273, _1517275)), hAPP(hAPP(c_Product__Type_OPair(_1517273, _1517275), 38337 ^ [_1517267, _1517269, _1517271, _1517273, _1517275, _1517277, _1517279, _1517281]), 38338 ^ [_1517267, _1517269, _1517271, _1517273, _1517275, _1517277, _1517279, _1517281])), _1517281)))], (38340 ^ _779142) ^ [] : [-(_1517271 = hAPP(hAPP(c_Product__Type_OPair(_1517267, _1517269), hAPP(_1517277, 38337 ^ [_1517267, _1517269, _1517271, _1517273, _1517275, _1517277, _1517279, _1517281])), hAPP(_1517279, 38338 ^ [_1517267, _1517269, _1517271, _1517273, _1517275, _1517277, _1517279, _1517281])))]]], (33720 ^ _779142) ^ [_1396409, _1396411, _1396413] : [-(hAPP(c_Product__Type_Osnd(_1396409, _1396411), _1396413) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1396409, _1396411, _1396411), hAPP(c_COMBK(tc_fun(_1396411, _1396411), _1396409), c_COMBI(_1396411))), _1396413))], (3808 ^ _779142) ^ [_836258, _836260] : [_836260 = _836258, -(c_Lazy__Sequence_Ohit__bound(_836260) = c_Lazy__Sequence_Ohit__bound(_836258))], (34987 ^ _779142) ^ [_1429007, _1429009, _1429011, _1429013, _1429015] : [-(_1429007 = c_Orderings_Obot__class_Obot(tc_fun(_1429009, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429009, tc_fun(_1429011, tc_HOL_Obool)), _1429007), hAPP(hAPP(c_COMBC(_1429009, tc_fun(_1429011, tc_HOL_Obool), tc_fun(_1429011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429011, tc_HOL_Obool), tc_fun(tc_fun(_1429011, tc_HOL_Obool), tc_fun(_1429011, tc_HOL_Obool)), _1429009), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429011, tc_HOL_Obool))), _1429013)), _1429015)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429011, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429009, tc_fun(_1429011, tc_HOL_Obool)), _1429007), _1429013)), _1429015))], (29255 ^ _779142) ^ [_1298266, _1298268, _1298270] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298266, tc_HOL_Obool)), _1298268), _1298270) = c_Orderings_Obot__class_Obot(tc_fun(_1298266, tc_HOL_Obool)), 29258 ^ _779142 : [(29259 ^ _779142) ^ [_1298390] : [hBOOL(hAPP(hAPP(c_member(_1298266), _1298390), _1298268)), 29262 ^ _779142 : [(29263 ^ _779142) ^ [_1298480] : [hBOOL(hAPP(hAPP(c_member(_1298266), _1298480), _1298270)), _1298390 = _1298480]]]]], (48068 ^ _779142) ^ [_1747925, _1747927] : [c_Wellfounded_Oacyclic(_1747925, hAPP(c_Set_OCollect(tc_prod(_1747925, _1747925)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747925, _1747925, tc_HOL_Obool), c_Predicate_Oconversep(_1747925, _1747925, _1747927)))), -(c_Wellfounded_Oacyclic(_1747925, hAPP(c_Set_OCollect(tc_prod(_1747925, _1747925)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747925, _1747925, tc_HOL_Obool), _1747927))))], (7804 ^ _779142) ^ [_907904, _907906, _907908] : [class_Orderings_Olinorder(_907904), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907904), _907906), _907908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907904), _907908), _907906)))], (32837 ^ _779142) ^ [_1378954, _1378956] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1378954), hAPP(c_Nat_OSuc, _1378956)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1378956), 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)), _1378956)), _1378954))], (152 ^ _779142) ^ [_781454, _781456, _781458, _781460, _781462, _781464] : [-(c_Finite__Set_Ofolding__one__idem(_781462, _781458, _781454)), c_Finite__Set_Ofolding__one__idem(_781464, _781460, _781456), _781464 = _781462, _781460 = _781458, _781456 = _781454], (46090 ^ _779142) ^ [_1706433, _1706435, _1706437] : [class_Orderings_Olinorder(_1706433), c_List_Olinorder__class_Osorted(_1706433, _1706435), -(c_List_Olinorder__class_Osorted(_1706433, hAPP(hAPP(c_List_Odrop(_1706433), _1706437), _1706435)))], (8875 ^ _779142) ^ [_928821, _928823, _928825, _928827, _928829] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928821), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), _928823), _928825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928821), _928827), _928829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928823), _928827)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928825), _928829))))], (34340 ^ _779142) ^ [_1410326, _1410328, _1410330, _1410332, _1410334, _1410336] : [class_Complete__Lattice_Ocomplete__lattice(_1410326), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410328, tc_fun(_1410330, _1410326)), _1410332), _1410334), _1410336) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410328, _1410326), _1410332), hAPP(hAPP(c_COMBC(_1410328, _1410330, _1410326), _1410334), _1410336)))], (25548 ^ _779142) ^ [_1228157, _1228159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228157), _1228159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1228157)), c_Int_OBit1(_1228159))))], (45330 ^ _779142) ^ [_1688905, _1688907, _1688909, _1688911, _1688913] : [c_Finite__Set_Ofun__left__comm(_1688905, _1688907, _1688909), -(hAPP(hAPP(c_Finite__Set_Ofold(_1688905, _1688907, _1688909), _1688911), hAPP(c_List_Oset(_1688905), _1688913)) = hAPP(c_List_Ofoldl(_1688907, _1688905, hAPP(c_COMBC(_1688905, _1688907, _1688907), _1688909), _1688911), c_List_Oremdups(_1688905, _1688913)))], (38300 ^ _779142) ^ [_1516298, _1516300, _1516302, _1516304, _1516306, _1516308, _1516310, _1516312] : [-(hAPP(c_Product__Type_Omap__pair(_1516298, _1516300, _1516302, _1516304, _1516306, _1516308), hAPP(hAPP(c_Product__Type_OPair(_1516298, _1516302), _1516310), _1516312)) = hAPP(hAPP(c_Product__Type_OPair(_1516300, _1516304), hAPP(_1516306, _1516310)), hAPP(_1516308, _1516312)))], (52297 ^ _779142) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (35625 ^ _779142) ^ [_1446389, _1446391, _1446393] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446389, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446389), _1446391), _1446393), -(_1446391 = c_Orderings_Obot__class_Obot(tc_fun(_1446389, tc_HOL_Obool)))], (35031 ^ _779142) ^ [_1430181, _1430183] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430181, 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(_1430181, tc_HOL_Obool)), tc_fun(_1430181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1430181, tc_HOL_Obool)), tc_fun(_1430181, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430181, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1430183)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430181, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430183))], (4646 ^ _779142) ^ [_849811, _849813] : [_849813 = _849811, -(c_Random__Sequence_Osingle(_849813) = c_Random__Sequence_Osingle(_849811))], (39260 ^ _779142) ^ [_1541439, _1541441, _1541443] : [hBOOL(hAPP(c_Predicate_OPowp(_1541439, _1541441), _1541443)), 39263 ^ _779142 : [(39264 ^ _779142) ^ [_1541523] : [hBOOL(hAPP(hAPP(c_member(_1541439), _1541523), _1541443)), -(hBOOL(hAPP(_1541441, _1541523)))]]], (7106 ^ _779142) ^ [_896603, _896605, _896607, _896609, _896611] : [class_Groups_Oordered__ab__group__add(_896603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896603), _896605), _896607) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896603), _896609), _896611), 7113 ^ _779142 : [(7120 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896603), _896609), _896611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896603), _896605), _896607)))], (7114 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896603), _896605), _896607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896603), _896609), _896611)))]]], (40809 ^ _779142) ^ [_1579414, _1579416, _1579418, _1579420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579414, _1579414)), hAPP(hAPP(c_Product__Type_OPair(_1579414, _1579414), _1579416), _1579418)), c_Transitive__Closure_Otrancl(_1579414, hAPP(c_Relation_Oconverse(_1579414, _1579414), _1579420)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579414, _1579414)), hAPP(hAPP(c_Product__Type_OPair(_1579414, _1579414), _1579416), _1579418)), hAPP(c_Relation_Oconverse(_1579414, _1579414), c_Transitive__Closure_Otrancl(_1579414, _1579420)))))], (44520 ^ _779142) ^ [_1670758, _1670760, _1670762, _1670764] : [-(hBOOL(hAPP(c_List_Odistinct(_1670758), hAPP(hAPP(c_List_Omap(_1670760, _1670758), _1670762), _1670764)))), hBOOL(hAPP(c_List_Odistinct(_1670760), _1670764)), c_Fun_Oinj__on(_1670760, _1670758, _1670762, hAPP(c_List_Oset(_1670760), _1670764))], (40743 ^ _779142) ^ [_1577947, _1577949, _1577951] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577947, _1577949)), hAPP(c_Relation_Oconverse(_1577949, _1577947), _1577951))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577949, _1577947)), _1577951)))], (3626 ^ _779142) ^ [_833429, _833431] : [_833431 = _833429, -(c_List_Oembed__list(_833431) = c_List_Oembed__list(_833429))], (30780 ^ _779142) ^ [_1330645, _1330647] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330645, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1330645, tc_HOL_Obool))), _1330647) = c_Orderings_Otop__class_Otop(tc_fun(_1330645, tc_HOL_Obool)))], (44448 ^ _779142) ^ [_1669128, _1669130, _1669132, _1669134, _1669136] : [-(hAPP(hAPP(c_List_Omap(_1669128, _1669130), _1669132), hAPP(hAPP(c_List_Olist_OCons(_1669128), _1669134), _1669136)) = hAPP(hAPP(c_List_Olist_OCons(_1669130), hAPP(_1669132, _1669134)), hAPP(hAPP(c_List_Omap(_1669128, _1669130), _1669132), _1669136)))], (13395 ^ _779142) ^ [_1011842, _1011844] : [class_Groups_Olinordered__ab__group__add(_1011842), 13398 ^ _779142 : [(13405 ^ _779142) ^ [] : [_1011844 = c_Groups_Ozero__class_Ozero(_1011842), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011842), _1011844), _1011844) = c_Groups_Ozero__class_Ozero(_1011842))], (13399 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011842), _1011844), _1011844) = c_Groups_Ozero__class_Ozero(_1011842), -(_1011844 = c_Groups_Ozero__class_Ozero(_1011842))]]], (12312 ^ _779142) ^ [_991697, _991699, _991701, _991703] : [class_Rings_Ocomm__semiring__1(_991697), class_Rings_Ono__zero__divisors(_991697), hBOOL(hAPP(c_Finite__Set_Ofinite(_991699), _991701)), 12323 ^ _779142 : [(12333 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_991699, _991697), _991703), _991701) = c_Groups_Ozero__class_Ozero(_991697)), 12334 ^ _779142 : [(12335 ^ _779142) ^ [_992075] : [hBOOL(hAPP(hAPP(c_member(_991699), _992075), _991701)), hAPP(_991703, _992075) = c_Groups_Ozero__class_Ozero(_991697)]]], (12324 ^ _779142) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_991699, _991697), _991703), _991701) = c_Groups_Ozero__class_Ozero(_991697), 12328 ^ _779142 : [(12331 ^ _779142) ^ [] : [-(hAPP(_991703, 12327 ^ [_991697, _991699, _991701, _991703]) = c_Groups_Ozero__class_Ozero(_991697))], (12329 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_991699), 12327 ^ [_991697, _991699, _991701, _991703]), _991701)))]]]]], (24009 ^ _779142) ^ [_1201921, _1201923] : [class_Int_Onumber__ring(_1201921), 24012 ^ _779142 : [(24019 ^ _779142) ^ [] : [c_Int_Oiszero(_1201921, hAPP(c_Int_Onumber__class_Onumber__of(_1201921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201923)))), -(c_Groups_Ozero__class_Ozero(_1201921) = hAPP(c_Int_Onumber__class_Onumber__of(_1201921), _1201923))], (24013 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_1201921) = hAPP(c_Int_Onumber__class_Onumber__of(_1201921), _1201923), -(c_Int_Oiszero(_1201921, hAPP(c_Int_Onumber__class_Onumber__of(_1201921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201923)))))]]], (31997 ^ _779142) ^ [_1358489, _1358491, _1358493, _1358495] : [-(_1358489 = c_Orderings_Obot__class_Obot(tc_fun(_1358491, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1358491, _1358493, hAPP(c_COMBK(_1358493, _1358491), _1358495)), _1358489) = hAPP(hAPP(c_Set_Oinsert(_1358493), _1358495), c_Orderings_Obot__class_Obot(tc_fun(_1358493, tc_HOL_Obool))))], (33355 ^ _779142) ^ [_1389643, _1389645, _1389647] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389643, _1389643), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389645), _1389647))), -(_1389643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42017 ^ _779142) ^ [_1613460, _1613462, _1613464] : [42019 ^ _779142 : [(42022 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1613460), 42018 ^ [_1613460, _1613462, _1613464]), _1613464))], (42020 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613460), 42018 ^ [_1613460, _1613462, _1613464]), hAPP(c_List_Oset(_1613460), _1613462))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613460)), _1613462), c_List_Olists(_1613460, _1613464))))], (34895 ^ _779142) ^ [_1426694, _1426696, _1426698, _1426700, _1426702] : [-(_1426694 = c_Orderings_Obot__class_Obot(tc_fun(_1426696, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426698, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426696, tc_fun(_1426698, tc_HOL_Obool)), _1426694), _1426700)), _1426702) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426696, tc_fun(_1426698, tc_HOL_Obool)), _1426694), hAPP(hAPP(c_COMBC(_1426696, tc_fun(_1426698, tc_HOL_Obool), tc_fun(_1426698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426698, tc_HOL_Obool), tc_fun(tc_fun(_1426698, tc_HOL_Obool), tc_fun(_1426698, tc_HOL_Obool)), _1426696), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426698, tc_HOL_Obool))), _1426700)), _1426702)))], (40727 ^ _779142) ^ [_1577609, _1577611, _1577613, _1577615] : [-(hAPP(c_Relation_Oconverse(_1577609, _1577611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1577609, _1577611), tc_HOL_Obool)), _1577613), _1577615)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1577611, _1577609), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1577609, _1577611), _1577613)), hAPP(c_Relation_Oconverse(_1577609, _1577611), _1577615)))], (48402 ^ _779142) ^ [_1755069, _1755071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755069), _1755071)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755069, _1755071) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (11460 ^ _779142) ^ [_976301, _976303, _976305] : [class_Groups_Oordered__comm__monoid__add(_976301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976301), c_Groups_Ozero__class_Ozero(_976301)), _976303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976301), c_Groups_Ozero__class_Ozero(_976301)), _976305)), 11471 ^ _779142 : [(11480 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976301), _976303), _976305) = c_Groups_Ozero__class_Ozero(_976301)), _976303 = c_Groups_Ozero__class_Ozero(_976301), _976305 = c_Groups_Ozero__class_Ozero(_976301)], (11472 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976301), _976303), _976305) = c_Groups_Ozero__class_Ozero(_976301), 11475 ^ _779142 : [(11478 ^ _779142) ^ [] : [-(_976305 = c_Groups_Ozero__class_Ozero(_976301))], (11476 ^ _779142) ^ [] : [-(_976303 = c_Groups_Ozero__class_Ozero(_976301))]]]]], (49841 ^ _779142) ^ [_1787013, _1787015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1787013), _1787015)), -(c_Quickcheck_Obeyond(_1787013, _1787015) = _1787015)], (43864 ^ _779142) ^ [_1656568, _1656570, _1656572, _1656574] : [class_Groups_Osemigroup__add(_1656568), -(hAPP(c_List_Ofoldl(_1656568, _1656568, c_Groups_Oplus__class_Oplus(_1656568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656568), _1656570), _1656572)), _1656574) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656568), _1656570), hAPP(c_List_Ofoldl(_1656568, _1656568, c_Groups_Oplus__class_Oplus(_1656568), _1656572), _1656574)))], (18543 ^ _779142) ^ [_1105626, _1105628] : [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)), _1105626)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1105626), _1105628)))], (48334 ^ _779142) ^ [_1753599, _1753601, _1753603] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1753599), hAPP(c_COMBK(_1753599, tc_Nat_Onat), _1753601)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753603)) = c_List_Oreplicate(_1753599, _1753603, _1753601))], (45276 ^ _779142) ^ [_1687758, _1687760, _1687762] : [hBOOL(hAPP(c_List_Odistinct(_1687758), _1687760)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687758)), c_Enum_On__lists(_1687758, _1687762, _1687760))))], (31388 ^ _779142) ^ [_1342027] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342027, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1342027, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1342027, tc_HOL_Obool)))], (7046 ^ _779142) ^ [_895286, _895288, _895290, _895292] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_895286, _895288, _895290), _895292)), _895290 = c_Orderings_Obot__class_Obot(tc_fun(_895286, tc_HOL_Obool))], (50202 ^ _779142) ^ [_1794157, _1794159, _1794161, _1794163] : [-(c_Product__Type_Ocurry(_1794157, _1794159, _1794161, hAPP(c_Product__Type_Oprod_Oprod__case(_1794157, _1794159, _1794161), _1794163)) = _1794163)], (48354 ^ _779142) ^ [_1753879, _1753881, _1753883] : [-(hAPP(c_List_Oset(_1753879), c_List_Oreplicate(_1753879, hAPP(c_Nat_OSuc, _1753881), _1753883)) = hAPP(hAPP(c_Set_Oinsert(_1753879), _1753883), c_Orderings_Obot__class_Obot(tc_fun(_1753879, tc_HOL_Obool))))], (43087 ^ _779142) ^ [_1638661, _1638663, _1638665, _1638667, _1638669] : [-(hAPP(hAPP(c_List_Oappend(_1638661), _1638663), _1638665) = hAPP(hAPP(c_List_Oappend(_1638661), _1638667), _1638669)), 43088 ^ _779142 : [(43095 ^ _779142) ^ [_1638885] : [hAPP(hAPP(c_List_Oappend(_1638661), _1638663), _1638885) = _1638667, _1638665 = hAPP(hAPP(c_List_Oappend(_1638661), _1638885), _1638669)], (43089 ^ _779142) ^ [_1638773] : [_1638663 = hAPP(hAPP(c_List_Oappend(_1638661), _1638667), _1638773), hAPP(hAPP(c_List_Oappend(_1638661), _1638773), _1638665) = _1638669]]], (26978 ^ _779142) ^ [_1255169, _1255171, _1255173, _1255175] : [class_Orderings_Olinorder(_1255169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255169), _1255171), _1255173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255169), _1255173), _1255175)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255169, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255169, _1255171), _1255173)), c_SetInterval_Oord__class_OatLeastAtMost(_1255169, _1255173, _1255175)) = c_SetInterval_Oord__class_OatLeastAtMost(_1255169, _1255171, _1255175))], (32347 ^ _779142) ^ [_1368457, _1368459] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1368457), _1368459))), -(hAPP(c_Finite__Set_Ocard(_1368457), _1368459) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10535 ^ _779142) ^ [_961478] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _961478)], (45849 ^ _779142) ^ [_1701556, _1701558] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1701556))), c_List_Otranspose(_1701556, _1701558)) = c_List_Ofoldr(tc_List_Olist(_1701556), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1701556)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1701556))), _1701558, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4212 ^ _779142) ^ [_842866, _842868] : [_842868 = _842866, -(c_List_Oappend(_842868) = c_List_Oappend(_842866))], (34389 ^ _779142) ^ [_1411851, _1411853, _1411855, _1411857] : [34391 ^ _779142 : [(34394 ^ _779142) ^ [] : [hAPP(_1411857, 34390 ^ [_1411851, _1411853, _1411855, _1411857]) = c_Orderings_Otop__class_Otop(tc_fun(_1411853, tc_HOL_Obool))], (34392 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411851), 34390 ^ [_1411851, _1411853, _1411855, _1411857]), _1411855)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411851, tc_fun(_1411853, tc_HOL_Obool)), _1411855), _1411857) = c_Orderings_Otop__class_Otop(tc_fun(_1411853, tc_HOL_Obool)))], (38683 ^ _779142) ^ [_1527886, _1527888, _1527890] : [c_Wellfounded_Owf(_1527886, _1527888), hBOOL(hAPP(hAPP(c_member(tc_prod(_1527886, _1527886)), hAPP(hAPP(c_Product__Type_OPair(_1527886, _1527886), _1527890), _1527890)), _1527888))], (19441 ^ _779142) ^ [_1121081, _1121083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121083)), -(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), _1121081), _1121083))))], (45640 ^ _779142) ^ [_1696058, _1696060, _1696062] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696058)), hAPP(c_List_Ofilter(_1696058, _1696060), _1696062))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696058)), hAPP(c_List_Ofilter(_1696058, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1696058), c_fNot), _1696060)), _1696062))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696058)), _1696062))], (44450 ^ _779142) ^ [_1669196, _1669198, _1669200, _1669202, _1669204] : [-(hAPP(hAPP(c_List_Omap(_1669196, _1669198), _1669200), hAPP(hAPP(c_List_Oappend(_1669196), _1669202), _1669204)) = hAPP(hAPP(c_List_Oappend(_1669198), hAPP(hAPP(c_List_Omap(_1669196, _1669198), _1669200), _1669202)), hAPP(hAPP(c_List_Omap(_1669196, _1669198), _1669200), _1669204)))], (31218 ^ _779142) ^ [] : [-(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))))], (33867 ^ _779142) ^ [_1399407, _1399409, _1399411] : [-(_1399407 = hAPP(hAPP(c_Product__Type_OPair(_1399409, _1399411), hAPP(c_Product__Type_Ofst(_1399409, _1399411), _1399407)), hAPP(c_Product__Type_Osnd(_1399409, _1399411), _1399407)))], (44672 ^ _779142) ^ [_1673953, _1673955, _1673957, _1673959] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673953)), _1673955) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673957)), _1673959), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673953, _1673957), _1673957), c_Product__Type_Osnd(_1673953, _1673957)), hAPP(hAPP(c_List_Ozip(_1673953, _1673957), _1673955), _1673959)) = _1673959)], (47209 ^ _779142) ^ [_1728800, _1728802, _1728804, _1728806, _1728808] : [-(c_List_Omaps(_1728800, _1728802, _1728804, hAPP(hAPP(c_List_Olist_OCons(_1728800), _1728806), _1728808)) = hAPP(hAPP(c_List_Oappend(_1728802), hAPP(_1728804, _1728806)), c_List_Omaps(_1728800, _1728802, _1728804, _1728808)))], (44474 ^ _779142) ^ [_1669799, _1669801, _1669803, _1669805, _1669807] : [c_Fun_Oinj__on(_1669799, _1669801, _1669803, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669799, tc_HOL_Obool)), hAPP(c_List_Oset(_1669799), _1669805)), hAPP(c_List_Oset(_1669799), _1669807))), 44477 ^ _779142 : [(44484 ^ _779142) ^ [] : [_1669805 = _1669807, -(hAPP(hAPP(c_List_Omap(_1669799, _1669801), _1669803), _1669805) = hAPP(hAPP(c_List_Omap(_1669799, _1669801), _1669803), _1669807))], (44478 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Omap(_1669799, _1669801), _1669803), _1669805) = hAPP(hAPP(c_List_Omap(_1669799, _1669801), _1669803), _1669807), -(_1669805 = _1669807)]]], (38424 ^ _779142) ^ [_1520320, _1520322] : [-(hAPP(c_Relation_ORange(_1520320, _1520322), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520320, _1520322), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1520322, tc_HOL_Obool)))], (33575 ^ _779142) ^ [_1393490, _1393492] : [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), _1393490), _1393492))), 33578 ^ _779142 : [(33585 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393492), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 33588 ^ _779142 : [(33597 ^ _779142) ^ [] : [-(c_Nitpick_Onorm__frac(_1393490, _1393492) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1393490), _1393492)), 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), _1393490))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393492)))), -(_1393490 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1393492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33589 ^ _779142) ^ [] : [33590 ^ _779142 : [(33593 ^ _779142) ^ [] : [_1393492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33591 ^ _779142) ^ [] : [_1393490 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1393490, _1393492) = 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)))]]], (33579 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393492), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1393490, _1393492) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393490), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393492)))]]], (48812 ^ _779142) ^ [_1764798, _1764800] : [c_Relation_Otrans(_1764798, _1764800), -(c_Transitive__Closure_Otrancl(_1764798, _1764800) = _1764800)], (52691 ^ _779142) ^ [_1836739, _1836741, _1836743, _1836745, _1836747, _1836749] : [-(hAPP(hAPP(hAPP(c_COMBS(_1836739, _1836741, _1836743), _1836745), _1836747), _1836749) = hAPP(hAPP(_1836745, _1836749), hAPP(_1836747, _1836749)))], (4130 ^ _779142) ^ [_841675, _841677] : [_841677 = _841675, -(c_List_Otl(_841677) = c_List_Otl(_841675))], (52231 ^ _779142) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10439 ^ _779142) ^ [_959974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _959974)), -(_959974 = hAPP(c_Nat_OSuc, 10442 ^ [_959974]))], (44506 ^ _779142) ^ [_1670506, _1670508, _1670510, _1670512, _1670514, _1670516] : [-(hBOOL(hAPP(hAPP(c_member(_1670506), _1670508), hAPP(c_List_Oset(_1670506), _1670510)))), -(hAPP(hAPP(c_List_Omap(_1670506, _1670512), c_Fun_Ofun__upd(_1670506, _1670512, _1670514, _1670508, _1670516)), _1670510) = hAPP(hAPP(c_List_Omap(_1670506, _1670512), _1670514), _1670510))], (52399 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (13577 ^ _779142) ^ [_1015326, _1015328, _1015330, _1015332] : [class_Rings_Odivision__ring(_1015326), -(_1015328 = c_Groups_Ozero__class_Ozero(_1015326)), 13584 ^ _779142 : [(13591 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015326), _1015330), _1015328) = _1015332, -(_1015330 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015326), _1015332), _1015328))], (13585 ^ _779142) ^ [] : [_1015330 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015326), _1015332), _1015328), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015326), _1015330), _1015328) = _1015332)]]], (4878 ^ _779142) ^ [_853409, _853411, _853413, _853415, _853417, _853419, _853421, _853423, _853425, _853427] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853427, _853423, _853419, _853415, _853411) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853425, _853421, _853417, _853413, _853409)), _853427 = _853425, _853423 = _853421, _853419 = _853417, _853415 = _853413, _853411 = _853409], (17811 ^ _779142) ^ [_1092992, _1092994, _1092996] : [class_Rings_Olinordered__semidom(_1092992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092992), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092992), _1092994)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092992), _1092996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1092994), _1092996)))], (33099 ^ _779142) ^ [_1385051, _1385053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385051)), 33102 ^ _779142 : [(33109 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385053))), 33112 ^ _779142 : [(33119 ^ _779142) ^ [] : [-(_1385051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1385051, _1385053) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385051), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385053))))], (33113 ^ _779142) ^ [] : [_1385051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1385051, _1385053) = 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)))]]], (33103 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385053)), -(c_Divides_Odivmod__int(_1385051, _1385053) = c_Divides_OposDivAlg(_1385051, _1385053))]]], (52537 ^ _779142) ^ [_1835055, _1835057] : [-(class_Nat_Osize(tc_sum(_1835055, _1835057)))], (1846 ^ _779142) ^ [_805159, _805161] : [-(class_Orderings_Oorder(_805159)), _805161 = _805159, class_Orderings_Oorder(_805161)], (22773 ^ _779142) ^ [_1180340, _1180342, _1180344] : [class_Groups_Ogroup__add(_1180340), 22776 ^ _779142 : [(22783 ^ _779142) ^ [] : [_1180342 = _1180344, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1180340), _1180342) = hAPP(c_Groups_Ouminus__class_Ouminus(_1180340), _1180344))], (22777 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1180340), _1180342) = hAPP(c_Groups_Ouminus__class_Ouminus(_1180340), _1180344), -(_1180342 = _1180344)]]], (52363 ^ _779142) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (9189 ^ _779142) ^ [_935770, _935772, _935774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935770), _935772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935770), _935774)), 9196 ^ _779142 : [(9203 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935772), _935774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935772), _935770)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935774), _935770))))], (9197 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935772), _935770)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935774), _935770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935772), _935774)))]]], (40749 ^ _779142) ^ [_1578062, _1578064, _1578066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578064, _1578062)), _1578066)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578062, _1578064)), hAPP(c_Relation_Oconverse(_1578064, _1578062), _1578066))))], (47371 ^ _779142) ^ [_1732655, _1732657, _1732659, _1732661, _1732663] : [47372 ^ _779142 : [(47375 ^ _779142) ^ [] : [hBOOL(hAPP(_1732663, hAPP(hAPP(c_List_Ozip(_1732655, _1732659), hAPP(hAPP(c_List_Otake(_1732655), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732655)), _1732657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732659)), _1732661))), _1732657)), hAPP(hAPP(c_List_Otake(_1732659), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732655)), _1732657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732659)), _1732661))), _1732661))))], (47373 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732655)), hAPP(hAPP(c_List_Otake(_1732655), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732655)), _1732657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732659)), _1732661))), _1732657)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732659)), hAPP(hAPP(c_List_Otake(_1732659), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732655)), _1732657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732659)), _1732661))), _1732661)))]], -(hBOOL(hAPP(_1732663, hAPP(hAPP(c_List_Ozip(_1732655, _1732659), _1732657), _1732661))))], (38792 ^ _779142) ^ [_1530272, _1530274, _1530276] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1530272, _1530274)), _1530276)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1530272), hAPP(c_Relation_ODomain(_1530272, _1530274), _1530276))))], (42061 ^ _779142) ^ [_1614590, _1614592, _1614594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614590), _1614592)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614590)), hAPP(c_Set_OCollect(tc_List_Olist(_1614590)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614590), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614590)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614590), tc_fun(_1614590, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614590, tc_HOL_Obool), tc_fun(tc_fun(_1614590, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614590)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614590, tc_HOL_Obool))), c_List_Oset(_1614590))), _1614592))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614590), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614590)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1614590)))), _1614594))))))], (29347 ^ _779142) ^ [_1300159, _1300161, _1300163, _1300165] : [hBOOL(hAPP(hAPP(c_member(_1300159), _1300161), _1300163)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300159, tc_HOL_Obool)), _1300163), hAPP(hAPP(c_Set_Oinsert(_1300159), _1300161), _1300165)) = hAPP(hAPP(c_Set_Oinsert(_1300159), _1300161), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300159, tc_HOL_Obool)), _1300163), _1300165)))], (12971 ^ _779142) ^ [_1003671, _1003673, _1003675] : [-(hBOOL(hAPP(_1003671, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003673), _1003675)))), 12974 ^ _779142 : [(12977 ^ _779142) ^ [] : [hBOOL(hAPP(_1003671, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12975 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003673), _1003675)))]], 12979 ^ _779142 : [(12982 ^ _779142) ^ [] : [hBOOL(hAPP(_1003671, 12978 ^ [_1003671, _1003673, _1003675]))], (12980 ^ _779142) ^ [] : [-(_1003673 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003675), 12978 ^ [_1003671, _1003673, _1003675]))]]], (6757 ^ _779142) ^ [_888723, _888725, _888727, _888729, _888731] : [c_Finite__Set_Ofolding__one(_888723, _888725, _888727), hBOOL(hAPP(c_Finite__Set_Ofinite(_888723), _888729)), hBOOL(hAPP(hAPP(c_member(_888723), _888731), _888729)), 6768 ^ _779142 : [(6775 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888723, tc_HOL_Obool)), _888729), hAPP(hAPP(c_Set_Oinsert(_888723), _888731), c_Orderings_Obot__class_Obot(tc_fun(_888723, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_888723, tc_HOL_Obool))), -(hAPP(_888727, _888729) = hAPP(hAPP(_888725, _888731), hAPP(_888727, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888723, tc_HOL_Obool)), _888729), hAPP(hAPP(c_Set_Oinsert(_888723), _888731), c_Orderings_Obot__class_Obot(tc_fun(_888723, tc_HOL_Obool)))))))], (6769 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888723, tc_HOL_Obool)), _888729), hAPP(hAPP(c_Set_Oinsert(_888723), _888731), c_Orderings_Obot__class_Obot(tc_fun(_888723, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_888723, tc_HOL_Obool)), -(hAPP(_888727, _888729) = _888731)]]], (16385 ^ _779142) ^ [_1067392, _1067394, _1067396] : [class_Orderings_Olinorder(_1067392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067392), _1067394)), hBOOL(hAPP(hAPP(c_member(_1067392), _1067396), _1067394)), 16396 ^ _779142 : [(16403 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1067392, tc_HOL_Obool)), _1067394), hAPP(hAPP(c_Set_Oinsert(_1067392), _1067396), c_Orderings_Obot__class_Obot(tc_fun(_1067392, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1067392, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1067392, c_Orderings_Oord__class_Omin(_1067392), _1067394) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067392), _1067396), c_Big__Operators_Olattice_OInf__fin(_1067392, c_Orderings_Oord__class_Omin(_1067392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1067392, tc_HOL_Obool)), _1067394), hAPP(hAPP(c_Set_Oinsert(_1067392), _1067396), c_Orderings_Obot__class_Obot(tc_fun(_1067392, tc_HOL_Obool)))))))], (16397 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1067392, tc_HOL_Obool)), _1067394), hAPP(hAPP(c_Set_Oinsert(_1067392), _1067396), c_Orderings_Obot__class_Obot(tc_fun(_1067392, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1067392, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1067392, c_Orderings_Oord__class_Omin(_1067392), _1067394) = _1067396)]]], (51723 ^ _779142) ^ [_1823761, _1823763, _1823765] : [class_Divides_Osemiring__div(_1823761), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823761), _1823763), _1823765)), -(c_Divides_Odiv__class_Omod(_1823761, _1823765, _1823763) = c_Groups_Ozero__class_Ozero(_1823761))], (18794 ^ _779142) ^ [_1110084, _1110086] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110084)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110084)), _1110086)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1110084))), _1110086))], (25112 ^ _779142) ^ [_1220504, _1220506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1220504), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220506), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1220504))))), -(_1220504 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220506), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1220504))))], (16361 ^ _779142) ^ [_1066886, _1066888, _1066890] : [class_Orderings_Olinorder(_1066886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066886), _1066888)), hBOOL(hAPP(hAPP(c_member(_1066886), _1066890), _1066888)), 16372 ^ _779142 : [(16379 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1066886, tc_HOL_Obool)), _1066888), hAPP(hAPP(c_Set_Oinsert(_1066886), _1066890), c_Orderings_Obot__class_Obot(tc_fun(_1066886, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1066886, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1066886, _1066888) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1066886), _1066890), c_Big__Operators_Olinorder__class_OMin(_1066886, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1066886, tc_HOL_Obool)), _1066888), hAPP(hAPP(c_Set_Oinsert(_1066886), _1066890), c_Orderings_Obot__class_Obot(tc_fun(_1066886, tc_HOL_Obool)))))))], (16373 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1066886, tc_HOL_Obool)), _1066888), hAPP(hAPP(c_Set_Oinsert(_1066886), _1066890), c_Orderings_Obot__class_Obot(tc_fun(_1066886, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1066886, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1066886, _1066888) = _1066890)]]], (39570 ^ _779142) ^ [_1549285, _1549287, _1549289] : [-(hAPP(c_Fun_Ocomp(_1549285, _1549287, _1549285, _1549289), c_Fun_Oid(_1549285)) = _1549289)], (52649 ^ _779142) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (19149 ^ _779142) ^ [_1115667, _1115669] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115667)))), 19152 ^ _779142 : [(19159 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115669)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115669)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115669))))], (19153 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115669))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115669)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115667))]]], (27396 ^ _779142) ^ [_1262480, _1262482, _1262484] : [class_Groups_Oordered__ab__group__add(_1262480), -(hAPP(c_Set_Oimage(_1262480, _1262480, c_Groups_Ouminus__class_Ouminus(_1262480)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262480, _1262482, _1262484)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1262480, hAPP(c_Groups_Ouminus__class_Ouminus(_1262480), _1262484)), hAPP(c_Groups_Ouminus__class_Ouminus(_1262480), _1262482)))], (19079 ^ _779142) ^ [_1114455] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1114455)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46726 ^ _779142) ^ [_1718684, _1718686, _1718688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718686)), _1718688))), -(hAPP(hAPP(c_List_Onth(_1718686), hAPP(c_List_Orev(_1718686), _1718688)), _1718684) = hAPP(hAPP(c_List_Onth(_1718686), _1718688), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718686)), _1718688)), hAPP(c_Nat_OSuc, _1718684))))], (35421 ^ _779142) ^ [_1440920, _1440922] : [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)), _1440920), 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)), _1440922), 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)), _1440920), _1440922)), c_Int_Ointrel)))], (26424 ^ _779142) ^ [_1243942, _1243944, _1243946] : [class_Lattices_Osemilattice__sup(_1243942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243942), _1243944), _1243946)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1243942), _1243946), _1243944) = _1243946)], (51011 ^ _779142) ^ [_1811712] : [_1811712 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811712), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (28895 ^ _779142) ^ [_1291268, _1291270, _1291272, _1291274] : [hBOOL(hAPP(hAPP(c_member(_1291268), _1291270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291268, tc_HOL_Obool)), _1291272), _1291274))), -(hBOOL(hAPP(hAPP(c_member(_1291268), _1291270), _1291272)))], (31689 ^ _779142) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (23463 ^ _779142) ^ [_1192470, _1192472, _1192474] : [class_Rings_Ocomm__ring__1(_1192470), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192470), _1192472), _1192474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192470), _1192472), hAPP(c_Groups_Ouminus__class_Ouminus(_1192470), _1192474)))], (51995 ^ _779142) ^ [_1828693, _1828695, _1828697, _1828699, _1828701] : [class_Groups_Ocomm__monoid__mult(_1828693), class_Rings_Odvd(_1828693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1828695), _1828697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1828695, tc_HOL_Obool)), _1828699), _1828697)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828693), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1828695, _1828693), _1828701), _1828699)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1828695, _1828693), _1828701), _1828697))))], (12986 ^ _779142) ^ [_1003982, _1003984, _1003986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003982), _1003984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003982), _1003986))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003984), _1003986)))], (5052 ^ _779142) ^ [_856172, _856174, _856176, _856178, _856180, _856182, _856184, _856186] : [-(c_Quotient_OBabs(_856186, _856182, _856178, _856174) = c_Quotient_OBabs(_856184, _856180, _856176, _856172)), _856186 = _856184, _856182 = _856180, _856178 = _856176, _856174 = _856172], (13637 ^ _779142) ^ [_1016400, _1016402, _1016404] : [class_Rings_Odivision__ring(_1016400), -(_1016402 = c_Groups_Ozero__class_Ozero(_1016400)), 13644 ^ _779142 : [(13651 ^ _779142) ^ [] : [_1016404 = _1016402, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016400), _1016404), _1016402) = c_Groups_Oone__class_Oone(_1016400))], (13645 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016400), _1016404), _1016402) = c_Groups_Oone__class_Oone(_1016400), -(_1016404 = _1016402)]]], (35175 ^ _779142) ^ [_1433979, _1433981, _1433983, _1433985, _1433987, _1433989, _1433991] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1433979, tc_fun(_1433981, tc_fun(_1433983, tc_HOL_Obool))), _1433985), _1433987), _1433989), _1433991)), 35178 ^ _779142 : [(35179 ^ _779142) ^ [_1434107] : [hBOOL(hAPP(hAPP(c_member(_1433979), _1434107), _1433985)), -(hBOOL(hAPP(hAPP(hAPP(_1433987, _1434107), _1433989), _1433991)))]]], (4186 ^ _779142) ^ [_842483, _842485] : [_842485 = _842483, -(c_List_Onth(_842485) = c_List_Onth(_842483))], (41288 ^ _779142) ^ [_1592273, _1592275, _1592277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592273), c_Nitpick_Oplus__frac(_1592273, _1592275, c_Nitpick_Ouminus__frac(_1592273, _1592277)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1592273, _1592275, _1592277))], (46724 ^ _779142) ^ [_1718611, _1718613, _1718615] : [-(hAPP(c_List_Orotate(_1718611, _1718613), hAPP(c_List_Orev(_1718611), _1718615)) = hAPP(c_List_Orev(_1718611), hAPP(c_List_Orotate(_1718611, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718611)), _1718615)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718613, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718611)), _1718615)))), _1718615)))], (2350 ^ _779142) ^ [_813491, _813493, _813495, _813497] : [-(c_Nitpick_Onat__gcd(_813497, _813493) = c_Nitpick_Onat__gcd(_813495, _813491)), _813497 = _813495, _813493 = _813491], (24834 ^ _779142) ^ [_1215829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1215829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1215829)))], (2468 ^ _779142) ^ [_815354, _815356, _815358, _815360] : [-(c_Nitpick_Onumber__of__frac(_815360, _815356) = c_Nitpick_Onumber__of__frac(_815358, _815354)), _815360 = _815358, _815356 = _815354], (39299 ^ _779142) ^ [_1542468, _1542470, _1542472, _1542474] : [39301 ^ _779142 : [(39304 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542468, _1542468, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542468, tc_fun(_1542468, _1542470), tc_fun(_1542468, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542470, tc_HOL_Obool), tc_fun(tc_fun(_1542468, _1542470), tc_fun(_1542468, tc_HOL_Obool)), _1542468), c_COMBB(_1542470, tc_HOL_Obool, _1542468)), hAPP(hAPP(c_COMBB(_1542470, tc_fun(_1542470, tc_HOL_Obool), _1542468), c_fequal), _1542474))), _1542474)), 39300 ^ [_1542468, _1542470, _1542472, _1542474]))], (39302 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542468, _1542468)), 39300 ^ [_1542468, _1542470, _1542472, _1542474]), _1542472)))]], -(c_Equiv__Relations_Ocongruent(_1542468, _1542470, _1542472, _1542474))], (8324 ^ _779142) ^ [_917698] : [class_Groups_Oab__semigroup__mult(_917698), -(c_Finite__Set_Ofun__left__comm(_917698, _917698, c_Groups_Otimes__class_Otimes(_917698)))], (6869 ^ _779142) ^ [_891254, _891256, _891258, _891260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891254, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891254, tc_HOL_Obool)), _891256), hAPP(hAPP(c_Set_Oinsert(_891254), _891258), c_Orderings_Obot__class_Obot(tc_fun(_891254, tc_HOL_Obool))))), _891260)), hBOOL(hAPP(hAPP(c_member(_891254), _891258), _891256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891254, tc_HOL_Obool)), _891256), hAPP(hAPP(c_Set_Oinsert(_891254), _891258), _891260))))], (43995 ^ _779142) ^ [_1659446, _1659448, _1659450] : [43996 ^ _779142 : [(43997 ^ _779142) ^ [_1659535, _1659537] : [_1659448 = hAPP(hAPP(c_List_Olist_OCons(_1659446), _1659537), _1659535)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659446), tc_List_Olist(_1659446))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659446), tc_List_Olist(_1659446)), c_List_Olist_ONil(_1659446)), _1659448)), c_List_Olexord(_1659446, _1659450))))], (49282 ^ _779142) ^ [_1775675, _1775677] : [-(c_Relation_Osym(_1775675, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775675, _1775675), tc_HOL_Obool)), _1775677), hAPP(c_Relation_Oconverse(_1775675, _1775675), _1775677))))], (18533 ^ _779142) ^ [_1105456] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1105456) = 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)), _1105456)))], (10831 ^ _779142) ^ [_966138, _966140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966138)), hAPP(c_Nat_OSuc, _966140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966138), _966140)))], (21254 ^ _779142) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (40438 ^ _779142) ^ [_1570657, _1570659] : [-(c_Relation_Orefl__on(_1570657, c_Orderings_Otop__class_Otop(tc_fun(_1570657, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570657, _1570659)))], (49368 ^ _779142) ^ [_1777011, _1777013, _1777015] : [c_Relation_Orefl__on(_1777011, _1777013, _1777015), c_Relation_Osym(_1777011, _1777015), c_Relation_Otrans(_1777011, _1777015), -(c_Equiv__Relations_Oequiv(_1777011, _1777013, _1777015))], (7632 ^ _779142) ^ [_905375, _905377, _905379, _905381] : [class_Orderings_Opreorder(_905375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905375), _905377), _905379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905375), _905379), _905381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905375), _905377), _905381)))], (9517 ^ _779142) ^ [_941206, _941208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941206), _941208)), _941206))], (39415 ^ _779142) ^ [_1545794, _1545796, _1545798, _1545800, _1545802] : [c_Fun_Oinj__on(_1545794, _1545796, _1545798, c_Orderings_Otop__class_Otop(tc_fun(_1545794, tc_HOL_Obool))), c_Fun_Oinj__on(_1545800, _1545794, _1545802, c_Orderings_Otop__class_Otop(tc_fun(_1545800, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1545800, _1545796, hAPP(c_Fun_Ocomp(_1545794, _1545796, _1545800, _1545798), _1545802), c_Orderings_Otop__class_Otop(tc_fun(_1545800, tc_HOL_Obool))))], (19735 ^ _779142) ^ [] : [-(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))))], (46072 ^ _779142) ^ [_1706169, _1706171] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1706169, _1706171)))], (43351 ^ _779142) ^ [_1644481, _1644483, _1644485, _1644487] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644483)), _1644485)))), -(hAPP(hAPP(c_List_Onth(_1644483), hAPP(hAPP(c_List_Oappend(_1644483), _1644485), _1644487)), _1644481) = hAPP(hAPP(c_List_Onth(_1644483), _1644487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644483)), _1644485))))], (5804 ^ _779142) ^ [_871072, _871074] : [class_Finite__Set_Ofinite(_871072), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871072), _871074)))], (30864 ^ _779142) ^ [] : [-(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)))], (16443 ^ _779142) ^ [_1068600, _1068602] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068600)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068602)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068600), _1068602)))], (52619 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (39922 ^ _779142) ^ [_1557317, _1557319, _1557321, _1557323, _1557325, _1557327, _1557329] : [c_Finite__Set_Ofolding__idem(_1557317, _1557319, _1557321, _1557323), -(hAPP(c_Fun_Ocomp(_1557319, _1557319, _1557325, hAPP(_1557321, _1557327)), hAPP(c_Fun_Ocomp(_1557319, _1557319, _1557325, hAPP(_1557321, _1557327)), _1557329)) = hAPP(c_Fun_Ocomp(_1557319, _1557319, _1557325, hAPP(_1557321, _1557327)), _1557329))], (31236 ^ _779142) ^ [_1339043, _1339045] : [class_Groups_Oordered__ab__group__add(_1339043), -(hAPP(c_Set_Oimage(_1339043, _1339043, c_Groups_Ouminus__class_Ouminus(_1339043)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1339043), _1339045)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1339043), hAPP(c_Groups_Ouminus__class_Ouminus(_1339043), _1339045)))], (19427 ^ _779142) ^ [_1120887, _1120889, _1120891] : [class_Fields_Olinordered__field(_1120887), -(_1120889 = c_Groups_Ozero__class_Ozero(_1120887)), -(hAPP(c_Groups_Oabs__class_Oabs(_1120887), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120887), _1120891), _1120889)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120887), hAPP(c_Groups_Oabs__class_Oabs(_1120887), _1120891)), hAPP(c_Groups_Oabs__class_Oabs(_1120887), _1120889)))], (9865 ^ _779142) ^ [_947266, _947268, _947270] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947266), _947268)), _947270) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947266), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947268), _947270)))], (49699 ^ _779142) ^ [_1783516, _1783518, _1783520, _1783522] : [hAPP(c_Set_Oimage(_1783516, _1783518, _1783520), c_Orderings_Otop__class_Otop(tc_fun(_1783516, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783518, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1783516, _1783518, _1783520), hAPP(c_Set_Oimage(_1783518, _1783516, c_Hilbert__Choice_Oinv__into(_1783516, _1783518, c_Orderings_Otop__class_Otop(tc_fun(_1783516, tc_HOL_Obool)), _1783520)), _1783522)) = _1783522)], (38312 ^ _779142) ^ [_1516616, _1516618, _1516620, _1516622, _1516624, _1516626] : [-(c_Product__Type_Omap__pair(_1516616, _1516618, _1516620, _1516622, _1516624, _1516626) = hAPP(c_Product__Type_Oprod_Oprod__case(_1516616, _1516620, tc_prod(_1516618, _1516622)), hAPP(hAPP(c_COMBC(_1516616, tc_fun(_1516620, _1516622), tc_fun(_1516620, tc_prod(_1516618, _1516622))), hAPP(hAPP(c_COMBB(tc_fun(_1516622, tc_prod(_1516618, _1516622)), tc_fun(tc_fun(_1516620, _1516622), tc_fun(_1516620, tc_prod(_1516618, _1516622))), _1516616), c_COMBB(_1516622, tc_prod(_1516618, _1516622), _1516620)), hAPP(hAPP(c_COMBB(_1516618, tc_fun(_1516622, tc_prod(_1516618, _1516622)), _1516616), c_Product__Type_OPair(_1516618, _1516622)), _1516624))), _1516626)))], (6580 ^ _779142) ^ [_884908, _884910, _884912, _884914, _884916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884908, tc_HOL_Obool)), _884910), hAPP(c_Set_Oimage(_884912, _884908, _884914), _884916))), 6584 ^ _779142 : [(6587 ^ _779142) ^ [] : [-(_884910 = hAPP(c_Set_Oimage(_884912, _884908, _884914), 6583 ^ [_884908, _884910, _884912, _884914, _884916]))], (6585 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884912, tc_HOL_Obool)), 6583 ^ [_884908, _884910, _884912, _884914, _884916]), _884916)))]]], (24722 ^ _779142) ^ [_1213902] : [_1213902 = c_Int_OMin, -(c_Int_OBit1(_1213902) = c_Int_OMin)], (13797 ^ _779142) ^ [_1019267, _1019269, _1019271, _1019273] : [class_Fields_Olinordered__field(_1019267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019267), c_Groups_Ozero__class_Ozero(_1019267)), _1019269)), 13804 ^ _779142 : [(13811 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019267), _1019271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019267), _1019273), _1019269))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019267), _1019271), _1019269)), _1019273)))], (13805 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019267), _1019271), _1019269)), _1019273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019267), _1019271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019267), _1019273), _1019269))))]]], (46688 ^ _779142) ^ [_1717839, _1717841, _1717843, _1717845, _1717847] : [-(c_List_Ofoldr(_1717839, _1717841, _1717843, _1717845, _1717847) = hAPP(c_List_Ofoldl(_1717841, _1717839, hAPP(c_COMBC(_1717839, _1717841, _1717841), _1717843), _1717847), hAPP(c_List_Orev(_1717839), _1717845)))], (37033 ^ _779142) ^ [_1477458, _1477460, _1477462] : [hBOOL(hAPP(hAPP(c_member(_1477458), _1477460), c_Wellfounded_Oacc(_1477458, _1477462))), 37036 ^ _779142 : [(37037 ^ _779142) ^ [_1477572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477458, _1477458)), hAPP(hAPP(c_Product__Type_OPair(_1477458, _1477458), _1477572), _1477460)), _1477462)), -(hBOOL(hAPP(hAPP(c_member(_1477458), _1477572), c_Wellfounded_Oacc(_1477458, _1477462))))]]], (42187 ^ _779142) ^ [_1619294, _1619296] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619294, _1619296)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619294, _1619296))], (8807 ^ _779142) ^ [_927469, _927471, _927473] : [class_Groups_Ogroup__add(_927469), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_927469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927469), _927471), _927473)), _927473) = _927471)], (38800 ^ _779142) ^ [_1530422, _1530424, _1530426, _1530428, _1530430] : [c_Relation_Orefl__on(_1530422, _1530424, _1530426), c_Relation_Orefl__on(_1530422, _1530428, _1530430), -(c_Relation_Orefl__on(_1530422, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530422, tc_HOL_Obool)), _1530424), _1530428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530422, _1530422), tc_HOL_Obool)), _1530426), _1530430)))], (2554 ^ _779142) ^ [_816709, _816711, _816713, _816715, _816717, _816719] : [-(c_Partial__Function_Oflat__lub(_816719, _816715, _816711) = c_Partial__Function_Oflat__lub(_816717, _816713, _816709)), _816719 = _816717, _816715 = _816713, _816711 = _816709], (25500 ^ _779142) ^ [_1227325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227325), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1227325)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35113 ^ _779142) ^ [_1432172, _1432174, _1432176, _1432178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1432172), _1432174)), 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)), _1432172), _1432176)), 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)), _1432174), _1432178)), 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)), _1432174), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1432176), _1432178))), c_FunDef_Omin__strict)))], (6637 ^ _779142) ^ [_886141, _886143, _886145, _886147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886141, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_886141), _886143), _886145)), _886147))), hBOOL(hAPP(hAPP(c_member(_886141), _886143), _886147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886141, tc_HOL_Obool)), _886145), _886147))], (44111 ^ _779142) ^ [_1661808, _1661810, _1661812, _1661814, _1661816] : [class_Orderings_Olinorder(_1661808), hBOOL(hAPP(c_List_Odistinct(_1661810), _1661812)), -(hBOOL(hAPP(c_List_Odistinct(_1661810), c_List_Olinorder__class_Oinsort__insert__key(_1661810, _1661808, _1661814, _1661816, _1661812))))], (43810 ^ _779142) ^ [_1655432, _1655434, _1655436] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655432, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655434)), _1655436)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1655434, _1655432), _1655436) = _1655436)], (41929 ^ _779142) ^ [_1611473, _1611475, _1611477, _1611479] : [hBOOL(hAPP(hAPP(c_member(_1611473), _1611475), hAPP(c_List_Oset(_1611473), hAPP(hAPP(c_List_Otake(_1611473), _1611477), _1611479)))), -(hBOOL(hAPP(hAPP(c_member(_1611473), _1611475), hAPP(c_List_Oset(_1611473), _1611479))))], (24740 ^ _779142) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (3690 ^ _779142) ^ [_834419, _834421, _834423, _834425] : [-(c_List_Omeasures(_834425, _834421) = c_List_Omeasures(_834423, _834419)), _834425 = _834423, _834421 = _834419], (48654 ^ _779142) ^ [_1760876, _1760878, _1760880, _1760882] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1760876, _1760878, _1760880, _1760882, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760878)) = _1760880)], (37175 ^ _779142) ^ [_1480855, _1480857, _1480859, _1480861, _1480863] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1480855, _1480857, _1480859), _1480861), _1480863)), -(hBOOL(hAPP(_1480861, hAPP(_1480859, _1480863))))], (13370 ^ _779142) ^ [_1011298, _1011300, _1011302, _1011304, _1011306] : [class_Groups_Ocomm__monoid__add(_1011298), class_Groups_Oordered__ab__semigroup__add(_1011298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011300), _1011302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011300, tc_HOL_Obool)), _1011304), _1011302)), 13388 ^ _779142 : [(13391 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011298), c_Groups_Ozero__class_Ozero(_1011298)), hAPP(_1011306, 13387 ^ [_1011298, _1011300, _1011302, _1011304, _1011306])))], (13389 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1011300), 13387 ^ [_1011298, _1011300, _1011302, _1011304, _1011306]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011300, tc_HOL_Obool)), _1011302), _1011304))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011298), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011300, _1011298), _1011306), _1011304)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011300, _1011298), _1011306), _1011302))))], (23119 ^ _779142) ^ [_1186178, _1186180, _1186182] : [class_Rings_Oring(_1186178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186178), hAPP(c_Groups_Ouminus__class_Ouminus(_1186178), _1186180)), _1186182) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186178), _1186180), hAPP(c_Groups_Ouminus__class_Ouminus(_1186178), _1186182)))], (33865 ^ _779142) ^ [_1399359, _1399361, _1399363] : [-(hAPP(hAPP(c_Product__Type_OPair(_1399359, _1399361), hAPP(c_Product__Type_Ofst(_1399359, _1399361), _1399363)), hAPP(c_Product__Type_Osnd(_1399359, _1399361), _1399363)) = _1399363)], (45258 ^ _779142) ^ [_1687161, _1687163] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1687161), tc_fun(_1687161, tc_HOL_Obool), c_List_Oset(_1687161)), hAPP(c_List_Oset(tc_List_Olist(_1687161)), c_Enum_Osublists(_1687161, _1687163))) = hAPP(c_Set_OPow(_1687161), hAPP(c_List_Oset(_1687161), _1687163)))], (45721 ^ _779142) ^ [_1697769, _1697771, _1697773] : [45723 ^ _779142 : [(45726 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1697771, 45722 ^ [_1697769, _1697771, _1697773])))], (45724 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697769), 45722 ^ [_1697769, _1697771, _1697773]), hAPP(c_List_Oset(_1697769), _1697773))))]], -(hAPP(c_List_Ofilter(_1697769, _1697771), _1697773) = c_List_Olist_ONil(_1697769))], (32151 ^ _779142) ^ [_1363507, _1363509, _1363511, _1363513, _1363515] : [class_Groups_Ocomm__monoid__add(_1363507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363509), _1363511)), 32158 ^ _779142 : [(32165 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1363509), _1363513), _1363511))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363509, _1363507), hAPP(hAPP(c_COMBC(_1363509, _1363507, _1363507), hAPP(hAPP(c_COMBS(_1363509, _1363507, tc_fun(_1363507, _1363507)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1363507, tc_fun(_1363507, _1363507)), _1363509), c_If(_1363507)), hAPP(hAPP(c_COMBC(_1363509, _1363509, tc_HOL_Obool), c_fequal), _1363513))), _1363515)), c_Groups_Ozero__class_Ozero(_1363507))), _1363511) = c_Groups_Ozero__class_Ozero(_1363507))], (32159 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1363509), _1363513), _1363511)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363509, _1363507), hAPP(hAPP(c_COMBC(_1363509, _1363507, _1363507), hAPP(hAPP(c_COMBS(_1363509, _1363507, tc_fun(_1363507, _1363507)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1363507, tc_fun(_1363507, _1363507)), _1363509), c_If(_1363507)), hAPP(hAPP(c_COMBC(_1363509, _1363509, tc_HOL_Obool), c_fequal), _1363513))), _1363515)), c_Groups_Ozero__class_Ozero(_1363507))), _1363511) = hAPP(_1363515, _1363513))]]], (33465 ^ _779142) ^ [_1391260, _1391262] : [-(_1391260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391262, _1391260), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391262), _1391260)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391262, _1391260)))))], (17543 ^ _779142) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52667 ^ _779142) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (25316 ^ _779142) ^ [_1224042, _1224044] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1224042)))), _1224044) = 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)))), _1224042)), _1224044))], (25490 ^ _779142) ^ [_1227159] : [c_Int_OMin = c_Int_OBit0(_1227159)], (17683 ^ _779142) ^ [_1090645, _1090647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090645), _1090647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090645)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090647))))], (26526 ^ _779142) ^ [] : [-(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))], (10297 ^ _779142) ^ [_957108, _957110, _957112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957108), _957110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957110), _957112))))], (11620 ^ _779142) ^ [_979077, _979079, _979081] : [class_Rings_Oordered__cancel__semiring(_979077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979077), c_Groups_Ozero__class_Ozero(_979077)), _979079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979077), _979081), c_Groups_Ozero__class_Ozero(_979077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979077), _979079), _979081)), c_Groups_Ozero__class_Ozero(_979077))))], (13231 ^ _779142) ^ [_1008488, _1008490, _1008492] : [class_Rings_Olinordered__ring(_1008488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008488), _1008490), _1008490)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008488), _1008492), _1008492))), c_Groups_Ozero__class_Ozero(_1008488)))], (16551 ^ _779142) ^ [_1070459] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1070459) = _1070459)], (44231 ^ _779142) ^ [_1663722, _1663724, _1663726, _1663728] : [hAPP(hAPP(c_List_Oappend(_1663722), _1663724), hAPP(hAPP(c_List_Olist_OCons(_1663722), _1663726), c_List_Olist_ONil(_1663722))) = _1663728, 44234 ^ _779142 : [(44239 ^ _779142) ^ [] : [-(c_List_Olast(_1663722, _1663728) = _1663726)], (44237 ^ _779142) ^ [] : [-(c_List_Obutlast(_1663722, _1663728) = _1663724)], (44235 ^ _779142) ^ [] : [_1663728 = c_List_Olist_ONil(_1663722)]]], (51033 ^ _779142) ^ [_1812067, _1812069, _1812071] : [class_Rings_Ocomm__ring__1(_1812067), 51036 ^ _779142 : [(51043 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812067), _1812069), _1812071)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812067), hAPP(c_Groups_Ouminus__class_Ouminus(_1812067), _1812069)), _1812071)))], (51037 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812067), hAPP(c_Groups_Ouminus__class_Ouminus(_1812067), _1812069)), _1812071)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812067), _1812069), _1812071)))]]], (40843 ^ _779142) ^ [_1580337, _1580339] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580337, _1580337)), _1580339)), c_Wellfounded_Oacyclic(_1580337, _1580339), -(c_Wellfounded_Owf(_1580337, hAPP(c_Relation_Oconverse(_1580337, _1580337), _1580339)))], (10839 ^ _779142) ^ [_966290, _966292] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966290)), _966292) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966290), _966292)))], (45685 ^ _779142) ^ [_1696965, _1696967, _1696969] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1696965), tc_List_Olist(_1696965)), c_List_Opartition(_1696965, _1696967, _1696969)) = hAPP(c_List_Ofilter(_1696965, _1696967), _1696969))], (3184 ^ _779142) ^ [_826530, _826532, _826534, _826536, _826538, _826540, _826542, _826544] : [-(c_Nitpick_Osetsum_H(_826544, _826540, _826536, _826532) = c_Nitpick_Osetsum_H(_826542, _826538, _826534, _826530)), _826544 = _826542, _826540 = _826538, _826536 = _826534, _826532 = _826530], (33417 ^ _779142) ^ [_1390572, _1390574, _1390576, _1390578] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1390572, _1390574), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390576), _1390578))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1390572), _1390574) = _1390576)], (41321 ^ _779142) ^ [_1592902, _1592904] : [-(c_List_Olenlex(_1592902, _1592904) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1592902)), tc_List_Olist(_1592902)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1592902), c_Wellfounded_Oless__than, c_List_Olex(_1592902, _1592904))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592902), tc_List_Olist(_1592902), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592902))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1592902), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592902))), tc_List_Olist(_1592902)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1592902))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592902)))), c_COMBI(tc_List_Olist(_1592902)))))], (8975 ^ _779142) ^ [_930768, _930770, _930772, _930774, _930776] : [class_Groups_Ocomm__monoid__add(_930768), hBOOL(hAPP(c_Finite__Set_Ofinite(_930770), _930772)), -(hBOOL(hAPP(hAPP(c_member(_930770), _930774), _930772))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_930770, _930768), _930776), hAPP(hAPP(c_Set_Oinsert(_930770), _930774), _930772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930768), hAPP(_930776, _930774)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_930770, _930768), _930776), _930772)))], (48052 ^ _779142) ^ [_1747521, _1747523, _1747525, _1747527] : [-(c_New__Random__Sequence_Opos__map(_1747521, _1747523, _1747525, _1747527) = c_New__Random__Sequence_Opos__bind(_1747521, _1747523, _1747527, hAPP(c_Fun_Ocomp(_1747523, 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(_1747523))))), _1747521, c_New__Random__Sequence_Opos__single(_1747523)), _1747525)))], (49052 ^ _779142) ^ [_1771094, _1771096] : [-(c_Equiv__Relations_Oequivp(_1771094, _1771096)), c_Predicate_Oreflp(_1771094, _1771096), c_Predicate_Osymp(_1771094, _1771096), c_Predicate_Otransp(_1771094, _1771096)], (42067 ^ _779142) ^ [_1614893, _1614895, _1614897] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614893), _1614895)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614893)), hAPP(c_Set_OCollect(tc_List_Olist(_1614893)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614893), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614893)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614893), tc_fun(_1614893, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614893, tc_HOL_Obool), tc_fun(tc_fun(_1614893, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614893)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614893, tc_HOL_Obool))), c_List_Oset(_1614893))), _1614895))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614893), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614893)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1614893)))), _1614897))))))], (44592 ^ _779142) ^ [_1672416, _1672418, _1672420, _1672422] : [class_Groups_Ocomm__monoid__add(_1672416), 44595 ^ _779142 : [(44602 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1672418), _1672420))), -(c_Nitpick_Osetsum_H(_1672418, _1672416, _1672422, _1672420) = c_Groups_Ozero__class_Ozero(_1672416))], (44596 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1672418), _1672420)), -(c_Nitpick_Osetsum_H(_1672418, _1672416, _1672422, _1672420) = hAPP(c_List_Omonoid__add__class_Olistsum(_1672416), hAPP(hAPP(c_List_Omap(_1672418, _1672416), _1672422), c_Hilbert__Choice_OEps(tc_List_Olist(_1672418), hAPP(hAPP(c_COMBS(tc_List_Olist(_1672418), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1672418)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1672418), tc_fun(_1672418, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1672418, tc_HOL_Obool), tc_fun(tc_fun(_1672418, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1672418)), c_fequal), c_List_Oset(_1672418))), _1672420))), c_List_Odistinct(_1672418))))))]]], (11187 ^ _779142) ^ [_971584] : [_971584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971584), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43163 ^ _779142) ^ [_1640436, _1640438, _1640440] : [hAPP(hAPP(c_List_Oappend(_1640436), _1640438), _1640440) = _1640440, -(_1640438 = c_List_Olist_ONil(_1640436))], (22955 ^ _779142) ^ [_1183369, _1183371, _1183373] : [class_Lattices_Oboolean__algebra(_1183369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183369), _1183371), _1183373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183369), hAPP(c_Groups_Ouminus__class_Ouminus(_1183369), _1183373)), hAPP(c_Groups_Ouminus__class_Ouminus(_1183369), _1183371))))], (26256 ^ _779142) ^ [_1240960] : [_1240960 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1240960) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32341 ^ _779142) ^ [_1368330, _1368332] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368330), _1368332)), -(hAPP(c_Finite__Set_Ocard(_1368330), _1368332) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1368330, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1368330), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1368332))], (18800 ^ _779142) ^ [_1110150, _1110152, _1110154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110150)), 18806 ^ _779142 : [(18809 ^ _779142) ^ [] : [hBOOL(hAPP(_1110152, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18805 ^ [_1110150, _1110152, _1110154]), _1110150)))], (18807 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1110152, 18805 ^ [_1110150, _1110152, _1110154])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110154)), 18814 ^ _779142 : [(18815 ^ _779142) ^ [_1110439] : [hBOOL(hAPP(_1110152, _1110439)), -(hBOOL(hAPP(_1110152, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1110439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1110154), _1110150)))))]]], (20149 ^ _779142) ^ [_1132871, _1132873, _1132875, _1132877] : [class_Divides_Osemiring__div(_1132871), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132871), _1132873), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132871), _1132875), _1132873))), c_Divides_Odiv__class_Omod(_1132871, _1132875, _1132873))), _1132877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132871), _1132875), _1132877))], (39481 ^ _779142) ^ [_1547229, _1547231] : [hBOOL(hAPP(_1547229, c_Hilbert__Choice_OEps(_1547231, _1547229))), -(hBOOL(hAPP(_1547229, 39484 ^ [_1547229, _1547231])))], (37207 ^ _779142) ^ [_1481703, _1481705, _1481707, _1481709, _1481711] : [hBOOL(hAPP(hAPP(c_member(_1481703), _1481705), hAPP(c_Set_Ovimage(_1481703, _1481707, _1481709), _1481711))), -(hBOOL(hAPP(hAPP(c_member(_1481707), hAPP(_1481709, _1481705)), _1481711)))], (35614 ^ _779142) ^ [_1446101, _1446103, _1446105, _1446107, _1446109] : [hBOOL(hAPP(hAPP(c_member(_1446101), _1446103), hAPP(c_Relation_OImage(_1446105, _1446101, _1446107), _1446109))), 35618 ^ _779142 : [(35621 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446105), 35617 ^ [_1446101, _1446103, _1446105, _1446107, _1446109]), _1446109)))], (35619 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446105, _1446101)), hAPP(hAPP(c_Product__Type_OPair(_1446105, _1446101), 35617 ^ [_1446101, _1446103, _1446105, _1446107, _1446109]), _1446103)), _1446107)))]]], (14984 ^ _779142) ^ [_1041044, _1041046, _1041048, _1041050] : [class_Rings_Olinordered__semidom(_1041044), 14990 ^ _779142 : [(14993 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041044), c_Groups_Ozero__class_Ozero(_1041044)), hAPP(_1041050, 14989 ^ [_1041044, _1041046, _1041048, _1041050])))], (14991 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041046), 14989 ^ [_1041044, _1041046, _1041048, _1041050]), _1041048)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041044), c_Groups_Ozero__class_Ozero(_1041044)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1041046, _1041044), _1041050), _1041048))))], (49182 ^ _779142) ^ [_1773275, _1773277, _1773279, _1773281] : [c_Relation_Oantisym(_1773275, _1773277), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773275, _1773275)), hAPP(hAPP(c_Product__Type_OPair(_1773275, _1773275), _1773279), _1773281)), _1773277)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773275, _1773275)), hAPP(hAPP(c_Product__Type_OPair(_1773275, _1773275), _1773281), _1773279)), _1773277)), -(_1773279 = _1773281)], (39051 ^ _779142) ^ [_1536343, _1536345, _1536347, _1536349] : [hBOOL(hAPP(hAPP(c_member(_1536343), _1536345), hAPP(c_Relation_ODomain(_1536343, _1536347), _1536349))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536343, _1536347)), hAPP(hAPP(c_Product__Type_OPair(_1536343, _1536347), _1536345), 39054 ^ [_1536343, _1536345, _1536347, _1536349])), _1536349)))], (44988 ^ _779142) ^ [_1681011, _1681013, _1681015, _1681017] : [-(hBOOL(hAPP(c_List_Olistsp(_1681011, _1681013), hAPP(hAPP(c_List_Oappend(_1681011), _1681015), _1681017)))), hBOOL(hAPP(c_List_Olistsp(_1681011, _1681013), _1681015)), hBOOL(hAPP(c_List_Olistsp(_1681011, _1681013), _1681017))], (29807 ^ _779142) ^ [_1310703, _1310705, _1310707, _1310709, _1310711] : [class_Groups_Ocomm__monoid__add(_1310703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310705), _1310707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310705), _1310709)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310705, tc_HOL_Obool)), _1310707), _1310709) = c_Orderings_Obot__class_Obot(tc_fun(_1310705, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1310705, _1310703), _1310711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310705, tc_HOL_Obool)), _1310707), _1310709)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1310703), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1310705, _1310703), _1310711), _1310707)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1310705, _1310703), _1310711), _1310709)))], (27792 ^ _779142) ^ [_1269951, _1269953, _1269955] : [class_Orderings_Olinorder(_1269951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269951), _1269953), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269951), _1269955), _1269953))))], (48826 ^ _779142) ^ [_1765008, _1765010] : [c_Relation_Otrans(_1765008, hAPP(c_Relation_Oconverse(_1765008, _1765008), _1765010)), -(c_Relation_Otrans(_1765008, _1765010))], (12646 ^ _779142) ^ [_997532, _997534, _997536, _997538] : [class_Rings_Olinordered__ring__strict(_997532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997532), c_Groups_Ozero__class_Ozero(_997532)), _997534)), 12653 ^ _779142 : [(12660 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997532), _997536), _997538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997532), _997534), _997536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997532), _997534), _997538))))], (12654 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997532), _997534), _997536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997532), _997534), _997538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997532), _997536), _997538)))]]], (1206 ^ _779142) ^ [_797159, _797161] : [-(class_Rings_Oordered__ring__abs(_797159)), _797161 = _797159, class_Rings_Oordered__ring__abs(_797161)], (52195 ^ _779142) ^ [_1831733, _1831735] : [class_Orderings_Oord(_1831733), -(class_Orderings_Oord(tc_fun(_1831735, _1831733)))], (51345 ^ _779142) ^ [_1817368, _1817370, _1817372] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817368), _1817370)), _1817370 = _1817372, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817368), _1817372)))], (32833 ^ _779142) ^ [_1378888, _1378890, _1378892, _1378894] : [-(c_Nat_Onat_Onat__case(_1378888, _1378890, _1378892, hAPP(c_Nat_OSuc, _1378894)) = hAPP(_1378892, _1378894))], (34379 ^ _779142) ^ [_1411622, _1411624, _1411626, _1411628] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411622, tc_fun(_1411624, tc_HOL_Obool)), _1411626), _1411628) = c_Orderings_Otop__class_Otop(tc_fun(_1411624, tc_HOL_Obool)), 34382 ^ _779142 : [(34383 ^ _779142) ^ [_1411738] : [hBOOL(hAPP(hAPP(c_member(_1411622), _1411738), _1411626)), -(hAPP(_1411628, _1411738) = c_Orderings_Otop__class_Otop(tc_fun(_1411624, tc_HOL_Obool)))]]], (25390 ^ _779142) ^ [_1225463, _1225465] : [c_Int_OBit0(_1225463) = c_Int_OBit0(_1225465), -(_1225463 = _1225465)], (50239 ^ _779142) ^ [_1795040, _1795042, _1795044, _1795046, _1795048, _1795050] : [c_Fun_Oinj__on(_1795040, _1795042, _1795044, _1795046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1795042, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795040, _1795042, _1795044), _1795046)), _1795048)), c_Fun_Oinj__on(_1795042, _1795040, _1795050, _1795048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1795040, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795042, _1795040, _1795050), _1795048)), _1795046)), -(c_Fun_Obij__betw(_1795040, _1795042, 50254 ^ [_1795040, _1795042, _1795044, _1795046, _1795048, _1795050], _1795046, _1795048))], (33247 ^ _779142) ^ [_1387723, _1387725] : [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), _1387723), _1387725))), 33250 ^ _779142 : [(33259 ^ _779142) ^ [] : [-(c_Divides_OnegDivAlg(_1387723, _1387725) = hAPP(c_Divides_Oadjust(_1387725), c_Divides_OnegDivAlg(_1387723, 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)))), _1387725)))), -(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), _1387723), _1387725)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387725), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33251 ^ _779142) ^ [] : [33252 ^ _779142 : [(33255 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387725), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33253 ^ _779142) ^ [] : [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), _1387723), _1387725)))]], -(c_Divides_OnegDivAlg(_1387723, _1387725) = 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), _1387723), _1387725)))]]], (33607 ^ _779142) ^ [_1393982, _1393984, _1393986] : [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), _1393982), _1393984))), -(hBOOL(hAPP(hAPP(_1393986, _1393982), _1393984))), 33614 ^ _779142 : [(33617 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1393986, 33612 ^ [_1393982, _1393984, _1393986]), 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)))), 33613 ^ [_1393982, _1393984, _1393986])))), -(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), 33612 ^ [_1393982, _1393984, _1393986]), 33613 ^ [_1393982, _1393984, _1393986])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 33613 ^ [_1393982, _1393984, _1393986]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33627 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1393986, 33612 ^ [_1393982, _1393984, _1393986]), 33613 ^ [_1393982, _1393984, _1393986]))], (33615 ^ _779142) ^ [] : [-(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), 33612 ^ [_1393982, _1393984, _1393986]), 33613 ^ [_1393982, _1393984, _1393986]))))]]], (51545 ^ _779142) ^ [_1820606, _1820608, _1820610] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820606), _1820608)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820608), _1820606))), 51560 ^ _779142 : [(51563 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820610), _1820606))], (51561 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820606), _1820610)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820608), _1820610)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820610), _1820608)))], (28030 ^ _779142) ^ [_1274103, _1274105, _1274107, _1274109] : [class_Orderings_Olinorder(_1274103), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274103), _1274105), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274103), _1274107), _1274109)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274103), _1274107), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274103), _1274105), _1274109)))], (4518 ^ _779142) ^ [_847745, _847747] : [_847747 = _847745, -(c_Code__Numeral_OSuc__code__numeral(_847747) = c_Code__Numeral_OSuc__code__numeral(_847745))], (21790 ^ _779142) ^ [_1161970, _1161972] : [-(_1161970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161972), _1161970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161972), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1161970), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (36294 ^ _779142) ^ [_1461676, _1461678, _1461680, _1461682] : [c_Fun_Oinj__on(_1461676, _1461678, _1461680, _1461682), 36297 ^ _779142 : [(36298 ^ _779142) ^ [_1461784] : [hBOOL(hAPP(hAPP(c_member(_1461676), _1461784), _1461682)), 36301 ^ _779142 : [(36302 ^ _779142) ^ [_1461886] : [hBOOL(hAPP(hAPP(c_member(_1461676), _1461886), _1461682)), hAPP(_1461680, _1461784) = hAPP(_1461680, _1461886), -(_1461784 = _1461886)]]]]], (17575 ^ _779142) ^ [_1088860, _1088862, _1088864, _1088866] : [class_Divides_Osemiring__div(_1088860), -(c_Divides_Odiv__class_Omod(_1088860, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088860), _1088862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088860), _1088864), _1088866)), _1088866) = c_Divides_Odiv__class_Omod(_1088860, _1088862, _1088866))], (51199 ^ _779142) ^ [_1815044, _1815046] : [class_Rings_Ocomm__semiring__1(_1815044), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815044), c_Groups_Oone__class_Oone(_1815044)), _1815046)))], (42059 ^ _779142) ^ [_1614464, _1614466] : [-(hAPP(c_List_Oset(_1614464), _1614466) = hAPP(c_Set_OCollect(_1614464), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1614464), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1614464, 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)), _1614464), 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)), _1614464), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1614464, tc_fun(tc_Nat_Onat, _1614464), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614464, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1614464), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1614464), c_COMBB(_1614464, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1614464), _1614466))))), 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(_1614464)), _1614466))))))], (48150 ^ _779142) ^ [_1750202, _1750204, _1750206, _1750208] : [-(c_Lazy__Sequence_Oproduct(_1750202, _1750204, _1750206, _1750208) = hAPP(c_Lazy__Sequence_Obind(_1750202, tc_prod(_1750202, _1750204), _1750206), hAPP(hAPP(c_COMBB(tc_fun(_1750204, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750202, _1750204))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750202, _1750204)), _1750202), c_Lazy__Sequence_Obind(_1750204, tc_prod(_1750202, _1750204), _1750208)), hAPP(hAPP(c_COMBB(tc_fun(_1750204, tc_prod(_1750202, _1750204)), tc_fun(_1750204, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750202, _1750204))), _1750202), hAPP(c_COMBB(tc_prod(_1750202, _1750204), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750202, _1750204)), _1750204), c_Lazy__Sequence_Osingle(tc_prod(_1750202, _1750204)))), c_Product__Type_OPair(_1750202, _1750204)))))], (28116 ^ _779142) ^ [_1275985, _1275987, _1275989] : [class_Groups_Olinordered__ab__group__add(_1275985), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275985), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275985), _1275987), _1275989)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275985), hAPP(c_Groups_Ouminus__class_Ouminus(_1275985), _1275987)), hAPP(c_Groups_Ouminus__class_Ouminus(_1275985), _1275989)))], (37189 ^ _779142) ^ [_1481134, _1481136, _1481138, _1481140, _1481142] : [-(hAPP(c_Set_Ovimage(_1481134, _1481136, _1481138), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481136, tc_HOL_Obool)), _1481140), _1481142)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481134, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481134, _1481136, _1481138), _1481140)), hAPP(c_Set_Ovimage(_1481134, _1481136, _1481138), _1481142)))], (32835 ^ _779142) ^ [_1378928] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1378928) = 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)))], (28697 ^ _779142) ^ [_1286585, _1286587] : [class_Orderings_Olinorder(_1286585), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286585), _1286587)), -(_1286587 = c_Orderings_Obot__class_Obot(tc_fun(_1286585, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1286585), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286585), 28710 ^ [_1286585, _1286587]), 28711 ^ [_1286585, _1286587])), hAPP(hAPP(c_Set_Oinsert(_1286585), 28710 ^ [_1286585, _1286587]), hAPP(hAPP(c_Set_Oinsert(_1286585), 28711 ^ [_1286585, _1286587]), c_Orderings_Obot__class_Obot(tc_fun(_1286585, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1286585), c_Big__Operators_Olattice_OSup__fin(_1286585, c_Orderings_Oord__class_Omax(_1286585), _1286587)), _1286587)))], (33141 ^ _779142) ^ [_1385658, _1385660] : [_1385658 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1385658, _1385660) = 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)))], (49392 ^ _779142) ^ [_1777349, _1777351, _1777353] : [-(c_Equiv__Relations_Oequiv(_1777349, _1777351, _1777353)), c_Relation_Orefl__on(_1777349, _1777351, _1777353), c_Relation_Osym(_1777349, _1777353), c_Relation_Otrans(_1777349, _1777353)], (25894 ^ _779142) ^ [_1234201, _1234203] : [class_Fields_Olinordered__field__inverse__zero(_1234201), class_Int_Onumber__ring(_1234201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234201), c_Groups_Ozero__class_Ozero(_1234201)), _1234203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234201), c_Groups_Ozero__class_Ozero(_1234201)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234201), _1234203), hAPP(c_Int_Onumber__class_Onumber__of(_1234201), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (30259 ^ _779142) ^ [_1320102, _1320104, _1320106] : [class_Lattices_Olattice(_1320102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320102), _1320104)), hBOOL(hAPP(hAPP(c_member(_1320102), _1320106), _1320104)), 30270 ^ _779142 : [(30277 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320102, tc_HOL_Obool)), _1320104), hAPP(hAPP(c_Set_Oinsert(_1320102), _1320106), c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1320102, _1320104) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320102), _1320106), c_Big__Operators_Olattice__class_OInf__fin(_1320102, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320102, tc_HOL_Obool)), _1320104), hAPP(hAPP(c_Set_Oinsert(_1320102), _1320106), c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool)))))))], (30271 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320102, tc_HOL_Obool)), _1320104), hAPP(hAPP(c_Set_Oinsert(_1320102), _1320106), c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320102, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1320102, _1320104) = _1320106)]]], (14938 ^ _779142) ^ [_1040268, _1040270, _1040272] : [class_Rings_Oring__1(_1040268), hBOOL(hAPP(hAPP(c_member(_1040268), _1040270), c_Int_Oring__1__class_OInts(_1040268))), hBOOL(hAPP(hAPP(c_member(_1040268), _1040272), c_Int_Oring__1__class_OInts(_1040268))), -(hBOOL(hAPP(hAPP(c_member(_1040268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040268), _1040270), _1040272)), c_Int_Oring__1__class_OInts(_1040268))))], (46148 ^ _779142) ^ [_1707278, _1707280] : [class_Orderings_Olinorder(_1707278), -(_1707280 = c_List_Olist_ONil(_1707278)), c_List_Olinorder__class_Osorted(_1707278, _1707280), -(c_List_Olinorder__class_Osorted(_1707278, c_List_Obutlast(_1707278, _1707280)))], (26190 ^ _779142) ^ [_1239581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1239581)), -(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), _1239581), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (45865 ^ _779142) ^ [_1702137, _1702139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702137), _1702139)), -(c_List_Oupt(_1702137, hAPP(c_Nat_OSuc, _1702139)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702137, _1702139)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702139), c_List_Olist_ONil(tc_Nat_Onat))))], (47069 ^ _779142) ^ [_1726011, _1726013] : [class_Orderings_Olinorder(_1726011), 47076 ^ _779142 : [(47081 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726011), hAPP(hAPP(c_List_Onth(_1726011), _1726013), 47074 ^ [_1726011, _1726013])), hAPP(hAPP(c_List_Onth(_1726011), _1726013), 47075 ^ [_1726011, _1726013])))], (47079 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47075 ^ [_1726011, _1726013]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726011)), _1726013))))], (47077 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47074 ^ [_1726011, _1726013]), 47075 ^ [_1726011, _1726013])))]], -(c_List_Olinorder__class_Osorted(_1726011, _1726013))], (27402 ^ _779142) ^ [_1262615, _1262617, _1262619] : [class_Orderings_Olinorder(_1262615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262615), _1262617), _1262619)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262615, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1262615), _1262617)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262615, _1262617, _1262619)) = hAPP(c_SetInterval_Oord__class_OatMost(_1262615), _1262619))], (2036 ^ _779142) ^ [_808618, _808620, _808622, _808624, _808626, _808628, _808630, _808632, _808634, _808636] : [-(c_Nitpick_Opair__box_Opair__box__case(_808636, _808632, _808628, _808624, _808620) = c_Nitpick_Opair__box_Opair__box__case(_808634, _808630, _808626, _808622, _808618)), _808636 = _808634, _808632 = _808630, _808628 = _808626, _808624 = _808622, _808620 = _808618], (35904 ^ _779142) ^ [_1452638, _1452640, _1452642, _1452644, _1452646] : [c_Equiv__Relations_Oequiv(_1452638, _1452640, _1452642), hBOOL(hAPP(hAPP(c_member(_1452638), _1452644), _1452640)), hBOOL(hAPP(hAPP(c_member(_1452638), _1452646), _1452640)), 35915 ^ _779142 : [(35922 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452638, _1452638)), hAPP(hAPP(c_Product__Type_OPair(_1452638, _1452638), _1452644), _1452646)), _1452642)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452638), hAPP(hAPP(c_Set_Oinsert(_1452638), _1452644), c_Orderings_Obot__class_Obot(tc_fun(_1452638, tc_HOL_Obool)))), _1452642) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452638), hAPP(hAPP(c_Set_Oinsert(_1452638), _1452646), c_Orderings_Obot__class_Obot(tc_fun(_1452638, tc_HOL_Obool)))), _1452642))], (35916 ^ _779142) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452638), hAPP(hAPP(c_Set_Oinsert(_1452638), _1452644), c_Orderings_Obot__class_Obot(tc_fun(_1452638, tc_HOL_Obool)))), _1452642) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452638), hAPP(hAPP(c_Set_Oinsert(_1452638), _1452646), c_Orderings_Obot__class_Obot(tc_fun(_1452638, tc_HOL_Obool)))), _1452642), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452638, _1452638)), hAPP(hAPP(c_Product__Type_OPair(_1452638, _1452638), _1452644), _1452646)), _1452642)))]]], (15235 ^ _779142) ^ [_1045813, _1045815, _1045817] : [class_Orderings_Olinorder(_1045813), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045813), _1045815), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045813), _1045815), _1045817)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045813), _1045815), _1045817))], (40622 ^ _779142) ^ [_1574941, _1574943] : [-(c_Relation_Oirrefl(_1574941, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1574941, _1574941), tc_HOL_Obool)), _1574943), c_Relation_OId(_1574941))))], (32663 ^ _779142) ^ [_1375686, _1375688] : [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), _1375686))), 32666 ^ _779142 : [(32673 ^ _779142) ^ [] : [-(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), _1375688)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375688), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375688), 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), _1375686)))))], (32667 ^ _779142) ^ [] : [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), _1375688)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375688), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686)) = 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), _1375688)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375686))))]]], (22674 ^ _779142) ^ [_1178555, _1178557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1178555), _1178557)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1178555, tc_HOL_Obool)), hAPP(c_Set_OPow(_1178555), _1178557)) = 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(_1178555), _1178557)))], (9719 ^ _779142) ^ [_944435, _944437, _944439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944435), _944437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944435), _944439)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944437), _944435)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944439), _944435)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944437), _944439))], (52609 ^ _779142) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (27734 ^ _779142) ^ [_1268800, _1268802, _1268804, _1268806] : [class_Orderings_Olinorder(_1268800), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268800), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268800), _1268802), _1268804)), _1268806) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268800), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268800), _1268802), _1268806)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268800), _1268804), _1268806)))], (12260 ^ _779142) ^ [_990869] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _990869)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _990869)], (35610 ^ _779142) ^ [_1445821, _1445823] : [-(c_Relation_OId__on(_1445821, _1445823) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1445821, tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool)), _1445823), hAPP(hAPP(c_COMBC(_1445821, tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool), tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1445821, _1445821), tc_fun(tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool), tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool)), _1445821), c_Set_Oinsert(tc_prod(_1445821, _1445821))), hAPP(hAPP(c_COMBS(_1445821, _1445821, tc_prod(_1445821, _1445821)), c_Product__Type_OPair(_1445821, _1445821)), c_COMBI(_1445821)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1445821, _1445821), tc_HOL_Obool)))))], (5838 ^ _779142) ^ [_871630, _871632, _871634] : [_871630 = c_Orderings_Obot__class_Obot(tc_fun(_871632, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_871632), _871634), _871630))], (52587 ^ _779142) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (47748 ^ _779142) ^ [_1741055, _1741057, _1741059] : [-(hBOOL(hAPP(hAPP(c_member(_1741055), _1741057), hAPP(c_List_Oset(_1741055), _1741059)))), 47749 ^ _779142 : [(47750 ^ _779142) ^ [_1741144] : [47751 ^ _779142 : [(47752 ^ _779142) ^ [_1741217] : [_1741059 = hAPP(hAPP(c_List_Oappend(_1741055), _1741144), hAPP(hAPP(c_List_Olist_OCons(_1741055), _1741057), _1741217))]], -(hBOOL(hAPP(hAPP(c_member(_1741055), _1741057), hAPP(c_List_Oset(_1741055), _1741144))))]]], (22965 ^ _779142) ^ [_1183548, _1183550] : [class_Groups_Olinordered__ab__group__add(_1183548), 22968 ^ _779142 : [(22975 ^ _779142) ^ [] : [_1183550 = c_Groups_Ozero__class_Ozero(_1183548), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1183548), _1183550) = _1183550)], (22969 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1183548), _1183550) = _1183550, -(_1183550 = c_Groups_Ozero__class_Ozero(_1183548))]]], (10195 ^ _779142) ^ [_954968, _954970, _954972, _954974] : [class_Rings_Ocomm__semiring__1(_954968), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954968), _954970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954968), _954972), _954974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954968), _954972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954968), _954970), _954974)))], (17789 ^ _779142) ^ [_1092611, _1092613] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1092611), _1092613)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092611)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092613)))], (10368 ^ _779142) ^ [_958523, _958525, _958527, _958529, _958531] : [class_Groups_Ocomm__monoid__mult(_958523), hBOOL(hAPP(c_Finite__Set_Ofinite(_958525), _958527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958525, tc_HOL_Obool)), _958529), _958527)), 10382 ^ _779142 : [(10385 ^ _779142) ^ [] : [hAPP(_958531, 10381 ^ [_958523, _958525, _958527, _958529, _958531]) = c_Groups_Oone__class_Oone(_958523)], (10383 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_958525), 10381 ^ [_958523, _958525, _958527, _958529, _958531]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958525, tc_HOL_Obool)), _958527), _958529))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_958525, _958523), _958531), _958529) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_958525, _958523), _958531), _958527))], (37898 ^ _779142) ^ [_1501115, _1501117] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501115), _1501117)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1501115, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1501115, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1501115, tc_HOL_Obool), tc_fun(_1501115, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1501115, tc_HOL_Obool))), _1501117)))))], (34156 ^ _779142) ^ [_1405751, _1405753, _1405755, _1405757, _1405759, _1405761] : [-(hAPP(c_Product__Type_Oapfst(_1405751, _1405753, _1405755, _1405757), hAPP(hAPP(c_Product__Type_OPair(_1405751, _1405755), _1405759), _1405761)) = hAPP(hAPP(c_Product__Type_OPair(_1405753, _1405755), hAPP(_1405757, _1405759)), _1405761))], (17237 ^ _779142) ^ [_1082515, _1082517] : [class_Int_Onumber__ring(_1082515), 17240 ^ _779142 : [(17247 ^ _779142) ^ [] : [-(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), _1082517)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082515), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082517)) = c_Groups_Ozero__class_Ozero(_1082515))], (17241 ^ _779142) ^ [] : [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), _1082517))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082515), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082517)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082515), _1082517))]]], (43498 ^ _779142) ^ [_1648521, _1648523] : [-(hAPP(hAPP(c_List_Odrop(_1648521), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648523) = _1648523)], (52665 ^ _779142) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (20315 ^ _779142) ^ [_1135640, _1135642] : [-(hBOOL(hAPP(_1135640, hAPP(c_Int_Onat, _1135642)))), 20319 ^ _779142 : [(20322 ^ _779142) ^ [] : [hBOOL(hAPP(_1135640, 20318 ^ [_1135640, _1135642]))], (20320 ^ _779142) ^ [] : [-(_1135642 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20318 ^ [_1135640, _1135642]))]], 20323 ^ _779142 : [(20326 ^ _779142) ^ [] : [hBOOL(hAPP(_1135640, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20324 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135642), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17271 ^ _779142) ^ [_1083078, _1083080] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083078), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083078)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083080)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083078), _1083080)))], (26840 ^ _779142) ^ [_1252133, _1252135, _1252137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252133, tc_HOL_Obool)), _1252135), _1252137)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252133, tc_HOL_Obool)), _1252137), _1252135) = _1252137)], (42535 ^ _779142) ^ [_1627004, _1627006] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1627004), _1627006)), -(c_Nitpick_Ocard_H(_1627004, _1627006) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627004)), c_Hilbert__Choice_OEps(tc_List_Olist(_1627004), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627004), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627004)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627004), tc_fun(_1627004, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1627004, tc_HOL_Obool), tc_fun(tc_fun(_1627004, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1627004)), c_fequal), c_List_Oset(_1627004))), _1627006))), c_List_Odistinct(_1627004)))))], (50317 ^ _779142) ^ [_1796563, _1796565, _1796567] : [hBOOL(hAPP(c_Quotient_ORespects(_1796563, _1796565), _1796567)), -(hBOOL(hAPP(hAPP(_1796565, _1796567), _1796567)))], (18756 ^ _779142) ^ [_1109329, _1109331, _1109333] : [-(hBOOL(hAPP(_1109329, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1109331, _1109333)))), 18759 ^ _779142 : [(18762 ^ _779142) ^ [] : [hBOOL(hAPP(_1109329, _1109331))], (18760 ^ _779142) ^ [] : [-(_1109333 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 18763 ^ _779142 : [(18768 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18766 ^ [_1109329, _1109331, _1109333]), _1109333)))], (18770 ^ _779142) ^ [] : [-(_1109331 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109333), 18765 ^ [_1109329, _1109331, _1109333])), 18766 ^ [_1109329, _1109331, _1109333]))], (18772 ^ _779142) ^ [] : [hBOOL(hAPP(_1109329, 18766 ^ [_1109329, _1109331, _1109333]))], (18764 ^ _779142) ^ [] : [_1109333 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (42389 ^ _779142) ^ [_1623722, _1623724, _1623726, _1623728] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623722), tc_List_Olist(_1623722))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623722), tc_List_Olist(_1623722)), _1623724), _1623726)), c_List_Olistrel1(_1623722, _1623728)))), 42390 ^ _779142 : [(42391 ^ _779142) ^ [_1623855, _1623857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623722, _1623722)), hAPP(hAPP(c_Product__Type_OPair(_1623722, _1623722), hAPP(hAPP(c_List_Onth(_1623722), _1623724), _1623855)), _1623857)), _1623728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623855), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623722)), _1623724))), _1623726 = hAPP(hAPP(c_List_Olist__update(_1623722, _1623724), _1623855), _1623857)]]], (42842 ^ _779142) ^ [_1632860, _1632862, _1632864, _1632866] : [-(_1632860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1632862), _1632860), hAPP(hAPP(c_List_Olist_OCons(_1632862), _1632864), _1632866)) = hAPP(hAPP(c_List_Olist_OCons(_1632862), _1632864), hAPP(hAPP(c_List_Otake(_1632862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632860), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632866)))], (35282 ^ _779142) ^ [_1436461, _1436463, _1436465, _1436467] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436461), _1436463)), 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)), _1436465), _1436461)), 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)), _1436467), _1436463)), c_FunDef_Omax__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436465), _1436467)), _1436463)), c_FunDef_Omax__weak)))], (45752 ^ _779142) ^ [_1698464, _1698466, _1698468] : [-(hAPP(c_List_Oset(_1698464), hAPP(c_List_Ofilter(_1698464, _1698466), _1698468)) = hAPP(c_Set_OCollect(_1698464), hAPP(hAPP(c_COMBS(_1698464, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1698464), c_fconj), hAPP(hAPP(c_COMBC(_1698464, tc_fun(_1698464, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698464)), hAPP(c_List_Oset(_1698464), _1698468)))), _1698466)))], (35156 ^ _779142) ^ [_1433537, _1433539, _1433541, _1433543, _1433545] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433537, tc_fun(_1433539, tc_HOL_Obool)), _1433541), _1433543), _1433545)), 35160 ^ _779142 : [(35163 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1433543, 35159 ^ [_1433537, _1433539, _1433541, _1433543, _1433545]), _1433545)))], (35161 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433537), 35159 ^ [_1433537, _1433539, _1433541, _1433543, _1433545]), _1433541)))]]], (47874 ^ _779142) ^ [_1743675, _1743677, _1743679, _1743681] : [c_List_Olist__all(_1743675, _1743677, hAPP(hAPP(c_List_Olist_OCons(_1743675), _1743679), _1743681)), 47877 ^ _779142 : [(47880 ^ _779142) ^ [] : [-(c_List_Olist__all(_1743675, _1743677, _1743681))], (47878 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1743677, _1743679)))]]], (11267 ^ _779142) ^ [_972769, _972771, _972773] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972769), _972771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972773), _972771), -(_972769 = _972773), -(_972771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21256 ^ _779142) ^ [_1152952, _1152954] : [c_Nat__Transfer_Ois__nat(_1152952), c_Nat__Transfer_Ois__nat(_1152954), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152952), _1152954)))], (50226 ^ _779142) ^ [_1794764, _1794766, _1794768, _1794770] : [c_Fun_Obij__betw(_1794764, _1794766, _1794768, c_Orderings_Otop__class_Otop(tc_fun(_1794764, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794766, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1794764, _1794766, _1794768), _1794770) = hAPP(c_Set_Oimage(_1794766, _1794764, c_Hilbert__Choice_Oinv__into(_1794764, _1794766, c_Orderings_Otop__class_Otop(tc_fun(_1794764, tc_HOL_Obool)), _1794768)), _1794770))], (31432 ^ _779142) ^ [_1342895, _1342897, _1342899] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342895, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342895, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342895, tc_HOL_Obool), _1342897)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342895, tc_HOL_Obool), _1342899))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342895, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1342895, tc_HOL_Obool), tc_HOL_Obool)), _1342897), _1342899)))))], (43289 ^ _779142) ^ [_1642847, _1642849, _1642851, _1642853] : [43290 ^ _779142 : [(43293 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642847), _1642849), hAPP(c_List_Oset(_1642847), c_List_Obutlast(_1642847, _1642853))))], (43291 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642847), _1642849), hAPP(c_List_Oset(_1642847), c_List_Obutlast(_1642847, _1642851))))]], -(hBOOL(hAPP(hAPP(c_member(_1642847), _1642849), hAPP(c_List_Oset(_1642847), c_List_Obutlast(_1642847, hAPP(hAPP(c_List_Oappend(_1642847), _1642851), _1642853))))))], (50777 ^ _779142) ^ [_1807332, _1807334, _1807336] : [class_Divides_Osemiring__div(_1807332), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807332), _1807334), _1807336)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807332), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807332), _1807336), _1807334)), _1807334) = _1807336)], (43872 ^ _779142) ^ [_1656782, _1656784, _1656786, _1656788, _1656790, _1656792] : [-(hAPP(c_List_Ofoldl(_1656782, _1656784, _1656786, _1656788), hAPP(hAPP(c_List_Oappend(_1656784), _1656790), _1656792)) = hAPP(c_List_Ofoldl(_1656782, _1656784, _1656786, hAPP(c_List_Ofoldl(_1656782, _1656784, _1656786, _1656788), _1656790)), _1656792))], (25140 ^ _779142) ^ [] : [-(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)))))], (17017 ^ _779142) ^ [_1078479, _1078481, _1078483, _1078485, _1078487, _1078489] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078479), _1078481)), _1078483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078485), _1078487)), _1078489), 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), _1078485), _1078487)), _1078489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078489), _1078485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078485), _1078479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078481), _1078487)))], (8034 ^ _779142) ^ [_911588, _911590, _911592, _911594, _911596, _911598, _911600] : [-(hBOOL(hAPP(hAPP(c_member(_911588), _911590), _911592))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911588, _911594, _911596, _911598, _911592), _911600)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911588, _911594, _911596, _911598, hAPP(hAPP(c_Set_Oinsert(_911588), _911590), _911592)), hAPP(hAPP(_911596, _911590), _911600))))], (39022 ^ _779142) ^ [_1535746, _1535748] : [c_Wellfounded_Owf(_1535746, _1535748), -(c_Wellfounded_Owf(tc_List_Olist(_1535746), c_List_Olex(_1535746, _1535748)))], (25870 ^ _779142) ^ [] : [-(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)))))], (37351 ^ _779142) ^ [_1485300, _1485302, _1485304, _1485306, _1485308, _1485310] : [-(hAPP(c_Set_Oimage(_1485300, tc_prod(_1485302, _1485304), hAPP(hAPP(c_COMBS(_1485300, _1485304, tc_prod(_1485302, _1485304)), hAPP(hAPP(c_COMBB(_1485302, tc_fun(_1485304, tc_prod(_1485302, _1485304)), _1485300), c_Product__Type_OPair(_1485302, _1485304)), _1485306)), _1485308)), _1485310) = hAPP(hAPP(c_Product__Type_OSigma(_1485302, _1485304), hAPP(c_Set_Oimage(_1485300, _1485302, _1485306), _1485310)), hAPP(hAPP(c_COMBB(tc_fun(_1485300, tc_HOL_Obool), tc_fun(_1485304, tc_HOL_Obool), _1485302), c_Set_Oimage(_1485300, _1485304, _1485308)), hAPP(hAPP(c_COMBC(_1485302, tc_fun(_1485300, tc_HOL_Obool), tc_fun(_1485300, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485300, tc_HOL_Obool), tc_fun(tc_fun(_1485300, tc_HOL_Obool), tc_fun(_1485300, tc_HOL_Obool)), _1485302), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485300, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1485302, tc_HOL_Obool), tc_fun(_1485300, tc_HOL_Obool), _1485302), c_Set_Ovimage(_1485300, _1485302, _1485306)), hAPP(hAPP(c_COMBC(_1485302, tc_fun(_1485302, tc_HOL_Obool), tc_fun(_1485302, tc_HOL_Obool)), c_Set_Oinsert(_1485302)), c_Orderings_Obot__class_Obot(tc_fun(_1485302, tc_HOL_Obool)))))), _1485310))))], (21478 ^ _779142) ^ [_1156526, _1156528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156526)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1156526, _1156528)))], (26108 ^ _779142) ^ [_1237870, _1237872, _1237874] : [class_Rings_Olinordered__idom(_1237870), 26111 ^ _779142 : [(26112 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237870), c_Groups_Ozero__class_Ozero(_1237870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237870), hAPP(hAPP(c_Power_Opower__class_Opower(_1237870), _1237872), 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(_1237870), _1237874), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1237872 = c_Groups_Ozero__class_Ozero(_1237870), _1237874 = c_Groups_Ozero__class_Ozero(_1237870)], (26122 ^ _779142) ^ [] : [26123 ^ _779142 : [(26126 ^ _779142) ^ [] : [-(_1237874 = c_Groups_Ozero__class_Ozero(_1237870))], (26124 ^ _779142) ^ [] : [-(_1237872 = c_Groups_Ozero__class_Ozero(_1237870))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237870), c_Groups_Ozero__class_Ozero(_1237870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237870), hAPP(hAPP(c_Power_Opower__class_Opower(_1237870), _1237872), 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(_1237870), _1237874), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (50015 ^ _779142) ^ [_1790689, _1790691, _1790693, _1790695, _1790697, _1790699, _1790701] : [c_Fun_Obij__betw(_1790689, _1790691, _1790693, _1790695, _1790697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1790689, tc_HOL_Obool)), _1790699), _1790695)), hAPP(c_Set_Oimage(_1790689, _1790691, _1790693), _1790699) = _1790701, -(c_Fun_Obij__betw(_1790689, _1790691, _1790693, _1790699, _1790701))], (48380 ^ _779142) ^ [_1754658, _1754660, _1754662, _1754664, _1754666] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1754658, _1754660, _1754662) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754658, _1754664, _1754666), 48383 ^ _779142 : [(48386 ^ _779142) ^ [] : [-(_1754662 = _1754666)], (48384 ^ _779142) ^ [] : [-(_1754660 = _1754664)]]], (26818 ^ _779142) ^ [_1251602, _1251604, _1251606, _1251608] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251602, tc_HOL_Obool)), _1251604), hAPP(hAPP(c_Set_Oinsert(_1251602), _1251606), _1251608)) = hAPP(hAPP(c_Set_Oinsert(_1251602), _1251606), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251602, tc_HOL_Obool)), _1251604), _1251608)))], (43460 ^ _779142) ^ [_1647678, _1647680, _1647682] : [-(hAPP(hAPP(c_List_Oappend(_1647678), hAPP(hAPP(c_List_Otake(_1647678), _1647680), _1647682)), hAPP(hAPP(c_List_Odrop(_1647678), _1647680), _1647682)) = _1647682)], (3292 ^ _779142) ^ [_828204, _828206, _828208, _828210] : [-(c_Product__Type_OSigma(_828210, _828206) = c_Product__Type_OSigma(_828208, _828204)), _828210 = _828208, _828206 = _828204], (18575 ^ _779142) ^ [_1106186, _1106188] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1106186), _1106188) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106186, _1106188)), _1106188))], (16661 ^ _779142) ^ [_1072450] : [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)), _1072450)), _1072450)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072450), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40178 ^ _779142) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (50767 ^ _779142) ^ [_1807119, _1807121, _1807123, _1807125] : [class_Divides_Osemiring__div(_1807119), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807119), _1807121), _1807123)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807119), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807119), _1807123), _1807121)), _1807125) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807119), _1807123), _1807125)), _1807121))], (9380 ^ _779142) ^ [_939068] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939068), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _939068)], (5448 ^ _779142) ^ [_862484, _862486] : [_862486 = _862484, -(c_Power_Opower__class_Opower(_862486) = c_Power_Opower__class_Opower(_862484))], (45919 ^ _779142) ^ [_1702985, _1702987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702985), _1702987)), -(c_List_Oupt(_1702987, _1702985) = c_List_Olist_ONil(tc_Nat_Onat))], (10117 ^ _779142) ^ [_952991, _952993, _952995] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952991), _952993)), _952995) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952991), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952993), _952995)))], (1926 ^ _779142) ^ [_806159, _806161] : [-(class_Rings_Odvd(_806159)), _806161 = _806159, class_Rings_Odvd(_806161)], (27342 ^ _779142) ^ [_1261489, _1261491, _1261493, _1261495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261489, tc_HOL_Obool)), _1261491), _1261493)), hBOOL(hAPP(_1261491, _1261495)), -(hBOOL(hAPP(_1261493, _1261495)))], (41830 ^ _779142) ^ [_1608840, _1608842, _1608844, _1608846] : [-(hAPP(hAPP(c_List_Onth(_1608840), hAPP(hAPP(c_List_Olist_OCons(_1608840), _1608842), _1608844)), _1608846) = c_Nat_Onat_Onat__case(_1608840, _1608842, hAPP(c_List_Onth(_1608840), _1608844), _1608846))], (33799 ^ _779142) ^ [_1398006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398006)), 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), _1398006)) = 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), _1398006))))))], (31394 ^ _779142) ^ [_1342172, _1342174, _1342176] : [class_Complete__Lattice_Ocomplete__lattice(_1342172), hBOOL(hAPP(hAPP(c_member(_1342172), _1342174), _1342176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342172), c_Complete__Lattice_OInf__class_OInf(_1342172, _1342176)), _1342174)))], (32932 ^ _779142) ^ [_1380954, _1380956, _1380958, _1380960, _1380962, _1380964, _1380966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1380954, _1380956)), hAPP(hAPP(c_Product__Type_OPair(_1380954, _1380956), _1380958), _1380960)), _1380962)), -(hBOOL(hAPP(hAPP(c_member(_1380964), hAPP(hAPP(_1380966, _1380958), _1380960)), hAPP(c_Set_Oimage(tc_prod(_1380954, _1380956), _1380964, hAPP(c_Product__Type_Oprod_Oprod__case(_1380954, _1380956, _1380964), _1380966)), _1380962))))], (52457 ^ _779142) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (40424 ^ _779142) ^ [_1570304, _1570306, _1570308, _1570310, _1570312] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570304, _1570304)), hAPP(hAPP(c_Product__Type_OPair(_1570304, _1570304), _1570306), _1570308)), _1570310)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570304, _1570304)), hAPP(hAPP(c_Product__Type_OPair(_1570304, _1570304), _1570308), _1570312)), c_Transitive__Closure_Ortrancl(_1570304, _1570310))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570304, _1570304)), hAPP(hAPP(c_Product__Type_OPair(_1570304, _1570304), _1570306), _1570312)), c_Transitive__Closure_Ortrancl(_1570304, _1570310))))], (44791 ^ _779142) ^ [_1676598, _1676600] : [_1676598 = _1676600, -(hAPP(c_Code__Numeral_Onat__of, _1676598) = hAPP(c_Code__Numeral_Onat__of, _1676600))], (12955 ^ _779142) ^ [_1003379, _1003381, _1003383] : [hBOOL(hAPP(_1003379, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003381), _1003383))), 12958 ^ _779142 : [(12965 ^ _779142) ^ [_1003570] : [_1003381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003383), _1003570), -(hBOOL(hAPP(_1003379, _1003570)))], (12959 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003381), _1003383)), -(hBOOL(hAPP(_1003379, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (12385 ^ _779142) ^ [_992843, _992845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992845), _992843)), -(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), _992843), _992845))))], (41471 ^ _779142) ^ [_1598206, _1598208, _1598210, _1598212] : [-(c_List_Olist_Olist__size(_1598206, _1598208, hAPP(hAPP(c_List_Olist_OCons(_1598206), _1598210), _1598212)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1598208, _1598210)), c_List_Olist_Olist__size(_1598206, _1598208, _1598212))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15627 ^ _779142) ^ [_1053144, _1053146, _1053148] : [class_Int_Onumber(_1053144), class_Orderings_Olinorder(_1053144), 15634 ^ _779142 : [(15641 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053144), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053148)), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053146)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053144), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053146)), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053148))))], (15635 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053144), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053146)), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053148))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053144), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053148)), hAPP(c_Int_Onumber__class_Onumber__of(_1053144), _1053146)))]]], (23691 ^ _779142) ^ [_1196436, _1196438] : [class_Groups_Oordered__ab__group__add__abs(_1196436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196436), _1196438), c_Groups_Ozero__class_Ozero(_1196436))), -(hAPP(c_Groups_Oabs__class_Oabs(_1196436), _1196438) = hAPP(c_Groups_Ouminus__class_Ouminus(_1196436), _1196438))], (6423 ^ _779142) ^ [_882040, _882042, _882044] : [class_Orderings_Oorder(_882040), 6426 ^ _779142 : [(6435 ^ _779142) ^ [] : [-(_882042 = _882044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882040), _882042), _882044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882040), _882044), _882042))], (6427 ^ _779142) ^ [] : [_882042 = _882044, 6430 ^ _779142 : [(6433 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882040), _882044), _882042)))], (6431 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882040), _882042), _882044)))]]]]], (43911 ^ _779142) ^ [_1657539, _1657541] : [class_Complete__Lattice_Ocomplete__lattice(_1657539), -(c_Complete__Lattice_OSup__class_OSup(_1657539, hAPP(c_List_Oset(_1657539), _1657541)) = hAPP(c_List_Ofoldl(_1657539, _1657539, c_Lattices_Osemilattice__sup__class_Osup(_1657539), c_Orderings_Obot__class_Obot(_1657539)), _1657541))], (38689 ^ _779142) ^ [_1528004, _1528006, _1528008, _1528010] : [c_Wellfounded_Owf(_1528004, _1528006), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528004, _1528004)), hAPP(hAPP(c_Product__Type_OPair(_1528004, _1528004), _1528008), _1528010)), _1528006)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528004, _1528004)), hAPP(hAPP(c_Product__Type_OPair(_1528004, _1528004), _1528010), _1528008)), _1528006))], (43269 ^ _779142) ^ [_1642353, _1642355, _1642357, _1642359, _1642361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642355)), _1642357))), -(hAPP(hAPP(c_List_Olist__update(_1642355, hAPP(hAPP(c_List_Oappend(_1642355), _1642357), _1642359)), _1642353), _1642361) = hAPP(hAPP(c_List_Oappend(_1642355), hAPP(hAPP(c_List_Olist__update(_1642355, _1642357), _1642353), _1642361)), _1642359))], (44315 ^ _779142) ^ [_1665290, _1665292, _1665294, _1665296, _1665298] : [-(hAPP(c_List_Orotate(_1665290, _1665292), hAPP(hAPP(c_List_Omap(_1665294, _1665290), _1665296), _1665298)) = hAPP(hAPP(c_List_Omap(_1665294, _1665290), _1665296), hAPP(c_List_Orotate(_1665294, _1665292), _1665298)))], (51253 ^ _779142) ^ [_1815926, _1815928] : [51260 ^ _779142 : [(51263 ^ _779142) ^ [] : [_1815926 = _1815928], (51261 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815926), _1815928)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815926), _1815928)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815928), _1815926)))], (426 ^ _779142) ^ [_785547, _785549, _785551, _785553, _785555, _785557] : [-(c_Relation_Osingle__valued(_785555, _785551, _785547)), c_Relation_Osingle__valued(_785557, _785553, _785549), _785557 = _785555, _785553 = _785551, _785549 = _785547], (45911 ^ _779142) ^ [_1702852, _1702854] : [45912 ^ _779142 : [(45915 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702854), _1702852))], (45913 ^ _779142) ^ [] : [_1702854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1702852, _1702854) = c_List_Olist_ONil(tc_Nat_Onat))], (33125 ^ _779142) ^ [_1385421, _1385423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385421))), 33128 ^ _779142 : [(33135 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385423))), -(c_Divides_Odivmod__int(_1385421, _1385423) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385421), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385423))))], (33129 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385423)), -(c_Divides_Odivmod__int(_1385421, _1385423) = c_Divides_OnegDivAlg(_1385421, _1385423))]]], (50457 ^ _779142) ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111] : [50460 ^ _779142 : [(50467 ^ _779142) ^ [] : [hAPP(hAPP(_1801109, 50458 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111]), 50462 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111]) = hAPP(hAPP(_1801109, 50459 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111]), 50463 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111])], (50465 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801105, _1801105)), hAPP(hAPP(c_Product__Type_OPair(_1801105, _1801105), 50462 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111]), 50463 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111])), _1801107)))], (50461 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801101, _1801101)), hAPP(hAPP(c_Product__Type_OPair(_1801101, _1801101), 50458 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111]), 50459 ^ [_1801101, _1801103, _1801105, _1801107, _1801109, _1801111])), _1801103)))]], -(c_Equiv__Relations_Ocongruent2(_1801101, _1801105, _1801111, _1801103, _1801107, _1801109))], (52495 ^ _779142) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (41603 ^ _779142) ^ [_1602225, _1602227, _1602229, _1602231, _1602233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602225), tc_List_Olist(_1602225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602225), tc_List_Olist(_1602225)), _1602227), _1602229)), c_List_Olistrel(_1602225, c_Transitive__Closure_Ortrancl(_1602225, _1602231)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602225), tc_List_Olist(_1602225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602225), tc_List_Olist(_1602225)), _1602229), _1602233)), c_List_Olistrel(_1602225, c_Transitive__Closure_Ortrancl(_1602225, _1602231)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602225), tc_List_Olist(_1602225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602225), tc_List_Olist(_1602225)), _1602227), _1602233)), c_List_Olistrel(_1602225, c_Transitive__Closure_Ortrancl(_1602225, _1602231)))))], (18416 ^ _779142) ^ [_1103520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103520), 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), _1103520)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34534 ^ _779142) ^ [_1416100, _1416102, _1416104, _1416106, _1416108] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416100, tc_fun(_1416102, tc_HOL_Obool)), _1416104), hAPP(hAPP(c_COMBC(_1416100, tc_fun(_1416102, tc_HOL_Obool), tc_fun(_1416102, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1416102, tc_HOL_Obool), tc_fun(tc_fun(_1416102, tc_HOL_Obool), tc_fun(_1416102, tc_HOL_Obool)), _1416100), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416102, tc_HOL_Obool))), _1416106)), _1416108)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416102, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416100, tc_fun(_1416102, tc_HOL_Obool)), _1416104), _1416106)), _1416108))], (48414 ^ _779142) ^ [_1755218, _1755220] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755218), _1755220))), 48417 ^ _779142 : [(48424 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755218), _1755220))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755218, _1755220) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755220), c_Lazy__Sequence_Osmall__lazy_H(_1755218, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755220), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48418 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755218), _1755220)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755218, _1755220) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (19289 ^ _779142) ^ [_1118345, _1118347] : [class_Rings_Olinordered__idom(_1118345), -(hAPP(c_Groups_Oabs__class_Oabs(_1118345), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1118345), _1118347)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1118345), _1118347))], (43060 ^ _779142) ^ [_1638018, _1638020, _1638022, _1638024] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638018)), hAPP(hAPP(c_List_Oappend(_1638018), _1638020), _1638022)), c_List_Olists(_1638018, _1638024)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638018)), _1638020), c_List_Olists(_1638018, _1638024))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638018)), _1638022), c_List_Olists(_1638018, _1638024)))], (12236 ^ _779142) ^ [_990487] : [class_Rings_Olinordered__semidom(_990487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990487), c_Groups_Oone__class_Oone(_990487)), c_Groups_Ozero__class_Ozero(_990487)))], (4604 ^ _779142) ^ [_849124, _849126] : [_849126 = _849124, -(c_DSequence_Osingle(_849126) = c_DSequence_Osingle(_849124))], (20155 ^ _779142) ^ [_1133038, _1133040, _1133042] : [class_Divides_Osemiring__div(_1133038), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133038), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133038), _1133040), _1133042)), _1133042)), c_Divides_Odiv__class_Omod(_1133038, _1133040, _1133042)) = _1133040)], (41997 ^ _779142) ^ [_1613016, _1613018, _1613020, _1613022, _1613024] : [hBOOL(hAPP(hAPP(c_member(_1613016), _1613018), hAPP(c_List_Oset(_1613016), _1613020))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1613022), hAPP(_1613024, _1613018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1613022), c_List_Olist_Olist__size(_1613016, _1613024, _1613020))))], (37908 ^ _779142) ^ [_1501451] : [-(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)))), _1501451))))], (29439 ^ _779142) ^ [_1302455, _1302457, _1302459] : [29441 ^ _779142 : [(29444 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302455, tc_HOL_Obool)), 29440 ^ [_1302455, _1302457, _1302459]), _1302459) = c_Orderings_Obot__class_Obot(tc_fun(_1302455, tc_HOL_Obool))], (29442 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1302455, tc_HOL_Obool)), 29440 ^ [_1302455, _1302457, _1302459]), _1302457)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302455, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1302455, tc_HOL_Obool), _1302457)), _1302459) = c_Orderings_Obot__class_Obot(tc_fun(_1302455, tc_HOL_Obool)))], (42032 ^ _779142) ^ [_1613801, _1613803, _1613805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613803)), _1613805))), -(hBOOL(hAPP(hAPP(c_member(_1613803), hAPP(hAPP(c_List_Onth(_1613803), _1613805), _1613801)), hAPP(c_List_Oset(_1613803), _1613805))))], (12940 ^ _779142) ^ [_1003076, _1003078, _1003080] : [-(hBOOL(hAPP(_1003076, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003078), _1003080)))), 12943 ^ _779142 : [(12946 ^ _779142) ^ [] : [hBOOL(hAPP(_1003076, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12944 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003078), _1003080)))]], 12948 ^ _779142 : [(12951 ^ _779142) ^ [] : [hBOOL(hAPP(_1003076, 12947 ^ [_1003076, _1003078, _1003080]))], (12949 ^ _779142) ^ [] : [-(_1003078 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003080), 12947 ^ [_1003076, _1003078, _1003080]))]]], (26637 ^ _779142) ^ [_1248026, _1248028, _1248030, _1248032] : [26641 ^ _779142 : [(26644 ^ _779142) ^ [] : [hBOOL(hAPP(_1248032, 26640 ^ [_1248026, _1248028, _1248030, _1248032]))], (26642 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248026), 26640 ^ [_1248026, _1248028, _1248030, _1248032]), _1248028)))]], 26646 ^ _779142 : [(26649 ^ _779142) ^ [] : [hBOOL(hAPP(_1248032, 26645 ^ [_1248026, _1248028, _1248030, _1248032]))], (26647 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248026), 26645 ^ [_1248026, _1248028, _1248030, _1248032]), _1248030)))]], 26650 ^ _779142 : [(26651 ^ _779142) ^ [_1248359] : [hBOOL(hAPP(hAPP(c_member(_1248026), _1248359), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248026, tc_HOL_Obool)), _1248028), _1248030))), -(hBOOL(hAPP(_1248032, _1248359)))]]], (42447 ^ _779142) ^ [_1625044, _1625046, _1625048] : [-(hBOOL(hAPP(c_List_Odistinct(_1625044), hAPP(hAPP(c_List_Olist_OCons(_1625044), _1625046), _1625048)))), -(hBOOL(hAPP(hAPP(c_member(_1625044), _1625046), hAPP(c_List_Oset(_1625044), _1625048)))), hBOOL(hAPP(c_List_Odistinct(_1625044), _1625048))], (20688 ^ _779142) ^ [_1142659, _1142661, _1142663, _1142665, _1142667] : [hBOOL(hAPP(hAPP(c_member(_1142659), _1142661), c_SetInterval_Oord_OatLeastAtMost(_1142659, _1142663, _1142665, _1142667))), 20691 ^ _779142 : [(20694 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1142663, _1142661), _1142667)))], (20692 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1142663, _1142665), _1142661)))]]], (40032 ^ _779142) ^ [_1560033, _1560035, _1560037, _1560039] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1560033, tc_HOL_Obool), tc_fun(_1560033, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1560033, tc_HOL_Obool), tc_fun(_1560033, tc_HOL_Obool)), _1560035), _1560037)), c_Wellfounded_Omax__ext(_1560033, _1560039)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560033), _1560035)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560033), _1560037)), -(_1560037 = c_Orderings_Obot__class_Obot(tc_fun(_1560033, tc_HOL_Obool))), 40046 ^ _779142 : [(40049 ^ _779142) ^ [_1560438] : [hBOOL(hAPP(hAPP(c_member(_1560033), _1560438), _1560037)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560033, _1560033)), hAPP(hAPP(c_Product__Type_OPair(_1560033, _1560033), 40045 ^ [_1560033, _1560035, _1560037, _1560039]), _1560438)), _1560039))], (40047 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560033), 40045 ^ [_1560033, _1560035, _1560037, _1560039]), _1560035)))]]], (30173 ^ _779142) ^ [_1318104, _1318106, _1318108, _1318110, _1318112] : [class_Groups_Ocomm__monoid__mult(_1318104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318106), _1318108)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318106), _1318110)), 30187 ^ _779142 : [(30190 ^ _779142) ^ [] : [hAPP(_1318112, 30186 ^ [_1318104, _1318106, _1318108, _1318110, _1318112]) = c_Groups_Oone__class_Oone(_1318104)], (30188 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318106), 30186 ^ [_1318104, _1318106, _1318108, _1318110, _1318112]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318106, tc_HOL_Obool)), _1318108), _1318110))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318106, _1318104), _1318112), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318106, tc_HOL_Obool)), _1318108), _1318110)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318104), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318106, _1318104), _1318112), _1318108)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318106, _1318104), _1318112), _1318110)))], (44803 ^ _779142) ^ [_1676789, _1676791] : [_1676789 = _1676791, -(hAPP(c_Code__Numeral_Onat__of, _1676789) = hAPP(c_Code__Numeral_Onat__of, _1676791))], (19439 ^ _779142) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30217 ^ _779142) ^ [_1319112, _1319114, _1319116, _1319118, _1319120] : [class_Groups_Ocomm__monoid__add(_1319112), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319114), _1319116)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319114), _1319118)), 30231 ^ _779142 : [(30234 ^ _779142) ^ [] : [hAPP(_1319120, 30230 ^ [_1319112, _1319114, _1319116, _1319118, _1319120]) = c_Groups_Ozero__class_Ozero(_1319112)], (30232 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319114), 30230 ^ [_1319112, _1319114, _1319116, _1319118, _1319120]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319114, tc_HOL_Obool)), _1319116), _1319118))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319114, _1319112), _1319120), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319114, tc_HOL_Obool)), _1319116), _1319118)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319112), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319114, _1319112), _1319120), _1319116)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319114, _1319112), _1319120), _1319118)))], (5914 ^ _779142) ^ [_872873, _872875, _872877, _872879] : [5915 ^ _779142 : [(5918 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_872873), _872875), _872879))], (5916 ^ _779142) ^ [] : [_872875 = _872877]], -(hBOOL(hAPP(hAPP(c_member(_872873), _872875), hAPP(hAPP(c_Set_Oinsert(_872873), _872877), _872879))))], (52431 ^ _779142) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (34951 ^ _779142) ^ [_1428196, _1428198, _1428200, _1428202] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428196, tc_fun(_1428198, tc_HOL_Obool)), _1428200), _1428202) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428198, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428196, tc_fun(_1428198, tc_HOL_Obool), _1428202), _1428200)))], (34310 ^ _779142) ^ [_1409268, _1409270, _1409272, _1409274] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409268, tc_fun(_1409270, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1409268, tc_HOL_Obool), _1409272)), _1409274) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1409268, tc_HOL_Obool), tc_fun(_1409270, tc_HOL_Obool)), _1409272), hAPP(hAPP(c_COMBC(tc_fun(_1409268, tc_HOL_Obool), tc_fun(_1409268, tc_fun(_1409270, tc_HOL_Obool)), tc_fun(_1409270, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409268, tc_fun(_1409270, tc_HOL_Obool))), _1409274)))], (29580 ^ _779142) ^ [_1305726, _1305728, _1305730, _1305732] : [class_Orderings_Olinorder(_1305726), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305726, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305726), _1305728)), c_SetInterval_Oord__class_OatLeastAtMost(_1305726, _1305730, _1305732)) = c_SetInterval_Oord__class_OatLeastAtMost(_1305726, _1305730, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305726), _1305728), _1305732)))], (45835 ^ _779142) ^ [_1701237, _1701239, _1701241, _1701243, _1701245, _1701247, _1701249] : [-(c_List_Ofoldr(_1701237, _1701239, _1701241, hAPP(hAPP(c_List_Omap(_1701243, _1701237), _1701245), _1701247), _1701249) = c_List_Ofoldr(_1701243, _1701239, hAPP(c_Fun_Ocomp(_1701237, tc_fun(_1701239, _1701239), _1701243, _1701241), _1701245), _1701247, _1701249))], (29329 ^ _779142) ^ [_1299710, _1299712, _1299714] : [class_Lattices_Oboolean__algebra(_1299710), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1299710), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299710), _1299712), _1299714)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299710), hAPP(c_Groups_Ouminus__class_Ouminus(_1299710), _1299712)), hAPP(c_Groups_Ouminus__class_Ouminus(_1299710), _1299714)))], (12379 ^ _779142) ^ [_992744, _992746] : [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), _992744), _992746))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992746), _992744)))], (21114 ^ _779142) ^ [_1150328, _1150330] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1150328, _1150330)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150330), hAPP(c_Nat_OSuc, _1150328)))], (52615 ^ _779142) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (38459 ^ _779142) ^ [_1521292, _1521294, _1521296, _1521298, _1521300] : [-(hAPP(c_Relation_ORange(_1521292, _1521294), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1521292, _1521294)), hAPP(hAPP(c_Product__Type_OPair(_1521292, _1521294), _1521296), _1521298)), _1521300)) = hAPP(hAPP(c_Set_Oinsert(_1521294), _1521298), hAPP(c_Relation_ORange(_1521292, _1521294), _1521300)))], (41310 ^ _779142) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34913 ^ _779142) ^ [_1427098, _1427100, _1427102, _1427104, _1427106] : [_1427098 = c_Orderings_Obot__class_Obot(tc_fun(_1427100, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427100, tc_fun(_1427102, tc_HOL_Obool)), _1427098), hAPP(hAPP(c_COMBC(_1427100, tc_fun(_1427102, tc_HOL_Obool), tc_fun(_1427102, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1427102, tc_HOL_Obool), tc_fun(tc_fun(_1427102, tc_HOL_Obool), tc_fun(_1427102, tc_HOL_Obool)), _1427100), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427102, tc_HOL_Obool))), _1427104)), _1427106)) = c_Orderings_Obot__class_Obot(tc_fun(_1427102, tc_HOL_Obool)))], (22000 ^ _779142) ^ [_1165798, _1165800, _1165802, _1165804] : [class_Rings_Olinordered__semidom(_1165798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165798), c_Groups_Oone__class_Oone(_1165798)), _1165800)), 22007 ^ _779142 : [(22014 ^ _779142) ^ [] : [_1165802 = _1165804, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1165798), _1165800), _1165802) = hAPP(hAPP(c_Power_Opower__class_Opower(_1165798), _1165800), _1165804))], (22008 ^ _779142) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1165798), _1165800), _1165802) = hAPP(hAPP(c_Power_Opower__class_Opower(_1165798), _1165800), _1165804), -(_1165802 = _1165804)]]], (16571 ^ _779142) ^ [_1070770, _1070772] : [16572 ^ _779142 : [(16575 ^ _779142) ^ [] : [_1070770 = _1070772], (16573 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070770), _1070772))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070772), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (6900 ^ _779142) ^ [_891964, _891966, _891968, _891970] : [_891968 = _891970, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_891964, _891966, hAPP(hAPP(c_Set_Oinsert(_891964), _891968), c_Orderings_Obot__class_Obot(tc_fun(_891964, tc_HOL_Obool)))), _891970)))], (41493 ^ _779142) ^ [_1598761, _1598763, _1598765, _1598767, _1598769] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598761), tc_List_Olist(_1598761))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598761), tc_List_Olist(_1598761)), _1598763), _1598765)), c_List_Olistrel1(_1598761, _1598767))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598761), tc_List_Olist(_1598761))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598761), tc_List_Olist(_1598761)), hAPP(hAPP(c_List_Olist_OCons(_1598761), _1598769), _1598763)), hAPP(hAPP(c_List_Olist_OCons(_1598761), _1598769), _1598765))), c_List_Olistrel1(_1598761, _1598767))))], (4704 ^ _779142) ^ [_850716, _850718] : [_850718 = _850716, -(c_Wellfounded_Ofinite__psubset(_850718) = c_Wellfounded_Ofinite__psubset(_850716))], (48064 ^ _779142) ^ [_1747823, _1747825, _1747827] : [-(c_List_Osplice(_1747823, hAPP(hAPP(c_List_Olist_OCons(_1747823), _1747825), _1747827), c_List_Olist_ONil(_1747823)) = hAPP(hAPP(c_List_Olist_OCons(_1747823), _1747825), _1747827))], (40980 ^ _779142) ^ [_1583761, _1583763, _1583765, _1583767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583761, _1583761)), hAPP(hAPP(c_Product__Type_OPair(_1583761, _1583761), _1583763), _1583765)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583761, _1583761), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583767))), -(_1583763 = _1583765)], (6025 ^ _779142) ^ [_875192, _875194, _875196] : [-(hAPP(c_Set_Oimage(_875192, _875194, _875196), c_Orderings_Obot__class_Obot(tc_fun(_875192, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_875194, tc_HOL_Obool)))], (11974 ^ _779142) ^ [_985714, _985716, _985718] : [class_Rings_Olinordered__ring__strict(_985714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985714), _985716), c_Groups_Ozero__class_Ozero(_985714))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985714), _985718), c_Groups_Ozero__class_Ozero(_985714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985714), c_Groups_Ozero__class_Ozero(_985714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985714), _985716), _985718))))], (188 ^ _779142) ^ [_781992, _781994, _781996, _781998, _782000, _782002, _782004, _782006, _782008, _782010] : [-(c_Big__Operators_Ocomm__monoid__big(_782008, _782004, _782000, _781996, _781992)), c_Big__Operators_Ocomm__monoid__big(_782010, _782006, _782002, _781998, _781994), _782010 = _782008, _782006 = _782004, _782002 = _782000, _781998 = _781996, _781994 = _781992], (39902 ^ _779142) ^ [_1556925, _1556927, _1556929, _1556931, _1556933, _1556935] : [c_Finite__Set_Ofolding__idem(_1556925, _1556927, _1556929, _1556931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556925), _1556933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556925, tc_HOL_Obool)), _1556935), _1556933)), -(hAPP(c_Fun_Ocomp(_1556927, _1556927, _1556927, hAPP(_1556931, _1556933)), hAPP(_1556931, _1556935)) = hAPP(_1556931, _1556933))], (25016 ^ _779142) ^ [_1219035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1219035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1219035)))], (30283 ^ _779142) ^ [_1320607, _1320609, _1320611] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1320607, tc_HOL_Obool)), _1320609), _1320611))), 30289 ^ _779142 : [(30293 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1320607, tc_HOL_Obool)), 30291 ^ [_1320607, _1320609, _1320611]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1320607, tc_HOL_Obool)), _1320609), _1320611))))], (30295 ^ _779142) ^ [] : [30288 ^ [_1320607, _1320609, _1320611] = 30291 ^ [_1320607, _1320609, _1320611]], (30297 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320607, tc_HOL_Obool)), 30288 ^ [_1320607, _1320609, _1320611]), 30291 ^ [_1320607, _1320609, _1320611]) = c_Orderings_Obot__class_Obot(tc_fun(_1320607, tc_HOL_Obool))], (30290 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1320607, tc_HOL_Obool)), 30288 ^ [_1320607, _1320609, _1320611]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1320607, tc_HOL_Obool)), _1320609), _1320611))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320607, tc_HOL_Obool)), _1320609), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1320607, tc_HOL_Obool), _1320611)) = c_Orderings_Obot__class_Obot(tc_fun(_1320607, tc_HOL_Obool)))], (43544 ^ _779142) ^ [_1649568, _1649570, _1649572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649568)), _1649572)), _1649570)), -(hAPP(hAPP(c_List_Odrop(_1649568), _1649570), _1649572) = c_List_Olist_ONil(_1649568))], (52357 ^ _779142) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (35476 ^ _779142) ^ [_1442229, _1442231, _1442233, _1442235, _1442237] : [-(hAPP(c_Relation_OImage(_1442229, _1442231, _1442233), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442229, tc_HOL_Obool)), _1442235), _1442237)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442231, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442229, _1442231, _1442233), _1442235)), hAPP(c_Relation_OImage(_1442229, _1442231, _1442233), _1442237)))], (14143 ^ _779142) ^ [_1025615, _1025617, _1025619, _1025621, _1025623] : [class_Fields_Ofield(_1025615), -(_1025617 = c_Groups_Ozero__class_Ozero(_1025615)), -(_1025619 = c_Groups_Ozero__class_Ozero(_1025615)), 14154 ^ _779142 : [(14161 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025615), _1025621), _1025619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025615), _1025623), _1025617), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025615), _1025621), _1025617) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025615), _1025623), _1025619))], (14155 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025615), _1025621), _1025617) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025615), _1025623), _1025619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025615), _1025621), _1025619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025615), _1025623), _1025617))]]], (38919 ^ _779142) ^ [_1533150, _1533152, _1533154, _1533156] : [c_Relation_Orefl__on(_1533150, _1533152, _1533154), hBOOL(hAPP(hAPP(c_member(_1533150), _1533156), _1533152)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533150, _1533150)), hAPP(hAPP(c_Product__Type_OPair(_1533150, _1533150), _1533156), _1533156)), _1533154)))], (32982 ^ _779142) ^ [_1382544, _1382546, _1382548, _1382550, _1382552] : [hBOOL(hAPP(hAPP(_1382544, _1382546), _1382548)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382550, _1382552, tc_HOL_Obool), _1382544), hAPP(hAPP(c_Product__Type_OPair(_1382550, _1382552), _1382546), _1382548))))], (42910 ^ _779142) ^ [_1634479, _1634481, _1634483] : [class_Orderings_Olinorder(_1634479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634479), _1634481)), -(c_List_Olinorder__class_Osorted__list__of__set(_1634479, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634479, tc_HOL_Obool)), _1634481), hAPP(hAPP(c_Set_Oinsert(_1634479), _1634483), c_Orderings_Obot__class_Obot(tc_fun(_1634479, tc_HOL_Obool))))) = c_List_Oremove1(_1634479, _1634483, c_List_Olinorder__class_Osorted__list__of__set(_1634479, _1634481)))], (24714 ^ _779142) ^ [_1213790] : [c_Int_OPls = c_Int_OBit1(_1213790)], (47390 ^ _779142) ^ [_1733330, _1733332, _1733334, _1733336, _1733338] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733330)), _1733332) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733334)), _1733336), 47396 ^ _779142 : [(47399 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1733338, hAPP(hAPP(c_List_Onth(_1733330), _1733332), 47395 ^ [_1733330, _1733332, _1733334, _1733336, _1733338])), hAPP(hAPP(c_List_Onth(_1733334), _1733336), 47395 ^ [_1733330, _1733332, _1733334, _1733336, _1733338])))], (47397 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47395 ^ [_1733330, _1733332, _1733334, _1733336, _1733338]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733330)), _1733332))))]], -(c_List_Olist__all2(_1733330, _1733334, _1733338, _1733332, _1733336))], (6534 ^ _779142) ^ [_883979, _883981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883979, tc_HOL_Obool)), _883981), c_Orderings_Obot__class_Obot(tc_fun(_883979, tc_HOL_Obool)))), -(_883981 = c_Orderings_Obot__class_Obot(tc_fun(_883979, tc_HOL_Obool)))], (27250 ^ _779142) ^ [] : [-(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))], (32171 ^ _779142) ^ [_1364045, _1364047, _1364049, _1364051, _1364053] : [hBOOL(hAPP(hAPP(c_member(_1364045), _1364047), _1364049)), -(hAPP(c_Set_Oimage(_1364045, _1364051, hAPP(c_COMBK(_1364051, _1364045), _1364053)), _1364049) = hAPP(hAPP(c_Set_Oinsert(_1364051), _1364053), c_Orderings_Obot__class_Obot(tc_fun(_1364051, tc_HOL_Obool))))], (29335 ^ _779142) ^ [_1299849, _1299851, _1299853] : [class_Lattices_Oboolean__algebra(_1299849), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1299849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299849), _1299851), _1299853)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299849), hAPP(c_Groups_Ouminus__class_Ouminus(_1299849), _1299851)), hAPP(c_Groups_Ouminus__class_Ouminus(_1299849), _1299853)))], (12499 ^ _779142) ^ [_994876, _994878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994876), _994878)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994876), _994878) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10327 ^ _779142) ^ [_957649, _957651, _957653] : [class_Lattices_Oab__semigroup__idem__mult(_957649), hAPP(_957651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957649), 10332 ^ [_957649, _957651, _957653]), 10333 ^ [_957649, _957651, _957653])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957649), hAPP(_957651, 10332 ^ [_957649, _957651, _957653])), hAPP(_957651, 10333 ^ [_957649, _957651, _957653])), hBOOL(hAPP(c_Finite__Set_Ofinite(_957649), _957653)), -(_957653 = c_Orderings_Obot__class_Obot(tc_fun(_957649, tc_HOL_Obool))), -(hAPP(_957651, hAPP(c_Finite__Set_Ofold1(_957649, c_Groups_Otimes__class_Otimes(_957649)), _957653)) = hAPP(c_Finite__Set_Ofold1(_957649, c_Groups_Otimes__class_Otimes(_957649)), hAPP(c_Set_Oimage(_957649, _957649, _957651), _957653)))], (24976 ^ _779142) ^ [_1218169, _1218171, _1218173, _1218175, _1218177] : [class_Groups_Ocomm__monoid__add(_1218169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218171), _1218173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218173), _1218175)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218169), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218169), _1218177), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218171), _1218173))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218169), _1218177), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218173), _1218175))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218169), _1218177), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218171), _1218175)))], (11079 ^ _779142) ^ [_970093, _970095, _970097] : [class_Groups_Oab__group__add(_970093), 11082 ^ _779142 : [(11089 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970093), _970095), _970097) = c_Groups_Ozero__class_Ozero(_970093), -(_970095 = _970097)], (11083 ^ _779142) ^ [] : [_970095 = _970097, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970093), _970095), _970097) = c_Groups_Ozero__class_Ozero(_970093))]]], (50055 ^ _779142) ^ [_1791474, _1791476, _1791478, _1791480, _1791482] : [-(c_Fun_Obij__betw(_1791474, _1791476, _1791478, _1791480, _1791482)), c_Fun_Oinj__on(_1791474, _1791476, _1791478, _1791480), hAPP(c_Set_Oimage(_1791474, _1791476, _1791478), _1791480) = _1791482], (48602 ^ _779142) ^ [_1759699, _1759701, _1759703] : [-(c_FunDef_OTHE__default(_1759701, _1759703, _1759699) = _1759703), 48604 ^ _779142 : [(48607 ^ _779142) ^ [_1759821] : [hBOOL(hAPP(_1759699, _1759821)), -(_1759821 = 48603 ^ [_1759699, _1759701, _1759703])], (48605 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1759699, 48603 ^ [_1759699, _1759701, _1759703])))]]], (38344 ^ _779142) ^ [_1517600, _1517602, _1517604, _1517606, _1517608] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517600, _1517602, _1517604), _1517606), _1517608) = hAPP(c_Set_OCollect(tc_prod(_1517600, _1517604)), hAPP(c_Product__Type_Oprod_Oprod__case(_1517600, _1517604, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1517604, tc_fun(_1517602, tc_HOL_Obool)), tc_fun(_1517604, tc_HOL_Obool), _1517600), hAPP(c_COMBB(tc_fun(_1517602, tc_HOL_Obool), tc_HOL_Obool, _1517604), c_HOL_OEx(_1517602))), hAPP(hAPP(c_COMBC(_1517600, tc_fun(_1517604, tc_fun(_1517602, tc_HOL_Obool)), tc_fun(_1517604, tc_fun(_1517602, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517602, tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), tc_fun(tc_fun(_1517604, tc_fun(_1517602, tc_HOL_Obool)), tc_fun(_1517604, tc_fun(_1517602, tc_HOL_Obool))), _1517600), c_COMBB(tc_fun(_1517602, tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool), _1517604)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517602, tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), _1517600), c_COMBS(_1517602, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_HOL_Obool), tc_fun(_1517602, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517600), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517602), c_fconj)), hAPP(hAPP(c_COMBC(_1517600, tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_fun(tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), _1517600), c_COMBC(_1517602, tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_prod(_1517600, _1517602)), tc_fun(_1517602, tc_fun(tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_HOL_Obool)), _1517600), hAPP(c_COMBB(tc_prod(_1517600, _1517602), tc_fun(tc_fun(tc_prod(_1517600, _1517602), tc_HOL_Obool), tc_HOL_Obool), _1517602), c_member(tc_prod(_1517600, _1517602)))), c_Product__Type_OPair(_1517600, _1517602)))), _1517606))))), hAPP(hAPP(c_COMBC(_1517604, tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_fun(tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_fun(_1517602, tc_HOL_Obool)), _1517604), c_COMBC(_1517602, tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517602, tc_prod(_1517602, _1517604)), tc_fun(_1517602, tc_fun(tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_HOL_Obool)), _1517604), hAPP(c_COMBB(tc_prod(_1517602, _1517604), tc_fun(tc_fun(tc_prod(_1517602, _1517604), tc_HOL_Obool), tc_HOL_Obool), _1517602), c_member(tc_prod(_1517602, _1517604)))), hAPP(c_COMBC(_1517602, _1517604, tc_prod(_1517602, _1517604)), c_Product__Type_OPair(_1517602, _1517604))))), _1517608))))))], (26558 ^ _779142) ^ [_1246413, _1246415, _1246417, _1246419] : [class_Lattices_Olattice(_1246413), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246413), _1246415), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246413), _1246417), _1246419)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246413), _1246417), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246413), _1246415), _1246419)))], (39752 ^ _779142) ^ [_1553524, _1553526, _1553528, _1553530, _1553532, _1553534] : [c_Finite__Set_Ofolding(_1553524, _1553526, _1553528, _1553530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553524), _1553532)), -(hAPP(c_Fun_Ocomp(_1553526, _1553526, _1553526, hAPP(_1553528, _1553534)), hAPP(_1553530, _1553532)) = hAPP(c_Fun_Ocomp(_1553526, _1553526, _1553526, hAPP(_1553530, _1553532)), hAPP(_1553528, _1553534)))], (21232 ^ _779142) ^ [_1152443, _1152445, _1152447, _1152449] : [class_Rings_Ocomm__semiring__1(_1152443), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1152443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152443), _1152445), _1152447)), _1152449) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152443), hAPP(hAPP(c_Power_Opower__class_Opower(_1152443), _1152445), _1152449)), hAPP(hAPP(c_Power_Opower__class_Opower(_1152443), _1152447), _1152449)))], (52013 ^ _779142) ^ [_1829026, _1829028, _1829030] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829026), _1829028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829026), _1829030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829026)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829028), _1829030)))], (40374 ^ _779142) ^ [_1569102, _1569104, _1569106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569102, _1569102), tc_HOL_Obool)), _1569104), c_Transitive__Closure_Ortrancl(_1569102, _1569106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569102, _1569102), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569102, _1569104)), c_Transitive__Closure_Ortrancl(_1569102, _1569106))))], (18676 ^ _779142) ^ [_1107870] : [class_Rings_Osemiring__1(_1107870), -(hBOOL(hAPP(hAPP(c_member(_1107870), c_Groups_Ozero__class_Ozero(_1107870)), c_Nat_Osemiring__1__class_ONats(_1107870))))], (27474 ^ _779142) ^ [_1264075, _1264077, _1264079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264075, tc_HOL_Obool)), _1264077), _1264079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1264075, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1264075, _1264077)), c_Predicate_OPowp(_1264075, _1264079))))], (26564 ^ _779142) ^ [_1246556, _1246558, _1246560, _1246562] : [class_Lattices_Osemilattice__sup(_1246556), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246556), _1246558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246556), _1246560), _1246562)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246556), _1246560), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246556), _1246558), _1246562)))], (5548 ^ _779142) ^ [_863930, _863932, _863934, _863936, _863938, _863940] : [-(c_COMBB(_863940, _863936, _863932) = c_COMBB(_863938, _863934, _863930)), _863940 = _863938, _863936 = _863934, _863932 = _863930], (50138 ^ _779142) ^ [_1792908, _1792910, _1792912] : [c_Fun_Obij__betw(_1792908, _1792908, c_Fun_Oid(_1792908), _1792910, _1792912), -(_1792910 = _1792912)], (48917 ^ _779142) ^ [_1766876, _1766878] : [c_Relation_Otrans(_1766876, _1766878), -(c_Relation_Otrans(_1766876, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1766876, _1766876), tc_HOL_Obool)), _1766878), c_Relation_OId(_1766876))))], (36874 ^ _779142) ^ [_1473920, _1473922, _1473924, _1473926, _1473928, _1473930] : [c_Typedef_Otype__definition(_1473920, _1473922, _1473924, _1473926, _1473928), -(hBOOL(hAPP(hAPP(c_member(_1473922), hAPP(_1473924, _1473930)), _1473928)))], (16973 ^ _779142) ^ [_1077619, _1077621, _1077623, _1077625, _1077627, _1077629] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077619), _1077621)), _1077623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077625), _1077627)), _1077629), 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), _1077625), _1077627)), _1077629)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077623), _1077619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077625), _1077619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077627), _1077621)))], (42700 ^ _779142) ^ [_1630127, _1630129] : [_1630129 = c_List_Olist_ONil(_1630127), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630127)), _1630129) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37289 ^ _779142) ^ [_1483639, _1483641, _1483643, _1483645] : [c_Fun_Oinj__on(_1483639, _1483641, _1483643, c_Orderings_Otop__class_Otop(tc_fun(_1483639, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1483639, _1483641, _1483643), hAPP(c_Set_Oimage(_1483639, _1483641, _1483643), _1483645)) = _1483645)], (32177 ^ _779142) ^ [_1364194, _1364196, _1364198, _1364200, _1364202] : [class_Groups_Ocomm__monoid__mult(_1364194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364196), _1364198)), 32184 ^ _779142 : [(32191 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364196), _1364200), _1364198))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1364196, _1364194), hAPP(hAPP(c_COMBC(_1364196, _1364194, _1364194), hAPP(hAPP(c_COMBS(_1364196, _1364194, tc_fun(_1364194, _1364194)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364194, tc_fun(_1364194, _1364194)), _1364196), c_If(_1364194)), hAPP(hAPP(c_COMBC(_1364196, _1364196, tc_HOL_Obool), c_fequal), _1364200))), _1364202)), c_Groups_Oone__class_Oone(_1364194))), _1364198) = c_Groups_Oone__class_Oone(_1364194))], (32185 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1364196), _1364200), _1364198)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1364196, _1364194), hAPP(hAPP(c_COMBC(_1364196, _1364194, _1364194), hAPP(hAPP(c_COMBS(_1364196, _1364194, tc_fun(_1364194, _1364194)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364194, tc_fun(_1364194, _1364194)), _1364196), c_If(_1364194)), hAPP(hAPP(c_COMBC(_1364196, _1364196, tc_HOL_Obool), c_fequal), _1364200))), _1364202)), c_Groups_Oone__class_Oone(_1364194))), _1364198) = hAPP(_1364202, _1364200))]]], (39786 ^ _779142) ^ [_1554271, _1554273, _1554275, _1554277, _1554279, _1554281, _1554283, _1554285] : [c_Finite__Set_Ofolding(_1554271, _1554273, _1554275, _1554277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554271), _1554279)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554271), _1554281)), -(hAPP(c_Fun_Ocomp(_1554273, _1554273, _1554283, hAPP(_1554277, _1554281)), hAPP(c_Fun_Ocomp(_1554273, _1554273, _1554283, hAPP(_1554277, _1554279)), _1554285)) = hAPP(c_Fun_Ocomp(_1554273, _1554273, _1554283, hAPP(_1554277, _1554279)), hAPP(c_Fun_Ocomp(_1554273, _1554273, _1554283, hAPP(_1554277, _1554281)), _1554285)))], (19051 ^ _779142) ^ [_1113971, _1113973, _1113975] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113971)))), 19054 ^ _779142 : [(19061 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113973)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113971)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113973)), _1113975)) = 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), _1113971), _1113973))), _1113975))], (19055 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113973))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113971)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113973)), _1113975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113971)), _1113975))]]], (42682 ^ _779142) ^ [_1629812, _1629814, _1629816] : [-(hAPP(hAPP(c_List_Ozip(_1629812, _1629814), _1629816), c_List_Olist_ONil(_1629814)) = c_List_Olist_ONil(tc_prod(_1629812, _1629814)))], (18929 ^ _779142) ^ [_1112077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112077)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1112077))], (35369 ^ _779142) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omin__strict), c_FunDef_Omin__weak)))], (15693 ^ _779142) ^ [_1054612, _1054614] : [class_Int_Onumber__ring(_1054612), -(hBOOL(hAPP(hAPP(c_member(_1054612), hAPP(c_Int_Onumber__class_Onumber__of(_1054612), _1054614)), c_Int_Oring__1__class_OInts(_1054612))))], (27836 ^ _779142) ^ [_1270694, _1270696, _1270698, _1270700] : [class_Orderings_Olinorder(_1270694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270694), _1270696), _1270698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270694), _1270696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270694), _1270698), _1270700))))], (35604 ^ _779142) ^ [_1445712, _1445714] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1445712, _1445712)), _1445714)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1445712), hAPP(c_Relation_OField(_1445712), _1445714))))], (49561 ^ _779142) ^ [_1780233, _1780235] : [c_Equiv__Relations_Opart__equivp(_1780233, _1780235), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1780233, tc_HOL_Obool)), 49564 ^ [_1780233, _1780235]), hAPP(hAPP(c_COMBB(tc_fun(_1780233, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1780233, tc_HOL_Obool)), c_HOL_OEx(_1780233)), hAPP(hAPP(c_COMBB(tc_fun(_1780233, tc_HOL_Obool), tc_fun(_1780233, tc_HOL_Obool), tc_fun(_1780233, tc_HOL_Obool)), hAPP(c_COMBS(_1780233, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780233), c_fconj), hAPP(hAPP(c_COMBS(_1780233, _1780233, tc_HOL_Obool), _1780235), c_COMBI(_1780233))))), hAPP(hAPP(c_COMBC(tc_fun(_1780233, tc_HOL_Obool), tc_fun(_1780233, tc_fun(_1780233, tc_HOL_Obool)), tc_fun(_1780233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780233, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1780233, tc_fun(_1780233, tc_HOL_Obool)), tc_fun(_1780233, tc_HOL_Obool)), tc_fun(_1780233, tc_HOL_Obool)), c_COMBB(tc_fun(_1780233, tc_HOL_Obool), tc_HOL_Obool, _1780233)), c_fequal)), _1780235))))))], (37257 ^ _779142) ^ [_1482948, _1482950, _1482952, _1482954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1482948), hAPP(c_Set_Ovimage(_1482948, _1482950, _1482952), _1482954))), hAPP(c_Set_Oimage(_1482948, _1482950, _1482952), c_Orderings_Otop__class_Otop(tc_fun(_1482948, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1482950, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1482950), _1482954)))], (17751 ^ _779142) ^ [_1091961, _1091963] : [17752 ^ _779142 : [(17753 ^ _779142) ^ [_1092014] : [_1091963 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091961), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092014))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091961), _1091963)))], (47778 ^ _779142) ^ [_1741901, _1741903, _1741905] : [c_List_Olist__all(_1741901, _1741903, _1741905), 47781 ^ _779142 : [(47782 ^ _779142) ^ [_1741990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741990), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741901)), _1741905))), -(hBOOL(hAPP(_1741903, hAPP(hAPP(c_List_Onth(_1741901), _1741905), _1741990))))]]], (44859 ^ _779142) ^ [_1677776, _1677778] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1677776), _1677778) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677776)), hAPP(c_Code__Numeral_Onat__of, _1677778))))], (49156 ^ _779142) ^ [_1772869] : [-(c_Relation_Oantisym(_1772869, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1772869, _1772869), tc_HOL_Obool))))], (26054 ^ _779142) ^ [_1236790, _1236792, _1236794] : [class_Rings_Ocomm__semiring__1(_1236790), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236790), _1236792), 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)))), _1236794)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236790), hAPP(hAPP(c_Power_Opower__class_Opower(_1236790), _1236792), _1236794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1236790), _1236792), _1236794)))], (7186 ^ _779142) ^ [_898210, _898212, _898214, _898216, _898218, _898220] : [c_Finite__Set_Ofun__left__comm__idem(_898210, _898212, _898214), hBOOL(hAPP(c_Finite__Set_Ofinite(_898210), _898216)), -(hAPP(hAPP(c_Finite__Set_Ofold(_898210, _898212, _898214), _898218), hAPP(hAPP(c_Set_Oinsert(_898210), _898220), _898216)) = hAPP(hAPP(_898214, _898220), hAPP(hAPP(c_Finite__Set_Ofold(_898210, _898212, _898214), _898218), _898216)))], (49242 ^ _779142) ^ [_1774732, _1774734] : [c_Relation_Osym(_1774732, _1774734), c_Relation_Otrans(_1774732, _1774734), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774732, _1774732), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774732, _1774732, _1774732), hAPP(c_Relation_Oconverse(_1774732, _1774732), _1774734)), _1774734)), _1774734)))], (34348 ^ _779142) ^ [_1410559, _1410561, _1410563, _1410565] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1410559, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410561, tc_fun(_1410559, tc_HOL_Obool)), _1410563), _1410565)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410561, tc_fun(_1410559, tc_HOL_Obool)), _1410563), hAPP(hAPP(c_COMBB(tc_fun(_1410559, tc_HOL_Obool), tc_fun(_1410559, tc_HOL_Obool), _1410561), c_Groups_Ouminus__class_Ouminus(tc_fun(_1410559, tc_HOL_Obool))), _1410565)))], (18080 ^ _779142) ^ [_1097586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1097586)), -(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), _1097586))))], (2996 ^ _779142) ^ [_823602, _823604, _823606, _823608] : [-(c_Wellfounded_Oacc(_823608, _823604) = c_Wellfounded_Oacc(_823606, _823602)), _823608 = _823606, _823604 = _823602], (2676 ^ _779142) ^ [_818612, _818614] : [_818614 = _818612, -(c_Set_OBall(_818614) = c_Set_OBall(_818612))], (37641 ^ _779142) ^ [_1492792, _1492794, _1492796, _1492798] : [-(hAPP(c_Set_Ovimage(_1492792, _1492794, _1492796), _1492798) = hAPP(c_Set_OCollect(_1492792), hAPP(hAPP(c_COMBC(_1492792, tc_fun(_1492794, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1492794, tc_fun(tc_fun(_1492794, tc_HOL_Obool), tc_HOL_Obool), _1492792), c_member(_1492794)), _1492796)), _1492798)))], (20049 ^ _779142) ^ [_1131056, _1131058] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1131056) = _1131058, 20052 ^ _779142 : [(20055 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131058)))], (20053 ^ _779142) ^ [] : [-(_1131056 = hAPP(c_Int_Onat, _1131058))]]], (9143 ^ _779142) ^ [_934717, _934719] : [class_Groups_Oab__semigroup__mult(_934717), hBOOL(hAPP(c_Finite__Set_Ofinite(_934717), _934719)), -(_934719 = c_Orderings_Obot__class_Obot(tc_fun(_934717, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_934717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934717), 9156 ^ [_934717, _934719]), 9157 ^ [_934717, _934719])), hAPP(hAPP(c_Set_Oinsert(_934717), 9156 ^ [_934717, _934719]), hAPP(hAPP(c_Set_Oinsert(_934717), 9157 ^ [_934717, _934719]), c_Orderings_Obot__class_Obot(tc_fun(_934717, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_934717), hAPP(c_Finite__Set_Ofold1(_934717, c_Groups_Otimes__class_Otimes(_934717)), _934719)), _934719)))], (4652 ^ _779142) ^ [_849896, _849898, _849900, _849902] : [-(c_Product__Type_Osnd(_849902, _849898) = c_Product__Type_Osnd(_849900, _849896)), _849902 = _849900, _849898 = _849896], (23605 ^ _779142) ^ [_1194915, _1194917] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1194915)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1194917), 23608 ^ _779142 : [(23611 ^ _779142) ^ [] : [-(_1194917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23609 ^ _779142) ^ [] : [-(_1194915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23259 ^ _779142) ^ [_1188928, _1188930, _1188932, _1188934, _1188936] : [hAPP(c_Set_Oimage(_1188928, _1188930, _1188932), _1188934) = _1188936, -(hAPP(c_Set_Oimage(tc_fun(_1188928, tc_HOL_Obool), tc_fun(_1188930, tc_HOL_Obool), c_Set_Oimage(_1188928, _1188930, _1188932)), hAPP(c_Set_OPow(_1188928), _1188934)) = hAPP(c_Set_OPow(_1188930), _1188936))], (32938 ^ _779142) ^ [_1381139, _1381141] : [class_Rings_Oring__1(_1381139), 32941 ^ _779142 : [(32948 ^ _779142) ^ [] : [-(_1381141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32951 ^ _779142 : [(32958 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381141), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1381139), _1381141) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1381139), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1381139, _1381139)), tc_fun(tc_Int_Oint, _1381139)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1381139, _1381139), _1381139), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1381139, _1381139)), tc_fun(tc_Int_Oint, _1381139)), tc_Int_Oint), c_COMBB(tc_fun(_1381139, _1381139), _1381139, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1381139, tc_fun(tc_fun(_1381139, _1381139), _1381139), tc_Int_Oint), c_HOL_OLet(_1381139, _1381139)), c_Int_Oring__1__class_Oof__int(_1381139)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1381139, _1381139), tc_fun(_1381139, _1381139)), hAPP(hAPP(c_COMBB(tc_fun(_1381139, tc_fun(_1381139, _1381139)), tc_fun(tc_fun(_1381139, _1381139), tc_fun(_1381139, _1381139)), tc_Int_Oint), c_COMBS(_1381139, _1381139, _1381139)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1381139, _1381139), tc_fun(_1381139, tc_fun(_1381139, _1381139))), hAPP(hAPP(c_COMBB(tc_fun(_1381139, tc_fun(_1381139, _1381139)), tc_fun(tc_fun(_1381139, _1381139), tc_fun(_1381139, tc_fun(_1381139, _1381139))), tc_Int_Oint), c_COMBB(_1381139, tc_fun(_1381139, _1381139), _1381139)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1381139, tc_fun(_1381139, _1381139)), tc_Int_Oint), c_If(_1381139)), 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(_1381139, _1381139, _1381139), c_Groups_Oplus__class_Oplus(_1381139)), c_COMBI(_1381139))))), hAPP(hAPP(c_COMBC(_1381139, _1381139, _1381139), hAPP(hAPP(c_COMBB(_1381139, tc_fun(_1381139, _1381139), _1381139), c_Groups_Oplus__class_Oplus(_1381139)), hAPP(hAPP(c_COMBS(_1381139, _1381139, _1381139), c_Groups_Oplus__class_Oplus(_1381139)), c_COMBI(_1381139)))), c_Groups_Oone__class_Oone(_1381139))))), c_Divides_Odivmod__int(_1381141, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (32952 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381141), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1381139), _1381141) = hAPP(c_Groups_Ouminus__class_Ouminus(_1381139), hAPP(c_Int_Oring__1__class_Oof__int(_1381139), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1381141))))]]], (32942 ^ _779142) ^ [] : [_1381141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1381139), _1381141) = c_Groups_Ozero__class_Ozero(_1381139))]]], (25038 ^ _779142) ^ [_1219358, _1219360] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219358), _1219360), hAPP(c_Int_Onumber__class_Onumber__of(_1219358), c_Int_OBit1(c_Int_OPls))) = _1219360), class_Fields_Ofield(_1219358), class_Int_Onumber__ring(_1219358)], (41417 ^ _779142) ^ [_1596506, _1596508, _1596510] : [-(c_Random_Oselect__weight(_1596506, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596506)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1596506), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1596508)), _1596510)) = c_Random_Oselect__weight(_1596506, _1596510))], (25452 ^ _779142) ^ [_1226553] : [c_Int_OPls = c_Int_OBit0(_1226553), -(c_Int_OPls = _1226553)], (37759 ^ _779142) ^ [_1496237, _1496239, _1496241, _1496243, _1496245, _1496247] : [-(hAPP(c_Set_Oimage(_1496237, _1496239, hAPP(hAPP(c_COMBS(_1496237, _1496239, _1496239), hAPP(hAPP(c_COMBS(_1496237, _1496239, tc_fun(_1496239, _1496239)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1496239, tc_fun(_1496239, _1496239)), _1496237), c_If(_1496239)), _1496241)), _1496243)), _1496245)), _1496247) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496239, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1496237, _1496239, _1496243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496237, tc_HOL_Obool)), _1496247), hAPP(c_Set_OCollect(_1496237), _1496241)))), hAPP(c_Set_Oimage(_1496237, _1496239, _1496245), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496237, tc_HOL_Obool)), _1496247), hAPP(c_Set_OCollect(_1496237), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496237), c_fNot), _1496241))))))], (3078 ^ _779142) ^ [_824869, _824871] : [_824871 = _824869, -(c_List_Orotate1(_824871) = c_List_Orotate1(_824869))], (25420 ^ _779142) ^ [_1225970, _1225972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225970), _1225972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1225970)), c_Int_OBit0(_1225972))))], (29011 ^ _779142) ^ [_1293331, _1293333, _1293335, _1293337] : [class_Lattices_Osemilattice__inf(_1293331), 29014 ^ _779142 : [(29023 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293331), _1293335), _1293337)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), _1293335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), _1293337))], (29015 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293331), _1293335), _1293337))), 29018 ^ _779142 : [(29021 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), _1293337)))], (29019 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293331), _1293333), _1293335)))]]]]], (27764 ^ _779142) ^ [_1269495, _1269497, _1269499, _1269501] : [class_Orderings_Olinorder(_1269495), 27767 ^ _779142 : [(27768 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269495), _1269499), _1269501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), _1269499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), _1269501)))], (27778 ^ _779142) ^ [] : [27779 ^ _779142 : [(27782 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), _1269501))], (27780 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), _1269499))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269495), _1269497), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269495), _1269499), _1269501))))]]], (33664 ^ _779142) ^ [_1395193, _1395195] : [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), _1395193), _1395195))), 33667 ^ _779142 : [(33674 ^ _779142) ^ [] : [-(_1395195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1395193, _1395195) = c_Nitpick_Onat__gcd(_1395195, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1395193, _1395195)))], (33668 ^ _779142) ^ [] : [_1395195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1395193, _1395195) = _1395193)]]], (38290 ^ _779142) ^ [_1515997, _1515999, _1516001, _1516003, _1516005, _1516007, _1516009, _1516011, _1516013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515997, _1515999)), hAPP(hAPP(c_Product__Type_OPair(_1515997, _1515999), _1516001), _1516003)), _1516005)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516007, _1516009)), hAPP(hAPP(c_Product__Type_OPair(_1516007, _1516009), hAPP(_1516011, _1516001)), hAPP(_1516013, _1516003))), hAPP(c_Set_Oimage(tc_prod(_1515997, _1515999), tc_prod(_1516007, _1516009), c_Product__Type_Omap__pair(_1515997, _1516007, _1515999, _1516009, _1516011, _1516013)), _1516005))))], (31671 ^ _779142) ^ [_1347739, _1347741, _1347743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1347739), _1347741))), -(c_Random_Ominus__shift(_1347743, _1347739, _1347741) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1347739), _1347741))], (52417 ^ _779142) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (26600 ^ _779142) ^ [_1247292, _1247294, _1247296] : [class_Lattices_Osemilattice__sup(_1247292), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247292), _1247294), _1247296) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247292), _1247296), _1247294))], (17231 ^ _779142) ^ [_1082469, _1082471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082469), _1082471))), -(c_Nat__Transfer_Otsub(_1082471, _1082469) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42836 ^ _779142) ^ [_1632749, _1632751, _1632753, _1632755] : [_1632749 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1632751), _1632749), hAPP(hAPP(c_List_Olist_OCons(_1632751), _1632753), _1632755)) = c_List_Olist_ONil(_1632751))], (42375 ^ _779142) ^ [_1623304, _1623306] : [-(c_List_Obutlast(_1623304, _1623306) = hAPP(hAPP(c_List_Otake(_1623304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623304)), _1623306)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1623306))], (17315 ^ _779142) ^ [_1083878, _1083880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083878), _1083880)), -(c_Nat__Transfer_Otsub(_1083880, _1083878) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1083880), _1083878))], (1686 ^ _779142) ^ [_803159, _803161] : [-(class_Rings_Oordered__semiring(_803159)), _803161 = _803159, class_Rings_Oordered__semiring(_803161)], (42582 ^ _779142) ^ [_1628093, _1628095] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1628093)), c_List_Olist_ONil(_1628093)), c_List_Olists(_1628093, _1628095))))], (8207 ^ _779142) ^ [_915480, _915482, _915484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_915480, tc_HOL_Obool)), _915482), _915484)), -(hBOOL(hAPP(hAPP(c_member(_915480), 8210 ^ [_915480, _915482, _915484]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915480, tc_HOL_Obool)), _915484), _915482))))], (5516 ^ _779142) ^ [_863462, _863464, _863466, _863468] : [-(tc_prod(_863468, _863464) = tc_prod(_863466, _863462)), _863468 = _863466, _863464 = _863462], (10993 ^ _779142) ^ [_968817, _968819] : [class_Rings_Omult__zero(_968817), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968817), c_Groups_Ozero__class_Ozero(_968817)), _968819) = c_Groups_Ozero__class_Ozero(_968817))], (31440 ^ _779142) ^ [_1343116, _1343118, _1343120] : [class_Complete__Lattice_Ocomplete__lattice(_1343116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343116), _1343118)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1343116), _1343120), c_Complete__Lattice_OInf__class_OInf(_1343116, _1343118)) = hAPP(hAPP(c_Finite__Set_Ofold(_1343116, _1343116, c_Lattices_Osemilattice__inf__class_Oinf(_1343116)), _1343120), _1343118))], (34208 ^ _779142) ^ [_1407027, _1407029, _1407031, _1407033, _1407035, _1407037] : [hBOOL(hAPP(hAPP(c_member(_1407027), _1407029), _1407031)), hBOOL(hAPP(hAPP(c_member(_1407033), _1407035), hAPP(_1407037, _1407029))), -(hBOOL(hAPP(hAPP(c_member(_1407033), _1407035), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407027, tc_fun(_1407033, tc_HOL_Obool)), _1407031), _1407037))))], (52625 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (17664 ^ _779142) ^ [_1090308] : [17665 ^ _779142 : [(17666 ^ _779142) ^ [_1090365] : [hBOOL(hAPP(_1090308, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090365)))]], 17668 ^ _779142 : [(17671 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1090308, 17667 ^ [_1090308])))], (17669 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17667 ^ [_1090308])))]]], (44630 ^ _779142) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3910 ^ _779142) ^ [_838123, _838125, _838127, _838129, _838131, _838133, _838135, _838137] : [-(c_Lazy__Sequence_Ohb__bind(_838137, _838133, _838129, _838125) = c_Lazy__Sequence_Ohb__bind(_838135, _838131, _838127, _838123)), _838137 = _838135, _838133 = _838131, _838129 = _838127, _838125 = _838123], (48286 ^ _779142) ^ [_1752740, _1752742, _1752744] : [c_List_Oreplicate(_1752740, _1752742, _1752744) = c_List_Olist_ONil(_1752740), -(_1752742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15043 ^ _779142) ^ [_1042302, _1042304, _1042306, _1042308] : [class_Fields_Olinordered__field__inverse__zero(_1042302), class_Int_Onumber(_1042302), 15050 ^ _779142 : [(15051 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1042302), _1042304), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))), _1042308)), 15054 ^ _779142 : [(15061 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)))), 15064 ^ _779142 : [(15071 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)), c_Groups_Ozero__class_Ozero(_1042302)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), _1042308)))], (15065 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)), c_Groups_Ozero__class_Ozero(_1042302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042302), _1042308), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))), _1042304)))]]], (15055 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), _1042304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042302), _1042308), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)))))]]], (15077 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1042302), _1042304), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))), _1042308))), 15080 ^ _779142 : [(15083 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), _1042304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042302), _1042308), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))))], (15081 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))))]], 15084 ^ _779142 : [(15087 ^ _779142) ^ [] : [15088 ^ _779142 : [(15091 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042302), _1042308), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306))), _1042304))], (15089 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)), c_Groups_Ozero__class_Ozero(_1042302))))]], 15092 ^ _779142 : [(15095 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), _1042308))], (15093 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)), c_Groups_Ozero__class_Ozero(_1042302)))]]], (15085 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042302), c_Groups_Ozero__class_Ozero(_1042302)), hAPP(c_Int_Onumber__class_Onumber__of(_1042302), _1042306)))]]]]], (18626 ^ _779142) ^ [_1107069, _1107071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107069), _1107071))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107069, _1107071) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1107069), _1107071), _1107071))], (48250 ^ _779142) ^ [_1752076, _1752078, _1752080, _1752082, _1752084] : [-(c_List_Oreplicate(_1752076, _1752078, _1752080) = c_List_Oreplicate(_1752076, _1752082, _1752084)), _1752078 = _1752082, 48255 ^ _779142 : [(48258 ^ _779142) ^ [] : [_1752080 = _1752084], (48256 ^ _779142) ^ [] : [_1752078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31056 ^ _779142) ^ [_1335632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335632), c_Orderings_Otop__class_Otop(tc_fun(_1335632, 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(_1335632), c_Orderings_Otop__class_Otop(tc_fun(_1335632, tc_HOL_Obool))))))], (8645 ^ _779142) ^ [_924334, _924336, _924338, _924340] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_924334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924334), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924334), _924336), _924338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924334), _924340), _924338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924334), _924336), _924340)))], (49308 ^ _779142) ^ [_1776075] : [-(c_Relation_Osym(_1776075, c_Relation_OId(_1776075)))], (42267 ^ _779142) ^ [_1620925, _1620927, _1620929, _1620931, _1620933] : [-(_1620925 = _1620927), -(hAPP(hAPP(c_List_Onth(_1620929), hAPP(hAPP(c_List_Olist__update(_1620929, _1620931), _1620925), _1620933)), _1620927) = hAPP(hAPP(c_List_Onth(_1620929), _1620931), _1620927))], (52465 ^ _779142) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (15813 ^ _779142) ^ [_1056515, _1056517, _1056519, _1056521] : [class_Fields_Ofield__inverse__zero(_1056515), class_Int_Onumber(_1056515), 15820 ^ _779142 : [(15821 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1056515), _1056517), hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519)) = _1056521, 15824 ^ _779142 : [(15831 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519) = c_Groups_Ozero__class_Ozero(_1056515), -(_1056521 = c_Groups_Ozero__class_Ozero(_1056515))], (15825 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519) = c_Groups_Ozero__class_Ozero(_1056515)), -(_1056517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056515), _1056521), hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519)))]]], (15837 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1056515), _1056517), hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519)) = _1056521), 15840 ^ _779142 : [(15843 ^ _779142) ^ [] : [_1056517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056515), _1056521), hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519))], (15841 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519) = c_Groups_Ozero__class_Ozero(_1056515)]], 15844 ^ _779142 : [(15847 ^ _779142) ^ [] : [_1056521 = c_Groups_Ozero__class_Ozero(_1056515)], (15845 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1056515), _1056519) = c_Groups_Ozero__class_Ozero(_1056515))]]]]], (12844 ^ _779142) ^ [_1001331, _1001333, _1001335, _1001337] : [class_Rings_Olinordered__semiring__strict(_1001331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001331), _1001333), _1001335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001331), _1001333), _1001337))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001331), c_Groups_Ozero__class_Ozero(_1001331)), _1001333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001331), _1001335), _1001337)))], (24465 ^ _779142) ^ [_1209595, _1209597] : [class_Rings_Olinordered__idom(_1209595), 24468 ^ _779142 : [(24475 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209597), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209595), hAPP(c_Int_Oring__1__class_Oof__int(_1209595), _1209597)), c_Groups_Ozero__class_Ozero(_1209595))))], (24469 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209595), hAPP(c_Int_Oring__1__class_Oof__int(_1209595), _1209597)), c_Groups_Ozero__class_Ozero(_1209595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209597), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (34937 ^ _779142) ^ [_1427727, _1427729, _1427731, _1427733, _1427735] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427727, tc_fun(_1427729, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1427727), _1427731), _1427733)), _1427735) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427729, tc_HOL_Obool)), hAPP(_1427735, _1427731)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427727, tc_fun(_1427729, tc_HOL_Obool)), _1427733), _1427735)))], (4542 ^ _779142) ^ [_848131, _848133, _848135, _848137, _848139, _848141, _848143, _848145] : [-(c_Random__Sequence_ORandom(_848145, _848141, _848137, _848133) = c_Random__Sequence_ORandom(_848143, _848139, _848135, _848131)), _848145 = _848143, _848141 = _848139, _848137 = _848135, _848133 = _848131], (50797 ^ _779142) ^ [_1807722, _1807724, _1807726] : [class_Divides_Osemiring__div(_1807722), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807722), _1807724), _1807726)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807722), _1807724), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807722), _1807726), _1807724)) = _1807726)], (38116 ^ _779142) ^ [_1509432, _1509434, _1509436] : [class_Lattices_Odistrib__lattice(_1509432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509432), _1509434)), -(_1509434 = c_Orderings_Obot__class_Obot(tc_fun(_1509432, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1509432), _1509436), c_Big__Operators_Olattice__class_OSup__fin(_1509432, _1509434)) = c_Big__Operators_Olattice__class_OSup__fin(_1509432, hAPP(c_Set_OCollect(_1509432), hAPP(hAPP(c_COMBB(tc_fun(_1509432, tc_HOL_Obool), tc_HOL_Obool, _1509432), c_HOL_OEx(_1509432)), hAPP(hAPP(c_COMBC(_1509432, tc_fun(_1509432, tc_HOL_Obool), tc_fun(_1509432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509432, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509432, tc_HOL_Obool), tc_fun(_1509432, tc_HOL_Obool)), _1509432), c_COMBS(_1509432, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509432, tc_HOL_Obool), tc_fun(_1509432, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509432), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509432), c_fconj)), hAPP(hAPP(c_COMBC(_1509432, tc_fun(_1509432, _1509432), tc_fun(_1509432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509432, tc_HOL_Obool), tc_fun(tc_fun(_1509432, _1509432), tc_fun(_1509432, tc_HOL_Obool)), _1509432), c_COMBB(_1509432, tc_HOL_Obool, _1509432)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1509432), _1509436))))), hAPP(hAPP(c_COMBC(_1509432, tc_fun(_1509432, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509432)), _1509434))))))], (39477 ^ _779142) ^ [_1547145, _1547147] : [-(c_Hilbert__Choice_OEps(_1547145, hAPP(c_fequal, _1547147)) = _1547147)], (28543 ^ _779142) ^ [_1283759, _1283761, _1283763] : [class_Orderings_Olinorder(_1283759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283759), _1283761)), -(_1283761 = c_Orderings_Obot__class_Obot(tc_fun(_1283759, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1283759, c_Orderings_Oord__class_Omax(_1283759), hAPP(hAPP(c_Set_Oinsert(_1283759), _1283763), _1283761)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1283759), _1283763), c_Big__Operators_Olattice_OSup__fin(_1283759, c_Orderings_Oord__class_Omax(_1283759), _1283761)))], (12036 ^ _779142) ^ [_986860, _986862, _986864] : [class_Rings_Olinordered__semiring__strict(_986860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986860), c_Groups_Ozero__class_Ozero(_986860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986860), _986862), _986864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986860), c_Groups_Ozero__class_Ozero(_986860)), _986862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986860), c_Groups_Ozero__class_Ozero(_986860)), _986864)))], (40193 ^ _779142) ^ [_1563863, _1563865, _1563867, _1563869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563863, _1563863)), hAPP(hAPP(c_Product__Type_OPair(_1563863, _1563863), _1563865), _1563867)), _1563869)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563863, _1563863)), hAPP(hAPP(c_Product__Type_OPair(_1563863, _1563863), _1563865), _1563867)), c_Transitive__Closure_Otrancl(_1563863, _1563869))))], (19409 ^ _779142) ^ [_1120418, _1120420, _1120422] : [class_Groups_Oordered__ab__group__add__abs(_1120418), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120418), hAPP(c_Groups_Oabs__class_Oabs(_1120418), _1120420)), hAPP(c_Groups_Oabs__class_Oabs(_1120418), _1120422))), hAPP(c_Groups_Oabs__class_Oabs(_1120418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120418), _1120422), _1120420)))))], (41838 ^ _779142) ^ [_1609017, _1609019, _1609021, _1609023] : [-(_1609017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1609019), hAPP(hAPP(c_List_Olist_OCons(_1609019), _1609021), _1609023)), _1609017) = hAPP(hAPP(c_List_Onth(_1609019), _1609023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1609017), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9336 ^ _779142) ^ [_938288, _938290, _938292, _938294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938288), _938290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938292), _938294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938288), _938292)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938290), _938294))))], (31166 ^ _779142) ^ [_1337766] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1337766)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1337766))], (51415 ^ _779142) ^ [_1818479, _1818481, _1818483] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818479), _1818481)), 51426 ^ _779142 : [(51429 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818483), _1818479))], (51427 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818479), _1818483)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818481), _1818483)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818483), _1818481)))], (44923 ^ _779142) ^ [_1679656, _1679658, _1679660] : [44925 ^ _779142 : [(44928 ^ _779142) ^ [] : [hBOOL(hAPP(_1679658, 44924 ^ [_1679656, _1679658, _1679660]))], (44926 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1679656), 44924 ^ [_1679656, _1679658, _1679660]), hAPP(c_List_Oset(_1679656), _1679660))))]], -(hBOOL(hAPP(c_List_Olistsp(_1679656, _1679658), _1679660)))], (42216 ^ _779142) ^ [_1619829, _1619831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619831), _1619829)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619831))))], (23763 ^ _779142) ^ [_1197694, _1197696] : [class_Int_Onumber__ring(_1197694), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197694), _1197696), hAPP(c_Int_Onumber__class_Onumber__of(_1197694), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1197694), _1197696))], (39734 ^ _779142) ^ [_1552969, _1552971, _1552973, _1552975, _1552977, _1552979] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552969, tc_fun(_1552971, tc_HOL_Obool)), _1552973), hAPP(c_Fun_Ocomp(_1552975, tc_fun(_1552971, tc_HOL_Obool), _1552969, _1552977), _1552979)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552975, tc_fun(_1552971, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1552969, _1552975, _1552979), _1552973)), _1552977))], (13683 ^ _779142) ^ [_1017038, _1017040, _1017042, _1017044] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017038), _1017040)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017042), _1017044)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1017038, _1017042)), c_Sum__Type_OPlus(_1017038, _1017042, _1017040, _1017044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1017038), _1017040)), hAPP(c_Finite__Set_Ocard(_1017042), _1017044)))], (17375 ^ _779142) ^ [_1084833, _1084835] : [class_Divides_Osemiring__div(_1084833), -(c_Divides_Odiv__class_Omod(_1084833, _1084835, _1084835) = c_Groups_Ozero__class_Ozero(_1084833))], (38947 ^ _779142) ^ [_1533742, _1533744, _1533746, _1533748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533742, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533742, _1533744), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1533742, _1533744), tc_HOL_Obool)), _1533746), _1533748))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533742, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533742, _1533744), _1533746)), hAPP(c_Relation_ODomain(_1533742, _1533744), _1533748)))))], (43682 ^ _779142) ^ [_1653123, _1653125, _1653127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653123), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653125)), _1653127))), -(hAPP(hAPP(c_List_Oappend(_1653125), hAPP(hAPP(c_List_Otake(_1653125), _1653123), _1653127)), hAPP(hAPP(c_List_Olist_OCons(_1653125), hAPP(c_List_Ohd(_1653125), hAPP(hAPP(c_List_Odrop(_1653125), _1653123), _1653127))), c_List_Olist_ONil(_1653125))) = hAPP(hAPP(c_List_Otake(_1653125), hAPP(c_Nat_OSuc, _1653123)), _1653127))], (32871 ^ _779142) ^ [_1379689, _1379691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1379689)), 32874 ^ _779142 : [(32881 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1379691), _1379689))), -(c_Divides_OposDivAlg(_1379691, _1379689) = hAPP(c_Divides_Oadjust(_1379689), c_Divides_OposDivAlg(_1379691, 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)))), _1379689))))], (32875 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1379691), _1379689)), -(c_Divides_OposDivAlg(_1379691, _1379689) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1379691))]]], (14869 ^ _779142) ^ [_1039020, _1039022, _1039024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039020), _1039022)), 14875 ^ _779142 : [(14878 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1039024, 14874 ^ [_1039020, _1039022, _1039024])))], (14876 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039020), 14874 ^ [_1039020, _1039022, _1039024]), _1039022)))]], -(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(_1039020, tc_Nat_Onat), _1039024), _1039022))))], (38174 ^ _779142) ^ [_1512134, _1512136, _1512138, _1512140, _1512142, _1512144, _1512146] : [class_Rings_Osemiring__0(_1512134), c_Fun_Oinj__on(tc_prod(_1512136, _1512138), _1512134, hAPP(c_Product__Type_Oprod_Oprod__case(_1512136, _1512138, _1512134), hAPP(hAPP(c_COMBC(_1512136, tc_fun(_1512138, _1512134), tc_fun(_1512138, _1512134)), hAPP(hAPP(c_COMBB(tc_fun(_1512134, _1512134), tc_fun(tc_fun(_1512138, _1512134), tc_fun(_1512138, _1512134)), _1512136), c_COMBB(_1512134, _1512134, _1512138)), hAPP(hAPP(c_COMBB(_1512134, tc_fun(_1512134, _1512134), _1512136), c_Groups_Otimes__class_Otimes(_1512134)), _1512140))), _1512142)), hAPP(hAPP(c_Product__Type_OSigma(_1512136, _1512138), _1512144), hAPP(c_COMBK(tc_fun(_1512138, tc_HOL_Obool), _1512136), _1512146))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512134), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512136, _1512134), _1512140), _1512144)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512138, _1512134), _1512142), _1512146)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512134, _1512134), c_Fun_Oid(_1512134)), hAPP(c_Set_OCollect(_1512134), hAPP(hAPP(c_COMBB(tc_fun(_1512136, tc_HOL_Obool), tc_HOL_Obool, _1512134), c_HOL_OEx(_1512136)), hAPP(hAPP(c_COMBB(tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool)), tc_fun(_1512136, tc_HOL_Obool), _1512134), hAPP(c_COMBB(tc_fun(_1512138, tc_HOL_Obool), tc_HOL_Obool, _1512136), c_HOL_OEx(_1512138))), hAPP(hAPP(c_COMBC(_1512134, tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool)), tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512136, tc_fun(tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool))), tc_fun(tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool)), tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool))), _1512134), c_COMBS(_1512136, tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512136, tc_fun(_1512138, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1512136, tc_fun(tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool))), _1512134), hAPP(c_COMBB(tc_fun(_1512138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool)), _1512136), c_COMBS(_1512138, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool)), tc_fun(_1512136, tc_fun(_1512138, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1512134), hAPP(c_COMBB(tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512136), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512138), c_fconj))), hAPP(hAPP(c_COMBC(_1512134, tc_fun(_1512136, tc_fun(_1512138, _1512134)), tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1512138, _1512134), tc_fun(_1512138, tc_HOL_Obool)), tc_fun(tc_fun(_1512136, tc_fun(_1512138, _1512134)), tc_fun(_1512136, tc_fun(_1512138, tc_HOL_Obool))), _1512134), c_COMBB(tc_fun(_1512138, _1512134), tc_fun(_1512138, tc_HOL_Obool), _1512136)), hAPP(hAPP(c_COMBB(tc_fun(_1512134, tc_HOL_Obool), tc_fun(tc_fun(_1512138, _1512134), tc_fun(_1512138, tc_HOL_Obool)), _1512134), c_COMBB(_1512134, tc_HOL_Obool, _1512138)), c_fequal))), hAPP(hAPP(c_COMBC(_1512136, tc_fun(_1512138, _1512134), tc_fun(_1512138, _1512134)), hAPP(hAPP(c_COMBB(tc_fun(_1512134, _1512134), tc_fun(tc_fun(_1512138, _1512134), tc_fun(_1512138, _1512134)), _1512136), c_COMBB(_1512134, _1512134, _1512138)), hAPP(hAPP(c_COMBB(_1512134, tc_fun(_1512134, _1512134), _1512136), c_Groups_Otimes__class_Otimes(_1512134)), _1512140))), _1512142)))))), hAPP(hAPP(c_COMBC(_1512136, tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1512138, tc_HOL_Obool), tc_fun(_1512138, tc_HOL_Obool)), _1512136), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512138)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512136), c_fconj), hAPP(hAPP(c_COMBC(_1512136, tc_fun(_1512136, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512136)), _1512144)))), hAPP(hAPP(c_COMBC(_1512138, tc_fun(_1512138, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512138)), _1512146))))))))], (28811 ^ _779142) ^ [_1289001, _1289003, _1289005, _1289007] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289001, tc_HOL_Obool)), _1289003), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289001, tc_HOL_Obool)), _1289005), _1289007)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289001, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289001, tc_HOL_Obool)), _1289003), _1289005)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289001, tc_HOL_Obool)), _1289003), _1289007)))], (17599 ^ _779142) ^ [] : [-(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))], (31713 ^ _779142) ^ [_1348404, _1348406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348404), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1348406)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1348404)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1348406))], (52657 ^ _779142) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (6233 ^ _779142) ^ [_878991, _878993, _878995, _878997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878991, tc_HOL_Obool)), _878993), _878995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878991, tc_HOL_Obool)), _878995), _878997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878991, tc_HOL_Obool)), _878993), _878997)))], (24706 ^ _779142) ^ [_1213640, _1213642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213640), _1213642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1213640)), c_Int_OBit1(_1213642))))], (25578 ^ _779142) ^ [_1228671, _1228673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228671)), c_Int_OBit0(_1228673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228671), _1228673)))], (8322 ^ _779142) ^ [_917660, _917662, _917664, _917666] : [-(c_Nitpick_Ofold__graph_H(_917660, _917662, _917664, _917666, c_Orderings_Obot__class_Obot(tc_fun(_917660, tc_HOL_Obool)), _917666))], (44536 ^ _779142) ^ [_1671086, _1671088, _1671090, _1671092] : [class_Groups_Oab__group__add(_1671086), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1671086), hAPP(c_List_Omonoid__add__class_Olistsum(_1671086), hAPP(hAPP(c_List_Omap(_1671088, _1671086), _1671090), _1671092))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671086), hAPP(hAPP(c_List_Omap(_1671088, _1671086), hAPP(c_Fun_Ocomp(_1671086, _1671086, _1671088, c_Groups_Ouminus__class_Ouminus(_1671086)), _1671090)), _1671092)))], (40402 ^ _779142) ^ [_1569730, _1569732] : [-(c_Transitive__Closure_Ortrancl(_1569730, c_Transitive__Closure_Ortrancl(_1569730, _1569732)) = c_Transitive__Closure_Ortrancl(_1569730, _1569732))], (42798 ^ _779142) ^ [_1631888, _1631890, _1631892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631888), tc_List_Olist(_1631888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631888), tc_List_Olist(_1631888)), c_List_Olist_ONil(_1631888)), _1631890)), c_List_Olistrel1(_1631888, _1631892)))], (33393 ^ _779142) ^ [_1390167, _1390169, _1390171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390167, tc_fun(_1390167, tc_HOL_Obool))), _1390169), _1390171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390167, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1390167, _1390171)), c_Wellfounded_Oaccp(_1390167, _1390169))))], (2234 ^ _779142) ^ [_811735, _811737] : [_811737 = _811735, -(c_Nat_Onat_Onat__size(_811737) = c_Nat_Onat_Onat__size(_811735))], (38230 ^ _779142) ^ [_1514657] : [-(hAPP(c_Set_Oimage(_1514657, _1514657, c_Fun_Oid(_1514657)), c_Orderings_Otop__class_Otop(tc_fun(_1514657, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514657, tc_HOL_Obool)))], (18911 ^ _779142) ^ [] : [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)], (23201 ^ _779142) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (37671 ^ _779142) ^ [_1493763, _1493765, _1493767, _1493769, _1493771, _1493773] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493763, _1493765)), hAPP(hAPP(c_Product__Type_OPair(_1493763, _1493765), _1493767), _1493769)), hAPP(hAPP(c_Product__Type_OSigma(_1493763, _1493765), _1493771), _1493773))), -(hBOOL(hAPP(hAPP(c_member(_1493765), _1493769), hAPP(_1493773, _1493767))))], (3006 ^ _779142) ^ [_823751, _823753, _823755, _823757] : [-(c_Nitpick_Ocard_H(_823757, _823753) = c_Nitpick_Ocard_H(_823755, _823751)), _823757 = _823755, _823753 = _823751], (31755 ^ _779142) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21218 ^ _779142) ^ [_1152246, _1152248] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1152246, _1152248))))], (17555 ^ _779142) ^ [_1088494] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088494), c_Int_OPls) = _1088494)], (16545 ^ _779142) ^ [_1070334, _1070336] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070334), _1070336) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070336), _1070334))], (33471 ^ _779142) ^ [_1391317, _1391319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1391317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1391319)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391317, _1391319), c_Divides_OposDivAlg(_1391317, _1391319))))], (25760 ^ _779142) ^ [_1231867] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1231867)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1231867)))], (39289 ^ _779142) ^ [_1542092, _1542094, _1542096, _1542098] : [c_Equiv__Relations_Ocongruent(_1542092, _1542094, _1542096, _1542098), 39292 ^ _779142 : [(39293 ^ _779142) ^ [_1542237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542092, _1542092)), _1542237), _1542096)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542092, _1542092, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542092, tc_fun(_1542092, _1542094), tc_fun(_1542092, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542094, tc_HOL_Obool), tc_fun(tc_fun(_1542092, _1542094), tc_fun(_1542092, tc_HOL_Obool)), _1542092), c_COMBB(_1542094, tc_HOL_Obool, _1542092)), hAPP(hAPP(c_COMBB(_1542094, tc_fun(_1542094, tc_HOL_Obool), _1542092), c_fequal), _1542098))), _1542098)), _1542237)))]]], (25384 ^ _779142) ^ [_1225321, _1225323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225321)), -(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)))), _1225323)), 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)))), _1225321)) = 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, _1225323, _1225321))))], (29365 ^ _779142) ^ [_1300491, _1300493, _1300495, _1300497] : [hBOOL(hAPP(hAPP(c_member(_1300491), _1300493), _1300495)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300491, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1300491), _1300493), _1300497)), _1300495) = hAPP(hAPP(c_Set_Oinsert(_1300491), _1300493), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300491, tc_HOL_Obool)), _1300497), _1300495)))], (34440 ^ _779142) ^ [_1413335, _1413337, _1413339, _1413341, _1413343] : [_1413335 = c_Orderings_Obot__class_Obot(tc_fun(_1413337, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413337, tc_fun(_1413339, tc_HOL_Obool)), _1413335), hAPP(hAPP(c_COMBB(tc_fun(_1413339, tc_HOL_Obool), tc_fun(_1413339, tc_HOL_Obool), _1413337), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413339, tc_HOL_Obool)), _1413341)), _1413343)) = c_Orderings_Otop__class_Otop(tc_fun(_1413339, tc_HOL_Obool)))], (36638 ^ _779142) ^ [_1468638, _1468640, _1468642, _1468644, _1468646, _1468648] : [c_Fun_Oinj__on(_1468638, _1468640, _1468642, _1468644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468640, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468638, _1468640, _1468642), _1468644)), _1468646)), c_Fun_Oinj__on(_1468640, _1468638, _1468648, _1468646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468638, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468640, _1468638, _1468648), _1468646)), _1468644)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468638), _1468644)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468640), _1468646)), -(hAPP(c_Finite__Set_Ocard(_1468638), _1468644) = hAPP(c_Finite__Set_Ocard(_1468640), _1468646))], (42469 ^ _779142) ^ [_1625476, _1625478, _1625480, _1625482] : [hBOOL(hAPP(c_List_Odistinct(_1625476), _1625478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625480), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625476)), _1625478))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625482), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625476)), _1625478))), 42480 ^ _779142 : [(42487 ^ _779142) ^ [] : [_1625480 = _1625482, -(hAPP(hAPP(c_List_Onth(_1625476), _1625478), _1625480) = hAPP(hAPP(c_List_Onth(_1625476), _1625478), _1625482))], (42481 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Onth(_1625476), _1625478), _1625480) = hAPP(hAPP(c_List_Onth(_1625476), _1625478), _1625482), -(_1625480 = _1625482)]]], (9563 ^ _779142) ^ [_941834, _941836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941834), _941836)), _941836 = _941834], (22044 ^ _779142) ^ [_1166649, _1166651, _1166653, _1166655] : [class_Fields_Ofield(_1166649), -(_1166651 = c_Groups_Ozero__class_Ozero(_1166649)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1166649), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166649), _1166653), _1166651)), _1166655) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166649), hAPP(hAPP(c_Power_Opower__class_Opower(_1166649), _1166653), _1166655)), hAPP(hAPP(c_Power_Opower__class_Opower(_1166649), _1166651), _1166655)))], (48201 ^ _779142) ^ [_1751166, _1751168, _1751170, _1751172] : [48202 ^ _779142 : [(48205 ^ _779142) ^ [] : [_1751168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48203 ^ _779142) ^ [] : [hBOOL(hAPP(_1751172, _1751170))]], 48206 ^ _779142 : [(48207 ^ _779142) ^ [_1751291] : [hBOOL(hAPP(hAPP(c_member(_1751166), _1751291), hAPP(c_List_Oset(_1751166), c_List_Oreplicate(_1751166, _1751168, _1751170)))), -(hBOOL(hAPP(_1751172, _1751291)))]]], (33293 ^ _779142) ^ [_1388561, _1388563, _1388565] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1388561, _1388563), _1388565)), 33296 ^ _779142 : [(33297 ^ _779142) ^ [_1388646] : [hBOOL(hAPP(hAPP(_1388563, _1388646), _1388565)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1388561, _1388563), _1388646)))]]], (14501 ^ _779142) ^ [_1031952, _1031954, _1031956, _1031958] : [class_Fields_Olinordered__field(_1031952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031952), c_Groups_Ozero__class_Ozero(_1031952)), _1031954)), 14508 ^ _779142 : [(14515 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031952), _1031956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031952), _1031958), _1031954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031952), _1031956), _1031954)), _1031958)))], (14509 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031952), _1031956), _1031954)), _1031958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031952), _1031956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031952), _1031958), _1031954))))]]], (2 ^ _779142) ^ [_779169] : [-(_779169 = _779169)], (23517 ^ _779142) ^ [_1193307, _1193309] : [class_Groups_Oordered__ab__group__add__abs(_1193307), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193307), hAPP(c_Groups_Ouminus__class_Ouminus(_1193307), _1193309)), hAPP(c_Groups_Oabs__class_Oabs(_1193307), _1193309))))], (18166 ^ _779142) ^ [_1098969, _1098971] : [class_Int_Onumber__ring(_1098969), class_Rings_Olinordered__idom(_1098969), 18173 ^ _779142 : [(18180 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098971), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098969), hAPP(c_Int_Onumber__class_Onumber__of(_1098969), _1098971)), c_Groups_Ozero__class_Ozero(_1098969))))], (18174 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098969), hAPP(c_Int_Onumber__class_Onumber__of(_1098969), _1098971)), c_Groups_Ozero__class_Ozero(_1098969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098971), c_Int_OPls)))]]], (2944 ^ _779142) ^ [_822734, _822736] : [_822736 = _822734, -(c_HOL_Obool_Obool__size(_822736) = c_HOL_Obool_Obool__size(_822734))], (47002 ^ _779142) ^ [_1724484, _1724486] : [-(c_List_OdropWhile(_1724484, _1724486, c_List_Olist_ONil(_1724484)) = c_List_Olist_ONil(_1724484))], (31769 ^ _779142) ^ [_1350675, _1350677, _1350679, _1350681] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350675, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1350675, tc_fun(_1350675, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350675)), _1350677)), hAPP(hAPP(c_COMBC(_1350675, tc_fun(_1350675, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350675)), _1350679)), _1350681)), -(hBOOL(hAPP(hAPP(c_member(_1350675), _1350681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350675, tc_HOL_Obool)), _1350677), _1350679))))], (25704 ^ _779142) ^ [_1230875, _1230877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230875), _1230877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1230875)), c_Int_OBit1(_1230877))))], (45791 ^ _779142) ^ [_1699383, _1699385, _1699387] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699383)), hAPP(c_List_Ofilter(_1699383, _1699385), _1699387)) = 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(_1699383)), _1699387)))), hAPP(hAPP(c_COMBB(_1699383, tc_HOL_Obool, tc_Nat_Onat), _1699385), hAPP(c_List_Onth(_1699383), _1699387))))))], (25716 ^ _779142) ^ [_1231098, _1231100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231098), _1231100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1231098)), c_Int_OBit0(_1231100))))], (39181 ^ _779142) ^ [_1539224, _1539226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539224, _1539224)), _1539226)), c_Wellfounded_Oacyclic(_1539224, _1539226), -(c_Wellfounded_Owf(_1539224, _1539226))], (24077 ^ _779142) ^ [_1203011, _1203013, _1203015] : [-(hBOOL(hAPP(hAPP(c_member(_1203011), _1203013), _1203015))), -(hBOOL(hAPP(hAPP(c_member(_1203011), _1203013), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203011, tc_HOL_Obool)), _1203015))))], (19067 ^ _779142) ^ [_1114302] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114302))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114302)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18342 ^ _779142) ^ [_1102119, _1102121, _1102123, _1102125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102121), _1102123)), -(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), _1102123), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1102125, _1102119))), _1102121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102123), _1102119))))], (45061 ^ _779142) ^ [_1682942, _1682944, _1682946, _1682948, _1682950, _1682952, _1682954] : [c_List_Olist__all2(_1682942, _1682950, hAPP(hAPP(c_COMBC(_1682942, tc_fun(_1682950, _1682944), tc_fun(_1682950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682944, tc_HOL_Obool), tc_fun(tc_fun(_1682950, _1682944), tc_fun(_1682950, tc_HOL_Obool)), _1682942), c_COMBB(_1682944, tc_HOL_Obool, _1682950)), _1682946)), _1682952), _1682948, _1682954), -(c_List_Olist__all2(_1682942, _1682944, _1682946, _1682948, hAPP(hAPP(c_List_Omap(_1682950, _1682944), _1682952), _1682954)))], (16549 ^ _779142) ^ [_1070422, _1070424] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070422), _1070424) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070424), _1070422))], (5826 ^ _779142) ^ [_871373, _871375, _871377, _871379] : [5827 ^ _779142 : [(5830 ^ _779142) ^ [] : [hBOOL(hAPP(_871377, _871379))], (5828 ^ _779142) ^ [] : [_871375 = _871379]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871373), _871375), _871377), _871379)))], (19725 ^ _779142) ^ [_1125798, _1125800, _1125802] : [class_Fields_Olinordered__field__inverse__zero(_1125798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125798), c_Groups_Ozero__class_Ozero(_1125798)), _1125800)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125798), hAPP(c_Groups_Oabs__class_Oabs(_1125798), _1125802)), _1125800) = hAPP(c_Groups_Oabs__class_Oabs(_1125798), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125798), _1125802), _1125800)))], (39840 ^ _779142) ^ [_1555327, _1555329, _1555331, _1555333, _1555335, _1555337] : [c_Finite__Set_Ofolding(_1555327, _1555329, _1555331, _1555333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555327), _1555335)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555327), _1555337)), -(hAPP(c_Fun_Ocomp(_1555329, _1555329, _1555329, hAPP(_1555333, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1555327, tc_HOL_Obool)), _1555335), _1555337))), hAPP(_1555333, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1555327, tc_HOL_Obool)), _1555335), _1555337))) = hAPP(c_Fun_Ocomp(_1555329, _1555329, _1555329, hAPP(_1555333, _1555335)), hAPP(_1555333, _1555337)))], (32197 ^ _779142) ^ [_1364732, _1364734, _1364736, _1364738, _1364740] : [class_Groups_Ocomm__monoid__mult(_1364732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364734), _1364736)), 32204 ^ _779142 : [(32211 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364734), _1364738), _1364736))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1364734, _1364732), hAPP(hAPP(c_COMBC(_1364734, _1364732, _1364732), hAPP(hAPP(c_COMBS(_1364734, _1364732, tc_fun(_1364732, _1364732)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364732, tc_fun(_1364732, _1364732)), _1364734), c_If(_1364732)), hAPP(c_fequal, _1364738))), _1364740)), c_Groups_Oone__class_Oone(_1364732))), _1364736) = c_Groups_Oone__class_Oone(_1364732))], (32205 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1364734), _1364738), _1364736)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1364734, _1364732), hAPP(hAPP(c_COMBC(_1364734, _1364732, _1364732), hAPP(hAPP(c_COMBS(_1364734, _1364732, tc_fun(_1364732, _1364732)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364732, tc_fun(_1364732, _1364732)), _1364734), c_If(_1364732)), hAPP(c_fequal, _1364738))), _1364740)), c_Groups_Oone__class_Oone(_1364732))), _1364736) = hAPP(_1364740, _1364738))]]], (22693 ^ _779142) ^ [_1178916, _1178918] : [-(_1178916 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22696 ^ _779142 : [(22703 ^ _779142) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178918, _1178916) = 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), _1178918)), _1178916) = 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), _1178918), _1178916))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22697 ^ _779142) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178918, _1178916) = 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), _1178918)), _1178916) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178918), _1178916)))]]], (43935 ^ _779142) ^ [_1658027, _1658029, _1658031] : [class_Orderings_Olinorder(_1658027), -(c_Big__Operators_Olinorder__class_OMin(_1658027, hAPP(c_List_Oset(_1658027), hAPP(hAPP(c_List_Olist_OCons(_1658027), _1658029), _1658031))) = hAPP(c_List_Ofoldl(_1658027, _1658027, c_Orderings_Oord__class_Omin(_1658027), _1658029), _1658031))], (40219 ^ _779142) ^ [_1564533, _1564535] : [-(hAPP(c_Relation_ODomain(_1564533, _1564533), c_Transitive__Closure_Otrancl(_1564533, _1564535)) = hAPP(c_Relation_ODomain(_1564533, _1564533), _1564535))], (10135 ^ _779142) ^ [_953470, _953472, _953474, _953476] : [class_Rings_Ocomm__semiring__1(_953470), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953470), _953472), _953474)), _953476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953470), _953472), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953470), _953474), _953476)))], (24942 ^ _779142) ^ [_1217564, _1217566] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217564), _1217566)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1217564)), hAPP(c_Nat_OSuc, _1217566)))], (27062 ^ _779142) ^ [_1256670, _1256672, _1256674, _1256676] : [class_Lattices_Osemilattice__sup(_1256670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256670), _1256672)), hBOOL(hAPP(hAPP(c_member(_1256670), _1256674), _1256672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256670), _1256674), _1256676)), hAPP(hAPP(c_Finite__Set_Ofold(_1256670, _1256670, c_Lattices_Osemilattice__sup__class_Osup(_1256670)), _1256676), _1256672))))], (49592 ^ _779142) ^ [_1781156, _1781158, _1781160, _1781162] : [c_Fun_Oinj__on(_1781156, _1781158, _1781160, c_Orderings_Otop__class_Otop(tc_fun(_1781156, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781158, _1781156, c_Hilbert__Choice_Oinv__into(_1781156, _1781158, c_Orderings_Otop__class_Otop(tc_fun(_1781156, tc_HOL_Obool)), _1781160)), hAPP(c_Set_Oimage(_1781156, _1781158, _1781160), _1781162)) = _1781162)], (25518 ^ _779142) ^ [_1227622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1227622)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227622), c_Int_OPls)))], (50272 ^ _779142) ^ [_1795645, _1795647, _1795649, _1795651, _1795653] : [50274 ^ _779142 : [(50277 ^ _779142) ^ [] : [c_Relation_Orefl__on(_1795649, hAPP(_1795651, 50273 ^ [_1795645, _1795647, _1795649, _1795651, _1795653]), hAPP(_1795653, 50273 ^ [_1795645, _1795647, _1795649, _1795651, _1795653]))], (50275 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795645), 50273 ^ [_1795645, _1795647, _1795649, _1795651, _1795653]), _1795647)))]], -(c_Relation_Orefl__on(_1795649, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795645, tc_fun(_1795649, tc_HOL_Obool)), _1795647), _1795651), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795645, tc_fun(tc_prod(_1795649, _1795649), tc_HOL_Obool)), _1795647), _1795653)))], (14073 ^ _779142) ^ [_1024312, _1024314, _1024316] : [class_Fields_Olinordered__field(_1024312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024312), c_Groups_Ozero__class_Ozero(_1024312)), _1024314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024312), _1024316), c_Groups_Ozero__class_Ozero(_1024312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024312), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024312), _1024314), _1024316)), c_Groups_Ozero__class_Ozero(_1024312))))], (34544 ^ _779142) ^ [_1416619, _1416621, _1416623, _1416625, _1416627, _1416629, _1416631] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416619, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416621, tc_fun(_1416619, tc_HOL_Obool)), _1416623), _1416625)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416627, tc_fun(_1416619, tc_HOL_Obool)), _1416629), _1416631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416621, tc_fun(_1416619, tc_HOL_Obool)), _1416623), hAPP(hAPP(c_COMBB(tc_fun(_1416627, tc_fun(_1416619, tc_HOL_Obool)), tc_fun(_1416619, tc_HOL_Obool), _1416621), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416627, tc_fun(_1416619, tc_HOL_Obool)), _1416629)), hAPP(hAPP(c_COMBC(_1416621, tc_fun(_1416627, tc_fun(_1416619, tc_HOL_Obool)), tc_fun(_1416627, tc_fun(_1416619, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1416619, tc_HOL_Obool), tc_fun(_1416619, tc_HOL_Obool)), tc_fun(tc_fun(_1416627, tc_fun(_1416619, tc_HOL_Obool)), tc_fun(_1416627, tc_fun(_1416619, tc_HOL_Obool))), _1416621), c_COMBB(tc_fun(_1416619, tc_HOL_Obool), tc_fun(_1416619, tc_HOL_Obool), _1416627)), hAPP(hAPP(c_COMBB(tc_fun(_1416619, tc_HOL_Obool), tc_fun(tc_fun(_1416619, tc_HOL_Obool), tc_fun(_1416619, tc_HOL_Obool)), _1416621), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416619, tc_HOL_Obool))), _1416625))), _1416631))))], (25542 ^ _779142) ^ [_1228056, _1228058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1228056)), c_Int_OBit1(_1228058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228056), _1228058)))], (18848 ^ _779142) ^ [_1111071] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111071)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1111071)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1111071)))], (37595 ^ _779142) ^ [_1491697, _1491699, _1491701] : [hBOOL(hAPP(_1491697, _1491699)), -(hAPP(c_Set_OCollect(_1491701), hAPP(hAPP(c_COMBS(_1491701, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491701), c_fconj), hAPP(hAPP(c_COMBC(_1491701, _1491701, tc_HOL_Obool), c_fequal), _1491699))), _1491697)) = hAPP(hAPP(c_Set_Oinsert(_1491701), _1491699), c_Orderings_Obot__class_Obot(tc_fun(_1491701, tc_HOL_Obool))))], (50747 ^ _779142) ^ [_1806691, _1806693, _1806695] : [class_Rings_Ocomm__semiring__1(_1806691), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806691), _1806693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806691), _1806693), _1806695))))], (24712 ^ _779142) ^ [_1213756] : [c_Int_OBit1(_1213756) = c_Int_OPls], (25842 ^ _779142) ^ [_1233266] : [-(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)))), _1233266) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233266)))], (37589 ^ _779142) ^ [_1491610, _1491612, _1491614] : [-(hBOOL(hAPP(_1491610, _1491612))), -(hAPP(c_Set_OCollect(_1491614), hAPP(hAPP(c_COMBS(_1491614, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491614), c_fconj), hAPP(c_fequal, _1491612))), _1491610)) = c_Orderings_Obot__class_Obot(tc_fun(_1491614, tc_HOL_Obool)))], (11320 ^ _779142) ^ [_973681, _973683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973681), hAPP(c_Nat_OSuc, _973683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973681), _973683)))], (27008 ^ _779142) ^ [_1255798, _1255800, _1255802] : [class_Orderings_Olinorder(_1255798), hBOOL(hAPP(c_Finite__Set_Ofinite(_1255798), _1255800)), hBOOL(hAPP(hAPP(c_member(_1255798), _1255802), _1255800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255798), _1255802), c_Big__Operators_Olinorder__class_OMax(_1255798, _1255800))))], (19553 ^ _779142) ^ [_1122896, _1122898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122898)), 19560 ^ _779142 : [(19567 ^ _779142) ^ [] : [_1122896 = _1122898, -(hAPP(c_Int_Onat, _1122896) = hAPP(c_Int_Onat, _1122898))], (19561 ^ _779142) ^ [] : [hAPP(c_Int_Onat, _1122896) = hAPP(c_Int_Onat, _1122898), -(_1122896 = _1122898)]]], (394 ^ _779142) ^ [_785085, _785087, _785089, _785091] : [-(c_Relation_Oirrefl(_785089, _785085)), c_Relation_Oirrefl(_785091, _785087), _785091 = _785089, _785087 = _785085], (8941 ^ _779142) ^ [_930103, _930105, _930107, _930109, _930111] : [class_Groups_Ocomm__monoid__mult(_930103), hBOOL(hAPP(c_Finite__Set_Ofinite(_930105), _930107)), -(hBOOL(hAPP(hAPP(c_member(_930105), _930109), _930107))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_930105, _930103), _930111), hAPP(hAPP(c_Set_Oinsert(_930105), _930109), _930107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930103), hAPP(_930111, _930109)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_930105, _930103), _930111), _930107)))], (52545 ^ _779142) ^ [_1835157] : [class_Enum_Oenum(_1835157), -(class_Enum_Oenum(tc_Option_Ooption(_1835157)))], (44530 ^ _779142) ^ [_1670945, _1670947] : [class_Groups_Oordered__ab__group__add__abs(_1670945), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670945), hAPP(c_Groups_Oabs__class_Oabs(_1670945), hAPP(c_List_Omonoid__add__class_Olistsum(_1670945), _1670947))), hAPP(c_List_Omonoid__add__class_Olistsum(_1670945), hAPP(hAPP(c_List_Omap(_1670945, _1670945), c_Groups_Oabs__class_Oabs(_1670945)), _1670947)))))], (51733 ^ _779142) ^ [_1823918, _1823920, _1823922] : [class_Divides_Osemiring__div(_1823918), 51736 ^ _779142 : [(51743 ^ _779142) ^ [] : [c_Divides_Odiv__class_Omod(_1823918, _1823922, _1823920) = c_Groups_Ozero__class_Ozero(_1823918), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823918), _1823920), _1823922)))], (51737 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823918), _1823920), _1823922)), -(c_Divides_Odiv__class_Omod(_1823918, _1823922, _1823920) = c_Groups_Ozero__class_Ozero(_1823918))]]], (31279 ^ _779142) ^ [_1339887, _1339889, _1339891, _1339893] : [class_Orderings_Olinorder(_1339887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339887), _1339889)), 31289 ^ _779142 : [(31292 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339887), 31288 ^ [_1339887, _1339889, _1339891, _1339893]), _1339891))], (31290 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339887), 31288 ^ [_1339887, _1339889, _1339891, _1339893]), _1339889)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339887), hAPP(hAPP(c_Finite__Set_Ofold(_1339887, _1339887, c_Orderings_Oord__class_Omax(_1339887)), _1339893), _1339889)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339887), _1339891), _1339893))))], (49066 ^ _779142) ^ [_1771277, _1771279] : [c_Predicate_Oreflp(_1771277, _1771279), c_Predicate_Osymp(_1771277, _1771279), c_Predicate_Otransp(_1771277, _1771279), -(c_Equiv__Relations_Oequivp(_1771277, _1771279))], (20097 ^ _779142) ^ [_1131865, _1131867, _1131869] : [-(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), _1131865), _1131867)), _1131867)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131865, _1131867))), _1131869) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1131865), _1131869))], (23089 ^ _779142) ^ [_1185523, _1185525, _1185527] : [class_Groups_Ogroup__add(_1185523), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185523), _1185525), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185523), hAPP(c_Groups_Ouminus__class_Ouminus(_1185523), _1185525)), _1185527)) = _1185527)], (45667 ^ _779142) ^ [_1696712, _1696714, _1696716, _1696718] : [-(hBOOL(hAPP(_1696712, _1696714))), -(c_List_Oremove1(_1696716, _1696714, hAPP(c_List_Ofilter(_1696716, _1696712), _1696718)) = hAPP(c_List_Ofilter(_1696716, _1696712), _1696718))], (52313 ^ _779142) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (9835 ^ _779142) ^ [_946634, _946636, _946638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946634), _946636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946636), _946638)), _946634))))], (39544 ^ _779142) ^ [_1548631, _1548633] : [39545 ^ _779142 : [(39546 ^ _779142) ^ [_1548677] : [hBOOL(hAPP(_1548631, _1548677))]], -(hBOOL(hAPP(_1548631, c_Hilbert__Choice_OEps(_1548633, _1548631))))], (27428 ^ _779142) ^ [_1263116, _1263118, _1263120] : [class_Orderings_Olinorder(_1263116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263116), _1263118), _1263120)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263116, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1263116), _1263118), c_Orderings_Obot__class_Obot(tc_fun(_1263116, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1263116, _1263118, _1263120)) = c_SetInterval_Oord__class_OatLeastAtMost(_1263116, _1263118, _1263120))], (52077 ^ _779142) ^ [_1830094, _1830096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1830094)), 52080 ^ _779142 : [(52087 ^ _779142) ^ [] : [_1830096 = 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), _1830096), _1830094)), _1830094)))], (52081 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1830096), _1830094)), _1830094)), -(_1830096 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6605 ^ _779142) ^ [_885508, _885510, _885512, _885514, _885516] : [c_Finite__Set_Ofolding__one__idem(_885508, _885510, _885512), hBOOL(hAPP(c_Finite__Set_Ofinite(_885508), _885514)), -(_885516 = c_Orderings_Obot__class_Obot(tc_fun(_885508, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885508, tc_HOL_Obool)), _885516), _885514)), -(hAPP(hAPP(_885510, hAPP(_885512, _885516)), hAPP(_885512, _885514)) = hAPP(_885512, _885514))], (43229 ^ _779142) ^ [_1641584, _1641586] : [-(hAPP(hAPP(c_List_Oappend(_1641584), _1641586), c_List_Olist_ONil(_1641584)) = _1641586)], (29239 ^ _779142) ^ [_1297836, _1297838, _1297840, _1297842, _1297844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297836, tc_HOL_Obool)), _1297838), _1297840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297836, tc_HOL_Obool)), _1297842), _1297844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297836, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297836, tc_HOL_Obool)), _1297838), _1297842)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297836, tc_HOL_Obool)), _1297840), _1297844))))], (48364 ^ _779142) ^ [_1754329, _1754331, _1754333] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1754329, _1754331), _1754333) = c_Lazy__Sequence_Oproduct(_1754329, _1754331, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754329, _1754333), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754331, _1754333))), class_Lazy__Sequence_Osmall__lazy(_1754329), class_Lazy__Sequence_Osmall__lazy(_1754331)], (5006 ^ _779142) ^ [_855483, _855485] : [_855485 = _855483, -(c_Orderings_Otop__class_Otop(_855485) = c_Orderings_Otop__class_Otop(_855483))], (26280 ^ _779142) ^ [_1241314, _1241316] : [class_Groups_Olinordered__ab__group__add(_1241314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1241314), _1241316)), -(_1241316 = c_Orderings_Obot__class_Obot(tc_fun(_1241314, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1241314), c_Big__Operators_Olinorder__class_OMax(_1241314, _1241316)) = c_Big__Operators_Olinorder__class_OMin(_1241314, hAPP(c_Set_Oimage(_1241314, _1241314, c_Groups_Ouminus__class_Ouminus(_1241314)), _1241316)))], (31604 ^ _779142) ^ [_1346447, _1346449, _1346451, _1346453] : [31606 ^ _779142 : [(31611 ^ _779142) ^ [] : [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(_1346451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31605 ^ [_1346447, _1346449, _1346451, _1346453]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1346451, 31605 ^ [_1346447, _1346449, _1346451, _1346453])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31609 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31605 ^ [_1346447, _1346449, _1346451, _1346453]), _1346449)))], (31607 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1346447), 31605 ^ [_1346447, _1346449, _1346451, _1346453])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1346447), _1346449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1346451, _1346447)), _1346453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1346453), hAPP(_1346451, _1346449))), 31625 ^ _779142 : [(31630 ^ _779142) ^ [] : [-(hAPP(_1346451, 31624 ^ [_1346447, _1346449, _1346451, _1346453]) = _1346453)], (31628 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31624 ^ [_1346447, _1346449, _1346451, _1346453]), _1346449)))], (31626 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1346447), 31624 ^ [_1346447, _1346449, _1346451, _1346453])))]]], (31132 ^ _779142) ^ [_1337155, _1337157, _1337159] : [class_Orderings_Olinorder(_1337155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337155), _1337157), _1337159)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337155, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1337155, _1337157, _1337159)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337155), _1337159)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1337155), _1337157))], (5490 ^ _779142) ^ [_863079, _863081, _863083, _863085] : [-(tc_sum(_863085, _863081) = tc_sum(_863083, _863079)), _863085 = _863083, _863081 = _863079], (41170 ^ _779142) ^ [_1588935, _1588937, _1588939, _1588941, _1588943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588935, _1588935)), hAPP(hAPP(c_Product__Type_OPair(_1588935, _1588935), _1588937), _1588939)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588935, _1588935), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1588941)), _1588943))), 41174 ^ _779142 : [(41177 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588935, _1588935)), hAPP(hAPP(c_Product__Type_OPair(_1588935, _1588935), 41173 ^ [_1588935, _1588937, _1588939, _1588941, _1588943]), _1588939)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588935, _1588935), tc_HOL_Obool), _1588941), _1588943))))], (41175 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588935, _1588935)), hAPP(hAPP(c_Product__Type_OPair(_1588935, _1588935), _1588937), 41173 ^ [_1588935, _1588937, _1588939, _1588941, _1588943])), _1588943)))]]], (40803 ^ _779142) ^ [_1579221, _1579223, _1579225, _1579227] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579221, _1579221)), hAPP(hAPP(c_Product__Type_OPair(_1579221, _1579221), _1579223), _1579225)), hAPP(c_Relation_Oconverse(_1579221, _1579221), c_Transitive__Closure_Otrancl(_1579221, _1579227)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579221, _1579221)), hAPP(hAPP(c_Product__Type_OPair(_1579221, _1579221), _1579223), _1579225)), c_Transitive__Closure_Otrancl(_1579221, hAPP(c_Relation_Oconverse(_1579221, _1579221), _1579227)))))], (19295 ^ _779142) ^ [_1118450] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118450) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28442 ^ _779142) ^ [_1281920, _1281922, _1281924] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281920, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1281920, tc_HOL_Obool), tc_HOL_Obool)), _1281922), _1281924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281920, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281920, tc_HOL_Obool), _1281922)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281920, tc_HOL_Obool), _1281924)))], (5562 ^ _779142) ^ [_864151, _864153, _864155, _864157, _864159, _864161] : [-(c_COMBC(_864161, _864157, _864153) = c_COMBC(_864159, _864155, _864151)), _864161 = _864159, _864157 = _864155, _864153 = _864151], (15673 ^ _779142) ^ [_1054126, _1054128, _1054130, _1054132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054126), _1054128), _1054130)), hAPP(c_Int_Onumber__class_Onumber__of(_1054126), _1054132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054126), _1054128), hAPP(c_Int_Onumber__class_Onumber__of(_1054126), _1054132))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054126), _1054130), hAPP(c_Int_Onumber__class_Onumber__of(_1054126), _1054132)))), class_Int_Onumber(_1054126), class_Rings_Oring(_1054126)], (44813 ^ _779142) ^ [_1676959, _1676961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1676959), _1676961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676959)), hAPP(c_Code__Numeral_Onat__of, _1676961))))], (532 ^ _779142) ^ [_787082, _787084, _787086, _787088, _787090, _787092] : [-(c_Finite__Set_Ofun__left__comm__idem(_787090, _787086, _787082)), c_Finite__Set_Ofun__left__comm__idem(_787092, _787088, _787084), _787092 = _787090, _787088 = _787086, _787084 = _787082], (43070 ^ _779142) ^ [_1638245, _1638247, _1638249, _1638251] : [-(hAPP(hAPP(c_List_Oappend(_1638245), hAPP(hAPP(c_List_Oappend(_1638245), _1638247), _1638249)), _1638251) = hAPP(hAPP(c_List_Oappend(_1638245), _1638247), hAPP(hAPP(c_List_Oappend(_1638245), _1638249), _1638251)))], (18469 ^ _779142) ^ [_1104369, _1104371] : [class_Int_Onumber__ring(_1104369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1104371)), -(hBOOL(hAPP(hAPP(c_member(_1104369), hAPP(c_Int_Onumber__class_Onumber__of(_1104369), _1104371)), c_Nat_Osemiring__1__class_ONats(_1104369))))], (52485 ^ _779142) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (30942 ^ _779142) ^ [_1333472, _1333474, _1333476, _1333478] : [-(hBOOL(hAPP(hAPP(c_member(_1333472), hAPP(_1333474, _1333476)), hAPP(c_Set_Oimage(_1333478, _1333472, _1333474), c_Orderings_Otop__class_Otop(tc_fun(_1333478, tc_HOL_Obool))))))], (20281 ^ _779142) ^ [_1135061, _1135063] : [20282 ^ _779142 : [(20285 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135063))], (20283 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135061))]], 20286 ^ _779142 : [(20293 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135061), _1135063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1135061)), hAPP(c_Int_Onat, _1135063))))], (20287 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1135061)), hAPP(c_Int_Onat, _1135063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135061), _1135063)))]]], (14349 ^ _779142) ^ [_1029155, _1029157, _1029159] : [class_Fields_Olinordered__field(_1029155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029155), c_Groups_Ozero__class_Ozero(_1029155)), _1029157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029155), _1029159), c_Groups_Ozero__class_Ozero(_1029155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029155), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029155), _1029157), _1029159)), c_Groups_Ozero__class_Ozero(_1029155))))], (11810 ^ _779142) ^ [_982664, _982666, _982668] : [class_Rings_Oordered__cancel__semiring(_982664), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982664), _982666), _982668)), c_Groups_Ozero__class_Ozero(_982664)))), 11815 ^ _779142 : [(11822 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982664), _982666), c_Groups_Ozero__class_Ozero(_982664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982664), c_Groups_Ozero__class_Ozero(_982664)), _982668))], (11816 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982664), c_Groups_Ozero__class_Ozero(_982664)), _982666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982664), _982668), c_Groups_Ozero__class_Ozero(_982664)))]]], (39532 ^ _779142) ^ [_1548330, _1548332, _1548334, _1548336, _1548338, _1548340, _1548342, _1548344, _1548346] : [hAPP(c_Fun_Ocomp(_1548330, _1548332, _1548334, _1548336), _1548338) = hAPP(c_Fun_Ocomp(_1548340, _1548332, _1548334, _1548342), _1548344), -(hAPP(_1548336, hAPP(_1548338, _1548346)) = hAPP(_1548342, hAPP(_1548344, _1548346)))], (45675 ^ _779142) ^ [_1696819, _1696821, _1696823, _1696825, _1696827, _1696829] : [class_Orderings_Olinorder(_1696819), -(hBOOL(hAPP(_1696821, _1696823))), -(hAPP(c_List_Ofilter(_1696825, _1696821), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696825, _1696819, _1696827), _1696823), _1696829)) = hAPP(c_List_Ofilter(_1696825, _1696821), _1696829))], (19915 ^ _779142) ^ [_1128785, _1128787, _1128789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128785), 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)), _1128787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1128787), _1128789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128785), _1128787)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128785), _1128789))))], (26612 ^ _779142) ^ [_1247492, _1247494] : [class_Lattices_Osemilattice__sup(_1247492), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247492), _1247494), _1247494) = _1247494)], (12894 ^ _779142) ^ [_1002246] : [class_Rings_Olinordered__semidom(_1002246), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002246), c_Groups_Ozero__class_Ozero(_1002246)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002246), c_Groups_Oone__class_Oone(_1002246)), c_Groups_Oone__class_Oone(_1002246)))))], (7536 ^ _779142) ^ [_903796, _903798, _903800] : [class_Orderings_Opreorder(_903796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903796), _903798), _903800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903796), _903800), _903798))], (16459 ^ _779142) ^ [_1068938, _1068940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068938)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1068938), _1068940)))], (3946 ^ _779142) ^ [_838725, _838727] : [_838727 = _838725, -(c_New__DSequence_Opos__empty(_838727) = c_New__DSequence_Opos__empty(_838725))], (18893 ^ _779142) ^ [] : [c_Int_OPls = c_Int_OMin], (42616 ^ _779142) ^ [_1628750, _1628752, _1628754] : [_1628750 = c_List_Olist_ONil(_1628752), -(c_List_Obutlast(_1628752, hAPP(hAPP(c_List_Olist_OCons(_1628752), _1628754), _1628750)) = c_List_Olist_ONil(_1628752))], (34079 ^ _779142) ^ [_1403998, _1404000, _1404002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1403998, tc_HOL_Obool), tc_fun(_1403998, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1403998, tc_HOL_Obool), tc_fun(_1403998, tc_HOL_Obool)), _1404000), _1404002)), c_Wellfounded_Ofinite__psubset(_1403998))), 34082 ^ _779142 : [(34085 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1403998), _1404002)))], (34083 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1403998, tc_HOL_Obool)), _1404000), _1404002)))]]], (16893 ^ _779142) ^ [_1076240, _1076242, _1076244] : [class_Orderings_Olinorder(_1076240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076240), _1076242)), -(c_Big__Operators_Olinorder__class_OMin(_1076240, hAPP(hAPP(c_Set_Oinsert(_1076240), _1076244), _1076242)) = hAPP(hAPP(c_Finite__Set_Ofold(_1076240, _1076240, c_Orderings_Oord__class_Omin(_1076240)), _1076244), _1076242))], (21138 ^ _779142) ^ [_1150674] : [c_Nat__Transfer_Onat__set(_1150674), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1150674) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1150674)))], (40504 ^ _779142) ^ [_1572211, _1572213, _1572215, _1572217, _1572219] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572211, _1572211)), hAPP(hAPP(c_Product__Type_OPair(_1572211, _1572211), _1572213), _1572215)), _1572217)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572211, _1572211)), hAPP(hAPP(c_Product__Type_OPair(_1572211, _1572211), _1572215), _1572219)), c_Transitive__Closure_Ortrancl(_1572211, _1572217))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572211, _1572211)), hAPP(hAPP(c_Product__Type_OPair(_1572211, _1572211), _1572213), _1572219)), c_Transitive__Closure_Otrancl(_1572211, _1572217))))], (45408 ^ _779142) ^ [_1690388, _1690390] : [_1690390 = c_List_Olist_ONil(_1690388), -(c_List_Oremdups(_1690388, _1690390) = c_List_Olist_ONil(_1690388))], (23497 ^ _779142) ^ [_1193011, _1193013, _1193015] : [class_Rings_Odivision__ring(_1193011), -(_1193013 = c_Groups_Ozero__class_Ozero(_1193011)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193011), hAPP(c_Groups_Ouminus__class_Ouminus(_1193011), _1193015)), hAPP(c_Groups_Ouminus__class_Ouminus(_1193011), _1193013)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193011), _1193015), _1193013))], (43947 ^ _779142) ^ [_1658285, _1658287, _1658289] : [class_Orderings_Olinorder(_1658285), -(c_Big__Operators_Olattice_OInf__fin(_1658285, c_Orderings_Oord__class_Omin(_1658285), hAPP(c_List_Oset(_1658285), hAPP(hAPP(c_List_Olist_OCons(_1658285), _1658287), _1658289))) = hAPP(c_List_Ofoldl(_1658285, _1658285, c_Orderings_Oord__class_Omin(_1658285), _1658287), _1658289))], (11123 ^ _779142) ^ [_970748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970748), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24734 ^ _779142) ^ [_1214070] : [c_Int_OMin = _1214070, -(c_Int_OMin = c_Int_OBit1(_1214070))], (26786 ^ _779142) ^ [_1250969, _1250971] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250969, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1250969, tc_HOL_Obool))), _1250971) = _1250971)], (24089 ^ _779142) ^ [_1203197, _1203199, _1203201] : [hBOOL(hAPP(hAPP(c_member(_1203197), _1203199), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203197, tc_HOL_Obool)), _1203201))), hBOOL(hAPP(hAPP(c_member(_1203197), _1203199), _1203201))], (5981 ^ _779142) ^ [_874279, _874281, _874283, _874285, _874287] : [-(hAPP(hAPP(c_Set_Oinsert(_874279), _874281), hAPP(hAPP(c_Set_Oinsert(_874279), _874283), c_Orderings_Obot__class_Obot(tc_fun(_874279, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_874279), _874285), hAPP(hAPP(c_Set_Oinsert(_874279), _874287), c_Orderings_Obot__class_Obot(tc_fun(_874279, tc_HOL_Obool))))), 5982 ^ _779142 : [(5989 ^ _779142) ^ [] : [_874281 = _874287, _874283 = _874285], (5983 ^ _779142) ^ [] : [_874281 = _874285, _874283 = _874287]]], (14269 ^ _779142) ^ [_1027631, _1027633, _1027635] : [class_Fields_Olinordered__field(_1027631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027631), _1027633), c_Groups_Ozero__class_Ozero(_1027631))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027631), c_Groups_Ozero__class_Ozero(_1027631)), _1027635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027631), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027631), _1027633), _1027635)), c_Groups_Ozero__class_Ozero(_1027631))))], (41040 ^ _779142) ^ [_1585389, _1585391, _1585393] : [41043 ^ _779142 : [(41049 ^ _779142) ^ [] : [41042 ^ [_1585389, _1585391, _1585393] = 41045 ^ [_1585389, _1585391, _1585393]], (41047 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585389, _1585391)), hAPP(hAPP(c_Product__Type_OPair(_1585389, _1585391), 41041 ^ [_1585389, _1585391, _1585393]), 41045 ^ [_1585389, _1585391, _1585393])), _1585393)))], (41044 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585389, _1585391)), hAPP(hAPP(c_Product__Type_OPair(_1585389, _1585391), 41041 ^ [_1585389, _1585391, _1585393]), 41042 ^ [_1585389, _1585391, _1585393])), _1585393)))]], -(c_Relation_Osingle__valued(_1585389, _1585391, _1585393))], (2796 ^ _779142) ^ [_820510, _820512, _820514, _820516] : [-(c_Relation_ODomain(_820516, _820512) = c_Relation_ODomain(_820514, _820510)), _820516 = _820514, _820512 = _820510], (7586 ^ _779142) ^ [_904567, _904569, _904571, _904573, _904575, _904577] : [c_Finite__Set_Ofun__left__comm(_904567, _904569, _904571), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_904567, _904569, _904571, _904573, _904575), _904577)), -(hAPP(hAPP(c_Finite__Set_Ofold(_904567, _904569, _904571), _904573), _904575) = _904577)], (23177 ^ _779142) ^ [_1187200, _1187202, _1187204] : [class_Rings_Odivision__ring(_1187200), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187200), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187200), _1187202), _1187204)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187200), hAPP(c_Groups_Ouminus__class_Ouminus(_1187200), _1187202)), _1187204))], (52049 ^ _779142) ^ [_1829643, _1829645, _1829647] : [class_Rings_Ocomm__semiring__1(_1829643), 52054 ^ _779142 : [(52057 ^ _779142) ^ [] : [_1829647 = c_Groups_Oone__class_Oone(_1829643)], (52055 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829645))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829643), _1829647), hAPP(hAPP(c_Power_Opower__class_Opower(_1829643), _1829647), _1829645))))], (288 ^ _779142) ^ [_783550, _783552] : [-(c_Nat__Transfer_Ois__nat(_783550)), _783552 = _783550, c_Nat__Transfer_Ois__nat(_783552)], (27786 ^ _779142) ^ [_1269844, _1269846, _1269848] : [class_Orderings_Olinorder(_1269844), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269844), _1269846), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269844), _1269846), _1269848))))], (33443 ^ _779142) ^ [_1390929, _1390931, _1390933, _1390935] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390929, _1390931), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390933), _1390935))), -(_1390931 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1390929), _1390931) = _1390933)], (24920 ^ _779142) ^ [_1217230] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1217230))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1217230)))))], (17976 ^ _779142) ^ [_1095767, _1095769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1095767), _1095769)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1095769)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1095767)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095769), _1095767)))], (43411 ^ _779142) ^ [_1646199, _1646201, _1646203, _1646205, _1646207, _1646209] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646199), tc_List_Olist(_1646199))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646199), tc_List_Olist(_1646199)), hAPP(hAPP(c_List_Oappend(_1646199), _1646201), hAPP(hAPP(c_List_Olist_OCons(_1646199), _1646203), c_List_Olist_ONil(_1646199)))), hAPP(hAPP(c_List_Oappend(_1646199), _1646205), hAPP(hAPP(c_List_Olist_OCons(_1646199), _1646207), c_List_Olist_ONil(_1646199))))), c_List_Olistrel1(_1646199, _1646209)))), 43412 ^ _779142 : [(43419 ^ _779142) ^ [] : [_1646201 = _1646205, hBOOL(hAPP(hAPP(c_member(tc_prod(_1646199, _1646199)), hAPP(hAPP(c_Product__Type_OPair(_1646199, _1646199), _1646203), _1646207)), _1646209))], (43413 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646199), tc_List_Olist(_1646199))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646199), tc_List_Olist(_1646199)), _1646201), _1646205)), c_List_Olistrel1(_1646199, _1646209))), _1646203 = _1646207]]], (43746 ^ _779142) ^ [_1654140, _1654142, _1654144] : [-(hAPP(c_List_Otl(_1654140), hAPP(hAPP(c_List_Olist_OCons(_1654140), _1654142), _1654144)) = _1654144)], (1236 ^ _779142) ^ [_797534, _797536] : [-(class_Groups_Oab__group__add(_797534)), _797536 = _797534, class_Groups_Oab__group__add(_797536)], (49969 ^ _779142) ^ [_1789663, _1789665, _1789667, _1789669, _1789671] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789663, _1789665, tc_HOL_Obool, _1789667), _1789669), _1789671)), -(hBOOL(hAPP(_1789667, hAPP(hAPP(c_Product__Type_OPair(_1789663, _1789665), _1789669), _1789671))))], (23849 ^ _779142) ^ [_1199220] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199220))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10531 ^ _779142) ^ [_961408] : [hAPP(c_Nat_OSuc, _961408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41282 ^ _779142) ^ [_1592162, _1592164, _1592166] : [c_Nitpick_Oless__frac(_1592162, _1592164, _1592166), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592162), c_Nitpick_Oplus__frac(_1592162, _1592164, c_Nitpick_Ouminus__frac(_1592162, _1592166)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28104 ^ _779142) ^ [_1275639, _1275641, _1275643, _1275645] : [class_Orderings_Olinorder(_1275639), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275639), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275639), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275639), _1275641), _1275643)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275639), _1275641), _1275645))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275639), _1275641), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275639), _1275643), _1275645)))))], (18549 ^ _779142) ^ [_1105752, _1105754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1105752), _1105754)), -(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)), _1105752)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105754))))], (38963 ^ _779142) ^ [_1534150, _1534152, _1534154] : [-(hAPP(c_Relation_ODomain(_1534150, _1534152), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1534150, _1534152), tc_HOL_Obool), _1534154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1534150, _1534152), tc_HOL_Obool), tc_fun(_1534150, tc_HOL_Obool)), _1534154), c_Relation_ODomain(_1534150, _1534152)))], (40656 ^ _779142) ^ [_1575673, _1575675, _1575677, _1575679, _1575681] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575673, _1575673)), hAPP(hAPP(c_Product__Type_OPair(_1575673, _1575673), hAPP(_1575675, hAPP(c_Nat_OSuc, 40657 ^ [_1575673, _1575675, _1575677, _1575679, _1575681]))), hAPP(_1575675, 40657 ^ [_1575673, _1575675, _1575677, _1575679, _1575681]))), c_Transitive__Closure_Ortrancl(_1575673, _1575677))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575673, _1575673)), hAPP(hAPP(c_Product__Type_OPair(_1575673, _1575673), hAPP(_1575675, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1575679), _1575681))), hAPP(_1575675, _1575679))), c_Transitive__Closure_Ortrancl(_1575673, _1575677))))], (44311 ^ _779142) ^ [_1665131, _1665133, _1665135, _1665137, _1665139, _1665141, _1665143] : [-(hAPP(c_List_Ofoldl(_1665131, _1665133, _1665135, _1665137), hAPP(hAPP(c_List_Omap(_1665139, _1665133), _1665141), _1665143)) = hAPP(c_List_Ofoldl(_1665131, _1665139, hAPP(hAPP(c_COMBC(_1665131, tc_fun(_1665139, _1665133), tc_fun(_1665139, _1665131)), hAPP(hAPP(c_COMBB(tc_fun(_1665133, _1665131), tc_fun(tc_fun(_1665139, _1665133), tc_fun(_1665139, _1665131)), _1665131), c_COMBB(_1665133, _1665131, _1665139)), _1665135)), _1665141), _1665137), _1665143))], (21684 ^ _779142) ^ [_1160087] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1160087) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49457 ^ _779142) ^ [_1778361, _1778363] : [c_Equiv__Relations_Opart__equivp(_1778361, _1778363), 49461 ^ _779142 : [(49474 ^ _779142) ^ [_1778703, _1778705] : [-(hBOOL(hAPP(hAPP(_1778363, _1778705), _1778703))), hBOOL(hAPP(hAPP(_1778363, _1778705), _1778705)), hBOOL(hAPP(hAPP(_1778363, _1778703), _1778703)), hAPP(_1778363, _1778705) = hAPP(_1778363, _1778703)], (49464 ^ _779142) ^ [_1778534, _1778536] : [hBOOL(hAPP(hAPP(_1778363, _1778536), _1778534)), 49467 ^ _779142 : [(49472 ^ _779142) ^ [] : [-(hAPP(_1778363, _1778536) = hAPP(_1778363, _1778534))], (49470 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778363, _1778534), _1778534)))], (49468 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778363, _1778536), _1778536)))]]], (49462 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778363, 49460 ^ [_1778361, _1778363]), 49460 ^ [_1778361, _1778363])))]]], (37401 ^ _779142) ^ [_1486685, _1486687, _1486689, _1486691, _1486693, _1486695] : [hBOOL(hAPP(hAPP(c_member(_1486685), _1486687), _1486689)), 37404 ^ _779142 : [(37411 ^ _779142) ^ [] : [_1486693 = _1486695, -(hAPP(hAPP(c_Product__Type_OSigma(_1486691, _1486685), _1486693), hAPP(c_COMBK(tc_fun(_1486685, tc_HOL_Obool), _1486691), _1486689)) = hAPP(hAPP(c_Product__Type_OSigma(_1486691, _1486685), _1486695), hAPP(c_COMBK(tc_fun(_1486685, tc_HOL_Obool), _1486691), _1486689)))], (37405 ^ _779142) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1486691, _1486685), _1486693), hAPP(c_COMBK(tc_fun(_1486685, tc_HOL_Obool), _1486691), _1486689)) = hAPP(hAPP(c_Product__Type_OSigma(_1486691, _1486685), _1486695), hAPP(c_COMBK(tc_fun(_1486685, tc_HOL_Obool), _1486691), _1486689)), -(_1486693 = _1486695)]]], (26020 ^ _779142) ^ [_1236367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236367), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1236367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1236367 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5648 ^ _779142) ^ [_868222, _868224] : [hAPP(_868222, 5649 ^ [_868222, _868224]) = hAPP(_868224, 5649 ^ [_868222, _868224]), -(_868222 = _868224)], (29103 ^ _779142) ^ [_1295104, _1295106, _1295108, _1295110] : [class_Lattices_Olattice(_1295104), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295104), _1295106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295104), _1295108), _1295110)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295104), _1295108), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295104), _1295106), _1295110)))], (43115 ^ _779142) ^ [_1639315, _1639317, _1639319, _1639321] : [hAPP(hAPP(c_List_Oappend(_1639315), _1639317), _1639319) = hAPP(hAPP(c_List_Oappend(_1639315), _1639321), _1639319), -(_1639317 = _1639321)], (31650 ^ _779142) ^ [_1347287, _1347289, _1347291] : [class_Divides_Osemiring__div(_1347287), -(_1347289 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347287), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347287), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1347287), _1347289), _1347291)), _1347291)), c_Divides_Odiv__class_Omod(_1347287, _1347289, _1347291)))], (41615 ^ _779142) ^ [_1602603, _1602605, _1602607, _1602609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602603), tc_List_Olist(_1602603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602603), tc_List_Olist(_1602603)), _1602605), _1602607)), c_List_Olistrel1(_1602603, _1602609))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602603), tc_List_Olist(_1602603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602603), tc_List_Olist(_1602603)), _1602605), _1602607)), c_List_Olistrel(_1602603, c_Transitive__Closure_Ortrancl(_1602603, _1602609)))))], (52499 ^ _779142) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (30856 ^ _779142) ^ [_1332078] : [c_Orderings_Otop__class_Otop(tc_fun(_1332078, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1332078, tc_HOL_Obool))], (6930 ^ _779142) ^ [_892541, _892543, _892545] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892541, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892541, tc_HOL_Obool)), _892543), _892545)), _892545) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892541, tc_HOL_Obool)), _892543), _892545))], (14101 ^ _779142) ^ [_1024822, _1024824, _1024826] : [class_Fields_Olinordered__field(_1024822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024822), _1024824), c_Groups_Ozero__class_Ozero(_1024822))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024822), _1024826), c_Groups_Ozero__class_Ozero(_1024822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024822), c_Groups_Ozero__class_Ozero(_1024822)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024822), _1024824), _1024826))))], (34268 ^ _779142) ^ [_1408277, _1408279, _1408281, _1408283, _1408285, _1408287, _1408289, _1408291] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408277, tc_fun(_1408279, tc_fun(_1408281, tc_HOL_Obool))), _1408283), _1408285), _1408287), _1408289)), -(hBOOL(hAPP(hAPP(hAPP(_1408285, _1408291), _1408287), _1408289))), hBOOL(hAPP(hAPP(c_member(_1408277), _1408291), _1408283))], (35590 ^ _779142) ^ [_1445305, _1445307, _1445309, _1445311] : [-(hAPP(c_Relation_OField(_1445305), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1445305, _1445305)), hAPP(hAPP(c_Product__Type_OPair(_1445305, _1445305), _1445307), _1445309)), _1445311)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445305, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1445305), _1445307), hAPP(hAPP(c_Set_Oinsert(_1445305), _1445309), c_Orderings_Obot__class_Obot(tc_fun(_1445305, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1445305), _1445311)))], (39528 ^ _779142) ^ [_1548213, _1548215, _1548217, _1548219, _1548221, _1548223, _1548225] : [-(hAPP(c_Fun_Ocomp(_1548213, _1548215, _1548217, _1548219), hAPP(c_Fun_Ocomp(_1548221, _1548213, _1548217, _1548223), _1548225)) = hAPP(c_Fun_Ocomp(_1548221, _1548215, _1548217, hAPP(c_Fun_Ocomp(_1548213, _1548215, _1548221, _1548219), _1548223)), _1548225))], (45520 ^ _779142) ^ [_1692508, _1692510] : [c_List_Olist_ONil(_1692508) = c_List_Oconcat(_1692508, _1692510), 45523 ^ _779142 : [(45524 ^ _779142) ^ [_1692599] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692508)), _1692599), hAPP(c_List_Oset(tc_List_Olist(_1692508)), _1692510))), -(_1692599 = c_List_Olist_ONil(_1692508))]]], (35669 ^ _779142) ^ [_1447421, _1447423, _1447425, _1447427] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447421, _1447421)), hAPP(hAPP(c_Product__Type_OPair(_1447421, _1447421), _1447423), _1447425)), c_Relation_OId__on(_1447421, _1447427)))), _1447423 = _1447425, hBOOL(hAPP(hAPP(c_member(_1447421), _1447423), _1447427))], (45266 ^ _779142) ^ [_1687445, _1687447] : [hBOOL(hAPP(c_List_Odistinct(_1687445), _1687447)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1687445, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687445), tc_fun(_1687445, tc_HOL_Obool)), c_List_Oset(_1687445)), c_Enum_Osublists(_1687445, _1687447)))))], (3844 ^ _779142) ^ [_836932, _836934, _836936, _836938, _836940, _836942, _836944, _836946] : [-(c_New__DSequence_Oneg__decr__bind(_836946, _836942, _836938, _836934) = c_New__DSequence_Oneg__decr__bind(_836944, _836940, _836936, _836932)), _836946 = _836944, _836942 = _836940, _836938 = _836936, _836934 = _836932], (25858 ^ _779142) ^ [_1233547] : [-(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)))), _1233547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1233547), _1233547))], (52367 ^ _779142) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (20872 ^ _779142) ^ [_1146124, _1146126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146126)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1146124)), hAPP(c_Int_Onat, _1146126)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1146124), _1146126)))], (37397 ^ _779142) ^ [_1486460, _1486462, _1486464, _1486466, _1486468] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486460, _1486462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486460, tc_HOL_Obool)), _1486464), _1486466)), hAPP(c_COMBK(tc_fun(_1486462, tc_HOL_Obool), _1486460), _1486468)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486460, _1486462), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486460, _1486462), _1486464), hAPP(c_COMBK(tc_fun(_1486462, tc_HOL_Obool), _1486460), _1486468))), hAPP(hAPP(c_Product__Type_OSigma(_1486460, _1486462), _1486466), hAPP(c_COMBK(tc_fun(_1486462, tc_HOL_Obool), _1486460), _1486468))))], (39612 ^ _779142) ^ [_1550203, _1550205, _1550207] : [-(c_Hilbert__Choice_OEps(tc_prod(_1550203, _1550205), _1550207) = c_Hilbert__Choice_OEps(tc_prod(_1550203, _1550205), hAPP(c_Product__Type_Oprod_Oprod__case(_1550203, _1550205, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1550205, tc_prod(_1550203, _1550205)), tc_fun(_1550205, tc_HOL_Obool), _1550203), hAPP(c_COMBB(tc_prod(_1550203, _1550205), tc_HOL_Obool, _1550205), _1550207)), c_Product__Type_OPair(_1550203, _1550205)))))], (29592 ^ _779142) ^ [_1305996, _1305998, _1306000] : [class_Orderings_Oorder(_1305996), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305996, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305996), _1305998)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1305996, _1305998, _1306000)) = c_Orderings_Obot__class_Obot(tc_fun(_1305996, tc_HOL_Obool)))], (18573 ^ _779142) ^ [_1106159] : [-(c_Int_Osucc(c_Int_Opred(_1106159)) = _1106159)], (52645 ^ _779142) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (28857 ^ _779142) ^ [_1290330, _1290332, _1290334, _1290336] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290330, tc_HOL_Obool)), _1290332), _1290334), _1290336)), -(hBOOL(hAPP(_1290334, _1290336)))], (10399 ^ _779142) ^ [_959203, _959205, _959207, _959209, _959211, _959213] : [class_Rings_Olinordered__semiring__1__strict(_959203), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959203), _959205), _959207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959203), _959209), _959207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959203), c_Groups_Ozero__class_Ozero(_959203)), _959211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959203), c_Groups_Ozero__class_Ozero(_959203)), _959213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959203), _959211), _959213) = c_Groups_Oone__class_Oone(_959203), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959203), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959203), _959211), _959205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959203), _959213), _959209))), _959207)))], (38080 ^ _779142) ^ [_1507847, _1507849, _1507851] : [class_Lattices_Odistrib__lattice(_1507847), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507847), _1507849)), -(_1507849 = c_Orderings_Obot__class_Obot(tc_fun(_1507847, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1507847), _1507851), c_Big__Operators_Olattice__class_OInf__fin(_1507847, _1507849)) = c_Big__Operators_Olattice__class_OInf__fin(_1507847, hAPP(c_Set_OCollect(_1507847), hAPP(hAPP(c_COMBB(tc_fun(_1507847, tc_HOL_Obool), tc_HOL_Obool, _1507847), c_HOL_OEx(_1507847)), hAPP(hAPP(c_COMBC(_1507847, tc_fun(_1507847, tc_HOL_Obool), tc_fun(_1507847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507847, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507847, tc_HOL_Obool), tc_fun(_1507847, tc_HOL_Obool)), _1507847), c_COMBS(_1507847, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507847, tc_HOL_Obool), tc_fun(_1507847, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507847), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507847), c_fconj)), hAPP(hAPP(c_COMBC(_1507847, tc_fun(_1507847, _1507847), tc_fun(_1507847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507847, tc_HOL_Obool), tc_fun(tc_fun(_1507847, _1507847), tc_fun(_1507847, tc_HOL_Obool)), _1507847), c_COMBB(_1507847, tc_HOL_Obool, _1507847)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1507847), _1507851))))), hAPP(hAPP(c_COMBC(_1507847, tc_fun(_1507847, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507847)), _1507849))))))], (31847 ^ _779142) ^ [_1352411, _1352413, _1352415, _1352417, _1352419] : [c_Finite__Set_Ofun__left__comm(_1352411, _1352413, _1352415), -(c_Finite__Set_Ofun__left__comm(_1352417, _1352413, hAPP(hAPP(c_COMBB(_1352411, tc_fun(_1352413, _1352413), _1352417), _1352415), _1352419)))], (35343 ^ _779142) ^ [_1437916, _1437918, _1437920, _1437922] : [c_Wellfounded_Omax__extp(_1437916, hAPP(hAPP(c_COMBC(_1437916, tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_fun(_1437916, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437916, tc_fun(tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_fun(_1437916, tc_HOL_Obool)), _1437916), c_COMBC(_1437916, tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1437916, tc_prod(_1437916, _1437916)), tc_fun(_1437916, tc_fun(tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_HOL_Obool)), _1437916), hAPP(c_COMBB(tc_prod(_1437916, _1437916), tc_fun(tc_fun(tc_prod(_1437916, _1437916), tc_HOL_Obool), tc_HOL_Obool), _1437916), c_member(tc_prod(_1437916, _1437916)))), c_Product__Type_OPair(_1437916, _1437916)))), _1437918), _1437920, _1437922), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437916, tc_HOL_Obool), tc_fun(_1437916, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437916, tc_HOL_Obool), tc_fun(_1437916, tc_HOL_Obool)), _1437920), _1437922)), c_Wellfounded_Omax__ext(_1437916, _1437918))))], (9841 ^ _779142) ^ [_946775, _946777, _946779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946775), _946777)), _946779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946779), _946777))))], (34097 ^ _779142) ^ [_1404422, _1404424, _1404426, _1404428, _1404430, _1404432] : [class_Groups_Oordered__ab__group__add(_1404422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404424), _1404426)), 34107 ^ _779142 : [(34110 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404422), c_Groups_Ozero__class_Ozero(_1404422)), hAPP(_1404428, 34106 ^ [_1404422, _1404424, _1404426, _1404428, _1404430, _1404432])))], (34108 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404424), 34106 ^ [_1404422, _1404424, _1404426, _1404428, _1404430, _1404432]), _1404426)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404424, _1404422), _1404428), _1404426) = _1404430, hBOOL(hAPP(hAPP(c_member(_1404424), _1404432), _1404426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404422), hAPP(_1404428, _1404432)), _1404430)))], (46670 ^ _779142) ^ [_1717497, _1717499, _1717501] : [_1717499 = hAPP(c_List_Orev(_1717497), _1717501), -(hAPP(c_List_Orev(_1717497), _1717499) = _1717501)], (33722 ^ _779142) ^ [_1396463, _1396465] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396463, _1396465) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1396463, _1396465)))], (8775 ^ _779142) ^ [_926855, _926857, _926859, _926861] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_926855), 8778 ^ _779142 : [(8785 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926855), _926859), _926861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926855), _926857), _926859)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926855), _926857), _926861))))], (8779 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926855), _926857), _926859)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926855), _926857), _926861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926855), _926859), _926861)))]]], (23569 ^ _779142) ^ [_1194220, _1194222, _1194224] : [class_Rings_Olinordered__idom(_1194220), 23572 ^ _779142 : [(23581 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), hAPP(c_Groups_Oabs__class_Oabs(_1194220), _1194222)), _1194224))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), _1194222), _1194224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), hAPP(c_Groups_Ouminus__class_Ouminus(_1194220), _1194222)), _1194224))], (23573 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), hAPP(c_Groups_Oabs__class_Oabs(_1194220), _1194222)), _1194224)), 23576 ^ _779142 : [(23579 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), hAPP(c_Groups_Ouminus__class_Ouminus(_1194220), _1194222)), _1194224)))], (23577 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194220), _1194222), _1194224)))]]]]], (41237 ^ _779142) ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590929, _1590931)), _1590933), hAPP(hAPP(c_Relation_Orel__comp(_1590929, _1590935, _1590931), _1590937), _1590939))), 41243 ^ _779142 : [(41248 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590935, _1590931)), hAPP(hAPP(c_Product__Type_OPair(_1590935, _1590931), 41241 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939]), 41242 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939])), _1590939)))], (41246 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590929, _1590935)), hAPP(hAPP(c_Product__Type_OPair(_1590929, _1590935), 41240 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939]), 41241 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939])), _1590937)))], (41244 ^ _779142) ^ [] : [-(_1590933 = hAPP(hAPP(c_Product__Type_OPair(_1590929, _1590931), 41240 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939]), 41242 ^ [_1590929, _1590931, _1590933, _1590935, _1590937, _1590939]))]]], (50200 ^ _779142) ^ [_1794116, _1794118, _1794120, _1794122] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1794116, _1794118, _1794120), c_Product__Type_Ocurry(_1794116, _1794118, _1794120, _1794122)) = _1794122)], (50961 ^ _779142) ^ [_1810823, _1810825] : [50962 ^ _779142 : [(50965 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810825), _1810823))], (50963 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810823), _1810825)))]], -(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)))), _1810823, _1810825) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (43462 ^ _779142) ^ [_1647729, _1647731, _1647733, _1647735] : [-(hAPP(hAPP(c_List_Odrop(_1647729), hAPP(c_Nat_OSuc, _1647731)), hAPP(hAPP(c_List_Olist_OCons(_1647729), _1647733), _1647735)) = hAPP(hAPP(c_List_Odrop(_1647729), _1647731), _1647735))], (52601 ^ _779142) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (14803 ^ _779142) ^ [_1037651, _1037653] : [class_Rings_Olinordered__idom(_1037651), hBOOL(hAPP(hAPP(c_member(_1037651), _1037653), c_Int_Oring__1__class_OInts(_1037651))), 14810 ^ _779142 : [(14817 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037651), _1037653), c_Groups_Ozero__class_Ozero(_1037651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037651), c_Groups_Oone__class_Oone(_1037651)), _1037653)), _1037653)), c_Groups_Ozero__class_Ozero(_1037651))))], (14811 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037651), c_Groups_Oone__class_Oone(_1037651)), _1037653)), _1037653)), c_Groups_Ozero__class_Ozero(_1037651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037651), _1037653), c_Groups_Ozero__class_Ozero(_1037651))))]]], (42804 ^ _779142) ^ [_1632095, _1632097, _1632099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632095), tc_List_Olist(_1632095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632095), tc_List_Olist(_1632095)), _1632097), c_List_Olist_ONil(_1632095))), c_List_Olex(_1632095, _1632099)))], (34523 ^ _779142) ^ [_1415780, _1415782, _1415784, _1415786] : [34525 ^ _779142 : [(34528 ^ _779142) ^ [] : [hAPP(_1415786, 34524 ^ [_1415780, _1415782, _1415784, _1415786]) = c_Orderings_Obot__class_Obot(tc_fun(_1415780, tc_HOL_Obool))], (34526 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415782), 34524 ^ [_1415780, _1415782, _1415784, _1415786]), _1415784)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1415780, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415782, tc_fun(_1415780, tc_HOL_Obool)), _1415784), _1415786))], (1566 ^ _779142) ^ [_801659, _801661] : [-(class_Rings_Olinordered__semiring__strict(_801659)), _801661 = _801659, class_Rings_Olinordered__semiring__strict(_801661)], (33237 ^ _779142) ^ [_1387454, _1387456, _1387458, _1387460, _1387462] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1387454, _1387456), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1387458), _1387460))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387456)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387462), _1387454), _1387456), 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), _1387462), _1387458)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387462), _1387460)), _1387456))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387462), _1387460), _1387456)))))], (7140 ^ _779142) ^ [_897210, _897212, _897214, _897216, _897218, _897220] : [c_Finite__Set_Ofun__left__comm(_897210, _897212, _897214), hBOOL(hAPP(c_Finite__Set_Ofinite(_897210), _897216)), -(hBOOL(hAPP(hAPP(c_member(_897210), _897218), _897216))), -(hAPP(hAPP(c_Finite__Set_Ofold(_897210, _897212, _897214), _897220), hAPP(hAPP(c_Set_Oinsert(_897210), _897218), _897216)) = hAPP(hAPP(_897214, _897218), hAPP(hAPP(c_Finite__Set_Ofold(_897210, _897212, _897214), _897220), _897216)))], (18658 ^ _779142) ^ [_1107553, _1107555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1107553)), _1107555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107553), _1107555)))], (51621 ^ _779142) ^ [_1821880, _1821882, _1821884, _1821886] : [class_Rings_Ocomm__semiring__1(_1821880), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821880), _1821882), _1821884)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821880), hAPP(hAPP(c_Power_Opower__class_Opower(_1821880), _1821882), _1821886)), hAPP(hAPP(c_Power_Opower__class_Opower(_1821880), _1821884), _1821886))))], (31064 ^ _779142) ^ [_1335767, _1335769, _1335771] : [class_Orderings_Olinorder(_1335767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335767), _1335769), _1335771)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335767, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1335767, _1335769), _1335771)), hAPP(c_SetInterval_Oord__class_OatLeast(_1335767), _1335771)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1335767), _1335769))], (48967 ^ _779142) ^ [_1768217, _1768219, _1768221, _1768223] : [class_Complete__Lattice_Ocomplete__lattice(_1768217), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768219, _1768217), _1768221), _1768223) = c_Complete__Lattice_OSup__class_OSup(_1768217, hAPP(c_Set_OCollect(_1768217), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool), tc_HOL_Obool, _1768217), c_HOL_OEx(tc_fun(_1768219, _1768217))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool), tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool), _1768217), hAPP(c_COMBS(tc_fun(_1768219, _1768217), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768219, _1768217)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768219, _1768217), tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768219, _1768217))), _1768221)))), hAPP(hAPP(c_COMBC(_1768217, tc_fun(tc_fun(_1768219, _1768217), _1768217), tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768217, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768219, _1768217), _1768217), tc_fun(tc_fun(_1768219, _1768217), tc_HOL_Obool)), _1768217), c_COMBB(_1768217, tc_HOL_Obool, tc_fun(_1768219, _1768217))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768219, _1768217), _1768219, _1768217), c_COMBI(tc_fun(_1768219, _1768217))), _1768223)))))))], (18947 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (48452 ^ _779142) ^ [_1755958, _1755960] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755958)), _1755960) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755958, tc_Lazy__Sequence_Olazy__sequence(_1755958)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755958, tc_Lazy__Sequence_Olazy__sequence(_1755958), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755958), tc_Nat_Onat), _1755958), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755958), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755958)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755958)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1755958), _1755960)))], (21876 ^ _779142) ^ [_1163591, _1163593] : [class_Groups_Omonoid__mult(_1163591), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163591), c_Groups_Oone__class_Oone(_1163591)), _1163593) = c_Groups_Oone__class_Oone(_1163591))], (39522 ^ _779142) ^ [_1548050, _1548052, _1548054, _1548056, _1548058, _1548060, _1548062, _1548064, _1548066, _1548068, _1548070] : [hAPP(_1548050, hAPP(_1548052, _1548054)) = hAPP(_1548056, hAPP(_1548058, _1548060)), -(hAPP(hAPP(c_Fun_Ocomp(_1548062, _1548064, _1548066, _1548050), _1548052), _1548054) = hAPP(hAPP(c_Fun_Ocomp(_1548068, _1548064, _1548070, _1548056), _1548058), _1548060))], (22472 ^ _779142) ^ [_1174629, _1174631, _1174633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174629)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1174631), _1174633)), 22479 ^ _779142 : [(22480 ^ _779142) ^ [_1174819] : [22482 ^ _779142 : [(22488 ^ _779142) ^ [] : [-(_1174819 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22484 ^ [_1174629, _1174631, _1174633, _1174819]), 22481 ^ [_1174629, _1174631, _1174633, _1174819]))], (22486 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22484 ^ [_1174629, _1174631, _1174633, _1174819]), _1174633)))], (22483 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22481 ^ [_1174629, _1174631, _1174633, _1174819]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1174629))))]], -(_1174819 = _1174631), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174819), _1174629) = _1174631]]], (48555 ^ _779142) ^ [_1758432, _1758434, _1758436, _1758438] : [class_Groups_Ocomm__monoid__add(_1758432), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1758434, tc_HOL_Obool)), _1758436)), 48565 ^ _779142 : [(48568 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1758434), 48564 ^ [_1758432, _1758434, _1758436, _1758438]))], (48566 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758434, tc_HOL_Obool)), 48564 ^ [_1758432, _1758434, _1758436, _1758438]), _1758436)))]], 48572 ^ _779142 : [(48576 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758434, tc_HOL_Obool)), 48574 ^ [_1758432, _1758434, _1758436, _1758438]), _1758436)))], (48573 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758434, tc_HOL_Obool)), 48571 ^ [_1758432, _1758434, _1758436, _1758438]), _1758436)))], (48585 ^ _779142) ^ [] : [hAPP(_1758438, 48579 ^ [_1758432, _1758434, _1758436, _1758438]) = c_Groups_Ozero__class_Ozero(_1758432)], (48581 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758434), 48579 ^ [_1758432, _1758434, _1758436, _1758438]), 48571 ^ [_1758432, _1758434, _1758436, _1758438])))], (48583 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758434), 48579 ^ [_1758432, _1758434, _1758436, _1758438]), 48574 ^ [_1758432, _1758434, _1758436, _1758438])))], (48578 ^ _779142) ^ [] : [48571 ^ [_1758432, _1758434, _1758436, _1758438] = 48574 ^ [_1758432, _1758434, _1758436, _1758438]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758434, _1758432), _1758438), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1758434, tc_HOL_Obool), _1758436)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1758434, tc_HOL_Obool), _1758432), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758434, _1758432), _1758438)), _1758436))], (18935 ^ _779142) ^ [_1112175] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1112175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112175), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52539 ^ _779142) ^ [_1835082] : [class_Finite__Set_Ofinite(_1835082), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1835082)))], (766 ^ _779142) ^ [_790651, _790653, _790655, _790657] : [-(c_Relation_Oantisym(_790655, _790651)), c_Relation_Oantisym(_790657, _790653), _790657 = _790655, _790653 = _790651], (30441 ^ _779142) ^ [_1323408, _1323410, _1323412] : [class_Lattices_Olattice(_1323408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323408), _1323410)), 30448 ^ _779142 : [(30455 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323408, tc_HOL_Obool)), _1323410), hAPP(hAPP(c_Set_Oinsert(_1323408), _1323412), c_Orderings_Obot__class_Obot(tc_fun(_1323408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323408, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1323408, hAPP(hAPP(c_Set_Oinsert(_1323408), _1323412), _1323410)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323408), _1323412), c_Big__Operators_Olattice__class_OInf__fin(_1323408, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323408, tc_HOL_Obool)), _1323410), hAPP(hAPP(c_Set_Oinsert(_1323408), _1323412), c_Orderings_Obot__class_Obot(tc_fun(_1323408, tc_HOL_Obool)))))))], (30449 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323408, tc_HOL_Obool)), _1323410), hAPP(hAPP(c_Set_Oinsert(_1323408), _1323412), c_Orderings_Obot__class_Obot(tc_fun(_1323408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323408, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1323408, hAPP(hAPP(c_Set_Oinsert(_1323408), _1323412), _1323410)) = _1323412)]]], (40618 ^ _779142) ^ [_1574765, _1574767] : [-(c_Relation_Orefl__on(_1574765, c_Orderings_Otop__class_Otop(tc_fun(_1574765, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574765, _1574765), tc_HOL_Obool)), _1574767), c_Relation_OId(_1574765))))], (9593 ^ _779142) ^ [_942355, _942357, _942359, _942361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942355), _942357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942359), _942361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942355), _942359)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942357), _942361))))], (24910 ^ _779142) ^ [_1217065] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217065), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (32479 ^ _779142) ^ [_1371342, _1371344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371342)), hAPP(c_Nat_OSuc, _1371344))), -(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(_1371342))), 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)), _1371344)))))], (112 ^ _779142) ^ [_780784, _780786] : [-(class_Fields_Olinordered__field__inverse__zero(_780784)), _780786 = _780784, class_Fields_Olinordered__field__inverse__zero(_780786)], (42816 ^ _779142) ^ [_1632443, _1632445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632443), _1632445))), -(c_List_Oupto(_1632443, _1632445) = c_List_Olist_ONil(tc_Int_Oint))], (24748 ^ _779142) ^ [_1214256, _1214258] : [class_Rings_Olinordered__idom(_1214256), 24751 ^ _779142 : [(24758 ^ _779142) ^ [] : [_1214258 = c_Groups_Ozero__class_Ozero(_1214256), -(c_Groups_Osgn__class_Osgn(_1214256, _1214258) = c_Groups_Ozero__class_Ozero(_1214256))], (24752 ^ _779142) ^ [] : [c_Groups_Osgn__class_Osgn(_1214256, _1214258) = c_Groups_Ozero__class_Ozero(_1214256), -(_1214258 = c_Groups_Ozero__class_Ozero(_1214256))]]], (17387 ^ _779142) ^ [_1085007, _1085009] : [class_Divides_Osemiring__div(_1085007), -(c_Divides_Odiv__class_Omod(_1085007, c_Groups_Ozero__class_Ozero(_1085007), _1085009) = c_Groups_Ozero__class_Ozero(_1085007))], (43576 ^ _779142) ^ [_1650313, _1650315, _1650317, _1650319] : [-(hAPP(hAPP(c_List_Odrop(_1650313), _1650315), hAPP(hAPP(c_List_Olist_OCons(_1650313), _1650317), _1650319)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1650313), hAPP(hAPP(c_List_Olist_OCons(_1650313), _1650317), _1650319), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1650313), tc_List_Olist(_1650313)), c_List_Odrop(_1650313)), _1650319), _1650315))], (4360 ^ _779142) ^ [_845270, _845272, _845274, _845276] : [-(c_Wellfounded_Oaccp(_845276, _845272) = c_Wellfounded_Oaccp(_845274, _845270)), _845276 = _845274, _845272 = _845270], (46246 ^ _779142) ^ [_1708809, _1708811, _1708813, _1708815, _1708817] : [class_Orderings_Olinorder(_1708809), c_List_Olinorder__class_Osorted(_1708809, hAPP(hAPP(c_List_Omap(_1708811, _1708809), _1708813), _1708815)), -(c_List_Olinorder__class_Osorted(_1708809, hAPP(hAPP(c_List_Omap(_1708811, _1708809), _1708813), c_List_Olinorder__class_Oinsort__insert__key(_1708811, _1708809, _1708813, _1708817, _1708815))))], (12788 ^ _779142) ^ [_1000255, _1000257, _1000259, _1000261] : [class_Rings_Olinordered__semiring__strict(_1000255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000255), _1000257), _1000259)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000255), _1000261), _1000259))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000255), c_Groups_Ozero__class_Ozero(_1000255)), _1000259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000255), _1000257), _1000261)))], (19271 ^ _779142) ^ [_1117998, _1118000] : [class_Rings_Olinordered__idom(_1117998), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117998), hAPP(c_Groups_Oabs__class_Oabs(_1117998), _1118000)), hAPP(c_Groups_Oabs__class_Oabs(_1117998), _1118000)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117998), _1118000), _1118000))], (948 ^ _779142) ^ [_793338, _793340, _793342, _793344] : [-(c_Wellfounded_Owf(_793342, _793338)), c_Wellfounded_Owf(_793344, _793340), _793344 = _793342, _793340 = _793338], (32393 ^ _779142) ^ [_1369236, _1369238, _1369240] : [-(hAPP(c_Divides_Oadjust(_1369236), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1369238), _1369240)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1369240), _1369236)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1369238)), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1369238)), _1369240))))], (20384 ^ _779142) ^ [_1136876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136876)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1136876) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (48374 ^ _779142) ^ [_1754492, _1754494, _1754496, _1754498] : [-(hAPP(c_New__DSequence_Opos__union(_1754492, _1754494, _1754496), _1754498) = c_Lazy__Sequence_Oappend(_1754492, hAPP(_1754494, _1754498), hAPP(_1754496, _1754498)))], (22735 ^ _779142) ^ [_1179648, _1179650] : [-(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), _1179648))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1179650))))], (30930 ^ _779142) ^ [_1333250, _1333252] : [class_Lattices_Obounded__lattice__top(_1333250), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1333250), c_Orderings_Otop__class_Otop(_1333250)), _1333252) = _1333252)], (44608 ^ _779142) ^ [_1672804, _1672806, _1672808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672804), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672806)), _1672808))), -(hAPP(c_Random_Opick(_1672806, hAPP(hAPP(c_List_Omap(_1672806, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672806)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672806), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672808)), hAPP(c_Code__Numeral_Oof__nat, _1672804)) = hAPP(hAPP(c_List_Onth(_1672806), _1672808), _1672804))], (10464 ^ _779142) ^ [_960360, _960362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960360), hAPP(c_Nat_OSuc, _960362))), -(_960360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10472 ^ _779142 : [(10475 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 10471 ^ [_960360, _960362]), _960362)))], (10473 ^ _779142) ^ [] : [-(_960360 = hAPP(c_Nat_OSuc, 10471 ^ [_960360, _960362]))]]], (42993 ^ _779142) ^ [_1636525, _1636527, _1636529, _1636531, _1636533] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636525), _1636527), _1636529) = hAPP(hAPP(c_List_Oappend(_1636525), _1636531), _1636533)), 42994 ^ _779142 : [(43001 ^ _779142) ^ [_1636708] : [hAPP(hAPP(c_List_Olist_OCons(_1636525), _1636527), _1636708) = _1636531, _1636529 = hAPP(hAPP(c_List_Oappend(_1636525), _1636708), _1636533)], (42995 ^ _779142) ^ [] : [_1636531 = c_List_Olist_ONil(_1636525), hAPP(hAPP(c_List_Olist_OCons(_1636525), _1636527), _1636529) = _1636533]]], (25480 ^ _779142) ^ [_1226959] : [-(c_Int_OBit0(_1226959) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226959), _1226959))], (20472 ^ _779142) ^ [_1138336, _1138338, _1138340] : [hBOOL(hAPP(_1138336, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138338), _1138340))), 20475 ^ _779142 : [(20500 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138340), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20503 ^ _779142 : [(20504 ^ _779142) ^ [_1139000] : [-(hBOOL(hAPP(_1138336, _1139000))), 20505 ^ _779142 : [(20506 ^ _779142) ^ [_1139074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138340), _1139074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139074), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1138338 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138340), _1139000)), _1139074)]]]]], (20482 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138340)), 20485 ^ _779142 : [(20486 ^ _779142) ^ [_1138670] : [-(hBOOL(hAPP(_1138336, _1138670))), 20487 ^ _779142 : [(20488 ^ _779142) ^ [_1138741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138741), _1138340)), _1138338 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138340), _1138670)), _1138741)]]]]], (20476 ^ _779142) ^ [] : [_1138340 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1138336, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (33877 ^ _779142) ^ [_1399645, _1399647, _1399649, _1399651, _1399653, _1399655] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1399645, _1399647), _1399647, _1399649), hAPP(hAPP(c_COMBB(_1399651, tc_fun(_1399647, _1399649), tc_prod(_1399645, _1399647)), _1399653), hAPP(hAPP(c_COMBB(_1399645, _1399651, tc_prod(_1399645, _1399647)), _1399655), c_Product__Type_Ofst(_1399645, _1399647)))), c_Product__Type_Osnd(_1399645, _1399647)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1399645, _1399647, _1399649), hAPP(hAPP(c_COMBB(_1399651, tc_fun(_1399647, _1399649), _1399645), _1399653), _1399655)))], (38603 ^ _779142) ^ [_1526584, _1526586, _1526588, _1526590] : [c_Wellfounded_Owf(_1526584, _1526586), c_Wellfounded_Owf(_1526588, _1526590), -(c_Wellfounded_Owf(tc_prod(_1526584, _1526588), c_Wellfounded_Olex__prod(_1526584, _1526588, _1526586, _1526590)))], (4154 ^ _779142) ^ [_842015, _842017, _842019, _842021] : [-(c_List_Olast(_842021, _842017) = c_List_Olast(_842019, _842015)), _842021 = _842019, _842017 = _842015], (43700 ^ _779142) ^ [_1653576, _1653578, _1653580] : [_1653576 = c_List_Olist_ONil(_1653578), -(hAPP(c_List_Ohd(_1653578), hAPP(hAPP(c_List_Oappend(_1653578), _1653576), _1653580)) = hAPP(c_List_Ohd(_1653578), _1653580))], (35623 ^ _779142) ^ [_1446325, _1446327] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446325), c_Orderings_Obot__class_Obot(tc_fun(_1446325, tc_HOL_Obool))), _1446327) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446325, tc_HOL_Obool), tc_HOL_Obool)))], (42265 ^ _779142) ^ [_1620885, _1620887, _1620889] : [-(hAPP(hAPP(c_List_Olist__update(_1620885, _1620887), _1620889), hAPP(hAPP(c_List_Onth(_1620885), _1620887), _1620889)) = _1620887)], (34554 ^ _779142) ^ [_1417137, _1417139, _1417141, _1417143, _1417145, _1417147] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417137, tc_fun(_1417139, tc_HOL_Obool)), _1417141), hAPP(hAPP(c_COMBB(_1417143, tc_fun(_1417139, tc_HOL_Obool), _1417137), _1417145), _1417147)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417143, tc_fun(_1417139, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1417137, _1417143, _1417147), _1417141)), _1417145))], (44847 ^ _779142) ^ [_1677553] : [-(c_Code__Numeral_OSuc__code__numeral(_1677553) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1677553))))], (12002 ^ _779142) ^ [_986224, _986226, _986228, _986230] : [class_Rings_Olinordered__ring__strict(_986224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986224), _986226), c_Groups_Ozero__class_Ozero(_986224))), 12009 ^ _779142 : [(12016 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986224), _986230), _986228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986224), _986226), _986228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986224), _986226), _986230))))], (12010 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986224), _986226), _986228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986224), _986226), _986230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986224), _986230), _986228)))]]], (27280 ^ _779142) ^ [_1260498, _1260500, _1260502] : [class_Orderings_Oorder(_1260498), 27283 ^ _779142 : [(27290 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260498), _1260500), _1260502))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1260498, _1260500, _1260502) = c_Orderings_Obot__class_Obot(tc_fun(_1260498, tc_HOL_Obool)))], (27284 ^ _779142) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1260498, _1260500, _1260502) = c_Orderings_Obot__class_Obot(tc_fun(_1260498, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260498), _1260500), _1260502))]]], (43706 ^ _779142) ^ [_1653689, _1653691, _1653693] : [-(_1653689 = c_List_Olist_ONil(_1653691)), -(hAPP(c_List_Ohd(_1653691), hAPP(hAPP(c_List_Oappend(_1653691), _1653689), _1653693)) = hAPP(c_List_Ohd(_1653691), _1653689))], (34031 ^ _779142) ^ [_1402655, _1402657, _1402659, _1402661, _1402663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1402655, _1402657)), hAPP(_1402655, _1402659))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402661, _1402661)), hAPP(hAPP(c_Product__Type_OPair(_1402661, _1402661), _1402657), _1402659)), c_Wellfounded_Omlex__prod(_1402661, _1402655, _1402663))))], (26830 ^ _779142) ^ [_1251914, _1251916, _1251918, _1251920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251914, tc_HOL_Obool)), _1251916), _1251918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251914, tc_HOL_Obool)), _1251920), _1251918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251914, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251914, tc_HOL_Obool)), _1251916), _1251920)), _1251918)))], (13038 ^ _779142) ^ [_1004961, _1004963, _1004965] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1004961), _1004963)), 13041 ^ _779142 : [(13061 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004961, tc_Nat_Onat), _1004965), _1004963) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 13062 ^ _779142 : [(13063 ^ _779142) ^ [_1005442] : [hBOOL(hAPP(hAPP(c_member(_1004961), _1005442), _1004963)), hAPP(_1004965, _1005442) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13071 ^ _779142 : [(13076 ^ _779142) ^ [] : [hAPP(_1004965, 13070 ^ [_1004961, _1004963, _1004965, _1005442]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13074 ^ _779142) ^ [] : [_1005442 = 13070 ^ [_1004961, _1004963, _1004965, _1005442]], (13072 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004961), 13070 ^ [_1004961, _1004963, _1004965, _1005442]), _1004963)))]]]]], (13042 ^ _779142) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004961, tc_Nat_Onat), _1004965), _1004963) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13046 ^ _779142 : [(13051 ^ _779142) ^ [_1005281] : [hBOOL(hAPP(hAPP(c_member(_1004961), _1005281), _1004963)), -(13045 ^ [_1004961, _1004963, _1004965] = _1005281), -(hAPP(_1004965, _1005281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13049 ^ _779142) ^ [] : [-(hAPP(_1004965, 13045 ^ [_1004961, _1004963, _1004965]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (13047 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004961), 13045 ^ [_1004961, _1004963, _1004965]), _1004963)))]]]]], (37553 ^ _779142) ^ [_1490569, _1490571, _1490573, _1490575] : [hBOOL(hAPP(hAPP(c_member(_1490569), _1490571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490569, tc_HOL_Obool)), _1490573), hAPP(c_Set_OCollect(_1490569), _1490575)))), 37556 ^ _779142 : [(37559 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1490575, _1490571)))], (37557 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490569), _1490571), _1490573)))]]], (35472 ^ _779142) ^ [_1442058, _1442060, _1442062, _1442064, _1442066, _1442068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442058, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442060, _1442058, _1442062), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442064, tc_fun(_1442060, tc_HOL_Obool)), _1442066), _1442068))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442064, tc_fun(_1442058, tc_HOL_Obool)), _1442066), hAPP(hAPP(c_COMBB(tc_fun(_1442060, tc_HOL_Obool), tc_fun(_1442058, tc_HOL_Obool), _1442064), c_Relation_OImage(_1442060, _1442058, _1442062)), _1442068)))))], (46007 ^ _779142) ^ [_1704610, _1704612] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704610), hAPP(c_List_Onth(_1704610), _1704612)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704610)), _1704612))) = _1704612)], (49807 ^ _779142) ^ [_1786450, _1786452] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786450), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786452, hAPP(c_Code__Numeral_Onat__of, 49812 ^ [_1786450, _1786452]))), -(hBOOL(hAPP(_1786452, _1786450)))], (45843 ^ _779142) ^ [_1701423, _1701425, _1701427] : [class_Groups_Omonoid__add(_1701423), -(hAPP(c_List_Ofoldl(_1701423, _1701423, c_Groups_Oplus__class_Oplus(_1701423), _1701425), _1701427) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1701423), _1701425), c_List_Ofoldr(_1701423, _1701423, c_Groups_Oplus__class_Oplus(_1701423), _1701427, c_Groups_Ozero__class_Ozero(_1701423))))], (9370 ^ _779142) ^ [_938925, _938927] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938925), _938927) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _938925 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _938927 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (20091 ^ _779142) ^ [_1131684, _1131686] : [-(_1131684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131686), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131684), _1131686))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131684, _1131686)))], (16447 ^ _779142) ^ [_1068707, _1068709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068707)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068707), _1068709)))], (9603 ^ _779142) ^ [_942546, _942548, _942550, _942552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942546), _942548)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942550), _942548) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942546), _942552), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942550), _942552)))], (39441 ^ _779142) ^ [_1546303, _1546305, _1546307, _1546309, _1546311, _1546313] : [c_Fun_Oinj__on(_1546303, _1546305, _1546307, _1546309), 39444 ^ _779142 : [(39451 ^ _779142) ^ [] : [c_Fun_Oinj__on(_1546303, _1546311, hAPP(c_Fun_Ocomp(_1546305, _1546311, _1546303, _1546313), _1546307), _1546309), -(c_Fun_Oinj__on(_1546305, _1546311, _1546313, hAPP(c_Set_Oimage(_1546303, _1546305, _1546307), _1546309)))], (39445 ^ _779142) ^ [] : [c_Fun_Oinj__on(_1546305, _1546311, _1546313, hAPP(c_Set_Oimage(_1546303, _1546305, _1546307), _1546309)), -(c_Fun_Oinj__on(_1546303, _1546311, hAPP(c_Fun_Ocomp(_1546305, _1546311, _1546303, _1546313), _1546307), _1546309))]]], (25728 ^ _779142) ^ [_1231321, _1231323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231321), _1231323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1231321)), c_Int_OBit0(_1231323))))], (21017 ^ _779142) ^ [_1148673, _1148675, _1148677, _1148679] : [hBOOL(hAPP(hAPP(_1148677, _1148675), _1148679)), -(hBOOL(hAPP(hAPP(c_member(_1148673), _1148675), c_SetInterval_Oord_OatMost(_1148673, _1148677, _1148679))))], (2478 ^ _779142) ^ [_815503, _815505, _815507, _815509] : [-(c_Nitpick_Onorm__frac(_815509, _815505) = c_Nitpick_Onorm__frac(_815507, _815503)), _815509 = _815507, _815505 = _815503], (28757 ^ _779142) ^ [_1287853, _1287855, _1287857, _1287859] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1287853), _1287855)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287853), _1287857)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287853, tc_Nat_Onat), _1287859), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287853, tc_HOL_Obool)), _1287855), _1287857)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287853, tc_Nat_Onat), _1287859), _1287855)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287853, tc_Nat_Onat), _1287859), _1287857))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287853, tc_Nat_Onat), _1287859), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287853, tc_HOL_Obool)), _1287855), _1287857))))], (29472 ^ _779142) ^ [_1303272, _1303274, _1303276, _1303278] : [class_Lattices_Osemilattice__inf(_1303272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303272), _1303274)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1303272, _1303272, c_Lattices_Osemilattice__inf__class_Oinf(_1303272)), _1303276), hAPP(hAPP(c_Set_Oinsert(_1303272), _1303278), _1303274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303272), _1303278), hAPP(hAPP(c_Finite__Set_Ofold(_1303272, _1303272, c_Lattices_Osemilattice__inf__class_Oinf(_1303272)), _1303276), _1303274)))], (39942 ^ _779142) ^ [_1557739, _1557741, _1557743, _1557745, _1557747, _1557749] : [c_Finite__Set_Ofolding__idem(_1557739, _1557741, _1557743, _1557745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557739), _1557747)), -(hAPP(_1557745, hAPP(hAPP(c_Set_Oinsert(_1557739), _1557749), _1557747)) = hAPP(c_Fun_Ocomp(_1557741, _1557741, _1557741, hAPP(_1557745, _1557747)), hAPP(_1557743, _1557749)))], (23113 ^ _779142) ^ [_1186049, _1186051, _1186053] : [class_Rings_Oring(_1186049), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1186049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186049), _1186051), _1186053)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186049), hAPP(c_Groups_Ouminus__class_Ouminus(_1186049), _1186051)), _1186053))], (38556 ^ _779142) ^ [_1525463, _1525465, _1525467] : [c_Wellfounded_Owf(_1525463, _1525465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525463, _1525463), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1525463, _1525463, _1525463), _1525465), _1525467)), _1525465)), -(c_FunDef_Oreduction__pair(_1525463, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1525463, _1525463), tc_HOL_Obool), tc_fun(tc_prod(_1525463, _1525463), tc_HOL_Obool)), _1525465), _1525467)))], (35555 ^ _779142) ^ [_1444434, _1444436, _1444438, _1444440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444434), _1444440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444438), _1444436))), -(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), _1444434), _1444436)), 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), _1444438), _1444440)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (48454 ^ _779142) ^ [_1756054, _1756056, _1756058] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1756054, _1756056), _1756058) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1756054, tc_Lazy__Sequence_Olazy__sequence(_1756054)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1756054, tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1756054, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat)), _1756054), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1756054), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1756054)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1756054, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756054), tc_Nat_Onat)), _1756054), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1756054))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1756054), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1756056))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1756054, _1756056))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1756054), _1756058)))], (19111 ^ _779142) ^ [_1115033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1115033)), 19115 ^ _779142 : [(19116 ^ _779142) ^ [_1115113] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1115113), _1115033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115113), 19114 ^ [_1115033])))]]], (21714 ^ _779142) ^ [_1160551, _1160553] : [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), _1160551), _1160553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160551))), -(_1160553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50677 ^ _779142) ^ [_1805432, _1805434, _1805436, _1805438] : [class_Rings_Ocomm__semiring__1(_1805432), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805432), _1805434), _1805436)), _1805438)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805432), _1805436), _1805438)))], (47801 ^ _779142) ^ [_1742390, _1742392, _1742394, _1742396] : [c_List_Olist__all(_1742390, _1742392, hAPP(hAPP(c_List_Oappend(_1742390), _1742394), _1742396)), 47804 ^ _779142 : [(47807 ^ _779142) ^ [] : [-(c_List_Olist__all(_1742390, _1742392, _1742396))], (47805 ^ _779142) ^ [] : [-(c_List_Olist__all(_1742390, _1742392, _1742394))]]], (12180 ^ _779142) ^ [_989473, _989475] : [class_Rings_Olinordered__ring(_989473), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989473), _989475), _989475)), c_Groups_Ozero__class_Ozero(_989473)))], (50549 ^ _779142) ^ [_1803236, _1803238, _1803240] : [-(c_Lazy__Sequence_Omap(_1803236, _1803238, _1803240, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803236)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803238))], (11027 ^ _779142) ^ [_969313, _969315, _969317] : [class_Rings_Ono__zero__divisors(_969313), -(_969315 = c_Groups_Ozero__class_Ozero(_969313)), -(_969317 = c_Groups_Ozero__class_Ozero(_969313)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969313), _969315), _969317) = c_Groups_Ozero__class_Ozero(_969313)], (27952 ^ _779142) ^ [_1272746, _1272748, _1272750, _1272752] : [class_Orderings_Olinorder(_1272746), 27955 ^ _779142 : [(27956 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272746), _1272750), _1272752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), _1272750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), _1272752)))], (27966 ^ _779142) ^ [] : [27967 ^ _779142 : [(27970 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), _1272752))], (27968 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), _1272750))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272746), _1272748), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272746), _1272750), _1272752))))]]], (9390 ^ _779142) ^ [_939223, _939225] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939223), _939225)), _939223 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _939225 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34759 ^ _779142) ^ [_1423299, _1423301, _1423303, _1423305] : [hBOOL(hAPP(hAPP(c_member(_1423301), _1423305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423299, tc_fun(_1423301, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423299, tc_HOL_Obool))), _1423303))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423299, tc_fun(_1423301, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423299, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1423301, tc_HOL_Obool), tc_fun(_1423301, tc_HOL_Obool), _1423299), hAPP(c_COMBC(_1423301, tc_fun(_1423301, tc_HOL_Obool), tc_HOL_Obool), c_member(_1423301))), _1423303)), _1423305)))], (6413 ^ _779142) ^ [_881895, _881897, _881899] : [class_Orderings_Opreorder(_881895), _881897 = _881899, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881895), _881897), _881899)))], (36422 ^ _779142) ^ [_1464214, _1464216, _1464218, _1464220, _1464222] : [c_Fun_Oinj__on(_1464214, _1464216, _1464218, c_Orderings_Otop__class_Otop(tc_fun(_1464214, tc_HOL_Obool))), 36425 ^ _779142 : [(36432 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464214), _1464220), _1464222)), -(hBOOL(hAPP(hAPP(c_member(_1464216), hAPP(_1464218, _1464220)), hAPP(c_Set_Oimage(_1464214, _1464216, _1464218), _1464222))))], (36426 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464216), hAPP(_1464218, _1464220)), hAPP(c_Set_Oimage(_1464214, _1464216, _1464218), _1464222))), -(hBOOL(hAPP(hAPP(c_member(_1464214), _1464220), _1464222)))]]], (11067 ^ _779142) ^ [_969903, _969905] : [class_Groups_Ogroup__add(_969903), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969903), _969905), c_Groups_Ozero__class_Ozero(_969903)) = _969905)], (1456 ^ _779142) ^ [_800284, _800286] : [-(class_Lattices_Olattice(_800284)), _800286 = _800284, class_Lattices_Olattice(_800286)], (27232 ^ _779142) ^ [_1259705, _1259707, _1259709, _1259711] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259705, tc_HOL_Obool)), _1259707), _1259709), _1259711)), -(hBOOL(hAPP(_1259707, _1259711))), -(hBOOL(hAPP(_1259709, _1259711)))], (24171 ^ _779142) ^ [_1204734, _1204736, _1204738, _1204740, _1204742] : [class_Orderings_Olinorder(_1204734), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204734, _1204736), _1204738) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204734, _1204740), _1204742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204734), _1204736), _1204738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204734), _1204740), _1204742)), -(_1204738 = _1204742)], (44277 ^ _779142) ^ [_1664520, _1664522, _1664524] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664520)), _1664522), c_List_Olists(_1664520, _1664524)))), 44278 ^ _779142 : [(44281 ^ _779142) ^ [_1664648, _1664650] : [_1664522 = hAPP(hAPP(c_List_Olist_OCons(_1664520), _1664650), _1664648), hBOOL(hAPP(hAPP(c_member(_1664520), _1664650), _1664524)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664520)), _1664648), c_List_Olists(_1664520, _1664524)))], (44279 ^ _779142) ^ [] : [_1664522 = c_List_Olist_ONil(_1664520)]]], (5340 ^ _779142) ^ [_860810, _860812, _860814, _860816, _860818, _860820] : [-(c_SetInterval_Oord_OatLeast(_860820, _860816, _860812) = c_SetInterval_Oord_OatLeast(_860818, _860814, _860810)), _860820 = _860818, _860816 = _860814, _860812 = _860810], (2902 ^ _779142) ^ [_822109, _822111, _822113, _822115, _822117, _822119] : [-(c_Nitpick_Oplus__frac(_822119, _822115, _822111) = c_Nitpick_Oplus__frac(_822117, _822113, _822109)), _822119 = _822117, _822115 = _822113, _822111 = _822109], (24964 ^ _779142) ^ [_1217995] : [class_Int_Onumber__ring(_1217995), -(c_Groups_Oone__class_Oone(_1217995) = hAPP(c_Int_Onumber__class_Onumber__of(_1217995), c_Int_OBit1(c_Int_OPls)))], (9581 ^ _779142) ^ [_942121, _942123, _942125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942121), _942123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942125), _942123))))], (51323 ^ _779142) ^ [_1817019, _1817021] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817019), _1817021)), -(_1817019 = _1817021), 51330 ^ _779142 : [(51333 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817021), _1817019))], (51331 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817019), _1817021)))]]], (23241 ^ _779142) ^ [_1188509, _1188511, _1188513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1188509, tc_HOL_Obool)), _1188511), _1188513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1188509, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1188509), _1188511)), hAPP(c_Set_OPow(_1188509), _1188513))))], (47689 ^ _779142) ^ [_1739950, _1739952, _1739954] : [c_List_Olist__ex(_1739950, _1739952, _1739954), 47693 ^ _779142 : [(47696 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1739952, 47692 ^ [_1739950, _1739952, _1739954])))], (47694 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739950), 47692 ^ [_1739950, _1739952, _1739954]), hAPP(c_List_Oset(_1739950), _1739954))))]]], (48172 ^ _779142) ^ [_1750727, _1750729, _1750731] : [-(_1750727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750729), c_List_Oreplicate(_1750729, _1750727, _1750731)) = _1750731)], (9310 ^ _779142) ^ [_937889, _937891] : [_937889 = _937891, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937889), _937891)))], (37661 ^ _779142) ^ [_1493497, _1493499] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493497, _1493499), c_Orderings_Otop__class_Otop(tc_fun(_1493497, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1493499, tc_HOL_Obool), _1493497), c_Orderings_Otop__class_Otop(tc_fun(_1493499, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1493497, _1493499), tc_HOL_Obool)))], (28971 ^ _779142) ^ [_1292651, _1292653, _1292655] : [class_Lattices_Osemilattice__inf(_1292651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292651), _1292653), _1292655)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1292651), _1292655), _1292653) = _1292653)], (43688 ^ _779142) ^ [_1653325, _1653327, _1653329] : [-(_1653325 = c_List_Olist_ONil(_1653327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653329), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653327)), _1653325))), -(hAPP(c_List_Ohd(_1653327), hAPP(hAPP(c_List_Odrop(_1653327), _1653329), _1653325)) = hAPP(hAPP(c_List_Onth(_1653327), _1653325), _1653329))], (6781 ^ _779142) ^ [_889245, _889247, _889249, _889251, _889253, _889255, _889257, _889259] : [c_Finite__Set_Ofolding__image__simple(_889245, _889247, _889249, _889251, _889253, _889255), hBOOL(hAPP(c_Finite__Set_Ofinite(_889247), _889257)), hBOOL(hAPP(hAPP(c_member(_889247), _889259), _889257)), -(hAPP(_889255, _889257) = hAPP(hAPP(_889249, hAPP(_889253, _889259)), hAPP(_889255, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889247, tc_HOL_Obool)), _889257), hAPP(hAPP(c_Set_Oinsert(_889247), _889259), c_Orderings_Obot__class_Obot(tc_fun(_889247, tc_HOL_Obool)))))))], (39806 ^ _779142) ^ [_1554701, _1554703, _1554705, _1554707, _1554709, _1554711] : [c_Finite__Set_Ofolding(_1554701, _1554703, _1554705, _1554707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554701), _1554709)), -(hAPP(hAPP(_1554707, _1554709), _1554711) = hAPP(hAPP(c_Finite__Set_Ofold(_1554701, _1554703, _1554705), _1554711), _1554709))], (41935 ^ _779142) ^ [_1611618, _1611620, _1611622, _1611624] : [hBOOL(hAPP(hAPP(c_member(_1611618), _1611620), hAPP(c_List_Oset(_1611618), c_List_Osublist(_1611618, _1611622, _1611624)))), -(hBOOL(hAPP(hAPP(c_member(_1611618), _1611620), hAPP(c_List_Oset(_1611618), _1611622))))], (1696 ^ _779142) ^ [_803284, _803286] : [-(class_Rings_Ono__zero__divisors(_803284)), _803286 = _803284, class_Rings_Ono__zero__divisors(_803286)], (24229 ^ _779142) ^ [_1205666] : [class_Rings_Oring__1(_1205666), -(hAPP(c_Int_Oring__1__class_Oof__int(_1205666), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1205666))], (50395 ^ _779142) ^ [_1798330, _1798332, _1798334, _1798336, _1798338, _1798340, _1798342] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332)), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798334), _1798336)), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798338), _1798340))), c_Transitive__Closure_Ortrancl(tc_prod(_1798330, _1798332), _1798342))), -(hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798334), _1798336) = hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798338), _1798340)), 50404 ^ _779142 : [(50407 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332)), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), 50402 ^ [_1798330, _1798332, _1798334, _1798336, _1798338, _1798340, _1798342]), 50403 ^ [_1798330, _1798332, _1798334, _1798336, _1798338, _1798340, _1798342])), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798338), _1798340))), c_Transitive__Closure_Ortrancl(tc_prod(_1798330, _1798332), _1798342))))], (50405 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798330, _1798332), tc_prod(_1798330, _1798332)), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), _1798334), _1798336)), hAPP(hAPP(c_Product__Type_OPair(_1798330, _1798332), 50402 ^ [_1798330, _1798332, _1798334, _1798336, _1798338, _1798340, _1798342]), 50403 ^ [_1798330, _1798332, _1798334, _1798336, _1798338, _1798340, _1798342]))), _1798342)))]]], (43181 ^ _779142) ^ [_1640745, _1640747, _1640749] : [_1640749 = c_List_Olist_ONil(_1640745), -(hAPP(hAPP(c_List_Oappend(_1640745), _1640747), _1640749) = _1640747)], (4288 ^ _779142) ^ [_844096, _844098, _844100, _844102, _844104, _844106, _844108, _844110, _844112, _844114, _844116, _844118] : [-(c_New__Random__Sequence_Opos__union(_844118, _844114, _844110, _844106, _844102, _844098) = c_New__Random__Sequence_Opos__union(_844116, _844112, _844108, _844104, _844100, _844096)), _844118 = _844116, _844114 = _844112, _844110 = _844108, _844106 = _844104, _844102 = _844100, _844098 = _844096], (20670 ^ _779142) ^ [_1142299, _1142301, _1142303, _1142305, _1142307] : [hBOOL(hAPP(hAPP(c_member(_1142299), _1142301), c_SetInterval_Oord_OgreaterThanLessThan(_1142299, _1142303, _1142305, _1142307))), 20673 ^ _779142 : [(20676 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1142303, _1142301), _1142307)))], (20674 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1142303, _1142305), _1142301)))]]], (31418 ^ _779142) ^ [_1342607] : [class_Complete__Lattice_Ocomplete__lattice(_1342607), -(c_Complete__Lattice_OInf__class_OInf(_1342607, c_Orderings_Otop__class_Otop(tc_fun(_1342607, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1342607))], (20798 ^ _779142) ^ [_1144751, _1144753] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144751), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144753), _1144751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144753), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144753, _1144751)))], (22412 ^ _779142) ^ [_1173522, _1173524] : [-(_1173522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1173524, _1173522) = c_Nitpick_Onat__gcd(_1173522, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1173524, _1173522)))], (52433 ^ _779142) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (32781 ^ _779142) ^ [_1377821, _1377823, _1377825] : [_1377821 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1377823, _1377823), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1377823, _1377823), tc_HOL_Obool)), _1377821), _1377825)))], (37924 ^ _779142) ^ [_1502182, _1502184, _1502186, _1502188, _1502190, _1502192] : [class_Groups_Ocomm__monoid__mult(_1502182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502184), _1502186)), 37934 ^ _779142 : [(37937 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502188), hAPP(_1502190, 37933 ^ [_1502182, _1502184, _1502186, _1502188, _1502190, _1502192])))], (37935 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502184), 37933 ^ [_1502182, _1502184, _1502186, _1502188, _1502190, _1502192]), _1502186)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502184, _1502182), hAPP(hAPP(c_COMBS(_1502184, tc_fun(_1502188, tc_HOL_Obool), _1502182), hAPP(hAPP(c_COMBB(tc_fun(_1502188, _1502182), tc_fun(tc_fun(_1502188, tc_HOL_Obool), _1502182), _1502184), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502188, _1502182)), _1502192)), _1502190)), _1502186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1502184, _1502188), _1502182), hAPP(c_Product__Type_Oprod_Oprod__case(_1502184, _1502188, _1502182), _1502192)), hAPP(hAPP(c_Product__Type_OSigma(_1502184, _1502188), _1502186), _1502190)))], (47856 ^ _779142) ^ [_1743335, _1743337, _1743339] : [c_FunDef_Ois__measure(_1743335, _1743337), -(c_FunDef_Ois__measure(tc_prod(_1743339, _1743335), hAPP(hAPP(c_COMBB(_1743335, tc_Nat_Onat, tc_prod(_1743339, _1743335)), _1743337), c_Product__Type_Osnd(_1743339, _1743335))))], (25584 ^ _779142) ^ [_1228772, _1228774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228772), _1228774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228772)), c_Int_OBit0(_1228774))))], (32013 ^ _779142) ^ [_1358844, _1358846, _1358848, _1358850] : [class_Rings_Osemiring__1(_1358844), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1358844), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358846, tc_Nat_Onat), _1358848), _1358850)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358846, _1358844), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1358844, _1358846), c_Nat_Osemiring__1__class_Oof__nat(_1358844)), _1358848)), _1358850))], (37683 ^ _779142) ^ [_1494106, _1494108, _1494110, _1494112, _1494114, _1494116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494106, _1494108)), hAPP(hAPP(c_Product__Type_OPair(_1494106, _1494108), _1494110), _1494112)), hAPP(hAPP(c_Product__Type_OSigma(_1494106, _1494108), _1494114), _1494116))), 37686 ^ _779142 : [(37689 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494108), _1494112), hAPP(_1494116, _1494110))))], (37687 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494106), _1494110), _1494114)))]]], (23641 ^ _779142) ^ [_1195492, _1195494] : [class_Rings_Oring__1(_1195492), hBOOL(hAPP(hAPP(c_member(_1195492), _1195494), c_Int_Oring__1__class_OInts(_1195492))), -(hBOOL(hAPP(hAPP(c_member(_1195492), hAPP(c_Groups_Ouminus__class_Ouminus(_1195492), _1195494)), c_Int_Oring__1__class_OInts(_1195492))))], (3700 ^ _779142) ^ [_834568, _834570, _834572, _834574, _834576, _834578, _834580, _834582] : [-(c_List_Ofoldl(_834582, _834578, _834574, _834570) = c_List_Ofoldl(_834580, _834576, _834572, _834568)), _834582 = _834580, _834578 = _834576, _834574 = _834572, _834570 = _834568], (52437 ^ _779142) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11676 ^ _779142) ^ [_980097, _980099, _980101, _980103] : [class_Rings_Oordered__semiring(_980097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980097), _980099), _980101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980097), c_Groups_Ozero__class_Ozero(_980097)), _980103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980097), _980099), _980103)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980097), _980101), _980103))))], (27326 ^ _779142) ^ [_1261201, _1261203] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1261201), _1261203) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1261201, _1261203))], (5032 ^ _779142) ^ [_855874, _855876, _855878, _855880] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855880, _855876) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855878, _855874)), _855880 = _855878, _855876 = _855874], (9867 ^ _779142) ^ [_947317, _947319, _947321] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947317), _947319)), _947321) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947317), _947321)), _947319))], (19283 ^ _779142) ^ [_1118254] : [class_Rings_Olinordered__idom(_1118254), -(hAPP(c_Groups_Oabs__class_Oabs(_1118254), c_Groups_Oone__class_Oone(_1118254)) = c_Groups_Oone__class_Oone(_1118254))], (45256 ^ _779142) ^ [_1687091, _1687093, _1687095, _1687097] : [-(hAPP(c_List_Oset(tc_prod(_1687091, _1687093)), c_Enum_Oproduct(_1687091, _1687093, _1687095, _1687097)) = hAPP(hAPP(c_Product__Type_OSigma(_1687091, _1687093), hAPP(c_List_Oset(_1687091), _1687095)), hAPP(c_COMBK(tc_fun(_1687093, tc_HOL_Obool), _1687091), hAPP(c_List_Oset(_1687093), _1687097))))], (48040 ^ _779142) ^ [_1747071, _1747073, _1747075, _1747077, _1747079, _1747081, _1747083] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1747071, _1747073, _1747075, _1747077), _1747079), _1747081), _1747083) = c_New__DSequence_Oneg__bind(_1747071, _1747073, hAPP(hAPP(hAPP(_1747075, _1747079), _1747081), _1747083), hAPP(hAPP(c_COMBC(_1747071, 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(_1747073)))), hAPP(hAPP(c_COMBC(_1747071, 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(_1747073))))), hAPP(hAPP(c_COMBC(_1747071, 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(_1747073)))))), _1747077), _1747079)), _1747081)), _1747083)))], (5388 ^ _779142) ^ [_861558, _861560, _861562, _861564, _861566, _861568, _861570, _861572] : [-(c_SetInterval_Oord_OatLeastAtMost(_861572, _861568, _861564, _861560) = c_SetInterval_Oord_OatLeastAtMost(_861570, _861566, _861562, _861558)), _861572 = _861570, _861568 = _861566, _861564 = _861562, _861560 = _861558], (35017 ^ _779142) ^ [_1429757, _1429759, _1429761, _1429763, _1429765] : [_1429757 = c_Orderings_Obot__class_Obot(tc_fun(_1429759, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429759, tc_fun(_1429761, tc_HOL_Obool)), _1429757), hAPP(hAPP(c_COMBC(_1429759, tc_fun(_1429761, tc_HOL_Obool), tc_fun(_1429761, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429761, tc_HOL_Obool), tc_fun(tc_fun(_1429761, tc_HOL_Obool), tc_fun(_1429761, tc_HOL_Obool)), _1429759), c_Groups_Ominus__class_Ominus(tc_fun(_1429761, tc_HOL_Obool))), _1429763)), _1429765)) = c_Orderings_Otop__class_Otop(tc_fun(_1429761, tc_HOL_Obool)))], (26246 ^ _779142) ^ [_1240753, _1240755] : [class_Rings_Osemiring__1(_1240753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240755)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1240753), 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)))), _1240755))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240753), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1240753), hAPP(c_Int_Onat, _1240755))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1240753), hAPP(c_Int_Onat, _1240755))))], (26136 ^ _779142) ^ [_1238389, _1238391, _1238393] : [class_Int_Onumber__ring(_1238389), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1238389), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238389), _1238391), _1238393)), 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(_1238389), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238389), hAPP(hAPP(c_Power_Opower__class_Opower(_1238389), _1238391), 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(_1238389), _1238393), 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(_1238389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238389), hAPP(c_Int_Onumber__class_Onumber__of(_1238389), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1238391)), _1238393)))], (26528 ^ _779142) ^ [_1245704, _1245706, _1245708, _1245710, _1245712] : [class_Lattices_Olattice(_1245704), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245706, _1245704)), _1245708), _1245710), _1245712) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245704), hAPP(_1245708, _1245712)), hAPP(_1245710, _1245712)))], (23379 ^ _779142) ^ [_1191008, _1191010] : [class_Rings_Olinordered__idom(_1191008), 23382 ^ _779142 : [(23389 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191008), _1191010), c_Groups_Ozero__class_Ozero(_1191008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191008), _1191010), hAPP(c_Groups_Ouminus__class_Ouminus(_1191008), _1191010))))], (23383 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191008), _1191010), hAPP(c_Groups_Ouminus__class_Ouminus(_1191008), _1191010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191008), _1191010), c_Groups_Ozero__class_Ozero(_1191008))))]]], (37203 ^ _779142) ^ [_1481551, _1481553, _1481555] : [-(hAPP(c_Set_Ovimage(_1481551, _1481553, _1481555), c_Orderings_Obot__class_Obot(tc_fun(_1481553, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1481551, tc_HOL_Obool)))], (45549 ^ _779142) ^ [_1693126, _1693128] : [45551 ^ _779142 : [(45554 ^ _779142) ^ [] : [45550 ^ [_1693126, _1693128] = c_List_Olist_ONil(_1693126)], (45552 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693126)), 45550 ^ [_1693126, _1693128]), hAPP(c_List_Oset(tc_List_Olist(_1693126)), _1693128))))]], -(c_List_Oconcat(_1693126, _1693128) = c_List_Olist_ONil(_1693126))], (18400 ^ _779142) ^ [_1103221, _1103223, _1103225] : [-(hBOOL(hAPP(_1103221, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103223), _1103225))))), 18403 ^ _779142 : [(18406 ^ _779142) ^ [] : [hBOOL(hAPP(_1103221, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103223)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103225))))], (18404 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103225), _1103223)))]], 18407 ^ _779142 : [(18410 ^ _779142) ^ [] : [hBOOL(hAPP(_1103221, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18408 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103223), _1103225)))]]], (38531 ^ _779142) ^ [_1524905, _1524907, _1524909, _1524911] : [38532 ^ _779142 : [(38533 ^ _779142) ^ [_1524959] : [hBOOL(hAPP(hAPP(_1524909, _1524959), _1524911))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1524905, _1524907, _1524909), _1524911)))], (23445 ^ _779142) ^ [_1192113, _1192115, _1192117] : [class_Groups_Ogroup__add(_1192113), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192113), _1192115), hAPP(c_Groups_Ouminus__class_Ouminus(_1192113), _1192117)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192113), _1192115), _1192117))], (16603 ^ _779142) ^ [_1071396, _1071398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071396), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1071398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071396), _1071398)))], (576 ^ _779142) ^ [_787796, _787798, _787800, _787802, _787804, _787806] : [-(c_Finite__Set_Ofun__left__comm(_787804, _787800, _787796)), c_Finite__Set_Ofun__left__comm(_787806, _787802, _787798), _787806 = _787804, _787802 = _787800, _787798 = _787796], (752 ^ _779142) ^ [_790458, _790460, _790462, _790464] : [-(c_Wellfounded_Oacyclic(_790462, _790458)), c_Wellfounded_Oacyclic(_790464, _790460), _790464 = _790462, _790460 = _790458], (40275 ^ _779142) ^ [_1565916, _1565918, _1565920, _1565922] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565916, _1565916)), _1565918), c_Transitive__Closure_Otrancl(_1565916, _1565920))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565916, _1565916), tc_HOL_Obool)), _1565920), _1565922)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565916, _1565916)), _1565918), c_Transitive__Closure_Otrancl(_1565916, _1565922))))], (28364 ^ _779142) ^ [_1280433, _1280435] : [class_Complete__Lattice_Ocomplete__lattice(_1280433), -(c_Complete__Lattice_OSup__class_OSup(_1280433, hAPP(hAPP(c_Set_Oinsert(_1280433), _1280435), c_Orderings_Obot__class_Obot(tc_fun(_1280433, tc_HOL_Obool)))) = _1280435)], (60 ^ _779142) ^ [_780072, _780074, _780076, _780078, _780080, _780082] : [-(c_Big__Operators_Osemilattice__big(_780080, _780076, _780072)), c_Big__Operators_Osemilattice__big(_780082, _780078, _780074), _780082 = _780080, _780078 = _780076, _780074 = _780072], (29371 ^ _779142) ^ [_1300656, _1300658, _1300660, _1300662] : [-(hBOOL(hAPP(hAPP(c_member(_1300656), _1300658), _1300660))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300656, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1300656), _1300658), _1300662)), _1300660) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300656, tc_HOL_Obool)), _1300662), _1300660))], (19219 ^ _779142) ^ [_1117054, _1117056] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117054), _1117056))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1117054))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1117056))))], (34178 ^ _779142) ^ [_1406394, _1406396, _1406398, _1406400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1406394), _1406396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1406398), _1406400)), -(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), _1406394), _1406398)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1406396), _1406400))), c_FunDef_Opair__less)))], (24409 ^ _779142) ^ [_1208669, _1208671] : [class_Rings_Oring__1(_1208669), -(hBOOL(hAPP(hAPP(c_member(_1208669), hAPP(c_Int_Oring__1__class_Oof__int(_1208669), _1208671)), c_Int_Oring__1__class_OInts(_1208669))))], (52325 ^ _779142) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (27814 ^ _779142) ^ [_1270314, _1270316, _1270318, _1270320] : [class_Orderings_Olinorder(_1270314), 27817 ^ _779142 : [(27826 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270314), _1270316), _1270318)), _1270320))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), _1270316), _1270320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), _1270318), _1270320))], (27818 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270314), _1270316), _1270318)), _1270320)), 27821 ^ _779142 : [(27824 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), _1270318), _1270320)))], (27822 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270314), _1270316), _1270320)))]]]]], (13311 ^ _779142) ^ [_1009954, _1009956, _1009958, _1009960, _1009962] : [class_Groups_Oordered__comm__monoid__add(_1009954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009956), _1009958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009956, tc_HOL_Obool)), _1009960), _1009958)), 13325 ^ _779142 : [(13328 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009954), c_Groups_Ozero__class_Ozero(_1009954)), hAPP(_1009962, 13324 ^ [_1009954, _1009956, _1009958, _1009960, _1009962])))], (13326 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009956), 13324 ^ [_1009954, _1009956, _1009958, _1009960, _1009962]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009956, tc_HOL_Obool)), _1009958), _1009960))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009954), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009956, _1009954), _1009962), _1009960)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009956, _1009954), _1009962), _1009958))))], (4334 ^ _779142) ^ [_844887, _844889] : [_844889 = _844887, -(c_Lazy__Sequence_Osingle(_844889) = c_Lazy__Sequence_Osingle(_844887))], (49158 ^ _779142) ^ [_1772915, _1772917] : [c_Relation_Oantisym(_1772915, hAPP(c_Relation_Oconverse(_1772915, _1772915), _1772917)), -(c_Relation_Oantisym(_1772915, _1772917))], (37163 ^ _779142) ^ [_1480594, _1480596, _1480598, _1480600, _1480602, _1480604] : [hAPP(_1480594, _1480596) = _1480598, hBOOL(hAPP(hAPP(c_member(_1480600), _1480598), _1480602)), -(hBOOL(hAPP(hAPP(c_member(_1480604), _1480596), hAPP(c_Set_Ovimage(_1480604, _1480600, _1480594), _1480602))))], (5042 ^ _779142) ^ [_856023, _856025, _856027, _856029] : [-(c_Quotient_ORespects(_856029, _856025) = c_Quotient_ORespects(_856027, _856023)), _856029 = _856027, _856025 = _856023], (2380 ^ _779142) ^ [_813938, _813940, _813942, _813944] : [-(c_Divides_OposDivAlg(_813944, _813940) = c_Divides_OposDivAlg(_813942, _813938)), _813944 = _813942, _813940 = _813938], (51829 ^ _779142) ^ [_1825661, _1825663, _1825665] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825661), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1825663), _1825665))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825661), _1825665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1825665), _1825663)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825661), _1825663)))], (40951 ^ _779142) ^ [_1582993, _1582995, _1582997, _1582999] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1582993, _1582995), tc_fun(_1582993, _1582995)), _1582997), c_Fun_Ocomp(_1582995, _1582995, _1582993, _1582999)) = c_Fun_Ocomp(_1582995, _1582995, _1582993, hAPP(hAPP(c_Nat_Ocompow(_1582995, _1582995), _1582997), _1582999)))], (41341 ^ _779142) ^ [_1593926, _1593928, _1593930] : [-(hAPP(c_List_Olexn(_1593926, _1593928), hAPP(c_Nat_OSuc, _1593930)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1593926), tc_List_Olist(_1593926)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1593926, tc_List_Olist(_1593926)), tc_prod(_1593926, tc_List_Olist(_1593926))), tc_prod(tc_List_Olist(_1593926), tc_List_Olist(_1593926)), c_Product__Type_Omap__pair(tc_prod(_1593926, tc_List_Olist(_1593926)), tc_List_Olist(_1593926), tc_prod(_1593926, tc_List_Olist(_1593926)), tc_List_Olist(_1593926), hAPP(c_Product__Type_Oprod_Oprod__case(_1593926, tc_List_Olist(_1593926), tc_List_Olist(_1593926)), c_List_Olist_OCons(_1593926)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593926, tc_List_Olist(_1593926), tc_List_Olist(_1593926)), c_List_Olist_OCons(_1593926)))), c_Wellfounded_Olex__prod(_1593926, tc_List_Olist(_1593926), _1593928, hAPP(c_List_Olexn(_1593926, _1593928), _1593930)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593926), tc_List_Olist(_1593926))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593926), tc_List_Olist(_1593926), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593926), tc_fun(tc_List_Olist(_1593926), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593926), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593926), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593926), tc_HOL_Obool)), tc_List_Olist(_1593926)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1593926))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593926)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593926), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593926)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593926)))), hAPP(c_Nat_OSuc, _1593930))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593926), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593926)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593926)))), hAPP(c_Nat_OSuc, _1593930)))))))], (17873 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (43852 ^ _779142) ^ [_1656316, _1656318, _1656320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656316), _1656318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656316), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656318), _1656320))))], (34154 ^ _779142) ^ [_1405673, _1405675, _1405677, _1405679, _1405681, _1405683, _1405685] : [-(hAPP(c_Product__Type_Oapsnd(_1405673, _1405675, _1405677, _1405679), hAPP(c_Product__Type_Oapfst(_1405681, _1405677, _1405673, _1405683), _1405685)) = hAPP(hAPP(c_Product__Type_OPair(_1405677, _1405675), hAPP(_1405683, hAPP(c_Product__Type_Ofst(_1405681, _1405673), _1405685))), hAPP(_1405679, hAPP(c_Product__Type_Osnd(_1405681, _1405673), _1405685))))], (42640 ^ _779142) ^ [_1629112, _1629114, _1629116] : [hAPP(hAPP(c_List_Olist_OCons(_1629112), _1629114), _1629116) = c_List_Olist_ONil(_1629112)], (18889 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (26364 ^ _779142) ^ [_1242819, _1242821, _1242823, _1242825] : [hBOOL(hAPP(hAPP(c_member(_1242819), _1242821), _1242823)), -(hBOOL(hAPP(hAPP(c_member(_1242819), _1242821), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242819, tc_HOL_Obool)), _1242825), _1242823))))], (27668 ^ _779142) ^ [_1267469, _1267471, _1267473] : [class_Lattices_Olattice(_1267469), hAPP(_1267471, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267469), 27673 ^ [_1267469, _1267471, _1267473]), 27674 ^ [_1267469, _1267471, _1267473])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267469), hAPP(_1267471, 27673 ^ [_1267469, _1267471, _1267473])), hAPP(_1267471, 27674 ^ [_1267469, _1267471, _1267473])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267469), _1267473)), -(_1267473 = c_Orderings_Obot__class_Obot(tc_fun(_1267469, tc_HOL_Obool))), -(hAPP(_1267471, c_Big__Operators_Olattice__class_OSup__fin(_1267469, _1267473)) = c_Big__Operators_Olattice__class_OSup__fin(_1267469, hAPP(c_Set_Oimage(_1267469, _1267469, _1267471), _1267473)))], (46851 ^ _779142) ^ [_1721373, _1721375, _1721377, _1721379, _1721381] : [-(hAPP(hAPP(c_List_Ozip(_1721373, _1721375), c_List_OtakeWhile(_1721373, _1721377, _1721379)), _1721381) = c_List_OtakeWhile(tc_prod(_1721373, _1721375), hAPP(c_Fun_Ocomp(_1721373, tc_HOL_Obool, tc_prod(_1721373, _1721375), _1721377), c_Product__Type_Ofst(_1721373, _1721375)), hAPP(hAPP(c_List_Ozip(_1721373, _1721375), _1721379), _1721381)))], (51059 ^ _779142) ^ [_1812510, _1812512, _1812514, _1812516] : [class_Rings_Ocomm__ring__1(_1812510), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812510), _1812512), _1812514)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812510), _1812512), _1812516)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812510), _1812512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1812510), _1812514), _1812516))))], (49778 ^ _779142) ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500] : [class_Groups_Ocomm__monoid__mult(_1785490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785492), _1785494)), 49788 ^ _779142 : [(49791 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785496), hAPP(_1785498, 49787 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500])))], (49789 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785492), 49787 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500]), _1785494)))]], 49795 ^ _779142 : [(49799 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785492), 49797 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500]), _1785494)))], (49801 ^ _779142) ^ [] : [49794 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500] = 49797 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500]], (49803 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785496, tc_HOL_Obool)), hAPP(_1785498, 49794 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500])), hAPP(_1785498, 49797 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500])) = c_Orderings_Obot__class_Obot(tc_fun(_1785496, tc_HOL_Obool))], (49796 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785492), 49794 ^ [_1785490, _1785492, _1785494, _1785496, _1785498, _1785500]), _1785494)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785490, _1785496, c_Groups_Otimes__class_Otimes(_1785490)), _1785500), c_Groups_Oone__class_Oone(_1785490)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785492, tc_fun(_1785496, tc_HOL_Obool)), _1785494), _1785498)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785490, _1785492, c_Groups_Otimes__class_Otimes(_1785490)), hAPP(hAPP(c_COMBB(tc_fun(_1785496, tc_HOL_Obool), _1785490, _1785492), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785490, _1785496, c_Groups_Otimes__class_Otimes(_1785490)), _1785500), c_Groups_Oone__class_Oone(_1785490))), _1785498)), c_Groups_Oone__class_Oone(_1785490)), _1785494))], (10529 ^ _779142) ^ [_961373] : [hAPP(c_Nat_OSuc, _961373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38591 ^ _779142) ^ [_1526368, _1526370, _1526372] : [-(hAPP(c_Relation_ODomain(_1526368, _1526370), hAPP(c_Set_OCollect(tc_prod(_1526368, _1526370)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526368, _1526370, tc_HOL_Obool), _1526372))) = hAPP(c_Set_OCollect(_1526368), hAPP(hAPP(c_COMBB(tc_fun(_1526370, tc_HOL_Obool), tc_HOL_Obool, _1526368), c_HOL_OEx(_1526370)), _1526372)))], (44490 ^ _779142) ^ [_1670124, _1670126, _1670128, _1670130, _1670132] : [hAPP(hAPP(c_List_Omap(_1670124, _1670126), _1670128), _1670130) = hAPP(hAPP(c_List_Omap(_1670124, _1670126), _1670128), _1670132), c_Fun_Oinj__on(_1670124, _1670126, _1670128, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1670124, tc_HOL_Obool)), hAPP(c_List_Oset(_1670124), _1670130)), hAPP(c_List_Oset(_1670124), _1670132))), -(_1670130 = _1670132)], (372 ^ _779142) ^ [_784732, _784734, _784736, _784738, _784740, _784742, _784744, _784746] : [-(c_Finite__Set_Ofolding__idem(_784744, _784740, _784736, _784732)), c_Finite__Set_Ofolding__idem(_784746, _784742, _784738, _784734), _784746 = _784744, _784742 = _784740, _784738 = _784736, _784734 = _784732], (52623 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (37607 ^ _779142) ^ [_1491952, _1491954, _1491956] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491952, tc_HOL_Obool)), _1491954), _1491956) = hAPP(c_Set_OCollect(_1491952), hAPP(hAPP(c_COMBS(_1491952, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491952), c_fconj), hAPP(hAPP(c_COMBC(_1491952, tc_fun(_1491952, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491952)), _1491954))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1491952), c_fNot), hAPP(hAPP(c_COMBC(_1491952, tc_fun(_1491952, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491952)), _1491956)))))], (2520 ^ _779142) ^ [_816190, _816192, _816194, _816196] : [-(c_Divides_Odivmod__nat(_816196, _816192) = c_Divides_Odivmod__nat(_816194, _816190)), _816196 = _816194, _816192 = _816190], (1376 ^ _779142) ^ [_799284, _799286] : [-(class_Orderings_Owellorder(_799284)), _799286 = _799284, class_Orderings_Owellorder(_799286)], (35331 ^ _779142) ^ [_1437484, _1437486, _1437488, _1437490, _1437492, _1437494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool)), _1437486), _1437488)), c_Wellfounded_Omax__ext(_1437484, _1437490))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool)), _1437492), _1437494)), c_Wellfounded_Omax__ext(_1437484, _1437490))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437484, tc_HOL_Obool), tc_fun(_1437484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437484, tc_HOL_Obool)), _1437486), _1437492)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437484, tc_HOL_Obool)), _1437488), _1437494))), c_Wellfounded_Omax__ext(_1437484, _1437490))))], (41689 ^ _779142) ^ [_1605124, _1605126, _1605128, _1605130, _1605132, _1605134] : [hBOOL(hAPP(hAPP(_1605124, _1605126), _1605128)), c_List_Olistrelp(_1605130, _1605124, _1605132, _1605134), -(c_List_Olistrelp(_1605130, _1605124, hAPP(hAPP(c_List_Olist_OCons(_1605130), _1605126), _1605132), hAPP(hAPP(c_List_Olist_OCons(_1605130), _1605128), _1605134)))], (20696 ^ _779142) ^ [_1142808, _1142810, _1142812, _1142814, _1142816] : [-(hBOOL(hAPP(hAPP(c_member(_1142808), _1142810), c_SetInterval_Oord_OatLeastAtMost(_1142808, _1142812, _1142814, _1142816)))), hBOOL(hAPP(hAPP(_1142812, _1142814), _1142810)), hBOOL(hAPP(hAPP(_1142812, _1142810), _1142816))], (8330 ^ _779142) ^ [_917777] : [class_Lattices_Oab__semigroup__idem__mult(_917777), -(c_Finite__Set_Ofun__left__comm__idem(_917777, _917777, c_Groups_Otimes__class_Otimes(_917777)))], (16351 ^ _779142) ^ [_1066699, _1066701, _1066703, _1066705, _1066707, _1066709] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1066699, _1066701, _1066703, _1066705, c_Nitpick_Opair__box_OPairBox(_1066699, _1066701, _1066707, _1066709)) = hAPP(hAPP(_1066705, _1066707), _1066709))], (52327 ^ _779142) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (41826 ^ _779142) ^ [_1608741, _1608743, _1608745] : [-(hAPP(hAPP(c_List_Onth(_1608741), hAPP(hAPP(c_List_Olist_OCons(_1608741), _1608743), _1608745)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1608743)], (34402 ^ _779142) ^ [_1412251, _1412253, _1412255, _1412257, _1412259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412251, tc_HOL_Obool)), _1412253), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412255, tc_fun(_1412251, tc_HOL_Obool)), _1412257), _1412259))), 34405 ^ _779142 : [(34406 ^ _779142) ^ [_1412384] : [hBOOL(hAPP(hAPP(c_member(_1412255), _1412384), _1412257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412251, tc_HOL_Obool)), _1412253), hAPP(_1412259, _1412384))))]]], (19599 ^ _779142) ^ [_1123571] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1123571)), -(hAPP(c_Int_Onat, _1123571) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31500 ^ _779142) ^ [_1344240, _1344242, _1344244] : [class_Orderings_Olinorder(_1344240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344240), _1344242)), 31510 ^ _779142 : [(31513 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344240), 31509 ^ [_1344240, _1344242, _1344244]), _1344244))], (31511 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344240), 31509 ^ [_1344240, _1344242, _1344244]), _1344242)))]], hBOOL(hAPP(hAPP(c_member(_1344240), _1344244), _1344242)), -(c_Big__Operators_Olinorder__class_OMax(_1344240, _1344242) = _1344244)], (46927 ^ _779142) ^ [_1722912] : [c_List_Onat__list(_1722912), -(c_List_Oembed__list(c_List_Oreturn__list(_1722912)) = _1722912)], (1856 ^ _779142) ^ [_805284, _805286] : [-(class_Rings_Osemiring(_805284)), _805286 = _805284, class_Rings_Osemiring(_805286)], (10903 ^ _779142) ^ [_967316, _967318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967316)), _967318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967316), _967318)))], (31430 ^ _779142) ^ [_1342821, _1342823, _1342825] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342821, tc_HOL_Obool)), _1342823), _1342825) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342821, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1342821, tc_HOL_Obool)), _1342823), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1342821, tc_HOL_Obool)), _1342825), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1342821, tc_HOL_Obool), tc_HOL_Obool))))))], (13179 ^ _779142) ^ [_1007720, _1007722] : [_1007720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007720), _1007722) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50633 ^ _779142) ^ [_1804716, _1804718, _1804720, _1804722] : [class_Rings_Oidom(_1804716), 50636 ^ _779142 : [(50637 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804716), _1804718), _1804720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804716), _1804722), _1804720))), -(_1804720 = c_Groups_Ozero__class_Ozero(_1804716)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804716), _1804718), _1804722)))], (50647 ^ _779142) ^ [] : [50648 ^ _779142 : [(50651 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804716), _1804718), _1804722))], (50649 ^ _779142) ^ [] : [_1804720 = c_Groups_Ozero__class_Ozero(_1804716)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804716), _1804718), _1804720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804716), _1804722), _1804720))))]]], (26698 ^ _779142) ^ [_1249386, _1249388, _1249390, _1249392] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249386, tc_HOL_Obool)), _1249388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249386, tc_HOL_Obool)), _1249390), _1249392)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249386, tc_HOL_Obool)), _1249390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249386, tc_HOL_Obool)), _1249388), _1249392)))], (15571 ^ _779142) ^ [_1051894, _1051896, _1051898] : [class_Int_Onumber__ring(_1051894), -(hAPP(c_Int_Onumber__class_Onumber__of(_1051894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051896), _1051898)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051894), hAPP(c_Int_Onumber__class_Onumber__of(_1051894), _1051896)), hAPP(c_Int_Onumber__class_Onumber__of(_1051894), _1051898)))], (12218 ^ _779142) ^ [_990149, _990151, _990153, _990155, _990157, _990159] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_990149), -(_990151 = c_Groups_Ozero__class_Ozero(_990149)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_990149), _990153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990149), _990151), _990157)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_990149), _990155), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990149), _990151), _990159)), _990153 = _990155, -(_990157 = _990159)], (37609 ^ _779142) ^ [_1492055, _1492057] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492055), hAPP(c_Set_OCollect(_1492055), _1492057))), 37612 ^ _779142 : [(37619 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492055), c_Orderings_Otop__class_Otop(tc_fun(_1492055, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492055), hAPP(c_Set_OCollect(_1492055), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492055), c_fNot), _1492057)))))], (37613 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492055), hAPP(c_Set_OCollect(_1492055), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492055), c_fNot), _1492057)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492055), c_Orderings_Otop__class_Otop(tc_fun(_1492055, tc_HOL_Obool)))))]]], (34714 ^ _779142) ^ [_1422189, _1422191, _1422193, _1422195, _1422197] : [class_Complete__Lattice_Ocomplete__lattice(_1422189), class_Orderings_Olinorder(_1422189), 34721 ^ _779142 : [(34731 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422189), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422191, _1422189), _1422193), _1422195)), _1422197))), 34732 ^ _779142 : [(34733 ^ _779142) ^ [_1422537] : [hBOOL(hAPP(hAPP(c_member(_1422191), _1422537), _1422193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422189), hAPP(_1422195, _1422537)), _1422197))]]], (34722 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422189), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422191, _1422189), _1422193), _1422195)), _1422197)), 34726 ^ _779142 : [(34729 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422189), hAPP(_1422195, 34725 ^ [_1422189, _1422191, _1422193, _1422195, _1422197])), _1422197)))], (34727 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422191), 34725 ^ [_1422189, _1422191, _1422193, _1422195, _1422197]), _1422193)))]]]]], (18046 ^ _779142) ^ [_1096984, _1096986, _1096988] : [class_Rings_Oring__1(_1096984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1096986), _1096988)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1096988), _1096986)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096984), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096984), _1096988)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096984), _1096986)))], (17225 ^ _779142) ^ [_1082370, _1082372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082370), _1082372)), -(c_Nat__Transfer_Otsub(_1082372, _1082370) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1082372), _1082370))], (4068 ^ _779142) ^ [_840698, _840700, _840702, _840704, _840706, _840708, _840710, _840712] : [-(c_New__Random__Sequence_Opos__bind(_840712, _840708, _840704, _840700) = c_New__Random__Sequence_Opos__bind(_840710, _840706, _840702, _840698)), _840712 = _840710, _840708 = _840706, _840704 = _840702, _840700 = _840698], (18567 ^ _779142) ^ [_1106068, _1106070] : [_1106068 = _1106070, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106068) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106070))], (33917 ^ _779142) ^ [_1400433, _1400435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400433), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400435), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1400433), _1400435) = 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), _1400433), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1400435)))))], (14535 ^ _779142) ^ [_1032602, _1032604, _1032606, _1032608] : [class_Fields_Olinordered__field(_1032602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032602), c_Groups_Ozero__class_Ozero(_1032602)), _1032604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032602), _1032606), _1032604)), _1032608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032602), _1032606), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032602), _1032608), _1032604))))], (49693 ^ _779142) ^ [_1783369, _1783371, _1783373, _1783375] : [hAPP(c_Set_Oimage(_1783369, _1783371, _1783373), c_Orderings_Otop__class_Otop(tc_fun(_1783369, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783371, tc_HOL_Obool)), -(hAPP(_1783373, hAPP(c_Hilbert__Choice_Oinv__into(_1783369, _1783371, c_Orderings_Otop__class_Otop(tc_fun(_1783369, tc_HOL_Obool)), _1783373), _1783375)) = _1783375)], (29482 ^ _779142) ^ [_1303495, _1303497, _1303499] : [class_Lattices_Olattice(_1303495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303495), _1303497)), hBOOL(hAPP(hAPP(c_member(_1303495), _1303499), _1303497)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303495), _1303499), c_Big__Operators_Olattice__class_OSup__fin(_1303495, _1303497)) = _1303499)], (46074 ^ _779142) ^ [_1706197, _1706199] : [class_Orderings_Olinorder(_1706197), -(c_List_Olinorder__class_Osorted(_1706197, c_List_Olinorder__class_Osort__key(_1706197, _1706197, c_COMBI(_1706197), _1706199)))], (22725 ^ _779142) ^ [_1179463, _1179465, _1179467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179463, tc_HOL_Obool)), _1179465), _1179467)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1179463, tc_HOL_Obool)), _1179465), hAPP(c_Set_OPow(_1179463), _1179467))))], (41899 ^ _779142) ^ [_1610759, _1610761, _1610763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610759)), _1610761)), _1610763)), -(hAPP(hAPP(c_List_Otake(_1610759), _1610763), _1610761) = _1610761)], (34961 ^ _779142) ^ [_1428364, _1428366, _1428368, _1428370, _1428372] : [class_Complete__Lattice_Ocomplete__lattice(_1428364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428366, tc_HOL_Obool)), _1428368), _1428370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428364), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428366, _1428364), _1428368), _1428372)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428366, _1428364), _1428370), _1428372))))], (52659 ^ _779142) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52143 ^ _779142) ^ [_1831051, _1831053] : [class_Lattices_Olattice(_1831051), -(class_Lattices_Osemilattice__inf(tc_fun(_1831053, _1831051)))], (17935 ^ _779142) ^ [_1095073, _1095075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095073), _1095075)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1095073, _1095075) = _1095073)], (7660 ^ _779142) ^ [_905841, _905843, _905845, _905847] : [class_Orderings_Opreorder(_905841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905841), _905843), _905845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905841), _905845), _905847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905841), _905843), _905847)))], (24638 ^ _779142) ^ [_1212425, _1212427, _1212429] : [_1212427 = _1212429, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212425, tc_HOL_Obool)), _1212427) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212425, tc_HOL_Obool)), _1212429))], (7382 ^ _779142) ^ [_901376, _901378, _901380] : [class_Orderings_Oorder(_901376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901376), _901378), _901380)), _901378 = _901380], (47054 ^ _779142) ^ [_1725620, _1725622, _1725624, _1725626, _1725628] : [class_Groups_Omonoid__add(_1725620), 47060 ^ _779142 : [(47065 ^ _779142) ^ [] : [hAPP(_1725628, 47059 ^ [_1725620, _1725622, _1725624, _1725626, _1725628]) = c_Groups_Ozero__class_Ozero(_1725620)], (47063 ^ _779142) ^ [] : [hBOOL(hAPP(_1725626, 47059 ^ [_1725620, _1725622, _1725624, _1725626, _1725628]))], (47061 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725622), 47059 ^ [_1725620, _1725622, _1725624, _1725626, _1725628]), hAPP(c_List_Oset(_1725622), _1725624))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1725620), hAPP(hAPP(c_List_Omap(_1725622, _1725620), _1725628), hAPP(c_List_Ofilter(_1725622, _1725626), _1725624))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1725620), hAPP(hAPP(c_List_Omap(_1725622, _1725620), _1725628), _1725624)))], (48062 ^ _779142) ^ [_1747792, _1747794] : [-(c_List_Osplice(_1747792, c_List_Olist_ONil(_1747792), _1747794) = _1747794)], (52265 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (50741 ^ _779142) ^ [_1806584, _1806586, _1806588] : [class_Rings_Ocomm__semiring__1(_1806584), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806584), _1806586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806584), _1806588), _1806586))))], (30854 ^ _779142) ^ [_1332028] : [-(hAPP(c_Set_OPow(_1332028), c_Orderings_Otop__class_Otop(tc_fun(_1332028, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1332028, tc_HOL_Obool), tc_HOL_Obool)))], (49630 ^ _779142) ^ [_1782008, _1782010, _1782012, _1782014, _1782016] : [c_Fun_Oinj__on(_1782008, _1782010, _1782012, _1782014), hBOOL(hAPP(hAPP(c_member(_1782008), _1782016), _1782014)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1782008, _1782010, _1782014, _1782012), hAPP(_1782012, _1782016)) = _1782016)], (4148 ^ _779142) ^ [_841930, _841932] : [_841932 = _841930, -(c_List_Ohd(_841932) = c_List_Ohd(_841930))], (52283 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (24107 ^ _779142) ^ [_1203639, _1203641, _1203643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203639, tc_HOL_Obool)), _1203641), _1203643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203639, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203639, tc_HOL_Obool)), _1203643)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203639, tc_HOL_Obool)), _1203641))))], (41767 ^ _779142) ^ [_1607050, _1607052, _1607054, _1607056] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607050), tc_List_Olist(_1607050))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607050), tc_List_Olist(_1607050)), _1607052), _1607054)), c_List_Olistrel(_1607050, _1607056))), 41770 ^ _779142 : [(41773 ^ _779142) ^ [_1607279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607050)), _1607052))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607050, _1607050)), hAPP(hAPP(c_Product__Type_OPair(_1607050, _1607050), hAPP(hAPP(c_List_Onth(_1607050), _1607052), _1607279)), hAPP(hAPP(c_List_Onth(_1607050), _1607054), _1607279))), _1607056)))], (41771 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607050)), _1607052) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607050)), _1607054))]]], (38296 ^ _779142) ^ [_1516216, _1516218] : [-(c_Product__Type_Omap__pair(_1516216, _1516216, _1516218, _1516218, c_Fun_Oid(_1516216), c_Fun_Oid(_1516218)) = c_Fun_Oid(tc_prod(_1516216, _1516218)))], (52245 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (21336 ^ _779142) ^ [_1154271, _1154273, _1154275] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1154271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1154273), _1154275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1154271), _1154273)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1154271), _1154275)))], (42305 ^ _779142) ^ [_1621807, _1621809, _1621811] : [hBOOL(hAPP(hAPP(c_member(_1621807), _1621809), hAPP(c_List_Oset(_1621807), c_List_Obutlast(_1621807, _1621811)))), -(hBOOL(hAPP(hAPP(c_member(_1621807), _1621809), hAPP(c_List_Oset(_1621807), _1621811))))], (42181 ^ _779142) ^ [_1619161, _1619163] : [class_Groups_Ocomm__monoid__add(_1619161), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619161), _1619163) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1619161), hAPP(c_List_Onth(_1619161), _1619163)), 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(_1619161)), _1619163))))], (35478 ^ _779142) ^ [_1442303, _1442305, _1442307] : [-(hAPP(c_Relation_OImage(_1442303, _1442305, _1442307), c_Orderings_Obot__class_Obot(tc_fun(_1442303, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1442305, tc_HOL_Obool)))], (254 ^ _779142) ^ [_783107, _783109] : [-(class_Fields_Ofield__inverse__zero(_783107)), _783109 = _783107, class_Fields_Ofield__inverse__zero(_783109)], (2932 ^ _779142) ^ [_822564, _822566] : [_822566 = _822564, -(c_Nitpick_Odenom(_822566) = c_Nitpick_Odenom(_822564))], (45430 ^ _779142) ^ [_1690800, _1690802, _1690804] : [hBOOL(hAPP(c_List_Odistinct(_1690800), _1690802)), -(c_List_Oremove1(_1690800, _1690804, c_List_Oremdups(_1690800, _1690802)) = c_List_Oremdups(_1690800, c_List_Oremove1(_1690800, _1690804, _1690802)))], (19905 ^ _779142) ^ [_1128620, _1128622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1128620), 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)), _1128622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128620), _1128622)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2926 ^ _779142) ^ [_822479, _822481] : [_822481 = _822479, -(c_Nitpick_Onum(_822481) = c_Nitpick_Onum(_822479))], (28374 ^ _779142) ^ [_1280594, _1280596, _1280598] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1280594, tc_HOL_Obool)), _1280596), _1280598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280594, tc_HOL_Obool)), _1280596), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1280594, tc_HOL_Obool), _1280598))))], (27220 ^ _779142) ^ [_1259575, _1259577] : [_1259575 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1259575, _1259577) = _1259577)], (31903 ^ _779142) ^ [_1354246, _1354248] : [-(hAPP(c_Set_Oimage(_1354246, _1354246, c_COMBI(_1354246)), _1354248) = _1354248)], (4598 ^ _779142) ^ [_849039, _849041] : [_849041 = _849039, -(c_DSequence_Oempty(_849041) = c_DSequence_Oempty(_849039))], (52329 ^ _779142) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (14221 ^ _779142) ^ [_1026882, _1026884, _1026886, _1026888] : [class_Fields_Ofield__inverse__zero(_1026882), 14224 ^ _779142 : [(14225 ^ _779142) ^ [] : [_1026884 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026882), _1026886), _1026888), 14228 ^ _779142 : [(14235 ^ _779142) ^ [] : [_1026888 = c_Groups_Ozero__class_Ozero(_1026882), -(_1026884 = c_Groups_Ozero__class_Ozero(_1026882))], (14229 ^ _779142) ^ [] : [-(_1026888 = c_Groups_Ozero__class_Ozero(_1026882)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026882), _1026884), _1026888) = _1026886)]]], (14241 ^ _779142) ^ [] : [-(_1026884 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026882), _1026886), _1026888)), 14244 ^ _779142 : [(14247 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026882), _1026884), _1026888) = _1026886], (14245 ^ _779142) ^ [] : [_1026888 = c_Groups_Ozero__class_Ozero(_1026882)]], 14248 ^ _779142 : [(14251 ^ _779142) ^ [] : [_1026884 = c_Groups_Ozero__class_Ozero(_1026882)], (14249 ^ _779142) ^ [] : [-(_1026888 = c_Groups_Ozero__class_Ozero(_1026882))]]]]], (8044 ^ _779142) ^ [_911802, _911804, _911806, _911808, _911810] : [class_Groups_Oab__group__add(_911802), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_911802), _911804), _911806) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_911802), _911808), _911810), 8051 ^ _779142 : [(8058 ^ _779142) ^ [] : [_911808 = _911810, -(_911804 = _911806)], (8052 ^ _779142) ^ [] : [_911804 = _911806, -(_911808 = _911810)]]], (45933 ^ _779142) ^ [_1703241, _1703243] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1703241), _1703243)) = c_List_Oupt(_1703241, _1703243))], (32839 ^ _779142) ^ [_1379002, _1379004] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379002)), _1379004) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1379002), 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), _1379002)), _1379004))], (50210 ^ _779142) ^ [_1794411, _1794413, _1794415, _1794417, _1794419] : [c_Fun_Obij__betw(_1794411, _1794413, _1794415, c_Orderings_Otop__class_Otop(tc_fun(_1794411, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794413, tc_HOL_Obool))), 50213 ^ _779142 : [(50220 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794413, tc_HOL_Obool)), _1794417), hAPP(c_Set_Oimage(_1794411, _1794413, _1794415), _1794419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794411, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794411, _1794413, _1794415), _1794417)), _1794419)))], (50214 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794411, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794411, _1794413, _1794415), _1794417)), _1794419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794413, tc_HOL_Obool)), _1794417), hAPP(c_Set_Oimage(_1794411, _1794413, _1794415), _1794419))))]]], (46877 ^ _779142) ^ [_1721859, _1721861, _1721863] : [hBOOL(hAPP(c_List_Odistinct(_1721859), _1721861)), -(hBOOL(hAPP(c_List_Odistinct(_1721859), c_List_OtakeWhile(_1721859, _1721863, _1721861))))], (46432 ^ _779142) ^ [_1712360, _1712362, _1712364] : [class_Orderings_Olinorder(_1712360), hBOOL(hAPP(hAPP(c_member(_1712360), _1712362), hAPP(c_List_Oset(_1712360), _1712364))), c_List_Olinorder__class_Osorted(_1712360, _1712364), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712360, _1712360, c_COMBI(_1712360)), _1712362), c_List_Oremove1(_1712360, _1712362, _1712364)) = _1712364)], (26154 ^ _779142) ^ [_1238890, _1238892, _1238894] : [class_Groups_Omonoid__mult(_1238890), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1238890), _1238892), 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)))), _1238894))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238890), _1238892), hAPP(hAPP(c_Power_Opower__class_Opower(_1238890), hAPP(hAPP(c_Power_Opower__class_Opower(_1238890), _1238892), _1238894)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (43556 ^ _779142) ^ [_1649816, _1649818, _1649820, _1649822] : [-(hAPP(hAPP(c_List_Odrop(_1649816), _1649818), hAPP(hAPP(c_List_Oappend(_1649816), _1649820), _1649822)) = hAPP(hAPP(c_List_Oappend(_1649816), hAPP(hAPP(c_List_Odrop(_1649816), _1649818), _1649820)), hAPP(hAPP(c_List_Odrop(_1649816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649818), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649816)), _1649820))), _1649822)))], (4192 ^ _779142) ^ [_842568, _842570, _842572, _842574] : [-(c_List_Ofilter(_842574, _842570) = c_List_Ofilter(_842572, _842568)), _842574 = _842572, _842570 = _842568], (26928 ^ _779142) ^ [_1254101, _1254103, _1254105, _1254107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254101, tc_HOL_Obool)), _1254103), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254101, tc_HOL_Obool)), _1254105), _1254107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254101, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254101, tc_HOL_Obool)), _1254103), _1254105)), _1254107)))], (30238 ^ _779142) ^ [_1319607, _1319609, _1319611, _1319613, _1319615] : [class_Groups_Ocomm__monoid__add(_1319607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319609), _1319611)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319609), _1319613)), 30252 ^ _779142 : [(30255 ^ _779142) ^ [] : [hAPP(_1319615, 30251 ^ [_1319607, _1319609, _1319611, _1319613, _1319615]) = c_Groups_Ozero__class_Ozero(_1319607)], (30253 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319609), 30251 ^ [_1319607, _1319609, _1319611, _1319613, _1319615]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319609, tc_HOL_Obool)), _1319611), _1319613))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319609, _1319607), _1319615), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319609, tc_HOL_Obool)), _1319611), _1319613)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319607), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319609, _1319607), _1319615), _1319611)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319609, _1319607), _1319615), _1319613)))], (16547 ^ _779142) ^ [_1070371, _1070373, _1070375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070371), _1070373)), _1070375) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070373), _1070375)))], (25656 ^ _779142) ^ [_1230038, _1230040] : [class_Int_Onumber__ring(_1230038), class_Int_Oring__char__0(_1230038), 25663 ^ _779142 : [(25670 ^ _779142) ^ [] : [c_Int_Oiszero(_1230038, hAPP(c_Int_Onumber__class_Onumber__of(_1230038), _1230040)), -(c_Int_Oiszero(_1230038, hAPP(c_Int_Onumber__class_Onumber__of(_1230038), c_Int_OBit0(_1230040))))], (25664 ^ _779142) ^ [] : [c_Int_Oiszero(_1230038, hAPP(c_Int_Onumber__class_Onumber__of(_1230038), c_Int_OBit0(_1230040))), -(c_Int_Oiszero(_1230038, hAPP(c_Int_Onumber__class_Onumber__of(_1230038), _1230040)))]]], (44646 ^ _779142) ^ [_1673499, _1673501] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673499), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673501), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44653 ^ _779142 : [(44660 ^ _779142) ^ [] : [_1673499 = _1673501, -(hAPP(c_Code__Numeral_Oof__nat, _1673499) = hAPP(c_Code__Numeral_Oof__nat, _1673501))], (44654 ^ _779142) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1673499) = hAPP(c_Code__Numeral_Oof__nat, _1673501), -(_1673499 = _1673501)]]], (2370 ^ _779142) ^ [_813789, _813791, _813793, _813795] : [-(c_Divides_OnegDivAlg(_813795, _813791) = c_Divides_OnegDivAlg(_813793, _813789)), _813795 = _813793, _813791 = _813789], (26570 ^ _779142) ^ [_1246699, _1246701, _1246703] : [class_Lattices_Osemilattice__sup(_1246699), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246699), _1246701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246699), _1246701), _1246703)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246699), _1246701), _1246703))], (27482 ^ _779142) ^ [_1264230, _1264232, _1264234] : [class_Lattices_Olattice(_1264230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264230), _1264232)), -(hBOOL(hAPP(hAPP(c_member(_1264230), _1264234), _1264232))), -(c_Big__Operators_Olattice__class_OSup__fin(_1264230, hAPP(hAPP(c_Set_Oinsert(_1264230), _1264234), _1264232)) = hAPP(hAPP(c_Finite__Set_Ofold(_1264230, _1264230, c_Lattices_Osemilattice__sup__class_Osup(_1264230)), _1264234), _1264232))], (26032 ^ _779142) ^ [_1236483, _1236485] : [class_Rings_Oring__1__no__zero__divisors(_1236483), 26035 ^ _779142 : [(26036 ^ _779142) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1236483), _1236485), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1236483), -(_1236485 = c_Groups_Oone__class_Oone(_1236483)), -(_1236485 = hAPP(c_Groups_Ouminus__class_Ouminus(_1236483), c_Groups_Oone__class_Oone(_1236483)))], (26046 ^ _779142) ^ [] : [26047 ^ _779142 : [(26050 ^ _779142) ^ [] : [_1236485 = hAPP(c_Groups_Ouminus__class_Ouminus(_1236483), c_Groups_Oone__class_Oone(_1236483))], (26048 ^ _779142) ^ [] : [_1236485 = c_Groups_Oone__class_Oone(_1236483)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236483), _1236485), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1236483))]]], (31985 ^ _779142) ^ [_1358216, _1358218, _1358220, _1358222, _1358224] : [class_Lattices_Olattice(_1358216), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358218, _1358216)), _1358220), _1358222), _1358224) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1358216), hAPP(_1358220, _1358224)), hAPP(_1358222, _1358224)))], (19165 ^ _779142) ^ [_1115940, _1115942, _1115944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1115942), 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), _1115942), _1115944))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1115940))), _1115944)))], (39105 ^ _779142) ^ [_1537619, _1537621, _1537623] : [c_Wellfounded_OwfP(_1537619, _1537621), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1537619, _1537621), _1537623)))], (27856 ^ _779142) ^ [_1271052, _1271054, _1271056] : [class_Orderings_Olinorder(_1271052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271052), _1271054), _1271056)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271052), _1271054), _1271056) = _1271056)], (14025 ^ _779142) ^ [_1023467, _1023469, _1023471] : [class_Fields_Olinordered__field__inverse__zero(_1023467), 14028 ^ _779142 : [(14043 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023467), _1023469), _1023471)), c_Groups_Ozero__class_Ozero(_1023467)))), 14044 ^ _779142 : [(14051 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), _1023469), c_Groups_Ozero__class_Ozero(_1023467))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), c_Groups_Ozero__class_Ozero(_1023467)), _1023471))], (14045 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), c_Groups_Ozero__class_Ozero(_1023467)), _1023469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), _1023471), c_Groups_Ozero__class_Ozero(_1023467)))]]], (14029 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023467), _1023469), _1023471)), c_Groups_Ozero__class_Ozero(_1023467))), 14034 ^ _779142 : [(14037 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), _1023471), c_Groups_Ozero__class_Ozero(_1023467))))], (14035 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), c_Groups_Ozero__class_Ozero(_1023467)), _1023469)))]], 14038 ^ _779142 : [(14041 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), c_Groups_Ozero__class_Ozero(_1023467)), _1023471)))], (14039 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023467), _1023469), c_Groups_Ozero__class_Ozero(_1023467))))]]]]], (38310 ^ _779142) ^ [_1516573, _1516575, _1516577, _1516579] : [-(c_Product__Type_Oapsnd(_1516573, _1516575, _1516577, _1516579) = c_Product__Type_Omap__pair(_1516577, _1516577, _1516573, _1516575, c_Fun_Oid(_1516577), _1516579))], (52309 ^ _779142) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (5472 ^ _779142) ^ [_862824, _862826] : [_862826 = _862824, -(c_Rings_Odvd__class_Odvd(_862826) = c_Rings_Odvd__class_Odvd(_862824))], (52463 ^ _779142) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (25168 ^ _779142) ^ [_1221505, _1221507] : [class_Rings_Olinordered__idom(_1221505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221505), c_Groups_Ozero__class_Ozero(_1221505)), _1221507)), -(c_Groups_Osgn__class_Osgn(_1221505, _1221507) = c_Groups_Oone__class_Oone(_1221505))], (52555 ^ _779142) ^ [_1835283, _1835285] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1835283, _1835285))), class_Lazy__Sequence_Osmall__lazy(_1835283), class_Lazy__Sequence_Osmall__lazy(_1835285)], (16591 ^ _779142) ^ [_1071165, _1071167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1071167), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071165), _1071167)))], (9420 ^ _779142) ^ [_939677, _939679] : [class_Groups_Omonoid__mult(_939677), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939677), c_Groups_Oone__class_Oone(_939677)), _939679) = _939679)], (7452 ^ _779142) ^ [_902454, _902456, _902458, _902460] : [class_Orderings_Oord(_902454), _902456 = _902458, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902454), _902458), _902460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902454), _902456), _902460)))], (40815 ^ _779142) ^ [_1579631, _1579633, _1579635, _1579637, _1579639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579631, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579633, _1579631, _1579635), _1579637)), _1579639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579633, tc_HOL_Obool)), _1579637), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579633, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579631, _1579633, hAPP(c_Relation_Oconverse(_1579633, _1579631), _1579635)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579631, tc_HOL_Obool)), _1579639))))))], (49262 ^ _779142) ^ [_1775197, _1775199] : [49265 ^ _779142 : [(49268 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775197, _1775197)), hAPP(hAPP(c_Product__Type_OPair(_1775197, _1775197), 49264 ^ [_1775197, _1775199]), 49263 ^ [_1775197, _1775199])), _1775199))], (49266 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775197, _1775197)), hAPP(hAPP(c_Product__Type_OPair(_1775197, _1775197), 49263 ^ [_1775197, _1775199]), 49264 ^ [_1775197, _1775199])), _1775199)))]], -(c_Relation_Osym(_1775197, _1775199))], (25090 ^ _779142) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (46861 ^ _779142) ^ [_1721591, _1721593, _1721595, _1721597] : [hBOOL(hAPP(_1721591, _1721593)), -(c_List_OtakeWhile(_1721595, _1721591, hAPP(hAPP(c_List_Olist_OCons(_1721595), _1721593), _1721597)) = hAPP(hAPP(c_List_Olist_OCons(_1721595), _1721593), c_List_OtakeWhile(_1721595, _1721591, _1721597)))], (7480 ^ _779142) ^ [_902892, _902894, _902896, _902898] : [class_Orderings_Oord(_902892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902892), _902894), _902896)), _902896 = _902898, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902892), _902894), _902898)))], (52749 ^ _779142) ^ [_1837525, _1837527] : [hBOOL(_1837525), -(hBOOL(hAPP(hAPP(c_fdisj, _1837527), _1837525)))], (22544 ^ _779142) ^ [_1176001, _1176003, _1176005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176001)), 22547 ^ _779142 : [(22548 ^ _779142) ^ [_1176135] : [22550 ^ _779142 : [(22556 ^ _779142) ^ [] : [-(_1176135 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22552 ^ [_1176001, _1176003, _1176005, _1176135]), 22549 ^ [_1176001, _1176003, _1176005, _1176135]))], (22554 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22552 ^ [_1176001, _1176003, _1176005, _1176135]), _1176003)))], (22551 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22549 ^ [_1176001, _1176003, _1176005, _1176135]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1176001))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176135), _1176005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176135), _1176001)), _1176005)))]]], (46214 ^ _779142) ^ [_1708319, _1708321, _1708323] : [class_Orderings_Olinorder(_1708319), c_List_Olinorder__class_Osorted(_1708319, _1708321), hBOOL(hAPP(c_List_Odistinct(_1708319), _1708321)), c_List_Olinorder__class_Osorted(_1708319, _1708323), hBOOL(hAPP(c_List_Odistinct(_1708319), _1708323)), hAPP(c_List_Oset(_1708319), _1708321) = hAPP(c_List_Oset(_1708319), _1708323), -(_1708321 = _1708323)], (35701 ^ _779142) ^ [_1448201, _1448203, _1448205, _1448207, _1448209] : [c_Equiv__Relations_Oequiv(_1448201, _1448203, _1448205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448201, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1448201, _1448201, _1448205), hAPP(hAPP(c_Set_Oinsert(_1448201), _1448207), c_Orderings_Obot__class_Obot(tc_fun(_1448201, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1448201, _1448201, _1448205), hAPP(hAPP(c_Set_Oinsert(_1448201), _1448209), c_Orderings_Obot__class_Obot(tc_fun(_1448201, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1448201), _1448207), _1448203)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448201, _1448201)), hAPP(hAPP(c_Product__Type_OPair(_1448201, _1448201), _1448209), _1448207)), _1448205)))], (37098 ^ _779142) ^ [_1478976, _1478978] : [-(c_Set_Othe__elem(_1478976, _1478978) = c_HOL_OThe(_1478976, hAPP(hAPP(c_COMBB(tc_fun(_1478976, tc_HOL_Obool), tc_HOL_Obool, _1478976), hAPP(c_fequal, _1478978)), hAPP(hAPP(c_COMBC(_1478976, tc_fun(_1478976, tc_HOL_Obool), tc_fun(_1478976, tc_HOL_Obool)), c_Set_Oinsert(_1478976)), c_Orderings_Obot__class_Obot(tc_fun(_1478976, tc_HOL_Obool))))))], (38860 ^ _779142) ^ [_1531640, _1531642, _1531644, _1531646] : [hBOOL(hAPP(hAPP(c_member(_1531640), _1531642), hAPP(c_Relation_ODomain(_1531640, _1531644), _1531646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531640, _1531644)), hAPP(hAPP(c_Product__Type_OPair(_1531640, _1531644), _1531642), 38863 ^ [_1531640, _1531642, _1531644, _1531646])), _1531646)))], (25194 ^ _779142) ^ [_1221907, _1221909, _1221911, _1221913] : [class_Groups_Ocomm__monoid__add(_1221907), 25197 ^ _779142 : [(25204 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221909), _1221911))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221907), _1221913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221911), hAPP(c_Nat_OSuc, _1221909))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221907), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221907), _1221913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221911), _1221909))), hAPP(_1221913, _1221909)))], (25198 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221909), _1221911)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221907), _1221913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221911), hAPP(c_Nat_OSuc, _1221909))) = c_Groups_Ozero__class_Ozero(_1221907))]]], (45232 ^ _779142) ^ [_1686615, _1686617, _1686619, _1686621, _1686623, _1686625, _1686627, _1686629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686615), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686617)), _1686619))), c_List_Olist__all2(_1686617, _1686621, _1686623, _1686619, _1686625), hBOOL(hAPP(hAPP(_1686623, _1686627), _1686629)), -(c_List_Olist__all2(_1686617, _1686621, _1686623, hAPP(hAPP(c_List_Olist__update(_1686617, _1686619), _1686615), _1686627), hAPP(hAPP(c_List_Olist__update(_1686621, _1686625), _1686615), _1686629)))], (42433 ^ _779142) ^ [_1624738, _1624740, _1624742, _1624744] : [hBOOL(hAPP(c_List_Odistinct(_1624738), _1624740)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624738, _1624742)), hAPP(hAPP(c_List_Ozip(_1624738, _1624742), _1624740), _1624744))))], (43195 ^ _779142) ^ [_1640993, _1640995, _1640997] : [-(hAPP(hAPP(c_List_Oappend(_1640993), _1640995), _1640997) = c_List_Olist_ONil(_1640993)), _1640995 = c_List_Olist_ONil(_1640993), _1640997 = c_List_Olist_ONil(_1640993)], (11606 ^ _779142) ^ [_978822, _978824, _978826] : [class_Rings_Oordered__cancel__semiring(_978822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978822), c_Groups_Ozero__class_Ozero(_978822)), _978824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978822), c_Groups_Ozero__class_Ozero(_978822)), _978826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978822), c_Groups_Ozero__class_Ozero(_978822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978822), _978824), _978826))))], (1726 ^ _779142) ^ [_803659, _803661] : [-(class_Groups_Osemigroup__add(_803659)), _803661 = _803659, class_Groups_Osemigroup__add(_803661)], (21324 ^ _779142) ^ [_1154019, _1154021, _1154023, _1154025] : [class_Rings_Ocomm__semiring__1(_1154019), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154019), hAPP(hAPP(c_Power_Opower__class_Opower(_1154019), _1154021), _1154023)), hAPP(hAPP(c_Power_Opower__class_Opower(_1154019), _1154021), _1154025)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1154019), _1154021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1154023), _1154025)))], (39336 ^ _779142) ^ [_1543706, _1543708, _1543710, _1543712] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543706), _1543708)), 39342 ^ _779142 : [(39345 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543710), hAPP(_1543712, 39341 ^ [_1543706, _1543708, _1543710, _1543712])))], (39343 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543706), 39341 ^ [_1543706, _1543708, _1543710, _1543712]), _1543708)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543710), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1543706, tc_fun(_1543710, tc_HOL_Obool)), _1543708), _1543712))))], (40988 ^ _779142) ^ [_1583962, _1583964, _1583966, _1583968, _1583970, _1583972] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583962, _1583962)), hAPP(hAPP(c_Product__Type_OPair(_1583962, _1583962), _1583964), _1583966)), _1583968)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583962, _1583962)), hAPP(hAPP(c_Product__Type_OPair(_1583962, _1583962), _1583966), _1583970)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583962, _1583962), tc_HOL_Obool), _1583972), _1583968))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583962, _1583962)), hAPP(hAPP(c_Product__Type_OPair(_1583962, _1583962), _1583964), _1583970)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583962, _1583962), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583972)), _1583968))))], (52343 ^ _779142) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (35894 ^ _779142) ^ [_1452357, _1452359, _1452361, _1452363, _1452365] : [c_Equiv__Relations_Oequiv(_1452357, _1452359, _1452361), hBOOL(hAPP(hAPP(c_member(tc_prod(_1452357, _1452357)), hAPP(hAPP(c_Product__Type_OPair(_1452357, _1452357), _1452363), _1452365)), _1452361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452357, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452357, _1452357, _1452361), hAPP(hAPP(c_Set_Oinsert(_1452357), _1452363), c_Orderings_Obot__class_Obot(tc_fun(_1452357, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1452357, _1452357, _1452361), hAPP(hAPP(c_Set_Oinsert(_1452357), _1452365), c_Orderings_Obot__class_Obot(tc_fun(_1452357, tc_HOL_Obool)))))))], (34939 ^ _779142) ^ [_1427804, _1427806, _1427808, _1427810] : [-(hAPP(c_Set_Oimage(_1427804, _1427806, _1427808), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427804, tc_HOL_Obool), _1427810)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1427804, tc_HOL_Obool), tc_fun(_1427806, tc_HOL_Obool)), _1427810), c_Set_Oimage(_1427804, _1427806, _1427808)))], (35127 ^ _779142) ^ [_1432453, _1432455, _1432457, _1432459, _1432461, _1432463] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432453, tc_fun(_1432455, tc_HOL_Obool)), _1432457), hAPP(hAPP(c_COMBC(_1432453, tc_fun(_1432459, tc_fun(_1432455, tc_HOL_Obool)), tc_fun(_1432455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432459, tc_HOL_Obool), tc_fun(tc_fun(_1432459, tc_fun(_1432455, tc_HOL_Obool)), tc_fun(_1432455, tc_HOL_Obool)), _1432453), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432459, tc_fun(_1432455, tc_HOL_Obool))), _1432461)), _1432463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432459, tc_fun(_1432455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432453, tc_fun(_1432459, tc_HOL_Obool)), _1432457), _1432461)), _1432463))], (49090 ^ _779142) ^ [_1771615, _1771617] : [c_Equiv__Relations_Oequivp(_1771615, _1771617), 49093 ^ _779142 : [(49098 ^ _779142) ^ [] : [-(c_Predicate_Otransp(_1771615, _1771617))], (49096 ^ _779142) ^ [] : [-(c_Predicate_Osymp(_1771615, _1771617))], (49094 ^ _779142) ^ [] : [-(c_Predicate_Oreflp(_1771615, _1771617))]]], (22805 ^ _779142) ^ [_1180822, _1180824, _1180826] : [class_Groups_Ogroup__add(_1180822), 22808 ^ _779142 : [(22815 ^ _779142) ^ [] : [_1180826 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180822), _1180824), -(_1180824 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180822), _1180826))], (22809 ^ _779142) ^ [] : [_1180824 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180822), _1180826), -(_1180826 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180822), _1180824))]]], (42644 ^ _779142) ^ [_1629201, _1629203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1629201), _1629203)), -(c_List_Oupto(_1629203, _1629201) = c_List_Olist_ONil(tc_Int_Oint))], (48460 ^ _779142) ^ [_1756342, _1756344, _1756346, _1756348, _1756350, _1756352] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756342, _1756344, _1756346, _1756348, c_Lazy__Sequence_Olazy__sequence_OInsert(_1756344, _1756350, _1756352)) = hAPP(hAPP(_1756348, _1756350), _1756352))], (25698 ^ _779142) ^ [_1230774, _1230776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1230774)), c_Int_OBit1(_1230776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230774), _1230776)))], (30874 ^ _779142) ^ [_1332365] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1332365, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1332365, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1332365, tc_HOL_Obool)))], (3328 ^ _779142) ^ [_828736, _828738, _828740, _828742] : [-(c_Enum_Oenum__the(_828742, _828738) = c_Enum_Oenum__the(_828740, _828736)), _828742 = _828740, _828738 = _828736], (29151 ^ _779142) ^ [_1296092, _1296094] : [class_Lattices_Osemilattice__inf(_1296092), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296092), _1296094), _1296094) = _1296094)], (52715 ^ _779142) ^ [_1837090] : [-(hBOOL(_1837090)), -(hBOOL(hAPP(c_fNot, _1837090)))], (44911 ^ _779142) ^ [_1679408, _1679410] : [-(hBOOL(hAPP(c_List_Olistsp(_1679408, _1679410), c_List_Olist_ONil(_1679408))))], (52237 ^ _779142) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (18595 ^ _779142) ^ [_1106584, _1106586] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106584, _1106586)) = _1106586, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1106584), _1106586) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17675 ^ _779142) ^ [_1090494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090494)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (48699 ^ _779142) ^ [_1761638, _1761640, _1761642, _1761644] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761638, _1761640, _1761642, c_Code__Numeral_OSuc__code__numeral(_1761644)) = hAPP(hAPP(_1761642, _1761644), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761638, _1761640, _1761642, _1761644)))], (44466 ^ _779142) ^ [_1669566, _1669568, _1669570, _1669572, _1669574] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669566), tc_List_Olist(_1669568), tc_List_Olist(_1669570), hAPP(c_List_Omap(_1669566, _1669568), _1669572)), hAPP(c_List_Omap(_1669570, _1669566), _1669574)) = hAPP(c_List_Omap(_1669570, _1669568), hAPP(c_Fun_Ocomp(_1669566, _1669568, _1669570, _1669572), _1669574)))], (41026 ^ _779142) ^ [_1585015, _1585017, _1585019] : [c_Relation_Osingle__valued(_1585015, _1585017, _1585019), 41029 ^ _779142 : [(41030 ^ _779142) ^ [_1585136, _1585138] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585015, _1585017)), hAPP(hAPP(c_Product__Type_OPair(_1585015, _1585017), _1585138), _1585136)), _1585019)), 41033 ^ _779142 : [(41034 ^ _779142) ^ [_1585262] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585015, _1585017)), hAPP(hAPP(c_Product__Type_OPair(_1585015, _1585017), _1585138), _1585262)), _1585019)), -(_1585136 = _1585262)]]]]], (37517 ^ _779142) ^ [_1489443, _1489445, _1489447, _1489449] : [hAPP(hAPP(c_Product__Type_OSigma(_1489443, _1489445), _1489447), hAPP(c_COMBK(tc_fun(_1489445, tc_HOL_Obool), _1489443), _1489449)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489443, _1489445), tc_HOL_Obool)), -(_1489447 = c_Orderings_Obot__class_Obot(tc_fun(_1489443, tc_HOL_Obool))), -(_1489449 = c_Orderings_Obot__class_Obot(tc_fun(_1489445, tc_HOL_Obool)))], (18965 ^ _779142) ^ [_1112601, _1112603] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112601), _1112603) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 18966 ^ _779142 : [(18973 ^ _779142) ^ [] : [_1112601 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1112603 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (18967 ^ _779142) ^ [] : [_1112601 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1112603 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (31632 ^ _779142) ^ [_1347082, _1347084] : [31633 ^ _779142 : [(31636 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1347084), _1347082))], (31634 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1347082), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1347082, _1347084) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (22446 ^ _779142) ^ [_1174119, _1174121] : [22448 ^ _779142 : [(22451 ^ _779142) ^ [] : [hBOOL(hAPP(_1174121, 22447 ^ [_1174119, _1174121]))], (22449 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 22447 ^ [_1174119, _1174121]), _1174119)))]], 22452 ^ _779142 : [(22453 ^ _779142) ^ [_1174270] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1174270), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1174119))), -(hBOOL(hAPP(_1174121, _1174270)))]]], (16747 ^ _779142) ^ [_1073821, _1073823] : [class_Orderings_Olinorder(_1073821), -(c_Big__Operators_Olattice_OInf__fin(_1073821, c_Orderings_Oord__class_Omin(_1073821), hAPP(hAPP(c_Set_Oinsert(_1073821), _1073823), c_Orderings_Obot__class_Obot(tc_fun(_1073821, tc_HOL_Obool)))) = _1073823)], (9400 ^ _779142) ^ [_939366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _939366) = _939366)], (18186 ^ _779142) ^ [_1099283, _1099285] : [class_Rings_Olinordered__semidom(_1099283), 18189 ^ _779142 : [(18196 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099283), c_Groups_Ozero__class_Ozero(_1099283)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099283), _1099285))))], (18190 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099283), c_Groups_Ozero__class_Ozero(_1099283)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099283), _1099285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099285)))]]], (24682 ^ _779142) ^ [_1213194, _1213196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213194), _1213196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1213194)), c_Int_OBit1(_1213196))))], (43754 ^ _779142) ^ [_1654301, _1654303, _1654305] : [hBOOL(hAPP(c_List_Odistinct(_1654301), _1654305)), -(hBOOL(hAPP(c_List_Odistinct(_1654301), hAPP(c_List_Orotate(_1654301, _1654303), _1654305))))], (26358 ^ _779142) ^ [_1242688, _1242690, _1242692, _1242694] : [hBOOL(hAPP(hAPP(c_member(_1242688), _1242690), _1242692)), -(hBOOL(hAPP(hAPP(c_member(_1242688), _1242690), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242688, tc_HOL_Obool)), _1242692), _1242694))))], (9360 ^ _779142) ^ [_938765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938765), _938765))))], (33322 ^ _779142) ^ [_1389137, _1389139, _1389141] : [33324 ^ _779142 : [(33327 ^ _779142) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1389137, _1389139), 33323 ^ [_1389137, _1389139, _1389141]))], (33325 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1389139, 33323 ^ [_1389137, _1389139, _1389141]), _1389141)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1389137, _1389139), _1389141)))], (48911 ^ _779142) ^ [_1766777, _1766779, _1766781, _1766783] : [c_Relation_Otrans(_1766777, _1766779), -(c_Relation_Otrans(_1766781, hAPP(hAPP(c_Relation_Oinv__image(_1766777, _1766781), _1766779), _1766783)))], (28068 ^ _779142) ^ [_1275039] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1275039) = c_Orderings_Oord__class_Omax(_1275039)), class_Lattices_Osemilattice__sup(_1275039), class_Orderings_Olinorder(_1275039)], (9239 ^ _779142) ^ [_936687, _936689, _936691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936687), _936689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936687), _936691)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936689), _936691))))], (30978 ^ _779142) ^ [_1334165, _1334167] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334165, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1334165, tc_HOL_Obool)), _1334167)), _1334167) = c_Orderings_Otop__class_Otop(tc_fun(_1334165, tc_HOL_Obool)))], (48487 ^ _779142) ^ [_1757003, _1757005, _1757007, _1757009] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757003), hAPP(hAPP(c_List_Olist_OCons(_1757003), _1757005), _1757007)), _1757009)), -(_1757005 = _1757009), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757003), _1757007), _1757009)))], (38899 ^ _779142) ^ [_1532760, _1532762, _1532764, _1532766, _1532768] : [c_Relation_Orefl__on(_1532760, _1532762, _1532764), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532760, _1532760)), hAPP(hAPP(c_Product__Type_OPair(_1532760, _1532760), _1532766), _1532768)), _1532764)), -(hBOOL(hAPP(hAPP(c_member(_1532760), _1532768), _1532762)))], (31919 ^ _779142) ^ [_1354594, _1354596, _1354598] : [_1354596 = _1354598, -(hAPP(hAPP(c_COMBC(_1354594, tc_fun(_1354594, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354594)), _1354596) = hAPP(hAPP(c_COMBC(_1354594, tc_fun(_1354594, tc_HOL_Obool), tc_HOL_Obool), c_member(_1354594)), _1354598))], (30152 ^ _779142) ^ [_1317608, _1317610, _1317612, _1317614, _1317616] : [class_Fields_Ofield(_1317608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317610), _1317612)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317610), _1317614)), 30166 ^ _779142 : [(30169 ^ _779142) ^ [] : [-(hAPP(_1317616, 30165 ^ [_1317608, _1317610, _1317612, _1317614, _1317616]) = c_Groups_Ozero__class_Ozero(_1317608))], (30167 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317610), 30165 ^ [_1317608, _1317610, _1317612, _1317614, _1317616]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317610, tc_HOL_Obool)), _1317612), _1317614))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317610, _1317608), _1317616), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317610, tc_HOL_Obool)), _1317612), _1317614)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317608), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317610, _1317608), _1317616), _1317612)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317610, _1317608), _1317616), _1317614))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317610, _1317608), _1317616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317610, tc_HOL_Obool)), _1317612), _1317614))))], (7254 ^ _779142) ^ [_899676, _899678, _899680, _899682, _899684, _899686] : [c_Finite__Set_Ofun__left__comm(_899676, _899678, _899680), -(hAPP(hAPP(_899680, _899682), hAPP(hAPP(_899680, _899684), _899686)) = hAPP(hAPP(_899680, _899684), hAPP(hAPP(_899680, _899682), _899686)))], (46042 ^ _779142) ^ [_1705618, _1705620, _1705622, _1705624, _1705626] : [class_Orderings_Olinorder(_1705618), hBOOL(hAPP(hAPP(c_member(_1705620), _1705622), hAPP(c_List_Oset(_1705620), _1705624))), c_List_Olinorder__class_Osorted(_1705618, hAPP(hAPP(c_List_Omap(_1705620, _1705618), _1705626), _1705624)), hAPP(c_List_Ohd(_1705620), hAPP(c_List_Ofilter(_1705620, hAPP(hAPP(c_COMBB(_1705618, tc_HOL_Obool, _1705620), hAPP(c_fequal, hAPP(_1705626, _1705622))), _1705626)), _1705624)) = _1705622, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705620, _1705618, _1705626), _1705622), c_List_Oremove1(_1705620, _1705622, _1705624)) = _1705624)], (6952 ^ _779142) ^ [_893060, _893062, _893064, _893066] : [-(hBOOL(hAPP(hAPP(c_member(_893060), _893062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893060, tc_HOL_Obool)), _893064), _893066)))), hBOOL(hAPP(hAPP(c_member(_893060), _893062), _893064)), -(hBOOL(hAPP(hAPP(c_member(_893060), _893062), _893066)))], (3352 ^ _779142) ^ [_829106, _829108, _829110, _829112, _829114, _829116] : [-(c_Enum_On__lists(_829116, _829112, _829108) = c_Enum_On__lists(_829114, _829110, _829106)), _829116 = _829114, _829112 = _829110, _829108 = _829106], (7412 ^ _779142) ^ [_901842, _901844, _901846] : [class_Orderings_Oorder(_901842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901842), _901844), _901846)), _901844 = _901846], (20740 ^ _779142) ^ [_1143632, _1143634] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143632), _1143634)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1143632)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1143634)))], (49272 ^ _779142) ^ [_1775462, _1775464, _1775466, _1775468] : [c_Relation_Osym(_1775462, _1775464), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775462, _1775462)), hAPP(hAPP(c_Product__Type_OPair(_1775462, _1775462), _1775466), _1775468)), _1775464)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775462, _1775462)), hAPP(hAPP(c_Product__Type_OPair(_1775462, _1775462), _1775468), _1775466)), _1775464)))], (31731 ^ _779142) ^ [_1348751, _1348753, _1348755, _1348757] : [class_Groups_Oordered__ab__group__add__abs(_1348751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348751), c_Groups_Ozero__class_Ozero(_1348751)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348753, _1348751), hAPP(hAPP(c_COMBB(_1348751, _1348751, _1348753), c_Groups_Oabs__class_Oabs(_1348751)), _1348755)), _1348757))))], (34298 ^ _779142) ^ [_1408950, _1408952, _1408954, _1408956] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1408954), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408950, tc_fun(_1408954, tc_HOL_Obool)), _1408952), _1408956)))), 34299 ^ _779142 : [(34300 ^ _779142) ^ [_1409024] : [hBOOL(hAPP(hAPP(c_member(_1408950), _1409024), _1408952)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408954), hAPP(_1408956, _1409024)))]]], (12686 ^ _779142) ^ [_998294, _998296, _998298, _998300, _998302] : [class_Rings_Olinordered__semiring__strict(_998294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998294), _998296), _998298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998294), _998300), _998302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998294), c_Groups_Ozero__class_Ozero(_998294)), _998298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998294), c_Groups_Ozero__class_Ozero(_998294)), _998300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998294), _998296), _998300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998294), _998298), _998302))))], (42614 ^ _779142) ^ [_1628708] : [-(c_List_Obutlast(_1628708, c_List_Olist_ONil(_1628708)) = c_List_Olist_ONil(_1628708))], (30782 ^ _779142) ^ [_1330706, _1330708] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1330706, _1330708)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1330706, _1330708), tc_HOL_Obool)))), 30785 ^ _779142 : [(30788 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330708), c_Orderings_Otop__class_Otop(tc_fun(_1330708, tc_HOL_Obool)))))], (30786 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330706), c_Orderings_Otop__class_Otop(tc_fun(_1330706, tc_HOL_Obool)))))]]], (20123 ^ _779142) ^ [_1132376, _1132378, _1132380] : [class_Divides_Osemiring__div(_1132376), -(_1132378 = c_Groups_Ozero__class_Ozero(_1132376)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132376), _1132378), _1132380)), _1132378) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132376), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132376), _1132380), _1132378)), c_Groups_Oone__class_Oone(_1132376)))], (41856 ^ _779142) ^ [_1609325, _1609327, _1609329, _1609331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609325), tc_List_Olist(_1609325))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609325), tc_List_Olist(_1609325)), _1609327), _1609329)), c_List_Olexord(_1609325, _1609331))), 41861 ^ _779142 : [(41864 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609325)), _1609327)), _1609329) = _1609327)], (41862 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609325)), _1609327)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609325)), _1609329))))]], 41866 ^ _779142 : [(41871 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609325, _1609325)), hAPP(hAPP(c_Product__Type_OPair(_1609325, _1609325), hAPP(hAPP(c_List_Onth(_1609325), _1609327), 41865 ^ [_1609325, _1609327, _1609329, _1609331])), hAPP(hAPP(c_List_Onth(_1609325), _1609329), 41865 ^ [_1609325, _1609327, _1609329, _1609331]))), _1609331)))], (41869 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609325), 41865 ^ [_1609325, _1609327, _1609329, _1609331]), _1609327) = hAPP(hAPP(c_List_Otake(_1609325), 41865 ^ [_1609325, _1609327, _1609329, _1609331]), _1609329))], (41867 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41865 ^ [_1609325, _1609327, _1609329, _1609331]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609325)), _1609327)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609325)), _1609329)))))]]], (43550 ^ _779142) ^ [_1649693, _1649695, _1649697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649693)), _1649695)), _1649697)), -(hAPP(hAPP(c_List_Odrop(_1649693), _1649697), _1649695) = c_List_Olist_ONil(_1649693))], (644 ^ _779142) ^ [_788828, _788830, _788832, _788834] : [-(c_FunDef_Ois__measure(_788832, _788828)), c_FunDef_Ois__measure(_788834, _788830), _788834 = _788832, _788830 = _788828], (40717 ^ _779142) ^ [_1577277, _1577279, _1577281, _1577283, _1577285] : [-(hAPP(c_Relation_Oconverse(_1577277, _1577279), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577281, tc_fun(tc_prod(_1577277, _1577279), tc_HOL_Obool)), _1577283), _1577285)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577281, tc_fun(tc_prod(_1577279, _1577277), tc_HOL_Obool)), _1577283), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1577277, _1577279), tc_HOL_Obool), tc_fun(tc_prod(_1577279, _1577277), tc_HOL_Obool), _1577281), c_Relation_Oconverse(_1577277, _1577279)), _1577285)))], (24860 ^ _779142) ^ [_1216255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1216255)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216255), c_Int_OMin)))], (52333 ^ _779142) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (5712 ^ _779142) ^ [_869392, _869394, _869396, _869398, _869400] : [hBOOL(hAPP(hAPP(c_member(_869392), _869394), _869396)), -(hAPP(hAPP(c_Set_Oinsert(_869398), hAPP(_869400, _869394)), hAPP(c_Set_Oimage(_869392, _869398, _869400), _869396)) = hAPP(c_Set_Oimage(_869392, _869398, _869400), _869396))], (43506 ^ _779142) ^ [_1648733, _1648735, _1648737] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648733)), hAPP(hAPP(c_List_Odrop(_1648733), _1648735), _1648737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648733)), _1648737)), _1648735))], (4228 ^ _779142) ^ [_843100, _843102, _843104, _843106, _843108, _843110] : [-(c_List_Oreplicate(_843110, _843106, _843102) = c_List_Oreplicate(_843108, _843104, _843100)), _843110 = _843108, _843106 = _843104, _843102 = _843100], (40699 ^ _779142) ^ [_1576915, _1576917, _1576919, _1576921, _1576923] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576915, _1576917)), hAPP(hAPP(c_Product__Type_OPair(_1576915, _1576917), _1576919), _1576921)), hAPP(c_Relation_Oconverse(_1576917, _1576915), _1576923))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576917, _1576915)), hAPP(hAPP(c_Product__Type_OPair(_1576917, _1576915), _1576921), _1576919)), _1576923)))], (24025 ^ _779142) ^ [_1202180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202180)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202180) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Int_Onat, _1202180))))], (48082 ^ _779142) ^ [_1748282, _1748284, _1748286, _1748288] : [-(c_Predicate_Oconversep(_1748282, _1748284, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748282, tc_fun(_1748284, tc_HOL_Obool))), _1748286), _1748288)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748284, tc_fun(_1748282, tc_HOL_Obool))), c_Predicate_Oconversep(_1748282, _1748284, _1748286)), c_Predicate_Oconversep(_1748282, _1748284, _1748288)))], (10825 ^ _779142) ^ [_966035, _966037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966035)), _966037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966035), _966037)))], (42102 ^ _779142) ^ [_1616985, _1616987, _1616989, _1616991] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1616985, _1616987))), hAPP(hAPP(c_List_Ozip(_1616985, _1616987), _1616989), _1616991)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616985)), _1616989)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616987)), _1616991)))], (25596 ^ _779142) ^ [_1228995, _1228997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228995), _1228997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228995)), c_Int_OBit0(_1228997))))], (46686 ^ _779142) ^ [_1717782, _1717784, _1717786, _1717788, _1717790] : [-(hAPP(c_List_Ofoldl(_1717782, _1717784, _1717786, _1717788), _1717790) = c_List_Ofoldr(_1717784, _1717782, hAPP(c_COMBC(_1717782, _1717784, _1717782), _1717786), hAPP(c_List_Orev(_1717784), _1717790), _1717788))], (49967 ^ _779142) ^ [_1789607, _1789609, _1789611, _1789613, _1789615, _1789617] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1789607, _1789609, _1789611, _1789613), _1789615), _1789617) = hAPP(_1789613, hAPP(hAPP(c_Product__Type_OPair(_1789607, _1789609), _1789615), _1789617)))], (2622 ^ _779142) ^ [_817771, _817773] : [_817773 = _817771, -(c_Int_Oint__ge__less__than2(_817773) = c_Int_Oint__ge__less__than2(_817771))], (3680 ^ _779142) ^ [_834270, _834272, _834274, _834276] : [-(c_List_Olex(_834276, _834272) = c_List_Olex(_834274, _834270)), _834276 = _834274, _834272 = _834270], (29544 ^ _779142) ^ [_1304880, _1304882, _1304884, _1304886] : [class_Orderings_Oorder(_1304880), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304880, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1304880, _1304882, _1304884)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1304880, _1304884, _1304886)) = c_Orderings_Obot__class_Obot(tc_fun(_1304880, tc_HOL_Obool)))], (39133 ^ _779142) ^ [_1538276, _1538278] : [c_Wellfounded_Owf(_1538276, _1538278), -(c_Wellfounded_OwfP(_1538276, hAPP(hAPP(c_COMBC(_1538276, tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_fun(_1538276, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538276, tc_fun(tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_fun(_1538276, tc_HOL_Obool)), _1538276), c_COMBC(_1538276, tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538276, tc_prod(_1538276, _1538276)), tc_fun(_1538276, tc_fun(tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_HOL_Obool)), _1538276), hAPP(c_COMBB(tc_prod(_1538276, _1538276), tc_fun(tc_fun(tc_prod(_1538276, _1538276), tc_HOL_Obool), tc_HOL_Obool), _1538276), c_member(tc_prod(_1538276, _1538276)))), c_Product__Type_OPair(_1538276, _1538276)))), _1538278)))], (38094 ^ _779142) ^ [_1508333, _1508335, _1508337] : [class_Lattices_Odistrib__lattice(_1508333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508333), _1508335)), -(_1508335 = c_Orderings_Obot__class_Obot(tc_fun(_1508333, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508333), _1508337)), -(_1508337 = c_Orderings_Obot__class_Obot(tc_fun(_1508333, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1508333), c_Big__Operators_Olattice__class_OInf__fin(_1508333, _1508335)), c_Big__Operators_Olattice__class_OInf__fin(_1508333, _1508337)) = c_Big__Operators_Olattice__class_OInf__fin(_1508333, hAPP(c_Set_OCollect(_1508333), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_HOL_Obool), tc_HOL_Obool, _1508333), c_HOL_OEx(_1508333)), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool)), tc_fun(_1508333, tc_HOL_Obool), _1508333), hAPP(c_COMBB(tc_fun(_1508333, tc_HOL_Obool), tc_HOL_Obool, _1508333), c_HOL_OEx(_1508333))), hAPP(hAPP(c_COMBC(_1508333, tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool)), tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_fun(tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool))), tc_fun(tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool)), tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool))), _1508333), c_COMBS(_1508333, tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_fun(_1508333, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1508333, tc_fun(tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool))), _1508333), hAPP(c_COMBB(tc_fun(_1508333, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool)), _1508333), c_COMBS(_1508333, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool)), tc_fun(_1508333, tc_fun(_1508333, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1508333), hAPP(c_COMBB(tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1508333), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508333), c_fconj))), hAPP(hAPP(c_COMBC(_1508333, tc_fun(_1508333, tc_fun(_1508333, _1508333)), tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1508333, _1508333), tc_fun(_1508333, tc_HOL_Obool)), tc_fun(tc_fun(_1508333, tc_fun(_1508333, _1508333)), tc_fun(_1508333, tc_fun(_1508333, tc_HOL_Obool))), _1508333), c_COMBB(tc_fun(_1508333, _1508333), tc_fun(_1508333, tc_HOL_Obool), _1508333)), hAPP(hAPP(c_COMBB(tc_fun(_1508333, tc_HOL_Obool), tc_fun(tc_fun(_1508333, _1508333), tc_fun(_1508333, tc_HOL_Obool)), _1508333), c_COMBB(_1508333, tc_HOL_Obool, _1508333)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1508333)))))), hAPP(hAPP(c_COMBC(_1508333, tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1508333, tc_HOL_Obool), tc_fun(_1508333, tc_HOL_Obool)), _1508333), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508333)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508333), c_fconj), hAPP(hAPP(c_COMBC(_1508333, tc_fun(_1508333, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508333)), _1508335)))), hAPP(hAPP(c_COMBC(_1508333, tc_fun(_1508333, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508333)), _1508337))))))))], (38044 ^ _779142) ^ [_1506234, _1506236, _1506238, _1506240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506234), hAPP(c_Set_OCollect(_1506234), _1506236))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506238), hAPP(c_Set_OCollect(_1506238), hAPP(hAPP(c_COMBB(tc_fun(_1506234, tc_HOL_Obool), tc_HOL_Obool, _1506238), c_HOL_OEx(_1506234)), hAPP(hAPP(c_COMBC(_1506238, tc_fun(_1506234, tc_HOL_Obool), tc_fun(_1506234, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506234, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506234, tc_HOL_Obool), tc_fun(_1506234, tc_HOL_Obool)), _1506238), c_COMBS(_1506234, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506234, tc_HOL_Obool), tc_fun(_1506234, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506238), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506234), c_fconj)), hAPP(hAPP(c_COMBC(_1506238, tc_fun(_1506234, _1506238), tc_fun(_1506234, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506238, tc_HOL_Obool), tc_fun(tc_fun(_1506234, _1506238), tc_fun(_1506234, tc_HOL_Obool)), _1506238), c_COMBB(_1506238, tc_HOL_Obool, _1506234)), c_fequal)), _1506240)))), _1506236))))))], (6403 ^ _779142) ^ [_881710, _881712, _881714, _881716, _881718] : [class_Orderings_Oord(_881710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881712, _881710)), _881714), _881716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881710), hAPP(_881714, _881718)), hAPP(_881716, _881718))))], (7972 ^ _779142) ^ [_910399, _910401, _910403] : [7973 ^ _779142 : [(7976 ^ _779142) ^ [] : [_910401 = _910403], (7974 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910399, tc_HOL_Obool)), _910401), _910403))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910399, tc_HOL_Obool)), _910401), _910403)))], (20103 ^ _779142) ^ [_1132020, _1132022, _1132024, _1132026] : [class_Divides_Osemiring__div(_1132020), -(_1132022 = c_Groups_Ozero__class_Ozero(_1132020)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132020), _1132024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132020), _1132026), _1132022))), _1132022) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132020), _1132026), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132020), _1132024), _1132022)))], (10651 ^ _779142) ^ [_963194, _963196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963196), _963194))))], (46969 ^ _779142) ^ [_1723834, _1723836, _1723838] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723834)), c_List_OdropWhile(_1723834, _1723836, _1723838))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723834)), _1723838))))], (45420 ^ _779142) ^ [_1690611, _1690613, _1690615, _1690617] : [-(_1690611 = _1690613), -(hAPP(c_List_OremoveAll(_1690615, _1690611), hAPP(hAPP(c_List_Olist_OCons(_1690615), _1690613), _1690617)) = hAPP(hAPP(c_List_Olist_OCons(_1690615), _1690613), hAPP(c_List_OremoveAll(_1690615, _1690611), _1690617)))], (45859 ^ _779142) ^ [_1701999, _1702001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701999), _1702001)), -(c_List_Oupt(_1701999, hAPP(c_Nat_OSuc, _1702001)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701999, _1702001)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702001), c_List_Olist_ONil(tc_Nat_Onat))))], (20652 ^ _779142) ^ [_1141929, _1141931, _1141933, _1141935, _1141937, _1141939] : [hBOOL(hAPP(hAPP(c_member(_1141929), _1141931), c_SetInterval_Oord_OatLeastLessThan(_1141929, _1141933, _1141935, _1141937, _1141939))), 20655 ^ _779142 : [(20658 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1141935, _1141931), _1141939)))], (20656 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1141933, _1141937), _1141931)))]]], (39078 ^ _779142) ^ [_1537144, _1537146] : [c_Wellfounded_OwfP(_1537144, _1537146), -(c_Wellfounded_Owf(_1537144, hAPP(c_Set_OCollect(tc_prod(_1537144, _1537144)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537144, _1537144, tc_HOL_Obool), _1537146))))], (28557 ^ _779142) ^ [_1283979, _1283981, _1283983] : [class_Orderings_Olinorder(_1283979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283979), _1283981)), -(_1283983 = c_Orderings_Obot__class_Obot(tc_fun(_1283979, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283979, tc_HOL_Obool)), _1283983), _1283981)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1283979), c_Big__Operators_Olattice_OSup__fin(_1283979, c_Orderings_Oord__class_Omax(_1283979), _1283983)), c_Big__Operators_Olattice_OSup__fin(_1283979, c_Orderings_Oord__class_Omax(_1283979), _1283981)) = c_Big__Operators_Olattice_OSup__fin(_1283979, c_Orderings_Oord__class_Omax(_1283979), _1283981))], (21434 ^ _779142) ^ [_1155853, _1155855, _1155857, _1155859] : [class_Orderings_Oorder(_1155853), 21437 ^ _779142 : [(21446 ^ _779142) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1155853, _1155855, _1155857) = hAPP(hAPP(c_Set_Oinsert(_1155853), _1155859), c_Orderings_Obot__class_Obot(tc_fun(_1155853, tc_HOL_Obool)))), _1155855 = _1155857, _1155857 = _1155859], (21438 ^ _779142) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1155853, _1155855, _1155857) = hAPP(hAPP(c_Set_Oinsert(_1155853), _1155859), c_Orderings_Obot__class_Obot(tc_fun(_1155853, tc_HOL_Obool))), 21441 ^ _779142 : [(21444 ^ _779142) ^ [] : [-(_1155857 = _1155859)], (21442 ^ _779142) ^ [] : [-(_1155855 = _1155857)]]]]], (10023 ^ _779142) ^ [_950779, _950781, _950783, _950785, _950787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950779), _950781)), 10026 ^ _779142 : [(10033 ^ _779142) ^ [] : [_950785 = 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), _950781), _950779)), _950783)), _950787), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950779), _950783)), _950785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950781), _950783)), _950787))], (10027 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950779), _950783)), _950785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950781), _950783)), _950787), -(_950785 = 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), _950781), _950779)), _950783)), _950787))]]], (44863 ^ _779142) ^ [_1677860] : [-(_1677860 = 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, _1677860)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1677860))))], (37124 ^ _779142) ^ [_1479617, _1479619, _1479621, _1479623, _1479625] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1479617, _1479619, _1479621), _1479623), _1479625) = c_HOL_OThe(_1479619, c_Finite__Set_Ofold__graph(_1479617, _1479619, _1479621, _1479623, _1479625)))], (45105 ^ _779142) ^ [_1683925, _1683927, _1683929, _1683931, _1683933, _1683935, _1683937] : [c_List_Olist__all2(_1683925, _1683927, _1683929, hAPP(hAPP(c_List_Olist_OCons(_1683925), _1683931), _1683933), hAPP(hAPP(c_List_Olist_OCons(_1683927), _1683935), _1683937)), 45108 ^ _779142 : [(45111 ^ _779142) ^ [] : [-(c_List_Olist__all2(_1683925, _1683927, _1683929, _1683933, _1683937))], (45109 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1683929, _1683931), _1683935)))]]], (14429 ^ _779142) ^ [_1030618, _1030620, _1030622, _1030624] : [class_Fields_Olinordered__field__inverse__zero(_1030618), 14432 ^ _779142 : [(14433 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1030618), _1030620), _1030622)), _1030624)), 14436 ^ _779142 : [(14443 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030622))), 14446 ^ _779142 : [(14453 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030622), c_Groups_Ozero__class_Ozero(_1030618)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030624)))], (14447 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030622), c_Groups_Ozero__class_Ozero(_1030618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030618), _1030624), _1030622)), _1030620)))]]], (14437 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030618), _1030624), _1030622))))]]], (14459 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1030618), _1030620), _1030622)), _1030624))), 14462 ^ _779142 : [(14465 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030618), _1030624), _1030622)))], (14463 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030622)))]], 14466 ^ _779142 : [(14469 ^ _779142) ^ [] : [14470 ^ _779142 : [(14473 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030618), _1030624), _1030622)), _1030620))], (14471 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030622), c_Groups_Ozero__class_Ozero(_1030618))))]], 14474 ^ _779142 : [(14477 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030624))], (14475 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), _1030622), c_Groups_Ozero__class_Ozero(_1030618)))]]], (14467 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030618), c_Groups_Ozero__class_Ozero(_1030618)), _1030622))]]]]], (8386 ^ _779142) ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005] : [c_Nitpick_Ofold__graph_H(_918993, _918995, _918997, _918999, _919001, hAPP(hAPP(_918997, _919003), _919005)), 8391 ^ _779142 : [(8394 ^ _779142) ^ [] : [-(hAPP(hAPP(_918997, _919003), _919005) = _918999)], (8392 ^ _779142) ^ [] : [-(_919001 = c_Orderings_Obot__class_Obot(tc_fun(_918993, tc_HOL_Obool)))]], 8397 ^ _779142 : [(8402 ^ _779142) ^ [] : [-(c_Nitpick_Ofold__graph_H(_918993, _918995, _918997, _918999, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918993, tc_HOL_Obool)), _919001), hAPP(hAPP(c_Set_Oinsert(_918993), 8395 ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005]), c_Orderings_Obot__class_Obot(tc_fun(_918993, tc_HOL_Obool)))), 8396 ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005]))], (8400 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918993), 8395 ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005]), _919001)))], (8398 ^ _779142) ^ [] : [-(hAPP(hAPP(_918997, _919003), _919005) = hAPP(hAPP(_918997, 8395 ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005]), 8396 ^ [_918993, _918995, _918997, _918999, _919001, _919003, _919005]))]]], (35470 ^ _779142) ^ [_1441974, _1441976, _1441978, _1441980, _1441982] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441974, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1441976, _1441974, _1441978), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441976, tc_HOL_Obool)), _1441980), _1441982))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441974, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1441976, _1441974, _1441978), _1441980)), hAPP(c_Relation_OImage(_1441976, _1441974, _1441978), _1441982)))))], (31931 ^ _779142) ^ [_1355305, _1355307, _1355309, _1355311] : [_1355309 = _1355311, -(hAPP(hAPP(c_COMBC(_1355305, tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_fun(_1355307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355307, tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_fun(_1355307, tc_HOL_Obool)), _1355305), c_COMBC(_1355307, tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355307, tc_prod(_1355305, _1355307)), tc_fun(_1355307, tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), _1355305), hAPP(c_COMBB(tc_prod(_1355305, _1355307), tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool), _1355307), c_member(tc_prod(_1355305, _1355307)))), c_Product__Type_OPair(_1355305, _1355307)))), _1355309) = hAPP(hAPP(c_COMBC(_1355305, tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_fun(_1355307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355307, tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_fun(_1355307, tc_HOL_Obool)), _1355305), c_COMBC(_1355307, tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355307, tc_prod(_1355305, _1355307)), tc_fun(_1355307, tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool)), _1355305), hAPP(c_COMBB(tc_prod(_1355305, _1355307), tc_fun(tc_fun(tc_prod(_1355305, _1355307), tc_HOL_Obool), tc_HOL_Obool), _1355307), c_member(tc_prod(_1355305, _1355307)))), c_Product__Type_OPair(_1355305, _1355307)))), _1355311))], (43874 ^ _779142) ^ [_1656847] : [class_Groups_Omonoid__add(_1656847), -(c_List_Omonoid__add__class_Olistsum(_1656847) = c_List_Ofoldl(_1656847, _1656847, c_Groups_Oplus__class_Oplus(_1656847), c_Groups_Ozero__class_Ozero(_1656847)))], (37503 ^ _779142) ^ [_1488928, _1488930, _1488932, _1488934] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1488928, _1488930), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1488928, tc_HOL_Obool), _1488932)), _1488934) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1488928, tc_HOL_Obool), tc_fun(tc_prod(_1488928, _1488930), tc_HOL_Obool)), _1488932), hAPP(hAPP(c_COMBC(tc_fun(_1488928, tc_HOL_Obool), tc_fun(_1488928, tc_fun(_1488930, tc_HOL_Obool)), tc_fun(tc_prod(_1488928, _1488930), tc_HOL_Obool)), c_Product__Type_OSigma(_1488928, _1488930)), _1488934)))], (9877 ^ _779142) ^ [_947584, _947586, _947588] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947584), _947586)), -(hBOOL(hAPP(hAPP(c_member(_947584), _947588), _947586))), -(hAPP(c_Finite__Set_Ocard(_947584), hAPP(hAPP(c_Set_Oinsert(_947584), _947588), _947586)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_947584), _947586)))], (48100 ^ _779142) ^ [_1748665, _1748667, _1748669, _1748671, _1748673] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748665, _1748667, _1748669), _1748671), _1748673)), -(hBOOL(hAPP(hAPP(_1748669, _1748673), _1748671)))], (39228 ^ _779142) ^ [_1540161, _1540163, _1540165] : [c_Relation_Orefl__on(_1540161, _1540163, _1540165), 39231 ^ _779142 : [(39238 ^ _779142) ^ [_1540645] : [hBOOL(hAPP(hAPP(c_member(_1540161), _1540645), _1540163)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540161, _1540161)), hAPP(hAPP(c_Product__Type_OPair(_1540161, _1540161), _1540645), _1540645)), _1540165)))], (39232 ^ _779142) ^ [_1540372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540161, _1540161)), _1540372), _1540165)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1540161, _1540161, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540161, tc_fun(_1540161, tc_HOL_Obool), tc_fun(_1540161, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540161, tc_HOL_Obool), tc_fun(_1540161, tc_HOL_Obool)), _1540161), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540161)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540161), c_fconj), hAPP(hAPP(c_COMBC(_1540161, tc_fun(_1540161, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540161)), _1540163)))), hAPP(hAPP(c_COMBC(_1540161, tc_fun(_1540161, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540161)), _1540163))), _1540372)))]]], (22859 ^ _779142) ^ [_1181672, _1181674, _1181676] : [class_Orderings_Olinorder(_1181672), 22862 ^ _779142 : [(22869 ^ _779142) ^ [] : [_1181674 = _1181676, -(hAPP(c_SetInterval_Oord__class_OatMost(_1181672), _1181674) = hAPP(c_SetInterval_Oord__class_OatMost(_1181672), _1181676))], (22863 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1181672), _1181674) = hAPP(c_SetInterval_Oord__class_OatMost(_1181672), _1181676), -(_1181674 = _1181676)]]], (10527 ^ _779142) ^ [_961338] : [hAPP(c_Nat_OSuc, _961338) = _961338], (36670 ^ _779142) ^ [_1469334, _1469336, _1469338, _1469340, _1469342] : [c_Fun_Oinj__on(_1469334, _1469336, _1469338, hAPP(hAPP(c_Set_Oinsert(_1469334), _1469340), _1469342)), 36673 ^ _779142 : [(36676 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1469336), hAPP(_1469338, _1469340)), hAPP(c_Set_Oimage(_1469334, _1469336, _1469338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469334, tc_HOL_Obool)), _1469342), hAPP(hAPP(c_Set_Oinsert(_1469334), _1469340), c_Orderings_Obot__class_Obot(tc_fun(_1469334, tc_HOL_Obool)))))))], (36674 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1469334, _1469336, _1469338, _1469342))]]], (39349 ^ _779142) ^ [_1543993, _1543995] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1543993, tc_HOL_Obool), _1543995) = hAPP(c_Set_OCollect(_1543993), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543993, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1543993), c_HOL_OAll(tc_fun(_1543993, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543993, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1543993, tc_HOL_Obool), tc_HOL_Obool), _1543993), hAPP(c_COMBS(tc_fun(_1543993, 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(_1543993, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1543993, tc_HOL_Obool), tc_fun(tc_fun(_1543993, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1543993, tc_HOL_Obool))), _1543995)))), c_member(_1543993)))))], (34398 ^ _779142) ^ [_1412081, _1412083] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1412081, tc_HOL_Obool), _1412083) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1412081, tc_HOL_Obool), tc_fun(_1412081, tc_HOL_Obool)), _1412083), c_COMBI(tc_fun(_1412081, tc_HOL_Obool))))], (35213 ^ _779142) ^ [_1435011, _1435013, _1435015, _1435017, _1435019] : [35215 ^ _779142 : [(35218 ^ _779142) ^ [] : [hBOOL(hAPP(_1435019, 35214 ^ [_1435011, _1435013, _1435015, _1435017, _1435019]))], (35216 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435011), 35214 ^ [_1435011, _1435013, _1435015, _1435017, _1435019]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435013, tc_fun(_1435011, tc_HOL_Obool)), _1435015), _1435017))))]], 35219 ^ _779142 : [(35220 ^ _779142) ^ [_1435233] : [hBOOL(hAPP(hAPP(c_member(_1435013), _1435233), _1435015)), 35223 ^ _779142 : [(35224 ^ _779142) ^ [_1435330] : [hBOOL(hAPP(hAPP(c_member(_1435011), _1435330), hAPP(_1435017, _1435233))), -(hBOOL(hAPP(_1435019, _1435330)))]]]]], (4868 ^ _779142) ^ [_853260, _853262, _853264, _853266] : [-(c_Quickcheck_Obeyond(_853266, _853262) = c_Quickcheck_Obeyond(_853264, _853260)), _853266 = _853264, _853262 = _853260], (17119 ^ _779142) ^ [_1080281] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080281) = _1080281)], (40821 ^ _779142) ^ [_1579822, _1579824, _1579826, _1579828, _1579830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579824, tc_HOL_Obool)), _1579828), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579824, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579822, _1579824, hAPP(c_Relation_Oconverse(_1579824, _1579822), _1579826)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579822, tc_HOL_Obool)), _1579830))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579822, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579824, _1579822, _1579826), _1579828)), _1579830)))], (49284 ^ _779142) ^ [_1775720, _1775722] : [c_Relation_Osym(_1775720, _1775722), -(c_Relation_Osym(_1775720, c_Transitive__Closure_Ortrancl(_1775720, _1775722)))], (50881 ^ _779142) ^ [_1809571, _1809573] : [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), _1809571, _1809573), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809571), _1809573))], (5922 ^ _779142) ^ [_873038, _873040, _873042] : [-(hBOOL(hAPP(hAPP(c_member(_873038), _873040), hAPP(hAPP(c_Set_Oinsert(_873038), _873040), _873042))))], (46907 ^ _779142) ^ [_1722468, _1722470] : [-(_1722468 = c_List_Olist_ONil(_1722470)), hBOOL(hAPP(c_List_Odistinct(_1722470), _1722468)), -(c_List_OtakeWhile(_1722470, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722470), c_fNot), hAPP(hAPP(c_COMBC(_1722470, _1722470, tc_HOL_Obool), c_fequal), c_List_Olast(_1722470, _1722468))), _1722468) = c_List_Obutlast(_1722470, _1722468))], (5442 ^ _779142) ^ [_862399, _862401] : [_862401 = _862399, -(c_Orderings_Oord__class_Oless__eq(_862401) = c_Orderings_Oord__class_Oless__eq(_862399))], (550 ^ _779142) ^ [_787351, _787353, _787355, _787357, _787359, _787361, _787363, _787365, _787367, _787369] : [-(c_Typedef_Otype__definition(_787367, _787363, _787359, _787355, _787351)), c_Typedef_Otype__definition(_787369, _787365, _787361, _787357, _787353), _787369 = _787367, _787365 = _787363, _787361 = _787359, _787357 = _787355, _787353 = _787351], (6369 ^ _779142) ^ [_881191, _881193, _881195, _881197] : [class_Orderings_Oord(_881191), _881193 = _881195, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881191), _881195), _881197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881191), _881193), _881197)))], (50047 ^ _779142) ^ [_1791345, _1791347, _1791349, _1791351, _1791353] : [c_Fun_Obij__betw(_1791345, _1791347, _1791349, _1791351, _1791353), 50050 ^ _779142 : [(50053 ^ _779142) ^ [] : [-(hAPP(c_Set_Oimage(_1791345, _1791347, _1791349), _1791351) = _1791353)], (50051 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1791345, _1791347, _1791349, _1791351))]]], (6514 ^ _779142) ^ [_883594, _883596, _883598, _883600] : [hBOOL(hAPP(hAPP(c_member(_883594), _883596), _883598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883594, tc_HOL_Obool)), _883598), _883600)), -(hBOOL(hAPP(hAPP(c_member(_883594), _883596), _883600)))], (10515 ^ _779142) ^ [_961153, _961155] : [hAPP(c_Nat_OSuc, _961153) = hAPP(c_Nat_OSuc, _961155), -(_961153 = _961155)], (5264 ^ _779142) ^ [_859556, _859558, _859560, _859562, _859564, _859566, _859568, _859570, _859572, _859574] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_859574, _859570, _859566, _859562, _859558) = c_SetInterval_Oord_OgreaterThanAtMost(_859572, _859568, _859564, _859560, _859556)), _859574 = _859572, _859570 = _859568, _859566 = _859564, _859562 = _859560, _859558 = _859556], (45764 ^ _779142) ^ [_1698721, _1698723, _1698725] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698721, tc_HOL_Obool)), hAPP(c_List_Oset(_1698721), _1698723)), hAPP(hAPP(c_Set_Oinsert(_1698721), _1698725), c_Orderings_Obot__class_Obot(tc_fun(_1698721, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698721), hAPP(c_List_Ofilter(_1698721, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698721), c_fNot), hAPP(hAPP(c_COMBC(_1698721, _1698721, tc_HOL_Obool), c_fequal), _1698725))), _1698723)))], (14997 ^ _779142) ^ [_1041340, _1041342, _1041344, _1041346] : [class_Rings_Olinordered__semidom(_1041340), 15003 ^ _779142 : [(15006 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041340), c_Groups_Ozero__class_Ozero(_1041340)), hAPP(_1041346, 15002 ^ [_1041340, _1041342, _1041344, _1041346])))], (15004 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041342), 15002 ^ [_1041340, _1041342, _1041344, _1041346]), _1041344)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041340), c_Groups_Ozero__class_Ozero(_1041340)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1041342, _1041340), _1041346), _1041344))))], (8679 ^ _779142) ^ [_924995, _924997, _924999, _925001] : [class_Groups_Oordered__ab__semigroup__add(_924995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924995), _924997), _924999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924995), _924997), _925001)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924995), _924999), _925001))))], (52461 ^ _779142) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (19605 ^ _779142) ^ [_1123652] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1123652))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1123652)) = _1123652)], (36183 ^ _779142) ^ [] : [-(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))], (25004 ^ _779142) ^ [_1218827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1218827)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218827), c_Int_OPls)))], (29462 ^ _779142) ^ [_1303105, _1303107] : [c_Nat__Transfer_Onat__set(_1303105), c_Nat__Transfer_Onat__set(_1303107), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1303105), _1303107) = 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), _1303105)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1303107))))], (12268 ^ _779142) ^ [_991010, _991012, _991014] : [class_Groups_Ocomm__monoid__add(_991010), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991012, _991010), _991014), c_Orderings_Obot__class_Obot(tc_fun(_991012, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_991010))], (40953 ^ _779142) ^ [_1583056, _1583058, _1583060, _1583062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583056, _1583056)), _1583058), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583056, _1583056), tc_HOL_Obool), _1583060), _1583062))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583056, _1583056)), _1583058), c_Transitive__Closure_Ortrancl(_1583056, _1583062))))], (25250 ^ _779142) ^ [_1222856, _1222858] : [class_Int_Onumber__ring(_1222856), class_Rings_Olinordered__idom(_1222856), 25257 ^ _779142 : [(25264 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1222858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222856), c_Groups_Oone__class_Oone(_1222856)), hAPP(c_Int_Onumber__class_Onumber__of(_1222856), _1222858))))], (25258 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222856), c_Groups_Oone__class_Oone(_1222856)), hAPP(c_Int_Onumber__class_Onumber__of(_1222856), _1222858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1222858)))]]], (23213 ^ _779142) ^ [_1187919, _1187921] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187919, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187921)) = 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), _1187919), _1187921)))], (23623 ^ _779142) ^ [_1195193, _1195195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195193)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195195))))], (52445 ^ _779142) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (29171 ^ _779142) ^ [_1296529, _1296531] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296529, tc_HOL_Obool)), _1296531), _1296531) = _1296531)], (45147 ^ _779142) ^ [_1684746, _1684748, _1684750, _1684752] : [c_List_Olist__all2(_1684746, _1684748, _1684750, _1684752, c_List_Olist_ONil(_1684748)), -(_1684752 = c_List_Olist_ONil(_1684746))], (48168 ^ _779142) ^ [_1750640, _1750642, _1750644] : [-(hAPP(c_List_Orev(_1750640), c_List_Oreplicate(_1750640, _1750642, _1750644)) = c_List_Oreplicate(_1750640, _1750642, _1750644))], (6159 ^ _779142) ^ [_877690, _877692, _877694, _877696, _877698] : [c_Finite__Set_Ofolding__one__idem(_877690, _877692, _877694), hBOOL(hAPP(c_Finite__Set_Ofinite(_877690), _877696)), hBOOL(hAPP(hAPP(c_member(_877690), _877698), _877696)), -(hAPP(hAPP(_877692, _877698), hAPP(_877694, _877696)) = hAPP(_877694, _877696))], (10433 ^ _779142) ^ [_959853, _959855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959853), _959855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959853)), hAPP(c_Nat_OSuc, _959855))))], (42782 ^ _779142) ^ [_1631603, _1631605] : [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(_1631603)), _1631605))), _1631605 = c_List_Olist_ONil(_1631603)], (9519 ^ _779142) ^ [_941254, _941256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941254), _941256)), _941256))], (17953 ^ _779142) ^ [_1095361, _1095363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095361)), -(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, _1095363, _1095361))))], (52315 ^ _779142) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (27866 ^ _779142) ^ [_1271213, _1271215, _1271217] : [class_Orderings_Olinorder(_1271213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271213), _1271215), _1271217)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271213), _1271217), _1271215) = _1271217)], (24764 ^ _779142) ^ [_1214482, _1214484, _1214486] : [class_Rings_Olinordered__idom(_1214482), -(c_Groups_Osgn__class_Osgn(_1214482, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214482), _1214484), _1214486)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214482), c_Groups_Osgn__class_Osgn(_1214482, _1214484)), c_Groups_Osgn__class_Osgn(_1214482, _1214486)))], (18491 ^ _779142) ^ [_1104752] : [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)), _1104752))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1104752)))], (26852 ^ _779142) ^ [_1252393, _1252395, _1252397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252393, tc_HOL_Obool)), _1252395), _1252397)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252393, tc_HOL_Obool)), _1252395), _1252397) = _1252397)], (11005 ^ _779142) ^ [_969015, _969017, _969019] : [class_Rings_Oring__no__zero__divisors(_969015), 11008 ^ _779142 : [(11009 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969015), _969017), _969019) = c_Groups_Ozero__class_Ozero(_969015), -(_969017 = c_Groups_Ozero__class_Ozero(_969015)), -(_969019 = c_Groups_Ozero__class_Ozero(_969015))], (11019 ^ _779142) ^ [] : [11020 ^ _779142 : [(11023 ^ _779142) ^ [] : [_969019 = c_Groups_Ozero__class_Ozero(_969015)], (11021 ^ _779142) ^ [] : [_969017 = c_Groups_Ozero__class_Ozero(_969015)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969015), _969017), _969019) = c_Groups_Ozero__class_Ozero(_969015))]]], (25766 ^ _779142) ^ [_1231978, _1231980] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1231978)), c_Int_OBit1(_1231980)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231978), c_Int_Osucc(_1231980))))], (2462 ^ _779142) ^ [_815269, _815271] : [_815271 = _815269, -(c_Nitpick_Oone__frac(_815271) = c_Nitpick_Oone__frac(_815269))], (17701 ^ _779142) ^ [_1091002, _1091004] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1091002, _1091004) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1091002 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1091004), 17704 ^ [_1091002, _1091004]))], (16099 ^ _779142) ^ [_1061981, _1061983, _1061985] : [class_Orderings_Olinorder(_1061981), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061981), _1061983)), hBOOL(hAPP(hAPP(c_member(_1061981), _1061985), _1061983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061981), hAPP(c_Finite__Set_Ofold1(_1061981, c_Orderings_Oord__class_Omin(_1061981)), _1061983)), _1061985)))], (48893 ^ _779142) ^ [_1766465, _1766467, _1766469] : [c_Relation_Otrans(_1766465, _1766467), c_Relation_Otrans(_1766465, _1766469), -(c_Relation_Otrans(_1766465, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1766465, _1766465), tc_HOL_Obool)), _1766467), _1766469)))], (29646 ^ _779142) ^ [_1307087, _1307089, _1307091] : [class_Lattices_Osemilattice__inf(_1307087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307087), _1307089)), -(_1307089 = c_Orderings_Obot__class_Obot(tc_fun(_1307087, tc_HOL_Obool))), 29657 ^ _779142 : [(29658 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307087), _1307091), hAPP(c_Finite__Set_Ofold1(_1307087, c_Lattices_Osemilattice__inf__class_Oinf(_1307087)), _1307089))), 29661 ^ _779142 : [(29662 ^ _779142) ^ [_1307380] : [hBOOL(hAPP(hAPP(c_member(_1307087), _1307380), _1307089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307087), _1307091), _1307380)))]]], (29668 ^ _779142) ^ [] : [29670 ^ _779142 : [(29673 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307087), _1307091), 29669 ^ [_1307087, _1307089, _1307091]))], (29671 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1307087), 29669 ^ [_1307087, _1307089, _1307091]), _1307089)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307087), _1307091), hAPP(c_Finite__Set_Ofold1(_1307087, c_Lattices_Osemilattice__inf__class_Oinf(_1307087)), _1307089))))]]], (19493 ^ _779142) ^ [_1121926] : [19494 ^ _779142 : [(19495 ^ _779142) ^ [_1121983] : [hBOOL(hAPP(_1121926, _1121983))]], 19497 ^ _779142 : [(19500 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1121926, hAPP(c_Int_Onat, 19496 ^ [_1121926]))))], (19498 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19496 ^ [_1121926])))]]], (45478 ^ _779142) ^ [_1691737, _1691739, _1691741] : [class_Orderings_Olinorder(_1691737), -(c_List_Olinorder__class_Osort__key(_1691739, _1691737, _1691741, c_List_Olist_ONil(_1691739)) = c_List_Olist_ONil(_1691739))], (50587 ^ _779142) ^ [_1803901, _1803903, _1803905] : [class_Rings_Odvd(_1803901), class_Rings_Osemiring__0(_1803901), 50594 ^ _779142 : [(50604 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1803903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1803901), _1803905), 50611 ^ [_1803901, _1803903, _1803905])))), 50605 ^ _779142 : [(50606 ^ _779142) ^ [_1804230] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803901), _1803905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1803901), _1804230), c_Groups_Ozero__class_Ozero(_1803901)))), hBOOL(hAPP(_1803903, _1804230))]]], (50595 ^ _779142) ^ [] : [50596 ^ _779142 : [(50597 ^ _779142) ^ [_1804093] : [hBOOL(hAPP(_1803903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1803901), _1803905), _1804093)))]], 50599 ^ _779142 : [(50602 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1803903, 50598 ^ [_1803901, _1803903, _1803905])))], (50600 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803901), _1803905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1803901), 50598 ^ [_1803901, _1803903, _1803905]), c_Groups_Ozero__class_Ozero(_1803901)))))]]]]], (39281 ^ _779142) ^ [_1541830, _1541832, _1541834] : [hBOOL(hAPP(hAPP(c_member(_1541832), _1541830), c_Orderings_Obot__class_Obot(tc_fun(_1541832, tc_HOL_Obool)))), -(hBOOL(hAPP(_1541834, _1541830)))], (2318 ^ _779142) ^ [_813023, _813025, _813027, _813029] : [-(c_Divides_Opdivmod(_813029, _813025) = c_Divides_Opdivmod(_813027, _813023)), _813029 = _813027, _813025 = _813023], (9823 ^ _779142) ^ [_946388, _946390, _946392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946388), _946390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946388), _946392)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946390), _946392))))], (10011 ^ _779142) ^ [_950503, _950505, _950507] : [class_Rings_Ocomm__semiring__1(_950503), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950503), _950505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950503), _950507), _950505)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950503), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950503), _950507), c_Groups_Oone__class_Oone(_950503))), _950505))], (44970 ^ _779142) ^ [_1680662, _1680664, _1680666, _1680668] : [-(hBOOL(hAPP(c_List_Olistsp(_1680662, _1680664), hAPP(hAPP(c_List_Olist_OCons(_1680662), _1680666), _1680668)))), hBOOL(hAPP(_1680664, _1680666)), hBOOL(hAPP(c_List_Olistsp(_1680662, _1680664), _1680668))], (35298 ^ _779142) ^ [_1436795, _1436797] : [hAPP(c_Int_ORep__Integ, _1436795) = hAPP(c_Int_ORep__Integ, _1436797), -(_1436795 = _1436797)], (33087 ^ _779142) ^ [_1384603, _1384605, _1384607, _1384609, _1384611, _1384613] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384603, _1384605, _1384607), _1384609), hAPP(hAPP(c_Product__Type_OPair(_1384603, _1384605), _1384611), _1384613)) = hAPP(hAPP(_1384609, _1384611), _1384613))], (34941 ^ _779142) ^ [_1427865, _1427867, _1427869] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427865, tc_HOL_Obool)), _1427867), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427865, tc_HOL_Obool), _1427869)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1427865, tc_HOL_Obool), tc_fun(_1427865, tc_HOL_Obool)), _1427869), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427865, tc_HOL_Obool)), _1427867)))], (40472 ^ _779142) ^ [_1571409, _1571411, _1571413, _1571415, _1571417] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571409, _1571409)), hAPP(hAPP(c_Product__Type_OPair(_1571409, _1571409), _1571411), _1571413)), c_Transitive__Closure_Otrancl(_1571409, _1571415))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571409, _1571409)), hAPP(hAPP(c_Product__Type_OPair(_1571409, _1571409), _1571413), _1571417)), c_Transitive__Closure_Ortrancl(_1571409, _1571415))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571409, _1571409)), hAPP(hAPP(c_Product__Type_OPair(_1571409, _1571409), _1571411), _1571417)), c_Transitive__Closure_Otrancl(_1571409, _1571415))))], (31691 ^ _779142) ^ [_1347945, _1347947] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1347945), _1347947) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1347945), _1347947))], (9245 ^ _779142) ^ [_936810, _936812, _936814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936810), _936812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936814), _936812))))], (52285 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (39762 ^ _779142) ^ [_1553737, _1553739, _1553741, _1553743, _1553745, _1553747, _1553749, _1553751] : [c_Finite__Set_Ofolding(_1553737, _1553739, _1553741, _1553743), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553737), _1553745)), -(hAPP(c_Fun_Ocomp(_1553739, _1553739, _1553747, hAPP(_1553741, _1553749)), hAPP(c_Fun_Ocomp(_1553739, _1553739, _1553747, hAPP(_1553743, _1553745)), _1553751)) = hAPP(c_Fun_Ocomp(_1553739, _1553739, _1553747, hAPP(_1553743, _1553745)), hAPP(c_Fun_Ocomp(_1553739, _1553739, _1553747, hAPP(_1553741, _1553749)), _1553751)))], (4470 ^ _779142) ^ [_846973, _846975] : [_846975 = _846973, -(c_Nat_Osize__class_Osize(_846975) = c_Nat_Osize__class_Osize(_846973))], (4476 ^ _779142) ^ [_847058, _847060, _847062, _847064] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847064, _847060) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847062, _847058)), _847064 = _847062, _847060 = _847058], (23183 ^ _779142) ^ [_1187329, _1187331, _1187333] : [class_Fields_Ofield__inverse__zero(_1187329), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187329), hAPP(c_Groups_Ouminus__class_Ouminus(_1187329), _1187331)), hAPP(c_Groups_Ouminus__class_Ouminus(_1187329), _1187333)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187329), _1187331), _1187333))], (23159 ^ _779142) ^ [_1186874, _1186876, _1186878, _1186880] : [class_Divides_Oring__div(_1186874), c_Divides_Odiv__class_Omod(_1186874, _1186876, _1186878) = c_Divides_Odiv__class_Omod(_1186874, _1186880, _1186878), -(c_Divides_Odiv__class_Omod(_1186874, hAPP(c_Groups_Ouminus__class_Ouminus(_1186874), _1186876), _1186878) = c_Divides_Odiv__class_Omod(_1186874, hAPP(c_Groups_Ouminus__class_Ouminus(_1186874), _1186880), _1186878))], (40729 ^ _779142) ^ [_1577702, _1577704, _1577706] : [c_Relation_Ototal__on(_1577702, _1577704, hAPP(c_Relation_Oconverse(_1577702, _1577702), _1577706)), -(c_Relation_Ototal__on(_1577702, _1577704, _1577706))], (52427 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (10757 ^ _779142) ^ [_965030, _965032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965030), _965032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965030)), hAPP(c_Nat_OSuc, _965032))))], (44632 ^ _779142) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18479 ^ _779142) ^ [_1104528, _1104530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104528)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104530)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1104530), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1104528))))], (33020 ^ _779142) ^ [_1383379, _1383381] : [-(c_Divides_Odivmod__nat(_1383381, _1383379) = 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), _1383381), _1383379), _1383379))), -(_1383379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1383381), _1383379)))], (44181 ^ _779142) ^ [_1662984, _1662986, _1662988] : [_1662984 = c_List_Olist_ONil(_1662986), -(c_List_Olast(_1662986, hAPP(hAPP(c_List_Olist_OCons(_1662986), _1662988), _1662984)) = _1662988)], (5834 ^ _779142) ^ [_871518, _871520, _871522, _871524] : [-(hAPP(hAPP(c_Set_Oinsert(_871518), _871520), hAPP(hAPP(c_Set_Oinsert(_871518), _871522), _871524)) = hAPP(hAPP(c_Set_Oinsert(_871518), _871522), hAPP(hAPP(c_Set_Oinsert(_871518), _871520), _871524)))], (41076 ^ _779142) ^ [_1586332, _1586334, _1586336, _1586338, _1586340] : [c_Relation_Osingle__valued(_1586332, _1586332, _1586334), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586332, _1586332)), hAPP(hAPP(c_Product__Type_OPair(_1586332, _1586332), _1586336), _1586338)), c_Transitive__Closure_Ortrancl(_1586332, _1586334))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586332, _1586332)), hAPP(hAPP(c_Product__Type_OPair(_1586332, _1586332), _1586336), _1586340)), c_Transitive__Closure_Ortrancl(_1586332, _1586334))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586332, _1586332)), hAPP(hAPP(c_Product__Type_OPair(_1586332, _1586332), _1586338), _1586340)), c_Transitive__Closure_Ortrancl(_1586332, _1586334)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586332, _1586332)), hAPP(hAPP(c_Product__Type_OPair(_1586332, _1586332), _1586340), _1586338)), c_Transitive__Closure_Ortrancl(_1586332, _1586334))))], (44857 ^ _779142) ^ [_1677730, _1677732] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1677730), _1677732) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677730)), hAPP(c_Code__Numeral_Onat__of, _1677732))))], (32463 ^ _779142) ^ [_1370889, _1370891, _1370893, _1370895] : [class_Groups_Oab__group__add(_1370889), 32466 ^ _779142 : [(32473 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370891), _1370893))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370889), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1370889, _1370889), hAPP(hAPP(c_COMBB(_1370889, tc_fun(_1370889, _1370889), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1370889)), _1370895)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370889, tc_Nat_Onat), _1370895), 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, _1370891, _1370893)) = c_Groups_Ozero__class_Ozero(_1370889))], (32467 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370891), _1370893)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370889), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1370889, _1370889), hAPP(hAPP(c_COMBB(_1370889, tc_fun(_1370889, _1370889), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1370889)), _1370895)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370889, tc_Nat_Onat), _1370895), 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, _1370891, _1370893)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1370889), hAPP(_1370895, _1370891)), hAPP(_1370895, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370893), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (40919 ^ _779142) ^ [_1582398, _1582400] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582398, _1582398), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1582400) = _1582400)], (43263 ^ _779142) ^ [_1642145, _1642147, _1642149, _1642151] : [-(hAPP(hAPP(c_List_Onth(_1642145), hAPP(hAPP(c_List_Oappend(_1642145), _1642147), hAPP(hAPP(c_List_Olist_OCons(_1642145), _1642149), _1642151))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642145)), _1642147)) = _1642149)], (14569 ^ _779142) ^ [_1033252, _1033254, _1033256, _1033258] : [class_Fields_Olinordered__field(_1033252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033252), _1033254), c_Groups_Ozero__class_Ozero(_1033252))), 14576 ^ _779142 : [(14583 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033252), _1033258), _1033254)), _1033256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033252), _1033256), _1033254)), _1033258)))], (14577 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033252), _1033256), _1033254)), _1033258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033252), _1033258), _1033254)), _1033256)))]]], (24828 ^ _779142) ^ [_1215716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215716), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1215716)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22821 ^ _779142) ^ [_1181063, _1181065, _1181067, _1181069] : [class_Groups_Ouminus(_1181063), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1181065, _1181063)), _1181067), _1181069) = hAPP(c_Groups_Ouminus__class_Ouminus(_1181063), hAPP(_1181067, _1181069)))], (10452 ^ _779142) ^ [_960177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960177), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_960177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4486 ^ _779142) ^ [_847207, _847209, _847211, _847213, _847215, _847217, _847219, _847221, _847223, _847225] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847225, _847221, _847217, _847213, _847209) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847223, _847219, _847215, _847211, _847207)), _847225 = _847223, _847221 = _847219, _847217 = _847215, _847213 = _847211, _847209 = _847207], (29203 ^ _779142) ^ [_1297100, _1297102, _1297104, _1297106] : [class_Lattices_Osemilattice__inf(_1297100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297100), _1297102), _1297104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297100), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297100), _1297102), _1297106)), _1297104)))], (31050 ^ _779142) ^ [_1335521, _1335523] : [class_Orderings_Olinorder(_1335521), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1335521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1335521), _1335523)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1335521), _1335523))], (24055 ^ _779142) ^ [_1202634, _1202636, _1202638] : [class_Int_Oring__char__0(_1202634), 24058 ^ _779142 : [(24065 ^ _779142) ^ [] : [_1202636 = _1202638, -(hAPP(c_Int_Oring__1__class_Oof__int(_1202634), _1202636) = hAPP(c_Int_Oring__1__class_Oof__int(_1202634), _1202638))], (24059 ^ _779142) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1202634), _1202636) = hAPP(c_Int_Oring__1__class_Oof__int(_1202634), _1202638), -(_1202636 = _1202638)]]], (1226 ^ _779142) ^ [_797409, _797411] : [-(class_Rings_Olinordered__idom(_797409)), _797411 = _797409, class_Rings_Olinordered__idom(_797411)], (44940 ^ _779142) ^ [_1680040, _1680042, _1680044, _1680046] : [-(hBOOL(hAPP(c_List_Olistsp(_1680040, hAPP(hAPP(c_COMBS(_1680040, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1680040), c_fconj), _1680042)), _1680044)), _1680046))), hBOOL(hAPP(c_List_Olistsp(_1680040, _1680042), _1680046)), hBOOL(hAPP(c_List_Olistsp(_1680040, _1680044), _1680046))], (52589 ^ _779142) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (17732 ^ _779142) ^ [_1091570, _1091572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091570), _1091572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091570)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091572))))], (34617 ^ _779142) ^ [_1418712, _1418714, _1418716, _1418718, _1418720, _1418722] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418712, tc_fun(_1418714, tc_fun(_1418716, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1418712, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_fun(_1418714, tc_fun(_1418716, tc_HOL_Obool)), _1418712), hAPP(c_COMBC(_1418714, tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_fun(_1418716, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418716, tc_fun(tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_fun(_1418716, tc_HOL_Obool)), _1418714), c_COMBC(_1418716, tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418716, tc_prod(_1418714, _1418716)), tc_fun(_1418716, tc_fun(tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_HOL_Obool)), _1418714), hAPP(c_COMBB(tc_prod(_1418714, _1418716), tc_fun(tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool), tc_HOL_Obool), _1418716), c_member(tc_prod(_1418714, _1418716)))), c_Product__Type_OPair(_1418714, _1418716))))), _1418718)), _1418720), _1418722)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1418714, _1418716)), hAPP(hAPP(c_Product__Type_OPair(_1418714, _1418716), _1418720), _1418722)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418712, tc_fun(tc_prod(_1418714, _1418716), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1418712, tc_HOL_Obool))), _1418718))))], (37201 ^ _779142) ^ [_1481477, _1481479, _1481481, _1481483, _1481485] : [-(hAPP(c_Set_Ovimage(_1481477, _1481479, _1481481), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481479, tc_HOL_Obool)), _1481483), _1481485)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481477, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481477, _1481479, _1481481), _1481483)), hAPP(c_Set_Ovimage(_1481477, _1481479, _1481481), _1481485)))], (15433 ^ _779142) ^ [_1049478, _1049480, _1049482, _1049484] : [class_Orderings_Olinorder(_1049478), 15436 ^ _779142 : [(15437 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049478), _1049480), _1049482)), _1049484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), _1049480), _1049484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), _1049482), _1049484)))], (15447 ^ _779142) ^ [] : [15448 ^ _779142 : [(15451 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), _1049482), _1049484))], (15449 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), _1049480), _1049484))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049478), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049478), _1049480), _1049482)), _1049484)))]]], (39058 ^ _779142) ^ [_1536508, _1536510] : [-(hAPP(c_List_Olexn(_1536508, _1536510), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1536508), tc_List_Olist(_1536508)), tc_HOL_Obool)))], (13103 ^ _779142) ^ [_1006231, _1006233, _1006235] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006231), _1006233)), -(hBOOL(hAPP(hAPP(c_member(_1006231), _1006235), _1006233))), -(hAPP(c_Finite__Set_Ocard(_1006231), hAPP(hAPP(c_Set_Oinsert(_1006231), _1006235), _1006233)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1006231), _1006233)))], (23613 ^ _779142) ^ [_1195032, _1195034] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195032)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195034)), _1195032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1195034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38717 ^ _779142) ^ [_1528575] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1528575)))], (28252 ^ _779142) ^ [_1278405, _1278407, _1278409] : [class_Orderings_Olinorder(_1278405), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278405), _1278407)), -(c_Big__Operators_Olinorder__class_OMax(_1278405, hAPP(hAPP(c_Set_Oinsert(_1278405), _1278409), _1278407)) = hAPP(hAPP(c_Finite__Set_Ofold(_1278405, _1278405, c_Orderings_Oord__class_Omax(_1278405)), _1278409), _1278407))], (29305 ^ _779142) ^ [_1299208, _1299210, _1299212, _1299214] : [class_Lattices_Olattice(_1299208), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299208), _1299210), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299208), _1299212), _1299214))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299208), _1299210), _1299212)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299208), _1299210), _1299214)))))], (17487 ^ _779142) ^ [_1087129, _1087131, _1087133, _1087135] : [class_Divides_Osemiring__div(_1087129), -(c_Divides_Odiv__class_Omod(_1087129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087129), _1087131), _1087133), _1087135) = c_Divides_Odiv__class_Omod(_1087129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087129), c_Divides_Odiv__class_Omod(_1087129, _1087131, _1087135)), _1087133), _1087135))], (52455 ^ _779142) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (26858 ^ _779142) ^ [_1252510, _1252512, _1252514] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252510, tc_HOL_Obool)), _1252512), _1252514) = _1252514, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252510, tc_HOL_Obool)), _1252512), _1252514)))], (40923 ^ _779142) ^ [_1582494, _1582496, _1582498, _1582500] : [-(hAPP(hAPP(c_Nat_Ocompow(_1582494, _1582494), _1582496), hAPP(hAPP(c_Nat_Ocompow(_1582494, _1582494), _1582498), _1582500)) = hAPP(hAPP(c_Nat_Ocompow(_1582494, _1582494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1582498), _1582496)), _1582500))], (29719 ^ _779142) ^ [_1308748, _1308750, _1308752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308748), _1308750)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308748), _1308752)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1308748), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308748, tc_HOL_Obool)), _1308750), _1308752))), hAPP(c_Finite__Set_Ocard(_1308748), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308748, tc_HOL_Obool)), _1308750), _1308752))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1308748), _1308750)), hAPP(c_Finite__Set_Ocard(_1308748), _1308752)))], (41387 ^ _779142) ^ [_1595269, _1595271, _1595273, _1595275, _1595277, _1595279] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595269), tc_List_Olist(_1595269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595269), tc_List_Olist(_1595269)), hAPP(hAPP(c_List_Olist_OCons(_1595269), _1595271), _1595273)), hAPP(hAPP(c_List_Olist_OCons(_1595269), _1595275), _1595277))), c_List_Olex(_1595269, _1595279)))), 41388 ^ _779142 : [(41395 ^ _779142) ^ [] : [_1595271 = _1595275, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595269), tc_List_Olist(_1595269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595269), tc_List_Olist(_1595269)), _1595273), _1595277)), c_List_Olex(_1595269, _1595279)))], (41389 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595269, _1595269)), hAPP(hAPP(c_Product__Type_OPair(_1595269, _1595269), _1595271), _1595275)), _1595279)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595269)), _1595273) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595269)), _1595277)]]], (7126 ^ _779142) ^ [_896958, _896960, _896962, _896964, _896966, _896968] : [c_Finite__Set_Ofun__left__comm(_896958, _896960, _896962), hBOOL(hAPP(c_Finite__Set_Ofinite(_896958), _896964)), -(hBOOL(hAPP(hAPP(c_member(_896958), _896966), _896964))), -(hAPP(hAPP(c_Finite__Set_Ofold(_896958, _896960, _896962), _896968), hAPP(hAPP(c_Set_Oinsert(_896958), _896966), _896964)) = hAPP(hAPP(c_Finite__Set_Ofold(_896958, _896960, _896962), hAPP(hAPP(_896962, _896966), _896968)), _896964))], (32131 ^ _779142) ^ [_1362997, _1362999, _1363001, _1363003, _1363005] : [class_Groups_Ocomm__monoid__add(_1362997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362999), _1363001)), 32138 ^ _779142 : [(32145 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362999), _1363003), _1363001))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362999, _1362997), hAPP(hAPP(c_COMBC(_1362999, _1362997, _1362997), hAPP(hAPP(c_COMBS(_1362999, _1362997, tc_fun(_1362997, _1362997)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1362997, tc_fun(_1362997, _1362997)), _1362999), c_If(_1362997)), hAPP(c_fequal, _1363003))), _1363005)), c_Groups_Ozero__class_Ozero(_1362997))), _1363001) = c_Groups_Ozero__class_Ozero(_1362997))], (32139 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1362999), _1363003), _1363001)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362999, _1362997), hAPP(hAPP(c_COMBC(_1362999, _1362997, _1362997), hAPP(hAPP(c_COMBS(_1362999, _1362997, tc_fun(_1362997, _1362997)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1362997, tc_fun(_1362997, _1362997)), _1362999), c_If(_1362997)), hAPP(c_fequal, _1363003))), _1363005)), c_Groups_Ozero__class_Ozero(_1362997))), _1363001) = hAPP(_1363005, _1363003))]]], (34664 ^ _779142) ^ [_1421177, _1421179, _1421181, _1421183, _1421185] : [class_Complete__Lattice_Ocomplete__lattice(_1421177), 34667 ^ _779142 : [(34668 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421177), _1421179), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1421181, _1421177), _1421183), _1421185))), 34671 ^ _779142 : [(34672 ^ _779142) ^ [_1421358] : [hBOOL(hAPP(hAPP(c_member(_1421181), _1421358), _1421183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421177), _1421179), hAPP(_1421185, _1421358))))]]], (34678 ^ _779142) ^ [] : [34680 ^ _779142 : [(34683 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421177), _1421179), hAPP(_1421185, 34679 ^ [_1421177, _1421179, _1421181, _1421183, _1421185])))], (34681 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421181), 34679 ^ [_1421177, _1421179, _1421181, _1421183, _1421185]), _1421183)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421177), _1421179), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1421181, _1421177), _1421183), _1421185))))]]], (26278 ^ _779142) ^ [] : [-(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)))], (23315 ^ _779142) ^ [_1189918, _1189920] : [class_Groups_Oordered__ab__group__add(_1189918), 23318 ^ _779142 : [(23325 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189918), _1189920), c_Groups_Ozero__class_Ozero(_1189918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189918), c_Groups_Ozero__class_Ozero(_1189918)), hAPP(c_Groups_Ouminus__class_Ouminus(_1189918), _1189920))))], (23319 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189918), c_Groups_Ozero__class_Ozero(_1189918)), hAPP(c_Groups_Ouminus__class_Ouminus(_1189918), _1189920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189918), _1189920), c_Groups_Ozero__class_Ozero(_1189918))))]]], (36634 ^ _779142) ^ [_1468551] : [-(c_Fun_Oinj__on(_1468551, tc_fun(_1468551, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468551, tc_fun(_1468551, tc_HOL_Obool), tc_fun(_1468551, tc_HOL_Obool)), c_Set_Oinsert(_1468551)), c_Orderings_Obot__class_Obot(tc_fun(_1468551, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1468551, tc_HOL_Obool))))], (30882 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (48680 ^ _779142) ^ [_1761281, _1761283, _1761285] : [c_List_Oall__interval__int(_1761281, _1761283, _1761285), 48683 ^ _779142 : [(48684 ^ _779142) ^ [_1761359] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1761359), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761283, _1761285))), -(hBOOL(hAPP(_1761281, _1761359)))]]], (31829 ^ _779142) ^ [_1352143, _1352145, _1352147, _1352149, _1352151, _1352153] : [_1352143 = _1352145, -(hAPP(c_Fun_Ofun__upd(_1352147, _1352149, _1352151, _1352145, _1352153), _1352143) = _1352153)], (2456 ^ _779142) ^ [_815184, _815186] : [_815186 = _815184, -(c_Nitpick_Ozero__frac(_815186) = c_Nitpick_Ozero__frac(_815184))], (16585 ^ _779142) ^ [_1071039, _1071041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071039), _1071041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071041), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (37657 ^ _779142) ^ [_1493396, _1493398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493396, _1493396), tc_HOL_Obool)), c_Relation_OId__on(_1493396, _1493398)), hAPP(hAPP(c_Product__Type_OSigma(_1493396, _1493396), _1493398), hAPP(c_COMBK(tc_fun(_1493396, tc_HOL_Obool), _1493396), _1493398)))))], (42748 ^ _779142) ^ [_1631002, _1631004] : [-(c_List_Olist_Olist__size(_1631002, _1631004, c_List_Olist_ONil(_1631002)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35379 ^ _779142) ^ [_1439354, _1439356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439354), _1439356)), -(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), _1439354), _1439356)), c_Wellfounded_Oless__than)))], (52201 ^ _779142) ^ [_1831812, _1831814] : [class_Orderings_Obot(_1831812), -(class_Orderings_Obot(tc_fun(_1831814, _1831812)))], (15247 ^ _779142) ^ [_1046063, _1046065, _1046067, _1046069] : [class_Orderings_Olinorder(_1046063), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046063), _1046065), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046063), _1046067), _1046069)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046063), _1046067), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046063), _1046065), _1046069)))], (17437 ^ _779142) ^ [_1086064, _1086066, _1086068] : [class_Divides_Osemiring__div(_1086064), -(c_Divides_Odiv__class_Omod(_1086064, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086064), _1086066), _1086068), _1086066) = c_Divides_Odiv__class_Omod(_1086064, _1086068, _1086066))], (33686 ^ _779142) ^ [_1395567, _1395569, _1395571, _1395573] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395567, _1395567)), hAPP(hAPP(c_Product__Type_OPair(_1395567, _1395567), _1395569), _1395571)), hAPP(c_Wellfounded_Omeasure(_1395567), _1395573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1395573, _1395569)), hAPP(_1395573, _1395571))))], (34817 ^ _779142) ^ [_1424590, _1424592, _1424594, _1424596, _1424598] : [-(_1424590 = c_Orderings_Obot__class_Obot(tc_fun(_1424592, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424594, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424592, tc_fun(_1424594, tc_HOL_Obool)), _1424590), _1424596)), _1424598) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424592, tc_fun(_1424594, tc_HOL_Obool)), _1424590), hAPP(hAPP(c_COMBC(_1424592, tc_fun(_1424594, tc_HOL_Obool), tc_fun(_1424594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1424594, tc_HOL_Obool), tc_fun(tc_fun(_1424594, tc_HOL_Obool), tc_fun(_1424594, tc_HOL_Obool)), _1424592), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424594, tc_HOL_Obool))), _1424596)), _1424598)))], (21582 ^ _779142) ^ [_1158181, _1158183, _1158185, _1158187] : [class_Rings_Olinordered__semidom(_1158181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158181), _1158183), _1158185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158181), c_Groups_Ozero__class_Ozero(_1158181)), _1158183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158181), hAPP(hAPP(c_Power_Opower__class_Opower(_1158181), _1158183), _1158187)), hAPP(hAPP(c_Power_Opower__class_Opower(_1158181), _1158185), _1158187))))], (24676 ^ _779142) ^ [_1213093, _1213095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1213093)), c_Int_OBit1(_1213095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213093), _1213095)))], (51219 ^ _779142) ^ [_1815360, _1815362] : [-(_1815360 = _1815362), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815360), _1815362)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815362), _1815360))], (45083 ^ _779142) ^ [_1683473, _1683475, _1683477, _1683479, _1683481, _1683483, _1683485] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683473)), _1683475) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683477)), _1683479), 45086 ^ _779142 : [(45095 ^ _779142) ^ [] : [-(c_List_Olist__all2(_1683473, _1683477, _1683481, hAPP(hAPP(c_List_Oappend(_1683473), _1683475), _1683483), hAPP(hAPP(c_List_Oappend(_1683477), _1683479), _1683485))), c_List_Olist__all2(_1683473, _1683477, _1683481, _1683475, _1683479), c_List_Olist__all2(_1683473, _1683477, _1683481, _1683483, _1683485)], (45087 ^ _779142) ^ [] : [c_List_Olist__all2(_1683473, _1683477, _1683481, hAPP(hAPP(c_List_Oappend(_1683473), _1683475), _1683483), hAPP(hAPP(c_List_Oappend(_1683477), _1683479), _1683485)), 45090 ^ _779142 : [(45093 ^ _779142) ^ [] : [-(c_List_Olist__all2(_1683473, _1683477, _1683481, _1683483, _1683485))], (45091 ^ _779142) ^ [] : [-(c_List_Olist__all2(_1683473, _1683477, _1683481, _1683475, _1683479))]]]]], (35137 ^ _779142) ^ [_1433072, _1433074, _1433076, _1433078, _1433080] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1433072, tc_fun(_1433074, tc_HOL_Obool)), _1433076), _1433078), _1433080)), 35140 ^ _779142 : [(35141 ^ _779142) ^ [_1433181] : [hBOOL(hAPP(hAPP(c_member(_1433072), _1433181), _1433076)), -(hBOOL(hAPP(hAPP(_1433078, _1433181), _1433080)))]]], (52497 ^ _779142) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (37138 ^ _779142) ^ [_1479961, _1479963, _1479965] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479961, tc_HOL_Obool)), _1479963), hAPP(hAPP(c_Set_Oinsert(_1479961), _1479965), c_Orderings_Obot__class_Obot(tc_fun(_1479961, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1479961, _1479965, _1479963) = c_HOL_OThe(_1479961, hAPP(hAPP(c_COMBC(_1479961, tc_fun(_1479961, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479961)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479961, tc_HOL_Obool)), _1479963), hAPP(hAPP(c_Set_Oinsert(_1479961), _1479965), c_Orderings_Obot__class_Obot(tc_fun(_1479961, tc_HOL_Obool)))))))], (42427 ^ _779142) ^ [_1624617, _1624619, _1624621, _1624623] : [hBOOL(hAPP(c_List_Odistinct(_1624617), _1624619)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624621, _1624617)), hAPP(hAPP(c_List_Ozip(_1624621, _1624617), _1624623), _1624619))))], (38965 ^ _779142) ^ [_1534228, _1534230] : [c_Predicate_Oreflp(_1534228, _1534230), -(c_Relation_Orefl__on(_1534228, c_Orderings_Otop__class_Otop(tc_fun(_1534228, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1534228, _1534228)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534228, _1534228, tc_HOL_Obool), _1534230))))], (25862 ^ _779142) ^ [_1233614, _1233616, _1233618] : [class_Groups_Omonoid__mult(_1233614), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233614), _1233616), 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)))), _1233618)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1233614), hAPP(hAPP(c_Power_Opower__class_Opower(_1233614), _1233616), _1233618)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (43987 ^ _779142) ^ [_1659263, _1659265, _1659267] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659263), tc_List_Olist(_1659263))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659263), tc_List_Olist(_1659263)), c_List_Olist_ONil(_1659263)), _1659265)), c_List_Olexord(_1659263, _1659267))), -(_1659265 = hAPP(hAPP(c_List_Olist_OCons(_1659263), 43990 ^ [_1659263, _1659265, _1659267]), 43991 ^ [_1659263, _1659265, _1659267]))], (33770 ^ _779142) ^ [_1397303, _1397305, _1397307] : [33772 ^ _779142 : [(33775 ^ _779142) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1397307, 33771 ^ [_1397303, _1397305, _1397307]))], (33773 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397303), 33771 ^ [_1397303, _1397305, _1397307]), _1397305)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1397303, tc_Int_Oint), _1397307), _1397305) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1397303, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1397303), c_Int_Onat), _1397307)), _1397305)))], (27798 ^ _779142) ^ [_1270058, _1270060, _1270062] : [class_Orderings_Olinorder(_1270058), 27801 ^ _779142 : [(27808 ^ _779142) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270058), _1270060), _1270062) = _1270062, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270058), _1270060), _1270062)))], (27802 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270058), _1270060), _1270062)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270058), _1270060), _1270062) = _1270062)]]], (3338 ^ _779142) ^ [_828885, _828887, _828889, _828891, _828893, _828895] : [-(c_Finite__Set_Ofold(_828895, _828891, _828887) = c_Finite__Set_Ofold(_828893, _828889, _828885)), _828895 = _828893, _828891 = _828889, _828887 = _828885], (21882 ^ _779142) ^ [_1163690, _1163692, _1163694] : [class_Rings_Osemiring__1(_1163690), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1163690), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1163692), _1163694)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163690), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1163690), _1163692)), _1163694))], (26618 ^ _779142) ^ [_1247604, _1247606, _1247608, _1247610] : [26620 ^ _779142 : [(26623 ^ _779142) ^ [] : [hBOOL(hAPP(_1247610, 26619 ^ [_1247604, _1247606, _1247608, _1247610]))], (26621 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1247604), 26619 ^ [_1247604, _1247606, _1247608, _1247610]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247604, tc_HOL_Obool)), _1247606), _1247608))))]], 26624 ^ _779142 : [(26631 ^ _779142) ^ [_1247921] : [hBOOL(hAPP(hAPP(c_member(_1247604), _1247921), _1247608)), -(hBOOL(hAPP(_1247610, _1247921)))], (26625 ^ _779142) ^ [_1247824] : [hBOOL(hAPP(hAPP(c_member(_1247604), _1247824), _1247606)), -(hBOOL(hAPP(_1247610, _1247824)))]]], (34953 ^ _779142) ^ [_1428253, _1428255, _1428257, _1428259] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428253, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428255, tc_fun(_1428253, tc_HOL_Obool), _1428257), _1428259)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428255, tc_fun(_1428253, tc_HOL_Obool)), _1428259), _1428257))], (1466 ^ _779142) ^ [_800409, _800411] : [-(class_Orderings_Otop(_800409)), _800411 = _800409, class_Orderings_Otop(_800411)], (2058 ^ _779142) ^ [_809007, _809009, _809011, _809013, _809015, _809017, _809019, _809021] : [-(c_Nitpick_Opair__box_OPairBox(_809021, _809017, _809013, _809009) = c_Nitpick_Opair__box_OPairBox(_809019, _809015, _809011, _809007)), _809021 = _809019, _809017 = _809015, _809013 = _809011, _809009 = _809007], (28621 ^ _779142) ^ [_1285104, _1285106, _1285108] : [class_Orderings_Olinorder(_1285104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285104), _1285106)), -(hBOOL(hAPP(hAPP(c_member(_1285104), _1285108), _1285106))), -(_1285106 = c_Orderings_Obot__class_Obot(tc_fun(_1285104, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1285104, c_Orderings_Oord__class_Omax(_1285104), hAPP(hAPP(c_Set_Oinsert(_1285104), _1285108), _1285106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285104), _1285108), c_Big__Operators_Olattice_OSup__fin(_1285104, c_Orderings_Oord__class_Omax(_1285104), _1285106)))], (38496 ^ _779142) ^ [_1523193, _1523195, _1523197, _1523199, _1523201, _1523203, _1523205] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1523193, _1523195, _1523197, hAPP(hAPP(c_COMBC(_1523193, tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_fun(_1523195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523195, tc_fun(tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_fun(_1523195, tc_HOL_Obool)), _1523193), c_COMBC(_1523195, tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523195, tc_prod(_1523193, _1523195)), tc_fun(_1523195, tc_fun(tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_HOL_Obool)), _1523193), hAPP(c_COMBB(tc_prod(_1523193, _1523195), tc_fun(tc_fun(tc_prod(_1523193, _1523195), tc_HOL_Obool), tc_HOL_Obool), _1523195), c_member(tc_prod(_1523193, _1523195)))), c_Product__Type_OPair(_1523193, _1523195)))), _1523199), hAPP(hAPP(c_COMBC(_1523195, tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_fun(_1523197, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523197, tc_fun(tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_fun(_1523197, tc_HOL_Obool)), _1523195), c_COMBC(_1523197, tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523197, tc_prod(_1523195, _1523197)), tc_fun(_1523197, tc_fun(tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_HOL_Obool)), _1523195), hAPP(c_COMBB(tc_prod(_1523195, _1523197), tc_fun(tc_fun(tc_prod(_1523195, _1523197), tc_HOL_Obool), tc_HOL_Obool), _1523197), c_member(tc_prod(_1523195, _1523197)))), c_Product__Type_OPair(_1523195, _1523197)))), _1523201)), _1523203), _1523205)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523193, _1523197)), hAPP(hAPP(c_Product__Type_OPair(_1523193, _1523197), _1523203), _1523205)), hAPP(hAPP(c_Relation_Orel__comp(_1523193, _1523195, _1523197), _1523199), _1523201))))], (34542 ^ _779142) ^ [_1416510, _1416512, _1416514, _1416516, _1416518] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416510, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416512, tc_fun(_1416510, tc_HOL_Obool)), _1416514), _1416516)), _1416518) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416512, tc_fun(_1416510, tc_HOL_Obool)), _1416514), hAPP(hAPP(c_COMBC(_1416512, tc_fun(_1416510, tc_HOL_Obool), tc_fun(_1416510, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1416510, tc_HOL_Obool), tc_fun(tc_fun(_1416510, tc_HOL_Obool), tc_fun(_1416510, tc_HOL_Obool)), _1416512), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416510, tc_HOL_Obool))), _1416516)), _1416518)))], (39952 ^ _779142) ^ [_1557946, _1557948, _1557950, _1557952, _1557954, _1557956, _1557958, _1557960] : [class_Groups_Ocomm__monoid__mult(_1557946), c_Fun_Oinj__on(_1557948, _1557950, _1557952, _1557954), _1557956 = hAPP(c_Set_Oimage(_1557948, _1557950, _1557952), _1557954), 39966 ^ _779142 : [(39969 ^ _779142) ^ [] : [hAPP(_1557958, 39965 ^ [_1557946, _1557948, _1557950, _1557952, _1557954, _1557956, _1557958, _1557960]) = hAPP(hAPP(c_Fun_Ocomp(_1557950, _1557946, _1557948, _1557960), _1557952), 39965 ^ [_1557946, _1557948, _1557950, _1557952, _1557954, _1557956, _1557958, _1557960])], (39967 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557948), 39965 ^ [_1557946, _1557948, _1557950, _1557952, _1557954, _1557956, _1557958, _1557960]), _1557954)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557950, _1557946), _1557960), _1557956) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557948, _1557946), _1557958), _1557954))], (42570 ^ _779142) ^ [_1627881, _1627883, _1627885, _1627887] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627881) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627883), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627881)), hAPP(hAPP(c_List_Olist_OCons(_1627883), _1627885), _1627887)) = c_List_Olist_ONil(_1627883))], (35649 ^ _779142) ^ [_1446887, _1446889] : [-(c_Relation_OId__on(_1446887, _1446889) = hAPP(c_Product__Type_Oprod_Oprod__case(_1446887, _1446887, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1446887, tc_HOL_Obool, tc_fun(_1446887, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446887, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1446887, tc_HOL_Obool)), _1446887), c_COMBC(_1446887, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446887, tc_HOL_Obool), tc_fun(_1446887, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1446887), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1446887), c_fconj)), c_fequal))), _1446889)))], (38471 ^ _779142) ^ [_1521898, _1521900, _1521902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521898, _1521898), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521898, _1521898, _1521898), _1521900), _1521902)), _1521900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1521898, _1521900)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1521898, _1521902)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1521898, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1521898, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1521898, tc_HOL_Obool), tc_fun(_1521898, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1521898, _1521900))))], (23717 ^ _779142) ^ [_1196841, _1196843, _1196845] : [class_Rings_Oring__1(_1196841), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1196841), hAPP(c_Groups_Ouminus__class_Ouminus(_1196841), _1196843)), _1196845) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196841), hAPP(hAPP(c_Power_Opower__class_Opower(_1196841), hAPP(c_Groups_Ouminus__class_Ouminus(_1196841), c_Groups_Oone__class_Oone(_1196841))), _1196845)), hAPP(hAPP(c_Power_Opower__class_Opower(_1196841), _1196843), _1196845)))], (32457 ^ _779142) ^ [_1370688, _1370690] : [class_Rings_Ocomm__semiring__1(_1370688), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1370688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370688), c_Groups_Oone__class_Oone(_1370688)), c_Groups_Oone__class_Oone(_1370688))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370688), c_Nat_Osemiring__1__class_Oof__nat(_1370688)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1370690))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1370688), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1370688), _1370690)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370688), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1370688), _1370690)), c_Groups_Oone__class_Oone(_1370688))))], (33163 ^ _779142) ^ [_1386096, _1386098] : [class_Rings_Osemiring__1(_1386096), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1386096), _1386098) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1386096, hAPP(hAPP(c_COMBC(_1386096, _1386096, _1386096), c_Groups_Oplus__class_Oplus(_1386096)), c_Groups_Oone__class_Oone(_1386096)), _1386098, c_Groups_Ozero__class_Ozero(_1386096)))], (11504 ^ _779142) ^ [_977025, _977027, _977029, _977031] : [class_Groups_Oordered__comm__monoid__add(_977025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977025), c_Groups_Ozero__class_Ozero(_977025)), _977027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977025), _977029), _977031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977025), _977029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977025), _977031), _977027))))], (21164 ^ _779142) ^ [_1151068, _1151070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151070)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1151070), _1151068)), _1151070) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1151070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1151068), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (38879 ^ _779142) ^ [_1532064, _1532066, _1532068, _1532070, _1532072] : [-(hAPP(c_Relation_ODomain(_1532064, _1532066), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1532064, _1532066)), hAPP(hAPP(c_Product__Type_OPair(_1532064, _1532066), _1532068), _1532070)), _1532072)) = hAPP(hAPP(c_Set_Oinsert(_1532064), _1532068), hAPP(c_Relation_ODomain(_1532064, _1532066), _1532072)))], (45709 ^ _779142) ^ [_1697483, _1697485, _1697487, _1697489] : [-(hAPP(c_List_Ofilter(_1697483, _1697485), hAPP(hAPP(c_List_Oappend(_1697483), _1697487), _1697489)) = hAPP(hAPP(c_List_Oappend(_1697483), hAPP(c_List_Ofilter(_1697483, _1697485), _1697487)), hAPP(c_List_Ofilter(_1697483, _1697485), _1697489)))], (17821 ^ _779142) ^ [_1093167, _1093169, _1093171] : [class_Rings_Olinordered__semidom(_1093167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093169), _1093171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093167), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093167), _1093169)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093167), _1093171))))], (9587 ^ _779142) ^ [_942232, _942234, _942236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942232), _942234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942232), _942236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942234), _942236))))], (24990 ^ _779142) ^ [_1218492, _1218494, _1218496, _1218498, _1218500] : [class_Groups_Oab__group__add(_1218492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218494), _1218496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218496), _1218498)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1218492), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218492), _1218500), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218494), _1218498))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218492), _1218500), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218494), _1218496))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218492), _1218500), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218496), _1218498)))], (26746 ^ _779142) ^ [_1250212, _1250214, _1250216, _1250218] : [class_Lattices_Osemilattice__sup(_1250212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250212), _1250214), _1250216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250212), _1250214), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1250212), _1250218), _1250216))))], (42085 ^ _779142) ^ [_1615946, _1615948, _1615950, _1615952] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615946), tc_List_Olist(_1615946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615946), tc_List_Olist(_1615946)), _1615948), _1615950)), c_List_Olistrel(_1615946, _1615952)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615946)), _1615948) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615946)), _1615950), 42091 ^ _779142 : [(42094 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615946, _1615946, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615946, tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_fun(_1615946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615946, tc_fun(tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_fun(_1615946, tc_HOL_Obool)), _1615946), c_COMBC(_1615946, tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615946, tc_prod(_1615946, _1615946)), tc_fun(_1615946, tc_fun(tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_HOL_Obool)), _1615946), hAPP(c_COMBB(tc_prod(_1615946, _1615946), tc_fun(tc_fun(tc_prod(_1615946, _1615946), tc_HOL_Obool), tc_HOL_Obool), _1615946), c_member(tc_prod(_1615946, _1615946)))), c_Product__Type_OPair(_1615946, _1615946)))), _1615952)), 42090 ^ [_1615946, _1615948, _1615950, _1615952]))], (42092 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615946, _1615946)), 42090 ^ [_1615946, _1615948, _1615950, _1615952]), hAPP(c_List_Oset(tc_prod(_1615946, _1615946)), hAPP(hAPP(c_List_Ozip(_1615946, _1615946), _1615948), _1615950)))))]]], (5940 ^ _779142) ^ [_873428, _873430, _873432, _873434, _873436] : [hBOOL(hAPP(hAPP(c_member(_873428), _873430), hAPP(c_Set_Oimage(_873432, _873428, _873434), _873436))), 5944 ^ _779142 : [(5947 ^ _779142) ^ [] : [-(_873430 = hAPP(_873434, 5943 ^ [_873428, _873430, _873432, _873434, _873436]))], (5945 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873432), 5943 ^ [_873428, _873430, _873432, _873434, _873436]), _873436)))]]], (31871 ^ _779142) ^ [_1353147, _1353149, _1353151, _1353153, _1353155, _1353157, _1353159] : [class_Rings_Osemiring__0(_1353147), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353147), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353149, _1353147), _1353151), _1353153)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353155, _1353147), _1353157), _1353159)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353149, _1353147), hAPP(hAPP(c_COMBC(_1353149, tc_fun(_1353155, tc_HOL_Obool), _1353147), hAPP(hAPP(c_COMBB(tc_fun(_1353155, _1353147), tc_fun(tc_fun(_1353155, tc_HOL_Obool), _1353147), _1353149), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353155, _1353147)), hAPP(hAPP(c_COMBC(_1353149, tc_fun(_1353155, _1353147), tc_fun(_1353155, _1353147)), hAPP(hAPP(c_COMBB(tc_fun(_1353147, _1353147), tc_fun(tc_fun(_1353155, _1353147), tc_fun(_1353155, _1353147)), _1353149), c_COMBB(_1353147, _1353147, _1353155)), hAPP(hAPP(c_COMBB(_1353147, tc_fun(_1353147, _1353147), _1353149), c_Groups_Otimes__class_Otimes(_1353147)), _1353151))), _1353157))), _1353159)), _1353153))], (25602 ^ _779142) ^ [_1229102, _1229104] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1229102)), c_Int_OBit0(_1229104)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1229102), _1229104)))], (32287 ^ _779142) ^ [_1366878, _1366880, _1366882] : [class_Groups_Ocomm__monoid__add(_1366878), class_Groups_Ocomm__monoid__mult(_1366878), c_Nat__Transfer_Onat__set(_1366880), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1366878), _1366882), _1366880) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1366878), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1366878, tc_Nat_Onat), _1366882), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1366880)))], (10727 ^ _779142) ^ [_964534, _964536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964536), hAPP(c_Nat_OSuc, _964534))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964534), _964536))], (43674 ^ _779142) ^ [_1652827, _1652829, _1652831, _1652833, _1652835] : [-(hAPP(hAPP(c_List_Ozip(_1652827, _1652829), hAPP(hAPP(c_List_Oappend(_1652827), _1652831), _1652833)), _1652835) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652827, _1652829)), hAPP(hAPP(c_List_Ozip(_1652827, _1652829), _1652831), hAPP(hAPP(c_List_Otake(_1652829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652827)), _1652831)), _1652835))), hAPP(hAPP(c_List_Ozip(_1652827, _1652829), _1652833), hAPP(hAPP(c_List_Odrop(_1652829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652827)), _1652831)), _1652835))))], (10129 ^ _779142) ^ [_953327, _953329, _953331, _953333] : [class_Rings_Ocomm__semiring__1(_953327), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953327), _953329), _953331)), _953333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953327), _953329), _953333)), _953331))], (37481 ^ _779142) ^ [_1488383, _1488385, _1488387] : [-(hAPP(c_Set_OCollect(_1488383), hAPP(hAPP(c_COMBS(_1488383, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488383), c_fconj), _1488385)), _1488387)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488383, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488383), _1488385)), hAPP(c_Set_OCollect(_1488383), _1488387)))], (52311 ^ _779142) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (50615 ^ _779142) ^ [_1804421, _1804423, _1804425] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804421), _1804423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804421), _1804425))), -(_1804421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1804423), _1804425)))], (15667 ^ _779142) ^ [_1053957, _1053959, _1053961, _1053963] : [class_Int_Onumber__ring(_1053957), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053957), hAPP(c_Int_Onumber__class_Onumber__of(_1053957), _1053959)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053957), hAPP(c_Int_Onumber__class_Onumber__of(_1053957), _1053961)), _1053963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053957), hAPP(c_Int_Onumber__class_Onumber__of(_1053957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1053959), _1053961))), _1053963))], (24700 ^ _779142) ^ [_1213539, _1213541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1213539)), c_Int_OBit1(_1213541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213539), _1213541)))], (22274 ^ _779142) ^ [_1170936, _1170938, _1170940, _1170942] : [class_Rings_Olinordered__semidom(_1170936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170938), _1170940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170936), c_Groups_Ozero__class_Ozero(_1170936)), _1170942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170936), _1170942), c_Groups_Oone__class_Oone(_1170936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170936), hAPP(hAPP(c_Power_Opower__class_Opower(_1170936), _1170942), _1170940)), hAPP(hAPP(c_Power_Opower__class_Opower(_1170936), _1170942), _1170938))))], (1616 ^ _779142) ^ [_802284, _802286] : [-(class_Rings_Oordered__comm__semiring(_802284)), _802286 = _802284, class_Rings_Oordered__comm__semiring(_802286)], (19073 ^ _779142) ^ [_1114393] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114393)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114393)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114393))], (29889 ^ _779142) ^ [_1312548, _1312550, _1312552] : [class_Groups_Oab__semigroup__mult(_1312548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312548), _1312550)), -(_1312550 = c_Orderings_Obot__class_Obot(tc_fun(_1312548, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312548), _1312552)), -(_1312552 = c_Orderings_Obot__class_Obot(tc_fun(_1312548, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312548, tc_HOL_Obool)), _1312550), _1312552) = c_Orderings_Obot__class_Obot(tc_fun(_1312548, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1312548, c_Groups_Otimes__class_Otimes(_1312548)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312548, tc_HOL_Obool)), _1312550), _1312552)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312548), hAPP(c_Finite__Set_Ofold1(_1312548, c_Groups_Otimes__class_Otimes(_1312548)), _1312550)), hAPP(c_Finite__Set_Ofold1(_1312548, c_Groups_Otimes__class_Otimes(_1312548)), _1312552)))], (2806 ^ _779142) ^ [_820659, _820661] : [_820661 = _820659, -(c_Nat_Ofunpow(_820661) = c_Nat_Ofunpow(_820659))], (30800 ^ _779142) ^ [_1331068] : [class_Finite__Set_Ofinite(_1331068), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1331068), c_Orderings_Otop__class_Otop(tc_fun(_1331068, tc_HOL_Obool)))))], (31404 ^ _779142) ^ [_1342337, _1342339, _1342341] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342337, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1342337, tc_HOL_Obool), tc_HOL_Obool)), _1342339), _1342341)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342337, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342337, tc_HOL_Obool), _1342339)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342337, tc_HOL_Obool), _1342341)))], (47493 ^ _779142) ^ [_1735890, _1735892, _1735894, _1735896, _1735898] : [hAPP(hAPP(c_List_Olist_OCons(_1735890), _1735892), _1735894) = hAPP(c_List_Ofilter(_1735890, _1735896), _1735898), 47498 ^ _779142 : [(47507 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1735896, _1735892)))], (47509 ^ _779142) ^ [] : [-(_1735894 = hAPP(c_List_Ofilter(_1735890, _1735896), 47497 ^ [_1735890, _1735892, _1735894, _1735896, _1735898]))], (47501 ^ _779142) ^ [_1736204] : [hBOOL(hAPP(hAPP(c_member(_1735890), _1736204), hAPP(c_List_Oset(_1735890), 47496 ^ [_1735890, _1735892, _1735894, _1735896, _1735898]))), hBOOL(hAPP(_1735896, _1736204))], (47499 ^ _779142) ^ [] : [-(_1735898 = hAPP(hAPP(c_List_Oappend(_1735890), 47496 ^ [_1735890, _1735892, _1735894, _1735896, _1735898]), hAPP(hAPP(c_List_Olist_OCons(_1735890), _1735892), 47497 ^ [_1735890, _1735892, _1735894, _1735896, _1735898])))]]], (20708 ^ _779142) ^ [_1143026, _1143028, _1143030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1143026), _1143028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143026), _1143030)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143028), _1143030))))], (52349 ^ _779142) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (36010 ^ _779142) ^ [_1455404, _1455406, _1455408] : [c_Equiv__Relations_Oequivp(_1455404, _1455406), -(hBOOL(hAPP(hAPP(_1455406, _1455408), _1455408)))], (39327 ^ _779142) ^ [_1543537, _1543539] : [39329 ^ _779142 : [(39332 ^ _779142) ^ [] : [hBOOL(hAPP(_1543537, hAPP(c_Int_OAbs__Integ, 39328 ^ [_1543537, _1543539])))], (39330 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39328 ^ [_1543537, _1543539]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1543537, _1543539)))], (19999 ^ _779142) ^ [_1130234] : [_1130234 = 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), _1130234)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (12604 ^ _779142) ^ [_996769, _996771, _996773, _996775] : [class_Groups_Oordered__comm__monoid__add(_996769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996769), c_Groups_Ozero__class_Ozero(_996769)), _996771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996769), _996773), _996775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996769), _996773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996769), _996771), _996775))))], (45697 ^ _779142) ^ [_1697284, _1697286, _1697288, _1697290] : [hBOOL(hAPP(_1697284, _1697286)), -(hAPP(c_List_Ofilter(_1697288, _1697284), hAPP(hAPP(c_List_Olist_OCons(_1697288), _1697286), _1697290)) = hAPP(hAPP(c_List_Olist_OCons(_1697288), _1697286), hAPP(c_List_Ofilter(_1697288, _1697284), _1697290)))], (6199 ^ _779142) ^ [_878384, _878386] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878384, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_878384, tc_HOL_Obool))), _878386)))], (30674 ^ _779142) ^ [_1328248, _1328250, _1328252, _1328254] : [class_Groups_Ocomm__monoid__mult(_1328248), 30677 ^ _779142 : [(30684 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1328250), _1328252))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328250, _1328248), _1328254), _1328252) = c_Groups_Oone__class_Oone(_1328248))], (30678 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1328250), _1328252)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328250, _1328248), _1328254), _1328252) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328248, _1328250, c_Groups_Otimes__class_Otimes(_1328248)), _1328254), c_Groups_Oone__class_Oone(_1328248)), _1328252))]]], (14859 ^ _779142) ^ [_1038834, _1038836] : [class_Int_Oring__char__0(_1038834), hBOOL(hAPP(hAPP(c_member(_1038834), _1038836), c_Int_Oring__1__class_OInts(_1038834))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038834), c_Groups_Oone__class_Oone(_1038834)), _1038836)), _1038836) = c_Groups_Ozero__class_Ozero(_1038834)], (47111 ^ _779142) ^ [_1726907, _1726909, _1726911, _1726913] : [47113 ^ _779142 : [(47116 ^ _779142) ^ [] : [hBOOL(hAPP(_1726909, hAPP(hAPP(c_List_Onth(_1726911), _1726913), 47112 ^ [_1726907, _1726909, _1726911, _1726913])))], (47114 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47112 ^ [_1726907, _1726909, _1726911, _1726913]), _1726907)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726911)), _1726913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726911)), c_List_OtakeWhile(_1726911, _1726909, _1726913)))))], (19347 ^ _779142) ^ [_1119325, _1119327] : [class_Groups_Oordered__ab__group__add__abs(_1119325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119325), c_Groups_Ozero__class_Ozero(_1119325)), _1119327)), -(hAPP(c_Groups_Oabs__class_Oabs(_1119325), _1119327) = _1119327)], (6041 ^ _779142) ^ [_875549, _875551] : [v_P(hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _875549)), _875551), hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_875549)))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), -(v_P(_875551, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _875549)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (39928 ^ _779142) ^ [_1557474, _1557476, _1557478, _1557480, _1557482, _1557484] : [c_Finite__Set_Ofolding__idem(_1557474, _1557476, _1557478, _1557480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557474), _1557482)), hBOOL(hAPP(hAPP(c_member(_1557474), _1557484), _1557482)), -(hAPP(c_Fun_Ocomp(_1557476, _1557476, _1557476, hAPP(_1557480, _1557482)), hAPP(_1557478, _1557484)) = hAPP(_1557480, _1557482))], (21848 ^ _779142) ^ [_1163062, _1163064] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1163062)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1163062)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1163064)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1163062)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1163064))))], (5816 ^ _779142) ^ [_871259, _871261, _871263, _871265] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871259), _871261), _871263), _871265)), -(_871261 = _871265), -(hBOOL(hAPP(_871263, _871265)))], (21428 ^ _779142) ^ [_1155744, _1155746] : [class_Orderings_Oorder(_1155744), -(c_SetInterval_Oord__class_OatLeastAtMost(_1155744, _1155746, _1155746) = hAPP(hAPP(c_Set_Oinsert(_1155744), _1155746), c_Orderings_Obot__class_Obot(tc_fun(_1155744, tc_HOL_Obool))))], (32831 ^ _779142) ^ [_1378856, _1378858, _1378860] : [-(c_Nat_Onat_Onat__case(_1378856, _1378858, _1378860, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1378858)], (11302 ^ _779142) ^ [_973327, _973329] : [11303 ^ _779142 : [(11304 ^ _779142) ^ [_973380] : [_973329 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973327), _973380))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973327), _973329)))], (38384 ^ _779142) ^ [_1519150, _1519152, _1519154, _1519156, _1519158, _1519160, _1519162] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519150, _1519152, _1519154), hAPP(hAPP(c_Relation_Orel__comp(_1519150, _1519156, _1519152), _1519158), _1519160)), _1519162) = hAPP(hAPP(c_Relation_Orel__comp(_1519150, _1519156, _1519154), _1519158), hAPP(hAPP(c_Relation_Orel__comp(_1519156, _1519152, _1519154), _1519160), _1519162)))], (3366 ^ _779142) ^ [_829327, _829329, _829331, _829333, _829335, _829337] : [-(c_List_Opartition(_829337, _829333, _829329) = c_List_Opartition(_829335, _829331, _829327)), _829337 = _829335, _829333 = _829331, _829329 = _829327], (13963 ^ _779142) ^ [_1022339, _1022341, _1022343, _1022345] : [class_Fields_Olinordered__field__inverse__zero(_1022339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022339), _1022341), _1022343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022339), c_Groups_Ozero__class_Ozero(_1022339)), _1022345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022339), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022339), _1022341), _1022345)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022339), _1022343), _1022345))))], (27600 ^ _779142) ^ [_1266133, _1266135, _1266137] : [class_Lattices_Olattice(_1266133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266133), _1266135)), -(c_Big__Operators_Olattice__class_OSup__fin(_1266133, hAPP(hAPP(c_Set_Oinsert(_1266133), _1266137), _1266135)) = hAPP(hAPP(c_Finite__Set_Ofold(_1266133, _1266133, c_Lattices_Osemilattice__sup__class_Osup(_1266133)), _1266137), _1266135))], (38426 ^ _779142) ^ [_1520364, _1520366, _1520368, _1520370, _1520372, _1520374, _1520376, _1520378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520364, _1520366), tc_HOL_Obool)), _1520368), hAPP(hAPP(c_Product__Type_OSigma(_1520364, _1520366), _1520370), hAPP(c_COMBK(tc_fun(_1520366, tc_HOL_Obool), _1520364), _1520372)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520366, _1520374), tc_HOL_Obool)), _1520376), hAPP(hAPP(c_Product__Type_OSigma(_1520366, _1520374), _1520372), hAPP(c_COMBK(tc_fun(_1520374, tc_HOL_Obool), _1520366), _1520378)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520364, _1520374), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520364, _1520366, _1520374), _1520368), _1520376)), hAPP(hAPP(c_Product__Type_OSigma(_1520364, _1520374), _1520370), hAPP(c_COMBK(tc_fun(_1520374, tc_HOL_Obool), _1520364), _1520378)))))], (25408 ^ _779142) ^ [_1225747, _1225749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225747), _1225749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1225747)), c_Int_OBit0(_1225749))))], (29073 ^ _779142) ^ [_1294395, _1294397, _1294399, _1294401, _1294403] : [class_Lattices_Olattice(_1294395), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294397, _1294395)), _1294399), _1294401), _1294403) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294395), hAPP(_1294399, _1294403)), hAPP(_1294401, _1294403)))], (8274 ^ _779142) ^ [_916936, _916938, _916940, _916942, _916944] : [c_Fun_Ofun__upd(_916936, _916938, _916940, _916942, _916944) = _916940, -(hAPP(_916940, _916942) = _916944)], (51919 ^ _779142) ^ [_1827338, _1827340, _1827342, _1827344, _1827346] : [class_Divides_Osemiring__div(_1827338), -(_1827340 = c_Groups_Ozero__class_Ozero(_1827338)), -(_1827342 = c_Groups_Ozero__class_Ozero(_1827338)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827338), _1827340), _1827344)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827338), _1827342), _1827346)), 51938 ^ _779142 : [(51945 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827338), _1827344), _1827342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827338), _1827340), _1827346), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827338), _1827344), _1827340) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827338), _1827346), _1827342))], (51939 ^ _779142) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827338), _1827344), _1827340) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827338), _1827346), _1827342), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827338), _1827344), _1827342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827338), _1827340), _1827346))]]], (25458 ^ _779142) ^ [_1226628] : [c_Int_OPls = _1226628, -(c_Int_OPls = c_Int_OBit0(_1226628))], (31949 ^ _779142) ^ [_1356124, _1356126, _1356128, _1356130] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1356124, tc_fun(_1356126, tc_HOL_Obool))), _1356128), _1356130)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1356124, _1356126)), hAPP(hAPP(c_Product__Type_OPair(_1356124, _1356126), _1356128), _1356130)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1356124, _1356126), tc_HOL_Obool)))))], (32567 ^ _779142) ^ [_1373619, _1373621, _1373623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373619), _1373621)), -(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)), _1373619)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1373623), _1373621)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373623), _1373619)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373621), _1373619)))], (17793 ^ _779142) ^ [_1092703, _1092705] : [class_Int_Onumber__ring(_1092703), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092703), _1092705), hAPP(c_Int_Onumber__class_Onumber__of(_1092703), c_Int_OPls)) = _1092705)], (21023 ^ _779142) ^ [_1148809, _1148811, _1148813, _1148815] : [hBOOL(hAPP(hAPP(c_member(_1148809), _1148811), c_SetInterval_Oord_OatLeast(_1148809, _1148813, _1148815))), -(hBOOL(hAPP(hAPP(_1148813, _1148815), _1148811)))], (15851 ^ _779142) ^ [_1057125, _1057127, _1057129, _1057131] : [class_Orderings_Olinorder(_1057125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057125), _1057127)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1057125, _1057125, c_Orderings_Oord__class_Omin(_1057125)), _1057129), hAPP(hAPP(c_Set_Oinsert(_1057125), _1057131), _1057127)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1057125), _1057131), hAPP(hAPP(c_Finite__Set_Ofold(_1057125, _1057125, c_Orderings_Oord__class_Omin(_1057125)), _1057129), _1057127)))], (49340 ^ _779142) ^ [_1776569, _1776571, _1776573] : [c_Relation_Osym(_1776569, _1776571), c_Relation_Osym(_1776569, _1776573), -(c_Relation_Osym(_1776569, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1776569, _1776569), tc_HOL_Obool)), _1776571), _1776573)))], (15155 ^ _779142) ^ [_1044485, _1044487, _1044489] : [class_Int_Onumber(_1044485), 15158 ^ _779142 : [(15165 ^ _779142) ^ [] : [_1044489 = hAPP(c_Int_Onumber__class_Onumber__of(_1044485), _1044487), -(hAPP(c_Int_Onumber__class_Onumber__of(_1044485), _1044487) = _1044489)], (15159 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1044485), _1044487) = _1044489, -(_1044489 = hAPP(c_Int_Onumber__class_Onumber__of(_1044485), _1044487))]]], (30980 ^ _779142) ^ [_1334214, _1334216] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1334214, tc_HOL_Obool)), _1334216) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334214, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1334214, tc_HOL_Obool))), _1334216))], (35509 ^ _779142) ^ [_1443078, _1443080, _1443082, _1443084] : [-(hAPP(c_Relation_OImage(_1443078, _1443080, _1443082), _1443084) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1443078, tc_fun(_1443080, tc_HOL_Obool)), _1443084), hAPP(hAPP(c_COMBB(tc_fun(_1443078, tc_HOL_Obool), tc_fun(_1443080, tc_HOL_Obool), _1443078), c_Relation_OImage(_1443078, _1443080, _1443082)), hAPP(hAPP(c_COMBC(_1443078, tc_fun(_1443078, tc_HOL_Obool), tc_fun(_1443078, tc_HOL_Obool)), c_Set_Oinsert(_1443078)), c_Orderings_Obot__class_Obot(tc_fun(_1443078, tc_HOL_Obool))))))], (40450 ^ _779142) ^ [_1570896, _1570898, _1570900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570896, _1570896)), hAPP(hAPP(c_Product__Type_OPair(_1570896, _1570896), _1570898), _1570900)), c_Relation_OId(_1570896))), -(_1570898 = _1570900)], (41523 ^ _779142) ^ [_1599849, _1599851, _1599853, _1599855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599849), tc_List_Olist(_1599849))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599849), tc_List_Olist(_1599849)), _1599851), _1599853)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599849), tc_List_Olist(_1599849)), c_List_Olistrel1(_1599849, _1599855)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599849), tc_List_Olist(_1599849))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599849), tc_List_Olist(_1599849)), _1599851), _1599853)), c_List_Olistrel1(_1599849, hAPP(c_Relation_Oconverse(_1599849, _1599849), _1599855)))))], (38197 ^ _779142) ^ [_1513698, _1513700, _1513702, _1513704, _1513706, _1513708] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513698), _1513700)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513702), _1513704)), 38207 ^ _779142 : [(38210 ^ _779142) ^ [] : [hAPP(c_Finite__Set_Ocard(_1513698), hAPP(c_Set_OCollect(_1513698), hAPP(hAPP(c_COMBS(_1513698, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513698), c_fconj), hAPP(hAPP(c_COMBC(_1513698, tc_fun(_1513698, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513698)), _1513700))), hAPP(hAPP(c_COMBC(_1513698, _1513702, tc_HOL_Obool), _1513706), 38206 ^ [_1513698, _1513700, _1513702, _1513704, _1513706, _1513708])))) = hAPP(_1513708, 38206 ^ [_1513698, _1513700, _1513702, _1513704, _1513706, _1513708])], (38208 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513702), 38206 ^ [_1513698, _1513700, _1513702, _1513704, _1513706, _1513708]), _1513704)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513698, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1513702, tc_HOL_Obool), tc_Nat_Onat, _1513698), c_Finite__Set_Ocard(_1513702)), hAPP(hAPP(c_COMBB(tc_fun(_1513702, tc_HOL_Obool), tc_fun(_1513702, tc_HOL_Obool), _1513698), c_Set_OCollect(_1513702)), hAPP(hAPP(c_COMBB(tc_fun(_1513702, tc_HOL_Obool), tc_fun(_1513702, tc_HOL_Obool), _1513698), hAPP(c_COMBS(_1513702, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513702), c_fconj), hAPP(hAPP(c_COMBC(_1513702, tc_fun(_1513702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513702)), _1513704)))), _1513706)))), _1513700) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513702, tc_Nat_Onat), _1513708), _1513704))], (9515 ^ _779142) ^ [_941166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941166), _941166))], (33303 ^ _779142) ^ [_1388747, _1388749, _1388751] : [33305 ^ _779142 : [(33308 ^ _779142) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1388747, _1388749), 33304 ^ [_1388747, _1388749, _1388751]))], (33306 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1388749, 33304 ^ [_1388747, _1388749, _1388751]), _1388751)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1388747, _1388749), _1388751)))], (41923 ^ _779142) ^ [_1611349, _1611351, _1611353, _1611355] : [-(hBOOL(hAPP(hAPP(c_member(_1611349), _1611351), hAPP(c_List_Oset(_1611349), _1611353)))), hBOOL(hAPP(hAPP(c_member(_1611349), _1611351), hAPP(c_List_Oset(_1611349), c_List_Osublist(_1611349, _1611353, _1611355))))], (9863 ^ _779142) ^ [_947229, _947231] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947229), _947231)), _947229) = _947231)], (47205 ^ _779142) ^ [_1728716, _1728718, _1728720, _1728722] : [-(c_List_Omaps(_1728716, _1728718, _1728720, _1728722) = c_List_Oconcat(_1728718, hAPP(hAPP(c_List_Omap(_1728716, tc_List_Olist(_1728718)), _1728720), _1728722)))], (30 ^ _779142) ^ [_779527, _779529, _779531, _779533, _779535, _779537, _779539, _779541, _779543, _779545, _779547, _779549] : [-(c_Nitpick_Ofold__graph_H(_779547, _779543, _779539, _779535, _779531, _779527)), c_Nitpick_Ofold__graph_H(_779549, _779545, _779541, _779537, _779533, _779529), _779549 = _779547, _779545 = _779543, _779541 = _779539, _779537 = _779535, _779533 = _779531, _779529 = _779527], (6623 ^ _779142) ^ [_885838, _885840, _885842, _885844, _885846, _885848] : [c_Finite__Set_Ofolding__image__simple(_885838, _885840, _885842, _885844, _885846, _885848), -(hAPP(_885848, c_Orderings_Obot__class_Obot(tc_fun(_885840, tc_HOL_Obool))) = _885844)], (50095 ^ _779142) ^ [_1792174, _1792176, _1792178, _1792180] : [c_Fun_Obij__betw(_1792174, _1792176, _1792178, _1792180, c_Orderings_Obot__class_Obot(tc_fun(_1792176, tc_HOL_Obool))), -(_1792180 = c_Orderings_Obot__class_Obot(tc_fun(_1792174, tc_HOL_Obool)))], (48398 ^ _779142) ^ [_1754938, _1754940, _1754942, _1754944, _1754946, _1754948] : [-(c_New__Random__Sequence_Opos__union(_1754938, _1754940, _1754942, _1754944, _1754946, _1754948) = c_New__DSequence_Opos__union(_1754938, hAPP(hAPP(hAPP(_1754940, _1754944), _1754946), _1754948), hAPP(hAPP(hAPP(_1754942, _1754944), _1754946), _1754948)))], (28901 ^ _779142) ^ [_1291399, _1291401, _1291403, _1291405] : [hBOOL(hAPP(hAPP(c_member(_1291399), _1291401), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291399, tc_HOL_Obool)), _1291403), _1291405))), -(hBOOL(hAPP(hAPP(c_member(_1291399), _1291401), _1291405)))], (1326 ^ _779142) ^ [_798659, _798661] : [-(class_Groups_Oabs__if(_798659)), _798661 = _798659, class_Groups_Oabs__if(_798661)], (44950 ^ _779142) ^ [_1680249, _1680251, _1680253, _1680255] : [hBOOL(hAPP(c_List_Olistsp(_1680249, _1680251), _1680253)), hBOOL(hAPP(c_List_Olistsp(_1680249, _1680255), _1680253)), -(hBOOL(hAPP(c_List_Olistsp(_1680249, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680249, tc_HOL_Obool)), _1680251), _1680255)), _1680253)))], (17553 ^ _779142) ^ [_1088468] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1088468) = c_Int_OPls)], (16875 ^ _779142) ^ [_1075926, _1075928, _1075930] : [class_Orderings_Olinorder(_1075926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075926), _1075928)), -(_1075930 = c_Orderings_Obot__class_Obot(tc_fun(_1075926, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075926, tc_HOL_Obool)), _1075930), _1075928)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075926), c_Big__Operators_Olinorder__class_OMin(_1075926, _1075930)), c_Big__Operators_Olinorder__class_OMin(_1075926, _1075928)) = c_Big__Operators_Olinorder__class_OMin(_1075926, _1075928))], (45468 ^ _779142) ^ [_1691493, _1691495, _1691497] : [-(hAPP(c_List_Oset(_1691493), hAPP(c_List_OremoveAll(_1691493, _1691495), _1691497)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691493, tc_HOL_Obool)), hAPP(c_List_Oset(_1691493), _1691497)), hAPP(hAPP(c_Set_Oinsert(_1691493), _1691495), c_Orderings_Obot__class_Obot(tc_fun(_1691493, tc_HOL_Obool)))))], (10537 ^ _779142) ^ [_961513] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _961513)], (14377 ^ _779142) ^ [_1029665, _1029667, _1029669, _1029671] : [class_Fields_Olinordered__field__inverse__zero(_1029665), 14380 ^ _779142 : [(14381 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029665), _1029669), _1029671))), 14384 ^ _779142 : [(14391 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), c_Groups_Ozero__class_Ozero(_1029665)), _1029671))), 14394 ^ _779142 : [(14401 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029671), c_Groups_Ozero__class_Ozero(_1029665)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029667), c_Groups_Ozero__class_Ozero(_1029665))))], (14395 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029671), c_Groups_Ozero__class_Ozero(_1029665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029665), _1029667), _1029671))))]]], (14385 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), c_Groups_Ozero__class_Ozero(_1029665)), _1029671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029665), _1029667), _1029671)), _1029669)))]]], (14407 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029665), _1029669), _1029671)))), 14410 ^ _779142 : [(14413 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029665), _1029667), _1029671)), _1029669))], (14411 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), c_Groups_Ozero__class_Ozero(_1029665)), _1029671)))]], 14414 ^ _779142 : [(14417 ^ _779142) ^ [] : [14418 ^ _779142 : [(14421 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029665), _1029667), _1029671)))], (14419 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029671), c_Groups_Ozero__class_Ozero(_1029665))))]], 14422 ^ _779142 : [(14425 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029667), c_Groups_Ozero__class_Ozero(_1029665)))], (14423 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), _1029671), c_Groups_Ozero__class_Ozero(_1029665)))]]], (14415 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029665), c_Groups_Ozero__class_Ozero(_1029665)), _1029671))]]]]], (42662 ^ _779142) ^ [_1629459, _1629461, _1629463] : [42663 ^ _779142 : [(42666 ^ _779142) ^ [] : [_1629463 = c_List_Olist_ONil(_1629459)], (42664 ^ _779142) ^ [] : [_1629461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1629459), _1629461), _1629463) = c_List_Olist_ONil(_1629459))], (51811 ^ _779142) ^ [_1825344, _1825346] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825344), 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)))), _1825346))), 51814 ^ _779142 : [(51817 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825344), _1825346))], (51815 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825346), _1825344)))]]], (28845 ^ _779142) ^ [_1290012, _1290014, _1290016, _1290018] : [class_Lattices_Odistrib__lattice(_1290012), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1290012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290012), _1290014), _1290016)), _1290018) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290012), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1290012), _1290014), _1290018)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1290012), _1290016), _1290018)))], (10953 ^ _779142) ^ [_968196, _968198] : [class_Groups_Ocomm__monoid__add(_968196), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968196), c_Groups_Ozero__class_Ozero(_968196)), _968198) = _968198)], (23559 ^ _779142) ^ [_1194041, _1194043, _1194045] : [class_Groups_Oordered__ab__group__add__abs(_1194041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194041), hAPP(c_Groups_Oabs__class_Oabs(_1194041), _1194043)), _1194045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194041), hAPP(c_Groups_Ouminus__class_Ouminus(_1194041), _1194043)), _1194045)))], (31925 ^ _779142) ^ [_1354756, _1354758, _1354760, _1354762] : [hAPP(hAPP(c_COMBC(_1354756, tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_fun(_1354758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354758, tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_fun(_1354758, tc_HOL_Obool)), _1354756), c_COMBC(_1354758, tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354758, tc_prod(_1354756, _1354758)), tc_fun(_1354758, tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), _1354756), hAPP(c_COMBB(tc_prod(_1354756, _1354758), tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool), _1354758), c_member(tc_prod(_1354756, _1354758)))), c_Product__Type_OPair(_1354756, _1354758)))), _1354760) = hAPP(hAPP(c_COMBC(_1354756, tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_fun(_1354758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354758, tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_fun(_1354758, tc_HOL_Obool)), _1354756), c_COMBC(_1354758, tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354758, tc_prod(_1354756, _1354758)), tc_fun(_1354758, tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool)), _1354756), hAPP(c_COMBB(tc_prod(_1354756, _1354758), tc_fun(tc_fun(tc_prod(_1354756, _1354758), tc_HOL_Obool), tc_HOL_Obool), _1354758), c_member(tc_prod(_1354756, _1354758)))), c_Product__Type_OPair(_1354756, _1354758)))), _1354762), -(_1354760 = _1354762)], (32355 ^ _779142) ^ [_1368606, _1368608] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1368606)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1368608)), hAPP(c_Int_Onat, _1368606)) = hAPP(c_Int_Onat, _1368608))], (41443 ^ _779142) ^ [_1597307, _1597309, _1597311, _1597313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597307), tc_List_Olist(_1597307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597307), tc_List_Olist(_1597307)), _1597309), _1597311)), c_List_Olex(_1597307, _1597313))), 41446 ^ _779142 : [(41449 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597307)), _1597309) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597307)), _1597311))], (41447 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597307), tc_List_Olist(_1597307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597307), tc_List_Olist(_1597307)), _1597309), _1597311)), c_List_Olexord(_1597307, _1597313))))]]], (38518 ^ _779142) ^ [_1524664, _1524666, _1524668, _1524670, _1524672] : [hBOOL(hAPP(hAPP(_1524664, _1524666), _1524668)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1524670, _1524672, _1524664), _1524668)))], (41637 ^ _779142) ^ [_1603238, _1603240, _1603242, _1603244, _1603246, _1603248] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603238, _1603238)), hAPP(hAPP(c_Product__Type_OPair(_1603238, _1603238), _1603240), _1603242)), _1603244)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603238), tc_List_Olist(_1603238))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603238), tc_List_Olist(_1603238)), _1603246), _1603248)), c_List_Olistrel(_1603238, _1603244))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603238), tc_List_Olist(_1603238))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603238), tc_List_Olist(_1603238)), hAPP(hAPP(c_List_Olist_OCons(_1603238), _1603240), _1603246)), hAPP(hAPP(c_List_Olist_OCons(_1603238), _1603242), _1603248))), c_List_Olistrel(_1603238, _1603244))))], (13693 ^ _779142) ^ [_1017249, _1017251, _1017253, _1017255] : [class_Fields_Olinordered__field__inverse__zero(_1017249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017249), _1017251), _1017253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017249), _1017255), c_Groups_Ozero__class_Ozero(_1017249))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017249), c_Groups_Ozero__class_Ozero(_1017249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017249), _1017251), _1017253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017249), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017249), _1017255), _1017251)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017249), _1017255), _1017253))))], (6478 ^ _779142) ^ [_882926, _882928] : [class_Orderings_Obot(_882926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882926), c_Orderings_Obot__class_Obot(_882926)), _882928)))], (28338 ^ _779142) ^ [_1279868, _1279870, _1279872] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1279868, _1279870, _1279872, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1279870)], (17757 ^ _779142) ^ [_1092081, _1092083] : [class_Rings_Olinordered__semidom(_1092081), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092081), c_Groups_Ozero__class_Ozero(_1092081)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092081), _1092083))))], (4006 ^ _779142) ^ [_839713, _839715] : [_839715 = _839713, -(c_New__Random__Sequence_Oneg__single(_839715) = c_New__Random__Sequence_Oneg__single(_839713))], (6085 ^ _779142) ^ [_876251, _876253, _876255, _876257, _876259] : [c_Finite__Set_Ofolding__one__idem(_876251, _876253, _876255), hBOOL(hAPP(c_Finite__Set_Ofinite(_876251), _876257)), -(_876257 = c_Orderings_Obot__class_Obot(tc_fun(_876251, tc_HOL_Obool))), -(hAPP(_876255, hAPP(hAPP(c_Set_Oinsert(_876251), _876259), _876257)) = hAPP(hAPP(_876253, _876259), hAPP(_876255, _876257)))], (52449 ^ _779142) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (34875 ^ _779142) ^ [_1426199, _1426201, _1426203, _1426205, _1426207] : [_1426199 = c_Orderings_Obot__class_Obot(tc_fun(_1426201, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1426203), _1426205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426201, tc_fun(_1426203, tc_HOL_Obool)), _1426199), _1426207)) = hAPP(hAPP(c_Set_Oinsert(_1426203), _1426205), c_Orderings_Obot__class_Obot(tc_fun(_1426203, tc_HOL_Obool))))], (34174 ^ _779142) ^ [_1406249, _1406251, _1406253, _1406255, _1406257, _1406259, _1406261] : [-(hAPP(c_Product__Type_Oapsnd(_1406249, _1406251, _1406253, _1406255), hAPP(c_Product__Type_Oapfst(_1406257, _1406253, _1406249, _1406259), _1406261)) = hAPP(c_Product__Type_Oapfst(_1406257, _1406253, _1406251, _1406259), hAPP(c_Product__Type_Oapsnd(_1406249, _1406251, _1406257, _1406255), _1406261)))], (10303 ^ _779142) ^ [_957219, _957221, _957223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957219), _957221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957223), _957221))))], (41621 ^ _779142) ^ [_1602810, _1602812, _1602814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602810, _1602810), tc_HOL_Obool)), _1602812), _1602814)), c_Relation_Orefl__on(_1602810, c_Orderings_Otop__class_Otop(tc_fun(_1602810, tc_HOL_Obool)), _1602814), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602810), tc_List_Olist(_1602810)), tc_HOL_Obool)), c_List_Olistrel1(_1602810, _1602812)), c_List_Olistrel(_1602810, _1602814))))], (41761 ^ _779142) ^ [_1606886, _1606888, _1606890] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606886)), _1606888), c_List_Olists(_1606886, c_Wellfounded_Oacc(_1606886, _1606890)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606886)), _1606888), c_Wellfounded_Oacc(tc_List_Olist(_1606886), c_List_Olistrel1(_1606886, _1606890)))))], (49614 ^ _779142) ^ [_1781694, _1781696, _1781698, _1781700, _1781702] : [c_Fun_Oinj__on(_1781694, _1781696, _1781698, c_Orderings_Otop__class_Otop(tc_fun(_1781694, tc_HOL_Obool))), hAPP(_1781698, _1781700) = _1781702, -(hAPP(c_Hilbert__Choice_Oinv__into(_1781694, _1781696, c_Orderings_Otop__class_Otop(tc_fun(_1781694, tc_HOL_Obool)), _1781698), _1781702) = _1781700)], (13529 ^ _779142) ^ [_1014538, _1014540, _1014542, _1014544] : [class_Rings_Odivision__ring(_1014538), -(_1014540 = c_Groups_Ozero__class_Ozero(_1014538)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014538), _1014542), _1014540) = _1014544, -(_1014542 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014538), _1014544), _1014540))], (17351 ^ _779142) ^ [_1084448, _1084450, _1084452] : [class_Nat_Osemiring__char__0(_1084448), 17354 ^ _779142 : [(17361 ^ _779142) ^ [] : [_1084450 = _1084452, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084448), _1084450) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084448), _1084452))], (17355 ^ _779142) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084448), _1084450) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084448), _1084452), -(_1084450 = _1084452)]]], (50787 ^ _779142) ^ [_1807509, _1807511, _1807513, _1807515] : [class_Divides_Osemiring__div(_1807509), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807509), _1807511), _1807513)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807509), _1807515), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807509), _1807513), _1807511)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807509), _1807515), _1807513)), _1807511))], (43792 ^ _779142) ^ [_1655037, _1655039] : [-(c_List_Orotate(_1655037, _1655039) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1655037), tc_List_Olist(_1655037)), _1655039), c_List_Orotate1(_1655037)))], (10913 ^ _779142) ^ [_967537, _967539, _967541] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967537)), _967539) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967537)), _967541), -(_967539 = _967541)], (48046 ^ _779142) ^ [_1747320, _1747322, _1747324, _1747326, _1747328] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1747320), _1747322), _1747324), _1747326), _1747328) = c_New__DSequence_Oneg__single(_1747320, _1747322))], (45539 ^ _779142) ^ [_1692920, _1692922] : [c_List_Oconcat(_1692920, _1692922) = c_List_Olist_ONil(_1692920), 45542 ^ _779142 : [(45543 ^ _779142) ^ [_1693011] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692920)), _1693011), hAPP(c_List_Oset(tc_List_Olist(_1692920)), _1692922))), -(_1693011 = c_List_Olist_ONil(_1692920))]]], (29391 ^ _779142) ^ [_1301078, _1301080, _1301082] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301078, tc_HOL_Obool)), _1301080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301078, tc_HOL_Obool)), _1301082), _1301080)) = c_Orderings_Obot__class_Obot(tc_fun(_1301078, tc_HOL_Obool)))], (43109 ^ _779142) ^ [_1639179, _1639181, _1639183, _1639185] : [_1639183 = _1639185, -(hAPP(hAPP(c_List_Oappend(_1639179), _1639181), _1639183) = hAPP(hAPP(c_List_Oappend(_1639179), _1639181), _1639185))], (52651 ^ _779142) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (21268 ^ _779142) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (46698 ^ _779142) ^ [_1718129, _1718131, _1718133, _1718135] : [_1718131 = hAPP(hAPP(c_List_Oappend(_1718129), hAPP(c_List_Orev(_1718129), _1718135)), hAPP(hAPP(c_List_Olist_OCons(_1718129), _1718133), c_List_Olist_ONil(_1718129))), -(hAPP(c_List_Orev(_1718129), _1718131) = hAPP(hAPP(c_List_Olist_OCons(_1718129), _1718133), _1718135))], (48186 ^ _779142) ^ [_1750866, _1750868, _1750870, _1750872, _1750874, _1750876] : [-(hAPP(hAPP(c_List_Ozip(_1750866, _1750868), c_List_Oreplicate(_1750866, _1750870, _1750872)), c_List_Oreplicate(_1750868, _1750874, _1750876)) = c_List_Oreplicate(tc_prod(_1750866, _1750868), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750870), _1750874), hAPP(hAPP(c_Product__Type_OPair(_1750866, _1750868), _1750872), _1750876)))], (45454 ^ _779142) ^ [_1691211, _1691213, _1691215] : [-(hBOOL(hAPP(hAPP(c_member(_1691211), _1691213), hAPP(c_List_Oset(_1691211), _1691215)))), -(c_List_Oremdups(_1691211, hAPP(hAPP(c_List_Olist_OCons(_1691211), _1691213), _1691215)) = hAPP(hAPP(c_List_Olist_OCons(_1691211), _1691213), c_List_Oremdups(_1691211, _1691215)))], (15421 ^ _779142) ^ [_1049264, _1049266, _1049268] : [class_Orderings_Olinorder(_1049264), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049264), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049264), _1049266), _1049268)), _1049268)))], (13173 ^ _779142) ^ [_1007534, _1007536, _1007538] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007534), _1007536)), -(hAPP(c_Finite__Set_Ocard(_1007534), hAPP(hAPP(c_Set_Oinsert(_1007534), _1007538), _1007536)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1007534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007534, tc_HOL_Obool)), _1007536), hAPP(hAPP(c_Set_Oinsert(_1007534), _1007538), c_Orderings_Obot__class_Obot(tc_fun(_1007534, tc_HOL_Obool)))))))], (13517 ^ _779142) ^ [_1014284, _1014286, _1014288, _1014290] : [class_Rings_Odivision__ring(_1014284), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014284), _1014286), _1014288)), _1014290) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014284), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014284), _1014286), _1014290)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014284), _1014288), _1014290)))], (32859 ^ _779142) ^ [_1379412, _1379414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1379412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1379414)), -(c_Divides_OposDivAlg(_1379412, _1379414) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1379412), _1379414)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1379412, _1379414)))], (37701 ^ _779142) ^ [_1494540, _1494542, _1494544, _1494546] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1494540, _1494542)), hAPP(hAPP(c_Product__Type_OSigma(_1494540, _1494542), hAPP(hAPP(c_Set_Oinsert(_1494540), _1494544), c_Orderings_Obot__class_Obot(tc_fun(_1494540, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1494542, tc_HOL_Obool), _1494540), _1494546))) = hAPP(c_Finite__Set_Ocard(_1494542), _1494546))], (10005 ^ _779142) ^ [_950358, _950360, _950362] : [class_Rings_Ocomm__semiring__1(_950358), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950358), _950360), _950362)), _950362) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950358), _950360), c_Groups_Oone__class_Oone(_950358))), _950362))], (16833 ^ _779142) ^ [_1075221, _1075223, _1075225] : [class_Orderings_Olinorder(_1075221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075221, tc_HOL_Obool)), _1075223), _1075225)), -(_1075223 = c_Orderings_Obot__class_Obot(tc_fun(_1075221, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075221), _1075225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075221), c_Big__Operators_Olinorder__class_OMin(_1075221, _1075225)), c_Big__Operators_Olinorder__class_OMin(_1075221, _1075223))))], (5012 ^ _779142) ^ [_855568, _855570, _855572, _855574, _855576, _855578] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855578, _855574, _855570) = c_SetInterval_Oord__class_OatLeastAtMost(_855576, _855572, _855568)), _855578 = _855576, _855574 = _855572, _855570 = _855568], (19319 ^ _779142) ^ [_1118874, _1118876] : [class_Divides_Osemiring__div(_1118874), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1118874), _1118876), c_Groups_Oone__class_Oone(_1118874)) = _1118876)], (10458 ^ _779142) ^ [_960258] : [_960258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960258), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (45813 ^ _779142) ^ [_1700576] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700576)), c_List_Otranspose__rel(_1700576)), c_List_Olist_ONil(tc_List_Olist(_1700576)))), -(c_List_Otranspose(_1700576, c_List_Olist_ONil(tc_List_Olist(_1700576))) = c_List_Olist_ONil(tc_List_Olist(_1700576)))], (5810 ^ _779142) ^ [_871155, _871157] : [class_Finite__Set_Ofinite(_871155), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871155), _871157)))], (18921 ^ _779142) ^ [_1112006] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1112006), c_Int_OMin) = c_Int_Osucc(_1112006))], (44560 ^ _779142) ^ [_1671676, _1671678, _1671680] : [c_Fun_Oinj__on(_1671676, _1671678, _1671680, c_Orderings_Otop__class_Otop(tc_fun(_1671676, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1671676), tc_List_Olist(_1671678), hAPP(c_List_Omap(_1671676, _1671678), _1671680), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671676), tc_HOL_Obool))))], (34431 ^ _779142) ^ [_1413054, _1413056, _1413058, _1413060, _1413062] : [34433 ^ _779142 : [(34436 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413054, tc_HOL_Obool)), hAPP(_1413060, 34432 ^ [_1413054, _1413056, _1413058, _1413060, _1413062])), _1413062))], (34434 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413056), 34432 ^ [_1413054, _1413056, _1413058, _1413060, _1413062]), _1413058)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413054, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413056, tc_fun(_1413054, tc_HOL_Obool)), _1413058), _1413060)), _1413062)))], (3718 ^ _779142) ^ [_834869, _834871] : [_834871 = _834869, -(c_Enum_Oenum__class_Oenum__ex(_834871) = c_Enum_Oenum__class_Oenum__ex(_834869))], (25618 ^ _779142) ^ [_1229414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229414), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1229414)), c_Int_OMin)))], (43490 ^ _779142) ^ [_1648289, _1648291, _1648293] : [-(hAPP(hAPP(c_List_Odrop(_1648289), _1648291), c_List_Obutlast(_1648289, _1648293)) = c_List_Obutlast(_1648289, hAPP(hAPP(c_List_Odrop(_1648289), _1648291), _1648293)))], (46990 ^ _779142) ^ [_1724309, _1724311, _1724313, _1724315] : [hBOOL(hAPP(_1724309, _1724311)), -(c_List_OdropWhile(_1724313, _1724309, hAPP(hAPP(c_List_Olist_OCons(_1724313), _1724311), _1724315)) = c_List_OdropWhile(_1724313, _1724309, _1724315))], (7942 ^ _779142) ^ [_909868, _909870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909868, tc_HOL_Obool)), _909870), c_Orderings_Obot__class_Obot(tc_fun(_909868, tc_HOL_Obool))))], (27266 ^ _779142) ^ [_1260273, _1260275] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1260273, _1260275))))], (7716 ^ _779142) ^ [_906594, _906596, _906598] : [class_Orderings_Olinorder(_906594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906594), _906596), _906598)), 7723 ^ _779142 : [(7730 ^ _779142) ^ [] : [_906596 = _906598, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906594), _906596), _906598))], (7724 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906594), _906596), _906598))), -(_906596 = _906598)]]], (4314 ^ _779142) ^ [_844581, _844583, _844585, _844587, _844589, _844591] : [-(c_New__DSequence_Opos__union(_844591, _844587, _844583) = c_New__DSequence_Opos__union(_844589, _844585, _844581)), _844591 = _844589, _844587 = _844585, _844583 = _844581], (46808 ^ _779142) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (9639 ^ _779142) ^ [_943199, _943201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943199), _943201)), 9642 ^ _779142 : [(9645 ^ _779142) ^ [] : [_943199 = _943201], (9643 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943199), _943201)))]]], (44255 ^ _779142) ^ [_1664157, _1664159] : [-(_1664157 = c_List_Olist_ONil(_1664159)), -(hAPP(hAPP(c_List_Oappend(_1664159), c_List_Obutlast(_1664159, _1664157)), hAPP(hAPP(c_List_Olist_OCons(_1664159), c_List_Olast(_1664159, _1664157)), c_List_Olist_ONil(_1664159))) = _1664157)], (4340 ^ _779142) ^ [_844972, _844974, _844976, _844978] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844978, _844974) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844976, _844972)), _844978 = _844976, _844974 = _844972], (37197 ^ _779142) ^ [_1481359, _1481361] : [-(hAPP(c_Set_Ovimage(_1481359, _1481359, c_COMBI(_1481359)), _1481361) = _1481361)], (3308 ^ _779142) ^ [_828438, _828440, _828442, _828444] : [-(c_HOL_OLet(_828444, _828440) = c_HOL_OLet(_828442, _828438)), _828444 = _828442, _828440 = _828438], (3232 ^ _779142) ^ [_827286, _827288, _827290, _827292] : [-(c_Code__Numeral_Onat__of__aux(_827292, _827288) = c_Code__Numeral_Onat__of__aux(_827290, _827286)), _827292 = _827290, _827288 = _827286], (47010 ^ _779142) ^ [_1724619, _1724621, _1724623] : [-(c_List_OdropWhile(_1724619, _1724621, _1724623) = c_List_Olist_ONil(_1724619)), hBOOL(hAPP(_1724621, hAPP(c_List_Ohd(_1724619), c_List_OdropWhile(_1724619, _1724621, _1724623))))], (45618 ^ _779142) ^ [_1695195, _1695197, _1695199, _1695201] : [-(c_List_Oconcat(_1695195, hAPP(hAPP(c_List_Omap(_1695197, tc_List_Olist(_1695195)), hAPP(hAPP(c_COMBC(_1695197, tc_List_Olist(_1695195), tc_List_Olist(_1695195)), hAPP(hAPP(c_COMBB(_1695195, tc_fun(tc_List_Olist(_1695195), tc_List_Olist(_1695195)), _1695197), c_List_Olist_OCons(_1695195)), _1695199)), c_List_Olist_ONil(_1695195))), _1695201)) = hAPP(hAPP(c_List_Omap(_1695197, _1695195), _1695199), _1695201))], (29389 ^ _779142) ^ [_1300994, _1300996, _1300998, _1301000, _1301002] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300994, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1300996, _1300994, _1300998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300996, tc_HOL_Obool)), _1301000), _1301002))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300994, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1300996, _1300994, _1300998), _1301000)), hAPP(c_Set_Oimage(_1300996, _1300994, _1300998), _1301002)))))], (50204 ^ _779142) ^ [_1794198, _1794200, _1794202, _1794204, _1794206, _1794208] : [c_Fun_Obij__betw(_1794198, _1794200, _1794202, c_Orderings_Otop__class_Otop(tc_fun(_1794198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794200, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1794198, _1794200, _1794202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1794204, tc_fun(_1794198, tc_HOL_Obool)), _1794206), _1794208)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1794204, tc_fun(_1794200, tc_HOL_Obool)), _1794206), hAPP(hAPP(c_COMBB(tc_fun(_1794198, tc_HOL_Obool), tc_fun(_1794200, tc_HOL_Obool), _1794204), c_Set_Oimage(_1794198, _1794200, _1794202)), _1794208)))], (41613 ^ _779142) ^ [_1602564, _1602566] : [-(c_List_Olistrel(_1602564, c_Transitive__Closure_Ortrancl(_1602564, _1602566)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602564), c_List_Olistrel1(_1602564, _1602566)))], (48505 ^ _779142) ^ [_1757320, _1757322, _1757324] : [hBOOL(hAPP(hAPP(c_member(_1757320), _1757322), hAPP(c_List_Oset(_1757320), _1757324))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757320), _1757324), _1757322)))], (52255 ^ _779142) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (38846 ^ _779142) ^ [_1531358, _1531360, _1531362] : [c_Wellfounded_Owf(_1531358, _1531360), c_Wellfounded_Owf(_1531358, _1531362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531358, _1531358), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531358, _1531358, _1531358), _1531360), _1531362)), _1531360)), -(c_Wellfounded_Owf(_1531358, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531358, _1531358), tc_HOL_Obool)), _1531360), _1531362)))], (40966 ^ _779142) ^ [_1583384, _1583386, _1583388] : [40967 ^ _779142 : [(40968 ^ _779142) ^ [_1583460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583384, _1583384)), _1583386), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583384, _1583384), tc_HOL_Obool), _1583460), _1583388)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583384, _1583384)), _1583386), c_Transitive__Closure_Ortrancl(_1583384, _1583388))))], (49586 ^ _779142) ^ [_1781009, _1781011, _1781013] : [hAPP(c_Set_Oimage(_1781009, _1781011, _1781013), c_Orderings_Otop__class_Otop(tc_fun(_1781009, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781011, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1781011, _1781009, c_Hilbert__Choice_Oinv__into(_1781009, _1781011, c_Orderings_Otop__class_Otop(tc_fun(_1781009, tc_HOL_Obool)), _1781013), c_Orderings_Otop__class_Otop(tc_fun(_1781011, tc_HOL_Obool))))], (36468 ^ _779142) ^ [_1465155, _1465157, _1465159, _1465161] : [-(_1465155 = c_Orderings_Obot__class_Obot(tc_fun(_1465157, tc_HOL_Obool))), 36471 ^ _779142 : [(36472 ^ _779142) ^ [] : [-(hAPP(c_Set_Oimage(_1465159, _1465157, 36479 ^ [_1465155, _1465157, _1465159, _1465161]), _1465161) = _1465155), 36473 ^ _779142 : [(36474 ^ _779142) ^ [_1465296] : [c_Fun_Oinj__on(_1465157, _1465159, _1465296, _1465155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465159, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465157, _1465159, _1465296), _1465155)), _1465161))]]], (36483 ^ _779142) ^ [] : [36484 ^ _779142 : [(36485 ^ _779142) ^ [_1465488] : [hAPP(c_Set_Oimage(_1465159, _1465157, _1465488), _1465161) = _1465155]], 36487 ^ _779142 : [(36490 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465159, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465157, _1465159, 36486 ^ [_1465155, _1465157, _1465159, _1465161]), _1465155)), _1465161)))], (36488 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1465157, _1465159, 36486 ^ [_1465155, _1465157, _1465159, _1465161], _1465155))]]]]], (48615 ^ _779142) ^ [_1759960, _1759962, _1759964, _1759966, _1759968, _1759970, _1759972] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1759960, tc_fun(_1759962, tc_fun(_1759964, tc_HOL_Obool))), _1759966), _1759968), _1759970), _1759972)), 48619 ^ _779142 : [(48622 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1759968, 48618 ^ [_1759960, _1759962, _1759964, _1759966, _1759968, _1759970, _1759972]), _1759970), _1759972)))], (48620 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759960), 48618 ^ [_1759960, _1759962, _1759964, _1759966, _1759968, _1759970, _1759972]), _1759966)))]]], (50409 ^ _779142) ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913)), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), _1798915), _1798917)), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), _1798919), _1798921))), c_Transitive__Closure_Ortrancl(tc_prod(_1798911, _1798913), _1798923))), hBOOL(hAPP(hAPP(_1798925, _1798915), _1798917)), 50420 ^ _779142 : [(50425 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913)), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), 50418 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]), 50419 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925])), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), 50422 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]), 50423 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]))), _1798923)))], (50427 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1798925, 50418 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]), 50419 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925])))], (50429 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1798925, 50422 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]), 50423 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]))], (50421 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798911, _1798913), tc_prod(_1798911, _1798913)), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), _1798915), _1798917)), hAPP(hAPP(c_Product__Type_OPair(_1798911, _1798913), 50418 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]), 50419 ^ [_1798911, _1798913, _1798915, _1798917, _1798919, _1798921, _1798923, _1798925]))), c_Transitive__Closure_Ortrancl(tc_prod(_1798911, _1798913), _1798923))))]], -(hBOOL(hAPP(hAPP(_1798925, _1798919), _1798921)))], (46240 ^ _779142) ^ [_1708702, _1708704, _1708706, _1708708] : [class_Orderings_Olinorder(_1708702), -(c_List_Olinorder__class_Osorted(_1708702, hAPP(hAPP(c_List_Omap(_1708704, _1708702), _1708706), c_List_Olinorder__class_Osort__key(_1708704, _1708702, _1708706, _1708708))))], (26212 ^ _779142) ^ [_1240086, _1240088, _1240090] : [class_Rings_Olinordered__idom(_1240086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240086), _1240088), c_Groups_Ozero__class_Ozero(_1240086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240086), hAPP(hAPP(c_Power_Opower__class_Opower(_1240086), _1240088), 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)))), _1240090)))), c_Groups_Ozero__class_Ozero(_1240086))))], (4218 ^ _779142) ^ [_842951, _842953, _842955, _842957] : [-(c_List_Omap(_842957, _842953) = c_List_Omap(_842955, _842951)), _842957 = _842955, _842953 = _842951], (29193 ^ _779142) ^ [_1296921, _1296923, _1296925, _1296927] : [class_Lattices_Osemilattice__inf(_1296921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296921), _1296923), _1296925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296921), _1296927), _1296923)), _1296925)))], (5699 ^ _779142) ^ [_869149, _869151] : [v_wt(_869149), 5705 ^ _779142 : [(5708 ^ _779142) ^ [] : [v_P(_869151, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, 5704 ^ [_869149, _869151])), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))], (5706 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 5704 ^ [_869149, _869151]), v_U)))]], -(v_P(_869151, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_869149)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (10733 ^ _779142) ^ [_964655, _964657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964655), hAPP(c_Nat_OSuc, _964657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964655), _964657))), -(_964655 = _964657)], (17613 ^ _779142) ^ [_1089435, _1089437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1089435, _1089437)), _1089435)))], (11662 ^ _779142) ^ [_979842, _979844, _979846] : [class_Rings_Oordered__ring(_979842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979842), _979844), c_Groups_Ozero__class_Ozero(_979842))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979842), _979846), c_Groups_Ozero__class_Ozero(_979842))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979842), c_Groups_Ozero__class_Ozero(_979842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979842), _979844), _979846))))], (26784 ^ _779142) ^ [_1250928, _1250930] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250928, tc_HOL_Obool)), _1250930), c_Orderings_Obot__class_Obot(tc_fun(_1250928, tc_HOL_Obool))) = _1250930)], (27648 ^ _779142) ^ [_1267025, _1267027] : [class_Lattices_Olattice(_1267025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267025), _1267027)), -(_1267027 = c_Orderings_Obot__class_Obot(tc_fun(_1267025, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1267025), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267025), 27661 ^ [_1267025, _1267027]), 27662 ^ [_1267025, _1267027])), hAPP(hAPP(c_Set_Oinsert(_1267025), 27661 ^ [_1267025, _1267027]), hAPP(hAPP(c_Set_Oinsert(_1267025), 27662 ^ [_1267025, _1267027]), c_Orderings_Obot__class_Obot(tc_fun(_1267025, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1267025), c_Big__Operators_Olattice__class_OSup__fin(_1267025, _1267027)), _1267027)))], (2752 ^ _779142) ^ [_819826, _819828, _819830, _819832] : [-(c_Wellfounded_Omax__ext(_819832, _819828) = c_Wellfounded_Omax__ext(_819830, _819826)), _819832 = _819830, _819828 = _819826], (6932 ^ _779142) ^ [_892601, _892603, _892605, _892607] : [hBOOL(hAPP(hAPP(c_member(_892601), _892603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892601, tc_HOL_Obool)), _892605), _892607))), hBOOL(hAPP(hAPP(c_member(_892601), _892603), _892607))], (39520 ^ _779142) ^ [_1547984, _1547986, _1547988, _1547990, _1547992, _1547994, _1547996] : [-(hAPP(c_Fun_Ocomp(_1547984, _1547986, _1547988, _1547990), c_Fun_Ofun__upd(_1547988, _1547984, _1547992, _1547994, _1547996)) = c_Fun_Ofun__upd(_1547988, _1547986, hAPP(c_Fun_Ocomp(_1547984, _1547986, _1547988, _1547990), _1547992), _1547994, hAPP(_1547990, _1547996)))], (47829 ^ _779142) ^ [_1742803, _1742805] : [-(c_FunDef_Ois__measure(_1742803, _1742805))], (4030 ^ _779142) ^ [_840099, _840101, _840103, _840105] : [-(c_New__DSequence_Oneg__single(_840105, _840101) = c_New__DSequence_Oneg__single(_840103, _840099)), _840105 = _840103, _840101 = _840099], (48098 ^ _779142) ^ [_1748606, _1748608, _1748610] : [-(c_Predicate_Oconversep(_1748606, _1748608, c_Predicate_Oconversep(_1748608, _1748606, _1748610)) = _1748610)], (3408 ^ _779142) ^ [_829998, _830000, _830002, _830004] : [-(c_Random_Oselect__weight(_830004, _830000) = c_Random_Oselect__weight(_830002, _829998)), _830004 = _830002, _830000 = _829998], (43808 ^ _779142) ^ [_1655346, _1655348, _1655350] : [-(hAPP(c_List_Otl(_1655346), hAPP(hAPP(c_List_Oappend(_1655346), _1655348), _1655350)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1655346), _1655346, hAPP(c_List_Otl(_1655346), _1655350), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1655346), tc_List_Olist(_1655346)), _1655346), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655346), tc_List_Olist(_1655346), tc_List_Olist(_1655346)), c_List_Oappend(_1655346)), _1655350))), _1655348))], (52503 ^ _779142) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (2688 ^ _779142) ^ [_818782, _818784, _818786, _818788, _818790, _818792] : [-(c_Predicate_ODomainP(_818792, _818788, _818784) = c_Predicate_ODomainP(_818790, _818786, _818782)), _818792 = _818790, _818788 = _818786, _818784 = _818782], (44470 ^ _779142) ^ [_1669708, _1669710, _1669712, _1669714, _1669716] : [-(c_List_Olist_Olist__size(_1669708, _1669710, hAPP(hAPP(c_List_Omap(_1669712, _1669708), _1669714), _1669716)) = c_List_Olist_Olist__size(_1669712, hAPP(c_Fun_Ocomp(_1669708, tc_Nat_Onat, _1669712, _1669710), _1669714), _1669716))], (50433 ^ _779142) ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043)), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), _1800045), _1800047)), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), _1800049), _1800051))), c_Transitive__Closure_Ortrancl(tc_prod(_1800041, _1800043), _1800053))), hBOOL(hAPP(hAPP(_1800055, _1800049), _1800051)), 50446 ^ _779142 : [(50449 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043)), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), 50444 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]), 50445 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055])), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), _1800049), _1800051))), c_Transitive__Closure_Ortrancl(tc_prod(_1800041, _1800043), _1800053))))], (50451 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1800055, 50444 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]), 50445 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055])))], (50453 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1800055, 50442 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]), 50443 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]))], (50447 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800041, _1800043), tc_prod(_1800041, _1800043)), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), 50442 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]), 50443 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055])), hAPP(hAPP(c_Product__Type_OPair(_1800041, _1800043), 50444 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]), 50445 ^ [_1800041, _1800043, _1800045, _1800047, _1800049, _1800051, _1800053, _1800055]))), _1800053)))]], -(hBOOL(hAPP(hAPP(_1800055, _1800045), _1800047)))], (44829 ^ _779142) ^ [] : [-(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))], (42369 ^ _779142) ^ [_1623157, _1623159, _1623161, _1623163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623157), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623159)), _1623161))), -(hBOOL(hAPP(hAPP(c_member(_1623159), _1623163), hAPP(c_List_Oset(_1623159), hAPP(hAPP(c_List_Olist__update(_1623159, _1623161), _1623157), _1623163)))))], (36763 ^ _779142) ^ [_1471704, _1471706, _1471708, _1471710, _1471712, _1471714, _1471716, _1471718] : [c_Fun_Oinj__on(_1471704, _1471706, _1471708, _1471710), 36769 ^ _779142 : [(36772 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471704, tc_HOL_Obool)), hAPP(_1471716, 36768 ^ [_1471704, _1471706, _1471708, _1471710, _1471712, _1471714, _1471716, _1471718])), _1471710))], (36770 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471712), 36768 ^ [_1471704, _1471706, _1471708, _1471710, _1471712, _1471714, _1471716, _1471718]), _1471714)))]], hBOOL(hAPP(hAPP(c_member(_1471712), _1471718), _1471714)), -(hAPP(c_Set_Oimage(_1471704, _1471706, _1471708), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471712, tc_fun(_1471704, tc_HOL_Obool)), _1471714), _1471716)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471712, tc_fun(_1471706, tc_HOL_Obool)), _1471714), hAPP(hAPP(c_COMBB(tc_fun(_1471704, tc_HOL_Obool), tc_fun(_1471706, tc_HOL_Obool), _1471712), c_Set_Oimage(_1471704, _1471706, _1471708)), _1471716)))], (14115 ^ _779142) ^ [_1025077, _1025079, _1025081, _1025083] : [class_Fields_Olinordered__field(_1025077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025077), _1025079), _1025081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025077), c_Groups_Ozero__class_Ozero(_1025077)), _1025083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025077), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025077), _1025079), _1025083)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025077), _1025081), _1025083))))], (26546 ^ _779142) ^ [_1246127, _1246129, _1246131, _1246133] : [class_Lattices_Osemilattice__sup(_1246127), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246127), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246127), _1246129), _1246131)), _1246133) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246127), _1246129), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246127), _1246131), _1246133)))], (18422 ^ _779142) ^ [_1103611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103611), 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), _1103611)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1103611)))], (52673 ^ _779142) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (47655 ^ _779142) ^ [_1739297, _1739299, _1739301] : [hBOOL(hAPP(hAPP(c_member(_1739297), _1739299), hAPP(c_List_Oset(_1739297), _1739301))), -(_1739301 = hAPP(hAPP(c_List_Oappend(_1739297), 47658 ^ [_1739297, _1739299, _1739301]), hAPP(hAPP(c_List_Olist_OCons(_1739297), _1739299), 47659 ^ [_1739297, _1739299, _1739301])))], (23417 ^ _779142) ^ [_1191637, _1191639] : [class_Groups_Ogroup__add(_1191637), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191637), hAPP(c_Groups_Ouminus__class_Ouminus(_1191637), _1191639)), _1191639) = c_Groups_Ozero__class_Ozero(_1191637))], (20025 ^ _779142) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48517 ^ _779142) ^ [_1757570, _1757572, _1757574] : [c_List_Olist__ex1(_1757570, _1757572, _1757574), 48521 ^ _779142 : [(48526 ^ _779142) ^ [_1757816] : [-(_1757816 = 48520 ^ [_1757570, _1757572, _1757574]), hBOOL(hAPP(hAPP(c_member(_1757570), _1757816), hAPP(c_List_Oset(_1757570), _1757574))), hBOOL(hAPP(_1757572, _1757816))], (48524 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1757572, 48520 ^ [_1757570, _1757572, _1757574])))], (48522 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757570), 48520 ^ [_1757570, _1757572, _1757574]), hAPP(c_List_Oset(_1757570), _1757574))))]]], (52247 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (9873 ^ _779142) ^ [_947470, _947472, _947474] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947470), _947472)), _947474) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947470), _947474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947472), _947474)))], (45628 ^ _779142) ^ [_1695826, _1695828, _1695830, _1695832, _1695834] : [class_Orderings_Olinorder(_1695826), -(hAPP(c_List_Ofilter(_1695828, _1695830), c_List_Olinorder__class_Osort__key(_1695828, _1695826, _1695832, _1695834)) = c_List_Olinorder__class_Osort__key(_1695828, _1695826, _1695832, hAPP(c_List_Ofilter(_1695828, _1695830), _1695834)))], (19611 ^ _779142) ^ [_1123694, _1123696, _1123698, _1123700] : [class_Divides_Osemiring__div(_1123694), 19614 ^ _779142 : [(19621 ^ _779142) ^ [] : [-(_1123696 = c_Groups_Ozero__class_Ozero(_1123694)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1123694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123694), _1123696), _1123698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123694), _1123696), _1123700)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1123694), _1123698), _1123700))], (19615 ^ _779142) ^ [] : [_1123696 = c_Groups_Ozero__class_Ozero(_1123694), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1123694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123694), _1123696), _1123698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123694), _1123696), _1123700)) = c_Groups_Ozero__class_Ozero(_1123694))]]], (43929 ^ _779142) ^ [_1657898, _1657900, _1657902] : [class_Lattices_Olattice(_1657898), -(c_Big__Operators_Olattice__class_OInf__fin(_1657898, hAPP(c_List_Oset(_1657898), hAPP(hAPP(c_List_Olist_OCons(_1657898), _1657900), _1657902))) = hAPP(c_List_Ofoldl(_1657898, _1657898, c_Lattices_Osemilattice__inf__class_Oinf(_1657898), _1657900), _1657902))], (44029 ^ _779142) ^ [_1660272, _1660274, _1660276, _1660278, _1660280] : [class_Orderings_Olinorder(_1660272), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660274)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660274, _1660272, _1660276), _1660278), _1660280)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660274)), _1660280)))], (47248 ^ _779142) ^ [_1729893, _1729895, _1729897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729893, _1729893)), hAPP(hAPP(c_Product__Type_OPair(_1729893, _1729893), _1729895), _1729897)), c_List_Omeasures(_1729893, c_List_Olist_ONil(tc_fun(_1729893, tc_Nat_Onat)))))], (5730 ^ _779142) ^ [_869793, _869795, _869797] : [hBOOL(hAPP(hAPP(c_member(_869793), _869795), hAPP(hAPP(c_Set_Oinsert(_869793), _869797), c_Orderings_Obot__class_Obot(tc_fun(_869793, tc_HOL_Obool))))), -(_869795 = _869797)], (49837 ^ _779142) ^ [_1786932] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49833 ^ [_1786932]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (7846 ^ _779142) ^ [_908442, _908444, _908446] : [class_Orderings_Opreorder(_908442), 7849 ^ _779142 : [(7858 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908442), _908444), _908446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908442), _908444), _908446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908442), _908446), _908444)))], (7850 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908442), _908444), _908446)), 7853 ^ _779142 : [(7856 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908442), _908446), _908444))], (7854 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908442), _908444), _908446)))]]]]], (24083 ^ _779142) ^ [_1203073, _1203075, _1203077] : [hBOOL(hAPP(hAPP(c_member(_1203073), _1203075), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203073, tc_HOL_Obool)), _1203077))), hBOOL(hAPP(hAPP(c_member(_1203073), _1203075), _1203077))], (52243 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (34538 ^ _779142) ^ [_1416330, _1416332, _1416334, _1416336, _1416338] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416330, tc_HOL_Obool)), _1416332), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416334, tc_fun(_1416330, tc_HOL_Obool)), _1416336), _1416338)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416334, tc_fun(_1416330, tc_HOL_Obool)), _1416336), hAPP(hAPP(c_COMBB(tc_fun(_1416330, tc_HOL_Obool), tc_fun(_1416330, tc_HOL_Obool), _1416334), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416330, tc_HOL_Obool)), _1416332)), _1416338)))], (28821 ^ _779142) ^ [_1289476, _1289478, _1289480] : [class_Lattices_Olattice(_1289476), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289476), _1289478), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289476), _1289478), _1289480)) = _1289478)], (46996 ^ _779142) ^ [_1724420, _1724422, _1724424, _1724426] : [-(hBOOL(hAPP(_1724420, _1724422))), -(c_List_OdropWhile(_1724424, _1724420, hAPP(hAPP(c_List_Olist_OCons(_1724424), _1724422), _1724426)) = hAPP(hAPP(c_List_Olist_OCons(_1724424), _1724422), _1724426))], (52689 ^ _779142) ^ [_1836687, _1836689, _1836691, _1836693, _1836695, _1836697] : [-(hAPP(hAPP(hAPP(c_COMBC(_1836687, _1836689, _1836691), _1836693), _1836695), _1836697) = hAPP(hAPP(_1836693, _1836697), _1836695))], (326 ^ _779142) ^ [_784061, _784063] : [-(c_Nitpick_Ounknown(_784061)), _784063 = _784061, c_Nitpick_Ounknown(_784063)], (27414 ^ _779142) ^ [_1262851, _1262853, _1262855, _1262857] : [class_Orderings_Olinorder(_1262851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262851), _1262853), _1262855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262851), _1262855), _1262857)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262851, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262851, _1262853, _1262855)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1262851, _1262855, _1262857)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1262851, _1262853, _1262857))], (18503 ^ _779142) ^ [_1104943, _1104945] : [_1104943 = _1104945, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1104943) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1104945))], (34957 ^ _779142) ^ [] : [-(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)))], (22875 ^ _779142) ^ [_1181913, _1181915, _1181917] : [class_Int_Onumber__ring(_1181913), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181913), hAPP(c_Groups_Ouminus__class_Ouminus(_1181913), hAPP(c_Int_Onumber__class_Onumber__of(_1181913), _1181915))), _1181917) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181913), hAPP(c_Int_Onumber__class_Onumber__of(_1181913), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181915))), _1181917))], (9847 ^ _779142) ^ [_946894, _946896, _946898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946898), _946896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946894), _946896)), _946898)))], (39538 ^ _779142) ^ [_1548477, _1548479, _1548481, _1548483, _1548485, _1548487, _1548489, _1548491] : [hAPP(c_Fun_Ocomp(_1548477, _1548479, _1548481, _1548483), _1548485) = hAPP(c_Fun_Ocomp(_1548487, _1548479, _1548481, _1548489), _1548491), 39541 ^ _779142 : [(39542 ^ _779142) ^ [_1548592] : [-(hAPP(_1548483, hAPP(_1548485, _1548592)) = hAPP(_1548489, hAPP(_1548491, _1548592)))]]], (19171 ^ _779142) ^ [_1116087, _1116089, _1116091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1116091), 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), _1116091), _1116089))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1116087)))))], (7596 ^ _779142) ^ [_904750, _904752, _904754, _904756] : [class_Orderings_Oord(_904750), 7599 ^ _779142 : [(7608 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904752, _904750)), _904754), _904756))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904752, _904750)), _904754), _904756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904752, _904750)), _904756), _904754)))], (7600 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904752, _904750)), _904754), _904756)), 7603 ^ _779142 : [(7606 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904752, _904750)), _904756), _904754))], (7604 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904752, _904750)), _904754), _904756)))]]]]], (16029 ^ _779142) ^ [_1060600, _1060602, _1060604, _1060606] : [class_Fields_Olinordered__field__inverse__zero(_1060600), class_Int_Onumber(_1060600), 16036 ^ _779142 : [(16037 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060602), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1060600), _1060604), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)))), 16040 ^ _779142 : [(16047 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), c_Groups_Ozero__class_Ozero(_1060600)), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)))), 16050 ^ _779142 : [(16057 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)), c_Groups_Ozero__class_Ozero(_1060600)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060602), c_Groups_Ozero__class_Ozero(_1060600))))], (16051 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)), c_Groups_Ozero__class_Ozero(_1060600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060600), _1060602), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)))))]]], (16041 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), c_Groups_Ozero__class_Ozero(_1060600)), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060600), _1060602), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))), _1060604)))]]], (16063 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060602), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1060600), _1060604), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))))), 16066 ^ _779142 : [(16069 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060600), _1060602), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))), _1060604))], (16067 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), c_Groups_Ozero__class_Ozero(_1060600)), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))))]], 16070 ^ _779142 : [(16073 ^ _779142) ^ [] : [16074 ^ _779142 : [(16077 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060600), _1060602), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606))))], (16075 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)), c_Groups_Ozero__class_Ozero(_1060600))))]], 16078 ^ _779142 : [(16081 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), _1060602), c_Groups_Ozero__class_Ozero(_1060600)))], (16079 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)), c_Groups_Ozero__class_Ozero(_1060600)))]]], (16071 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060600), c_Groups_Ozero__class_Ozero(_1060600)), hAPP(c_Int_Onumber__class_Onumber__of(_1060600), _1060606)))]]]]], (52391 ^ _779142) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (9755 ^ _779142) ^ [_945096, _945098, _945100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945096), _945098)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945098), _945096)), _945100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945098), _945100)), _945096))], (28863 ^ _779142) ^ [_1290441, _1290443, _1290445, _1290447] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290441, tc_HOL_Obool)), _1290443), _1290445), _1290447)), -(hBOOL(hAPP(_1290443, _1290447)))], (30690 ^ _779142) ^ [_1328520, _1328522, _1328524, _1328526] : [class_Groups_Ocomm__monoid__mult(_1328520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328522), _1328524)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328522, _1328520), _1328526), _1328524) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328520, _1328522, c_Groups_Otimes__class_Otimes(_1328520)), _1328526), c_Groups_Oone__class_Oone(_1328520)), _1328524))], (5602 ^ _779142) ^ [_864763, _864765, _864767, _864769, _864771, _864773] : [-(c_Set_Oimage(_864773, _864769, _864765) = c_Set_Oimage(_864771, _864767, _864763)), _864773 = _864771, _864769 = _864767, _864765 = _864763], (35928 ^ _779142) ^ [_1453192, _1453194, _1453196, _1453198, _1453200, _1453202, _1453204, _1453206, _1453208, _1453210] : [c_Equiv__Relations_Oequiv(_1453192, _1453194, _1453196), c_Equiv__Relations_Oequiv(_1453198, _1453200, _1453202), c_Equiv__Relations_Ocongruent2(_1453192, _1453198, tc_fun(_1453204, tc_HOL_Obool), _1453196, _1453202, _1453206), hBOOL(hAPP(hAPP(c_member(_1453192), _1453208), _1453194)), hBOOL(hAPP(hAPP(c_member(_1453198), _1453210), _1453200)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453192, tc_fun(_1453204, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453192, _1453192, _1453196), hAPP(hAPP(c_Set_Oinsert(_1453192), _1453208), c_Orderings_Obot__class_Obot(tc_fun(_1453192, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1453198, tc_fun(_1453204, tc_HOL_Obool)), tc_fun(_1453204, tc_HOL_Obool), _1453192), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453198, tc_fun(_1453204, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453198, _1453198, _1453202), hAPP(hAPP(c_Set_Oinsert(_1453198), _1453210), c_Orderings_Obot__class_Obot(tc_fun(_1453198, tc_HOL_Obool)))))), _1453206)) = hAPP(hAPP(_1453206, _1453208), _1453210))], (48322 ^ _779142) ^ [_1753364, _1753366, _1753368, _1753370] : [-(hBOOL(hAPP(hAPP(c_member(_1753364), _1753366), hAPP(c_List_Oset(_1753364), c_List_Oreplicate(_1753364, _1753368, _1753370))))), _1753366 = _1753370, -(_1753368 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21104 ^ _779142) ^ [_1150187, _1150189] : [c_Nat__Transfer_Onat__set(_1150187), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1150189), _1150187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150189)))], (37213 ^ _779142) ^ [_1481830, _1481832, _1481834, _1481836, _1481838] : [hBOOL(hAPP(hAPP(c_member(_1481834), hAPP(_1481836, _1481832)), _1481838)), -(hBOOL(hAPP(hAPP(c_member(_1481830), _1481832), hAPP(c_Set_Ovimage(_1481830, _1481834, _1481836), _1481838))))], (17183 ^ _779142) ^ [] : [-(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))))], (50258 ^ _779142) ^ [_1795407, _1795409] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795407), _1795409)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1795407, 50261 ^ [_1795407, _1795409], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795407), _1795409)), _1795409))], (30519 ^ _779142) ^ [_1324917, _1324919] : [class_Lattices_Olattice(_1324917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324917), _1324919)), -(_1324919 = c_Orderings_Obot__class_Obot(tc_fun(_1324917, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324917), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324917), 30532 ^ [_1324917, _1324919]), 30533 ^ [_1324917, _1324919])), hAPP(hAPP(c_Set_Oinsert(_1324917), 30532 ^ [_1324917, _1324919]), hAPP(hAPP(c_Set_Oinsert(_1324917), 30533 ^ [_1324917, _1324919]), c_Orderings_Obot__class_Obot(tc_fun(_1324917, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324917), c_Big__Operators_Olattice__class_OInf__fin(_1324917, _1324919)), _1324919)))], (21216 ^ _779142) ^ [_1152199, _1152201] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1152199, _1152201)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152201), _1152199)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (336 ^ _779142) ^ [_784186, _784188, _784190, _784192] : [-(c_Wellfounded_OwfP(_784190, _784186)), c_Wellfounded_OwfP(_784192, _784188), _784192 = _784190, _784188 = _784186], (43518 ^ _779142) ^ [_1649043, _1649045] : [hAPP(c_List_Orotate1(_1649043), _1649045) = c_List_Olist_ONil(_1649043), -(_1649045 = c_List_Olist_ONil(_1649043))], (34320 ^ _779142) ^ [_1409673, _1409675, _1409677, _1409679, _1409681] : [-(hAPP(hAPP(c_Set_Oinsert(_1409673), _1409675), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409677, tc_fun(_1409673, tc_HOL_Obool)), _1409679), _1409681)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409677, tc_fun(_1409673, tc_HOL_Obool)), _1409679), hAPP(hAPP(c_COMBB(tc_fun(_1409673, tc_HOL_Obool), tc_fun(_1409673, tc_HOL_Obool), _1409677), hAPP(c_Set_Oinsert(_1409673), _1409675)), _1409681)))], (34847 ^ _779142) ^ [_1425363, _1425365, _1425367, _1425369] : [hBOOL(hAPP(hAPP(c_member(_1425365), _1425369), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425363, tc_fun(_1425365, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425363, tc_HOL_Obool))), _1425367))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425363, tc_fun(_1425365, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425363, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1425365, tc_HOL_Obool), tc_fun(_1425365, tc_HOL_Obool), _1425363), hAPP(c_COMBC(_1425365, tc_fun(_1425365, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425365))), _1425367)), _1425369)))], (7986 ^ _779142) ^ [_910677, _910679, _910681, _910683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910677, tc_HOL_Obool)), _910679), _910681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910677, tc_HOL_Obool)), _910681), _910683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910677, tc_HOL_Obool)), _910679), _910683)))], (39203 ^ _779142) ^ [_1539502, _1539504] : [-(c_Nitpick_Owf_H(_1539502, _1539504)), c_Wellfounded_Oacyclic(_1539502, _1539504), 39208 ^ _779142 : [(39211 ^ _779142) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (39209 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539502, _1539502)), _1539504))]]], (45426 ^ _779142) ^ [_1690681, _1690683, _1690685, _1690687] : [-(hAPP(c_List_OremoveAll(_1690681, _1690683), hAPP(hAPP(c_List_Oappend(_1690681), _1690685), _1690687)) = hAPP(hAPP(c_List_Oappend(_1690681), hAPP(c_List_OremoveAll(_1690681, _1690683), _1690685)), hAPP(c_List_OremoveAll(_1690681, _1690683), _1690687)))], (49879 ^ _779142) ^ [_1787727, _1787729, _1787731, _1787733, _1787735, _1787737] : [c_Fun_Obij__betw(_1787727, _1787729, _1787731, _1787733, _1787735), hBOOL(hAPP(hAPP(c_member(_1787727), _1787737), _1787733)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787729, _1787727, _1787735, c_Hilbert__Choice_Oinv__into(_1787727, _1787729, _1787733, _1787731)), _1787737) = hAPP(_1787731, _1787737))], (40368 ^ _779142) ^ [_1568911, _1568913, _1568915] : [-(c_Transitive__Closure_Ortrancl(_1568911, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568911, _1568911), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568911, _1568913)), c_Transitive__Closure_Ortrancl(_1568911, _1568915))) = c_Transitive__Closure_Ortrancl(_1568911, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568911, _1568911), tc_HOL_Obool)), _1568913), _1568915)))], (43239 ^ _779142) ^ [_1641766, _1641768, _1641770] : [-(c_List_Olist_ONil(_1641766) = hAPP(hAPP(c_List_Oappend(_1641766), _1641768), _1641770)), _1641768 = c_List_Olist_ONil(_1641766), _1641770 = c_List_Olist_ONil(_1641766)], (19331 ^ _779142) ^ [_1119072, _1119074] : [class_Groups_Oordered__ab__group__add__abs(_1119072), 19334 ^ _779142 : [(19341 ^ _779142) ^ [] : [_1119074 = c_Groups_Ozero__class_Ozero(_1119072), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119072), hAPP(c_Groups_Oabs__class_Oabs(_1119072), _1119074)), c_Groups_Ozero__class_Ozero(_1119072))))], (19335 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119072), hAPP(c_Groups_Oabs__class_Oabs(_1119072), _1119074)), c_Groups_Ozero__class_Ozero(_1119072))), -(_1119074 = c_Groups_Ozero__class_Ozero(_1119072))]]], (28018 ^ _779142) ^ [_1273853, _1273855, _1273857] : [class_Orderings_Olinorder(_1273853), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273853), _1273855), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273853), _1273855), _1273857)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273853), _1273855), _1273857))], (2270 ^ _779142) ^ [_812267, _812269] : [_812269 = _812267, -(c_Int_Opred(_812269) = c_Int_Opred(_812267))], (6484 ^ _779142) ^ [_883019, _883021, _883023, _883025, _883027, _883029, _883031] : [c_Finite__Set_Ofolding__image__simple__idem(_883019, _883021, _883023, _883025, _883027, _883029), -(hAPP(hAPP(_883023, _883031), _883031) = _883031)], (33093 ^ _779142) ^ [_1384787, _1384789, _1384791, _1384793, _1384795, _1384797, _1384799, _1384801] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384787, _1384789, _1384791), _1384793), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384795, _1384797, tc_prod(_1384787, _1384789)), _1384799), _1384801)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384795, _1384797, _1384791), hAPP(hAPP(c_COMBB(tc_fun(_1384797, tc_prod(_1384787, _1384789)), tc_fun(_1384797, _1384791), _1384795), hAPP(c_COMBB(tc_prod(_1384787, _1384789), _1384791, _1384797), hAPP(c_Product__Type_Oprod_Oprod__case(_1384787, _1384789, _1384791), _1384793))), _1384799)), _1384801))], (2574 ^ _779142) ^ [_817015, _817017, _817019, _817021, _817023, _817025, _817027, _817029] : [-(c_Nitpick_Oprod(_817029, _817025, _817021, _817017) = c_Nitpick_Oprod(_817027, _817023, _817019, _817015)), _817029 = _817027, _817025 = _817023, _817021 = _817019, _817017 = _817015], (20027 ^ _779142) ^ [_1130660, _1130662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1130662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130660), _1130662)), _1130660)))], (32869 ^ _779142) ^ [_1379587, _1379589, _1379591, _1379593] : [-(c_Nat_Onat_Onat__case(_1379587, _1379589, _1379591, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379593)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1379587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1379593))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1379587, _1379587), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1379587, tc_fun(_1379587, _1379587)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1379587, tc_fun(_1379587, _1379587)), tc_Int_Oint), c_If(_1379587)), c_Nat__Numeral_Oneg)), _1379589)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379587, tc_Int_Oint), _1379591), c_Int_Onat))))], (2498 ^ _779142) ^ [_815801, _815803, _815805, _815807, _815809, _815811, _815813, _815815, _815817, _815819] : [-(c_Finite__Set_Ofold__graph(_815819, _815815, _815811, _815807, _815803) = c_Finite__Set_Ofold__graph(_815817, _815813, _815809, _815805, _815801)), _815819 = _815817, _815815 = _815813, _815811 = _815809, _815807 = _815805, _815803 = _815801], (16561 ^ _779142) ^ [_1070652, _1070654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070654), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070652), _1070654))), -(_1070652 = _1070654)], (17547 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (45811 ^ _779142) ^ [_1700513, _1700515] : [-(c_Random_Opick(_1700513, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700513), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700513, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700513, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700513)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700515)) = c_Random_Opick(_1700513, _1700515))], (1196 ^ _779142) ^ [_797034, _797036] : [-(class_Groups_Oordered__ab__group__add(_797034)), _797036 = _797034, class_Groups_Oordered__ab__group__add(_797036)], (27746 ^ _779142) ^ [_1269118, _1269120, _1269122, _1269124] : [class_Orderings_Olinorder(_1269118), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269118), _1269120), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269118), _1269122), _1269124)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269118), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269118), _1269120), _1269122)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269118), _1269120), _1269124)))], (20882 ^ _779142) ^ [_1146303, _1146305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146303)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1146303), _1146305)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1146303)), hAPP(c_Int_Onat, _1146305)))], (39475 ^ _779142) ^ [_1547095, _1547097, _1547099, _1547101, _1547103, _1547105] : [-(hAPP(hAPP(c_Fun_Ocomp(_1547095, _1547097, _1547099, _1547101), _1547103), _1547105) = hAPP(_1547101, hAPP(_1547103, _1547105)))], (39121 ^ _779142) ^ [_1537867, _1537869] : [c_Wellfounded_Owf(_1537867, _1537869), -(c_Wellfounded_OwfP(_1537867, c_FunDef_Oin__rel(_1537867, _1537867, _1537869)))], (1886 ^ _779142) ^ [_805659, _805661] : [-(class_Power_Opower(_805659)), _805661 = _805659, class_Power_Opower(_805661)], (10093 ^ _779142) ^ [_952525, _952527, _952529] : [_952525 = _952529, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952525), _952527) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952529), _952527))], (50077 ^ _779142) ^ [_1791853, _1791855, _1791857, _1791859, _1791861] : [c_Fun_Obij__betw(_1791853, _1791855, _1791857, _1791859, _1791861), -(c_Fun_Obij__betw(_1791855, _1791853, c_Fun_Othe__inv__into(_1791853, _1791855, _1791859, _1791857), _1791861, _1791859))], (34352 ^ _779142) ^ [_1410723, _1410725, _1410727, _1410729, _1410731] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410723, tc_fun(_1410725, tc_HOL_Obool)), _1410727), hAPP(hAPP(c_COMBB(tc_fun(_1410725, tc_HOL_Obool), tc_fun(_1410725, tc_HOL_Obool), _1410723), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410725, tc_HOL_Obool)), _1410729)), _1410731)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410725, tc_HOL_Obool)), _1410729), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410723, tc_fun(_1410725, tc_HOL_Obool)), _1410727), _1410731)))], (45821 ^ _779142) ^ [_1700800, _1700802, _1700804, _1700806] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700800)), _1700802))), c_List_Ofoldr(tc_List_Olist(_1700804), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700804)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700804))), _1700806, 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(_1700800)), _1700802)), c_List_Ofoldr(tc_List_Olist(_1700804), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700804)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700804), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700804)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700804)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700804), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700804)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700804), tc_List_Olist(_1700804), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700804)))), _1700806), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (42680 ^ _779142) ^ [_1629781, _1629783] : [-(c_List_Olistrelp(_1629781, _1629783, c_List_Olist_ONil(_1629781), c_List_Olist_ONil(_1629781)))], (42904 ^ _779142) ^ [_1634165, _1634167, _1634169, _1634171] : [-(hAPP(c_List_Olist_Olist__case(_1634165, _1634167, _1634169, _1634171), c_List_Olist_ONil(_1634167)) = _1634169)], (10017 ^ _779142) ^ [_950648, _950650] : [class_Rings_Ocomm__semiring__1(_950648), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950648), _950650), _950650) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950648), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950648), c_Groups_Oone__class_Oone(_950648)), c_Groups_Oone__class_Oone(_950648))), _950650))], (30824 ^ _779142) ^ [_1331521] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331521), c_Orderings_Otop__class_Otop(tc_fun(_1331521, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1331521)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1331521), tc_HOL_Obool)))))], (34598 ^ _779142) ^ [_1418228, _1418230, _1418232, _1418234, _1418236] : [hBOOL(hAPP(hAPP(c_member(_1418228), _1418230), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418232, tc_fun(_1418228, tc_HOL_Obool)), _1418234), _1418236))), 34602 ^ _779142 : [(34605 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418228), _1418230), hAPP(_1418236, 34601 ^ [_1418228, _1418230, _1418232, _1418234, _1418236]))))], (34603 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418232), 34601 ^ [_1418228, _1418230, _1418232, _1418234, _1418236]), _1418234)))]]], (32223 ^ _779142) ^ [_1365387, _1365389, _1365391] : [class_Int_Onumber__ring(_1365387), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1365387), _1365389), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1365391))) = hAPP(hAPP(c_HOL_OLet(_1365387, _1365387), hAPP(hAPP(c_Power_Opower__class_Opower(_1365387), _1365389), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365391))), hAPP(hAPP(c_COMBS(_1365387, _1365387, _1365387), c_Groups_Otimes__class_Otimes(_1365387)), c_COMBI(_1365387))))], (36230 ^ _779142) ^ [_1460572, _1460574, _1460576, _1460578, _1460580, _1460582] : [c_Fun_Oinj__on(_1460572, _1460574, _1460576, _1460578), hBOOL(hAPP(hAPP(c_member(_1460572), _1460580), _1460578)), hBOOL(hAPP(hAPP(c_member(_1460572), _1460582), _1460578)), 36241 ^ _779142 : [(36248 ^ _779142) ^ [] : [_1460580 = _1460582, -(hAPP(_1460576, _1460580) = hAPP(_1460576, _1460582))], (36242 ^ _779142) ^ [] : [hAPP(_1460576, _1460580) = hAPP(_1460576, _1460582), -(_1460580 = _1460582)]]], (26896 ^ _779142) ^ [_1253360, _1253362, _1253364] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1253360), _1253362)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253360, tc_HOL_Obool)), _1253362), _1253364) = hAPP(hAPP(c_Finite__Set_Ofold(_1253360, tc_fun(_1253360, tc_HOL_Obool), c_Set_Oinsert(_1253360)), _1253364), _1253362))], (35230 ^ _779142) ^ [_1435447, _1435449, _1435451, _1435453, _1435455] : [35232 ^ _779142 : [(35238 ^ _779142) ^ [] : [hBOOL(hAPP(_1435455, 35234 ^ [_1435447, _1435449, _1435451, _1435453, _1435455]))], (35236 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435447), 35234 ^ [_1435447, _1435449, _1435451, _1435453, _1435455]), hAPP(_1435453, 35231 ^ [_1435447, _1435449, _1435451, _1435453, _1435455]))))], (35233 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435449), 35231 ^ [_1435447, _1435449, _1435451, _1435453, _1435455]), _1435451)))]], 35239 ^ _779142 : [(35240 ^ _779142) ^ [_1435757] : [hBOOL(hAPP(hAPP(c_member(_1435447), _1435757), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435449, tc_fun(_1435447, tc_HOL_Obool)), _1435451), _1435453))), -(hBOOL(hAPP(_1435455, _1435757)))]]], (22682 ^ _779142) ^ [_1178720, _1178722, _1178724] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1178720, _1178722) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1178724, _1178722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1178724), _1178720)), -(_1178720 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1178724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178722), 22689 ^ [_1178720, _1178722, _1178724])))], (11634 ^ _779142) ^ [_979332, _979334, _979336] : [class_Rings_Oordered__cancel__semiring(_979332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979332), c_Groups_Ozero__class_Ozero(_979332)), _979334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979332), _979336), c_Groups_Ozero__class_Ozero(_979332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979332), _979336), _979334)), c_Groups_Ozero__class_Ozero(_979332))))], (42361 ^ _779142) ^ [_1622968, _1622970, _1622972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622970)), _1622972))), -(hAPP(hAPP(c_List_Otake(_1622970), _1622968), c_List_Obutlast(_1622970, _1622972)) = hAPP(hAPP(c_List_Otake(_1622970), _1622968), _1622972))], (28871 ^ _779142) ^ [_1290636, _1290638, _1290640, _1290642] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290636, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290636, tc_HOL_Obool)), _1290638), _1290640)), _1290642) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290636, tc_HOL_Obool)), _1290638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290636, tc_HOL_Obool)), _1290640), _1290642)))], (42210 ^ _779142) ^ [_1619700, _1619702, _1619704] : [class_Groups_Omonoid__add(_1619700), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619700), hAPP(hAPP(c_List_Olist_OCons(_1619700), _1619702), _1619704)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619700), _1619702), hAPP(c_List_Omonoid__add__class_Olistsum(_1619700), _1619704)))], (12112 ^ _779142) ^ [_988261, _988263, _988265, _988267] : [class_Rings_Olinordered__ring__strict(_988261), 12115 ^ _779142 : [(12130 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988261), _988263), _988265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988261), _988263), _988267)))), 12131 ^ _779142 : [(12138 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988263), c_Groups_Ozero__class_Ozero(_988261))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988267), _988265))], (12132 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), c_Groups_Ozero__class_Ozero(_988261)), _988263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988265), _988267))]]], (12116 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988261), _988263), _988265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988261), _988263), _988267))), 12121 ^ _779142 : [(12124 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988265), _988267)))], (12122 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), c_Groups_Ozero__class_Ozero(_988261)), _988263)))]], 12125 ^ _779142 : [(12128 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988267), _988265)))], (12126 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988261), _988263), c_Groups_Ozero__class_Ozero(_988261))))]]]]], (44783 ^ _779142) ^ [_1676469] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676469)) = _1676469)], (44797 ^ _779142) ^ [_1676704, _1676706] : [hAPP(c_Code__Numeral_Onat__of, _1676704) = hAPP(c_Code__Numeral_Onat__of, _1676706), -(_1676704 = _1676706)], (37653 ^ _779142) ^ [_1493200, _1493202, _1493204, _1493206, _1493208] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493200, _1493202), _1493204), hAPP(hAPP(c_COMBS(_1493200, tc_fun(_1493202, tc_HOL_Obool), tc_fun(_1493202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493202, tc_HOL_Obool), tc_fun(tc_fun(_1493202, tc_HOL_Obool), tc_fun(_1493202, tc_HOL_Obool)), _1493200), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493202, tc_HOL_Obool))), _1493206)), _1493208)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493200, _1493202), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493200, _1493202), _1493204), _1493206)), hAPP(hAPP(c_Product__Type_OSigma(_1493200, _1493202), _1493204), _1493208)))], (13603 ^ _779142) ^ [_1015767, _1015769, _1015771, _1015773] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1015767, _1015769)), c_Sum__Type_OPlus(_1015767, _1015769, _1015771, _1015773))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1015767), _1015771)))], (47809 ^ _779142) ^ [_1742515, _1742517, _1742519, _1742521] : [-(c_List_Olist__all(_1742515, _1742517, hAPP(hAPP(c_List_Oappend(_1742515), _1742519), _1742521))), c_List_Olist__all(_1742515, _1742517, _1742519), c_List_Olist__all(_1742515, _1742517, _1742521)], (13977 ^ _779142) ^ [_1022608, _1022610, _1022612, _1022614] : [class_Fields_Olinordered__field__inverse__zero(_1022608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022608), _1022610), _1022612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022608), _1022614), c_Groups_Ozero__class_Ozero(_1022608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022608), _1022612), _1022614)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022608), _1022610), _1022614))))], (52293 ^ _779142) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (34238 ^ _779142) ^ [_1407662, _1407664, _1407666, _1407668, _1407670, _1407672] : [hBOOL(hAPP(hAPP(c_member(_1407662), _1407664), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407666, tc_fun(_1407662, tc_HOL_Obool)), _1407668), _1407670))), hBOOL(hAPP(hAPP(c_member(_1407666), _1407672), _1407668)), -(hBOOL(hAPP(hAPP(c_member(_1407662), _1407664), hAPP(_1407670, _1407672))))], (19313 ^ _779142) ^ [_1118775, _1118777] : [class_Divides_Osemiring__div(_1118775), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1118775), c_Groups_Ozero__class_Ozero(_1118775)), _1118777) = c_Groups_Ozero__class_Ozero(_1118775))], (38276 ^ _779142) ^ [_1515730, _1515732] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515730), _1515732)), -(_1515732 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1515730, 38280 ^ [_1515730, _1515732]), 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)), 38279 ^ [_1515730, _1515732]))))], (26330 ^ _779142) ^ [_1242168, _1242170, _1242172, _1242174] : [hBOOL(hAPP(hAPP(c_member(_1242168), _1242170), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242168, tc_HOL_Obool)), _1242172), _1242174))), -(hBOOL(hAPP(hAPP(c_member(_1242168), _1242170), _1242172))), -(hBOOL(hAPP(hAPP(c_member(_1242168), _1242170), _1242174)))], (36364 ^ _779142) ^ [_1463137, _1463139, _1463141, _1463143] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1463137), hAPP(c_Set_Oimage(_1463139, _1463137, _1463141), _1463143))), c_Fun_Oinj__on(_1463139, _1463137, _1463141, _1463143), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463139), _1463143)))], (16753 ^ _779142) ^ [_1073934, _1073936] : [class_Orderings_Olinorder(_1073934), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073934), _1073936)), -(_1073936 = c_Orderings_Obot__class_Obot(tc_fun(_1073934, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1073934), c_Big__Operators_Olinorder__class_OMin(_1073934, _1073936)), _1073936)))], (39582 ^ _779142) ^ [_1549535, _1549537, _1549539, _1549541, _1549543, _1549545, _1549547, _1549549] : [class_Groups_Ocomm__monoid__mult(_1549535), c_Fun_Oinj__on(_1549537, _1549539, _1549541, _1549543), _1549545 = hAPP(c_Set_Oimage(_1549537, _1549539, _1549541), _1549543), _1549547 = hAPP(c_Fun_Ocomp(_1549539, _1549535, _1549537, _1549549), _1549541), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549539, _1549535), _1549549), _1549545) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549537, _1549535), _1549547), _1549543))], (38836 ^ _779142) ^ [_1531181, _1531183, _1531185] : [c_Wellfounded_Owf(_1531181, _1531183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531181, tc_HOL_Obool)), _1531185), hAPP(c_Relation_OImage(_1531181, _1531181, _1531183), _1531185))), -(_1531185 = c_Orderings_Obot__class_Obot(tc_fun(_1531181, tc_HOL_Obool)))], (37862 ^ _779142) ^ [_1499782, _1499784, _1499786, _1499788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499784, _1499782), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1499782, tc_prod(_1499784, _1499782), 37858 ^ [_1499782, _1499784, _1499786, _1499788]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499784, tc_fun(_1499782, tc_HOL_Obool)), _1499786), _1499788))), hAPP(hAPP(c_Product__Type_OSigma(_1499784, _1499782), _1499786), _1499788))))], (9561 ^ _779142) ^ [_941806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941806), _941806))], (50281 ^ _779142) ^ [_1795913, _1795915, _1795917] : [c_Equiv__Relations_Oequivp(_1795913, _1795915), 50284 ^ _779142 : [(50285 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1795917, 50292 ^ [_1795913, _1795915, _1795917]))), 50286 ^ _779142 : [(50287 ^ _779142) ^ [_1796035] : [hBOOL(hAPP(hAPP(c_member(_1795913), _1796035), c_Quotient_ORespects(_1795913, _1795915))), hBOOL(hAPP(_1795917, _1796035))]]], (50296 ^ _779142) ^ [] : [50297 ^ _779142 : [(50298 ^ _779142) ^ [_1796202] : [hBOOL(hAPP(_1795917, _1796202))]], 50300 ^ _779142 : [(50303 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1795917, 50299 ^ [_1795913, _1795915, _1795917])))], (50301 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795913), 50299 ^ [_1795913, _1795915, _1795917]), c_Quotient_ORespects(_1795913, _1795915))))]]]]], (5326 ^ _779142) ^ [_860589, _860591, _860593, _860595, _860597, _860599] : [-(c_SetInterval_Oord_OatMost(_860599, _860595, _860591) = c_SetInterval_Oord_OatMost(_860597, _860593, _860589)), _860599 = _860597, _860595 = _860593, _860591 = _860589], (49443 ^ _779142) ^ [_1778142, _1778144] : [49444 ^ _779142 : [(49445 ^ _779142) ^ [_1778198] : [hBOOL(hAPP(hAPP(_1778142, _1778198), _1778198))]], c_Predicate_Osymp(_1778144, _1778142), c_Predicate_Otransp(_1778144, _1778142), -(c_Equiv__Relations_Opart__equivp(_1778144, _1778142))], (25470 ^ _779142) ^ [_1226796] : [_1226796 = c_Int_OPls, -(c_Int_OBit0(_1226796) = c_Int_OPls)], (18821 ^ _779142) ^ [_1110562, _1110564, _1110566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110562)), 18827 ^ _779142 : [(18830 ^ _779142) ^ [] : [hBOOL(hAPP(_1110564, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18826 ^ [_1110562, _1110564, _1110566]), _1110562)))], (18828 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1110564, 18826 ^ [_1110562, _1110564, _1110566])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110566)), 18835 ^ _779142 : [(18836 ^ _779142) ^ [_1110851] : [hBOOL(hAPP(_1110564, _1110851)), -(hBOOL(hAPP(_1110564, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1110566), _1110562)))))]]], (19695 ^ _779142) ^ [_1125029, _1125031, _1125033] : [class_Rings_Oordered__ring__abs(_1125029), -(hAPP(c_Groups_Oabs__class_Oabs(_1125029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125029), _1125031), _1125033)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125029), hAPP(c_Groups_Oabs__class_Oabs(_1125029), _1125031)), hAPP(c_Groups_Oabs__class_Oabs(_1125029), _1125033))), 19702 ^ _779142 : [(19705 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125029), _1125031), c_Groups_Ozero__class_Ozero(_1125029)))], (19703 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125029), c_Groups_Ozero__class_Ozero(_1125029)), _1125031))]], 19706 ^ _779142 : [(19709 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125029), _1125033), c_Groups_Ozero__class_Ozero(_1125029)))], (19707 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125029), c_Groups_Ozero__class_Ozero(_1125029)), _1125033))]]], (20173 ^ _779142) ^ [_1133449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1133449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133449)))], (8567 ^ _779142) ^ [_922965, _922967, _922969, _922971] : [class_Groups_Oab__semigroup__add(_922965), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922965), _922967), _922969)), _922971) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922965), _922967), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922965), _922969), _922971)))], (45159 ^ _779142) ^ [_1684955, _1684957, _1684959, _1684961] : [c_List_Olist__all2(_1684955, _1684957, _1684959, c_List_Olist_ONil(_1684955), _1684961), -(_1684961 = c_List_Olist_ONil(_1684957))], (21830 ^ _779142) ^ [_1162767, _1162769] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162767))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162767)), _1162769) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162769))], (44682 ^ _779142) ^ [_1674194, _1674196] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674194)), hAPP(c_Code__Numeral_Oof__nat, _1674196)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674194), _1674196)))], (10183 ^ _779142) ^ [_954682, _954684, _954686, _954688] : [class_Rings_Ocomm__semiring__1(_954682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954682), _954684), _954686)), _954688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954682), _954684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954682), _954686), _954688)))], (17431 ^ _779142) ^ [_1085929, _1085931, _1085933, _1085935] : [class_Divides_Osemiring__div(_1085929), -(c_Divides_Odiv__class_Omod(_1085929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085929), _1085931), _1085933), _1085935) = c_Divides_Odiv__class_Omod(_1085929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085929), _1085931), c_Divides_Odiv__class_Omod(_1085929, _1085933, _1085935)), _1085935))], (23051 ^ _779142) ^ [_1184838, _1184840, _1184842] : [class_Groups_Oordered__ab__group__add(_1184838), 23054 ^ _779142 : [(23061 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184838), hAPP(c_Groups_Ouminus__class_Ouminus(_1184838), _1184842)), _1184840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184838), hAPP(c_Groups_Ouminus__class_Ouminus(_1184838), _1184840)), _1184842)))], (23055 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184838), hAPP(c_Groups_Ouminus__class_Ouminus(_1184838), _1184840)), _1184842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184838), hAPP(c_Groups_Ouminus__class_Ouminus(_1184838), _1184842)), _1184840)))]]], (18555 ^ _779142) ^ [_1105857, _1105859] : [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)), _1105857)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1105857), _1105859)))], (38284 ^ _779142) ^ [_1515861, _1515863] : [38285 ^ _779142 : [(38286 ^ _779142) ^ [_1515925, _1515927] : [_1515863 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1515861, _1515925), 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)), _1515927)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515861), _1515863)))], (48184 ^ _779142) ^ [_1750815, _1750817, _1750819, _1750821] : [-(hAPP(hAPP(c_List_Otake(_1750815), _1750817), c_List_Oreplicate(_1750815, _1750819, _1750821)) = c_List_Oreplicate(_1750815, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750817), _1750819), _1750821))], (658 ^ _779142) ^ [_789021, _789023, _789025, _789027, _789029, _789031, _789033, _789035] : [-(c_Nat__Transfer_Otransfer__morphism(_789033, _789029, _789025, _789021)), c_Nat__Transfer_Otransfer__morphism(_789035, _789031, _789027, _789023), _789035 = _789033, _789031 = _789029, _789027 = _789025, _789023 = _789021], (29933 ^ _779142) ^ [_1313403, _1313405, _1313407] : [class_Lattices_Olattice(_1313403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313403), _1313405)), -(_1313405 = c_Orderings_Obot__class_Obot(tc_fun(_1313403, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313403), _1313407)), -(_1313407 = c_Orderings_Obot__class_Obot(tc_fun(_1313403, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313403, tc_HOL_Obool)), _1313405), _1313407) = c_Orderings_Obot__class_Obot(tc_fun(_1313403, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1313403, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313403, tc_HOL_Obool)), _1313405), _1313407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1313403), c_Big__Operators_Olattice__class_OSup__fin(_1313403, _1313405)), c_Big__Operators_Olattice__class_OSup__fin(_1313403, _1313407)))], (21358 ^ _779142) ^ [_1154640, _1154642, _1154644] : [class_Orderings_Oorder(_1154640), 21361 ^ _779142 : [(21368 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), _1154642), _1154644))), -(c_Orderings_Obot__class_Obot(tc_fun(_1154640, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1154640, _1154642, _1154644))], (21362 ^ _779142) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1154640, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1154640, _1154642, _1154644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), _1154642), _1154644))]]], (44452 ^ _779142) ^ [_1669266, _1669268, _1669270, _1669272] : [-(_1669266 = c_List_Olist_ONil(_1669268)), -(hAPP(c_List_Ohd(_1669270), hAPP(hAPP(c_List_Omap(_1669268, _1669270), _1669272), _1669266)) = hAPP(_1669272, hAPP(c_List_Ohd(_1669268), _1669266)))], (52251 ^ _779142) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (32019 ^ _779142) ^ [_1358993, _1358995, _1358997, _1358999, _1359001] : [class_Groups_Ocomm__monoid__mult(_1358993), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358995), _1358997)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358995, _1358993), hAPP(hAPP(c_COMBS(_1358995, _1358993, _1358993), hAPP(hAPP(c_COMBB(_1358993, tc_fun(_1358993, _1358993), _1358995), c_Groups_Otimes__class_Otimes(_1358993)), _1358999)), _1359001)), _1358997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358993), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358995, _1358993), _1358999), _1358997)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358995, _1358993), _1359001), _1358997)))], (3648 ^ _779142) ^ [_833748, _833750, _833752, _833754, _833756, _833758] : [-(c_List_Oinsert(_833758, _833754, _833750) = c_List_Oinsert(_833756, _833752, _833748)), _833758 = _833756, _833754 = _833752, _833750 = _833748], (19045 ^ _779142) ^ [_1113833, _1113835, _1113837] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113833))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113833)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113835)), _1113837)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113835)), _1113837))], (37479 ^ _779142) ^ [_1488330, _1488332] : [-(hAPP(c_Set_OCollect(_1488330), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1488330), c_fNot), _1488332)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1488330, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488330), _1488332)))], (43275 ^ _779142) ^ [_1642528, _1642530, _1642532, _1642534, _1642536] : [-(hAPP(hAPP(c_List_Olist__update(_1642528, hAPP(hAPP(c_List_Oappend(_1642528), _1642530), hAPP(hAPP(c_List_Olist_OCons(_1642528), _1642532), _1642534))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642528)), _1642530)), _1642536) = hAPP(hAPP(c_List_Oappend(_1642528), _1642530), hAPP(hAPP(c_List_Olist_OCons(_1642528), _1642536), _1642534)))], (24383 ^ _779142) ^ [_1208181, _1208183, _1208185, _1208187, _1208189] : [class_Orderings_Olinorder(_1208181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208181, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208181, _1208183), _1208185)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208181, _1208187), _1208189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208181), _1208185), _1208183))), 24394 ^ _779142 : [(24397 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208181), _1208185), _1208189)))], (24395 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208181), _1208187), _1208183)))]]], (19593 ^ _779142) ^ [_1123438] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1123438) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123438)))], (41308 ^ _779142) ^ [_1592671] : [-(c_Nitpick_Odenom(_1592671) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592671, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592671)))], (38463 ^ _779142) ^ [_1521445, _1521447, _1521449, _1521451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521445, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521445, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521447, _1521445), _1521449)), hAPP(c_Relation_ORange(_1521447, _1521445), _1521451))), hAPP(c_Relation_ORange(_1521447, _1521445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1521447, _1521445), tc_HOL_Obool)), _1521449), _1521451)))))], (17539 ^ _779142) ^ [_1088251, _1088253, _1088255] : [-(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, _1088251, _1088253)), _1088255), _1088253) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088251), _1088255), _1088253))], (18521 ^ _779142) ^ [_1105240, _1105242] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1105240), _1105242)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105240)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105242))))], (32743 ^ _779142) ^ [_1377044, _1377046, _1377048, _1377050, _1377052, _1377054] : [32744 ^ _779142 : [(32747 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1377050, _1377046), _1377048))], (32745 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1377044, _1377046), _1377048))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377052, tc_fun(_1377054, tc_HOL_Obool))), _1377050), _1377044), _1377046), _1377048)))], (15917 ^ _779142) ^ [_1058462, _1058464, _1058466, _1058468] : [class_Fields_Olinordered__field__inverse__zero(_1058462), class_Int_Onumber(_1058462), 15924 ^ _779142 : [(15925 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1058462), _1058464), _1058466)), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468))), 15928 ^ _779142 : [(15935 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), _1058466))), 15938 ^ _779142 : [(15945 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058466), c_Groups_Ozero__class_Ozero(_1058462)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468))))], (15939 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058466), c_Groups_Ozero__class_Ozero(_1058462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058462), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)), _1058466)), _1058464)))]]], (15929 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), _1058466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058462), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)), _1058466))))]]], (15951 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1058462), _1058464), _1058466)), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)))), 15954 ^ _779142 : [(15957 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058462), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)), _1058466)))], (15955 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), _1058466)))]], 15958 ^ _779142 : [(15961 ^ _779142) ^ [] : [15962 ^ _779142 : [(15965 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058462), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)), _1058466)), _1058464))], (15963 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058466), c_Groups_Ozero__class_Ozero(_1058462))))]], 15966 ^ _779142 : [(15969 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), hAPP(c_Int_Onumber__class_Onumber__of(_1058462), _1058468)))], (15967 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), _1058466), c_Groups_Ozero__class_Ozero(_1058462)))]]], (15959 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058462), c_Groups_Ozero__class_Ozero(_1058462)), _1058466))]]]]], (51793 ^ _779142) ^ [_1825012, _1825014] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825012), 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)))), _1825014))), 51796 ^ _779142 : [(51799 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825014), _1825012))], (51797 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825012), _1825014)))]]], (46959 ^ _779142) ^ [_1723695, _1723697, _1723699] : [class_Orderings_Olinorder(_1723695), c_List_Olinorder__class_Osorted(_1723695, _1723697), -(c_List_Olinorder__class_Osorted(_1723695, c_List_OdropWhile(_1723695, _1723699, _1723697)))], (13332 ^ _779142) ^ [_1010458, _1010460, _1010462] : [hAPP(c_Finite__Set_Ocard(_1010458), _1010460) = hAPP(c_Nat_OSuc, _1010462), 13337 ^ _779142 : [(13340 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1010458), 13335 ^ [_1010458, _1010460, _1010462]), 13336 ^ [_1010458, _1010460, _1010462]))], (13342 ^ _779142) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1010458), 13336 ^ [_1010458, _1010460, _1010462]) = _1010462)], (13344 ^ _779142) ^ [] : [_1010462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(13336 ^ [_1010458, _1010460, _1010462] = c_Orderings_Obot__class_Obot(tc_fun(_1010458, tc_HOL_Obool)))], (13338 ^ _779142) ^ [] : [-(_1010460 = hAPP(hAPP(c_Set_Oinsert(_1010458), 13335 ^ [_1010458, _1010460, _1010462]), 13336 ^ [_1010458, _1010460, _1010462]))]]], (42906 ^ _779142) ^ [_1634204, _1634206, _1634208] : [-(c_List_Olistset(_1634204, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1634204, tc_HOL_Obool)), _1634206), _1634208)) = c_List_Oset__Cons(_1634204, _1634206, c_List_Olistset(_1634204, _1634208)))], (17581 ^ _779142) ^ [_1088987, _1088989] : [class_Divides_Osemiring__div(_1088987), -(c_Divides_Odiv__class_Omod(_1088987, _1088989, c_Groups_Oone__class_Oone(_1088987)) = c_Groups_Ozero__class_Ozero(_1088987))], (40620 ^ _779142) ^ [_1574812] : [-(c_Relation_OId(_1574812) = hAPP(c_Set_OCollect(tc_prod(_1574812, _1574812)), hAPP(hAPP(c_COMBB(tc_fun(_1574812, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1574812, _1574812)), c_HOL_OEx(_1574812)), hAPP(hAPP(c_COMBC(tc_prod(_1574812, _1574812), tc_fun(_1574812, tc_prod(_1574812, _1574812)), tc_fun(_1574812, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1574812, _1574812), tc_HOL_Obool), tc_fun(tc_fun(_1574812, tc_prod(_1574812, _1574812)), tc_fun(_1574812, tc_HOL_Obool)), tc_prod(_1574812, _1574812)), c_COMBB(tc_prod(_1574812, _1574812), tc_HOL_Obool, _1574812)), c_fequal)), hAPP(hAPP(c_COMBS(_1574812, _1574812, tc_prod(_1574812, _1574812)), c_Product__Type_OPair(_1574812, _1574812)), c_COMBI(_1574812))))))], (33901 ^ _779142) ^ [_1400133] : [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), _1400133))), -(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), _1400133)) = 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), _1400133))))], (50382 ^ _779142) ^ [_1797933, _1797935, _1797937, _1797939, _1797941, _1797943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797933, tc_HOL_Obool)), _1797935), _1797937)), 50388 ^ _779142 : [(50391 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797939, tc_HOL_Obool)), hAPP(_1797941, 50387 ^ [_1797933, _1797935, _1797937, _1797939, _1797941, _1797943])), hAPP(_1797943, 50387 ^ [_1797933, _1797935, _1797937, _1797939, _1797941, _1797943])))], (50389 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797933), 50387 ^ [_1797933, _1797935, _1797937, _1797939, _1797941, _1797943]), _1797937)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797939, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797933, tc_fun(_1797939, tc_HOL_Obool)), _1797937), _1797941)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797933, tc_fun(_1797939, tc_HOL_Obool)), _1797937), _1797943))))], (43772 ^ _779142) ^ [_1654652, _1654654, _1654656] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654652)), hAPP(c_List_Orotate(_1654652, _1654654), _1654656)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654652)), _1654656))], (34889 ^ _779142) ^ [_1426561, _1426563, _1426565, _1426567, _1426569] : [_1426561 = c_Orderings_Obot__class_Obot(tc_fun(_1426563, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426565, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426563, tc_fun(_1426565, tc_HOL_Obool)), _1426561), _1426567)), _1426569) = _1426569)], (40675 ^ _779142) ^ [_1576212, _1576214] : [-(c_Transitive__Closure_Ortrancl(_1576212, hAPP(c_Relation_Oconverse(_1576212, _1576212), _1576214)) = hAPP(c_Relation_Oconverse(_1576212, _1576212), c_Transitive__Closure_Ortrancl(_1576212, _1576214)))], (40115 ^ _779142) ^ [_1562103, _1562105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562103), _1562105)), -(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), _1562103), _1562105)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30003 ^ _779142) ^ [_1314705, _1314707, _1314709] : [class_Orderings_Olinorder(_1314705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314705), _1314707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314705), _1314709)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314705, tc_HOL_Obool)), _1314707), _1314709) = c_Orderings_Obot__class_Obot(tc_fun(_1314705, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1314705), c_Big__Operators_Olinorder__class_OMax(_1314705, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314705, tc_HOL_Obool)), _1314707), _1314709))), c_Big__Operators_Olinorder__class_OMax(_1314705, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314705, tc_HOL_Obool)), _1314707), _1314709))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1314705), c_Big__Operators_Olinorder__class_OMax(_1314705, _1314707)), c_Big__Operators_Olinorder__class_OMax(_1314705, _1314709)))], (22054 ^ _779142) ^ [_1166827, _1166829, _1166831] : [class_Fields_Ofield__inverse__zero(_1166827), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166827), c_Groups_Oone__class_Oone(_1166827)), hAPP(hAPP(c_Power_Opower__class_Opower(_1166827), _1166829), _1166831)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1166827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166827), c_Groups_Oone__class_Oone(_1166827)), _1166829)), _1166831))], (41222 ^ _779142) ^ [_1590529, _1590531, _1590533, _1590535, _1590537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590529, tc_HOL_Obool)), _1590531), _1590533)), 41228 ^ _779142 : [(41233 ^ _779142) ^ [] : [hBOOL(hAPP(_1590537, 41227 ^ [_1590529, _1590531, _1590533, _1590535, _1590537]))], (41231 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1590535, 41227 ^ [_1590529, _1590531, _1590533, _1590535, _1590537])))], (41229 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590529), 41227 ^ [_1590529, _1590531, _1590533, _1590535, _1590537]), _1590531)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590529, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590529, tc_HOL_Obool)), _1590531), hAPP(c_Set_OCollect(_1590529), _1590535))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590529, tc_HOL_Obool)), _1590533), hAPP(c_Set_OCollect(_1590529), _1590537)))))], (30215 ^ _779142) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (4412 ^ _779142) ^ [_846114, _846116] : [_846116 = _846114, -(c_Lazy__Sequence_Oyield(_846116) = c_Lazy__Sequence_Oyield(_846114))], (37920 ^ _779142) ^ [_1502090] : [-(c_Int_Oint__ge__less__than(_1502090) = 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), _1502090)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (1516 ^ _779142) ^ [_801034, _801036] : [-(class_Enum_Oenum(_801034)), _801036 = _801034, class_Enum_Oenum(_801036)], (20442 ^ _779142) ^ [_1137849, _1137851, _1137853, _1137855] : [_1137849 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1137851), _1137853)), _1137855), -(_1137851 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1137849), _1137851) = _1137853), 20449 ^ _779142 : [(20452 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137855), _1137851))], (20450 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137851)))]], 20457 ^ _779142 : [(20460 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137851), _1137855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137855), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20458 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137851))]]], (8765 ^ _779142) ^ [_926660, _926662, _926664, _926666] : [class_Groups_Oordered__cancel__ab__semigroup__add(_926660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926660), _926662), _926664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926660), _926662), _926666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926660), _926664), _926666))))], (52261 ^ _779142) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (38489 ^ _779142) ^ [_1522998, _1523000, _1523002, _1523004] : [hBOOL(hAPP(hAPP(c_member(_1522998), _1523000), hAPP(c_Relation_ORange(_1523002, _1522998), _1523004))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523002, _1522998)), hAPP(hAPP(c_Product__Type_OPair(_1523002, _1522998), 38492 ^ [_1522998, _1523000, _1523002, _1523004]), _1523000)), _1523004)))], (5228 ^ _779142) ^ [_858954, _858956, _858958, _858960, _858962, _858964, _858966, _858968] : [-(c_Lazy__Sequence_Omap(_858968, _858964, _858960, _858956) = c_Lazy__Sequence_Omap(_858966, _858962, _858958, _858954)), _858968 = _858966, _858964 = _858962, _858960 = _858958, _858956 = _858954], (25782 ^ _779142) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (9893 ^ _779142) ^ [_947919, _947921, _947923] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947919), _947921)), hBOOL(hAPP(hAPP(c_member(_947919), _947923), _947921)), -(hAPP(c_Finite__Set_Ocard(_947919), _947921) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_947919), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947919, tc_HOL_Obool)), _947921), hAPP(hAPP(c_Set_Oinsert(_947919), _947923), c_Orderings_Obot__class_Obot(tc_fun(_947919, tc_HOL_Obool)))))))], (31200 ^ _779142) ^ [_1338358, _1338360] : [class_Orderings_Olinorder(_1338358), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1338358, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338358), _1338360)) = hAPP(c_SetInterval_Oord__class_OatMost(_1338358), _1338360))], (38374 ^ _779142) ^ [_1518883, _1518885, _1518887, _1518889, _1518891, _1518893, _1518895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518883, _1518885), tc_HOL_Obool)), _1518887), _1518889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518885, _1518891), tc_HOL_Obool)), _1518893), _1518895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518883, _1518891), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518883, _1518885, _1518891), _1518887), _1518893)), hAPP(hAPP(c_Relation_Orel__comp(_1518883, _1518885, _1518891), _1518889), _1518895))))], (37853 ^ _779142) ^ [_1499553, _1499555] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1499553)), -(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)), _1499553))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1499555))))) = 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)), _1499553))), 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, _1499555))))))], (34791 ^ _779142) ^ [_1423965, _1423967, _1423969, _1423971, _1423973, _1423975] : [hBOOL(hAPP(hAPP(c_member(_1423965), _1423967), _1423969)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423965, tc_fun(_1423971, tc_HOL_Obool)), _1423969), hAPP(hAPP(c_COMBB(tc_fun(_1423971, tc_HOL_Obool), tc_fun(_1423971, tc_HOL_Obool), _1423965), hAPP(c_Set_Oinsert(_1423971), _1423973)), _1423975)) = hAPP(hAPP(c_Set_Oinsert(_1423971), _1423973), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423965, tc_fun(_1423971, tc_HOL_Obool)), _1423969), _1423975)))], (46534 ^ _779142) ^ [_1714562, _1714564, _1714566, _1714568] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714562), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714562))), _1714564))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714566), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714562))), c_List_Otranspose(_1714562, _1714564)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714568), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714562))), hAPP(c_List_Ofilter(tc_List_Olist(_1714562), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714562)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714566)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714562)))), _1714564)))), -(hAPP(hAPP(c_List_Onth(_1714562), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714562)), c_List_Otranspose(_1714562, _1714564)), _1714566)), _1714568) = hAPP(hAPP(c_List_Onth(_1714562), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714562)), _1714564), _1714568)), _1714566))], (29049 ^ _779142) ^ [_1293967, _1293969, _1293971] : [class_Lattices_Osemilattice__inf(_1293967), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293967), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293967), _1293969), _1293971)), _1293971)))], (50831 ^ _779142) ^ [_1808512, _1808514, _1808516, _1808518] : [class_Rings_Ocomm__ring(_1808512), class_Rings_Odvd(_1808512), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808512), _1808514), _1808516)), 50842 ^ _779142 : [(50849 ^ _779142) ^ [_1808938, _1808940] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808512), _1808514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808512), _1808940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808512), _1808938), _1808516))), _1808518))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808512), _1808514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808512), _1808940), _1808518))))], (50843 ^ _779142) ^ [_1808765, _1808767] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808512), _1808514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808512), _1808767), _1808518))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808512), _1808514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808512), _1808767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808512), _1808765), _1808516))), _1808518))))]]], (46684 ^ _779142) ^ [_1717738, _1717740] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717738)), hAPP(c_List_Orev(_1717738), _1717740)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717738)), _1717740))], (46612 ^ _779142) ^ [_1716223, _1716225, _1716227] : [-(hAPP(c_List_Orev(_1716223), hAPP(hAPP(c_List_Oappend(_1716223), _1716225), _1716227)) = hAPP(hAPP(c_List_Oappend(_1716223), hAPP(c_List_Orev(_1716223), _1716227)), hAPP(c_List_Orev(_1716223), _1716225)))], (12774 ^ _779142) ^ [_999986, _999988, _999990, _999992] : [class_Rings_Olinordered__semiring(_999986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999986), _999988), _999990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999986), _999992), _999990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999986), c_Groups_Ozero__class_Ozero(_999986)), _999990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999986), _999988), _999992)))], (42694 ^ _779142) ^ [_1630036, _1630038] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630036)), _1630038) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1630038 = c_List_Olist_ONil(_1630036))], (21642 ^ _779142) ^ [_1159300, _1159302, _1159304, _1159306] : [class_Rings_Olinordered__semidom(_1159300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159300), c_Groups_Oone__class_Oone(_1159300)), _1159302)), 21649 ^ _779142 : [(21656 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159304), _1159306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159300), hAPP(hAPP(c_Power_Opower__class_Opower(_1159300), _1159302), _1159304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1159300), _1159302), _1159306))))], (21650 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159300), hAPP(hAPP(c_Power_Opower__class_Opower(_1159300), _1159302), _1159304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1159300), _1159302), _1159306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159304), _1159306)))]]], (28216 ^ _779142) ^ [_1277821, _1277823, _1277825] : [class_Orderings_Olinorder(_1277821), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277821), _1277823)), hBOOL(hAPP(hAPP(c_member(_1277821), _1277825), _1277823)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277821), _1277825), c_Big__Operators_Olattice_OInf__fin(_1277821, c_Orderings_Oord__class_Omin(_1277821), _1277823)) = _1277825)], (33949 ^ _779142) ^ [_1401156, _1401158, _1401160] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1401156, _1401158), _1401160)), 33952 ^ _779142 : [(33961 ^ _779142) ^ [] : [-(_1401158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 33964 ^ _779142 : [(33973 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401158))), 33976 ^ _779142 : [(33979 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401160)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33977 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401158), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401160))))]]], (33965 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401158)), 33968 ^ _779142 : [(33971 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401160)), _1401158)))], (33969 ^ _779142) ^ [] : [-(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), _1401160))))]]]]], (33955 ^ _779142) ^ [] : [_1401158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1401160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33953 ^ _779142) ^ [] : [-(_1401156 = 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), _1401160)), _1401158)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401160)))]]], (38578 ^ _779142) ^ [_1526019, _1526021, _1526023] : [-(c_Relation_Orefl__on(_1526019, _1526021, _1526023)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526019, _1526019), tc_HOL_Obool)), _1526023), hAPP(hAPP(c_Product__Type_OSigma(_1526019, _1526019), _1526021), hAPP(c_COMBK(tc_fun(_1526019, tc_HOL_Obool), _1526019), _1526021)))), 38584 ^ _779142 : [(38587 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526019, _1526019)), hAPP(hAPP(c_Product__Type_OPair(_1526019, _1526019), 38583 ^ [_1526019, _1526021, _1526023]), 38583 ^ [_1526019, _1526021, _1526023])), _1526023))], (38585 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526019), 38583 ^ [_1526019, _1526021, _1526023]), _1526021)))]]], (7312 ^ _779142) ^ [_900597, _900599, _900601] : [class_Orderings_Olinorder(_900597), 7315 ^ _779142 : [(7316 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900597), _900599), _900601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900597), _900601), _900599))), -(_900599 = _900601)], (7326 ^ _779142) ^ [] : [7327 ^ _779142 : [(7330 ^ _779142) ^ [] : [_900599 = _900601], (7328 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900597), _900601), _900599))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900597), _900599), _900601))]]], (34452 ^ _779142) ^ [_1413630, _1413632, _1413634, _1413636, _1413638] : [_1413630 = c_Orderings_Obot__class_Obot(tc_fun(_1413632, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413634, tc_HOL_Obool)), _1413636), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413632, tc_fun(_1413634, tc_HOL_Obool)), _1413630), _1413638)) = _1413636)], (52693 ^ _779142) ^ [_1836794, _1836796] : [hBOOL(hAPP(hAPP(c_fequal, _1836794), _1836796)), -(_1836794 = _1836796)], (34228 ^ _779142) ^ [_1407441, _1407443, _1407445, _1407447, _1407449, _1407451] : [hBOOL(hAPP(hAPP(c_member(_1407441), _1407443), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407445, tc_fun(_1407441, tc_HOL_Obool)), _1407447), _1407449))), -(hBOOL(hAPP(hAPP(c_member(_1407441), _1407443), hAPP(_1407449, _1407451)))), hBOOL(hAPP(hAPP(c_member(_1407445), _1407451), _1407447))], (39698 ^ _779142) ^ [_1552107, _1552109, _1552111, _1552113, _1552115, _1552117] : [c_Finite__Set_Ofolding(_1552107, _1552109, _1552111, _1552113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552107), _1552115)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552107), _1552117)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1552107, tc_HOL_Obool)), _1552115), _1552117) = c_Orderings_Obot__class_Obot(tc_fun(_1552107, tc_HOL_Obool)), -(hAPP(_1552113, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552107, tc_HOL_Obool)), _1552115), _1552117)) = hAPP(c_Fun_Ocomp(_1552109, _1552109, _1552109, hAPP(_1552113, _1552115)), hAPP(_1552113, _1552117)))], (14589 ^ _779142) ^ [_1033633, _1033635, _1033637, _1033639] : [class_Fields_Olinordered__field(_1033633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033633), _1033635), _1033637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033633), c_Groups_Ozero__class_Ozero(_1033633)), _1033639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033633), c_Groups_Ozero__class_Ozero(_1033633)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033633), _1033637), _1033635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033633), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033633), _1033639), _1033637)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033633), _1033639), _1033635))))], (12666 ^ _779142) ^ [_997913, _997915, _997917, _997919] : [class_Rings_Olinordered__ring__strict(_997913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997913), _997915), c_Groups_Ozero__class_Ozero(_997913))), 12673 ^ _779142 : [(12680 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997913), _997919), _997917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997913), _997915), _997917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997913), _997915), _997919))))], (12674 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997913), _997915), _997917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997913), _997915), _997919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997913), _997919), _997917)))]]], (25320 ^ _779142) ^ [_1224146] : [_1224146 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1224146) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45448 ^ _779142) ^ [_1691086, _1691088, _1691090] : [hBOOL(hAPP(hAPP(c_member(_1691086), _1691088), hAPP(c_List_Oset(_1691086), _1691090))), -(c_List_Oremdups(_1691086, hAPP(hAPP(c_List_Olist_OCons(_1691086), _1691088), _1691090)) = c_List_Oremdups(_1691086, _1691090))], (42100 ^ _779142) ^ [_1616909, _1616911, _1616913, _1616915, _1616917] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1616909, _1616911)), _1616913), hAPP(hAPP(c_List_Ozip(_1616909, _1616911), _1616915), _1616917)) = hAPP(hAPP(c_List_Ozip(_1616909, _1616911), hAPP(hAPP(c_List_Otake(_1616909), _1616913), _1616915)), hAPP(hAPP(c_List_Otake(_1616911), _1616913), _1616917)))], (49835 ^ _779142) ^ [_1786904] : [-(_1786904 = hAPP(c_Code__Numeral_Oof__nat, 49833 ^ [_1786904]))], (29425 ^ _779142) ^ [_1302071, _1302073] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302071, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302071, tc_HOL_Obool)), _1302073)), _1302073) = c_Orderings_Obot__class_Obot(tc_fun(_1302071, tc_HOL_Obool)))], (26370 ^ _779142) ^ [_1242950, _1242952, _1242954, _1242956] : [class_Lattices_Osemilattice__sup(_1242950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242950), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1242950), _1242952), _1242954)), _1242956)), 26377 ^ _779142 : [(26380 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242950), _1242954), _1242956)))], (26378 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242950), _1242952), _1242956)))]]], (14187 ^ _779142) ^ [_1026388, _1026390, _1026392, _1026394] : [class_Fields_Ofield__inverse__zero(_1026388), 14190 ^ _779142 : [(14191 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026388), _1026390), _1026392) = _1026394, 14194 ^ _779142 : [(14201 ^ _779142) ^ [] : [_1026392 = c_Groups_Ozero__class_Ozero(_1026388), -(_1026394 = c_Groups_Ozero__class_Ozero(_1026388))], (14195 ^ _779142) ^ [] : [-(_1026392 = c_Groups_Ozero__class_Ozero(_1026388)), -(_1026390 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026388), _1026394), _1026392))]]], (14207 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026388), _1026390), _1026392) = _1026394), 14210 ^ _779142 : [(14213 ^ _779142) ^ [] : [_1026390 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026388), _1026394), _1026392)], (14211 ^ _779142) ^ [] : [_1026392 = c_Groups_Ozero__class_Ozero(_1026388)]], 14214 ^ _779142 : [(14217 ^ _779142) ^ [] : [_1026394 = c_Groups_Ozero__class_Ozero(_1026388)], (14215 ^ _779142) ^ [] : [-(_1026392 = c_Groups_Ozero__class_Ozero(_1026388))]]]]], (4960 ^ _779142) ^ [_854740, _854742, _854744, _854746, _854748, _854750] : [-(c_Product__Type_Oprod_Oprod__case(_854750, _854746, _854742) = c_Product__Type_Oprod_Oprod__case(_854748, _854744, _854740)), _854750 = _854748, _854746 = _854744, _854742 = _854740], (39459 ^ _779142) ^ [_1546657, _1546659, _1546661, _1546663, _1546665] : [hAPP(c_Set_Oimage(_1546657, _1546659, _1546661), c_Orderings_Otop__class_Otop(tc_fun(_1546657, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546659, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1546659, _1546663, _1546665), c_Orderings_Otop__class_Otop(tc_fun(_1546659, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546663, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1546657, _1546663, hAPP(c_Fun_Ocomp(_1546659, _1546663, _1546657, _1546665), _1546661)), c_Orderings_Otop__class_Otop(tc_fun(_1546657, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546663, tc_HOL_Obool)))], (21662 ^ _779142) ^ [_1159675, _1159677, _1159679, _1159681] : [class_Rings_Olinordered__semidom(_1159675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159677), _1159679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159675), c_Groups_Ozero__class_Ozero(_1159675)), _1159681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159675), _1159681), c_Groups_Oone__class_Oone(_1159675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159675), hAPP(hAPP(c_Power_Opower__class_Opower(_1159675), _1159681), _1159679)), hAPP(hAPP(c_Power_Opower__class_Opower(_1159675), _1159681), _1159677))))], (18004 ^ _779142) ^ [_1096271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096271), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096271))], (44211 ^ _779142) ^ [_1663417, _1663419, _1663421] : [-(_1663417 = c_List_Olist_ONil(_1663419)), -(c_List_Olast(_1663419, hAPP(hAPP(c_List_Oappend(_1663419), _1663421), _1663417)) = c_List_Olast(_1663419, _1663417))], (39502 ^ _779142) ^ [_1547605, _1547607, _1547609, _1547611, _1547613, _1547615, _1547617] : [hAPP(c_Fun_Ocomp(_1547605, _1547607, _1547609, _1547611), _1547613) = _1547615, -(hAPP(_1547611, hAPP(_1547613, _1547617)) = hAPP(_1547615, _1547617))], (30808 ^ _779142) ^ [_1331199, _1331201] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331199), c_Orderings_Otop__class_Otop(tc_fun(_1331199, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331201), c_Orderings_Otop__class_Otop(tc_fun(_1331201, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1331199, _1331201)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1331199, _1331201), tc_HOL_Obool)))))], (10321 ^ _779142) ^ [_957538, _957540, _957542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957538), _957540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957538), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957540), _957542))))], (41631 ^ _779142) ^ [_1603027, _1603029, _1603031, _1603033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603027), tc_List_Olist(_1603027))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603027), tc_List_Olist(_1603027)), _1603029), _1603031)), c_List_Olistrel(_1603027, _1603033))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603027), tc_List_Olist(_1603027))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603027), tc_List_Olist(_1603027)), _1603029), _1603031)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603027), c_List_Olistrel1(_1603027, _1603033)))))], (40295 ^ _779142) ^ [_1566663, _1566665, _1566667, _1566669] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1566663, tc_fun(_1566663, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1566663, tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_fun(_1566663, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566663, tc_fun(tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_fun(_1566663, tc_HOL_Obool)), _1566663), c_COMBC(_1566663, tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566663, tc_prod(_1566663, _1566663)), tc_fun(_1566663, tc_fun(tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_HOL_Obool)), _1566663), hAPP(c_COMBB(tc_prod(_1566663, _1566663), tc_fun(tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool), tc_HOL_Obool), _1566663), c_member(tc_prod(_1566663, _1566663)))), c_Product__Type_OPair(_1566663, _1566663)))), _1566665)), c_fequal), _1566667), _1566669)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566663, _1566663)), hAPP(hAPP(c_Product__Type_OPair(_1566663, _1566663), _1566667), _1566669)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566663, _1566663), tc_HOL_Obool)), _1566665), c_Relation_OId(_1566663)))))], (23723 ^ _779142) ^ [_1197006] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197006)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197006)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1197006)))], (40340 ^ _779142) ^ [_1568171, _1568173] : [-(c_Transitive__Closure_Otrancl(_1568171, _1568173) = hAPP(hAPP(c_Relation_Orel__comp(_1568171, _1568171, _1568171), _1568173), c_Transitive__Closure_Ortrancl(_1568171, _1568173)))], (8404 ^ _779142) ^ [_919430, _919432, _919434, _919436, _919438, _919440, _919442] : [-(c_Nitpick_Ofold__graph_H(_919430, _919432, _919434, _919436, _919438, hAPP(hAPP(_919434, _919440), _919442))), 8405 ^ _779142 : [(8412 ^ _779142) ^ [_919659, _919661] : [hAPP(hAPP(_919434, _919440), _919442) = hAPP(hAPP(_919434, _919661), _919659), hBOOL(hAPP(hAPP(c_member(_919430), _919661), _919438)), c_Nitpick_Ofold__graph_H(_919430, _919432, _919434, _919436, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919430, tc_HOL_Obool)), _919438), hAPP(hAPP(c_Set_Oinsert(_919430), _919661), c_Orderings_Obot__class_Obot(tc_fun(_919430, tc_HOL_Obool)))), _919659)], (8406 ^ _779142) ^ [] : [_919438 = c_Orderings_Obot__class_Obot(tc_fun(_919430, tc_HOL_Obool)), hAPP(hAPP(_919434, _919440), _919442) = _919436]]], (37767 ^ _779142) ^ [_1496557, _1496559, _1496561, _1496563] : [-(_1496557 = c_Orderings_Obot__class_Obot(tc_fun(_1496559, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1496561, _1496559), _1496561, c_Product__Type_Ofst(_1496561, _1496559)), hAPP(hAPP(c_Product__Type_OSigma(_1496561, _1496559), _1496563), hAPP(c_COMBK(tc_fun(_1496559, tc_HOL_Obool), _1496561), _1496557))) = _1496563)], (50573 ^ _779142) ^ [_1803644, _1803646, _1803648, _1803650, _1803652] : [class_Rings_Ocomm__semiring__1(_1803644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803646), _1803648)), hBOOL(hAPP(hAPP(c_member(_1803646), _1803650), _1803648)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803644), hAPP(_1803652, _1803650)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1803646, _1803644), _1803652), _1803648))))], (45260 ^ _779142) ^ [_1687220, _1687222] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687220))), c_Enum_Osublists(_1687220, _1687222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687220)), _1687222)))], (45030 ^ _779142) ^ [_1682060, _1682062, _1682064, _1682066, _1682068] : [-(c_List_Olist__all2(_1682060, _1682062, _1682064, _1682066, _1682068)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682060)), _1682066) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682062)), _1682068), 45036 ^ _779142 : [(45039 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1682060, _1682062, tc_HOL_Obool), _1682064), 45035 ^ [_1682060, _1682062, _1682064, _1682066, _1682068]))], (45037 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682060, _1682062)), 45035 ^ [_1682060, _1682062, _1682064, _1682066, _1682068]), hAPP(c_List_Oset(tc_prod(_1682060, _1682062)), hAPP(hAPP(c_List_Ozip(_1682060, _1682062), _1682066), _1682068)))))]]], (15465 ^ _779142) ^ [_1050006, _1050008, _1050010, _1050012] : [class_Orderings_Olinorder(_1050006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050006), _1050008), _1050010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050006), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1050006), _1050008), _1050012)), _1050010)))], (40229 ^ _779142) ^ [_1564735, _1564737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564735, _1564735)), _1564737)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564735, _1564735)), c_Transitive__Closure_Otrancl(_1564735, _1564737))))], (43736 ^ _779142) ^ [_1653964, _1653966, _1653968] : [-(_1653964 = c_List_Olist_ONil(_1653966)), -(hAPP(c_List_Ohd(_1653966), hAPP(c_List_Orotate(_1653966, _1653968), _1653964)) = hAPP(hAPP(c_List_Onth(_1653966), _1653964), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1653968, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653966)), _1653964))))], (8449 ^ _779142) ^ [_920482, _920484, _920486, _920488, _920490] : [class_Groups_Ocomm__monoid__add(_920482), hBOOL(hAPP(c_Finite__Set_Ofinite(_920484), _920486)), hBOOL(hAPP(hAPP(c_member(_920484), _920488), _920486)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920484, _920482), _920490), _920486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920482), hAPP(_920490, _920488)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920484, _920482), _920490), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920484, tc_HOL_Obool)), _920486), hAPP(hAPP(c_Set_Oinsert(_920484), _920488), c_Orderings_Obot__class_Obot(tc_fun(_920484, tc_HOL_Obool)))))))], (45165 ^ _779142) ^ [_1685046, _1685048, _1685050, _1685052] : [_1685052 = c_List_Olist_ONil(_1685048), -(c_List_Olist__all2(_1685046, _1685048, _1685050, c_List_Olist_ONil(_1685046), _1685052))], (5661 ^ _779142) ^ [_868459, _868461, _868463] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868459), _868461)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868459), hAPP(hAPP(c_Set_Oinsert(_868459), _868463), _868461))))], (47569 ^ _779142) ^ [_1737577, _1737579] : [class_Enum_Oenum(_1737577), 47572 ^ _779142 : [(47580 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737577), _1737579)), 47583 ^ _779142 : [(47584 ^ _779142) ^ [_1737795] : [-(hBOOL(hAPP(_1737579, _1737795)))]]], (47573 ^ _779142) ^ [] : [hBOOL(hAPP(_1737579, 47574 ^ [_1737577, _1737579])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737577), _1737579)))]]], (32263 ^ _779142) ^ [_1366325, _1366327, _1366329] : [class_Groups_Ocomm__monoid__add(_1366325), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1366325), _1366327), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1366329))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366325), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1366325), _1366327), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1366329))), hAPP(_1366327, _1366329)))], (52687 ^ _779142) ^ [_1836635, _1836637, _1836639, _1836641, _1836643, _1836645] : [-(hAPP(hAPP(hAPP(c_COMBB(_1836635, _1836637, _1836639), _1836641), _1836643), _1836645) = hAPP(_1836641, hAPP(_1836643, _1836645)))], (43724 ^ _779142) ^ [_1653850, _1653852] : [-(_1653850 = c_List_Olist_ONil(_1653852)), -(hAPP(c_List_Ohd(_1653852), _1653850) = hAPP(hAPP(c_List_Onth(_1653852), _1653850), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33853 ^ _779142) ^ [_1399105, _1399107, _1399109] : [-(hAPP(c_Product__Type_Ofst(_1399105, _1399107), _1399109) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399105, _1399107, _1399105), c_COMBK(_1399105, _1399107)), _1399109))], (19959 ^ _779142) ^ [_1129574, _1129576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1129574)), hAPP(c_Int_Onat, _1129576))), 19962 ^ _779142 : [(19965 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129574), _1129576)))], (19963 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129576)))]]], (46524 ^ _779142) ^ [_1714235, _1714237, _1714239] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714235), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714235))), _1714237))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714239), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714235))), _1714237))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714235), _1714235), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714235), tc_Nat_Onat, _1714235), c_List_Onth(_1714235)), _1714239)), hAPP(c_List_Ofilter(tc_List_Olist(_1714235), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714235)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714239)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714235)))), c_List_Otranspose(_1714235, _1714237))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714235)), _1714237), _1714239))], (20920 ^ _779142) ^ [_1147013, _1147015, _1147017] : [hBOOL(hAPP(_1147013, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1147015), _1147017))), 20925 ^ _779142 : [(20928 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1147013, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20926 ^ _779142) ^ [] : [-(_1147017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20930 ^ _779142 : [(20935 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1147013, 20929 ^ [_1147013, _1147015, _1147017])))], (20933 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147017), hAPP(c_Nat_OSuc, 20929 ^ [_1147013, _1147015, _1147017])))))], (20931 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147017), 20929 ^ [_1147013, _1147015, _1147017])), _1147015)))]]], (33312 ^ _779142) ^ [_1388951, _1388953, _1388955] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1388951, _1388953), _1388955)), 33315 ^ _779142 : [(33316 ^ _779142) ^ [_1389036] : [hBOOL(hAPP(hAPP(_1388953, _1389036), _1388955)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1388951, _1388953), _1389036)))]]], (35637 ^ _779142) ^ [_1446647, _1446649, _1446651] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446647), _1446649), _1446651) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446647, tc_HOL_Obool), tc_HOL_Obool)), -(_1446649 = c_Orderings_Obot__class_Obot(tc_fun(_1446647, tc_HOL_Obool)))], (17619 ^ _779142) ^ [_1089534, _1089536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089534), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089534), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1089536, _1089534))))], (38130 ^ _779142) ^ [_1509918, _1509920, _1509922] : [class_Lattices_Odistrib__lattice(_1509918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509918), _1509920)), -(_1509920 = c_Orderings_Obot__class_Obot(tc_fun(_1509918, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509918), _1509922)), -(_1509922 = c_Orderings_Obot__class_Obot(tc_fun(_1509918, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1509918), c_Big__Operators_Olattice__class_OSup__fin(_1509918, _1509920)), c_Big__Operators_Olattice__class_OSup__fin(_1509918, _1509922)) = c_Big__Operators_Olattice__class_OSup__fin(_1509918, hAPP(c_Set_OCollect(_1509918), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_HOL_Obool), tc_HOL_Obool, _1509918), c_HOL_OEx(_1509918)), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool)), tc_fun(_1509918, tc_HOL_Obool), _1509918), hAPP(c_COMBB(tc_fun(_1509918, tc_HOL_Obool), tc_HOL_Obool, _1509918), c_HOL_OEx(_1509918))), hAPP(hAPP(c_COMBC(_1509918, tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool)), tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_fun(tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool))), tc_fun(tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool)), tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool))), _1509918), c_COMBS(_1509918, tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_fun(_1509918, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1509918, tc_fun(tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool))), _1509918), hAPP(c_COMBB(tc_fun(_1509918, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool)), _1509918), c_COMBS(_1509918, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool)), tc_fun(_1509918, tc_fun(_1509918, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1509918), hAPP(c_COMBB(tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509918), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509918), c_fconj))), hAPP(hAPP(c_COMBC(_1509918, tc_fun(_1509918, tc_fun(_1509918, _1509918)), tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1509918, _1509918), tc_fun(_1509918, tc_HOL_Obool)), tc_fun(tc_fun(_1509918, tc_fun(_1509918, _1509918)), tc_fun(_1509918, tc_fun(_1509918, tc_HOL_Obool))), _1509918), c_COMBB(tc_fun(_1509918, _1509918), tc_fun(_1509918, tc_HOL_Obool), _1509918)), hAPP(hAPP(c_COMBB(tc_fun(_1509918, tc_HOL_Obool), tc_fun(tc_fun(_1509918, _1509918), tc_fun(_1509918, tc_HOL_Obool)), _1509918), c_COMBB(_1509918, tc_HOL_Obool, _1509918)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1509918)))))), hAPP(hAPP(c_COMBC(_1509918, tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1509918, tc_HOL_Obool), tc_fun(_1509918, tc_HOL_Obool)), _1509918), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509918)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509918), c_fconj), hAPP(hAPP(c_COMBC(_1509918, tc_fun(_1509918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509918)), _1509920)))), hAPP(hAPP(c_COMBC(_1509918, tc_fun(_1509918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509918)), _1509922))))))))], (20852 ^ _779142) ^ [_1145702, _1145704, _1145706] : [-(hBOOL(hAPP(_1145702, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1145704), _1145706)))), 20855 ^ _779142 : [(20858 ^ _779142) ^ [] : [hBOOL(hAPP(_1145702, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20856 ^ _779142) ^ [] : [-(_1145706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20859 ^ _779142 : [(20864 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20862 ^ [_1145702, _1145704, _1145706]), _1145706)))], (20866 ^ _779142) ^ [] : [-(_1145704 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145706), 20861 ^ [_1145702, _1145704, _1145706])), 20862 ^ [_1145702, _1145704, _1145706]))], (20868 ^ _779142) ^ [] : [hBOOL(hAPP(_1145702, 20861 ^ [_1145702, _1145704, _1145706]))], (20860 ^ _779142) ^ [] : [_1145706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (52039 ^ _779142) ^ [_1829490, _1829492] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829490), _1829492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1829490), _1829492)))], (49028 ^ _779142) ^ [_1770727, _1770729, _1770731, _1770733, _1770735] : [c_Predicate_Otransp(_1770727, _1770729), hBOOL(hAPP(hAPP(_1770729, _1770731), _1770733)), hBOOL(hAPP(hAPP(_1770729, _1770733), _1770735)), -(hBOOL(hAPP(hAPP(_1770729, _1770731), _1770735)))], (29169 ^ _779142) ^ [_1296480, _1296482, _1296484] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296480, tc_HOL_Obool)), _1296482), _1296484) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296480, tc_HOL_Obool)), _1296484), _1296482))], (20095 ^ _779142) ^ [_1131804, _1131806, _1131808] : [-(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), _1131804), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131806), _1131804))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131806, _1131804))), _1131808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1131806), _1131808))], (42670 ^ _779142) ^ [_1629602, _1629604] : [-(hAPP(hAPP(c_List_Otake(_1629602), _1629604), c_List_Olist_ONil(_1629602)) = c_List_Olist_ONil(_1629602))], (2780 ^ _779142) ^ [_820276, _820278] : [_820278 = _820276, -(c_Relation_OField(_820278) = c_Relation_OField(_820276))], (8286 ^ _779142) ^ [_917136, _917138, _917140, _917142, _917144, _917146] : [-(c_Fun_Ofun__upd(_917136, _917138, c_Fun_Ofun__upd(_917136, _917138, _917140, _917142, _917144), _917142, _917146) = c_Fun_Ofun__upd(_917136, _917138, _917140, _917142, _917146))], (41955 ^ _779142) ^ [_1612027, _1612029, _1612031] : [-(hAPP(c_List_Oset(_1612027), hAPP(hAPP(c_List_Olist_OCons(_1612027), _1612029), _1612031)) = hAPP(hAPP(c_Set_Oinsert(_1612027), _1612029), hAPP(c_List_Oset(_1612027), _1612031)))], (45486 ^ _779142) ^ [_1691884, _1691886] : [-(c_List_Oconcat(_1691884, _1691886) = hAPP(c_List_Ofoldl(tc_List_Olist(_1691884), tc_List_Olist(_1691884), c_List_Oappend(_1691884), c_List_Olist_ONil(_1691884)), _1691886))], (39530 ^ _779142) ^ [_1548280, _1548282, _1548284, _1548286, _1548288, _1548290] : [-(hAPP(hAPP(c_Fun_Ocomp(_1548280, _1548282, _1548284, _1548286), _1548288), _1548290) = hAPP(_1548286, hAPP(_1548288, _1548290)))], (40211 ^ _779142) ^ [_1564366, _1564368, _1564370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564366, _1564366)), _1564368), _1564370)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564366, _1564366)), _1564368), c_Transitive__Closure_Otrancl(_1564366, _1564370))))], (18716 ^ _779142) ^ [_1108570, _1108572] : [class_Rings_Osemiring__1(_1108570), -(hBOOL(hAPP(hAPP(c_member(_1108570), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1108570), _1108572)), c_Nat_Osemiring__1__class_ONats(_1108570))))], (28084 ^ _779142) ^ [_1275247, _1275249, _1275251] : [class_Int_Onumber(_1275247), class_Orderings_Oord(_1275247), 28091 ^ _779142 : [(28098 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275247), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275249)), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275251)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275247), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275249)), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275251)) = hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275249))], (28092 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275247), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275249)), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275251))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275247), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275249)), hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275251)) = hAPP(c_Int_Onumber__class_Onumber__of(_1275247), _1275251))]]], (43369 ^ _779142) ^ [_1644862, _1644864, _1644866, _1644868] : [-(c_List_Osublist(_1644862, hAPP(hAPP(c_List_Oappend(_1644862), _1644864), _1644866), _1644868) = hAPP(hAPP(c_List_Oappend(_1644862), c_List_Osublist(_1644862, _1644864, _1644868)), c_List_Osublist(_1644862, _1644866, 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(_1644862)), _1644864)))), _1644868)))))], (38627 ^ _779142) ^ [_1527022, _1527024] : [c_Wellfounded_Owf(_1527022, hAPP(hAPP(c_Relation_Orel__comp(_1527022, _1527022, _1527022), _1527024), _1527024)), -(c_Wellfounded_Owf(_1527022, _1527024))], (44241 ^ _779142) ^ [_1663911, _1663913, _1663915, _1663917] : [-(hAPP(hAPP(c_List_Oappend(_1663911), _1663913), hAPP(hAPP(c_List_Olist_OCons(_1663911), _1663915), c_List_Olist_ONil(_1663911))) = _1663917), -(_1663917 = c_List_Olist_ONil(_1663911)), c_List_Obutlast(_1663911, _1663917) = _1663913, c_List_Olast(_1663911, _1663917) = _1663915], (43211 ^ _779142) ^ [_1641269, _1641271, _1641273] : [_1641273 = c_List_Olist_ONil(_1641271), -(_1641269 = hAPP(hAPP(c_List_Oappend(_1641271), _1641273), _1641269))], (7756 ^ _779142) ^ [_907169, _907171, _907173] : [class_Orderings_Oorder(_907169), -(_907171 = _907173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907169), _907173), _907171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907169), _907173), _907171)))], (34687 ^ _779142) ^ [_1421671, _1421673, _1421675, _1421677, _1421679] : [class_Complete__Lattice_Ocomplete__lattice(_1421671), class_Orderings_Olinorder(_1421671), 34694 ^ _779142 : [(34704 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421671), _1421673), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421675, _1421671), _1421677), _1421679)))), 34705 ^ _779142 : [(34706 ^ _779142) ^ [_1422019] : [hBOOL(hAPP(hAPP(c_member(_1421675), _1422019), _1421677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421671), _1421673), hAPP(_1421679, _1422019)))]]], (34695 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421671), _1421673), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421675, _1421671), _1421677), _1421679))), 34699 ^ _779142 : [(34702 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421671), _1421673), hAPP(_1421679, 34698 ^ [_1421671, _1421673, _1421675, _1421677, _1421679]))))], (34700 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421675), 34698 ^ [_1421671, _1421673, _1421675, _1421677, _1421679]), _1421677)))]]]]], (26938 ^ _779142) ^ [_1254379, _1254381] : [class_Orderings_Olinorder(_1254379), -(c_Big__Operators_Olinorder__class_OMax(_1254379, hAPP(hAPP(c_Set_Oinsert(_1254379), _1254381), c_Orderings_Obot__class_Obot(tc_fun(_1254379, tc_HOL_Obool)))) = _1254381)], (31955 ^ _779142) ^ [_1356281, _1356283, _1356285, _1356287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1356281, _1356283)), hAPP(hAPP(c_Product__Type_OPair(_1356281, _1356283), _1356285), _1356287)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1356281, _1356283), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1356281, tc_fun(_1356283, tc_HOL_Obool))), _1356285), _1356287)))], (45304 ^ _779142) ^ [_1688270, _1688272, _1688274, _1688276, _1688278] : [45306 ^ _779142 : [(45309 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1688270, _1688272, tc_HOL_Obool), _1688278), 45305 ^ [_1688270, _1688272, _1688274, _1688276, _1688278]))], (45307 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1688270, _1688272)), 45305 ^ [_1688270, _1688272, _1688274, _1688276, _1688278]), hAPP(c_List_Oset(tc_prod(_1688270, _1688272)), hAPP(hAPP(c_List_Ozip(_1688270, _1688272), _1688274), _1688276)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688270)), _1688274) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688272)), _1688276), -(c_List_Olist__all2(_1688270, _1688272, _1688278, _1688274, _1688276))], (26700 ^ _779142) ^ [_1249459, _1249461, _1249463] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249459, tc_HOL_Obool)), _1249461), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249459, tc_HOL_Obool)), _1249461), _1249463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249459, tc_HOL_Obool)), _1249461), _1249463))], (21290 ^ _779142) ^ [_1153396, _1153398] : [c_Nat__Transfer_Ois__nat(_1153396), c_Nat__Transfer_Ois__nat(_1153398), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1153396), _1153398)))], (37181 ^ _779142) ^ [_1480962, _1480964, _1480966, _1480968, _1480970] : [hBOOL(hAPP(_1480968, hAPP(_1480966, _1480970))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1480962, _1480964, _1480966), _1480968), _1480970)))], (25824 ^ _779142) ^ [] : [-(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))))], (44762 ^ _779142) ^ [_1675987, _1675989, _1675991, _1675993, _1675995] : [class_Groups_Omonoid__add(_1675987), class_Groups_Oordered__ab__semigroup__add(_1675987), 44772 ^ _779142 : [(44775 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675987), hAPP(_1675993, 44771 ^ [_1675987, _1675989, _1675991, _1675993, _1675995])), hAPP(_1675995, 44771 ^ [_1675987, _1675989, _1675991, _1675993, _1675995])))], (44773 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675989), 44771 ^ [_1675987, _1675989, _1675991, _1675993, _1675995]), hAPP(c_List_Oset(_1675989), _1675991))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675987), hAPP(c_List_Omonoid__add__class_Olistsum(_1675987), hAPP(hAPP(c_List_Omap(_1675989, _1675987), _1675993), _1675991))), hAPP(c_List_Omonoid__add__class_Olistsum(_1675987), hAPP(hAPP(c_List_Omap(_1675989, _1675987), _1675995), _1675991)))))], (5590 ^ _779142) ^ [_864593, _864595] : [_864595 = _864593, -(c_Finite__Set_Ofinite(_864595) = c_Finite__Set_Ofinite(_864593))], (50083 ^ _779142) ^ [_1791958, _1791960, _1791962, _1791964, _1791966] : [c_Fun_Obij__betw(_1791958, _1791960, _1791962, _1791964, _1791966), -(hAPP(c_Finite__Set_Ocard(_1791958), _1791964) = hAPP(c_Finite__Set_Ocard(_1791960), _1791966))], (11291 ^ _779142) ^ [_973121, _973123] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973121), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973121), _973123)))))], (52291 ^ _779142) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (9619 ^ _779142) ^ [_942838, _942840, _942842] : [9620 ^ _779142 : [(9623 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_942842, _942840), _942838))], (9621 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942838), _942840)))]], 9626 ^ _779142 : [(9629 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_942842, _942840), _942838))], (9627 ^ _779142) ^ [] : [-(_942838 = _942840)]], 9632 ^ _779142 : [(9635 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_942842, _942840), _942838))], (9633 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942840), _942838)))]], -(hBOOL(hAPP(hAPP(_942842, _942840), _942838)))], (43454 ^ _779142) ^ [_1647485, _1647487, _1647489, _1647491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647485), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647487)), _1647489))), -(hAPP(hAPP(c_List_Olist__update(_1647487, _1647489), _1647485), _1647491) = hAPP(hAPP(c_List_Oappend(_1647487), hAPP(hAPP(c_List_Otake(_1647487), _1647485), _1647489)), hAPP(hAPP(c_List_Olist_OCons(_1647487), _1647491), hAPP(hAPP(c_List_Odrop(_1647487), hAPP(c_Nat_OSuc, _1647485)), _1647489))))], (48735 ^ _779142) ^ [_1762820, _1762822, _1762824, _1762826] : [-(hAPP(c_Relation_OImage(_1762820, _1762822, hAPP(c_Set_OCollect(tc_prod(_1762820, _1762822)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762820, _1762822, tc_HOL_Obool), _1762824))), _1762826) = hAPP(c_Set_OCollect(_1762822), hAPP(hAPP(c_COMBB(tc_fun(_1762820, tc_HOL_Obool), tc_HOL_Obool, _1762822), c_HOL_OEx(_1762820)), hAPP(hAPP(c_COMBB(tc_fun(_1762820, tc_HOL_Obool), tc_fun(_1762820, tc_HOL_Obool), _1762822), hAPP(c_COMBS(_1762820, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762820), c_fconj), hAPP(hAPP(c_COMBC(_1762820, tc_fun(_1762820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762820)), _1762826)))), hAPP(c_COMBC(_1762820, _1762822, tc_HOL_Obool), _1762824)))))], (244 ^ _779142) ^ [_782982, _782984] : [-(class_Fields_Olinordered__field(_782982)), _782984 = _782982, class_Fields_Olinordered__field(_782984)], (350 ^ _779142) ^ [_784379, _784381, _784383, _784385, _784387, _784389, _784391, _784393] : [-(c_Finite__Set_Ofolding(_784391, _784387, _784383, _784379)), c_Finite__Set_Ofolding(_784393, _784389, _784385, _784381), _784393 = _784391, _784389 = _784387, _784385 = _784383, _784381 = _784379], (52605 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (30958 ^ _779142) ^ [_1333797] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1333797, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1333797, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1333797, tc_HOL_Obool)))], (44758 ^ _779142) ^ [_1675815, _1675817] : [-(c_Random_Oselect__weight(_1675815, _1675817) = 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(_1675815, 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, _1675815), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675815)), _1675817)))), hAPP(hAPP(c_COMBB(_1675815, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675815, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675815, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1675815, _1675817))))], (37827 ^ _779142) ^ [_1498280, _1498282, _1498284, _1498286, _1498288, _1498290, _1498292, _1498294] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1498280, _1498282), tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498280, _1498282), _1498288), hAPP(c_COMBK(tc_fun(_1498282, tc_HOL_Obool), _1498280), _1498290))), hAPP(c_Product__Type_Oprod_Oprod__case(_1498280, _1498282, tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1498280, tc_fun(_1498282, tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool))), tc_fun(_1498282, tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool)), tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool)), tc_fun(tc_fun(_1498282, tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool))), tc_fun(_1498282, tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool))), _1498280), c_COMBB(tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool)), tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool), _1498282)), hAPP(hAPP(c_COMBB(tc_fun(_1498284, tc_HOL_Obool), tc_fun(tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool)), tc_fun(tc_prod(_1498284, _1498286), tc_HOL_Obool)), _1498280), c_Product__Type_OSigma(_1498284, _1498286)), _1498292))), hAPP(hAPP(c_COMBB(tc_fun(_1498286, tc_HOL_Obool), tc_fun(_1498284, tc_fun(_1498286, tc_HOL_Obool)), _1498282), c_COMBK(tc_fun(_1498286, tc_HOL_Obool), _1498284)), _1498294)))) = hAPP(hAPP(c_Product__Type_OSigma(_1498284, _1498286), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498280, tc_fun(_1498284, tc_HOL_Obool)), _1498288), _1498292)), hAPP(c_COMBK(tc_fun(_1498286, tc_HOL_Obool), _1498284), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498282, tc_fun(_1498286, tc_HOL_Obool)), _1498290), _1498294))))], (22092 ^ _779142) ^ [_1167572, _1167574, _1167576, _1167578] : [class_Rings_Olinordered__semidom(_1167572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167572), hAPP(hAPP(c_Power_Opower__class_Opower(_1167572), _1167574), hAPP(c_Nat_OSuc, _1167576))), hAPP(hAPP(c_Power_Opower__class_Opower(_1167572), _1167578), hAPP(c_Nat_OSuc, _1167576)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167572), c_Groups_Ozero__class_Ozero(_1167572)), _1167578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167572), _1167574), _1167578)))], (4050 ^ _779142) ^ [_840397, _840399, _840401, _840403, _840405, _840407, _840409, _840411] : [-(c_New__Random__Sequence_Opos__map(_840411, _840407, _840403, _840399) = c_New__Random__Sequence_Opos__map(_840409, _840405, _840401, _840397)), _840411 = _840409, _840407 = _840405, _840403 = _840401, _840399 = _840397], (7026 ^ _779142) ^ [_894636, _894638, _894640] : [-(hAPP(hAPP(c_Set_Oinsert(_894636), _894638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894636, tc_HOL_Obool)), _894640), hAPP(hAPP(c_Set_Oinsert(_894636), _894638), c_Orderings_Obot__class_Obot(tc_fun(_894636, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_894636), _894638), _894640))], (46947 ^ _779142) ^ [_1723355, _1723357, _1723359] : [hBOOL(hAPP(c_List_Odistinct(_1723355), _1723357)), hBOOL(hAPP(hAPP(c_member(_1723355), _1723359), hAPP(c_List_Oset(_1723355), _1723357))), -(c_List_OdropWhile(_1723355, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723355), c_fNot), hAPP(hAPP(c_COMBC(_1723355, _1723355, tc_HOL_Obool), c_fequal), _1723359)), hAPP(c_List_Orev(_1723355), _1723357)) = hAPP(hAPP(c_List_Olist_OCons(_1723355), _1723359), hAPP(c_List_Orev(_1723355), c_List_OtakeWhile(_1723355, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723355), c_fNot), hAPP(hAPP(c_COMBC(_1723355, _1723355, tc_HOL_Obool), c_fequal), _1723359)), _1723357))))], (51189 ^ _779142) ^ [_1814895, _1814897] : [class_Rings_Ocomm__semiring__1(_1814895), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814895), c_Groups_Ozero__class_Ozero(_1814895)), _1814897)), -(_1814897 = c_Groups_Ozero__class_Ozero(_1814895))], (3216 ^ _779142) ^ [_827052, _827054, _827056, _827058] : [-(c_Random_Oselect(_827058, _827054) = c_Random_Oselect(_827056, _827052)), _827058 = _827056, _827054 = _827052], (39020 ^ _779142) ^ [] : [-(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))))], (18869 ^ _779142) ^ [_1111352, _1111354] : [class_Int_Onumber__ring(_1111352), 18872 ^ _779142 : [(18879 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111354)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1111354)) = hAPP(c_Int_Onumber__class_Onumber__of(_1111352), _1111354))], (18873 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111354))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1111352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1111354)) = c_Groups_Ozero__class_Ozero(_1111352))]]], (25444 ^ _779142) ^ [_1226416, _1226418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226416), _1226418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1226416)), c_Int_OBit0(_1226418))))], (40624 ^ _779142) ^ [_1574997, _1574999] : [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), _1574997), _1574999)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1574997), _1574999)))], (1346 ^ _779142) ^ [_798909, _798911] : [-(class_Rings_Oring(_798909)), _798911 = _798909, class_Rings_Oring(_798911)], (47046 ^ _779142) ^ [_1725383, _1725385, _1725387] : [-(c_List_OdropWhile(_1725383, _1725385, _1725387) = hAPP(hAPP(c_List_Odrop(_1725383), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725383)), c_List_OtakeWhile(_1725383, _1725385, _1725387))), _1725387))], (24620 ^ _779142) ^ [_1212102, _1212104] : [class_Rings_Olinordered__idom(_1212102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212102), _1212104), c_Groups_Ozero__class_Ozero(_1212102))), -(c_Groups_Osgn__class_Osgn(_1212102, _1212104) = hAPP(c_Groups_Ouminus__class_Ouminus(_1212102), c_Groups_Oone__class_Oone(_1212102)))], (30976 ^ _779142) ^ [_1334116, _1334118] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334116, tc_HOL_Obool)), _1334118), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1334116, tc_HOL_Obool)), _1334118)) = c_Orderings_Otop__class_Otop(tc_fun(_1334116, tc_HOL_Obool)))], (1014 ^ _779142) ^ [_794429, _794431, _794433, _794435, _794437, _794439] : [-(c_List_Olist__all(_794437, _794433, _794429)), c_List_Olist__all(_794439, _794435, _794431), _794439 = _794437, _794435 = _794433, _794431 = _794429], (31392 ^ _779142) ^ [_1342130] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342130, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1342130, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1342130, tc_HOL_Obool)))], (34400 ^ _779142) ^ [_1412132, _1412134, _1412136, _1412138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1412132, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412134, tc_fun(tc_fun(_1412132, tc_HOL_Obool), tc_HOL_Obool)), _1412136), hAPP(hAPP(c_COMBB(tc_fun(_1412132, tc_HOL_Obool), tc_fun(tc_fun(_1412132, tc_HOL_Obool), tc_HOL_Obool), _1412134), c_Set_OPow(_1412132)), _1412138))), hAPP(c_Set_OPow(_1412132), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412134, tc_fun(_1412132, tc_HOL_Obool)), _1412136), _1412138)))))], (21053 ^ _779142) ^ [_1149408, _1149410, _1149412, _1149414] : [hBOOL(hAPP(hAPP(_1149412, _1149414), _1149410)), -(hBOOL(hAPP(hAPP(c_member(_1149408), _1149410), c_SetInterval_Oord_OgreaterThan(_1149408, _1149412, _1149414))))], (24970 ^ _779142) ^ [_1218082] : [class_Int_Onumber__ring(_1218082), -(hAPP(c_Int_Onumber__class_Onumber__of(_1218082), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1218082))], (40013 ^ _779142) ^ [_1559527, _1559529, _1559531, _1559533] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1559527, tc_HOL_Obool), tc_fun(_1559527, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1559527, tc_HOL_Obool), tc_fun(_1559527, tc_HOL_Obool)), _1559529), _1559531)), c_Wellfounded_Omax__ext(_1559527, _1559533))), 40016 ^ _779142 : [(40019 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559527), _1559531)))], (40021 ^ _779142) ^ [] : [_1559531 = c_Orderings_Obot__class_Obot(tc_fun(_1559527, tc_HOL_Obool))], (40023 ^ _779142) ^ [_1559821] : [hBOOL(hAPP(hAPP(c_member(_1559527), _1559821), _1559529)), 40027 ^ _779142 : [(40030 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559527, _1559527)), hAPP(hAPP(c_Product__Type_OPair(_1559527, _1559527), _1559821), 40026 ^ [_1559527, _1559529, _1559531, _1559533, _1559821])), _1559533)))], (40028 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559527), 40026 ^ [_1559527, _1559529, _1559531, _1559533, _1559821]), _1559531)))]]], (40017 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559527), _1559529)))]]], (15565 ^ _779142) ^ [_1051735, _1051737, _1051739, _1051741] : [class_Groups_Oordered__ab__group__add(_1051735), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051735), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1051735), _1051737), _1051739)), _1051741) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1051735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051735), _1051737), _1051741)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051735), _1051739), _1051741)))], (21041 ^ _779142) ^ [_1149163, _1149165, _1149167, _1149169] : [hBOOL(hAPP(hAPP(_1149167, _1149165), _1149169)), -(hBOOL(hAPP(hAPP(c_member(_1149163), _1149165), c_SetInterval_Oord_OlessThan(_1149163, _1149167, _1149169))))], (29574 ^ _779142) ^ [_1305583, _1305585, _1305587, _1305589] : [class_Orderings_Olinorder(_1305583), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305583, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1305583, _1305585, _1305587)), hAPP(c_SetInterval_Oord__class_OatMost(_1305583), _1305589)) = c_SetInterval_Oord__class_OatLeastAtMost(_1305583, _1305585, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305583), _1305587), _1305589)))], (26922 ^ _779142) ^ [_1253940, _1253942, _1253944, _1253946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253940, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253940, tc_HOL_Obool)), _1253942), _1253944)), _1253946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253940, tc_HOL_Obool)), _1253942), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253940, tc_HOL_Obool)), _1253944), _1253946))))], (46885 ^ _779142) ^ [_1721990, _1721992, _1721994, _1721996, _1721998] : [hBOOL(hAPP(hAPP(c_member(_1721990), _1721992), hAPP(c_List_Oset(_1721990), _1721994))), -(hBOOL(hAPP(_1721996, _1721992))), -(c_List_OtakeWhile(_1721990, _1721996, hAPP(hAPP(c_List_Oappend(_1721990), _1721994), _1721998)) = c_List_OtakeWhile(_1721990, _1721996, _1721994))], (14703 ^ _779142) ^ [_1035735, _1035737, _1035739, _1035741] : [class_Fields_Ofield(_1035735), -(_1035737 = c_Groups_Ozero__class_Ozero(_1035735)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035735), _1035739), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035735), _1035741), _1035737)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035735), _1035737), _1035739)), _1035741)), _1035737))], (15041 ^ _779142) ^ [_1042240, _1042242, _1042244, _1042246, _1042248, _1042250] : [-(c_Nitpick_Opair__box_Opair__box__size(_1042240, _1042242, _1042244, _1042246, c_Nitpick_Opair__box_OPairBox(_1042240, _1042242, _1042248, _1042250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1042244, _1042248)), hAPP(_1042246, _1042250))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3742 ^ _779142) ^ [_835255, _835257] : [_835257 = _835255, -(c_New__DSequence_Opos__not__seq(_835257) = c_New__DSequence_Opos__not__seq(_835255))], (45673 ^ _779142) ^ [_1696770, _1696772, _1696774, _1696776] : [-(hAPP(c_List_Ofilter(_1696770, _1696772), c_List_Oremove1(_1696770, _1696774, _1696776)) = c_List_Oremove1(_1696770, _1696774, hAPP(c_List_Ofilter(_1696770, _1696772), _1696776)))], (32627 ^ _779142) ^ [_1374886, _1374888] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374886)), hAPP(c_Nat_OSuc, _1374888)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1374886))), 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)), _1374888)))))], (6055 ^ _779142) ^ [_875822, _875824, _875826, _875828, _875830] : [c_Finite__Set_Ofolding__one(_875822, _875824, _875826), hBOOL(hAPP(c_Finite__Set_Ofinite(_875822), _875828)), -(hBOOL(hAPP(hAPP(c_member(_875822), _875830), _875828))), -(_875828 = c_Orderings_Obot__class_Obot(tc_fun(_875822, tc_HOL_Obool))), -(hAPP(_875826, hAPP(hAPP(c_Set_Oinsert(_875822), _875830), _875828)) = hAPP(hAPP(_875824, _875830), hAPP(_875826, _875828)))], (11131 ^ _779142) ^ [_970814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970814)), _970814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31973 ^ _779142) ^ [_1356896, _1356898, _1356900, _1356902, _1356904, _1356906] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356896, tc_fun(_1356898, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1356896, tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_fun(_1356898, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1356898, tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_fun(_1356898, tc_HOL_Obool)), _1356896), c_COMBC(_1356898, tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1356898, tc_prod(_1356896, _1356898)), tc_fun(_1356898, tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), _1356896), hAPP(c_COMBB(tc_prod(_1356896, _1356898), tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool), _1356898), c_member(tc_prod(_1356896, _1356898)))), c_Product__Type_OPair(_1356896, _1356898)))), _1356900)), hAPP(hAPP(c_COMBC(_1356896, tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_fun(_1356898, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1356898, tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_fun(_1356898, tc_HOL_Obool)), _1356896), c_COMBC(_1356898, tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1356898, tc_prod(_1356896, _1356898)), tc_fun(_1356898, tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool)), _1356896), hAPP(c_COMBB(tc_prod(_1356896, _1356898), tc_fun(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool), tc_HOL_Obool), _1356898), c_member(tc_prod(_1356896, _1356898)))), c_Product__Type_OPair(_1356896, _1356898)))), _1356902)), _1356904), _1356906)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1356896, _1356898)), hAPP(hAPP(c_Product__Type_OPair(_1356896, _1356898), _1356904), _1356906)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1356896, _1356898), tc_HOL_Obool)), _1356900), _1356902))))], (7702 ^ _779142) ^ [_906422, _906424, _906426] : [class_Orderings_Oorder(_906422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906422), _906424), _906426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906422), _906424), _906426))), -(_906424 = _906426)], (33189 ^ _779142) ^ [_1386609, _1386611] : [_1386609 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1386611, _1386609) = 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), _1386611)))], (32411 ^ _779142) ^ [_1369817, _1369819] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369817) = hAPP(c_Nat_OSuc, _1369819), -(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(_1369817))), 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)), _1369819))))))], (45472 ^ _779142) ^ [_1691626, _1691628] : [class_Orderings_Olinorder(_1691626), -(c_List_Olinorder__class_Osorted__list__of__set(_1691626, hAPP(c_List_Oset(_1691626), _1691628)) = c_List_Olinorder__class_Osort__key(_1691626, _1691626, c_COMBI(_1691626), c_List_Oremdups(_1691626, _1691628)))], (37581 ^ _779142) ^ [_1491386, _1491388] : [-(hAPP(c_Set_OCollect(_1491386), hAPP(hAPP(c_COMBC(_1491386, _1491386, tc_HOL_Obool), c_fequal), _1491388)) = hAPP(hAPP(c_Set_Oinsert(_1491386), _1491388), c_Orderings_Obot__class_Obot(tc_fun(_1491386, tc_HOL_Obool))))], (35029 ^ _779142) ^ [_1430091, _1430093, _1430095, _1430097] : [-(hAPP(c_Set_Oimage(_1430091, _1430093, _1430095), _1430097) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430091, tc_fun(_1430093, tc_HOL_Obool)), _1430097), hAPP(hAPP(c_COMBC(_1430091, tc_fun(_1430093, tc_HOL_Obool), tc_fun(_1430093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1430093, tc_fun(tc_fun(_1430093, tc_HOL_Obool), tc_fun(_1430093, tc_HOL_Obool)), _1430091), c_Set_Oinsert(_1430093)), _1430095)), c_Orderings_Obot__class_Obot(tc_fun(_1430093, tc_HOL_Obool)))))], (47185 ^ _779142) ^ [_1728323, _1728325, _1728327] : [-(c_List_Oinsert(_1728323, _1728325, c_List_Oremdups(_1728323, _1728327)) = c_List_Oremdups(_1728323, c_List_Oinsert(_1728323, _1728325, _1728327)))], (35373 ^ _779142) ^ [_1439249, _1439251] : [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), _1439249), _1439251)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439249), _1439251)))], (45564 ^ _779142) ^ [_1693489, _1693491, _1693493, _1693495, _1693497] : [class_Orderings_Olinorder(_1693489), -(c_List_Olinorder__class_Osort__key(_1693491, _1693489, _1693493, hAPP(hAPP(c_List_Olist_OCons(_1693491), _1693495), _1693497)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693491, _1693489, _1693493), _1693495), c_List_Olinorder__class_Osort__key(_1693491, _1693489, _1693493, _1693497)))], (51441 ^ _779142) ^ [_1818906, _1818908] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818906), _1818908)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818908), _1818906))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818908), _1818906)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818906), _1818908)))], (34765 ^ _779142) ^ [_1423524, _1423526, _1423528, _1423530, _1423532] : [hBOOL(hAPP(hAPP(c_member(_1423524), _1423526), _1423528)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423530, tc_HOL_Obool)), hAPP(_1423532, _1423526)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423524, tc_fun(_1423530, tc_HOL_Obool)), _1423528), _1423532)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423524, tc_fun(_1423530, tc_HOL_Obool)), _1423528), _1423532))], (1276 ^ _779142) ^ [_798034, _798036] : [-(class_Divides_Oring__div(_798034)), _798036 = _798034, class_Divides_Oring__div(_798036)], (33539 ^ _779142) ^ [_1392806, _1392808, _1392810, _1392812, _1392814, _1392816, _1392818] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1392806, _1392808), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1392810), _1392812))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1392814, _1392808), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1392816), _1392818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1392808)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392806), _1392814), _1392808), 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), _1392810), _1392816)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392812), _1392818)), _1392808))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392812), _1392818), _1392808)))))], (18909 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (29496 ^ _779142) ^ [_1303742, _1303744, _1303746] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1303742, tc_HOL_Obool)), _1303744), _1303746) = c_Orderings_Obot__class_Obot(tc_fun(_1303742, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303742, tc_HOL_Obool)), _1303744), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1303742, tc_HOL_Obool)), _1303746))))], (17887 ^ _779142) ^ [_1094280] : [class_Rings_Osemiring__1(_1094280), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094280), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1094280))], (4328 ^ _779142) ^ [_844802, _844804] : [_844804 = _844802, -(c_Lazy__Sequence_Oempty(_844804) = c_Lazy__Sequence_Oempty(_844802))], (21226 ^ _779142) ^ [_1152358, _1152360] : [c_Nat__Transfer_Ois__nat(_1152358), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1152358), _1152360)))], (51205 ^ _779142) ^ [_1815137, _1815139] : [class_Rings_Ocomm__semiring__1(_1815137), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815137), _1815139), _1815139)))], (30998 ^ _779142) ^ [_1334531, _1334533, _1334535] : [class_Orderings_Oorder(_1334531), 31001 ^ _779142 : [(31008 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334531), _1334535), _1334533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334531, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1334531), _1334533)), hAPP(c_SetInterval_Oord__class_OatLeast(_1334531), _1334535))))], (31002 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334531, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1334531), _1334533)), hAPP(c_SetInterval_Oord__class_OatLeast(_1334531), _1334535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334531), _1334535), _1334533)))]]], (5070 ^ _779142) ^ [_856473, _856475, _856477, _856479] : [-(c_Transitive__Closure_Otrancl(_856479, _856475) = c_Transitive__Closure_Otrancl(_856477, _856473)), _856479 = _856477, _856475 = _856473], (50041 ^ _779142) ^ [_1791216, _1791218, _1791220, _1791222] : [c_Fun_Oinj__on(_1791216, _1791218, _1791220, _1791222), -(c_Fun_Obij__betw(_1791216, _1791218, _1791220, _1791222, hAPP(c_Set_Oimage(_1791216, _1791218, _1791220), _1791222)))], (35545 ^ _779142) ^ [_1444130, _1444132] : [-(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), _1444130), _1444132)), 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), _1444130), _1444132))], (48138 ^ _779142) ^ [_1749430, _1749432, _1749434, _1749436, _1749438] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749430, _1749432, hAPP(hAPP(c_COMBC(_1749430, tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_fun(_1749432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749432, tc_fun(tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_fun(_1749432, tc_HOL_Obool)), _1749430), c_COMBC(_1749432, tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749432, tc_prod(_1749430, _1749432)), tc_fun(_1749432, tc_fun(tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_HOL_Obool)), _1749430), hAPP(c_COMBB(tc_prod(_1749430, _1749432), tc_fun(tc_fun(tc_prod(_1749430, _1749432), tc_HOL_Obool), tc_HOL_Obool), _1749432), c_member(tc_prod(_1749430, _1749432)))), c_Product__Type_OPair(_1749430, _1749432)))), _1749434)), _1749436), _1749438)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749432, _1749430)), hAPP(hAPP(c_Product__Type_OPair(_1749432, _1749430), _1749436), _1749438)), hAPP(c_Relation_Oconverse(_1749430, _1749432), _1749434))))], (44131 ^ _779142) ^ [_1662146, _1662148, _1662150] : [class_Orderings_Olinorder(_1662146), -(hAPP(c_List_Oset(_1662146), c_List_Olinorder__class_Oinsort__insert__key(_1662146, _1662146, c_COMBI(_1662146), _1662148, _1662150)) = hAPP(hAPP(c_Set_Oinsert(_1662146), _1662148), hAPP(c_List_Oset(_1662146), _1662150)))], (18414 ^ _779142) ^ [] : [-(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))))], (6251 ^ _779142) ^ [_879337, _879339, _879341] : [class_Orderings_Olinorder(_879337), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879337), _879339), _879341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879337), _879341), _879339)))], (23741 ^ _779142) ^ [_1197315, _1197317, _1197319] : [class_Orderings_Oord(_1197315), 23744 ^ _779142 : [(23751 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197315), _1197317), _1197319)), -(hBOOL(hAPP(hAPP(c_member(_1197315), _1197317), hAPP(c_SetInterval_Oord__class_OlessThan(_1197315), _1197319))))], (23745 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1197315), _1197317), hAPP(c_SetInterval_Oord__class_OlessThan(_1197315), _1197319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197315), _1197317), _1197319)))]]], (52685 ^ _779142) ^ [_1836597, _1836599, _1836601, _1836603] : [-(hAPP(hAPP(c_COMBK(_1836597, _1836599), _1836601), _1836603) = _1836601)], (31184 ^ _779142) ^ [_1338066, _1338068, _1338070] : [class_Orderings_Olinorder(_1338066), 31187 ^ _779142 : [(31194 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338066), _1338070), _1338068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338066, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338066), _1338068)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338066), _1338070))))], (31188 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338066, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338066), _1338068)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338066), _1338070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338066), _1338070), _1338068)))]]], (32497 ^ _779142) ^ [_1371762, _1371764] : [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(_1371764))), 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), _1371762)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1371762)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371764))))], (27312 ^ _779142) ^ [_1260936, _1260938, _1260940, _1260942] : [class_Orderings_Olinorder(_1260936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260936), _1260938), _1260940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260936), _1260940), _1260942)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260936, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1260936, _1260938, _1260940)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1260936, _1260940, _1260942)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1260936, _1260938, _1260942))], (49550 ^ _779142) ^ [_1780073, _1780075] : [c_Equiv__Relations_Opart__equivp(_1780073, _1780075), 49554 ^ _779142 : [(49559 ^ _779142) ^ [] : [-(c_Predicate_Otransp(_1780073, _1780075))], (49557 ^ _779142) ^ [] : [-(c_Predicate_Osymp(_1780073, _1780075))], (49555 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1780075, 49553 ^ [_1780073, _1780075]), 49553 ^ [_1780073, _1780075])))]]], (30399 ^ _779142) ^ [_1322800, _1322802] : [class_Lattices_Olattice(_1322800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322800), _1322802)), -(_1322802 = c_Orderings_Obot__class_Obot(tc_fun(_1322800, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322800), c_Big__Operators_Olattice__class_OInf__fin(_1322800, _1322802)), c_Big__Operators_Olattice__class_OSup__fin(_1322800, _1322802))))], (33433 ^ _779142) ^ [_1390803, _1390805, _1390807, _1390809] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390803, _1390805), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390807), _1390809))), -(_1390805 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390803, _1390805) = _1390809)], (28128 ^ _779142) ^ [_1276263, _1276265] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1276263), _1276265)), _1276265) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1276263), _1276265))], (25884 ^ _779142) ^ [] : [-(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))))], (23781 ^ _779142) ^ [_1197999, _1198001, _1198003] : [class_Int_Onumber__ring(_1197999), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197999), hAPP(c_Int_Onumber__class_Onumber__of(_1197999), _1198001)), hAPP(c_Int_Onumber__class_Onumber__of(_1197999), _1198003)) = hAPP(c_Int_Onumber__class_Onumber__of(_1197999), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198001), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198003))))], (20358 ^ _779142) ^ [_1136409, _1136411] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136409) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136411)), _1136409 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136411)), 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), _1136411)))], (48030 ^ _779142) ^ [_1746714, _1746716, _1746718, _1746720, _1746722, _1746724, _1746726] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1746714, _1746716, _1746718, _1746720, _1746722, _1746724, _1746726) = c_New__DSequence_Oneg__decr__bind(_1746714, _1746716, hAPP(hAPP(hAPP(_1746718, _1746722), _1746724), _1746726), hAPP(hAPP(c_COMBC(_1746714, 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(_1746716)))), hAPP(hAPP(c_COMBC(_1746714, 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(_1746716))))), hAPP(hAPP(c_COMBC(_1746714, 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(_1746716)))))), _1746720), _1746722)), _1746724)), _1746726)))], (20802 ^ _779142) ^ [_1144845, _1144847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144847), _1144845))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144847), _1144845) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144847), _1144845)), _1144845)))], (36054 ^ _779142) ^ [_1456130, _1456132, _1456134, _1456136, _1456138, _1456140, _1456142, _1456144, _1456146, _1456148] : [c_Equiv__Relations_Ocongruent2(_1456130, _1456132, _1456134, _1456136, _1456138, _1456140), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456130, _1456130)), hAPP(hAPP(c_Product__Type_OPair(_1456130, _1456130), _1456142), _1456144)), _1456136)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456132, _1456132)), hAPP(hAPP(c_Product__Type_OPair(_1456132, _1456132), _1456146), _1456148)), _1456138)), -(hAPP(hAPP(_1456140, _1456142), _1456146) = hAPP(hAPP(_1456140, _1456144), _1456148))], (3768 ^ _779142) ^ [_835646, _835648, _835650, _835652, _835654, _835656] : [-(c_List_OtakeWhile(_835656, _835652, _835648) = c_List_OtakeWhile(_835654, _835650, _835646)), _835656 = _835654, _835652 = _835650, _835648 = _835646], (24119 ^ _779142) ^ [_1203885] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203885) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1203885))], (25064 ^ _779142) ^ [_1219777, _1219779] : [class_Rings_Olinordered__idom(_1219777), 25067 ^ _779142 : [(25074 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219777), c_Groups_Ozero__class_Ozero(_1219777)), _1219779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219777), c_Groups_Ozero__class_Ozero(_1219777)), c_Groups_Osgn__class_Osgn(_1219777, _1219779))))], (25068 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219777), c_Groups_Ozero__class_Ozero(_1219777)), c_Groups_Osgn__class_Osgn(_1219777, _1219779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219777), c_Groups_Ozero__class_Ozero(_1219777)), _1219779)))]]], (32887 ^ _779142) ^ [_1379929, _1379931] : [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), _1379929))), 32890 ^ _779142 : [(32897 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379931)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379929)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379931), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379929)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379929)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379931), 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), _1379929)))))], (32891 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379931)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379929))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379931), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379929)) = 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), _1379931)))]]], (34053 ^ _779142) ^ [_1403256, _1403258, _1403260, _1403262, _1403264, _1403266, _1403268, _1403270] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1403256, _1403258), tc_prod(_1403256, _1403258))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1403256, _1403258), tc_prod(_1403256, _1403258)), hAPP(hAPP(c_Product__Type_OPair(_1403256, _1403258), _1403260), _1403262)), hAPP(hAPP(c_Product__Type_OPair(_1403256, _1403258), _1403264), _1403266))), c_Wellfounded_Olex__prod(_1403256, _1403258, _1403268, _1403270)))), 34054 ^ _779142 : [(34057 ^ _779142) ^ [] : [_1403260 = _1403264, hBOOL(hAPP(hAPP(c_member(tc_prod(_1403258, _1403258)), hAPP(hAPP(c_Product__Type_OPair(_1403258, _1403258), _1403262), _1403266)), _1403270))], (34055 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1403256, _1403256)), hAPP(hAPP(c_Product__Type_OPair(_1403256, _1403256), _1403260), _1403264)), _1403268))]]], (11195 ^ _779142) ^ [_971697] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971697), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _971697)], (42642 ^ _779142) ^ [_1629164, _1629166, _1629168] : [c_List_Olist_ONil(_1629164) = hAPP(hAPP(c_List_Olist_OCons(_1629164), _1629166), _1629168)], (52595 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (19277 ^ _779142) ^ [_1118125, _1118127, _1118129] : [class_Groups_Oordered__ab__group__add__abs(_1118125), -(hAPP(c_Groups_Oabs__class_Oabs(_1118125), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118125), _1118127), _1118129)) = hAPP(c_Groups_Oabs__class_Oabs(_1118125), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118125), _1118129), _1118127)))], (52317 ^ _779142) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (20957 ^ _779142) ^ [_1147724, _1147726] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147724))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147724)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147726)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41300 ^ _779142) ^ [_1592519, _1592521, _1592523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592519), c_Nitpick_Oplus__frac(_1592519, _1592521, c_Nitpick_Ouminus__frac(_1592519, _1592523)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1592519, _1592521, _1592523))], (44460 ^ _779142) ^ [_1669395] : [-(hAPP(c_List_Omap(_1669395, _1669395), c_COMBI(_1669395)) = c_Fun_Oid(tc_List_Olist(_1669395)))], (27544 ^ _779142) ^ [_1265231] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1265231)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1265231)], (49080 ^ _779142) ^ [_1771458, _1771460, _1771462, _1771464] : [c_Predicate_Osymp(_1771458, _1771460), hBOOL(hAPP(hAPP(_1771460, _1771462), _1771464)), -(hBOOL(hAPP(hAPP(_1771460, _1771464), _1771462)))], (5090 ^ _779142) ^ [_856771, _856773, _856775, _856777] : [-(c_Transitive__Closure_Ortrancl(_856777, _856773) = c_Transitive__Closure_Ortrancl(_856775, _856771)), _856777 = _856775, _856773 = _856771], (31250 ^ _779142) ^ [_1339340, _1339342] : [-(hBOOL(hAPP(hAPP(c_member(_1339340), _1339342), c_Orderings_Otop__class_Otop(tc_fun(_1339340, tc_HOL_Obool)))))], (27628 ^ _779142) ^ [_1266555, _1266557, _1266559] : [class_Lattices_Olattice(_1266555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266555), _1266557)), 27635 ^ _779142 : [(27642 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266555, tc_HOL_Obool)), _1266557), hAPP(hAPP(c_Set_Oinsert(_1266555), _1266559), c_Orderings_Obot__class_Obot(tc_fun(_1266555, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1266555, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1266555, hAPP(hAPP(c_Set_Oinsert(_1266555), _1266559), _1266557)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266555), _1266559), c_Big__Operators_Olattice__class_OSup__fin(_1266555, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266555, tc_HOL_Obool)), _1266557), hAPP(hAPP(c_Set_Oinsert(_1266555), _1266559), c_Orderings_Obot__class_Obot(tc_fun(_1266555, tc_HOL_Obool)))))))], (27636 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266555, tc_HOL_Obool)), _1266557), hAPP(hAPP(c_Set_Oinsert(_1266555), _1266559), c_Orderings_Obot__class_Obot(tc_fun(_1266555, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1266555, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1266555, hAPP(hAPP(c_Set_Oinsert(_1266555), _1266559), _1266557)) = _1266559)]]], (34360 ^ _779142) ^ [_1411142, _1411144, _1411146, _1411148] : [c_Orderings_Otop__class_Otop(tc_fun(_1411142, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411144, tc_fun(_1411142, tc_HOL_Obool)), _1411146), _1411148), 34363 ^ _779142 : [(34364 ^ _779142) ^ [_1411258] : [hBOOL(hAPP(hAPP(c_member(_1411144), _1411258), _1411146)), -(hAPP(_1411148, _1411258) = c_Orderings_Otop__class_Otop(tc_fun(_1411142, tc_HOL_Obool)))]]], (36096 ^ _779142) ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105] : [c_Equiv__Relations_Oequiv(_1457093, _1457095, _1457097), c_Equiv__Relations_Ocongruent(_1457093, tc_fun(_1457099, tc_HOL_Obool), _1457097, _1457101), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457093, tc_fun(_1457099, tc_HOL_Obool)), _1457103), _1457101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457093, tc_fun(_1457099, tc_HOL_Obool)), _1457105), _1457101), hBOOL(hAPP(hAPP(c_member(tc_fun(_1457093, tc_HOL_Obool)), _1457103), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457093), _1457095), _1457097))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1457093, tc_HOL_Obool)), _1457105), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457093), _1457095), _1457097))), 36118 ^ _779142 : [(36122 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457093), 36120 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105]), _1457095)))], (36124 ^ _779142) ^ [] : [-(hAPP(_1457101, 36117 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105]) = hAPP(_1457101, 36120 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105]))], (36126 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457093, _1457093)), hAPP(hAPP(c_Product__Type_OPair(_1457093, _1457093), 36117 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105]), 36120 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105])), _1457097))], (36119 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457093), 36117 ^ [_1457093, _1457095, _1457097, _1457099, _1457101, _1457103, _1457105]), _1457095)))]], -(_1457103 = _1457105)], (23469 ^ _779142) ^ [_1192589, _1192591] : [class_Rings_Oring__1__no__zero__divisors(_1192589), 23472 ^ _779142 : [(23473 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192589), _1192591), _1192591) = c_Groups_Oone__class_Oone(_1192589), -(_1192591 = c_Groups_Oone__class_Oone(_1192589)), -(_1192591 = hAPP(c_Groups_Ouminus__class_Ouminus(_1192589), c_Groups_Oone__class_Oone(_1192589)))], (23483 ^ _779142) ^ [] : [23484 ^ _779142 : [(23487 ^ _779142) ^ [] : [_1192591 = hAPP(c_Groups_Ouminus__class_Ouminus(_1192589), c_Groups_Oone__class_Oone(_1192589))], (23485 ^ _779142) ^ [] : [_1192591 = c_Groups_Oone__class_Oone(_1192589)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192589), _1192591), _1192591) = c_Groups_Oone__class_Oone(_1192589))]]], (28006 ^ _779142) ^ [_1273635, _1273637, _1273639] : [class_Orderings_Olinorder(_1273635), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273635), _1273637), _1273639) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273635), _1273639), _1273637))], (14283 ^ _779142) ^ [_1027886, _1027888, _1027890, _1027892, _1027894] : [class_Fields_Olinordered__field(_1027886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027886), c_Groups_Ozero__class_Ozero(_1027886)), _1027888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027886), _1027888), _1027890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027886), c_Groups_Ozero__class_Ozero(_1027886)), _1027892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027886), _1027892), _1027894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027886), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027886), _1027888), _1027894)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027886), _1027890), _1027892))))], (42345 ^ _779142) ^ [_1622672, _1622674, _1622676, _1622678, _1622680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622672), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622674)), _1622676))), 42348 ^ _779142 : [(42355 ^ _779142) ^ [] : [-(_1622672 = _1622678), -(hAPP(hAPP(c_List_Onth(_1622674), hAPP(hAPP(c_List_Olist__update(_1622674, _1622676), _1622672), _1622680)), _1622678) = hAPP(hAPP(c_List_Onth(_1622674), _1622676), _1622678))], (42349 ^ _779142) ^ [] : [_1622672 = _1622678, -(hAPP(hAPP(c_List_Onth(_1622674), hAPP(hAPP(c_List_Olist__update(_1622674, _1622676), _1622672), _1622680)), _1622678) = _1622680)]]], (42898 ^ _779142) ^ [_1633859] : [-(c_List_Olistset(_1633859, c_List_Olist_ONil(tc_fun(_1633859, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633859)), c_List_Olist_ONil(_1633859)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633859), tc_HOL_Obool))))], (38983 ^ _779142) ^ [_1534836, _1534838, _1534840, _1534842] : [hBOOL(hAPP(hAPP(c_member(_1534836), _1534842), hAPP(c_Relation_ODomain(_1534836, _1534838), _1534840))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1534836, _1534838, hAPP(hAPP(c_COMBC(_1534836, tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_fun(_1534838, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534838, tc_fun(tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_fun(_1534838, tc_HOL_Obool)), _1534836), c_COMBC(_1534838, tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534838, tc_prod(_1534836, _1534838)), tc_fun(_1534838, tc_fun(tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_HOL_Obool)), _1534836), hAPP(c_COMBB(tc_prod(_1534836, _1534838), tc_fun(tc_fun(tc_prod(_1534836, _1534838), tc_HOL_Obool), tc_HOL_Obool), _1534838), c_member(tc_prod(_1534836, _1534838)))), c_Product__Type_OPair(_1534836, _1534838)))), _1534840)), _1534842)))], (1876 ^ _779142) ^ [_805534, _805536] : [-(class_Groups_Ominus(_805534)), _805536 = _805534, class_Groups_Ominus(_805536)], (36502 ^ _779142) ^ [_1465792, _1465794, _1465796] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465792), _1465794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465792, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465792, _1465792, _1465796), _1465794)), _1465794)), c_Fun_Oinj__on(_1465792, _1465792, _1465796, _1465794), -(hAPP(c_Set_Oimage(_1465792, _1465792, _1465796), _1465794) = _1465794)], (21600 ^ _779142) ^ [_1158510, _1158512, _1158514, _1158516] : [class_Fields_Ofield(_1158510), -(_1158512 = c_Groups_Ozero__class_Ozero(_1158510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158514), _1158516)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158510), _1158512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158516), _1158514)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158510), hAPP(hAPP(c_Power_Opower__class_Opower(_1158510), _1158512), _1158516)), hAPP(hAPP(c_Power_Opower__class_Opower(_1158510), _1158512), _1158514)))], (33724 ^ _779142) ^ [_1396498, _1396500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396498), 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)), _1396500)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396498, _1396500) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1396498, _1396500)))], (11197 ^ _779142) ^ [_971726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971726), _971726) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17899 ^ _779142) ^ [_1094482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1094482)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1094482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3538 ^ _779142) ^ [_832053, _832055, _832057, _832059, _832061, _832063] : [-(c_List_Oremove1(_832063, _832059, _832055) = c_List_Oremove1(_832061, _832057, _832053)), _832063 = _832061, _832059 = _832057, _832055 = _832053], (32847 ^ _779142) ^ [_1379168, _1379170] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379168), _1379170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379168)), _1379170)))], (35541 ^ _779142) ^ [_1443985] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1443985) = 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), _1443985), 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))))))], (25928 ^ _779142) ^ [_1234792, _1234794, _1234796] : [class_Rings_Olinordered__semidom(_1234792), hAPP(hAPP(c_Power_Opower__class_Opower(_1234792), _1234794), 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(_1234792), _1234796), 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(_1234792), c_Groups_Ozero__class_Ozero(_1234792)), _1234794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234792), c_Groups_Ozero__class_Ozero(_1234792)), _1234796)), -(_1234794 = _1234796)], (29977 ^ _779142) ^ [_1314228, _1314230, _1314232] : [class_Orderings_Olinorder(_1314228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314228), _1314230)), -(_1314230 = c_Orderings_Obot__class_Obot(tc_fun(_1314228, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314228), _1314232)), -(_1314232 = c_Orderings_Obot__class_Obot(tc_fun(_1314228, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314228, tc_HOL_Obool)), _1314230), _1314232) = c_Orderings_Obot__class_Obot(tc_fun(_1314228, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1314228, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314228, tc_HOL_Obool)), _1314230), _1314232)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314228), c_Big__Operators_Olinorder__class_OMin(_1314228, _1314230)), c_Big__Operators_Olinorder__class_OMin(_1314228, _1314232)))], (4242 ^ _779142) ^ [_843321, _843323] : [_843323 = _843321, -(c_If(_843323) = c_If(_843321))], (12517 ^ _779142) ^ [_995186, _995188] : [_995186 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995186), _995188), -(_995188 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_995186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21894 ^ _779142) ^ [_1163954, _1163956, _1163958, _1163960] : [class_Fields_Ofield__inverse__zero(_1163954), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163954), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163954), _1163956), _1163958)), _1163960) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163954), hAPP(hAPP(c_Power_Opower__class_Opower(_1163954), _1163956), _1163960)), hAPP(hAPP(c_Power_Opower__class_Opower(_1163954), _1163958), _1163960)))], (41711 ^ _779142) ^ [_1605708, _1605710, _1605712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605708, _1605708), tc_HOL_Obool)), _1605710), hAPP(hAPP(c_Product__Type_OSigma(_1605708, _1605708), _1605712), hAPP(c_COMBK(tc_fun(_1605708, tc_HOL_Obool), _1605708), _1605712)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1605708), tc_List_Olist(_1605708)), tc_HOL_Obool)), c_List_Olistrel(_1605708, _1605710)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1605708), tc_List_Olist(_1605708)), c_List_Olists(_1605708, _1605712)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1605708), tc_HOL_Obool), tc_List_Olist(_1605708)), c_List_Olists(_1605708, _1605712))))))], (21063 ^ _779142) ^ [_1149584] : [c_Nat__Transfer_Onat__set(_1149584), 21066 ^ _779142 : [(21067 ^ _779142) ^ [_1149650] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1149650), _1149584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149650)))]]], (52295 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (47681 ^ _779142) ^ [_1739789, _1739791, _1739793, _1739795] : [47682 ^ _779142 : [(47685 ^ _779142) ^ [] : [c_List_Olist__ex(_1739789, _1739791, _1739795)], (47683 ^ _779142) ^ [] : [c_List_Olist__ex(_1739789, _1739791, _1739793)]], -(c_List_Olist__ex(_1739789, _1739791, hAPP(hAPP(c_List_Oappend(_1739789), _1739793), _1739795)))], (13609 ^ _779142) ^ [_1015880, _1015882, _1015884, _1015886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015880), _1015882)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015884), _1015886)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1015880, _1015884)), c_Sum__Type_OPlus(_1015880, _1015884, _1015882, _1015886))))], (49234 ^ _779142) ^ [_1774436, _1774438] : [c_Wellfounded_Oacyclic(_1774436, _1774438), -(c_Relation_Oantisym(_1774436, c_Transitive__Closure_Ortrancl(_1774436, _1774438)))], (14882 ^ _779142) ^ [_1039281, _1039283, _1039285, _1039287] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039281, tc_Nat_Onat), _1039283), _1039285) = hAPP(c_Nat_OSuc, _1039287), 14886 ^ _779142 : [(14889 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1039283, 14885 ^ [_1039281, _1039283, _1039285, _1039287]))))], (14887 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039281), 14885 ^ [_1039281, _1039283, _1039285, _1039287]), _1039285)))]]], (20267 ^ _779142) ^ [_1134837, _1134839] : [-(hAPP(c_Int_Onat, _1134837) = _1134839), 20270 ^ _779142 : [(20273 ^ _779142) ^ [] : [_1134837 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134839)], (20271 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134837)))]], 20274 ^ _779142 : [(20277 ^ _779142) ^ [] : [_1134839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20275 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134837))]]], (9047 ^ _779142) ^ [_932167, _932169, _932171, _932173, _932175, _932177] : [class_Rings_Oordered__ring(_932167), 9050 ^ _779142 : [(9057 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932167), _932173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932167), _932175), _932169)), _932171)), _932177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), _932169), _932171)), _932173)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), _932175), _932171)), _932177))))], (9051 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), _932169), _932171)), _932173)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), _932175), _932171)), _932177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932167), _932173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932167), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932167), _932175), _932169)), _932171)), _932177))))]]], (43802 ^ _779142) ^ [_1655198, _1655200, _1655202] : [-(hAPP(c_List_Orotate(_1655198, _1655200), _1655202) = hAPP(c_List_Orotate(_1655198, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655200, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655198)), _1655202))), _1655202))], (46375 ^ _779142) ^ [_1711324, _1711326, _1711328, _1711330, _1711332, _1711334] : [class_Orderings_Olinorder(_1711324), c_List_Olinorder__class_Osorted(_1711324, hAPP(hAPP(c_List_Omap(_1711326, _1711324), _1711328), _1711330)), hBOOL(hAPP(_1711332, _1711334)), -(hAPP(c_List_Ofilter(_1711326, _1711332), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711326, _1711324, _1711328), _1711334), _1711330)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711326, _1711324, _1711328), _1711334), hAPP(c_List_Ofilter(_1711326, _1711332), _1711330)))], (29067 ^ _779142) ^ [_1294288, _1294290, _1294292] : [class_Lattices_Olattice(_1294288), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294288), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294288), _1294290), _1294292)), _1294290)))], (49765 ^ _779142) ^ [_1785164, _1785166, _1785168, _1785170, _1785172] : [c_Fun_Oinj__on(_1785164, _1785166, _1785168, c_Orderings_Otop__class_Otop(tc_fun(_1785164, tc_HOL_Obool))), 49771 ^ _779142 : [(49774 ^ _779142) ^ [] : [hBOOL(hAPP(_1785170, hAPP(c_Hilbert__Choice_Oinv__into(_1785164, _1785166, c_Orderings_Otop__class_Otop(tc_fun(_1785164, tc_HOL_Obool)), _1785168), 49770 ^ [_1785164, _1785166, _1785168, _1785170, _1785172])))], (49772 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785166), 49770 ^ [_1785164, _1785166, _1785168, _1785170, _1785172]), hAPP(c_Set_Oimage(_1785164, _1785166, _1785168), c_Orderings_Otop__class_Otop(tc_fun(_1785164, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1785170, _1785172)))], (16113 ^ _779142) ^ [_1062218, _1062220, _1062222] : [class_Orderings_Olinorder(_1062218), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062218), _1062220)), -(_1062220 = c_Orderings_Obot__class_Obot(tc_fun(_1062218, tc_HOL_Obool))), 16124 ^ _779142 : [(16125 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062218), _1062222), hAPP(c_Finite__Set_Ofold1(_1062218, c_Orderings_Oord__class_Omin(_1062218)), _1062220))), 16128 ^ _779142 : [(16129 ^ _779142) ^ [_1062511] : [hBOOL(hAPP(hAPP(c_member(_1062218), _1062511), _1062220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062218), _1062222), _1062511)))]]], (16135 ^ _779142) ^ [] : [16137 ^ _779142 : [(16140 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062218), _1062222), 16136 ^ [_1062218, _1062220, _1062222]))], (16138 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062218), 16136 ^ [_1062218, _1062220, _1062222]), _1062220)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062218), _1062222), hAPP(c_Finite__Set_Ofold1(_1062218, c_Orderings_Oord__class_Omin(_1062218)), _1062220))))]]], (16409 ^ _779142) ^ [_1067916, _1067918, _1067920] : [class_Orderings_Olinorder(_1067916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067916), _1067918)), -(hBOOL(hAPP(hAPP(c_member(_1067916), _1067920), _1067918))), -(c_Big__Operators_Olinorder__class_OMin(_1067916, hAPP(hAPP(c_Set_Oinsert(_1067916), _1067920), _1067918)) = hAPP(hAPP(c_Finite__Set_Ofold(_1067916, _1067916, c_Orderings_Oord__class_Omin(_1067916)), _1067920), _1067918))], (31807 ^ _779142) ^ [_1351653, _1351655, _1351657, _1351659] : [class_Groups_Ouminus(_1351653), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1351655, _1351653)), _1351657), _1351659) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351653), hAPP(_1351657, _1351659)))], (16541 ^ _779142) ^ [_1070232, _1070234, _1070236] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070232), _1070234)), _1070236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070234), _1070236)))], (4584 ^ _779142) ^ [_848818, _848820, _848822, _848824, _848826, _848828] : [-(c_Random__Sequence_Oempty(_848828, _848824, _848820) = c_Random__Sequence_Oempty(_848826, _848822, _848818)), _848828 = _848826, _848824 = _848822, _848820 = _848818], (42848 ^ _779142) ^ [_1632949, _1632951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632949)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632951))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632949), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632951)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632949)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632949)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632951))))], (41154 ^ _779142) ^ [_1588376, _1588378, _1588380, _1588382, _1588384] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588376, _1588376)), hAPP(hAPP(c_Product__Type_OPair(_1588376, _1588376), _1588378), _1588380)), c_Transitive__Closure_Ortrancl(_1588376, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588376, _1588376), tc_HOL_Obool)), _1588382), _1588384)))), 41160 ^ _779142 : [(41166 ^ _779142) ^ [] : [41159 ^ [_1588376, _1588378, _1588380, _1588382, _1588384] = 41162 ^ [_1588376, _1588378, _1588380, _1588382, _1588384]], (41164 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588376, _1588376)), hAPP(hAPP(c_Product__Type_OPair(_1588376, _1588376), 41159 ^ [_1588376, _1588378, _1588380, _1588382, _1588384]), 41162 ^ [_1588376, _1588378, _1588380, _1588382, _1588384])), _1588384)))], (41161 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588376, _1588376)), hAPP(hAPP(c_Product__Type_OPair(_1588376, _1588376), _1588378), 41159 ^ [_1588376, _1588378, _1588380, _1588382, _1588384])), c_Transitive__Closure_Ortrancl(_1588376, _1588382))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588376, _1588376)), hAPP(hAPP(c_Product__Type_OPair(_1588376, _1588376), _1588378), _1588380)), c_Transitive__Closure_Ortrancl(_1588376, _1588382))))], (31112 ^ _779142) ^ [_1336800, _1336802] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1336800, _1336802)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1336800, _1336802), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1336802), c_Orderings_Otop__class_Otop(tc_fun(_1336802, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1336800), c_Orderings_Otop__class_Otop(tc_fun(_1336800, tc_HOL_Obool)))))], (35362 ^ _779142) ^ [_1438972, _1438974, _1438976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438972, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35363 ^ [_1438972, _1438974, _1438976])), _1438974)), _1438976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438972, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1438974)), _1438976)))], (49598 ^ _779142) ^ [_1781299, _1781301, _1781303, _1781305] : [c_Fun_Oinj__on(_1781299, _1781301, _1781303, c_Orderings_Otop__class_Otop(tc_fun(_1781299, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781301, _1781299, c_Hilbert__Choice_Oinv__into(_1781299, _1781301, c_Orderings_Otop__class_Otop(tc_fun(_1781299, tc_HOL_Obool)), _1781303)), hAPP(c_Set_Oimage(_1781299, _1781301, _1781303), _1781305)) = _1781305)], (25104 ^ _779142) ^ [_1220382] : [class_Int_Onumber__ring(_1220382), c_Int_Oiszero(_1220382, hAPP(c_Int_Onumber__class_Onumber__of(_1220382), c_Int_OBit1(c_Int_OPls)))], (24809 ^ _779142) ^ [_1215372, _1215374] : [24817 ^ _779142 : [(24820 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1215374, 24816 ^ [_1215372, _1215374])))], (24818 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24816 ^ [_1215372, _1215374]), _1215372)))]], 24810 ^ _779142 : [(24811 ^ _779142) ^ [_1215440] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1215440), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215372))), hBOOL(hAPP(_1215374, _1215440))]]], (48152 ^ _779142) ^ [_1750319, _1750321, _1750323] : [-(_1750319 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1750321), c_List_Oreplicate(_1750321, _1750319, _1750323)) = c_List_Oreplicate(_1750321, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750319), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1750323))], (6189 ^ _779142) ^ [_878199, _878201, _878203, _878205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878199, tc_HOL_Obool)), _878201), _878203)), hBOOL(hAPP(hAPP(c_member(_878199), _878205), _878201)), -(hBOOL(hAPP(hAPP(c_member(_878199), _878205), _878203)))], (15405 ^ _779142) ^ [_1049008, _1049010, _1049012] : [class_Orderings_Olinorder(_1049008), 15408 ^ _779142 : [(15415 ^ _779142) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049008), _1049010), _1049012) = _1049010, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049008), _1049010), _1049012)))], (15409 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049008), _1049010), _1049012)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049008), _1049010), _1049012) = _1049010)]]], (19667 ^ _779142) ^ [_1124580, _1124582] : [class_Divides_Osemiring__div(_1124580), -(_1124582 = c_Groups_Ozero__class_Ozero(_1124580)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124580), _1124582), _1124582) = c_Groups_Oone__class_Oone(_1124580))], (38050 ^ _779142) ^ [_1506595, _1506597] : [-(hAPP(c_Set_OPow(_1506595), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506595, tc_HOL_Obool)), _1506597)) = hAPP(c_Set_OCollect(tc_fun(_1506595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506595, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1506595, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1506595, tc_HOL_Obool), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1506595, tc_HOL_Obool)), c_COMBS(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1506595, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1506595, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1506595, tc_HOL_Obool), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_fun(_1506595, tc_HOL_Obool)), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_fun(_1506595, tc_HOL_Obool)), tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1506595, tc_HOL_Obool)), c_COMBB(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506595, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1506595, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506595, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1506595, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1506595, tc_HOL_Obool)), _1506597)), c_Set_OPow(_1506595))))))], (26718 ^ _779142) ^ [_1249790, _1249792] : [class_Lattices_Obounded__lattice__bot(_1249790), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1249790), _1249792), c_Orderings_Obot__class_Obot(_1249790)) = _1249792)], (40221 ^ _779142) ^ [_1564573, _1564575] : [-(hAPP(c_Relation_ORange(_1564573, _1564573), c_Transitive__Closure_Otrancl(_1564573, _1564575)) = hAPP(c_Relation_ORange(_1564573, _1564573), _1564575))], (31943 ^ _779142) ^ [_1355986, _1355988] : [hBOOL(hAPP(hAPP(c_member(_1355986), _1355988), c_Orderings_Obot__class_Obot(tc_fun(_1355986, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1355986, tc_HOL_Obool)), _1355988)))], (15775 ^ _779142) ^ [_1055920, _1055922, _1055924, _1055926] : [class_Fields_Ofield__inverse__zero(_1055920), class_Int_Onumber(_1055920), 15782 ^ _779142 : [(15783 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1055920), _1055922), _1055924) = hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926), 15786 ^ _779142 : [(15793 ^ _779142) ^ [] : [_1055924 = c_Groups_Ozero__class_Ozero(_1055920), -(hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926) = c_Groups_Ozero__class_Ozero(_1055920))], (15787 ^ _779142) ^ [] : [-(_1055924 = c_Groups_Ozero__class_Ozero(_1055920)), -(_1055922 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055920), hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926)), _1055924))]]], (15799 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1055920), _1055922), _1055924) = hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926)), 15802 ^ _779142 : [(15805 ^ _779142) ^ [] : [_1055922 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055920), hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926)), _1055924)], (15803 ^ _779142) ^ [] : [_1055924 = c_Groups_Ozero__class_Ozero(_1055920)]], 15806 ^ _779142 : [(15809 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1055920), _1055926) = c_Groups_Ozero__class_Ozero(_1055920)], (15807 ^ _779142) ^ [] : [-(_1055924 = c_Groups_Ozero__class_Ozero(_1055920))]]]]], (35262 ^ _779142) ^ [_1436043, _1436045, _1436047, _1436049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1436043), _1436045)), -(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), _1436043), _1436047)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1436045), _1436049))), c_FunDef_Opair__leq)))], (10113 ^ _779142) ^ [_952903, _952905, _952907] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952905), _952907)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952903), _952907)))], (23219 ^ _779142) ^ [_1188047, _1188049] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1188047, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1188047, tc_HOL_Obool))), hAPP(c_Set_OPow(_1188047), _1188049))))], (40004 ^ _779142) ^ [_1559279, _1559281, _1559283] : [-(hBOOL(hAPP(hAPP(c_member(_1559279), _1559281), c_Wellfounded_Oacc(_1559279, _1559283)))), 40008 ^ _779142 : [(40011 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1559279), 40007 ^ [_1559279, _1559281, _1559283]), c_Wellfounded_Oacc(_1559279, _1559283)))], (40009 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559279, _1559279)), hAPP(hAPP(c_Product__Type_OPair(_1559279, _1559279), 40007 ^ [_1559279, _1559281, _1559283]), _1559281)), _1559283)))]]], (28078 ^ _779142) ^ [_1275168] : [class_Orderings_Olinorder(_1275168), -(c_Finite__Set_Ofun__left__comm__idem(_1275168, _1275168, c_Orderings_Oord__class_Omax(_1275168)))], (37625 ^ _779142) ^ [_1492364, _1492366, _1492368] : [-(hAPP(hAPP(c_Set_Oinsert(_1492364), _1492366), _1492368) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1492364, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1492364), hAPP(hAPP(c_COMBC(_1492364, _1492364, tc_HOL_Obool), c_fequal), _1492366))), _1492368))], (20185 ^ _779142) ^ [_1133625, _1133627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133627)), 20192 ^ _779142 : [(20199 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133625), _1133627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1133625)), hAPP(c_Int_Onat, _1133627))))], (20193 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1133625)), hAPP(c_Int_Onat, _1133627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133625), _1133627)))]]], (20828 ^ _779142) ^ [_1145265, _1145267, _1145269] : [hBOOL(hAPP(_1145265, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1145267), _1145269))), 20831 ^ _779142 : [(20838 ^ _779142) ^ [] : [-(_1145269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20841 ^ _779142 : [(20842 ^ _779142) ^ [_1145517, _1145519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145517), _1145269)), _1145267 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145269), _1145519)), _1145517), -(hBOOL(hAPP(_1145265, _1145519)))]]], (20832 ^ _779142) ^ [] : [_1145269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1145265, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (38719 ^ _779142) ^ [_1528600, _1528602, _1528604] : [c_Wellfounded_Owf(_1528600, _1528602), c_Wellfounded_Owf(_1528600, _1528604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528600, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1528600, _1528600), _1528602)), hAPP(c_Relation_ORange(_1528600, _1528600), _1528604)) = c_Orderings_Obot__class_Obot(tc_fun(_1528600, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1528600, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528600, _1528600), tc_HOL_Obool)), _1528602), _1528604)))], (35089 ^ _779142) ^ [_1431688, _1431690, _1431692, _1431694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431688), _1431690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431692), _1431694)), -(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), _1431688), _1431692)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1431690), _1431694))), c_FunDef_Opair__leq)))], (23247 ^ _779142) ^ [_1188672, _1188674, _1188676] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1188672, tc_HOL_Obool)), _1188674), hAPP(c_Set_OPow(_1188672), _1188676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1188672, tc_HOL_Obool)), _1188674), _1188676)))], (35304 ^ _779142) ^ [_1436880, _1436882] : [_1436880 = _1436882, -(hAPP(c_Int_ORep__Integ, _1436880) = hAPP(c_Int_ORep__Integ, _1436882))], (3594 ^ _779142) ^ [_832961, _832963] : [_832963 = _832961, -(c_Orderings_Oord__class_Omax(_832963) = c_Orderings_Oord__class_Omax(_832961))], (9449 ^ _779142) ^ [_940192, _940194] : [class_Rings_Olinordered__semidom(_940192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940192), _940194), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940192), _940194), c_Groups_Oone__class_Oone(_940192)))))], (38649 ^ _779142) ^ [] : [-(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)))))], (21704 ^ _779142) ^ [_1160355, _1160357, _1160359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1160355), _1160357)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1160355), _1160359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160357), _1160359)))], (41731 ^ _779142) ^ [_1606225, _1606227, _1606229] : [c_Relation_Orefl__on(_1606225, _1606227, _1606229), -(c_Relation_Orefl__on(tc_List_Olist(_1606225), c_List_Olists(_1606225, _1606227), c_List_Olistrel(_1606225, _1606229)))], (51693 ^ _779142) ^ [_1823218, _1823220, _1823222, _1823224] : [-(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), _1823218, _1823220)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823222, _1823224)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823222), _1823224)), 51696 ^ _779142 : [(51699 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823222), _1823218)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823220), _1823224)), 51706 ^ _779142 : [(51713 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823220), _1823224)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823224), _1823220)))], (51707 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823222), _1823218)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823218), _1823222)))]]], (51697 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823218), _1823220)))]]], (52655 ^ _779142) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (21348 ^ _779142) ^ [_1154511, _1154513] : [c_Nat__Transfer_Ois__nat(_1154511), c_Nat__Transfer_Ois__nat(_1154513), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1154511, _1154513)))], (49911 ^ _779142) ^ [_1788505, _1788507, _1788509, _1788511, _1788513, _1788515, _1788517, _1788519] : [c_Fun_Obij__betw(_1788505, _1788507, _1788509, _1788511, _1788513), 49914 ^ _779142 : [(49921 ^ _779142) ^ [] : [c_Fun_Obij__betw(_1788505, _1788515, hAPP(c_Fun_Ocomp(_1788507, _1788515, _1788505, _1788517), _1788509), _1788511, _1788519), -(c_Fun_Obij__betw(_1788507, _1788515, _1788517, _1788513, _1788519))], (49915 ^ _779142) ^ [] : [c_Fun_Obij__betw(_1788507, _1788515, _1788517, _1788513, _1788519), -(c_Fun_Obij__betw(_1788505, _1788515, hAPP(c_Fun_Ocomp(_1788507, _1788515, _1788505, _1788517), _1788509), _1788511, _1788519))]]], (44408 ^ _779142) ^ [_1668204, _1668206, _1668208, _1668210, _1668212] : [class_Groups_Oab__group__add(_1668204), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668204), hAPP(hAPP(c_List_Omap(_1668206, _1668204), hAPP(hAPP(c_COMBS(_1668206, _1668204, _1668204), hAPP(hAPP(c_COMBB(_1668204, tc_fun(_1668204, _1668204), _1668206), c_Groups_Ominus__class_Ominus(_1668204)), _1668208)), _1668210)), _1668212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1668204), hAPP(c_List_Omonoid__add__class_Olistsum(_1668204), hAPP(hAPP(c_List_Omap(_1668206, _1668204), _1668208), _1668212))), hAPP(c_List_Omonoid__add__class_Olistsum(_1668204), hAPP(hAPP(c_List_Omap(_1668206, _1668204), _1668210), _1668212))))], (12427 ^ _779142) ^ [_993609, _993611, _993613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993609), _993611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993613), _993611))), 12430 ^ _779142 : [(12433 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993609), _993613)))], (12431 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993611)))]]], (6299 ^ _779142) ^ [_880088, _880090, _880092, _880094] : [class_Orderings_Opreorder(_880088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880088), _880090), _880092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880088), _880092), _880094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880088), _880090), _880094)))], (47964 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45414 ^ _779142) ^ [_1690496, _1690498, _1690500, _1690502] : [_1690496 = _1690498, -(hAPP(c_List_OremoveAll(_1690500, _1690496), hAPP(hAPP(c_List_Olist_OCons(_1690500), _1690498), _1690502)) = hAPP(c_List_OremoveAll(_1690500, _1690496), _1690502))], (37425 ^ _779142) ^ [_1487204, _1487206, _1487208] : [hBOOL(hAPP(_1487208, _1487206)), -(hBOOL(hAPP(hAPP(c_member(_1487204), _1487206), hAPP(c_Set_OCollect(_1487204), _1487208))))], (27534 ^ _779142) ^ [_1265074, _1265076] : [class_Lattices_Olattice(_1265074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265074), _1265076)), -(c_Big__Operators_Olattice__class_OSup__fin(_1265074, _1265076) = hAPP(c_Finite__Set_Ofold1(_1265074, c_Lattices_Osemilattice__sup__class_Osup(_1265074)), _1265076))], (5852 ^ _779142) ^ [_871907, _871909] : [-(_871909 = c_Orderings_Obot__class_Obot(tc_fun(_871907, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_871907), 5855 ^ [_871907, _871909]), _871909)))], (8234 ^ _779142) ^ [_916099, _916101, _916103, _916105, _916107] : [class_Rings_Oring(_916099), hBOOL(hAPP(c_Finite__Set_Ofinite(_916101), _916103)), hBOOL(hAPP(hAPP(c_member(_916101), _916105), _916103)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_916101, _916099), _916107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916101, tc_HOL_Obool)), _916103), hAPP(hAPP(c_Set_Oinsert(_916101), _916105), c_Orderings_Obot__class_Obot(tc_fun(_916101, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_916099), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_916101, _916099), _916107), _916103)), hAPP(_916107, _916105)))], (52467 ^ _779142) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (26508 ^ _779142) ^ [_1245365, _1245367, _1245369] : [class_Lattices_Olattice(_1245365), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245365), _1245367), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245365), _1245369), _1245367))))], (10389 ^ _779142) ^ [_958974, _958976, _958978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_958974), _958976)), hBOOL(hAPP(hAPP(c_member(_958974), _958978), _958976)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_958974), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958974, tc_HOL_Obool)), _958976), hAPP(hAPP(c_Set_Oinsert(_958974), _958978), c_Orderings_Obot__class_Obot(tc_fun(_958974, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_958974), _958976))], (1486 ^ _779142) ^ [_800659, _800661] : [-(class_Groups_Ouminus(_800659)), _800661 = _800659, class_Groups_Ouminus(_800661)], (8669 ^ _779142) ^ [_924800, _924802, _924804, _924806] : [class_Groups_Oordered__ab__semigroup__add(_924800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924800), _924802), _924804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924800), _924806), _924802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924800), _924806), _924804))))], (48717 ^ _779142) ^ [_1762291, _1762293, _1762295, _1762297] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1762291), _1762293), _1762295), _1762297) = 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(_1762291)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1762291), _1762293)))], (17763 ^ _779142) ^ [_1092184, _1092186] : [class_Rings_Olinordered__semidom(_1092184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092184), c_Groups_Ozero__class_Ozero(_1092184)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092184), _1092186))))], (25348 ^ _779142) ^ [_1224541, _1224543] : [class_Int_Onumber__ring(_1224541), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224541), hAPP(c_Int_Onumber__class_Onumber__of(_1224541), _1224543)), c_Groups_Oone__class_Oone(_1224541)) = hAPP(c_Int_Onumber__class_Onumber__of(_1224541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224543), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (34334 ^ _779142) ^ [_1410175, _1410177, _1410179, _1410181, _1410183, _1410185] : [class_Complete__Lattice_Ocomplete__lattice(_1410175), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410177, tc_fun(_1410179, _1410175)), _1410181), _1410183), _1410185) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410177, _1410175), _1410181), hAPP(hAPP(c_COMBC(_1410177, _1410179, _1410175), _1410183), _1410185)))], (31937 ^ _779142) ^ [_1355875, _1355877] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1355875, tc_HOL_Obool)), _1355877)), -(hBOOL(hAPP(hAPP(c_member(_1355875), _1355877), c_Orderings_Obot__class_Obot(tc_fun(_1355875, tc_HOL_Obool)))))], (41832 ^ _779142) ^ [_1608910, _1608912, _1608914, _1608916] : [_1608910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608912), hAPP(hAPP(c_List_Olist_OCons(_1608912), _1608914), _1608916)), _1608910) = _1608914)], (9469 ^ _779142) ^ [_940556, _940558, _940560] : [class_Groups_Ocomm__monoid__mult(_940556), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_940558, _940556), _940560), c_Orderings_Obot__class_Obot(tc_fun(_940558, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_940556))], (30878 ^ _779142) ^ [_1332448, _1332450] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332448, tc_HOL_Obool)), _1332450), c_Orderings_Otop__class_Otop(tc_fun(_1332448, tc_HOL_Obool))) = _1332450)], (42870 ^ _779142) ^ [_1633475, _1633477, _1633479] : [-(hBOOL(hAPP(hAPP(c_member(_1633475), _1633477), hAPP(c_List_Oset(_1633475), _1633479)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633475)), c_List_Oremove1(_1633475, _1633477, _1633479)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633475)), _1633479))], (41653 ^ _779142) ^ [_1603971, _1603973, _1603975, _1603977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603971), tc_List_Olist(_1603971))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603971), tc_List_Olist(_1603971)), _1603975), _1603977)), c_List_Olistrel(_1603971, _1603973))), -(c_List_Olistrelp(_1603971, hAPP(hAPP(c_COMBC(_1603971, tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_fun(_1603971, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603971, tc_fun(tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_fun(_1603971, tc_HOL_Obool)), _1603971), c_COMBC(_1603971, tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603971, tc_prod(_1603971, _1603971)), tc_fun(_1603971, tc_fun(tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_HOL_Obool)), _1603971), hAPP(c_COMBB(tc_prod(_1603971, _1603971), tc_fun(tc_fun(tc_prod(_1603971, _1603971), tc_HOL_Obool), tc_HOL_Obool), _1603971), c_member(tc_prod(_1603971, _1603971)))), c_Product__Type_OPair(_1603971, _1603971)))), _1603973), _1603975, _1603977))], (33223 ^ _779142) ^ [_1387147, _1387149, _1387151, _1387153, _1387155] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1387147, _1387149), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1387151), _1387153))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387155)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1387147, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387149), _1387155)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1387151), _1387155)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387149), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1387151, _1387155))), _1387153)))))], (47094 ^ _779142) ^ [_1726503, _1726505, _1726507, _1726509] : [47096 ^ _779142 : [(47101 ^ _779142) ^ [] : [hBOOL(hAPP(_1726509, hAPP(hAPP(c_List_Onth(_1726505), _1726507), 47095 ^ [_1726503, _1726505, _1726507, _1726509])))], (47099 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47095 ^ [_1726503, _1726505, _1726507, _1726509]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726505)), _1726507))))], (47097 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47095 ^ [_1726503, _1726505, _1726507, _1726509]), _1726503)))]], 47104 ^ _779142 : [(47107 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1726509, hAPP(hAPP(c_List_Onth(_1726505), _1726507), _1726503))))], (47105 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726503), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726505)), _1726507))))]], -(c_List_OtakeWhile(_1726505, _1726509, _1726507) = hAPP(hAPP(c_List_Otake(_1726505), _1726503), _1726507))], (17535 ^ _779142) ^ [_1088149, _1088151, _1088153] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088149), _1088151), _1088153) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088149), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1088151, _1088153)), _1088153))], (41064 ^ _779142) ^ [_1586011, _1586013, _1586015] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586011, _1586011)), _1586013), c_Transitive__Closure_Otrancl(_1586011, _1586015)))), 41065 ^ _779142 : [(41066 ^ _779142) ^ [_1586090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1586090)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586011, _1586011)), _1586013), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586011, _1586011), tc_HOL_Obool), _1586090), _1586015)))]]], (26382 ^ _779142) ^ [_1243173, _1243175, _1243177, _1243179, _1243181] : [class_Lattices_Osemilattice__sup(_1243173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243173), _1243175), _1243177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243173), _1243179), _1243181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243173), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1243173), _1243175), _1243179)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1243173), _1243177), _1243181))))], (29532 ^ _779142) ^ [_1304622, _1304624, _1304626] : [class_Orderings_Oorder(_1304622), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304622, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1304622), _1304624)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304622, _1304624), _1304626)) = c_Orderings_Obot__class_Obot(tc_fun(_1304622, tc_HOL_Obool)))], (38733 ^ _779142) ^ [_1528886, _1528888] : [c_Wellfounded_Owf(_1528886, _1528888), 38736 ^ _779142 : [(38737 ^ _779142) ^ [_1528955] : [-(hBOOL(hAPP(hAPP(c_member(_1528886), _1528955), c_Wellfounded_Oacc(_1528886, _1528888))))]]], (3448 ^ _779142) ^ [_830602, _830604] : [_830604 = _830602, -(c_SetInterval_Oord__class_OlessThan(_830604) = c_SetInterval_Oord__class_OlessThan(_830602))], (23981 ^ _779142) ^ [_1201523, _1201525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201523)), -(c_SMT_Oz3mod(_1201525, _1201523) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201525, _1201523))], (10431 ^ _779142) ^ [_959822] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959822), hAPP(c_Nat_OSuc, _959822))))], (19297 ^ _779142) ^ [_1118476, _1118478, _1118480] : [class_Fields_Olinordered__field__inverse__zero(_1118476), -(hAPP(c_Groups_Oabs__class_Oabs(_1118476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118476), _1118478), _1118480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118476), hAPP(c_Groups_Oabs__class_Oabs(_1118476), _1118478)), hAPP(c_Groups_Oabs__class_Oabs(_1118476), _1118480)))], (8184 ^ _779142) ^ [_915072, _915074, _915076, _915078, _915080, _915082] : [hBOOL(hAPP(hAPP(c_member(_915072), _915074), _915076)), -(hAPP(c_Set_Oimage(_915072, _915078, c_Fun_Ofun__upd(_915072, _915078, _915080, _915074, _915082)), _915076) = hAPP(hAPP(c_Set_Oinsert(_915078), _915082), hAPP(c_Set_Oimage(_915072, _915078, _915080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915072, tc_HOL_Obool)), _915076), hAPP(hAPP(c_Set_Oinsert(_915072), _915074), c_Orderings_Obot__class_Obot(tc_fun(_915072, tc_HOL_Obool)))))))], (22060 ^ _779142) ^ [_1166976, _1166978, _1166980, _1166982] : [class_Rings_Olinordered__semidom(_1166976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166976), hAPP(hAPP(c_Power_Opower__class_Opower(_1166976), _1166978), _1166980)), hAPP(hAPP(c_Power_Opower__class_Opower(_1166976), _1166982), _1166980))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166976), c_Groups_Ozero__class_Ozero(_1166976)), _1166982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166976), _1166978), _1166982)))], (29165 ^ _779142) ^ [_1296347, _1296349, _1296351, _1296353] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296347, tc_HOL_Obool)), _1296349), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296347, tc_HOL_Obool)), _1296351), _1296353)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296347, tc_HOL_Obool)), _1296351), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296347, tc_HOL_Obool)), _1296349), _1296353)))], (31739 ^ _779142) ^ [_1348935, _1348937, _1348939, _1348941] : [class_Groups_Ocomm__monoid__add(_1348935), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348935), _1348937), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348939), hAPP(c_Nat_OSuc, _1348941))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348935), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348935, tc_Nat_Onat), _1348937), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348939, _1348941)))], (41559 ^ _779142) ^ [_1600909, _1600911, _1600913, _1600915, _1600917] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600909, _1600909)), hAPP(hAPP(c_Product__Type_OPair(_1600909, _1600909), _1600911), _1600913)), _1600915)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600909), tc_List_Olist(_1600909))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600909), tc_List_Olist(_1600909)), hAPP(hAPP(c_List_Olist_OCons(_1600909), _1600911), _1600917)), hAPP(hAPP(c_List_Olist_OCons(_1600909), _1600913), _1600917))), c_List_Olistrel1(_1600909, _1600915))))], (26998 ^ _779142) ^ [_1255599, _1255601, _1255603] : [class_Orderings_Olinorder(_1255599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255599), _1255601), _1255603)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255599, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1255599), _1255601)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255599, _1255601), _1255603)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1255599), _1255603))], (24742 ^ _779142) ^ [_1214169] : [class_Groups_Osgn__if(_1214169), -(c_Groups_Osgn__class_Osgn(_1214169, c_Groups_Ozero__class_Ozero(_1214169)) = c_Groups_Ozero__class_Ozero(_1214169))], (40771 ^ _779142) ^ [_1578473, _1578475] : [c_Wellfounded_Owf(_1578473, hAPP(c_Relation_Oconverse(_1578473, _1578473), _1578475)), -(c_Wellfounded_Owf(_1578473, hAPP(c_Relation_Oconverse(_1578473, _1578473), c_Transitive__Closure_Otrancl(_1578473, _1578475))))], (52501 ^ _779142) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (27060 ^ _779142) ^ [_1256588, _1256590, _1256592] : [-(hAPP(c_Set_OPow(_1256588), hAPP(hAPP(c_Set_Oinsert(_1256588), _1256590), _1256592)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1256588, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1256588), _1256592)), hAPP(c_Set_Oimage(tc_fun(_1256588, tc_HOL_Obool), tc_fun(_1256588, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1256588), _1256590)), hAPP(c_Set_OPow(_1256588), _1256592))))], (44620 ^ _779142) ^ [_1673077, _1673079] : [_1673077 = _1673079, -(hAPP(c_Code__Numeral_Oof__nat, _1673077) = hAPP(c_Code__Numeral_Oof__nat, _1673079))], (630 ^ _779142) ^ [_788635, _788637, _788639, _788641] : [-(c_List_Olinorder__class_Osorted(_788639, _788635)), c_List_Olinorder__class_Osorted(_788641, _788637), _788641 = _788639, _788637 = _788635], (35742 ^ _779142) ^ [_1449116, _1449118, _1449120, _1449122, _1449124] : [c_Equiv__Relations_Oequiv(_1449116, _1449118, _1449120), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449116, tc_HOL_Obool)), _1449122), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449116), _1449118), _1449120))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449116, tc_HOL_Obool)), _1449124), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449116), _1449118), _1449120))), -(_1449122 = _1449124), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449116, tc_HOL_Obool)), _1449122), _1449124) = c_Orderings_Obot__class_Obot(tc_fun(_1449116, tc_HOL_Obool)))], (35129 ^ _779142) ^ [_1432572, _1432574, _1432576, _1432578, _1432580, _1432582] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432572, tc_fun(_1432574, tc_HOL_Obool)), _1432576), hAPP(hAPP(c_COMBC(_1432572, tc_fun(_1432578, tc_fun(_1432574, tc_HOL_Obool)), tc_fun(_1432574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432578, tc_HOL_Obool), tc_fun(tc_fun(_1432578, tc_fun(_1432574, tc_HOL_Obool)), tc_fun(_1432574, tc_HOL_Obool)), _1432572), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432578, tc_fun(_1432574, tc_HOL_Obool))), _1432580)), _1432582)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432578, tc_fun(_1432574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432572, tc_fun(_1432578, tc_HOL_Obool)), _1432576), _1432580)), _1432582))], (7196 ^ _779142) ^ [_898433, _898435, _898437, _898439, _898441] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_898433, _898433, _898435, _898437, _898439), _898441)), -(hBOOL(hAPP(hAPP(c_member(_898433), _898437), _898439))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_898433, _898435, hAPP(hAPP(c_Set_Oinsert(_898433), _898437), _898439)), _898441)))], (14305 ^ _779142) ^ [_1028309, _1028311, _1028313, _1028315, _1028317] : [class_Fields_Olinordered__field(_1028309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028309), c_Groups_Ozero__class_Ozero(_1028309)), _1028311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028309), _1028311), _1028313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028309), c_Groups_Ozero__class_Ozero(_1028309)), _1028315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028309), _1028315), _1028317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028309), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028309), _1028311), _1028317)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028309), _1028313), _1028315))))], (25834 ^ _779142) ^ [_1233141, _1233143] : [class_Groups_Omonoid__mult(_1233141), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233141), _1233143), 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(_1233141), _1233143), _1233143))], (22238 ^ _779142) ^ [_1170300, _1170302, _1170304, _1170306] : [class_Rings_Olinordered__semidom(_1170300), hAPP(hAPP(c_Power_Opower__class_Opower(_1170300), _1170302), _1170304) = hAPP(hAPP(c_Power_Opower__class_Opower(_1170300), _1170306), _1170304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170300), c_Groups_Ozero__class_Ozero(_1170300)), _1170302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170300), c_Groups_Ozero__class_Ozero(_1170300)), _1170306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170304)), -(_1170302 = _1170306)], (38066 ^ _779142) ^ [_1507361, _1507363, _1507365] : [class_Groups_Olinordered__ab__semigroup__add(_1507361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507361), _1507363)), -(_1507363 = c_Orderings_Obot__class_Obot(tc_fun(_1507361, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1507361), _1507365), c_Big__Operators_Olinorder__class_OMin(_1507361, _1507363)) = c_Big__Operators_Olinorder__class_OMin(_1507361, hAPP(c_Set_OCollect(_1507361), hAPP(hAPP(c_COMBB(tc_fun(_1507361, tc_HOL_Obool), tc_HOL_Obool, _1507361), c_HOL_OEx(_1507361)), hAPP(hAPP(c_COMBC(_1507361, tc_fun(_1507361, tc_HOL_Obool), tc_fun(_1507361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507361, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507361, tc_HOL_Obool), tc_fun(_1507361, tc_HOL_Obool)), _1507361), c_COMBS(_1507361, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507361, tc_HOL_Obool), tc_fun(_1507361, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507361), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507361), c_fconj)), hAPP(hAPP(c_COMBC(_1507361, tc_fun(_1507361, _1507361), tc_fun(_1507361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507361, tc_HOL_Obool), tc_fun(tc_fun(_1507361, _1507361), tc_fun(_1507361, tc_HOL_Obool)), _1507361), c_COMBB(_1507361, tc_HOL_Obool, _1507361)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1507361), _1507365))))), hAPP(hAPP(c_COMBC(_1507361, tc_fun(_1507361, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507361)), _1507363))))))], (38764 ^ _779142) ^ [_1529550, _1529552, _1529554] : [c_Wellfounded_Owf(_1529550, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529550, _1529550), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529550, _1529550), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529550, _1529550, _1529550), _1529552), _1529552)), hAPP(hAPP(c_Relation_Orel__comp(_1529550, _1529550, _1529550), _1529554), _1529552))), _1529554)), -(c_Wellfounded_Owf(_1529550, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529550, _1529550), tc_HOL_Obool)), _1529552), _1529554)))], (34548 ^ _779142) ^ [_1416899, _1416901, _1416903, _1416905, _1416907, _1416909] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416899, tc_fun(_1416901, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1416903, _1416899, _1416905), _1416907)), _1416909) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416903, tc_fun(_1416901, tc_HOL_Obool)), _1416907), hAPP(hAPP(c_COMBB(_1416899, tc_fun(_1416901, tc_HOL_Obool), _1416903), _1416909), _1416905)))], (45336 ^ _779142) ^ [_1689056, _1689058, _1689060, _1689062, _1689064] : [c_Fun_Oinj__on(_1689056, _1689058, _1689060, hAPP(hAPP(c_Set_Oinsert(_1689056), _1689062), hAPP(c_List_Oset(_1689056), _1689064))), -(hAPP(hAPP(c_List_Omap(_1689056, _1689058), _1689060), hAPP(c_List_OremoveAll(_1689056, _1689062), _1689064)) = hAPP(c_List_OremoveAll(_1689058, hAPP(_1689060, _1689062)), hAPP(hAPP(c_List_Omap(_1689056, _1689058), _1689060), _1689064)))], (37801 ^ _779142) ^ [_1497409, _1497411, _1497413, _1497415, _1497417, _1497419] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497409, _1497411), hAPP(hAPP(c_Set_Oinsert(_1497409), _1497413), _1497415)), hAPP(c_COMBK(tc_fun(_1497411, tc_HOL_Obool), _1497409), hAPP(hAPP(c_Set_Oinsert(_1497411), _1497417), _1497419))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1497409, _1497411)), hAPP(hAPP(c_Product__Type_OPair(_1497409, _1497411), _1497413), _1497417)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1497409, _1497411), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497409, _1497411), _1497415), hAPP(c_COMBK(tc_fun(_1497411, tc_HOL_Obool), _1497409), hAPP(hAPP(c_Set_Oinsert(_1497411), _1497417), _1497419)))), hAPP(hAPP(c_Product__Type_OSigma(_1497409, _1497411), hAPP(hAPP(c_Set_Oinsert(_1497409), _1497413), _1497415)), hAPP(c_COMBK(tc_fun(_1497411, tc_HOL_Obool), _1497409), _1497419)))))], (9223 ^ _779142) ^ [_936385, _936387, _936389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936385), _936387)), _936389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936387), _936389)))], (38372 ^ _779142) ^ [_1518792, _1518794, _1518796, _1518798, _1518800, _1518802] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518792, _1518794, _1518796), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518792, _1518794), tc_HOL_Obool)), _1518798), _1518800)), _1518802) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518792, _1518796), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518792, _1518794, _1518796), _1518798), _1518802)), hAPP(hAPP(c_Relation_Orel__comp(_1518792, _1518794, _1518796), _1518800), _1518802)))], (52675 ^ _779142) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (27578 ^ _779142) ^ [_1265784, _1265786, _1265788] : [class_Lattices_Olattice(_1265784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265784), _1265786)), -(_1265786 = c_Orderings_Obot__class_Obot(tc_fun(_1265784, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265784), _1265788)), -(_1265788 = c_Orderings_Obot__class_Obot(tc_fun(_1265784, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1265784, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265784, tc_HOL_Obool)), _1265786), _1265788)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265784), c_Big__Operators_Olattice__class_OSup__fin(_1265784, _1265786)), c_Big__Operators_Olattice__class_OSup__fin(_1265784, _1265788)))], (17163 ^ _779142) ^ [_1081081, _1081083] : [class_Orderings_Olinorder(_1081081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081081), _1081083)), -(_1081083 = c_Orderings_Obot__class_Obot(tc_fun(_1081081, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1081081), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081081), 17176 ^ [_1081081, _1081083]), 17177 ^ [_1081081, _1081083])), hAPP(hAPP(c_Set_Oinsert(_1081081), 17176 ^ [_1081081, _1081083]), hAPP(hAPP(c_Set_Oinsert(_1081081), 17177 ^ [_1081081, _1081083]), c_Orderings_Obot__class_Obot(tc_fun(_1081081, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1081081), c_Big__Operators_Olinorder__class_OMin(_1081081, _1081083)), _1081083)))], (34536 ^ _779142) ^ [_1416209, _1416211, _1416213, _1416215, _1416217] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416209, tc_fun(_1416211, tc_HOL_Obool)), _1416213), hAPP(hAPP(c_COMBS(_1416209, tc_fun(_1416211, tc_HOL_Obool), tc_fun(_1416211, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1416211, tc_HOL_Obool), tc_fun(tc_fun(_1416211, tc_HOL_Obool), tc_fun(_1416211, tc_HOL_Obool)), _1416209), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416211, tc_HOL_Obool))), _1416215)), _1416217)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416211, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416209, tc_fun(_1416211, tc_HOL_Obool)), _1416213), _1416215)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416209, tc_fun(_1416211, tc_HOL_Obool)), _1416213), _1416217)))], (48873 ^ _779142) ^ [_1766096, _1766098] : [-(hBOOL(hAPP(_1766098, 48880 ^ [_1766096, _1766098]))), 48874 ^ _779142 : [(48875 ^ _779142) ^ [_1766157] : [hBOOL(hAPP(hAPP(c_member(_1766096), _1766157), c_Orderings_Otop__class_Otop(tc_fun(_1766096, tc_HOL_Obool)))), hBOOL(hAPP(_1766098, _1766157))]]], (9408 ^ _779142) ^ [_939487, _939489] : [class_Groups_Omonoid__mult(_939487), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939487), _939489), c_Groups_Oone__class_Oone(_939487)) = _939489)], (24952 ^ _779142) ^ [_1217793, _1217795] : [class_Int_Onumber__ring(_1217793), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217793), hAPP(c_Int_Onumber__class_Onumber__of(_1217793), c_Int_OBit1(c_Int_OPls))), _1217795) = _1217795)], (43103 ^ _779142) ^ [_1639070, _1639072, _1639074, _1639076] : [hAPP(hAPP(c_List_Oappend(_1639070), _1639072), _1639074) = hAPP(hAPP(c_List_Oappend(_1639070), _1639072), _1639076), -(_1639074 = _1639076)], (36782 ^ _779142) ^ [_1472211, _1472213, _1472215, _1472217, _1472219, _1472221] : [c_Fun_Oinj__on(_1472211, _1472213, _1472215, _1472217), hBOOL(hAPP(hAPP(c_member(_1472213), _1472219), hAPP(c_Set_Oimage(_1472211, _1472213, _1472215), _1472217))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472211, tc_HOL_Obool)), _1472217), _1472221)), -(hBOOL(hAPP(hAPP(c_member(_1472211), hAPP(c_Fun_Othe__inv__into(_1472211, _1472213, _1472217, _1472215), _1472219)), _1472221)))], (37464 ^ _779142) ^ [_1488092, _1488094] : [hAPP(c_Set_OCollect(_1488092), _1488094) = c_Orderings_Obot__class_Obot(tc_fun(_1488092, tc_HOL_Obool)), 37467 ^ _779142 : [(37468 ^ _779142) ^ [_1488177] : [hBOOL(hAPP(_1488094, _1488177))]]], (36588 ^ _779142) ^ [_1467572, _1467574, _1467576, _1467578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467572), _1467574)), hAPP(c_Finite__Set_Ocard(_1467576), hAPP(c_Set_Oimage(_1467572, _1467576, _1467578), _1467574)) = hAPP(c_Finite__Set_Ocard(_1467572), _1467574), -(c_Fun_Oinj__on(_1467572, _1467576, _1467578, _1467574))], (48777 ^ _779142) ^ [_1763953, _1763955] : [48780 ^ _779142 : [(48786 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763953, _1763953)), hAPP(hAPP(c_Product__Type_OPair(_1763953, _1763953), 48778 ^ [_1763953, _1763955]), 48782 ^ [_1763953, _1763955])), _1763955))], (48784 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763953, _1763953)), hAPP(hAPP(c_Product__Type_OPair(_1763953, _1763953), 48779 ^ [_1763953, _1763955]), 48782 ^ [_1763953, _1763955])), _1763955)))], (48781 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763953, _1763953)), hAPP(hAPP(c_Product__Type_OPair(_1763953, _1763953), 48778 ^ [_1763953, _1763955]), 48779 ^ [_1763953, _1763955])), _1763955)))]], -(c_Relation_Otrans(_1763953, _1763955))], (14723 ^ _779142) ^ [_1036128, _1036130, _1036132] : [class_Fields_Olinordered__field(_1036128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036128), _1036130), _1036132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036128), _1036130), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1036128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036128), _1036130), _1036132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036128), c_Groups_Oone__class_Oone(_1036128)), c_Groups_Oone__class_Oone(_1036128))))))], (4 ^ _779142) ^ [_779192, _779194] : [_779194 = _779192, -(_779192 = _779194)], (8573 ^ _779142) ^ [_923108, _923110, _923112, _923114] : [class_Groups_Ocancel__semigroup__add(_923108), 8576 ^ _779142 : [(8583 ^ _779142) ^ [] : [_923112 = _923114, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923108), _923110), _923112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923108), _923110), _923114))], (8577 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923108), _923110), _923112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923108), _923110), _923114), -(_923112 = _923114)]]], (9257 ^ _779142) ^ [_937050, _937052, _937054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937050), _937052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937050), _937054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937052), _937054)))], (14733 ^ _779142) ^ [_1036343, _1036345, _1036347, _1036349] : [class_Fields_Olinordered__field__inverse__zero(_1036343), 14736 ^ _779142 : [(14737 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1036343), _1036347), _1036349))), 14740 ^ _779142 : [(14747 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), c_Groups_Ozero__class_Ozero(_1036343)), _1036349))), 14750 ^ _779142 : [(14757 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), _1036349), c_Groups_Ozero__class_Ozero(_1036343)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036345), c_Groups_Ozero__class_Ozero(_1036343))))], (14751 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), _1036349), c_Groups_Ozero__class_Ozero(_1036343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036343), _1036345), _1036349))))]]], (14741 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), c_Groups_Ozero__class_Ozero(_1036343)), _1036349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036343), _1036345), _1036349)), _1036347)))]]], (14763 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1036343), _1036347), _1036349)))), 14766 ^ _779142 : [(14769 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036343), _1036345), _1036349)), _1036347))], (14767 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), c_Groups_Ozero__class_Ozero(_1036343)), _1036349)))]], 14770 ^ _779142 : [(14773 ^ _779142) ^ [] : [14774 ^ _779142 : [(14777 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036343), _1036345), _1036349)))], (14775 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), _1036349), c_Groups_Ozero__class_Ozero(_1036343))))]], 14778 ^ _779142 : [(14781 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036343), _1036345), c_Groups_Ozero__class_Ozero(_1036343)))], (14779 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), _1036349), c_Groups_Ozero__class_Ozero(_1036343)))]]], (14771 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036343), c_Groups_Ozero__class_Ozero(_1036343)), _1036349))]]]]], (13014 ^ _779142) ^ [_1004516, _1004518, _1004520] : [13015 ^ _779142 : [(13018 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004516), _1004520))], (13016 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004518)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004516), _1004518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004520), _1004518))))], (52679 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (8358 ^ _779142) ^ [_918406, _918408, _918410, _918412, _918414] : [class_Groups_Oab__group__add(_918406), hBOOL(hAPP(c_Finite__Set_Ofinite(_918408), _918410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918408, tc_HOL_Obool)), _918412), _918410)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918408, _918406), _918414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918408, tc_HOL_Obool)), _918410), _918412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918406), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918408, _918406), _918414), _918410)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918408, _918406), _918414), _918412)))], (17695 ^ _779142) ^ [_1090876, _1090878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090876), _1090878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090876)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090878))))], (31683 ^ _779142) ^ [_1347880, _1347882] : [-(_1347880 = _1347882), -(c_Random_Oinc__shift(_1347880, _1347882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1347882), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (52259 ^ _779142) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (1496 ^ _779142) ^ [_800784, _800786] : [-(class_Lazy__Sequence_Osmall__lazy(_800784)), _800786 = _800784, class_Lazy__Sequence_Osmall__lazy(_800786)], (34065 ^ _779142) ^ [_1403631] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1403631) = _1403631)], (10115 ^ _779142) ^ [_952954, _952956] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952954), _952956) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952956), _952954))], (4424 ^ _779142) ^ [_846284, _846286] : [_846286 = _846284, -(c_List_Olist_OCons(_846286) = c_List_Olist_OCons(_846284))], (11386 ^ _779142) ^ [_974842, _974844, _974846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974844), _974846)), -(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, _974842)), _974844)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974842)), _974846))))], (29341 ^ _779142) ^ [_1299988, _1299990, _1299992, _1299994] : [hBOOL(hAPP(hAPP(c_member(_1299988), _1299990), _1299992)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299988, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1299988), _1299990), _1299994)), _1299992) = hAPP(hAPP(c_Set_Oinsert(_1299988), _1299990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299988, tc_HOL_Obool)), _1299994), _1299992)))], (21338 ^ _779142) ^ [_1154328, _1154330, _1154332] : [class_Rings_Oring__1(_1154328), hBOOL(hAPP(hAPP(c_member(_1154328), _1154330), c_Int_Oring__1__class_OInts(_1154328))), -(hBOOL(hAPP(hAPP(c_member(_1154328), hAPP(hAPP(c_Power_Opower__class_Opower(_1154328), _1154330), _1154332)), c_Int_Oring__1__class_OInts(_1154328))))], (32915 ^ _779142) ^ [_1380547, _1380549] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1380547, _1380549) = 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), _1380547), _1380549)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1380547, _1380549)))], (12078 ^ _779142) ^ [_987625, _987627, _987629] : [class_Rings_Olinordered__semiring__strict(_987625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987625), c_Groups_Ozero__class_Ozero(_987625)), _987627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987625), c_Groups_Ozero__class_Ozero(_987625)), _987629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987625), c_Groups_Ozero__class_Ozero(_987625)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987625), _987627), _987629))))], (1176 ^ _779142) ^ [_796784, _796786] : [-(class_Rings_Oring__no__zero__divisors(_796784)), _796786 = _796784, class_Rings_Oring__no__zero__divisors(_796786)], (40448 ^ _779142) ^ [_1570839, _1570841, _1570843] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570839, _1570841, _1570841), _1570843), c_Relation_OId(_1570841)) = _1570843)], (36206 ^ _779142) ^ [_1460176, _1460178] : [class_Groups_Oordered__ab__group__add(_1460176), -(c_Fun_Oinj__on(_1460176, _1460176, c_Groups_Ouminus__class_Ouminus(_1460176), _1460178))], (42958 ^ _779142) ^ [_1635705, _1635707, _1635709, _1635711] : [-(c_List_Osublist(_1635705, hAPP(hAPP(c_List_Olist_OCons(_1635705), _1635707), _1635709), _1635711) = hAPP(hAPP(c_List_Oappend(_1635705), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1635705)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635711)), hAPP(hAPP(c_List_Olist_OCons(_1635705), _1635707), c_List_Olist_ONil(_1635705))), c_List_Olist_ONil(_1635705))), c_List_Osublist(_1635705, _1635709, 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)), _1635711)))))], (35543 ^ _779142) ^ [_1444029, _1444031, _1444033, _1444035] : [-(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), _1444029), _1444031)), 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), _1444033), _1444035)), 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), _1444029), _1444033)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444031), _1444035))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (52149 ^ _779142) ^ [_1831130, _1831132] : [class_Lattices_Odistrib__lattice(_1831130), -(class_Lattices_Odistrib__lattice(tc_fun(_1831132, _1831130)))], (7944 ^ _779142) ^ [_909926, _909928, _909930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909926, tc_HOL_Obool)), _909928), _909930)), 7947 ^ _779142 : [(7950 ^ _779142) ^ [] : [_909928 = _909930], (7948 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909926, tc_HOL_Obool)), _909928), _909930)))]]], (20005 ^ _779142) ^ [_1130327, _1130329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130329)), 20012 ^ _779142 : [(20019 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130327), _1130329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1130327)), hAPP(c_Int_Onat, _1130329))))], (20013 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1130327)), hAPP(c_Int_Onat, _1130329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130327), _1130329)))]]], (40346 ^ _779142) ^ [_1568307, _1568309, _1568311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568307, _1568307), tc_HOL_Obool)), c_Relation_OId(_1568307)), _1568309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568307, _1568307), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1568307, _1568307, _1568307), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1568307, _1568307), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568307, _1568311)), _1568309)), _1568311)), _1568309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568307, _1568307), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568307, _1568311)), _1568309)))], (9929 ^ _779142) ^ [_948780, _948782, _948784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948780), _948782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948780), _948784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948784), _948782)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948784), _948780))))], (38298 ^ _779142) ^ [_1516257, _1516259] : [-(c_Product__Type_Omap__pair(_1516257, _1516257, _1516259, _1516259, c_COMBI(_1516257), c_COMBI(_1516259)) = c_Fun_Oid(tc_prod(_1516257, _1516259)))], (17475 ^ _779142) ^ [_1086843, _1086845, _1086847, _1086849] : [class_Divides_Osemiring__div(_1086843), -(c_Divides_Odiv__class_Omod(_1086843, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086843), _1086845), _1086847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086843), _1086845), _1086849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086843), _1086845), c_Divides_Odiv__class_Omod(_1086843, _1086847, _1086849)))], (21174 ^ _779142) ^ [_1151253, _1151255] : [-(c_Nitpick_Oint__lcm(_1151253, _1151255) = 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), _1151253)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151255)))))], (43427 ^ _779142) ^ [_1646667, _1646669, _1646671, _1646673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646667), tc_List_Olist(_1646667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646667), tc_List_Olist(_1646667)), _1646669), _1646671)), c_List_Olistrel1(_1646667, _1646673))), 43432 ^ _779142 : [(43439 ^ _779142) ^ [] : [-(_1646671 = hAPP(hAPP(c_List_Oappend(_1646667), 43434 ^ [_1646667, _1646669, _1646671, _1646673]), hAPP(hAPP(c_List_Olist_OCons(_1646667), 43431 ^ [_1646667, _1646669, _1646671, _1646673]), 43435 ^ [_1646667, _1646669, _1646671, _1646673])))], (43437 ^ _779142) ^ [] : [-(_1646669 = hAPP(hAPP(c_List_Oappend(_1646667), 43434 ^ [_1646667, _1646669, _1646671, _1646673]), hAPP(hAPP(c_List_Olist_OCons(_1646667), 43430 ^ [_1646667, _1646669, _1646671, _1646673]), 43435 ^ [_1646667, _1646669, _1646671, _1646673])))], (43433 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646667, _1646667)), hAPP(hAPP(c_Product__Type_OPair(_1646667, _1646667), 43430 ^ [_1646667, _1646669, _1646671, _1646673]), 43431 ^ [_1646667, _1646669, _1646671, _1646673])), _1646673)))]]], (39244 ^ _779142) ^ [_1540780, _1540782, _1540784] : [-(c_Relation_Orefl__on(_1540780, _1540782, _1540784)), 39248 ^ _779142 : [(39251 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1540780, _1540780, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540780, tc_fun(_1540780, tc_HOL_Obool), tc_fun(_1540780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540780, tc_HOL_Obool), tc_fun(_1540780, tc_HOL_Obool)), _1540780), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540780)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540780), c_fconj), hAPP(hAPP(c_COMBC(_1540780, tc_fun(_1540780, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540780)), _1540782)))), hAPP(hAPP(c_COMBC(_1540780, tc_fun(_1540780, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540780)), _1540782))), 39247 ^ [_1540780, _1540782, _1540784]))], (39249 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540780, _1540780)), 39247 ^ [_1540780, _1540782, _1540784]), _1540784)))]], 39253 ^ _779142 : [(39256 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540780, _1540780)), hAPP(hAPP(c_Product__Type_OPair(_1540780, _1540780), 39252 ^ [_1540780, _1540782, _1540784]), 39252 ^ [_1540780, _1540782, _1540784])), _1540784))], (39254 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540780), 39252 ^ [_1540780, _1540782, _1540784]), _1540782)))]]], (38358 ^ _779142) ^ [_1518410, _1518412, _1518414, _1518416, _1518418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518410, _1518412)), hAPP(hAPP(c_Product__Type_OPair(_1518410, _1518412), _1518414), _1518416)), _1518418)), -(hBOOL(hAPP(hAPP(c_member(_1518412), _1518416), hAPP(c_Relation_ORange(_1518410, _1518412), _1518418))))], (40893 ^ _779142) ^ [_1581757, _1581759, _1581761, _1581763, _1581765, _1581767] : [c_Relation_Osingle__valued(_1581757, _1581759, hAPP(c_Relation_Oconverse(_1581759, _1581757), _1581761)), -(_1581763 = c_Orderings_Obot__class_Obot(tc_fun(_1581765, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1581759, _1581757, _1581761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581765, tc_fun(_1581759, tc_HOL_Obool)), _1581763), _1581767)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581765, tc_fun(_1581757, tc_HOL_Obool)), _1581763), hAPP(hAPP(c_COMBB(tc_fun(_1581759, tc_HOL_Obool), tc_fun(_1581757, tc_HOL_Obool), _1581765), c_Relation_OImage(_1581759, _1581757, _1581761)), _1581767)))], (33501 ^ _779142) ^ [_1392007, _1392009, _1392011, _1392013] : [_1392007 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1392009), _1392011)), _1392013), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1392007, _1392009), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1392011), _1392013)))), 33508 ^ _779142 : [(33511 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392013), _1392009))], (33509 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392009)))]], 33516 ^ _779142 : [(33519 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392009), _1392013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1392013), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33517 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392009))]]], (13493 ^ _779142) ^ [_1013784, _1013786] : [class_Rings_Odivision__ring__inverse__zero(_1013784), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1013784), _1013786), c_Groups_Ozero__class_Ozero(_1013784)) = c_Groups_Ozero__class_Ozero(_1013784))], (8849 ^ _779142) ^ [_928256, _928258, _928260, _928262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_928256), _928258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_928260), hAPP(c_Set_Oimage(_928256, _928260, _928262), _928258))), hAPP(c_Finite__Set_Ocard(_928256), _928258))))], (25852 ^ _779142) ^ [_1233430, _1233432] : [class_Rings_Oring__1(_1233430), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233430), hAPP(c_Groups_Ouminus__class_Ouminus(_1233430), _1233432)), 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(_1233430), _1233432), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35433 ^ _779142) ^ [_1441188, _1441190, _1441192, _1441194, _1441196] : [class_Groups_Ocomm__monoid__add(_1441188), class_Groups_Ocomm__monoid__mult(_1441188), _1441190 = _1441192, c_Nat__Transfer_Onat__set(_1441192), 35451 ^ _779142 : [(35454 ^ _779142) ^ [] : [hAPP(_1441194, 35450 ^ [_1441188, _1441190, _1441192, _1441194, _1441196]) = hAPP(_1441196, 35450 ^ [_1441188, _1441190, _1441192, _1441194, _1441196])], (35452 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35450 ^ [_1441188, _1441190, _1441192, _1441194, _1441196])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441188), _1441194), _1441190) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441188), _1441196), _1441192))], (15455 ^ _779142) ^ [_1049827, _1049829, _1049831, _1049833] : [class_Orderings_Olinorder(_1049827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049827), _1049829), _1049831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049827), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049827), _1049833), _1049829)), _1049831)))], (6540 ^ _779142) ^ [_884092, _884094] : [_884094 = c_Orderings_Obot__class_Obot(tc_fun(_884092, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884092, tc_HOL_Obool)), _884094), c_Orderings_Obot__class_Obot(tc_fun(_884092, tc_HOL_Obool)))))], (46333 ^ _779142) ^ [_1710476, _1710478, _1710480] : [class_Orderings_Olinorder(_1710476), 46336 ^ _779142 : [(46355 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710476, hAPP(hAPP(c_List_Oappend(_1710476), _1710478), _1710480))), c_List_Olinorder__class_Osorted(_1710476, _1710478), c_List_Olinorder__class_Osorted(_1710476, _1710480), 46365 ^ _779142 : [(46371 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710476), 46364 ^ [_1710476, _1710478, _1710480]), 46367 ^ [_1710476, _1710478, _1710480]))], (46369 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710476), 46367 ^ [_1710476, _1710478, _1710480]), hAPP(c_List_Oset(_1710476), _1710480))))], (46366 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710476), 46364 ^ [_1710476, _1710478, _1710480]), hAPP(c_List_Oset(_1710476), _1710478))))]]], (46337 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1710476, hAPP(hAPP(c_List_Oappend(_1710476), _1710478), _1710480)), 46340 ^ _779142 : [(46345 ^ _779142) ^ [_1710712] : [hBOOL(hAPP(hAPP(c_member(_1710476), _1710712), hAPP(c_List_Oset(_1710476), _1710478))), 46348 ^ _779142 : [(46349 ^ _779142) ^ [_1710822] : [hBOOL(hAPP(hAPP(c_member(_1710476), _1710822), hAPP(c_List_Oset(_1710476), _1710480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710476), _1710712), _1710822)))]]], (46343 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710476, _1710480))], (46341 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710476, _1710478))]]]]], (24399 ^ _779142) ^ [_1208462, _1208464, _1208466, _1208468] : [class_Orderings_Olinorder(_1208462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208462), _1208464), _1208466)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1208462, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208462, _1208464), _1208468)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208462, _1208464), _1208466)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208462, _1208466), _1208468))], (9657 ^ _779142) ^ [_943495, _943497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943495), _943497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943495), _943497))), -(_943495 = _943497)], (21990 ^ _779142) ^ [_1165643, _1165645] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1165643), c_Groups_Ozero__class_Ozero(_1165643)), hAPP(c_Nat_OSuc, _1165645)) = c_Groups_Ozero__class_Ozero(_1165643)), class_Power_Opower(_1165643), class_Rings_Osemiring__0(_1165643)], (42098 ^ _779142) ^ [_1616684, _1616686, _1616688, _1616690] : [-(hAPP(c_List_Oset(tc_prod(_1616684, _1616686)), hAPP(hAPP(c_List_Ozip(_1616684, _1616686), _1616688), _1616690)) = hAPP(c_Set_OCollect(tc_prod(_1616684, _1616686)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1616684, _1616686)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1616684, _1616686), 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(_1616684, _1616686)), 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(_1616684, _1616686)), 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(_1616684, _1616686), tc_fun(tc_Nat_Onat, tc_prod(_1616684, _1616686)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616684, _1616686), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1616684, _1616686)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616684, _1616686)), c_COMBB(tc_prod(_1616684, _1616686), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1616686, tc_prod(_1616684, _1616686)), hAPP(hAPP(c_COMBB(_1616684, tc_fun(_1616686, tc_prod(_1616684, _1616686)), tc_Nat_Onat), c_Product__Type_OPair(_1616684, _1616686)), hAPP(c_List_Onth(_1616684), _1616688))), hAPP(c_List_Onth(_1616686), _1616690)))))), 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(_1616684)), _1616688)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616686)), _1616690)))))))], (11041 ^ _779142) ^ [_969533, _969535, _969537] : [class_Rings_Ono__zero__divisors(_969533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969533), _969535), _969537) = c_Groups_Ozero__class_Ozero(_969533), -(_969535 = c_Groups_Ozero__class_Ozero(_969533)), -(_969537 = c_Groups_Ozero__class_Ozero(_969533))], (40404 ^ _779142) ^ [_1569764, _1569766, _1569768, _1569770, _1569772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569764, _1569764)), hAPP(hAPP(c_Product__Type_OPair(_1569764, _1569764), _1569766), _1569768)), c_Transitive__Closure_Ortrancl(_1569764, _1569770))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569764, _1569764)), hAPP(hAPP(c_Product__Type_OPair(_1569764, _1569764), _1569768), _1569772)), c_Transitive__Closure_Ortrancl(_1569764, _1569770))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569764, _1569764)), hAPP(hAPP(c_Product__Type_OPair(_1569764, _1569764), _1569766), _1569772)), c_Transitive__Closure_Ortrancl(_1569764, _1569770))))], (32509 ^ _779142) ^ [_1372055, _1372057] : [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(_1372055))), 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)), _1372057)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372055)), hAPP(c_Nat_OSuc, _1372057))))], (12527 ^ _779142) ^ [_995288, _995290, _995292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995288), _995290)), 12530 ^ _779142 : [(12531 ^ _779142) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_995288, tc_Nat_Onat), _995292), _995290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 12534 ^ _779142 : [(12535 ^ _779142) ^ [_995450] : [hBOOL(hAPP(hAPP(c_member(_995288), _995450), _995290)), -(hAPP(_995292, _995450) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (12541 ^ _779142) ^ [] : [12543 ^ _779142 : [(12546 ^ _779142) ^ [] : [hAPP(_995292, 12542 ^ [_995288, _995290, _995292]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12544 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_995288), 12542 ^ [_995288, _995290, _995292]), _995290)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_995288, tc_Nat_Onat), _995292), _995290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44317 ^ _779142) ^ [_1665351, _1665353] : [-(hAPP(hAPP(c_List_Ozip(_1665351, _1665351), _1665353), _1665353) = hAPP(hAPP(c_List_Omap(_1665351, tc_prod(_1665351, _1665351)), hAPP(hAPP(c_COMBS(_1665351, _1665351, tc_prod(_1665351, _1665351)), c_Product__Type_OPair(_1665351, _1665351)), c_COMBI(_1665351))), _1665353))], (52257 ^ _779142) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (29632 ^ _779142) ^ [_1306850, _1306852, _1306854] : [class_Lattices_Osemilattice__inf(_1306850), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306850), _1306852)), hBOOL(hAPP(hAPP(c_member(_1306850), _1306854), _1306852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306850), hAPP(c_Finite__Set_Ofold1(_1306850, c_Lattices_Osemilattice__inf__class_Oinf(_1306850)), _1306852)), _1306854)))], (24047 ^ _779142) ^ [_1202541, _1202543, _1202545] : [-(hBOOL(hAPP(hAPP(c_member(_1202541), _1202543), _1202545))), -(hBOOL(hAPP(hAPP(c_member(_1202541), _1202543), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1202541, tc_HOL_Obool)), _1202545))))], (46576 ^ _779142) ^ [_1715487, _1715489] : [hAPP(c_List_Orev(_1715487), _1715489) = c_List_Olist_ONil(_1715487), -(_1715489 = c_List_Olist_ONil(_1715487))], (20776 ^ _779142) ^ [_1144278, _1144280, _1144282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144278)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144278), _1144280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144278), _1144282)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144280), _1144282))], (9539 ^ _779142) ^ [_941504, _941506, _941508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941504), _941506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941504), _941508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941506), _941508)))], (17587 ^ _779142) ^ [_1089090] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1089090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1089090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52277 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (19237 ^ _779142) ^ [_1117377, _1117379] : [class_Groups_Oordered__ab__group__add__abs(_1117377), 19240 ^ _779142 : [(19247 ^ _779142) ^ [] : [_1117379 = c_Groups_Ozero__class_Ozero(_1117377), -(hAPP(c_Groups_Oabs__class_Oabs(_1117377), _1117379) = c_Groups_Ozero__class_Ozero(_1117377))], (19241 ^ _779142) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1117377), _1117379) = c_Groups_Ozero__class_Ozero(_1117377), -(_1117379 = c_Groups_Ozero__class_Ozero(_1117377))]]], (33187 ^ _779142) ^ [_1386544, _1386546] : [-(c_Divides_Opdivmod(_1386544, _1386546) = 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), _1386544)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1386546))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1386544), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1386546))))], (44726 ^ _779142) ^ [_1675156, _1675158, _1675160] : [-(c_List_Olist_Olist__size(_1675156, _1675158, _1675160) = 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(_1675156, tc_Nat_Onat), _1675158), _1675160))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675156)), _1675160)))], (47788 ^ _779142) ^ [_1742115, _1742117, _1742119] : [47790 ^ _779142 : [(47793 ^ _779142) ^ [] : [hBOOL(hAPP(_1742117, hAPP(hAPP(c_List_Onth(_1742115), _1742119), 47789 ^ [_1742115, _1742117, _1742119])))], (47791 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47789 ^ [_1742115, _1742117, _1742119]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742115)), _1742119))))]], -(c_List_Olist__all(_1742115, _1742117, _1742119))], (23363 ^ _779142) ^ [_1190734, _1190736] : [class_Groups_Oordered__ab__group__add(_1190734), 23366 ^ _779142 : [(23373 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190734), _1190736), c_Groups_Ozero__class_Ozero(_1190734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190734), c_Groups_Ozero__class_Ozero(_1190734)), hAPP(c_Groups_Ouminus__class_Ouminus(_1190734), _1190736))))], (23367 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190734), c_Groups_Ozero__class_Ozero(_1190734)), hAPP(c_Groups_Ouminus__class_Ouminus(_1190734), _1190736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190734), _1190736), c_Groups_Ozero__class_Ozero(_1190734))))]]], (20350 ^ _779142) ^ [_1136276, _1136278] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136276) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136278), 20353 ^ _779142 : [(20356 ^ _779142) ^ [] : [-(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), _1136278))))], (20354 ^ _779142) ^ [] : [-(_1136276 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136278)))]]], (17061 ^ _779142) ^ [_1079327, _1079329, _1079331] : [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), _1079327), _1079329)), _1079331)), 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)), _1079331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079329), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7566 ^ _779142) ^ [_904212, _904214, _904216, _904218, _904220] : [class_Groups_Oordered__ab__group__add(_904212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_904212), _904214), _904216) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_904212), _904218), _904220), 7573 ^ _779142 : [(7580 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904212), _904218), _904220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904212), _904214), _904216)))], (7574 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904212), _904214), _904216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904212), _904218), _904220)))]]], (46626 ^ _779142) ^ [_1716626, _1716628] : [-(hAPP(c_List_Oset(_1716626), hAPP(c_List_Orev(_1716626), _1716628)) = hAPP(c_List_Oset(_1716626), _1716628))], (32039 ^ _779142) ^ [_1359527, _1359529, _1359531, _1359533, _1359535] : [class_Groups_Ominus(_1359527), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359529, _1359527)), _1359531), _1359533), _1359535) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1359527), hAPP(_1359531, _1359535)), hAPP(_1359533, _1359535)))], (52435 ^ _779142) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (41597 ^ _779142) ^ [_1602056, _1602058, _1602060, _1602062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602056), tc_List_Olist(_1602056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602056), tc_List_Olist(_1602056)), _1602058), _1602060)), c_List_Olistrel(_1602056, _1602062))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602056)), _1602058) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602056)), _1602060))], (3434 ^ _779142) ^ [_830381, _830383, _830385, _830387, _830389, _830391] : [-(c_List_Osublist(_830391, _830387, _830383) = c_List_Osublist(_830389, _830385, _830381)), _830391 = _830389, _830387 = _830385, _830383 = _830381], (51107 ^ _779142) ^ [_1813452, _1813454, _1813456, _1813458] : [class_Divides_Osemiring__div(_1813452), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813452), _1813454), _1813456)), 51114 ^ _779142 : [(51121 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813452), _1813454), _1813458)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813452), _1813454), c_Divides_Odiv__class_Omod(_1813452, _1813458, _1813456))))], (51115 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813452), _1813454), c_Divides_Odiv__class_Omod(_1813452, _1813458, _1813456))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813452), _1813454), _1813458)))]]], (37643 ^ _779142) ^ [_1492864, _1492866, _1492868] : [c_Equiv__Relations_Oequiv(_1492864, _1492866, _1492868), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492864, _1492864), tc_HOL_Obool)), _1492868), hAPP(hAPP(c_Product__Type_OSigma(_1492864, _1492864), _1492866), hAPP(c_COMBK(tc_fun(_1492864, tc_HOL_Obool), _1492864), _1492866)))))], (12708 ^ _779142) ^ [_998717, _998719, _998721, _998723, _998725] : [class_Rings_Olinordered__semiring__strict(_998717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998717), _998719), _998721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998717), _998723), _998725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998717), c_Groups_Ozero__class_Ozero(_998717)), _998719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998717), c_Groups_Ozero__class_Ozero(_998717)), _998723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998717), _998719), _998723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998717), _998721), _998725))))], (33169 ^ _779142) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (6355 ^ _779142) ^ [_880972, _880974, _880976, _880978] : [class_Orderings_Oorder(_880972), _880974 = _880976, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880972), _880978), _880976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880972), _880978), _880974)))], (34999 ^ _779142) ^ [_1429321, _1429323, _1429325, _1429327, _1429329] : [-(_1429321 = c_Orderings_Obot__class_Obot(tc_fun(_1429323, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429323, tc_fun(_1429325, tc_HOL_Obool)), _1429321), hAPP(hAPP(c_COMBB(tc_fun(_1429325, tc_HOL_Obool), tc_fun(_1429325, tc_HOL_Obool), _1429323), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429325, tc_HOL_Obool)), _1429327)), _1429329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429325, tc_HOL_Obool)), _1429327), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429323, tc_fun(_1429325, tc_HOL_Obool)), _1429321), _1429329)))], (38234 ^ _779142) ^ [_1514742, _1514744, _1514746, _1514748] : [class_Groups_Ocomm__monoid__add(_1514742), c_Fun_Oinj__on(_1514744, _1514742, _1514746, _1514748), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514744, _1514742), _1514746), _1514748) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514742, _1514742), c_Fun_Oid(_1514742)), hAPP(c_Set_Oimage(_1514744, _1514742, _1514746), _1514748)))], (40444 ^ _779142) ^ [_1570766, _1570768] : [-(hAPP(c_Relation_OImage(_1570766, _1570766, c_Relation_OId(_1570766)), _1570768) = _1570768)], (52383 ^ _779142) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (32423 ^ _779142) ^ [_1370084, _1370086] : [hAPP(c_Nat_OSuc, _1370084) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370086), -(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(_1370086))), 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)), _1370084))))))], (24940 ^ _779142) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (10077 ^ _779142) ^ [_952093, _952095, _952097, _952099, _952101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952093), _952095)), -(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), _952095), _952097)), _952099)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952093), _952097)), _952101)) = 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), _952095), _952093)), _952097)), _952099)), _952101))], (50311 ^ _779142) ^ [_1796434, _1796436, _1796438] : [hBOOL(hAPP(hAPP(_1796438, _1796436), _1796436)), -(hBOOL(hAPP(hAPP(c_member(_1796434), _1796436), c_Quotient_ORespects(_1796434, _1796438))))], (44335 ^ _779142) ^ [_1666280, _1666282, _1666284, _1666286] : [_1666286 = c_List_Olist_ONil(_1666282), -(c_List_Olist_ONil(_1666280) = hAPP(hAPP(c_List_Omap(_1666282, _1666280), _1666284), _1666286))], (23859 ^ _779142) ^ [_1199403, _1199405] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199403, _1199405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199403, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199403, _1199405)), _1199405))], (3016 ^ _779142) ^ [_823900, _823902, _823904, _823906, _823908, _823910] : [-(c_List_Oset__Cons(_823910, _823906, _823902) = c_List_Oset__Cons(_823908, _823904, _823900)), _823910 = _823908, _823906 = _823904, _823902 = _823900], (39479 ^ _779142) ^ [_1547176, _1547178] : [-(c_Hilbert__Choice_OEps(_1547176, hAPP(hAPP(c_COMBC(_1547176, _1547176, tc_HOL_Obool), c_fequal), _1547178)) = _1547178)], (42806 ^ _779142) ^ [_1632169, _1632171, _1632173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632169), tc_List_Olist(_1632169))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632169), tc_List_Olist(_1632169)), c_List_Olist_ONil(_1632169)), _1632171)), c_List_Olex(_1632169, _1632173)))], (49100 ^ _779142) ^ [_1771767, _1771769, _1771771, _1771773] : [c_Wellfounded_Omax__extp(_1771767, _1771769, _1771771, _1771773), 49103 ^ _779142 : [(49106 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771767), _1771773)))], (49108 ^ _779142) ^ [] : [_1771773 = c_Orderings_Obot__class_Obot(tc_fun(_1771767, tc_HOL_Obool))], (49110 ^ _779142) ^ [_1771983] : [hBOOL(hAPP(hAPP(c_member(_1771767), _1771983), _1771771)), 49114 ^ _779142 : [(49117 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1771769, _1771983), 49113 ^ [_1771767, _1771769, _1771771, _1771773, _1771983])))], (49115 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771767), 49113 ^ [_1771767, _1771769, _1771771, _1771773, _1771983]), _1771773)))]]], (49104 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771767), _1771771)))]]], (730 ^ _779142) ^ [_790105, _790107, _790109, _790111, _790113, _790115, _790117, _790119] : [-(c_Wellfounded_Omax__extp(_790117, _790113, _790109, _790105)), c_Wellfounded_Omax__extp(_790119, _790115, _790111, _790107), _790119 = _790117, _790115 = _790113, _790111 = _790109, _790107 = _790105], (52487 ^ _779142) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (43516 ^ _779142) ^ [_1648973, _1648975, _1648977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648973, tc_HOL_Obool)), hAPP(c_List_Oset(_1648973), hAPP(hAPP(c_List_Odrop(_1648973), _1648975), _1648977))), hAPP(c_List_Oset(_1648973), _1648977))))], (45601 ^ _779142) ^ [_1694554, _1694556, _1694558] : [c_List_Oconcat(_1694554, _1694556) = c_List_Oconcat(_1694554, _1694558), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694554))), _1694556) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694554))), _1694558), 45611 ^ _779142 : [(45614 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1694554), tc_List_Olist(_1694554), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694554), tc_fun(tc_List_Olist(_1694554), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694554), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1694554), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694554), tc_HOL_Obool)), tc_List_Olist(_1694554)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1694554))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1694554)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1694554))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1694554)))), 45610 ^ [_1694554, _1694556, _1694558]))], (45612 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694554), tc_List_Olist(_1694554))), 45610 ^ [_1694554, _1694556, _1694558]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1694554), tc_List_Olist(_1694554))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1694554), tc_List_Olist(_1694554)), _1694556), _1694558)))))]], -(_1694556 = _1694558)], (5320 ^ _779142) ^ [_860504, _860506] : [_860506 = _860504, -(c_Groups_Oplus__class_Oplus(_860506) = c_Groups_Oplus__class_Oplus(_860504))], (23945 ^ _779142) ^ [_1200830, _1200832] : [class_Int_Onumber__ring(_1200830), -(hAPP(c_Int_Onumber__class_Onumber__of(_1200830), c_Int_Opred(_1200832)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200830), hAPP(c_Groups_Ouminus__class_Ouminus(_1200830), c_Groups_Oone__class_Oone(_1200830))), hAPP(c_Int_Onumber__class_Onumber__of(_1200830), _1200832)))], (28803 ^ _779142) ^ [_1288838, _1288840, _1288842] : [28804 ^ _779142 : [(28807 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1288838), _1288842))], (28805 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1288838), _1288840))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1288838), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288838, tc_HOL_Obool)), _1288840), _1288842))))], (29323 ^ _779142) ^ [_1299591, _1299593, _1299595] : [class_Lattices_Oboolean__algebra(_1299591), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1299591), _1299593), _1299595) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299591), _1299593), hAPP(c_Groups_Ouminus__class_Ouminus(_1299591), _1299595)))], (43283 ^ _779142) ^ [_1642769, _1642771, _1642773, _1642775] : [-(hBOOL(hAPP(hAPP(c_member(_1642769), _1642771), hAPP(c_List_Oset(_1642769), _1642773)))), -(c_List_Oremove1(_1642769, _1642771, hAPP(hAPP(c_List_Oappend(_1642769), _1642773), _1642775)) = hAPP(hAPP(c_List_Oappend(_1642769), _1642773), c_List_Oremove1(_1642769, _1642771, _1642775)))], (29145 ^ _779142) ^ [_1295983, _1295985, _1295987] : [class_Lattices_Osemilattice__inf(_1295983), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295983), _1295985), _1295987) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295983), _1295987), _1295985))], (35661 ^ _779142) ^ [_1447260, _1447262, _1447264, _1447266] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447260, _1447260)), hAPP(hAPP(c_Product__Type_OPair(_1447260, _1447260), _1447262), _1447264)), c_Relation_OId__on(_1447260, _1447266))), 35664 ^ _779142 : [(35667 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447260), _1447262), _1447266)))], (35665 ^ _779142) ^ [] : [-(_1447262 = _1447264)]]], (39614 ^ _779142) ^ [_1550281, _1550283, _1550285, _1550287, _1550289] : [class_Groups_Ocomm__monoid__add(_1550281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550283), _1550285)), c_Fun_Oinj__on(_1550283, _1550283, _1550287, _1550285), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550283, _1550281), _1550289), hAPP(c_Set_Oimage(_1550283, _1550283, _1550287), _1550285)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550283, _1550281), hAPP(c_Fun_Ocomp(_1550283, _1550281, _1550283, _1550289), _1550287)), _1550285))], (25680 ^ _779142) ^ [_1230391, _1230393] : [class_Int_Onumber__ring(_1230391), -(hAPP(c_Int_Onumber__class_Onumber__of(_1230391), c_Int_OBit0(_1230393)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230391), c_Groups_Ozero__class_Ozero(_1230391)), hAPP(c_Int_Onumber__class_Onumber__of(_1230391), _1230393))), hAPP(c_Int_Onumber__class_Onumber__of(_1230391), _1230393)))], (36194 ^ _779142) ^ [_1459793, _1459795, _1459797] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459793), _1459795)), c_Fun_Oinj__on(_1459793, tc_fun(tc_fun(_1459793, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1459793, tc_fun(tc_prod(_1459793, _1459793), tc_HOL_Obool), tc_fun(tc_fun(_1459793, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459793, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1459793, _1459793), tc_HOL_Obool), tc_fun(tc_fun(_1459793, tc_HOL_Obool), tc_HOL_Obool)), _1459793), c_Equiv__Relations_Oquotient(_1459793)), hAPP(hAPP(c_COMBC(_1459793, tc_fun(_1459793, tc_HOL_Obool), tc_fun(_1459793, tc_HOL_Obool)), c_Set_Oinsert(_1459793)), c_Orderings_Obot__class_Obot(tc_fun(_1459793, tc_HOL_Obool))))), _1459797), _1459795), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1459793, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1459793), _1459795), _1459797)) = hAPP(c_Finite__Set_Ocard(_1459793), _1459795))], (17519 ^ _779142) ^ [_1087825, _1087827, _1087829, _1087831] : [class_Divides_Oring__div(_1087825), -(c_Divides_Odiv__class_Omod(_1087825, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087825), _1087827), _1087829), _1087831) = c_Divides_Odiv__class_Omod(_1087825, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087825), c_Divides_Odiv__class_Omod(_1087825, _1087827, _1087831)), _1087829), _1087831))], (44698 ^ _779142) ^ [_1674517, _1674519, _1674521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1674517), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674519), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674519)), _1674521)))), -(hBOOL(hAPP(hAPP(c_member(_1674519), hAPP(c_Random_Opick(_1674519, _1674521), _1674517)), hAPP(c_List_Oset(_1674519), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674519), _1674519), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674519)), _1674521)))))], (2164 ^ _779142) ^ [_810614, _810616, _810618, _810620, _810622, _810624, _810626, _810628] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810628, _810624, _810620, _810616) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810626, _810622, _810618, _810614)), _810628 = _810626, _810624 = _810622, _810620 = _810618, _810616 = _810614], (30778 ^ _779142) ^ [_1330599, _1330601] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330599, tc_HOL_Obool)), _1330601), c_Orderings_Otop__class_Otop(tc_fun(_1330599, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1330599, tc_HOL_Obool)))], (40903 ^ _779142) ^ [_1581983, _1581985, _1581987] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581983, _1581983)), _1581985), c_Transitive__Closure_Ortrancl(_1581983, _1581987))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581983, _1581983)), _1581985), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1581983, _1581983), 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(_1581983, _1581983), tc_HOL_Obool), tc_fun(tc_prod(_1581983, _1581983), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1581983, _1581983), tc_HOL_Obool)), _1581987)))))], (44472 ^ _779142) ^ [_1669764] : [-(hAPP(c_List_Omap(_1669764, _1669764), c_Fun_Oid(_1669764)) = c_Fun_Oid(tc_List_Olist(_1669764)))], (33698 ^ _779142) ^ [_1395867, _1395869, _1395871, _1395873] : [-(hAPP(c_Product__Type_Osnd(_1395867, _1395869), hAPP(hAPP(c_Product__Type_OPair(_1395867, _1395869), _1395871), _1395873)) = _1395873)], (10539 ^ _779142) ^ [_961554, _961556] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961554), _961556), 10544 ^ _779142 : [(10547 ^ _779142) ^ [] : [-(_961556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10545 ^ _779142) ^ [] : [-(_961554 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10548 ^ _779142 : [(10551 ^ _779142) ^ [] : [-(_961556 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10549 ^ _779142) ^ [] : [-(_961554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43223 ^ _779142) ^ [_1641483, _1641485, _1641487] : [_1641487 = c_List_Olist_ONil(_1641485), -(_1641483 = hAPP(hAPP(c_List_Oappend(_1641485), _1641483), _1641487))], (36973 ^ _779142) ^ [_1476175, _1476177, _1476179, _1476181] : [c_Wellfounded_Omax__extp(_1476175, _1476177, _1476179, _1476181), 36976 ^ _779142 : [(36979 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476175), _1476181)))], (36981 ^ _779142) ^ [] : [_1476181 = c_Orderings_Obot__class_Obot(tc_fun(_1476175, tc_HOL_Obool))], (36983 ^ _779142) ^ [_1476391] : [hBOOL(hAPP(hAPP(c_member(_1476175), _1476391), _1476179)), 36987 ^ _779142 : [(36990 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1476177, _1476391), 36986 ^ [_1476175, _1476177, _1476179, _1476181, _1476391])))], (36988 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476175), 36986 ^ [_1476175, _1476177, _1476179, _1476181, _1476391]), _1476181)))]]], (36977 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476175), _1476179)))]]], (39060 ^ _779142) ^ [_1536551, _1536553, _1536555, _1536557] : [39062 ^ _779142 : [(39065 ^ _779142) ^ [] : [c_Wellfounded_Owf(_1536553, hAPP(_1536555, 39061 ^ [_1536551, _1536553, _1536555, _1536557]))], (39063 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1536551, 39061 ^ [_1536551, _1536553, _1536555, _1536557])))]], -(c_Wellfounded_Owf(tc_prod(_1536557, _1536553), c_Recdef_Osame__fst(_1536557, _1536553, _1536551, _1536555)))], (8791 ^ _779142) ^ [_927162, _927164, _927166, _927168] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927162), 8794 ^ _779142 : [(8801 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927162), _927164), _927168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927162), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927162), _927164), _927166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927162), _927168), _927166))))], (8795 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927162), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927162), _927164), _927166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927162), _927168), _927166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927162), _927164), _927168)))]]], (8477 ^ _779142) ^ [_921132, _921134, _921136] : [class_Groups_Oab__semigroup__mult(_921132), hBOOL(hAPP(c_Finite__Set_Ofinite(_921132), _921134)), -(hBOOL(hAPP(hAPP(c_member(_921132), _921136), _921134))), -(hAPP(c_Finite__Set_Ofold1(_921132, c_Groups_Otimes__class_Otimes(_921132)), hAPP(hAPP(c_Set_Oinsert(_921132), _921136), _921134)) = hAPP(hAPP(c_Finite__Set_Ofold(_921132, _921132, c_Groups_Otimes__class_Otimes(_921132)), _921136), _921134))], (24367 ^ _779142) ^ [_1207956, _1207958, _1207960] : [class_Orderings_Oorder(_1207956), 24370 ^ _779142 : [(24377 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207956), _1207958), _1207960))), -(c_Orderings_Obot__class_Obot(tc_fun(_1207956, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207956, _1207958), _1207960))], (24371 ^ _779142) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1207956, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207956, _1207958), _1207960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207956), _1207958), _1207960))]]], (11690 ^ _779142) ^ [_980366, _980368, _980370, _980372] : [class_Rings_Oordered__semiring(_980366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980366), _980368), _980370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980366), c_Groups_Ozero__class_Ozero(_980366)), _980372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980366), _980372), _980368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980366), _980372), _980370))))], (15265 ^ _779142) ^ [_1046492, _1046494, _1046496, _1046498] : [class_Orderings_Olinorder(_1046492), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046492), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046492), _1046494), _1046496)), _1046498) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046492), _1046494), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046492), _1046496), _1046498)))], (24223 ^ _779142) ^ [_1205541, _1205543] : [_1205543 = c_Orderings_Obot__class_Obot(tc_fun(_1205541, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205541, tc_HOL_Obool)), _1205543), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205541, tc_HOL_Obool)), _1205543))))], (37655 ^ _779142) ^ [_1493315, _1493317, _1493319] : [-(hAPP(c_Set_OCollect(_1493315), hAPP(hAPP(c_COMBS(_1493315, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1493315), c_fimplies), _1493317)), _1493319)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493315, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493315, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1493315), _1493317))), hAPP(c_Set_OCollect(_1493315), _1493319)))], (6341 ^ _779142) ^ [_880753, _880755, _880757, _880759] : [class_Orderings_Oord(_880753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880753), _880755), _880757)), _880757 = _880759, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880753), _880755), _880759)))], (37309 ^ _779142) ^ [_1484060, _1484062, _1484064, _1484066, _1484068] : [c_Fun_Oinj__on(_1484060, _1484062, _1484064, c_Orderings_Otop__class_Otop(tc_fun(_1484060, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484062, tc_HOL_Obool)), _1484066), hAPP(c_Set_Oimage(_1484060, _1484062, _1484064), _1484068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484060, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1484060, _1484062, _1484064), _1484066)), _1484068)))], (1586 ^ _779142) ^ [_801909, _801911] : [-(class_Groups_Oordered__comm__monoid__add(_801909)), _801911 = _801909, class_Groups_Oordered__comm__monoid__add(_801911)], (26888 ^ _779142) ^ [_1253222] : [class_Lattices_Osemilattice__sup(_1253222), -(c_Finite__Set_Ofun__left__comm__idem(_1253222, _1253222, c_Lattices_Osemilattice__sup__class_Osup(_1253222)))], (44666 ^ _779142) ^ [_1673796, _1673798, _1673800, _1673802] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673796)), _1673798) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673800)), _1673802), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673796, _1673800), _1673796), c_Product__Type_Ofst(_1673796, _1673800)), hAPP(hAPP(c_List_Ozip(_1673796, _1673800), _1673798), _1673802)) = _1673798)], (4732 ^ _779142) ^ [_851120, _851122, _851124, _851126] : [-(c_Complete__Lattice_OSup__class_OSup(_851126, _851122) = c_Complete__Lattice_OSup__class_OSup(_851124, _851120)), _851126 = _851124, _851122 = _851120], (8463 ^ _779142) ^ [_920807, _920809, _920811, _920813, _920815] : [class_Groups_Ocomm__monoid__add(_920807), hBOOL(hAPP(c_Finite__Set_Ofinite(_920809), _920811)), hBOOL(hAPP(hAPP(c_member(_920809), _920813), _920811)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920809, _920807), _920815), _920811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920807), hAPP(_920815, _920813)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920809, _920807), _920815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920809, tc_HOL_Obool)), _920811), hAPP(hAPP(c_Set_Oinsert(_920809), _920813), c_Orderings_Obot__class_Obot(tc_fun(_920809, tc_HOL_Obool)))))))], (20430 ^ _779142) ^ [_1137673] : [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, _1137673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1137673)))], (26308 ^ _779142) ^ [_1241714, _1241716, _1241718, _1241720] : [class_Orderings_Olinorder(_1241714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241714), _1241716), _1241718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241714), _1241718), _1241720)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241714, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1241714, _1241716, _1241718)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1241714, _1241718, _1241720)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241714, _1241716), _1241720))], (30608 ^ _779142) ^ [_1327038, _1327040, _1327042, _1327044, _1327046, _1327048, _1327050] : [c_Finite__Set_Ofolding__image__simple(_1327038, _1327040, _1327042, _1327044, _1327046, _1327048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327040), _1327050)), -(hAPP(_1327048, _1327050) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1327038, _1327040, _1327042), _1327046), _1327044), _1327050))], (20800 ^ _779142) ^ [_1144798, _1144800] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144798, _1144800) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144798), _1144800)), _1144800)))], (32005 ^ _779142) ^ [_1358615, _1358617, _1358619] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358615, tc_Nat_Onat), _1358617), _1358619) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358615, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1358615), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1358617)), _1358619)))], (45634 ^ _779142) ^ [_1695951, _1695953, _1695955] : [hBOOL(hAPP(c_List_Odistinct(_1695951), _1695953)), -(hBOOL(hAPP(c_List_Odistinct(_1695951), hAPP(c_List_Ofilter(_1695951, _1695955), _1695953))))], (23837 ^ _779142) ^ [_1199027, _1199029] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199027)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199029))))), _1199027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1199029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21029 ^ _779142) ^ [_1148918, _1148920, _1148922, _1148924] : [hBOOL(hAPP(hAPP(_1148922, _1148924), _1148920)), -(hBOOL(hAPP(hAPP(c_member(_1148918), _1148920), c_SetInterval_Oord_OatLeast(_1148918, _1148922, _1148924))))], (25678 ^ _779142) ^ [_1230362] : [-(c_Int_Osucc(c_Int_OBit0(_1230362)) = c_Int_OBit1(_1230362))], (17259 ^ _779142) ^ [_1082886, _1082888, _1082890] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082886), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082888)), _1082890)) = 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), _1082886), _1082888))), _1082890))], (48804 ^ _779142) ^ [_1764686, _1764688] : [-(c_Relation_Otrans(_1764686, c_Transitive__Closure_Ortrancl(_1764686, _1764688)))], (18535 ^ _779142) ^ [] : [-(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))))], (40791 ^ _779142) ^ [_1578859, _1578861, _1578863, _1578865] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578859, _1578859)), hAPP(hAPP(c_Product__Type_OPair(_1578859, _1578859), _1578861), _1578863)), c_Transitive__Closure_Ortrancl(_1578859, _1578865))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578859, _1578859)), hAPP(hAPP(c_Product__Type_OPair(_1578859, _1578859), _1578863), _1578861)), c_Transitive__Closure_Ortrancl(_1578859, hAPP(c_Relation_Oconverse(_1578859, _1578859), _1578865)))))], (45346 ^ _779142) ^ [_1689329, _1689331] : [c_List_Oremdups(_1689329, _1689331) = _1689331, -(hBOOL(hAPP(c_List_Odistinct(_1689329), _1689331)))], (32930 ^ _779142) ^ [_1380893] : [-(c_Divides_Oadjust(_1380893) = 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)), _1380893))))), 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)), _1380893))))), 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))))))))], (4116 ^ _779142) ^ [_841454, _841456, _841458, _841460, _841462, _841464] : [-(c_Predicate_Oconversep(_841464, _841460, _841456) = c_Predicate_Oconversep(_841462, _841458, _841454)), _841464 = _841462, _841460 = _841458, _841456 = _841454], (21220 ^ _779142) ^ [_1152277, _1152279] : [c_Nat__Transfer_Ois__nat(_1152277), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1152277, _1152279)))], (31044 ^ _779142) ^ [_1335410, _1335412] : [class_Orderings_Olinorder(_1335410), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1335410, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1335410), _1335412)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1335410), _1335412))], (38566 ^ _779142) ^ [_1525702, _1525704, _1525706] : [c_Relation_Orefl__on(_1525702, _1525704, _1525706), 38569 ^ _779142 : [(38572 ^ _779142) ^ [_1525884] : [hBOOL(hAPP(hAPP(c_member(_1525702), _1525884), _1525704)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525702, _1525702)), hAPP(hAPP(c_Product__Type_OPair(_1525702, _1525702), _1525884), _1525884)), _1525706)))], (38570 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525702, _1525702), tc_HOL_Obool)), _1525706), hAPP(hAPP(c_Product__Type_OSigma(_1525702, _1525702), _1525704), hAPP(c_COMBK(tc_fun(_1525702, tc_HOL_Obool), _1525702), _1525704)))))]]], (33734 ^ _779142) ^ [_1396661, _1396663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396663)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396661, _1396663) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1396661, _1396663)))], (47911 ^ _779142) ^ [_1744373, _1744375, _1744377] : [c_List_Olist__all(_1744373, _1744375, _1744377), 47914 ^ _779142 : [(47915 ^ _779142) ^ [_1744454] : [hBOOL(hAPP(hAPP(c_member(_1744373), _1744454), hAPP(c_List_Oset(_1744373), _1744377))), -(hBOOL(hAPP(_1744375, _1744454)))]]], (44752 ^ _779142) ^ [_1675618, _1675620, _1675622] : [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, _1675618), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675618)), _1675620)))), -(hBOOL(hAPP(hAPP(c_member(_1675618), hAPP(c_Product__Type_Ofst(_1675618, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1675618, _1675620), _1675622))), hAPP(c_List_Oset(_1675618), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1675618), _1675618), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1675618)), _1675620)))))], (43768 ^ _779142) ^ [_1654566] : [-(c_List_Orotate(_1654566, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1654566)))], (52475 ^ _779142) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (35539 ^ _779142) ^ [] : [-(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))))))], (23457 ^ _779142) ^ [_1192351, _1192353, _1192355] : [class_Groups_Ogroup__add(_1192351), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192351), _1192353), _1192355) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192351), _1192353), hAPP(c_Groups_Ouminus__class_Ouminus(_1192351), _1192355)))], (2634 ^ _779142) ^ [_817941, _817943, _817945, _817947, _817949, _817951, _817953, _817955] : [-(c_Recdef_Osame__fst(_817955, _817951, _817947, _817943) = c_Recdef_Osame__fst(_817953, _817949, _817945, _817941)), _817955 = _817953, _817951 = _817949, _817947 = _817945, _817943 = _817941], (52341 ^ _779142) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (42706 ^ _779142) ^ [_1630224] : [-(hAPP(c_List_Oset(_1630224), c_List_Olist_ONil(_1630224)) = c_Orderings_Obot__class_Obot(tc_fun(_1630224, tc_HOL_Obool)))], (43660 ^ _779142) ^ [_1652400, _1652402, _1652404, _1652406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652400), _1652402)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652404)), _1652406))), -(hAPP(hAPP(c_List_Otake(_1652404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652400), _1652402)), _1652406) = hAPP(hAPP(c_List_Oappend(_1652404), hAPP(hAPP(c_List_Otake(_1652404), _1652400), _1652406)), hAPP(hAPP(c_List_Otake(_1652404), _1652402), hAPP(hAPP(c_List_Odrop(_1652404), _1652400), _1652406))))], (41206 ^ _779142) ^ [_1590127, _1590129, _1590131, _1590133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590127, _1590127)), hAPP(hAPP(c_Product__Type_OPair(_1590127, _1590127), _1590129), _1590131)), c_Transitive__Closure_Otrancl(_1590127, _1590133))), 41210 ^ _779142 : [(41213 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590127, _1590127)), hAPP(hAPP(c_Product__Type_OPair(_1590127, _1590127), 41209 ^ [_1590127, _1590129, _1590131, _1590133]), _1590131)), _1590133)))], (41211 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590127, _1590127)), hAPP(hAPP(c_Product__Type_OPair(_1590127, _1590127), _1590129), 41209 ^ [_1590127, _1590129, _1590131, _1590133])), c_Transitive__Closure_Ortrancl(_1590127, _1590133))))]]], (44341 ^ _779142) ^ [_1666389, _1666391, _1666393] : [-(hAPP(hAPP(c_List_Omap(_1666389, _1666391), _1666393), c_List_Olist_ONil(_1666389)) = c_List_Olist_ONil(_1666391))], (44895 ^ _779142) ^ [_1678548, _1678550, _1678552, _1678554] : [-(c_List_Opartition(_1678548, _1678550, hAPP(hAPP(c_List_Olist_OCons(_1678548), _1678552), _1678554)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1678548), tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1678548), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678548), tc_fun(tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), tc_fun(tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), tc_List_Olist(_1678548)), c_COMBS(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_fun(tc_List_Olist(_1678548), tc_fun(tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), tc_List_Olist(_1678548)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_fun(tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_List_Olist(_1678548)), hAPP(c_If(tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), hAPP(_1678550, _1678552)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1678548), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_List_Olist(_1678548)), c_Product__Type_OPair(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), hAPP(c_List_Olist_OCons(_1678548), _1678552))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1678548), tc_fun(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548))), tc_fun(tc_fun(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_fun(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), tc_List_Olist(_1678548)), c_COMBB(tc_List_Olist(_1678548), tc_prod(tc_List_Olist(_1678548), tc_List_Olist(_1678548)), tc_List_Olist(_1678548))), c_Product__Type_OPair(tc_List_Olist(_1678548), tc_List_Olist(_1678548)))), hAPP(c_List_Olist_OCons(_1678548), _1678552)))), c_List_Opartition(_1678548, _1678550, _1678554)))], (43646 ^ _779142) ^ [_1652107, _1652109, _1652111, _1652113] : [-(hAPP(c_List_Orotate1(_1652109), hAPP(hAPP(c_List_Olist_OCons(_1652109), _1652111), _1652113)) = hAPP(hAPP(c_List_Oappend(_1652109), _1652113), hAPP(hAPP(c_List_Olist_OCons(_1652109), _1652111), c_List_Olist_ONil(_1652109))))], (6079 ^ _779142) ^ [_876154, _876156, _876158] : [class_Orderings_Obot(_876154), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_876156, _876154)), _876158) = c_Orderings_Obot__class_Obot(_876154))], (40540 ^ _779142) ^ [_1573059] : [-(hAPP(c_Relation_ORange(_1573059, _1573059), c_Relation_OId(_1573059)) = c_Orderings_Otop__class_Otop(tc_fun(_1573059, tc_HOL_Obool)))], (26464 ^ _779142) ^ [_1244622, _1244624, _1244626, _1244628] : [class_Lattices_Osemilattice__sup(_1244622), 26467 ^ _779142 : [(26476 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1244622), _1244624), _1244626)), _1244628))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), _1244624), _1244628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), _1244626), _1244628))], (26468 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1244622), _1244624), _1244626)), _1244628)), 26471 ^ _779142 : [(26474 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), _1244626), _1244628)))], (26472 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244622), _1244624), _1244628)))]]]]], (2786 ^ _779142) ^ [_820361, _820363, _820365, _820367] : [-(c_Relation_ORange(_820367, _820363) = c_Relation_ORange(_820365, _820361)), _820367 = _820365, _820363 = _820361], (39310 ^ _779142) ^ [_1543008, _1543010] : [class_Complete__Lattice_Ocomplete__lattice(_1543008), -(c_Complete__Lattice_OInf__class_OInf(_1543008, _1543010) = c_Complete__Lattice_OSup__class_OSup(_1543008, hAPP(c_Set_OCollect(_1543008), hAPP(hAPP(c_COMBB(tc_fun(_1543008, tc_HOL_Obool), tc_HOL_Obool, _1543008), c_HOL_OAll(_1543008)), hAPP(hAPP(c_COMBB(tc_fun(_1543008, tc_HOL_Obool), tc_fun(_1543008, tc_HOL_Obool), _1543008), hAPP(c_COMBS(_1543008, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543008), c_fimplies), hAPP(hAPP(c_COMBC(_1543008, tc_fun(_1543008, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543008)), _1543010)))), c_Orderings_Oord__class_Oless__eq(_1543008))))))], (28036 ^ _779142) ^ [_1274246, _1274248, _1274250, _1274252] : [class_Orderings_Olinorder(_1274246), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274246), _1274248), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274246), _1274250), _1274252)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274246), _1274250), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274246), _1274248), _1274252)))], (41337 ^ _779142) ^ [_1593304, _1593306] : [-(c_List_Olenlex(_1593304, _1593306) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593304), tc_List_Olist(_1593304), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593304), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), tc_List_Olist(_1593304)), c_COMBS(tc_List_Olist(_1593304), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593304)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593304)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593304), tc_fun(tc_List_Olist(_1593304), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593304), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), tc_List_Olist(_1593304)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593304))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593304)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1593304))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593304)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593304), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), tc_List_Olist(_1593304)), c_COMBS(tc_List_Olist(_1593304), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593304)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593304)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593304), tc_fun(tc_List_Olist(_1593304), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593304), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), tc_List_Olist(_1593304)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593304))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593304)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593304))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593304)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593304), tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593304), tc_HOL_Obool)), tc_List_Olist(_1593304)), c_COMBC(tc_List_Olist(_1593304), tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593304), tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304))), tc_fun(tc_List_Olist(_1593304), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1593304)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1593304)), c_member(tc_prod(tc_List_Olist(_1593304), tc_List_Olist(_1593304))))), c_Product__Type_OPair(tc_List_Olist(_1593304), tc_List_Olist(_1593304))))), c_List_Olex(_1593304, _1593306)))))))], (23935 ^ _779142) ^ [_1200649, _1200651] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1200649), hAPP(c_Int_Onumber__class_Onumber__of(_1200649), c_Int_OMin)), _1200651) = hAPP(c_Groups_Ouminus__class_Ouminus(_1200649), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1200649), c_Groups_Oone__class_Oone(_1200649)), _1200651))), class_Fields_Ofield__inverse__zero(_1200649), class_Int_Onumber__ring(_1200649)], (49871 ^ _779142) ^ [_1787592, _1787594] : [-(c_Fun_Obij__betw(_1787592, _1787592, c_Fun_Oid(_1787592), _1787594, _1787594))], (3862 ^ _779142) ^ [_837233, _837235, _837237, _837239, _837241, _837243, _837245, _837247, _837249, _837251, _837253, _837255, _837257, _837259] : [-(c_New__Random__Sequence_Opos__decr__bind(_837259, _837255, _837251, _837247, _837243, _837239, _837235) = c_New__Random__Sequence_Opos__decr__bind(_837257, _837253, _837249, _837245, _837241, _837237, _837233)), _837259 = _837257, _837255 = _837253, _837251 = _837249, _837247 = _837245, _837243 = _837241, _837239 = _837237, _837235 = _837233], (46550 ^ _779142) ^ [_1715033, _1715035] : [hBOOL(hAPP(c_List_Odistinct(_1715033), hAPP(c_List_Orev(_1715033), _1715035))), -(hBOOL(hAPP(c_List_Odistinct(_1715033), _1715035)))], (44442 ^ _779142) ^ [_1668955, _1668957, _1668959, _1668961, _1668963] : [-(hAPP(hAPP(c_List_Otake(_1668955), _1668957), hAPP(hAPP(c_List_Omap(_1668959, _1668955), _1668961), _1668963)) = hAPP(hAPP(c_List_Omap(_1668959, _1668955), _1668961), hAPP(hAPP(c_List_Otake(_1668959), _1668957), _1668963)))], (48690 ^ _779142) ^ [_1761462, _1761464, _1761466] : [48692 ^ _779142 : [(48695 ^ _779142) ^ [] : [hBOOL(hAPP(_1761462, 48691 ^ [_1761462, _1761464, _1761466]))], (48693 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48691 ^ [_1761462, _1761464, _1761466]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761464, _1761466))))]], -(c_List_Oall__interval__int(_1761462, _1761464, _1761466))], (10795 ^ _779142) ^ [_965624, _965626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965624), _965626)), -(hAPP(c_Nat_OSuc, _965624) = _965626), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965624)), _965626)))], (27268 ^ _779142) ^ [_1260304, _1260306] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1260304, _1260306))))], (40332 ^ _779142) ^ [_1568002, _1568004] : [-(c_Transitive__Closure_Otrancl(_1568002, c_Transitive__Closure_Ortrancl(_1568002, _1568004)) = c_Transitive__Closure_Ortrancl(_1568002, _1568004))], (3802 ^ _779142) ^ [_836173, _836175] : [_836175 = _836173, -(c_Nat_Osemiring__1__class_Oof__nat(_836175) = c_Nat_Osemiring__1__class_Oof__nat(_836173))], (21806 ^ _779142) ^ [_1162323, _1162325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162323)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1162323)), _1162325) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1162323), _1162325)))], (13197 ^ _779142) ^ [_1007957, _1007959] : [-(_1007957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007957), _1007959) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1007957), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1007959)))], (3084 ^ _779142) ^ [_824954, _824956, _824958, _824960] : [-(c_Finite__Set_Ofold1(_824960, _824956) = c_Finite__Set_Ofold1(_824958, _824954)), _824960 = _824958, _824956 = _824954], (50481 ^ _779142) ^ [_1801923, _1801925, _1801927] : [-(c_Lazy__Sequence_Oflat(_1801923, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1801923), _1801925, _1801927)) = c_Lazy__Sequence_Oappend(_1801923, _1801925, c_Lazy__Sequence_Oflat(_1801923, _1801927)))], (43452 ^ _779142) ^ [_1647391, _1647393] : [-(hAPP(c_List_Orotate1(_1647391), _1647393) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1647391), _1647391, c_List_Olist_ONil(_1647391), hAPP(hAPP(c_COMBB(tc_List_Olist(_1647391), tc_fun(tc_List_Olist(_1647391), tc_List_Olist(_1647391)), _1647391), hAPP(c_COMBC(tc_List_Olist(_1647391), tc_List_Olist(_1647391), tc_List_Olist(_1647391)), c_List_Oappend(_1647391))), hAPP(hAPP(c_COMBC(_1647391, tc_List_Olist(_1647391), tc_List_Olist(_1647391)), c_List_Olist_OCons(_1647391)), c_List_Olist_ONil(_1647391)))), _1647393))], (22224 ^ _779142) ^ [_1170017, _1170019, _1170021] : [class_Rings_Olinordered__semidom(_1170017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170017), c_Groups_Ozero__class_Ozero(_1170017)), _1170019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170017), _1170019), c_Groups_Oone__class_Oone(_1170017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170017), _1170019), hAPP(hAPP(c_Power_Opower__class_Opower(_1170017), _1170019), _1170021))), hAPP(hAPP(c_Power_Opower__class_Opower(_1170017), _1170019), _1170021))))], (24872 ^ _779142) ^ [_1216463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1216463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1216463)))], (49042 ^ _779142) ^ [_1770971, _1770973] : [c_Equiv__Relations_Oequivp(_1770971, _1770973), 49045 ^ _779142 : [(49050 ^ _779142) ^ [] : [-(c_Predicate_Otransp(_1770971, _1770973))], (49048 ^ _779142) ^ [] : [-(c_Predicate_Osymp(_1770971, _1770973))], (49046 ^ _779142) ^ [] : [-(c_Predicate_Oreflp(_1770971, _1770973))]]], (51049 ^ _779142) ^ [_1812335, _1812337, _1812339] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812335), _1812337)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812335), _1812339)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1812337), _1812339))))], (48036 ^ _779142) ^ [_1747003, _1747005] : [-(hAPP(c_New__DSequence_Opos__empty(_1747003), _1747005) = c_Lazy__Sequence_Oempty(_1747003))], (16999 ^ _779142) ^ [_1078124, _1078126, _1078128, _1078130, _1078132] : [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), _1078124), _1078126)), _1078128)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078124), _1078130)), _1078132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078132), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078124), _1078132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078124), _1078128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078130), _1078126)))], (3528 ^ _779142) ^ [_831904, _831906, _831908, _831910] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831910, _831906) = c_List_Olinorder__class_Osorted__list__of__set(_831908, _831904)), _831910 = _831908, _831906 = _831904], (29456 ^ _779142) ^ [_1302978, _1302980, _1302982, _1302984] : [class_Orderings_Oorder(_1302978), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302978, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1302978, _1302980, _1302982)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1302978, _1302982, _1302984)) = c_Orderings_Obot__class_Obot(tc_fun(_1302978, tc_HOL_Obool)))], (41517 ^ _779142) ^ [_1599620, _1599622, _1599624, _1599626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599620), tc_List_Olist(_1599620))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599620), tc_List_Olist(_1599620)), _1599622), _1599624)), c_List_Olistrel1(_1599620, hAPP(c_Relation_Oconverse(_1599620, _1599620), _1599626)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599620), tc_List_Olist(_1599620))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599620), tc_List_Olist(_1599620)), _1599622), _1599624)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599620), tc_List_Olist(_1599620)), c_List_Olistrel1(_1599620, _1599626)))))], (49873 ^ _779142) ^ [_1787622, _1787624, _1787626, _1787628, _1787630] : [c_Fun_Obij__betw(_1787622, _1787624, _1787626, _1787628, _1787630), -(c_Fun_Obij__betw(_1787624, _1787622, c_Hilbert__Choice_Oinv__into(_1787622, _1787624, _1787628, _1787626), _1787630, _1787628))], (44147 ^ _779142) ^ [_1662469, _1662471, _1662473, _1662475] : [-(_1662469 = c_List_Olist_ONil(_1662471)), 44150 ^ _779142 : [(44157 ^ _779142) ^ [] : [-(_1662473 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662471)), _1662469)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1662471, hAPP(hAPP(c_List_Olist__update(_1662471, _1662469), _1662473), _1662475)) = c_List_Olast(_1662471, _1662469))], (44151 ^ _779142) ^ [] : [_1662473 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662471)), _1662469)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1662471, hAPP(hAPP(c_List_Olist__update(_1662471, _1662469), _1662473), _1662475)) = _1662475)]]], (31376 ^ _779142) ^ [_1341747, _1341749, _1341751] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1341747, tc_HOL_Obool)), _1341749), _1341751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341747, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341747, tc_HOL_Obool), _1341751)), _1341749)))], (31693 ^ _779142) ^ [_1347982, _1347984, _1347986] : [-(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), _1347982)), 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))), _1347984))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1347986))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1347986)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1347982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1347982), 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), _1347986), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1347984)))))], (19513 ^ _779142) ^ [_1122260] : [hBOOL(hAPP(_1122260, 19514 ^ [_1122260])), 19517 ^ _779142 : [(19518 ^ _779142) ^ [_1122354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122354)), -(hBOOL(hAPP(_1122260, hAPP(c_Int_Onat, _1122354))))]]], (38752 ^ _779142) ^ [_1529220, _1529222] : [hAPP(hAPP(c_Relation_Orel__comp(_1529220, _1529220, _1529220), _1529222), _1529222) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529220, _1529220), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1529220, _1529222))], (49316 ^ _779142) ^ [_1776200, _1776202] : [c_Relation_Osym(_1776200, _1776202), -(c_Relation_Osym(_1776200, hAPP(c_Relation_Oconverse(_1776200, _1776200), _1776202)))], (33008 ^ _779142) ^ [_1383158, _1383160, _1383162, _1383164] : [-(hAPP(c_Nat_Onat_Onat__rec(_1383158, _1383160, _1383162), hAPP(c_Nat_OSuc, _1383164)) = hAPP(hAPP(_1383162, _1383164), hAPP(c_Nat_Onat_Onat__rec(_1383158, _1383160, _1383162), _1383164)))], (27930 ^ _779142) ^ [_1272366, _1272368, _1272370, _1272372] : [class_Orderings_Olinorder(_1272366), 27933 ^ _779142 : [(27942 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272366), _1272368), _1272370)), _1272372))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), _1272368), _1272372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), _1272370), _1272372))], (27934 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272366), _1272368), _1272370)), _1272372)), 27937 ^ _779142 : [(27940 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), _1272370), _1272372)))], (27938 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272366), _1272368), _1272372)))]]]]], (52189 ^ _779142) ^ [_1831654, _1831656] : [class_Orderings_Otop(_1831654), -(class_Orderings_Otop(tc_fun(_1831656, _1831654)))], (8174 ^ _779142) ^ [_914812, _914814, _914816, _914818, _914820, _914822, _914824] : [hBOOL(hAPP(hAPP(c_member(_914812), _914814), _914816)), c_Nitpick_Ofold__graph_H(_914812, _914818, _914820, _914822, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914812, tc_HOL_Obool)), _914816), hAPP(hAPP(c_Set_Oinsert(_914812), _914814), c_Orderings_Obot__class_Obot(tc_fun(_914812, tc_HOL_Obool)))), _914824), -(c_Nitpick_Ofold__graph_H(_914812, _914818, _914820, _914822, _914816, hAPP(hAPP(_914820, _914814), _914824)))], (42808 ^ _779142) ^ [_1632228, _1632230, _1632232, _1632234] : [-(hAPP(hAPP(c_List_Otake(_1632228), _1632230), hAPP(hAPP(c_List_Olist_OCons(_1632228), _1632232), _1632234)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1632228), c_List_Olist_ONil(_1632228), hAPP(hAPP(c_COMBB(tc_List_Olist(_1632228), tc_List_Olist(_1632228), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1632228), _1632232)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1632228), tc_List_Olist(_1632228)), c_List_Otake(_1632228)), _1632234)), _1632230))], (16539 ^ _779142) ^ [_1070175, _1070177, _1070179] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070175), _1070177)), _1070179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070175), _1070179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070177), _1070179)))], (52731 ^ _779142) ^ [_1837264, _1837266] : [hBOOL(hAPP(hAPP(c_fconj, _1837264), _1837266)), -(hBOOL(_1837264))], (15683 ^ _779142) ^ [_1054369, _1054371, _1054373, _1054375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054369), hAPP(c_Int_Onumber__class_Onumber__of(_1054369), _1054371)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054369), _1054373), _1054375)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054369), hAPP(c_Int_Onumber__class_Onumber__of(_1054369), _1054371)), _1054373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054369), hAPP(c_Int_Onumber__class_Onumber__of(_1054369), _1054371)), _1054375))), class_Int_Onumber(_1054369), class_Rings_Oring(_1054369)], (44430 ^ _779142) ^ [_1668728, _1668730, _1668732, _1668734, _1668736] : [hAPP(hAPP(c_List_Omap(_1668728, _1668730), _1668732), _1668734) = hAPP(hAPP(c_List_Omap(_1668728, _1668730), _1668732), _1668736), c_Fun_Oinj__on(_1668728, _1668730, _1668732, c_Orderings_Otop__class_Otop(tc_fun(_1668728, tc_HOL_Obool))), -(_1668734 = _1668736)], (37144 ^ _779142) ^ [_1480070, _1480072, _1480074, _1480076] : [c_Fun_Oinj__on(_1480070, _1480072, _1480074, c_Orderings_Otop__class_Otop(tc_fun(_1480070, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480070, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1480070, _1480072, _1480074), hAPP(hAPP(c_Set_Oinsert(_1480072), _1480076), c_Orderings_Obot__class_Obot(tc_fun(_1480072, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1480070), c_HOL_OThe(_1480070, hAPP(hAPP(c_COMBC(_1480070, _1480072, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1480072, tc_fun(_1480072, tc_HOL_Obool), _1480070), c_fequal), _1480074)), _1480076))), c_Orderings_Obot__class_Obot(tc_fun(_1480070, tc_HOL_Obool))))))], (39147 ^ _779142) ^ [_1538729, _1538731] : [-(c_HOL_OThe(_1538729, hAPP(hAPP(c_COMBC(_1538729, _1538729, tc_HOL_Obool), c_fequal), _1538731)) = _1538731)], (3952 ^ _779142) ^ [_838810, _838812, _838814, _838816, _838818, _838820, _838822, _838824] : [-(c_New__DSequence_Oneg__bind(_838824, _838820, _838816, _838812) = c_New__DSequence_Oneg__bind(_838822, _838818, _838814, _838810)), _838824 = _838822, _838820 = _838818, _838816 = _838814, _838812 = _838810], (9382 ^ _779142) ^ [_939112, _939114] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939112), _939114), 9385 ^ _779142 : [(9388 ^ _779142) ^ [] : [-(_939114 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9386 ^ _779142) ^ [] : [-(_939112 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (34312 ^ _779142) ^ [_1409358, _1409360, _1409362, _1409364] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1409358, tc_HOL_Obool), tc_fun(_1409360, tc_HOL_Obool)), _1409362), hAPP(hAPP(c_COMBC(tc_fun(_1409358, tc_HOL_Obool), tc_fun(_1409358, tc_fun(_1409360, tc_HOL_Obool)), tc_fun(_1409360, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409358, tc_fun(_1409360, tc_HOL_Obool))), _1409364)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409358, tc_fun(_1409360, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1409358, tc_HOL_Obool), _1409362)), _1409364))], (39191 ^ _779142) ^ [_1539382, _1539384] : [c_Nitpick_Owf_H(_1539382, _1539384), 39194 ^ _779142 : [(39197 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539382, _1539382)), _1539384))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (39195 ^ _779142) ^ [] : [-(c_Wellfounded_Oacyclic(_1539382, _1539384))]]], (40076 ^ _779142) ^ [_1561070, _1561072, _1561074, _1561076, _1561078, _1561080, _1561082, _1561084] : [class_Groups_Ocomm__monoid__add(_1561070), c_Fun_Oinj__on(_1561072, _1561074, _1561076, _1561078), _1561080 = hAPP(c_Set_Oimage(_1561072, _1561074, _1561076), _1561078), 40090 ^ _779142 : [(40093 ^ _779142) ^ [] : [hAPP(_1561082, 40089 ^ [_1561070, _1561072, _1561074, _1561076, _1561078, _1561080, _1561082, _1561084]) = hAPP(_1561084, hAPP(_1561076, 40089 ^ [_1561070, _1561072, _1561074, _1561076, _1561078, _1561080, _1561082, _1561084]))], (40091 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561072), 40089 ^ [_1561070, _1561072, _1561074, _1561076, _1561078, _1561080, _1561082, _1561084]), _1561078)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561074, _1561070), _1561084), _1561080) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561072, _1561070), _1561082), _1561078))], (3632 ^ _779142) ^ [_833514, _833516] : [_833516 = _833514, -(c_List_Omonoid__add__class_Olistsum(_833516) = c_List_Omonoid__add__class_Olistsum(_833514))], (49927 ^ _779142) ^ [_1788796, _1788798, _1788800, _1788802, _1788804, _1788806, _1788808, _1788810] : [c_Fun_Obij__betw(_1788796, _1788798, _1788800, _1788802, _1788804), c_Fun_Obij__betw(_1788798, _1788806, _1788808, _1788804, _1788810), -(c_Fun_Obij__betw(_1788796, _1788806, hAPP(c_Fun_Ocomp(_1788798, _1788806, _1788796, _1788808), _1788800), _1788802, _1788810))], (41306 ^ _779142) ^ [_1592636] : [-(c_Nitpick_Onum(_1592636) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592636, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592636)))], (46003 ^ _779142) ^ [_1704537, _1704539] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1704537, _1704539) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704537), _1704539)))], (1266 ^ _779142) ^ [_797909, _797911] : [-(class_Groups_Ogroup__add(_797909)), _797911 = _797909, class_Groups_Ogroup__add(_797911)], (39562 ^ _779142) ^ [_1549107, _1549109, _1549111, _1549113, _1549115, _1549117, _1549119] : [hAPP(c_Fun_Ocomp(_1549107, _1549109, _1549111, _1549113), _1549115) = hAPP(c_Fun_Ocomp(_1549109, _1549109, _1549111, c_Fun_Oid(_1549109)), _1549117), -(hAPP(_1549113, hAPP(_1549115, _1549119)) = hAPP(_1549117, _1549119))], (15583 ^ _779142) ^ [_1052164, _1052166, _1052168, _1052170] : [class_Int_Onumber__ring(_1052164), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052164), hAPP(c_Int_Onumber__class_Onumber__of(_1052164), _1052166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052164), hAPP(c_Int_Onumber__class_Onumber__of(_1052164), _1052168)), _1052170)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052164), hAPP(c_Int_Onumber__class_Onumber__of(_1052164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052166), _1052168))), _1052170))], (37561 ^ _779142) ^ [_1490736, _1490738, _1490740, _1490742] : [-(hBOOL(hAPP(hAPP(c_member(_1490736), _1490738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490736, tc_HOL_Obool)), _1490740), hAPP(c_Set_OCollect(_1490736), _1490742))))), hBOOL(hAPP(hAPP(c_member(_1490736), _1490738), _1490740)), hBOOL(hAPP(_1490742, _1490738))], (10207 ^ _779142) ^ [_955220, _955222, _955224, _955226, _955228] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_955220), 10210 ^ _779142 : [(10211 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955222), _955224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955226), _955228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955222), _955228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955226), _955224)), -(_955222 = _955226), -(_955224 = _955228)], (10221 ^ _779142) ^ [] : [10222 ^ _779142 : [(10225 ^ _779142) ^ [] : [_955224 = _955228], (10223 ^ _779142) ^ [] : [_955222 = _955226]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955222), _955224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955226), _955228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955222), _955228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955220), _955226), _955224)))]]], (22745 ^ _779142) ^ [_1179877, _1179879] : [class_Int_Onumber__ring(_1179877), -(hAPP(c_Int_Onumber__class_Onumber__of(_1179877), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179879)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1179877), hAPP(c_Int_Onumber__class_Onumber__of(_1179877), _1179879)))], (34771 ^ _779142) ^ [_1423697, _1423699, _1423701, _1423703] : [class_Complete__Lattice_Ocomplete__lattice(_1423697), -(_1423699 = c_Orderings_Obot__class_Obot(tc_fun(_1423701, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423701, _1423697), _1423699), hAPP(c_COMBK(_1423697, _1423701), _1423703)) = _1423703)], (43524 ^ _779142) ^ [_1649134, _1649136] : [_1649136 = c_List_Olist_ONil(_1649134), -(hAPP(c_List_Orotate1(_1649134), _1649136) = c_List_Olist_ONil(_1649134))], (52553 ^ _779142) ^ [_1835256, _1835258] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1835256, _1835258)))], (1826 ^ _779142) ^ [_804909, _804911] : [-(class_Rings_Osemiring__0(_804909)), _804911 = _804909, class_Rings_Osemiring__0(_804911)], (16719 ^ _779142) ^ [_1073347, _1073349, _1073351] : [class_Orderings_Olinorder(_1073347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073347), _1073349)), hBOOL(hAPP(hAPP(c_member(_1073347), _1073351), _1073349)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073347), _1073351), c_Big__Operators_Olattice_OInf__fin(_1073347, c_Orderings_Oord__class_Omin(_1073347), _1073349)) = c_Big__Operators_Olattice_OInf__fin(_1073347, c_Orderings_Oord__class_Omin(_1073347), _1073349))], (37829 ^ _779142) ^ [_1498554, _1498556, _1498558, _1498560] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1498554, _1498556), _1498558), _1498560) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498554, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), _1498558), hAPP(hAPP(c_COMBS(_1498554, tc_fun(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498556, tc_HOL_Obool), tc_fun(tc_fun(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), _1498554), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), _1498560)), hAPP(hAPP(c_COMBC(_1498554, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1498556, tc_fun(tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), _1498554), c_COMBC(_1498556, tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1498556, tc_prod(_1498554, _1498556)), tc_fun(_1498556, tc_fun(tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))), _1498554), hAPP(c_COMBB(tc_prod(_1498554, _1498556), tc_fun(tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool), tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool)), _1498556), c_Set_Oinsert(tc_prod(_1498554, _1498556)))), c_Product__Type_OPair(_1498554, _1498556)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1498554, _1498556), tc_HOL_Obool))))))], (27904 ^ _779142) ^ [_1271872, _1271874, _1271876, _1271878, _1271880] : [class_Orderings_Olinorder(_1271872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271872), _1271874), _1271876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271872), _1271878), _1271880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271872), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271872), _1271874), _1271878)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271872), _1271876), _1271880))))], (43965 ^ _779142) ^ [_1658726, _1658728, _1658730, _1658732] : [class_Complete__Lattice_Ocomplete__lattice(_1658726), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658728, _1658726), hAPP(c_List_Oset(_1658728), _1658730)), _1658732) = hAPP(c_List_Ofoldl(_1658726, _1658728, hAPP(c_COMBC(_1658728, _1658726, _1658726), hAPP(hAPP(c_COMBB(_1658726, tc_fun(_1658726, _1658726), _1658728), c_Lattices_Osemilattice__inf__class_Oinf(_1658726)), _1658732)), c_Orderings_Otop__class_Otop(_1658726)), _1658730))], (23229 ^ _779142) ^ [_1188269, _1188271] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1188269), _1188271)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1188269, tc_HOL_Obool)), hAPP(c_Set_OPow(_1188269), _1188271))))], (37225 ^ _779142) ^ [_1482094, _1482096, _1482098, _1482100, _1482102] : [hBOOL(hAPP(hAPP(c_member(_1482094), hAPP(_1482096, _1482098)), _1482100)), -(hBOOL(hAPP(hAPP(c_member(_1482102), _1482098), hAPP(c_Set_Ovimage(_1482102, _1482094, _1482096), _1482100))))], (28110 ^ _779142) ^ [_1275812, _1275814, _1275816, _1275818] : [class_Orderings_Olinorder(_1275812), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275812), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275812), _1275814), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275812), _1275816), _1275818))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275812), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275812), _1275814), _1275816)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1275812), _1275814), _1275818)))))], (22741 ^ _779142) ^ [_1179799, _1179801] : [hAPP(c_Set_OPow(_1179799), _1179801) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1179799, tc_HOL_Obool), tc_HOL_Obool))], (38709 ^ _779142) ^ [_1528432, _1528434, _1528436] : [c_Wellfounded_Owf(_1528432, _1528434), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528432, _1528432)), hAPP(hAPP(c_Product__Type_OPair(_1528432, _1528432), _1528436), _1528436)), _1528434))], (45695 ^ _779142) ^ [_1697234, _1697236] : [-(hAPP(c_List_Ofilter(_1697234, _1697236), c_List_Olist_ONil(_1697234)) = c_List_Olist_ONil(_1697234))], (3202 ^ _779142) ^ [_826831, _826833, _826835, _826837, _826839, _826841] : [-(c_List_Olist_Olist__size(_826841, _826837, _826833) = c_List_Olist_Olist__size(_826839, _826835, _826831)), _826841 = _826839, _826837 = _826835, _826833 = _826831], (52323 ^ _779142) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11163 ^ _779142) ^ [_971234, _971236] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971234), _971236) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _971236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40986 ^ _779142) ^ [_1583904, _1583906, _1583908] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583904, _1583904)), hAPP(hAPP(c_Product__Type_OPair(_1583904, _1583904), _1583906), _1583906)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583904, _1583904), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583908))))], (31032 ^ _779142) ^ [_1335110, _1335112] : [class_Lattices_Oboolean__algebra(_1335110), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1335110), hAPP(c_Groups_Ouminus__class_Ouminus(_1335110), _1335112)), _1335112) = c_Orderings_Otop__class_Otop(_1335110))], (49733 ^ _779142) ^ [_1784330, _1784332, _1784334, _1784336, _1784338] : [c_Fun_Oinj__on(_1784330, _1784332, _1784334, c_Orderings_Otop__class_Otop(tc_fun(_1784330, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784332, _1784336, _1784330, hAPP(c_Fun_Ocomp(_1784330, _1784336, _1784332, _1784338), c_Hilbert__Choice_Oinv__into(_1784330, _1784332, c_Orderings_Otop__class_Otop(tc_fun(_1784330, tc_HOL_Obool)), _1784334))), _1784334) = _1784338)], (44325 ^ _779142) ^ [_1665881, _1665883, _1665885, _1665887, _1665889, _1665891] : [-(hAPP(hAPP(c_List_Ozip(_1665881, _1665883), hAPP(hAPP(c_List_Omap(_1665885, _1665881), _1665887), _1665889)), _1665891) = hAPP(hAPP(c_List_Omap(tc_prod(_1665885, _1665883), tc_prod(_1665881, _1665883)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665885, _1665883, tc_prod(_1665881, _1665883)), hAPP(hAPP(c_COMBB(_1665881, tc_fun(_1665883, tc_prod(_1665881, _1665883)), _1665885), c_Product__Type_OPair(_1665881, _1665883)), _1665887))), hAPP(hAPP(c_List_Ozip(_1665885, _1665883), _1665889), _1665891)))], (42301 ^ _779142) ^ [_1621685, _1621687, _1621689, _1621691] : [-(hAPP(hAPP(c_List_Olist__update(_1621685, hAPP(hAPP(c_List_Olist_OCons(_1621685), _1621687), _1621689)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1621691) = hAPP(hAPP(c_List_Olist_OCons(_1621685), _1621691), _1621689))], (52631 ^ _779142) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (1716 ^ _779142) ^ [_803534, _803536] : [-(class_Rings_Ocomm__semiring__1(_803534)), _803536 = _803534, class_Rings_Ocomm__semiring__1(_803536)], (5526 ^ _779142) ^ [_863611, _863613] : [_863613 = _863611, -(tc_Lazy__Sequence_Olazy__sequence(_863613) = tc_Lazy__Sequence_Olazy__sequence(_863611))], (44825 ^ _779142) ^ [_1677175] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677175)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36961 ^ _779142) ^ [_1475466, _1475468, _1475470] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475466, hAPP(hAPP(c_COMBC(_1475466, tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_fun(_1475466, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475466, tc_fun(tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_fun(_1475466, tc_HOL_Obool)), _1475466), c_COMBC(_1475466, tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475466, tc_prod(_1475466, _1475466)), tc_fun(_1475466, tc_fun(tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_HOL_Obool)), _1475466), hAPP(c_COMBB(tc_prod(_1475466, _1475466), tc_fun(tc_fun(tc_prod(_1475466, _1475466), tc_HOL_Obool), tc_HOL_Obool), _1475466), c_member(tc_prod(_1475466, _1475466)))), c_Product__Type_OPair(_1475466, _1475466)))), _1475468)), _1475470)), -(hBOOL(hAPP(hAPP(c_member(_1475466), _1475470), c_Wellfounded_Oacc(_1475466, _1475468))))], (43345 ^ _779142) ^ [_1644334, _1644336, _1644338, _1644340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644334), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644336)), _1644338))), -(hAPP(hAPP(c_List_Onth(_1644336), hAPP(hAPP(c_List_Oappend(_1644336), _1644338), _1644340)), _1644334) = hAPP(hAPP(c_List_Onth(_1644336), _1644338), _1644334))], (20794 ^ _779142) ^ [_1144641, _1144643, _1144645] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144641, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144643), _1144645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144643), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144641), _1144643), _1144645))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144641, _1144643)))], (30321 ^ _779142) ^ [_1321537, _1321539, _1321541] : [class_Lattices_Olattice(_1321537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321537), _1321539)), hBOOL(hAPP(hAPP(c_member(_1321537), _1321541), _1321539)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321537), _1321541), c_Big__Operators_Olattice__class_OInf__fin(_1321537, _1321539)) = c_Big__Operators_Olattice__class_OInf__fin(_1321537, _1321539))], (50355 ^ _779142) ^ [_1797228, _1797230, _1797232, _1797234, _1797236] : [hBOOL(hAPP(hAPP(c_member(_1797228), _1797230), _1797232)), -(hAPP(c_Quotient_OBabs(_1797228, _1797234, _1797232, _1797236), _1797230) = hAPP(_1797236, _1797230))], (34421 ^ _779142) ^ [_1412796, _1412798, _1412800, _1412802, _1412804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412796, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412798, tc_fun(_1412796, tc_HOL_Obool)), _1412800), _1412802)), _1412804)), 34424 ^ _779142 : [(34425 ^ _779142) ^ [_1412929] : [hBOOL(hAPP(hAPP(c_member(_1412798), _1412929), _1412800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412796, tc_HOL_Obool)), hAPP(_1412802, _1412929)), _1412804)))]]], (48348 ^ _779142) ^ [_1753819, _1753821, _1753823] : [-(_1753819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753821), c_List_Oreplicate(_1753821, _1753819, _1753823)) = hAPP(hAPP(c_Set_Oinsert(_1753821), _1753823), c_Orderings_Obot__class_Obot(tc_fun(_1753821, tc_HOL_Obool))))], (48074 ^ _779142) ^ [_1748066, _1748068] : [c_Wellfounded_Oacyclic(_1748066, hAPP(c_Set_OCollect(tc_prod(_1748066, _1748066)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748066, _1748066, tc_HOL_Obool), _1748068))), -(c_Wellfounded_Oacyclic(_1748066, hAPP(c_Set_OCollect(tc_prod(_1748066, _1748066)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748066, _1748066, tc_HOL_Obool), c_Predicate_Oconversep(_1748066, _1748066, _1748068)))))], (7618 ^ _779142) ^ [_905142, _905144, _905146, _905148] : [class_Orderings_Oorder(_905142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905142), _905144), _905146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905142), _905148), _905144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905142), _905148), _905146)))], (39045 ^ _779142) ^ [_1536248, _1536250, _1536252] : [c_Wellfounded_Owf(_1536248, _1536250), -(c_Wellfounded_Owf(tc_List_Olist(_1536248), hAPP(c_List_Olexn(_1536248, _1536250), _1536252)))], (10751 ^ _779142) ^ [_964925, _964927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964925)), hAPP(c_Nat_OSuc, _964927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964925), _964927)))], (7006 ^ _779142) ^ [_894182, _894184, _894186] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894182, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894182, tc_HOL_Obool)), _894184), _894186)), _894184)))], (40978 ^ _779142) ^ [_1583722, _1583724] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583722, _1583722), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583724) = c_Relation_OId(_1583722))], (23909 ^ _779142) ^ [_1200122, _1200124] : [class_Int_Onumber__ring(_1200122), class_Rings_Olinordered__idom(_1200122), 23916 ^ _779142 : [(23923 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200122), hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124)), c_Groups_Ozero__class_Ozero(_1200122)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1200122), hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124)) = hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124))], (23917 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200122), hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124)), c_Groups_Ozero__class_Ozero(_1200122))), -(hAPP(c_Groups_Oabs__class_Oabs(_1200122), hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1200122), hAPP(c_Int_Onumber__class_Onumber__of(_1200122), _1200124)))]]], (45205 ^ _779142) ^ [_1685956, _1685958, _1685960, _1685962, _1685964] : [-(c_List_Olist__all2(_1685956, _1685958, _1685960, _1685962, _1685964)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685956)), _1685962) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685958)), _1685964), 45211 ^ _779142 : [(45214 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1685960, hAPP(hAPP(c_List_Onth(_1685956), _1685962), 45210 ^ [_1685956, _1685958, _1685960, _1685962, _1685964])), hAPP(hAPP(c_List_Onth(_1685958), _1685964), 45210 ^ [_1685956, _1685958, _1685960, _1685962, _1685964])))], (45212 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45210 ^ [_1685956, _1685958, _1685960, _1685962, _1685964]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685956)), _1685962))))]]], (42026 ^ _779142) ^ [_1613680, _1613682, _1613684] : [hBOOL(hAPP(hAPP(c_member(_1613680), _1613682), hAPP(c_List_Oset(_1613680), _1613684))), -(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(_1613680)), _1613684))))], (52517 ^ _779142) ^ [_1834797, _1834799] : [-(class_Finite__Set_Ofinite(tc_sum(_1834797, _1834799))), class_Finite__Set_Ofinite(_1834797), class_Finite__Set_Ofinite(_1834799)], (18991 ^ _779142) ^ [_1112929] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1112929))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1112929) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45073 ^ _779142) ^ [_1683274, _1683276, _1683278, _1683280, _1683282, _1683284, _1683286] : [c_List_Olist__all2(_1683274, _1683276, _1683278, _1683280, _1683282), c_List_Olist__all2(_1683274, _1683276, _1683278, _1683284, _1683286), -(c_List_Olist__all2(_1683274, _1683276, _1683278, hAPP(hAPP(c_List_Oappend(_1683274), _1683280), _1683284), hAPP(hAPP(c_List_Oappend(_1683276), _1683282), _1683286)))], (6795 ^ _779142) ^ [_889570, _889572, _889574, _889576, _889578] : [c_Finite__Set_Ofolding__one(_889570, _889572, _889574), hBOOL(hAPP(c_Finite__Set_Ofinite(_889570), _889576)), 6802 ^ _779142 : [(6809 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889570, tc_HOL_Obool)), _889576), hAPP(hAPP(c_Set_Oinsert(_889570), _889578), c_Orderings_Obot__class_Obot(tc_fun(_889570, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889570, tc_HOL_Obool))), -(hAPP(_889574, hAPP(hAPP(c_Set_Oinsert(_889570), _889578), _889576)) = hAPP(hAPP(_889572, _889578), hAPP(_889574, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889570, tc_HOL_Obool)), _889576), hAPP(hAPP(c_Set_Oinsert(_889570), _889578), c_Orderings_Obot__class_Obot(tc_fun(_889570, tc_HOL_Obool)))))))], (6803 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889570, tc_HOL_Obool)), _889576), hAPP(hAPP(c_Set_Oinsert(_889570), _889578), c_Orderings_Obot__class_Obot(tc_fun(_889570, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889570, tc_HOL_Obool)), -(hAPP(_889574, hAPP(hAPP(c_Set_Oinsert(_889570), _889578), _889576)) = _889578)]]], (40390 ^ _779142) ^ [_1569454, _1569456, _1569458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569454, _1569454), tc_HOL_Obool)), _1569456), _1569458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569454, _1569454), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569454, _1569456)), c_Transitive__Closure_Ortrancl(_1569454, _1569458))))], (49252 ^ _779142) ^ [_1774934, _1774936] : [c_Relation_Osym(_1774934, _1774936), 49255 ^ _779142 : [(49256 ^ _779142) ^ [_1775040, _1775042] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774934, _1774934)), hAPP(hAPP(c_Product__Type_OPair(_1774934, _1774934), _1775042), _1775040)), _1774936)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774934, _1774934)), hAPP(hAPP(c_Product__Type_OPair(_1774934, _1774934), _1775040), _1775042)), _1774936)))]]], (9263 ^ _779142) ^ [_937169, _937171, _937173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937171), _937173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937169), _937171)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937169), _937173))))], (30944 ^ _779142) ^ [_1333523, _1333525] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333523, tc_HOL_Obool)), _1333525), c_Orderings_Otop__class_Otop(tc_fun(_1333523, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1333523, tc_HOL_Obool)))], (44932 ^ _779142) ^ [_1679867, _1679869, _1679871, _1679873] : [hBOOL(hAPP(c_List_Olistsp(_1679867, hAPP(hAPP(c_COMBS(_1679867, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1679867), c_fconj), _1679869)), _1679871)), _1679873)), 44935 ^ _779142 : [(44938 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679867, _1679871), _1679873)))], (44936 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679867, _1679869), _1679873)))]]], (32917 ^ _779142) ^ [_1380606, _1380608] : [c_Nitpick_Orefl_H(_1380606, _1380608), 32920 ^ _779142 : [(32921 ^ _779142) ^ [_1380684] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1380606, _1380606)), hAPP(hAPP(c_Product__Type_OPair(_1380606, _1380606), _1380684), _1380684)), _1380608)))]]], (5144 ^ _779142) ^ [_857588, _857590, _857592, _857594, _857596, _857598, _857600, _857602] : [-(c_Fun_Ocomp(_857602, _857598, _857594, _857590) = c_Fun_Ocomp(_857600, _857596, _857592, _857588)), _857602 = _857600, _857598 = _857596, _857594 = _857592, _857590 = _857588], (31677 ^ _779142) ^ [_1347803, _1347805] : [_1347803 = _1347805, -(c_Random_Oinc__shift(_1347803, _1347805) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (11890 ^ _779142) ^ [_984114, _984116, _984118] : [class_Groups_Oordered__comm__monoid__add(_984114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984114), _984116), c_Groups_Ozero__class_Ozero(_984114))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984114), _984118), c_Groups_Ozero__class_Ozero(_984114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984114), _984116), _984118)), c_Groups_Ozero__class_Ozero(_984114))))], (21011 ^ _779142) ^ [_1148564, _1148566, _1148568, _1148570] : [hBOOL(hAPP(hAPP(c_member(_1148564), _1148566), c_SetInterval_Oord_OatMost(_1148564, _1148568, _1148570))), -(hBOOL(hAPP(hAPP(_1148568, _1148566), _1148570)))], (36852 ^ _779142) ^ [_1473499, _1473501, _1473503, _1473505, _1473507] : [c_Fun_Oinj__on(_1473499, _1473501, _1473503, _1473505), hBOOL(hAPP(hAPP(c_member(_1473501), _1473507), hAPP(c_Set_Oimage(_1473499, _1473501, _1473503), _1473505))), -(hAPP(_1473503, hAPP(c_Fun_Othe__inv__into(_1473499, _1473501, _1473505, _1473503), _1473507)) = _1473507)], (48944 ^ _779142) ^ [_1767499, _1767501, _1767503] : [c_List_Olist__ex(_1767499, _1767501, _1767503), 48948 ^ _779142 : [(48951 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1767501, 48947 ^ [_1767499, _1767501, _1767503])))], (48949 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767499), 48947 ^ [_1767499, _1767501, _1767503]), hAPP(c_List_Oset(_1767499), _1767503))))]]], (18056 ^ _779142) ^ [_1097198, _1097200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097198)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097198), _1097200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097198), c_Int_OPls)))], (52387 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (50101 ^ _779142) ^ [_1792281, _1792283, _1792285, _1792287, _1792289] : [c_Fun_Obij__betw(_1792281, _1792283, _1792285, _1792287, _1792289), 50104 ^ _779142 : [(50111 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792283), _1792289)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792281), _1792287)))], (50105 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792281), _1792287)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792283), _1792289)))]]], (23701 ^ _779142) ^ [_1196601, _1196603] : [class_Groups_Oabs__if(_1196601), 23704 ^ _779142 : [(23711 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196601), _1196603), c_Groups_Ozero__class_Ozero(_1196601)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1196601), _1196603) = _1196603)], (23705 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196601), _1196603), c_Groups_Ozero__class_Ozero(_1196601))), -(hAPP(c_Groups_Oabs__class_Oabs(_1196601), _1196603) = hAPP(c_Groups_Ouminus__class_Ouminus(_1196601), _1196603))]]], (28460 ^ _779142) ^ [_1282248] : [class_Orderings_Oord(_1282248), -(c_Orderings_Oord__class_Omax(_1282248) = c_Orderings_Oord_Omax(_1282248, c_Orderings_Oord__class_Oless__eq(_1282248)))], (52575 ^ _779142) ^ [_1835541, _1835543] : [-(class_Enum_Oenum(tc_prod(_1835541, _1835543))), class_Enum_Oenum(_1835541), class_Enum_Oenum(_1835543)], (34959 ^ _779142) ^ [] : [-(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)))], (12445 ^ _779142) ^ [_993941, _993943, _993945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993941), _993943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993941), _993945)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993943), _993945))))], (39014 ^ _779142) ^ [_1535610, _1535612, _1535614, _1535616] : [39015 ^ _779142 : [(39016 ^ _779142) ^ [_1535664] : [hBOOL(hAPP(hAPP(_1535614, _1535616), _1535664))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1535610, _1535612, _1535614), _1535616)))], (44299 ^ _779142) ^ [_1664944, _1664946, _1664948] : [c_Fun_Oinj__on(_1664944, _1664946, _1664948, c_Orderings_Otop__class_Otop(tc_fun(_1664944, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1664944), tc_List_Olist(_1664946), hAPP(c_List_Omap(_1664944, _1664946), _1664948), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664944), tc_HOL_Obool))))], (43205 ^ _779142) ^ [_1641174, _1641176, _1641178] : [_1641174 = hAPP(hAPP(c_List_Oappend(_1641176), _1641178), _1641174), -(_1641178 = c_List_Olist_ONil(_1641176))], (11876 ^ _779142) ^ [_983859, _983861, _983863] : [class_Groups_Oordered__comm__monoid__add(_983859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983859), c_Groups_Ozero__class_Ozero(_983859)), _983861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983859), c_Groups_Ozero__class_Ozero(_983859)), _983863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983859), c_Groups_Ozero__class_Ozero(_983859)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983859), _983861), _983863))))], (21084 ^ _779142) ^ [_1149914, _1149916] : [c_Nat__Transfer_Onat__set(_1149914), c_Nat__Transfer_Onat__set(_1149916), 21091 ^ _779142 : [(21098 ^ _779142) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1149914) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1149916), -(_1149914 = _1149916)], (21092 ^ _779142) ^ [] : [_1149914 = _1149916, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1149914) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1149916))]]], (43832 ^ _779142) ^ [_1655842, _1655844, _1655846] : [-(hAPP(c_List_Orotate(_1655842, _1655844), _1655846) = hAPP(hAPP(c_List_Oappend(_1655842), hAPP(hAPP(c_List_Odrop(_1655842), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655844, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655842)), _1655846))), _1655846)), hAPP(hAPP(c_List_Otake(_1655842), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655844, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655842)), _1655846))), _1655846)))], (51759 ^ _779142) ^ [_1824397, _1824399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1824397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1824397), _1824399)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824399), _1824397))], (45945 ^ _779142) ^ [_1703452, _1703454] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1703452, _1703454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703454), _1703452))], (21732 ^ _779142) ^ [_1160794, _1160796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1160794)), -(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), _1160794), _1160796))))], (16353 ^ _779142) ^ [_1066749, _1066751, _1066753, _1066755, _1066757, _1066759] : [-(c_Nitpick_Opair__box_Opair__box__case(_1066749, _1066751, _1066753, _1066755, c_Nitpick_Opair__box_OPairBox(_1066749, _1066751, _1066757, _1066759)) = hAPP(hAPP(_1066755, _1066757), _1066759))], (43730 ^ _779142) ^ [_1653897, _1653899] : [-(_1653897 = c_List_Olist_ONil(_1653899)), -(hAPP(c_List_Orotate1(_1653899), _1653897) = hAPP(hAPP(c_List_Oappend(_1653899), hAPP(c_List_Otl(_1653899), _1653897)), hAPP(hAPP(c_List_Olist_OCons(_1653899), hAPP(c_List_Ohd(_1653899), _1653897)), c_List_Olist_ONil(_1653899))))], (52787 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))], (962 ^ _779142) ^ [_793531, _793533, _793535, _793537, _793539, _793541, _793543, _793545, _793547, _793549, _793551, _793553] : [-(c_Equiv__Relations_Ocongruent2(_793551, _793547, _793543, _793539, _793535, _793531)), c_Equiv__Relations_Ocongruent2(_793553, _793549, _793545, _793541, _793537, _793533), _793553 = _793551, _793549 = _793547, _793545 = _793543, _793541 = _793539, _793537 = _793535, _793533 = _793531], (18086 ^ _779142) ^ [_1097677, _1097679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1097677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097677), _1097679)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1097677, _1097679) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097677), _1097679))], (29061 ^ _779142) ^ [_1294181, _1294183, _1294185] : [class_Lattices_Osemilattice__inf(_1294181), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294181), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294181), _1294183), _1294185)), _1294183)))], (38977 ^ _779142) ^ [_1534485, _1534487, _1534489, _1534491] : [hBOOL(hAPP(c_Predicate_ODomainP(_1534485, _1534487, hAPP(hAPP(c_COMBC(_1534485, tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_fun(_1534487, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534487, tc_fun(tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_fun(_1534487, tc_HOL_Obool)), _1534485), c_COMBC(_1534487, tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534487, tc_prod(_1534485, _1534487)), tc_fun(_1534487, tc_fun(tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_HOL_Obool)), _1534485), hAPP(c_COMBB(tc_prod(_1534485, _1534487), tc_fun(tc_fun(tc_prod(_1534485, _1534487), tc_HOL_Obool), tc_HOL_Obool), _1534487), c_member(tc_prod(_1534485, _1534487)))), c_Product__Type_OPair(_1534485, _1534487)))), _1534489)), _1534491)), -(hBOOL(hAPP(hAPP(c_member(_1534485), _1534491), hAPP(c_Relation_ODomain(_1534485, _1534487), _1534489))))], (52361 ^ _779142) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (38546 ^ _779142) ^ [_1525243, _1525245, _1525247, _1525249, _1525251, _1525253, _1525255] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1525243, _1525245, _1525247, _1525249, _1525251), _1525253), _1525255))), 38547 ^ _779142 : [(38548 ^ _779142) ^ [_1525314] : [hBOOL(hAPP(hAPP(_1525249, _1525253), _1525314)), hBOOL(hAPP(hAPP(_1525251, _1525314), _1525255))]]], (48471 ^ _779142) ^ [_1756677, _1756679, _1756681] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756677), _1756679), _1756681)), -(hBOOL(hAPP(hAPP(c_member(_1756677), _1756681), hAPP(c_List_Oset(_1756677), _1756679))))], (31737 ^ _779142) ^ [_1348890, _1348892] : [-(hAPP(c_Finite__Set_Ocard(_1348890), _1348892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348890, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1348890), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1348892))], (43466 ^ _779142) ^ [_1647828, _1647830, _1647832, _1647834, _1647836] : [hAPP(hAPP(c_List_Odrop(_1647828), _1647830), _1647832) = hAPP(hAPP(c_List_Olist_OCons(_1647828), _1647834), _1647836), -(hAPP(hAPP(c_List_Onth(_1647828), _1647832), _1647830) = _1647834)], (28611 ^ _779142) ^ [_1284913, _1284915, _1284917] : [class_Orderings_Olinorder(_1284913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284913), _1284915)), -(c_Big__Operators_Olattice_OSup__fin(_1284913, c_Orderings_Oord__class_Omax(_1284913), hAPP(hAPP(c_Set_Oinsert(_1284913), _1284917), _1284915)) = hAPP(hAPP(c_Finite__Set_Ofold(_1284913, _1284913, c_Orderings_Oord__class_Omax(_1284913)), _1284917), _1284915))], (32075 ^ _779142) ^ [_1360562] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1360562) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1360562)))], (6047 ^ _779142) ^ [_875688] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _875688), v_U)), -(v_wt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_875688))))], (52423 ^ _779142) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (12562 ^ _779142) ^ [_996006, _996008, _996010] : [class_Groups_Oordered__comm__monoid__add(_996006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996006), c_Groups_Ozero__class_Ozero(_996006)), _996008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996006), c_Groups_Ozero__class_Ozero(_996006)), _996010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996006), c_Groups_Ozero__class_Ozero(_996006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996006), _996008), _996010))))], (19679 ^ _779142) ^ [_1124723, _1124725, _1124727] : [class_Divides_Osemiring__div(_1124723), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124723), c_Divides_Odiv__class_Omod(_1124723, _1124725, _1124727)), _1124727) = c_Groups_Ozero__class_Ozero(_1124723))], (51265 ^ _779142) ^ [_1816118, _1816120] : [51272 ^ _779142 : [(51275 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816120), _1816118))], (51273 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816118), _1816120)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816118), _1816120)), -(_1816118 = _1816120)], (43654 ^ _779142) ^ [_1652319, _1652321, _1652323, _1652325] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1652321), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652319)), hAPP(hAPP(c_List_Olist_OCons(_1652321), _1652323), _1652325)) = hAPP(hAPP(c_List_Odrop(_1652321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652319)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1652325))], (15229 ^ _779142) ^ [_1045704, _1045706, _1045708] : [class_Orderings_Olinorder(_1045704), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045704), _1045706), _1045708) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045704), _1045708), _1045706))], (52635 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (35594 ^ _779142) ^ [_1445459] : [-(hAPP(c_Relation_OField(_1445459), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1445459, _1445459), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1445459, tc_HOL_Obool)))], (19597 ^ _779142) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36840 ^ _779142) ^ [_1473263, _1473265, _1473267, _1473269] : [c_Fun_Oinj__on(_1473263, _1473265, _1473267, _1473269), -(hAPP(c_Set_Oimage(_1473265, _1473263, c_Fun_Othe__inv__into(_1473263, _1473265, _1473269, _1473267)), hAPP(c_Set_Oimage(_1473263, _1473265, _1473267), _1473269)) = _1473269)], (6472 ^ _779142) ^ [_882831, _882833, _882835, _882837] : [c_Finite__Set_Ofolding__one__idem(_882831, _882833, _882835), -(hAPP(hAPP(_882833, _882837), _882837) = _882837)], (9521 ^ _779142) ^ [_941299, _941301] : [-(_941299 = _941301), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941299), _941301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941301), _941299)))], (38715 ^ _779142) ^ [_1528550] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1528550)))], (35579 ^ _779142) ^ [_1445183, _1445185] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445183, _1445183)), hAPP(hAPP(c_Product__Type_OPair(_1445183, _1445183), 35580 ^ [_1445183, _1445185]), 35580 ^ [_1445183, _1445185])), _1445185))), -(c_Relation_Oirrefl(_1445183, _1445185))], (35460 ^ _779142) ^ [_1441735, _1441737, _1441739, _1441741, _1441743, _1441745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1441735, _1441737), tc_HOL_Obool)), _1441739), _1441741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441735, tc_HOL_Obool)), _1441743), _1441745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441737, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1441735, _1441737, _1441739), _1441743)), hAPP(c_Relation_OImage(_1441735, _1441737, _1441741), _1441745))))], (31991 ^ _779142) ^ [_1358368, _1358370, _1358372, _1358374] : [_1358368 = c_Orderings_Obot__class_Obot(tc_fun(_1358370, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1358370, _1358372, hAPP(c_COMBK(_1358372, _1358370), _1358374)), _1358368) = c_Orderings_Obot__class_Obot(tc_fun(_1358372, tc_HOL_Obool)))], (34308 ^ _779142) ^ [_1409178, _1409180, _1409182, _1409184] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409178, tc_fun(_1409180, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1409178, tc_HOL_Obool), _1409182)), _1409184) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1409178, tc_HOL_Obool), tc_fun(_1409180, tc_HOL_Obool)), _1409182), hAPP(hAPP(c_COMBC(tc_fun(_1409178, tc_HOL_Obool), tc_fun(_1409178, tc_fun(_1409180, tc_HOL_Obool)), tc_fun(_1409180, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409178, tc_fun(_1409180, tc_HOL_Obool))), _1409184)))], (44357 ^ _779142) ^ [_1666758, _1666760, _1666762, _1666764, _1666766] : [hAPP(hAPP(c_List_Omap(_1666758, _1666760), _1666762), _1666764) = hAPP(hAPP(c_List_Omap(_1666758, _1666760), _1666766), _1666764), 44360 ^ _779142 : [(44361 ^ _779142) ^ [_1666881] : [hBOOL(hAPP(hAPP(c_member(_1666758), _1666881), hAPP(c_List_Oset(_1666758), _1666764))), -(hAPP(_1666762, _1666881) = hAPP(_1666766, _1666881))]]], (26262 ^ _779142) ^ [_1241036] : [-(_1241036 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 26265 ^ _779142 : [(26272 ^ _779142) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1241036, 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, _1241036) = 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), _1241036), 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)))], (26266 ^ _779142) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1241036, 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, _1241036) = 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), _1241036), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (10121 ^ _779142) ^ [_953079, _953081, _953083, _953085] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953079), _953081)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953083), _953081)), _953085)) = 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), _953079), _953083)), _953081)), _953085))], (19677 ^ _779142) ^ [_1124694] : [-(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)), _1124694)) = _1124694)], (46732 ^ _779142) ^ [_1718861, _1718863, _1718865, _1718867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718861), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718863)), _1718865))), -(hAPP(c_List_Orev(_1718863), hAPP(hAPP(c_List_Olist__update(_1718863, _1718865), _1718861), _1718867)) = hAPP(hAPP(c_List_Olist__update(_1718863, hAPP(c_List_Orev(_1718863), _1718865)), 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(_1718863)), _1718865)), _1718861)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718867))], (48050 ^ _779142) ^ [_1747485, _1747487, _1747489] : [-(hAPP(c_New__DSequence_Oneg__single(_1747485, _1747487), _1747489) = c_Lazy__Sequence_Ohb__single(_1747485, _1747487))], (48058 ^ _779142) ^ [_1747690, _1747692, _1747694, _1747696, _1747698] : [-(c_List_Osplice(_1747690, hAPP(hAPP(c_List_Olist_OCons(_1747690), _1747692), _1747694), hAPP(hAPP(c_List_Olist_OCons(_1747690), _1747696), _1747698)) = hAPP(hAPP(c_List_Olist_OCons(_1747690), _1747692), hAPP(hAPP(c_List_Olist_OCons(_1747690), _1747696), c_List_Osplice(_1747690, _1747694, _1747698))))], (29789 ^ _779142) ^ [_1310347, _1310349, _1310351, _1310353, _1310355] : [c_Finite__Set_Ofolding__one(_1310347, _1310349, _1310351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310347), _1310353)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310347), _1310355)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310347, tc_HOL_Obool)), _1310353), _1310355) = c_Orderings_Obot__class_Obot(tc_fun(_1310347, tc_HOL_Obool))), -(hAPP(hAPP(_1310349, hAPP(_1310351, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310347, tc_HOL_Obool)), _1310353), _1310355))), hAPP(_1310351, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310347, tc_HOL_Obool)), _1310353), _1310355))) = hAPP(hAPP(_1310349, hAPP(_1310351, _1310353)), hAPP(_1310351, _1310355)))], (31424 ^ _779142) ^ [_1342700, _1342702, _1342704] : [class_Complete__Lattice_Ocomplete__lattice(_1342700), -(c_Complete__Lattice_OInf__class_OInf(_1342700, hAPP(hAPP(c_Set_Oinsert(_1342700), _1342702), _1342704)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1342700), _1342702), c_Complete__Lattice_OInf__class_OInf(_1342700, _1342704)))], (15861 ^ _779142) ^ [_1057348, _1057350, _1057352, _1057354] : [class_Fields_Olinordered__field__inverse__zero(_1057348), class_Int_Onumber(_1057348), 15868 ^ _779142 : [(15869 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1057348), _1057350), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))), _1057354)), 15872 ^ _779142 : [(15879 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)))), 15882 ^ _779142 : [(15889 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)), c_Groups_Ozero__class_Ozero(_1057348)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), _1057354)))], (15883 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)), c_Groups_Ozero__class_Ozero(_1057348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057348), _1057354), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))), _1057350)))]]], (15873 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), _1057350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057348), _1057354), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)))))]]], (15895 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1057348), _1057350), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))), _1057354))), 15898 ^ _779142 : [(15901 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), _1057350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057348), _1057354), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))))], (15899 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))))]], 15902 ^ _779142 : [(15905 ^ _779142) ^ [] : [15906 ^ _779142 : [(15909 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057348), _1057354), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352))), _1057350))], (15907 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)), c_Groups_Ozero__class_Ozero(_1057348))))]], 15910 ^ _779142 : [(15913 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), _1057354))], (15911 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)), c_Groups_Ozero__class_Ozero(_1057348)))]]], (15903 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057348), c_Groups_Ozero__class_Ozero(_1057348)), hAPP(c_Int_Onumber__class_Onumber__of(_1057348), _1057352)))]]]]], (48715 ^ _779142) ^ [_1762242, _1762244, _1762246] : [-(c_Random__Sequence_Oempty(_1762242, _1762244, _1762246) = 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(_1762242)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1762242)))], (25654 ^ _779142) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (30858 ^ _779142) ^ [_1332111, _1332113] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1332111, _1332113)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1332111, _1332113), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1332113), c_Orderings_Otop__class_Otop(tc_fun(_1332113, tc_HOL_Obool)))))], (38621 ^ _779142) ^ [_1526929, _1526931] : [c_Wellfounded_Owf(_1526929, _1526931), -(c_Wellfounded_Owf(_1526929, hAPP(hAPP(c_Relation_Orel__comp(_1526929, _1526929, _1526929), _1526931), _1526931)))], (27724 ^ _779142) ^ [_1268586] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1268586), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1268586)], (11918 ^ _779142) ^ [_984638, _984640, _984642, _984644] : [class_Rings_Olinordered__ring__strict(_984638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984638), _984640), _984642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984638), _984644), c_Groups_Ozero__class_Ozero(_984638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984638), _984642), _984644)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984638), _984640), _984644))))], (48751 ^ _779142) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (23819 ^ _779142) ^ [_1198724, _1198726] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1198724), _1198726), hAPP(c_Int_Onumber__class_Onumber__of(_1198724), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1198724), _1198726)), class_Fields_Ofield__inverse__zero(_1198724), class_Int_Onumber__ring(_1198724)], (43644 ^ _779142) ^ [_1652072, _1652074, _1652076, _1652078] : [-(hAPP(c_List_Orotate1(_1652072), c_List_Olist_ONil(_1652072)) = c_List_Olist_ONil(_1652072))], (52249 ^ _779142) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (40285 ^ _779142) ^ [_1566131, _1566133] : [-(c_Transitive__Closure_Otrancl(_1566131, _1566133) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566131, _1566131), tc_HOL_Obool)), _1566133), hAPP(hAPP(c_Relation_Orel__comp(_1566131, _1566131, _1566131), c_Transitive__Closure_Otrancl(_1566131, _1566133)), _1566133)))], (38222 ^ _779142) ^ [_1514534, _1514536] : [-(c_Product__Type_Oapfst(_1514534, _1514534, _1514536, c_Fun_Oid(_1514534)) = c_Fun_Oid(tc_prod(_1514534, _1514536)))], (1606 ^ _779142) ^ [_802159, _802161] : [-(class_Rings_Oordered__cancel__semiring(_802159)), _802161 = _802159, class_Rings_Oordered__cancel__semiring(_802161)], (35517 ^ _779142) ^ [_1443364, _1443366, _1443368, _1443370, _1443372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1443368, _1443364)), hAPP(hAPP(c_Product__Type_OPair(_1443368, _1443364), _1443372), _1443366)), _1443370)), -(hBOOL(hAPP(hAPP(c_member(_1443364), _1443366), hAPP(c_Relation_OImage(_1443368, _1443364, _1443370), hAPP(hAPP(c_Set_Oinsert(_1443368), _1443372), c_Orderings_Obot__class_Obot(tc_fun(_1443368, tc_HOL_Obool)))))))], (40186 ^ _779142) ^ [_1563789, _1563791] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563789, _1563789)), hAPP(hAPP(c_Product__Type_OPair(_1563789, _1563789), 40187 ^ [_1563789, _1563791]), 40187 ^ [_1563789, _1563791])), c_Transitive__Closure_Otrancl(_1563789, _1563791)))), -(c_Wellfounded_Oacyclic(_1563789, _1563791))], (29677 ^ _779142) ^ [_1307665, _1307667, _1307669, _1307671, _1307673] : [class_Groups_Ocomm__monoid__add(_1307665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307667), _1307669)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307667), _1307671)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1307665), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1307667, _1307665), _1307673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307667, tc_HOL_Obool)), _1307669), _1307671))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1307667, _1307665), _1307673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307667, tc_HOL_Obool)), _1307669), _1307671))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1307665), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1307667, _1307665), _1307673), _1307669)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1307667, _1307665), _1307673), _1307671)))], (16237 ^ _779142) ^ [_1064474, _1064476, _1064478, _1064480] : [class_Fields_Olinordered__field__inverse__zero(_1064474), class_Int_Onumber(_1064474), 16244 ^ _779142 : [(16245 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1064474), _1064478), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)))), 16248 ^ _779142 : [(16255 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), c_Groups_Ozero__class_Ozero(_1064474)), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)))), 16258 ^ _779142 : [(16265 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)), c_Groups_Ozero__class_Ozero(_1064474)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064476), c_Groups_Ozero__class_Ozero(_1064474))))], (16259 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)), c_Groups_Ozero__class_Ozero(_1064474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064474), _1064476), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)))))]]], (16249 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), c_Groups_Ozero__class_Ozero(_1064474)), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064474), _1064476), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))), _1064478)))]]], (16271 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1064474), _1064478), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))))), 16274 ^ _779142 : [(16277 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064474), _1064476), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))), _1064478))], (16275 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), c_Groups_Ozero__class_Ozero(_1064474)), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))))]], 16278 ^ _779142 : [(16281 ^ _779142) ^ [] : [16282 ^ _779142 : [(16285 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064474), _1064476), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480))))], (16283 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)), c_Groups_Ozero__class_Ozero(_1064474))))]], 16286 ^ _779142 : [(16289 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064474), _1064476), c_Groups_Ozero__class_Ozero(_1064474)))], (16287 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)), c_Groups_Ozero__class_Ozero(_1064474)))]]], (16279 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064474), c_Groups_Ozero__class_Ozero(_1064474)), hAPP(c_Int_Onumber__class_Onumber__of(_1064474), _1064480)))]]]]], (8424 ^ _779142) ^ [_919951, _919953, _919955, _919957, _919959] : [class_Groups_Ocomm__monoid__add(_919951), class_Groups_Oordered__cancel__ab__semigroup__add(_919951), hBOOL(hAPP(c_Finite__Set_Ofinite(_919953), _919955)), -(_919955 = c_Orderings_Obot__class_Obot(tc_fun(_919953, tc_HOL_Obool))), 8442 ^ _779142 : [(8445 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919951), hAPP(_919957, 8441 ^ [_919951, _919953, _919955, _919957, _919959])), hAPP(_919959, 8441 ^ [_919951, _919953, _919955, _919957, _919959])))], (8443 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919953), 8441 ^ [_919951, _919953, _919955, _919957, _919959]), _919955)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919951), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_919953, _919951), _919957), _919955)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_919953, _919951), _919959), _919955))))], (13265 ^ _779142) ^ [_1009171, _1009173] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009171), hAPP(c_Nat_OSuc, _1009173)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009171), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1009173))], (812 ^ _779142) ^ [_791306, _791308, _791310, _791312] : [-(c_Relation_Osym(_791310, _791306)), c_Relation_Osym(_791312, _791308), _791312 = _791310, _791308 = _791306], (38410 ^ _779142) ^ [_1520007, _1520009, _1520011] : [-(hAPP(c_Relation_ORange(_1520007, _1520009), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1520007, _1520009), tc_HOL_Obool), _1520011)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1520007, _1520009), tc_HOL_Obool), tc_fun(_1520009, tc_HOL_Obool)), _1520011), c_Relation_ORange(_1520007, _1520009)))], (52379 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (42179 ^ _779142) ^ [_1619114, _1619116] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1619114, _1619116) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619114), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619116), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (444 ^ _779142) ^ [_785816, _785818] : [-(class_Rings_Oinverse(_785816)), _785818 = _785816, class_Rings_Oinverse(_785818)], (3610 ^ _779142) ^ [_833195, _833197, _833199, _833201] : [-(c_List_Obutlast(_833201, _833197) = c_List_Obutlast(_833199, _833195)), _833201 = _833199, _833197 = _833195], (22839 ^ _779142) ^ [_1181370] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181370)) = _1181370)], (23101 ^ _779142) ^ [_1185781, _1185783, _1185785] : [class_Groups_Oab__group__add(_1185781), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1185781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185781), _1185783), _1185785)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185781), hAPP(c_Groups_Ouminus__class_Ouminus(_1185781), _1185783)), hAPP(c_Groups_Ouminus__class_Ouminus(_1185781), _1185785)))], (50655 ^ _779142) ^ [_1805074, _1805076, _1805078, _1805080] : [class_Rings_Oidom(_1805074), 50658 ^ _779142 : [(50659 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805074), _1805076), _1805078)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805074), _1805076), _1805080))), -(_1805076 = c_Groups_Ozero__class_Ozero(_1805074)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805074), _1805078), _1805080)))], (50669 ^ _779142) ^ [] : [50670 ^ _779142 : [(50673 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805074), _1805078), _1805080))], (50671 ^ _779142) ^ [] : [_1805076 = c_Groups_Ozero__class_Ozero(_1805074)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805074), _1805076), _1805078)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805074), _1805076), _1805080))))]]], (17893 ^ _779142) ^ [_1094367, _1094369] : [class_Rings_Oring__1(_1094367), -(hBOOL(hAPP(hAPP(c_member(_1094367), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094367), _1094369)), c_Int_Oring__1__class_OInts(_1094367))))], (17805 ^ _779142) ^ [_1092905] : [class_Rings_Osemiring__1(_1092905), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092905), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1092905))], (40833 ^ _779142) ^ [_1580158, _1580160, _1580162] : [hAPP(hAPP(c_Relation_Orel__comp(_1580158, _1580158, _1580158), hAPP(c_Relation_Oconverse(_1580158, _1580158), _1580160)), _1580160) = _1580160, hAPP(c_Relation_ODomain(_1580158, _1580158), _1580160) = _1580162, -(c_Equiv__Relations_Oequiv(_1580158, _1580162, _1580160))], (3390 ^ _779142) ^ [_829697, _829699, _829701, _829703, _829705, _829707, _829709, _829711] : [-(c_List_Olist_Olist__case(_829711, _829707, _829703, _829699) = c_List_Olist_Olist__case(_829709, _829705, _829701, _829697)), _829711 = _829709, _829707 = _829705, _829703 = _829701, _829699 = _829697], (25512 ^ _779142) ^ [_1227521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1227521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1227521))))], (52155 ^ _779142) ^ [_1831209, _1831211] : [class_Lattices_Oboolean__algebra(_1831209), -(class_Lattices_Oboolean__algebra(tc_fun(_1831211, _1831209)))], (42590 ^ _779142) ^ [_1628279, _1628281, _1628283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628279), tc_List_Olist(_1628279))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628279), tc_List_Olist(_1628279)), c_List_Olist_ONil(_1628279)), _1628281)), c_List_Olistrel(_1628279, _1628283))), -(_1628281 = c_List_Olist_ONil(_1628279))], (43766 ^ _779142) ^ [_1654513, _1654515, _1654517, _1654519] : [-(hAPP(c_List_Orotate(_1654513, _1654515), hAPP(c_List_Orotate(_1654513, _1654517), _1654519)) = hAPP(c_List_Orotate(_1654513, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654515), _1654517)), _1654519))], (15621 ^ _779142) ^ [_1053065] : [class_Orderings_Olinorder(_1053065), -(c_Finite__Set_Ofun__left__comm__idem(_1053065, _1053065, c_Orderings_Oord__class_Omin(_1053065)))], (48656 ^ _779142) ^ [_1760931, _1760933, _1760935] : [c_List_Olist__all(tc_Int_Oint, _1760931, c_List_Oupto(_1760933, _1760935)), -(c_List_Oall__interval__int(_1760931, _1760933, _1760935))], (48332 ^ _779142) ^ [_1753538, _1753540, _1753542] : [-(hAPP(hAPP(c_List_Oappend(_1753538), c_List_Oreplicate(_1753538, _1753540, _1753542)), hAPP(hAPP(c_List_Olist_OCons(_1753538), _1753542), c_List_Olist_ONil(_1753538))) = hAPP(hAPP(c_List_Olist_OCons(_1753538), _1753542), c_List_Oreplicate(_1753538, _1753540, _1753542)))], (52419 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (21035 ^ _779142) ^ [_1149054, _1149056, _1149058, _1149060] : [hBOOL(hAPP(hAPP(c_member(_1149054), _1149056), c_SetInterval_Oord_OlessThan(_1149054, _1149058, _1149060))), -(hBOOL(hAPP(hAPP(_1149058, _1149056), _1149060)))], (49580 ^ _779142) ^ [_1780876, _1780878, _1780880] : [c_Fun_Oinj__on(_1780876, _1780878, _1780880, c_Orderings_Otop__class_Otop(tc_fun(_1780876, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780878, _1780876, _1780876, c_Hilbert__Choice_Oinv__into(_1780876, _1780878, c_Orderings_Otop__class_Otop(tc_fun(_1780876, tc_HOL_Obool)), _1780880)), _1780880) = c_Fun_Oid(_1780876))], (39488 ^ _779142) ^ [_1547328, _1547330] : [39489 ^ _779142 : [(39490 ^ _779142) ^ [_1547374] : [hBOOL(hAPP(_1547328, _1547374))]], -(hBOOL(hAPP(_1547328, c_Hilbert__Choice_OEps(_1547330, _1547328))))], (122 ^ _779142) ^ [_780909, _780911, _780913, _780915, _780917, _780919, _780921, _780923, _780925, _780927, _780929, _780931] : [-(c_Finite__Set_Ofolding__image__simple__idem(_780929, _780925, _780921, _780917, _780913, _780909)), c_Finite__Set_Ofolding__image__simple__idem(_780931, _780927, _780923, _780919, _780915, _780911), _780931 = _780929, _780927 = _780925, _780923 = _780921, _780919 = _780917, _780915 = _780913, _780911 = _780909], (17449 ^ _779142) ^ [_1086282, _1086284, _1086286, _1086288, _1086290, _1086292] : [class_Divides_Osemiring__div(_1086282), c_Divides_Odiv__class_Omod(_1086282, _1086284, _1086286) = c_Divides_Odiv__class_Omod(_1086282, _1086288, _1086286), c_Divides_Odiv__class_Omod(_1086282, _1086290, _1086286) = c_Divides_Odiv__class_Omod(_1086282, _1086292, _1086286), -(c_Divides_Odiv__class_Omod(_1086282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086282), _1086284), _1086290), _1086286) = c_Divides_Odiv__class_Omod(_1086282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086282), _1086288), _1086292), _1086286))], (5426 ^ _779142) ^ [_862165, _862167] : [_862167 = _862165, -(c_Int_Onumber__class_Onumber__of(_862167) = c_Int_Onumber__class_Onumber__of(_862165))], (34087 ^ _779142) ^ [_1404193, _1404195, _1404197] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404193, tc_HOL_Obool), tc_fun(_1404193, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404193, tc_HOL_Obool), tc_fun(_1404193, tc_HOL_Obool)), _1404195), _1404197)), c_Wellfounded_Ofinite__psubset(_1404193)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1404193, tc_HOL_Obool)), _1404195), _1404197)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404193), _1404197))], (35724 ^ _779142) ^ [] : [-(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))], (24958 ^ _779142) ^ [_1217894, _1217896] : [class_Int_Onumber__ring(_1217894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217894), _1217896), hAPP(c_Int_Onumber__class_Onumber__of(_1217894), c_Int_OBit1(c_Int_OPls))) = _1217896)], (48923 ^ _779142) ^ [_1766985, _1766987] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1766985, tc_HOL_Obool), _1766987) = hAPP(c_Set_OCollect(_1766985), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766985, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1766985), c_HOL_OEx(tc_fun(_1766985, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766985, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1766985, tc_HOL_Obool), tc_HOL_Obool), _1766985), hAPP(c_COMBS(tc_fun(_1766985, 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(_1766985, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1766985, tc_HOL_Obool), tc_fun(tc_fun(_1766985, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1766985, tc_HOL_Obool))), _1766987)))), c_member(_1766985)))))], (12242 ^ _779142) ^ [_990583] : [class_Rings_Olinordered__semidom(_990583), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990583), c_Groups_Ozero__class_Ozero(_990583)), c_Groups_Oone__class_Oone(_990583))))], (17294 ^ _779142) ^ [_1083506, _1083508, _1083510] : [class_Orderings_Olinorder(_1083506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083506), _1083508)), 17304 ^ _779142 : [(17307 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083506), _1083510), 17303 ^ [_1083506, _1083508, _1083510]))], (17305 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083506), 17303 ^ [_1083506, _1083508, _1083510]), _1083508)))]], hBOOL(hAPP(hAPP(c_member(_1083506), _1083510), _1083508)), -(c_Big__Operators_Olinorder__class_OMin(_1083506, _1083508) = _1083510)], (51017 ^ _779142) ^ [_1811799, _1811801, _1811803] : [class_Rings_Ocomm__ring__1(_1811799), 51020 ^ _779142 : [(51027 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811799), _1811801), _1811803)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811799), _1811801), hAPP(c_Groups_Ouminus__class_Ouminus(_1811799), _1811803))))], (51021 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811799), _1811801), hAPP(c_Groups_Ouminus__class_Ouminus(_1811799), _1811803))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811799), _1811801), _1811803)))]]], (10189 ^ _779142) ^ [_954825, _954827, _954829, _954831] : [class_Rings_Ocomm__semiring__1(_954825), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954825), _954827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954825), _954829), _954831)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954825), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954825), _954827), _954829)), _954831))], (9163 ^ _779142) ^ [_935171, _935173, _935175] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_935171), _935173)), 9166 ^ _779142 : [(9173 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_935171), _935175), _935173))), -(hAPP(c_Finite__Set_Ocard(_935171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935171, tc_HOL_Obool)), _935173), hAPP(hAPP(c_Set_Oinsert(_935171), _935175), c_Orderings_Obot__class_Obot(tc_fun(_935171, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_935171), _935173))], (9167 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_935171), _935175), _935173)), -(hAPP(c_Finite__Set_Ocard(_935171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935171, tc_HOL_Obool)), _935173), hAPP(hAPP(c_Set_Oinsert(_935171), _935175), c_Orderings_Obot__class_Obot(tc_fun(_935171, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_935171), _935173)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (24071 ^ _779142) ^ [_1202893, _1202895, _1202897] : [hBOOL(hAPP(hAPP(c_member(_1202893), _1202895), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1202893, tc_HOL_Obool)), _1202897))), hBOOL(hAPP(hAPP(c_member(_1202893), _1202895), _1202897))], (38651 ^ _779142) ^ [_1527387, _1527389] : [-(c_Relation_Orefl__on(_1527387, _1527389, c_Relation_OId__on(_1527387, _1527389)))], (12996 ^ _779142) ^ [_1004159, _1004161, _1004163] : [12997 ^ _779142 : [(13000 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004161), _1004163))], (12998 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004159)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004159), _1004161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004159), _1004163))))], (5200 ^ _779142) ^ [_858480, _858482] : [_858482 = _858480, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858482) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858480))], (14645 ^ _779142) ^ [_1034707, _1034709, _1034711, _1034713] : [class_Fields_Ofield__inverse__zero(_1034707), -(_1034709 = c_Groups_Ozero__class_Ozero(_1034707)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034707), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034707), _1034711), _1034709)), _1034713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034707), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034707), _1034711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034707), _1034713), _1034709))), _1034709))], (41138 ^ _779142) ^ [_1587817, _1587819, _1587821, _1587823, _1587825] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587817, _1587817)), hAPP(hAPP(c_Product__Type_OPair(_1587817, _1587817), _1587819), _1587821)), c_Transitive__Closure_Ortrancl(_1587817, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587817, _1587817), tc_HOL_Obool)), _1587823), _1587825)))), 41144 ^ _779142 : [(41150 ^ _779142) ^ [] : [41146 ^ [_1587817, _1587819, _1587821, _1587823, _1587825] = 41143 ^ [_1587817, _1587819, _1587821, _1587823, _1587825]], (41148 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587817, _1587817)), hAPP(hAPP(c_Product__Type_OPair(_1587817, _1587817), 41146 ^ [_1587817, _1587819, _1587821, _1587823, _1587825]), 41143 ^ [_1587817, _1587819, _1587821, _1587823, _1587825])), _1587825)))], (41145 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587817, _1587817)), hAPP(hAPP(c_Product__Type_OPair(_1587817, _1587817), 41143 ^ [_1587817, _1587819, _1587821, _1587823, _1587825]), _1587821)), c_Transitive__Closure_Ortrancl(_1587817, _1587823))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587817, _1587817)), hAPP(hAPP(c_Product__Type_OPair(_1587817, _1587817), _1587819), _1587821)), c_Transitive__Closure_Ortrancl(_1587817, _1587823))))], (3242 ^ _779142) ^ [_827435, _827437] : [_827437 = _827435, -(c_Lazy__Sequence_Ohb__not__seq(_827437) = c_Lazy__Sequence_Ohb__not__seq(_827435))], (2082 ^ _779142) ^ [_809393, _809395, _809397, _809399] : [-(c_Int_Onat__aux(_809399, _809395) = c_Int_Onat__aux(_809397, _809393)), _809399 = _809397, _809395 = _809393], (50493 ^ _779142) ^ [_1802171, _1802173, _1802175] : [50495 ^ _779142 : [(50498 ^ _779142) ^ [] : [hBOOL(hAPP(_1802171, 50494 ^ [_1802171, _1802173, _1802175]))], (50496 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50494 ^ [_1802171, _1802173, _1802175]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802173), _1802175))))]], -(c_List_Oall__interval__nat(_1802171, _1802173, _1802175))], (27560 ^ _779142) ^ [_1265470, _1265472, _1265474] : [class_Lattices_Olattice(_1265470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265470), _1265472)), -(_1265474 = c_Orderings_Obot__class_Obot(tc_fun(_1265470, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265470, tc_HOL_Obool)), _1265474), _1265472)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265470), c_Big__Operators_Olattice__class_OSup__fin(_1265470, _1265474)), c_Big__Operators_Olattice__class_OSup__fin(_1265470, _1265472)) = c_Big__Operators_Olattice__class_OSup__fin(_1265470, _1265472))], (13163 ^ _779142) ^ [_1007368, _1007370] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1007368), _1007370)))), -(_1007370 = c_Orderings_Obot__class_Obot(tc_fun(_1007368, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007368), _1007370))], (4844 ^ _779142) ^ [_852890, _852892, _852894, _852896] : [-(c_Hilbert__Choice_OEps(_852896, _852892) = c_Hilbert__Choice_OEps(_852894, _852890)), _852896 = _852894, _852892 = _852890], (33089 ^ _779142) ^ [_1384661, _1384663, _1384665, _1384667, _1384669, _1384671] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384661, _1384663, _1384665), _1384667), hAPP(hAPP(c_Product__Type_OPair(_1384661, _1384663), _1384669), _1384671)) = hAPP(hAPP(_1384667, _1384669), _1384671))], (17781 ^ _779142) ^ [_1092478] : [class_Int_Onumber__ring(_1092478), -(c_Groups_Ozero__class_Ozero(_1092478) = hAPP(c_Int_Onumber__class_Onumber__of(_1092478), c_Int_OPls))], (11430 ^ _779142) ^ [_975763, _975765] : [class_Groups_Olinordered__ab__group__add(_975763), 11433 ^ _779142 : [(11440 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975763), _975765), c_Groups_Ozero__class_Ozero(_975763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975763), _975765), _975765)), c_Groups_Ozero__class_Ozero(_975763))))], (11434 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975763), _975765), _975765)), c_Groups_Ozero__class_Ozero(_975763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975763), _975765), c_Groups_Ozero__class_Ozero(_975763))))]]], (35005 ^ _779142) ^ [_1429447, _1429449, _1429451, _1429453, _1429455] : [_1429447 = c_Orderings_Obot__class_Obot(tc_fun(_1429449, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429451, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429449, tc_fun(_1429451, tc_HOL_Obool)), _1429447), _1429453)), _1429455) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429451, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1429451, tc_HOL_Obool))), _1429455))], (10119 ^ _779142) ^ [_953042, _953044] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953042), _953044) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953044), _953042))], (38438 ^ _779142) ^ [_1520795, _1520797, _1520799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1520795, _1520797)), _1520799)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520797), hAPP(c_Relation_ORange(_1520795, _1520797), _1520799))))], (30091 ^ _779142) ^ [_1316397, _1316399, _1316401] : [class_Orderings_Olinorder(_1316397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316397), _1316399)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316397), _1316401)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316397, tc_HOL_Obool)), _1316399), _1316401) = c_Orderings_Obot__class_Obot(tc_fun(_1316397, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316397), c_Big__Operators_Olattice_OSup__fin(_1316397, c_Orderings_Oord__class_Omax(_1316397), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316397, tc_HOL_Obool)), _1316399), _1316401))), c_Big__Operators_Olattice_OSup__fin(_1316397, c_Orderings_Oord__class_Omax(_1316397), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316397, tc_HOL_Obool)), _1316399), _1316401))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316397), c_Big__Operators_Olattice_OSup__fin(_1316397, c_Orderings_Oord__class_Omax(_1316397), _1316399)), c_Big__Operators_Olattice_OSup__fin(_1316397, c_Orderings_Oord__class_Omax(_1316397), _1316401)))], (38613 ^ _779142) ^ [_1526737, _1526739] : [-(c_Wellfounded_Owf(_1526737, hAPP(c_Wellfounded_Omeasure(_1526737), _1526739)))], (37881 ^ _779142) ^ [_1500425, _1500427, _1500429, _1500431, _1500433, _1500435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500425), _1500427)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500429), _1500431)), 37891 ^ _779142 : [(37894 ^ _779142) ^ [] : [hAPP(c_Finite__Set_Ocard(_1500425), hAPP(c_Set_OCollect(_1500425), hAPP(hAPP(c_COMBS(_1500425, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500425), c_fconj), hAPP(hAPP(c_COMBC(_1500425, tc_fun(_1500425, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500425)), _1500427))), hAPP(hAPP(c_COMBC(_1500425, _1500429, tc_HOL_Obool), _1500433), 37890 ^ [_1500425, _1500427, _1500429, _1500431, _1500433, _1500435])))) = _1500435], (37892 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500429), 37890 ^ [_1500425, _1500427, _1500429, _1500431, _1500433, _1500435]), _1500431)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500425, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1500429, tc_HOL_Obool), tc_Nat_Onat, _1500425), c_Finite__Set_Ocard(_1500429)), hAPP(hAPP(c_COMBB(tc_fun(_1500429, tc_HOL_Obool), tc_fun(_1500429, tc_HOL_Obool), _1500425), c_Set_OCollect(_1500429)), hAPP(hAPP(c_COMBB(tc_fun(_1500429, tc_HOL_Obool), tc_fun(_1500429, tc_HOL_Obool), _1500425), hAPP(c_COMBS(_1500429, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500429), c_fconj), hAPP(hAPP(c_COMBC(_1500429, tc_fun(_1500429, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500429)), _1500431)))), _1500433)))), _1500427) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1500435), hAPP(c_Finite__Set_Ocard(_1500429), _1500431)))], (18664 ^ _779142) ^ [_1107656] : [-(c_Int_Opred(_1107656) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1107656), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37507 ^ _779142) ^ [_1489057, _1489059, _1489061] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489057, _1489059), c_Orderings_Obot__class_Obot(tc_fun(_1489057, tc_HOL_Obool))), _1489061) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489057, _1489059), tc_HOL_Obool)))], (3724 ^ _779142) ^ [_834954, _834956, _834958, _834960, _834962, _834964, _834966, _834968] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_834968, _834964, _834960, _834956) = c_New__Random__Sequence_Opos__not__random__dseq(_834966, _834962, _834958, _834954)), _834968 = _834966, _834964 = _834962, _834960 = _834958, _834956 = _834954], (15559 ^ _779142) ^ [_1051576, _1051578, _1051580, _1051582] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1051576), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051576), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1051576), _1051578), _1051580)), _1051582) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1051576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051576), _1051578), _1051582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051576), _1051580), _1051582)))], (3094 ^ _779142) ^ [_825103, _825105, _825107, _825109] : [-(c_Big__Operators_Olattice__class_OSup__fin(_825109, _825105) = c_Big__Operators_Olattice__class_OSup__fin(_825107, _825103)), _825109 = _825107, _825105 = _825103], (35549 ^ _779142) ^ [_1444241, _1444243, _1444245, _1444247] : [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), _1444241), _1444243)), 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), _1444245), _1444247)), 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), _1444241), _1444247)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444245), _1444243))))], (46756 ^ _779142) ^ [_1719397, _1719399, _1719401] : [class_Orderings_Olinorder(_1719397), c_List_Olinorder__class_Osorted(_1719397, hAPP(c_List_Orev(_1719397), _1719399)), 46763 ^ _779142 : [(46770 ^ _779142) ^ [] : [-(_1719399 = c_List_Olist_ONil(_1719397)), -(c_List_Ofoldr(_1719397, _1719397, c_Orderings_Oord__class_Omax(_1719397), _1719399, _1719401) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1719397), hAPP(hAPP(c_List_Onth(_1719397), _1719399), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1719401))], (46764 ^ _779142) ^ [] : [_1719399 = c_List_Olist_ONil(_1719397), -(c_List_Ofoldr(_1719397, _1719397, c_Orderings_Oord__class_Omax(_1719397), _1719399, _1719401) = _1719401)]]], (5750 ^ _779142) ^ [_870175, _870177, _870179, _870181] : [_870175 = _870177, hBOOL(hAPP(hAPP(c_member(_870179), _870177), _870181)), -(hBOOL(hAPP(hAPP(c_member(_870179), _870175), _870181)))], (52113 ^ _779142) ^ [_1830656, _1830658] : [class_Lattices_Obounded__lattice(_1830656), -(class_Lattices_Obounded__lattice(tc_fun(_1830658, _1830656)))], (4818 ^ _779142) ^ [_852507, _852509, _852511, _852513] : [-(c_Relation_Oconverse(_852513, _852509) = c_Relation_Oconverse(_852511, _852507)), _852513 = _852511, _852509 = _852507], (6327 ^ _779142) ^ [_880534, _880536, _880538, _880540] : [class_Orderings_Oorder(_880534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880534), _880536), _880538)), _880536 = _880540, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880534), _880540), _880538)))], (38953 ^ _779142) ^ [_1533959, _1533961, _1533963, _1533965] : [c_Wellfounded_Owf(_1533959, _1533961), c_Fun_Oinj__on(_1533959, _1533963, _1533965, c_Orderings_Otop__class_Otop(tc_fun(_1533959, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1533963, hAPP(c_Set_Oimage(tc_prod(_1533959, _1533959), tc_prod(_1533963, _1533963), c_Product__Type_Omap__pair(_1533959, _1533963, _1533959, _1533963, _1533965, _1533965)), _1533961)))], (51775 ^ _779142) ^ [_1824667, _1824669] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824667), _1824669)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824667), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824669))))], (32353 ^ _779142) ^ [_1368504] : [-(c_Finite__Set_Ofun__left__comm__idem(_1368504, tc_fun(_1368504, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1368504, tc_HOL_Obool), tc_fun(tc_fun(_1368504, tc_HOL_Obool), tc_fun(_1368504, tc_HOL_Obool)), _1368504), hAPP(c_COMBC(tc_fun(_1368504, tc_HOL_Obool), tc_fun(_1368504, tc_HOL_Obool), tc_fun(_1368504, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1368504, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1368504, tc_fun(_1368504, tc_HOL_Obool), tc_fun(_1368504, tc_HOL_Obool)), c_Set_Oinsert(_1368504)), c_Orderings_Obot__class_Obot(tc_fun(_1368504, tc_HOL_Obool))))))], (16955 ^ _779142) ^ [_1077382, _1077384, _1077386] : [class_Orderings_Olinorder(_1077382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077382), _1077384)), -(hBOOL(hAPP(hAPP(c_member(_1077382), _1077386), _1077384))), -(_1077384 = c_Orderings_Obot__class_Obot(tc_fun(_1077382, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1077382, hAPP(hAPP(c_Set_Oinsert(_1077382), _1077386), _1077384)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1077382), _1077386), c_Big__Operators_Olinorder__class_OMin(_1077382, _1077384)))], (52351 ^ _779142) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (28262 ^ _779142) ^ [_1278590, _1278592, _1278594] : [class_Complete__Lattice_Ocomplete__lattice(_1278590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278590), _1278592)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278590), _1278594), c_Complete__Lattice_OSup__class_OSup(_1278590, _1278592)) = hAPP(hAPP(c_Finite__Set_Ofold(_1278590, _1278590, c_Lattices_Osemilattice__sup__class_Osup(_1278590)), _1278594), _1278592))], (38444 ^ _779142) ^ [_1520908, _1520910, _1520912] : [-(hAPP(c_Set_Oimage(tc_prod(_1520908, _1520910), _1520910, c_Product__Type_Osnd(_1520908, _1520910)), _1520912) = hAPP(c_Relation_ORange(_1520908, _1520910), _1520912))], (26080 ^ _779142) ^ [_1237331, _1237333, _1237335] : [class_Rings_Olinordered__idom(_1237331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237331), c_Groups_Ozero__class_Ozero(_1237331)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237331), hAPP(hAPP(c_Power_Opower__class_Opower(_1237331), _1237333), 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(_1237331), _1237335), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (48485 ^ _779142) ^ [_1756955] : [-(c_List_Omember(_1756955) = c_List_Oset(_1756955))], (25230 ^ _779142) ^ [_1222551, _1222553] : [class_Int_Onumber__ring(_1222551), class_Rings_Olinordered__idom(_1222551), 25237 ^ _779142 : [(25244 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1222553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222551), c_Groups_Oone__class_Oone(_1222551)), hAPP(c_Int_Onumber__class_Onumber__of(_1222551), _1222553))))], (25238 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222551), c_Groups_Oone__class_Oone(_1222551)), hAPP(c_Int_Onumber__class_Onumber__of(_1222551), _1222553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1222553)))]]], (25764 ^ _779142) ^ [_1231933, _1231935] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1231933)), c_Int_OBit1(_1231935)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1231933)), _1231935)))], (7066 ^ _779142) ^ [_895673, _895675, _895677, _895679, _895681] : [c_Finite__Set_Ofolding__one__idem(_895673, _895675, _895677), hBOOL(hAPP(c_Finite__Set_Ofinite(_895673), _895679)), -(hAPP(_895677, hAPP(hAPP(c_Set_Oinsert(_895673), _895681), _895679)) = hAPP(hAPP(c_Finite__Set_Ofold(_895673, _895673, _895675), _895681), _895679))], (52347 ^ _779142) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (33869 ^ _779142) ^ [_1399455, _1399457, _1399459, _1399461, _1399463] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399455, _1399457, _1399459), _1399461), _1399463) = hAPP(hAPP(_1399461, hAPP(c_Product__Type_Ofst(_1399455, _1399457), _1399463)), hAPP(c_Product__Type_Osnd(_1399455, _1399457), _1399463)))], (46646 ^ _779142) ^ [_1717053, _1717055, _1717057, _1717059, _1717061] : [c_List_Olist__all2(_1717053, _1717055, _1717057, _1717059, _1717061), -(c_List_Olist__all2(_1717053, _1717055, _1717057, hAPP(c_List_Orev(_1717053), _1717059), hAPP(c_List_Orev(_1717055), _1717061)))], (31098 ^ _779142) ^ [_1336510, _1336512] : [class_Groups_Oordered__ab__group__add(_1336510), -(hAPP(c_Set_Oimage(_1336510, _1336510, c_Groups_Ouminus__class_Ouminus(_1336510)), hAPP(c_SetInterval_Oord__class_OatLeast(_1336510), _1336512)) = hAPP(c_SetInterval_Oord__class_OatMost(_1336510), hAPP(c_Groups_Ouminus__class_Ouminus(_1336510), _1336512)))], (16479 ^ _779142) ^ [_1069296, _1069298] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069296), _1069298))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069296), _1069298)), -(_1069296 = _1069298)], (30335 ^ _779142) ^ [_1321772, _1321774] : [class_Lattices_Olattice(_1321772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321772), _1321774)), -(c_Big__Operators_Olattice__class_OInf__fin(_1321772, _1321774) = hAPP(c_Finite__Set_Ofold1(_1321772, c_Lattices_Osemilattice__inf__class_Oinf(_1321772)), _1321774))], (37319 ^ _779142) ^ [_1484304, _1484306, _1484308, _1484310, _1484312, _1484314] : [hBOOL(hAPP(hAPP(c_member(_1484304), _1484306), _1484308)), 37322 ^ _779142 : [(37329 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484304), _1484310), _1484308))), -(hAPP(c_Set_Ovimage(_1484312, _1484304, hAPP(hAPP(c_COMBC(_1484312, _1484304, _1484304), hAPP(hAPP(c_COMBC(_1484312, _1484304, tc_fun(_1484304, _1484304)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484304, tc_fun(_1484304, _1484304)), _1484312), c_If(_1484304)), hAPP(hAPP(c_COMBC(_1484312, tc_fun(_1484312, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484312)), _1484314))), _1484306)), _1484310)), _1484308) = _1484314)], (37323 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484304), _1484310), _1484308)), -(hAPP(c_Set_Ovimage(_1484312, _1484304, hAPP(hAPP(c_COMBC(_1484312, _1484304, _1484304), hAPP(hAPP(c_COMBC(_1484312, _1484304, tc_fun(_1484304, _1484304)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484304, tc_fun(_1484304, _1484304)), _1484312), c_If(_1484304)), hAPP(hAPP(c_COMBC(_1484312, tc_fun(_1484312, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484312)), _1484314))), _1484306)), _1484310)), _1484308) = c_Orderings_Otop__class_Otop(tc_fun(_1484312, tc_HOL_Obool)))]]], (39098 ^ _779142) ^ [_1537501, _1537503] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1537501, _1537503), 39099 ^ [_1537501, _1537503])), -(c_Wellfounded_OwfP(_1537501, _1537503))], (46292 ^ _779142) ^ [_1709673, _1709675, _1709677, _1709679, _1709681] : [class_Orderings_Olinorder(_1709673), -(c_List_Olinorder__class_Osorted(_1709673, hAPP(hAPP(c_List_Omap(_1709675, _1709673), _1709677), hAPP(c_List_Ofilter(_1709675, hAPP(hAPP(c_COMBC(_1709675, _1709673, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1709673, tc_fun(_1709673, tc_HOL_Obool), _1709675), c_fequal), _1709677)), hAPP(_1709679, _1709681))), _1709681))))], (52299 ^ _779142) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (48048 ^ _779142) ^ [_1747368, _1747370, _1747372, _1747374, _1747376, _1747378, _1747380] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1747368, _1747370, _1747372, _1747374), _1747376), _1747378), _1747380) = c_New__DSequence_Opos__bind(_1747368, _1747370, hAPP(hAPP(hAPP(_1747372, _1747376), _1747378), _1747380), hAPP(hAPP(c_COMBC(_1747368, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747370))), hAPP(hAPP(c_COMBC(_1747368, 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(_1747370)))), hAPP(hAPP(c_COMBC(_1747368, 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(_1747370))))), _1747374), _1747376)), _1747378)), _1747380)))], (23223 ^ _779142) ^ [_1188164, _1188166] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1188164, tc_HOL_Obool)), hAPP(c_Set_OPow(_1188164), _1188166))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1188164), _1188166)))], (36868 ^ _779142) ^ [_1473807, _1473809, _1473811, _1473813, _1473815] : [c_Typedef_Otype__definition(_1473807, _1473809, _1473811, _1473813, _1473815), -(hAPP(c_Set_Oimage(_1473809, _1473807, _1473813), _1473815) = c_Orderings_Otop__class_Otop(tc_fun(_1473807, tc_HOL_Obool)))], (8250 ^ _779142) ^ [_916462, _916464, _916466, _916468] : [class_Groups_Oab__semigroup__mult(_916462), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916462), _916464), _916466)), _916468) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916462), _916464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916462), _916466), _916468)))], (46935 ^ _779142) ^ [_1723036] : [-(c_List_Oembed__list(_1723036) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1723036))], (42708 ^ _779142) ^ [_1630274, _1630276] : [c_Orderings_Obot__class_Obot(tc_fun(_1630274, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630274), _1630276), -(_1630276 = c_List_Olist_ONil(_1630274))], (21552 ^ _779142) ^ [_1157735, _1157737] : [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), _1157735)), _1157737))), _1157735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1157737 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35316 ^ _779142) ^ [_1437066] : [-(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)), _1437066), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (25308 ^ _779142) ^ [_1223846, _1223848] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1223846))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223848)) = 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)))), _1223846), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223848)))], (22981 ^ _779142) ^ [_1183774, _1183776] : [class_Groups_Ogroup__add(_1183774), 22984 ^ _779142 : [(22991 ^ _779142) ^ [] : [_1183776 = c_Groups_Ozero__class_Ozero(_1183774), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1183774), _1183776) = c_Groups_Ozero__class_Ozero(_1183774))], (22985 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1183774), _1183776) = c_Groups_Ozero__class_Ozero(_1183774), -(_1183776 = c_Groups_Ozero__class_Ozero(_1183774))]]], (37535 ^ _779142) ^ [_1489798, _1489800, _1489802] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489798, _1489800), _1489802), hAPP(c_COMBK(tc_fun(_1489800, tc_HOL_Obool), _1489798), c_Orderings_Obot__class_Obot(tc_fun(_1489800, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489798, _1489800), tc_HOL_Obool)))], (38412 ^ _779142) ^ [_1520088, _1520090, _1520092] : [hAPP(c_Relation_ORange(_1520088, _1520090), _1520092) = c_Orderings_Obot__class_Obot(tc_fun(_1520090, tc_HOL_Obool)), -(_1520092 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520088, _1520090), tc_HOL_Obool)))], (45871 ^ _779142) ^ [_1702260, _1702262] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702260), _1702262))), -(c_List_Oupt(_1702260, hAPP(c_Nat_OSuc, _1702262)) = c_List_Olist_ONil(tc_Nat_Onat))], (29399 ^ _779142) ^ [_1301286, _1301288, _1301290, _1301292] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301286, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301286, tc_HOL_Obool)), _1301288), _1301290)), _1301292) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301286, tc_HOL_Obool)), _1301288), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301286, tc_HOL_Obool)), _1301290), _1301292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301286, tc_HOL_Obool)), _1301292), _1301288)))], (45620 ^ _779142) ^ [_1695282, _1695284, _1695286] : [-(c_Enum_On__lists(_1695282, hAPP(c_Nat_OSuc, _1695284), _1695286) = c_List_Oconcat(tc_List_Olist(_1695282), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695282), tc_List_Olist(tc_List_Olist(_1695282))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695282), tc_List_Olist(_1695282), tc_List_Olist(tc_List_Olist(_1695282))), hAPP(hAPP(c_COMBB(tc_fun(_1695282, tc_List_Olist(_1695282)), tc_fun(tc_List_Olist(_1695282), tc_List_Olist(tc_List_Olist(_1695282))), tc_List_Olist(_1695282)), c_List_Omap(_1695282, tc_List_Olist(_1695282))), hAPP(c_COMBC(_1695282, tc_List_Olist(_1695282), tc_List_Olist(_1695282)), c_List_Olist_OCons(_1695282)))), _1695286)), c_Enum_On__lists(_1695282, _1695284, _1695286))))], (16621 ^ _779142) ^ [_1071721, _1071723, _1071725, _1071727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071721), _1071723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071725), _1071727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071721), _1071725)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071723), _1071727))))], (29857 ^ _779142) ^ [_1311854, _1311856, _1311858, _1311860, _1311862] : [class_Groups_Ocomm__monoid__mult(_1311854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311856), _1311858)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311856), _1311860)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311856, tc_HOL_Obool)), _1311858), _1311860) = c_Orderings_Obot__class_Obot(tc_fun(_1311856, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311856, _1311854), _1311862), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311856, tc_HOL_Obool)), _1311858), _1311860)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311854), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311856, _1311854), _1311862), _1311858)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311856, _1311854), _1311862), _1311860)))], (22897 ^ _779142) ^ [_1182341, _1182343, _1182345] : [class_Groups_Oordered__ab__group__add(_1182341), 22900 ^ _779142 : [(22907 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182341), hAPP(c_Groups_Ouminus__class_Ouminus(_1182341), _1182345)), _1182343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182341), hAPP(c_Groups_Ouminus__class_Ouminus(_1182341), _1182343)), _1182345)))], (22901 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182341), hAPP(c_Groups_Ouminus__class_Ouminus(_1182341), _1182343)), _1182345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182341), hAPP(c_Groups_Ouminus__class_Ouminus(_1182341), _1182345)), _1182343)))]]], (41485 ^ _779142) ^ [_1598563, _1598565] : [-(c_List_Olistrel1(_1598563, hAPP(c_Relation_Oconverse(_1598563, _1598563), _1598565)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1598563), tc_List_Olist(_1598563)), c_List_Olistrel1(_1598563, _1598565)))], (44811 ^ _779142) ^ [] : [-(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))))], (40998 ^ _779142) ^ [_1584275, _1584277, _1584279, _1584281, _1584283, _1584285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584275, _1584275)), hAPP(hAPP(c_Product__Type_OPair(_1584275, _1584275), _1584277), _1584279)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584275, _1584275), tc_HOL_Obool), _1584281), _1584283))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584275, _1584275)), hAPP(hAPP(c_Product__Type_OPair(_1584275, _1584275), _1584279), _1584285)), _1584283)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584275, _1584275)), hAPP(hAPP(c_Product__Type_OPair(_1584275, _1584275), _1584277), _1584285)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584275, _1584275), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1584281)), _1584283))))], (27450 ^ _779142) ^ [_1263569, _1263571, _1263573] : [class_Lattices_Olattice(_1263569), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263569), _1263571)), hBOOL(hAPP(hAPP(c_member(_1263569), _1263573), _1263571)), 27461 ^ _779142 : [(27468 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1263569, tc_HOL_Obool)), _1263571), hAPP(hAPP(c_Set_Oinsert(_1263569), _1263573), c_Orderings_Obot__class_Obot(tc_fun(_1263569, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1263569, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1263569, _1263571) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263569), _1263573), c_Big__Operators_Olattice__class_OSup__fin(_1263569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1263569, tc_HOL_Obool)), _1263571), hAPP(hAPP(c_Set_Oinsert(_1263569), _1263573), c_Orderings_Obot__class_Obot(tc_fun(_1263569, tc_HOL_Obool)))))))], (27462 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1263569, tc_HOL_Obool)), _1263571), hAPP(hAPP(c_Set_Oinsert(_1263569), _1263573), c_Orderings_Obot__class_Obot(tc_fun(_1263569, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1263569, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1263569, _1263571) = _1263573)]]], (44458 ^ _779142) ^ [_1669330, _1669332, _1669334, _1669336, _1669338] : [-(hAPP(hAPP(c_List_Odrop(_1669330), _1669332), hAPP(hAPP(c_List_Omap(_1669334, _1669330), _1669336), _1669338)) = hAPP(hAPP(c_List_Omap(_1669334, _1669330), _1669336), hAPP(hAPP(c_List_Odrop(_1669334), _1669332), _1669338)))], (52331 ^ _779142) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (48284 ^ _779142) ^ [_1752684, _1752686] : [-(c_List_Oconcat(_1752684, c_List_Oreplicate(tc_List_Olist(_1752684), _1752686, c_List_Olist_ONil(_1752684))) = c_List_Olist_ONil(_1752684))], (11193 ^ _779142) ^ [_971671] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971671) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16471 ^ _779142) ^ [_1069169, _1069171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069169), _1069171)), 16474 ^ _779142 : [(16477 ^ _779142) ^ [] : [_1069169 = _1069171], (16475 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069169), _1069171)))]]], (38657 ^ _779142) ^ [_1527478, _1527480] : [c_Wellfounded_Owf(_1527478, _1527480), -(c_Wellfounded_Owf(tc_fun(_1527478, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1527478, _1527480)))], (37539 ^ _779142) ^ [_1489948, _1489950, _1489952] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1489948, _1489950), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1489948, _1489950), c_Orderings_Otop__class_Otop(tc_fun(_1489948, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1489950, tc_HOL_Obool), _1489948), _1489952))) = hAPP(hAPP(c_Product__Type_OSigma(_1489948, _1489950), c_Orderings_Otop__class_Otop(tc_fun(_1489948, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1489950, tc_HOL_Obool), _1489948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1489950, tc_HOL_Obool)), _1489952))))], (39560 ^ _779142) ^ [_1549012, _1549014, _1549016, _1549018, _1549020, _1549022, _1549024, _1549026, _1549028, _1549030] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1549012, _1549014), tc_prod(_1549016, _1549018), tc_prod(_1549020, _1549022), c_Product__Type_Omap__pair(_1549012, _1549016, _1549014, _1549018, _1549024, _1549026)), c_Product__Type_Omap__pair(_1549020, _1549012, _1549022, _1549014, _1549028, _1549030)) = c_Product__Type_Omap__pair(_1549020, _1549016, _1549022, _1549018, hAPP(c_Fun_Ocomp(_1549012, _1549016, _1549020, _1549024), _1549028), hAPP(c_Fun_Ocomp(_1549014, _1549018, _1549022, _1549026), _1549030)))], (46168 ^ _779142) ^ [_1707547, _1707549, _1707551, _1707553] : [class_Orderings_Olinorder(_1707547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707547), _1707549), _1707551)), c_List_Olinorder__class_Osorted(_1707547, hAPP(hAPP(c_List_Olist_OCons(_1707547), _1707551), _1707553)), -(c_List_Olinorder__class_Osorted(_1707547, hAPP(hAPP(c_List_Olist_OCons(_1707547), _1707549), hAPP(hAPP(c_List_Olist_OCons(_1707547), _1707551), _1707553))))], (1986 ^ _779142) ^ [_807755, _807757] : [_807757 = _807755, -(c_Com_Obody(_807757) = c_Com_Obody(_807755))], (34164 ^ _779142) ^ [_1405989, _1405991, _1405993, _1405995, _1405997, _1405999] : [hAPP(_1405995, hAPP(c_Product__Type_Ofst(_1405989, _1405993), _1405997)) = hAPP(_1405999, hAPP(c_Product__Type_Ofst(_1405989, _1405993), _1405997)), -(hAPP(c_Product__Type_Oapfst(_1405989, _1405991, _1405993, _1405995), _1405997) = hAPP(c_Product__Type_Oapfst(_1405989, _1405991, _1405993, _1405999), _1405997))], (29450 ^ _779142) ^ [_1302791, _1302793, _1302795] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302791, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302791, tc_HOL_Obool)), _1302793), _1302795)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302791, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302791, tc_HOL_Obool)), _1302793)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1302791, tc_HOL_Obool)), _1302795)))], (34358 ^ _779142) ^ [_1411012, _1411014, _1411016, _1411018, _1411020] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411012, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411014, tc_fun(_1411012, tc_HOL_Obool)), _1411016), _1411018)), _1411020) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411014, tc_fun(_1411012, tc_HOL_Obool)), _1411016), hAPP(hAPP(c_COMBC(_1411014, tc_fun(_1411012, tc_HOL_Obool), tc_fun(_1411012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411012, tc_HOL_Obool), tc_fun(tc_fun(_1411012, tc_HOL_Obool), tc_fun(_1411012, tc_HOL_Obool)), _1411014), c_Groups_Ominus__class_Ominus(tc_fun(_1411012, tc_HOL_Obool))), _1411018)), _1411020)))], (50933 ^ _779142) ^ [_1810338, _1810340] : [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)))), _1810338, _1810340) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810338), _1810340)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810340), _1810338)))], (24546 ^ _779142) ^ [_1210925, _1210927] : [class_Int_Onumber__ring(_1210925), 24549 ^ _779142 : [(24556 ^ _779142) ^ [] : [c_Int_Oiszero(_1210925, hAPP(c_Int_Onumber__class_Onumber__of(_1210925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1210927), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1210925), _1210927) = c_Groups_Oone__class_Oone(_1210925))], (24550 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1210925), _1210927) = c_Groups_Oone__class_Oone(_1210925), -(c_Int_Oiszero(_1210925, hAPP(c_Int_Onumber__class_Onumber__of(_1210925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1210927), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (47768 ^ _779142) ^ [_1741611, _1741613, _1741615] : [-(hBOOL(hAPP(hAPP(c_member(_1741611), _1741613), hAPP(c_List_Oset(_1741611), _1741615)))), 47769 ^ _779142 : [(47770 ^ _779142) ^ [_1741700, _1741702] : [_1741615 = hAPP(hAPP(c_List_Oappend(_1741611), _1741702), hAPP(hAPP(c_List_Olist_OCons(_1741611), _1741613), _1741700)), -(hBOOL(hAPP(hAPP(c_member(_1741611), _1741613), hAPP(c_List_Oset(_1741611), _1741700))))]]], (41587 ^ _779142) ^ [_1601792, _1601794, _1601796] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601792), tc_List_Olist(_1601792))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601792), tc_List_Olist(_1601792)), _1601794), _1601794)), c_List_Olistrel(_1601792, c_Transitive__Closure_Ortrancl(_1601792, _1601796)))))], (12730 ^ _779142) ^ [_999140, _999142, _999144, _999146, _999148] : [class_Rings_Olinordered__semiring__strict(_999140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999140), _999142), _999144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999140), _999146), _999148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999140), c_Groups_Ozero__class_Ozero(_999140)), _999142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999140), c_Groups_Ozero__class_Ozero(_999140)), _999146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999140), _999142), _999146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999140), _999144), _999148))))], (9647 ^ _779142) ^ [_943326, _943328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943326), _943328))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943326), _943328)), -(_943326 = _943328)], (39308 ^ _779142) ^ [_1542843, _1542845, _1542847, _1542849] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1542843, tc_fun(_1542845, tc_HOL_Obool)), _1542847), _1542849) = hAPP(c_Set_OCollect(_1542845), hAPP(hAPP(c_COMBB(tc_fun(_1542843, tc_HOL_Obool), tc_HOL_Obool, _1542845), c_HOL_OAll(_1542843)), hAPP(hAPP(c_COMBB(tc_fun(_1542843, tc_HOL_Obool), tc_fun(_1542843, tc_HOL_Obool), _1542845), hAPP(c_COMBS(_1542843, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542843), c_fimplies), hAPP(hAPP(c_COMBC(_1542843, tc_fun(_1542843, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542843)), _1542847)))), hAPP(hAPP(c_COMBC(_1542845, tc_fun(_1542843, tc_fun(_1542845, tc_HOL_Obool)), tc_fun(_1542843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542845, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542843, tc_fun(_1542845, tc_HOL_Obool)), tc_fun(_1542843, tc_HOL_Obool)), _1542845), c_COMBB(tc_fun(_1542845, tc_HOL_Obool), tc_HOL_Obool, _1542843)), c_member(_1542845))), _1542849)))))], (31793 ^ _779142) ^ [_1351331, _1351333, _1351335] : [class_Groups_Ocomm__monoid__mult(_1351331), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351333, _1351331), hAPP(c_COMBK(_1351331, _1351333), c_Groups_Oone__class_Oone(_1351331))), _1351335) = c_Groups_Oone__class_Oone(_1351331))], (43578 ^ _779142) ^ [_1650404, _1650406, _1650408, _1650410] : [_1650404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1650406), _1650404), hAPP(hAPP(c_List_Olist_OCons(_1650406), _1650408), _1650410)) = hAPP(hAPP(c_List_Olist_OCons(_1650406), _1650408), _1650410))], (18923 ^ _779142) ^ [_1112043] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1112043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112043)))], (40334 ^ _779142) ^ [_1568036, _1568038] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568036, _1568036), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1568036, _1568038)), c_Relation_OId(_1568036)) = c_Transitive__Closure_Ortrancl(_1568036, _1568038))], (35531 ^ _779142) ^ [] : [-(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))))))], (46102 ^ _779142) ^ [_1706608, _1706610, _1706612] : [class_Orderings_Olinorder(_1706608), c_List_Olinorder__class_Osorted(_1706608, _1706610), -(c_List_Olinorder__class_Osorted(_1706608, hAPP(hAPP(c_List_Otake(_1706608), _1706612), _1706610)))], (28991 ^ _779142) ^ [_1292973, _1292975, _1292977, _1292979] : [class_Lattices_Osemilattice__inf(_1292973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292973), _1292975), _1292977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292973), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1292973), _1292979), _1292975)), _1292977)))], (33718 ^ _779142) ^ [_1396355, _1396357, _1396359, _1396361, _1396363] : [-(hAPP(c_Product__Type_Osnd(_1396355, _1396357), hAPP(c_Product__Type_Oapsnd(_1396359, _1396357, _1396355, _1396361), _1396363)) = hAPP(_1396361, hAPP(c_Product__Type_Osnd(_1396355, _1396359), _1396363)))], (5638 ^ _779142) ^ [_865299, _865301, _865303, _865305] : [-(tc_fun(_865305, _865301) = tc_fun(_865303, _865299)), _865305 = _865303, _865301 = _865299], (7890 ^ _779142) ^ [_909135, _909137, _909139] : [class_Orderings_Olinorder(_909135), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909135), _909137), _909139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909135), _909139), _909137)))], (17557 ^ _779142) ^ [_1088523, _1088525, _1088527] : [class_Divides_Osemiring__div(_1088523), -(c_Divides_Odiv__class_Omod(_1088523, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088523), _1088525), _1088527), _1088525) = c_Groups_Ozero__class_Ozero(_1088523))], (24189 ^ _779142) ^ [_1205041, _1205043] : [class_Rings_Osemiring__1(_1205041), 24192 ^ _779142 : [(24199 ^ _779142) ^ [] : [_1205043 = c_Groups_Ozero__class_Ozero(_1205041), -(c_Int_Oiszero(_1205041, _1205043))], (24193 ^ _779142) ^ [] : [c_Int_Oiszero(_1205041, _1205043), -(_1205043 = c_Groups_Ozero__class_Ozero(_1205041))]]], (17265 ^ _779142) ^ [_1082973, _1082975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082973), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082973)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082975)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1596 ^ _779142) ^ [_802034, _802036] : [-(class_Groups_Ocancel__ab__semigroup__add(_802034)), _802036 = _802034, class_Groups_Ocancel__ab__semigroup__add(_802036)], (45827 ^ _779142) ^ [_1701065, _1701067, _1701069, _1701071, _1701073, _1701075] : [-(c_List_Ofoldr(_1701065, _1701067, _1701069, hAPP(hAPP(c_List_Oappend(_1701065), _1701071), _1701073), _1701075) = c_List_Ofoldr(_1701065, _1701067, _1701069, _1701071, c_List_Ofoldr(_1701065, _1701067, _1701069, _1701073, _1701075)))], (37906 ^ _779142) ^ [_1501331, _1501333] : [-(c_Fun_Oinj__on(tc_fun(_1501331, _1501333), tc_fun(tc_prod(_1501331, _1501333), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1501331, _1501333), tc_HOL_Obool), tc_fun(tc_prod(_1501331, _1501333), tc_HOL_Obool), tc_fun(_1501331, _1501333)), c_Set_OCollect(tc_prod(_1501331, _1501333))), hAPP(hAPP(c_COMBB(tc_fun(_1501331, tc_fun(_1501333, tc_HOL_Obool)), tc_fun(tc_prod(_1501331, _1501333), tc_HOL_Obool), tc_fun(_1501331, _1501333)), c_Product__Type_Oprod_Oprod__case(_1501331, _1501333, tc_HOL_Obool)), hAPP(c_COMBB(_1501333, tc_fun(_1501333, tc_HOL_Obool), _1501331), hAPP(c_COMBC(_1501333, _1501333, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1501331, _1501333), tc_HOL_Obool))))], (13267 ^ _779142) ^ [_1009217] : [-(hAPP(c_Nat_OSuc, _1009217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1009217), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (28827 ^ _779142) ^ [_1289585, _1289587, _1289589] : [class_Lattices_Olattice(_1289585), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289585), _1289587), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289585), _1289587), _1289589)) = _1289587)], (35203 ^ _779142) ^ [_1434734, _1434736, _1434738, _1434740, _1434742, _1434744, _1434746] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434734, tc_fun(_1434736, tc_fun(_1434738, tc_HOL_Obool))), _1434740), _1434742), _1434744), _1434746))), 35204 ^ _779142 : [(35205 ^ _779142) ^ [_1434819] : [hBOOL(hAPP(hAPP(c_member(_1434734), _1434819), _1434740)), hBOOL(hAPP(hAPP(hAPP(_1434742, _1434819), _1434744), _1434746))]]], (9749 ^ _779142) ^ [_944959, _944961, _944963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944959), _944961)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944961), _944963)), _944959) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944961), _944959)), _944963))], (24866 ^ _779142) ^ [_1216350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216350), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1216350)), c_Int_OMin)))], (37043 ^ _779142) ^ [_1477711, _1477713, _1477715] : [37045 ^ _779142 : [(37048 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1477711), 37044 ^ [_1477711, _1477713, _1477715]), c_Wellfounded_Oacc(_1477711, _1477715)))], (37046 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477711, _1477711)), hAPP(hAPP(c_Product__Type_OPair(_1477711, _1477711), 37044 ^ [_1477711, _1477713, _1477715]), _1477713)), _1477715)))]], -(hBOOL(hAPP(hAPP(c_member(_1477711), _1477713), c_Wellfounded_Oacc(_1477711, _1477715))))], (52629 ^ _779142) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (42104 ^ _779142) ^ [_1617053, _1617055, _1617057, _1617059, _1617061, _1617063] : [-(hAPP(hAPP(c_List_Ozip(_1617053, _1617055), hAPP(hAPP(c_List_Olist_OCons(_1617053), _1617057), _1617059)), hAPP(hAPP(c_List_Olist_OCons(_1617055), _1617061), _1617063)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1617053, _1617055)), hAPP(hAPP(c_Product__Type_OPair(_1617053, _1617055), _1617057), _1617061)), hAPP(hAPP(c_List_Ozip(_1617053, _1617055), _1617059), _1617063)))], (21047 ^ _779142) ^ [_1149299, _1149301, _1149303, _1149305] : [hBOOL(hAPP(hAPP(c_member(_1149299), _1149301), c_SetInterval_Oord_OgreaterThan(_1149299, _1149303, _1149305))), -(hBOOL(hAPP(hAPP(_1149303, _1149305), _1149301)))], (3454 ^ _779142) ^ [_830687, _830689, _830691, _830693, _830695, _830697] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830697, _830693, _830689) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830695, _830691, _830687)), _830697 = _830695, _830693 = _830691, _830689 = _830687], (29825 ^ _779142) ^ [_1311098, _1311100, _1311102, _1311104, _1311106] : [class_Groups_Oab__group__add(_1311098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311100), _1311102)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311100), _1311104)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311100, _1311098), _1311106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311100, tc_HOL_Obool)), _1311102), _1311104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1311098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311098), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311100, _1311098), _1311106), _1311102)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311100, _1311098), _1311106), _1311104))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311100, _1311098), _1311106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311100, tc_HOL_Obool)), _1311102), _1311104))))], (21466 ^ _779142) ^ [_1156374] : [c_Nat__Transfer_Ois__nat(_1156374), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156374)))], (20554 ^ _779142) ^ [_1140010, _1140012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140010)), 20557 ^ _779142 : [(20564 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140010), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1140010)), _1140012)))], (20558 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1140010)), _1140012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140010), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140012))))]]], (21300 ^ _779142) ^ [_1153531, _1153533, _1153535] : [class_Rings_Ocomm__semiring__1(_1153531), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153531), hAPP(hAPP(c_Power_Opower__class_Opower(_1153531), _1153533), _1153535)), _1153533) = hAPP(hAPP(c_Power_Opower__class_Opower(_1153531), _1153533), hAPP(c_Nat_OSuc, _1153535)))], (45809 ^ _779142) ^ [_1700450, _1700452] : [-(c_Random_Oselect__weight(_1700450, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700450), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700450, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700450, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700450)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700452)) = c_Random_Oselect__weight(_1700450, _1700452))], (12363 ^ _779142) ^ [_992525, _992527] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_992525), _992527))), -(hAPP(c_Finite__Set_Ocard(_992525), _992527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44827 ^ _779142) ^ [_1677206] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1677206)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1677206))], (14904 ^ _779142) ^ [_1039663] : [class_Rings_Oring__1(_1039663), -(hBOOL(hAPP(hAPP(c_member(_1039663), c_Groups_Ozero__class_Ozero(_1039663)), c_Int_Oring__1__class_OInts(_1039663))))], (24840 ^ _779142) ^ [_1215912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1215912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1215912))))], (33875 ^ _779142) ^ [_1399586, _1399588, _1399590, _1399592, _1399594] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399586, _1399588, _1399590), _1399592), _1399594) = hAPP(hAPP(_1399592, hAPP(c_Product__Type_Ofst(_1399586, _1399588), _1399594)), hAPP(c_Product__Type_Osnd(_1399586, _1399588), _1399594)))], (18601 ^ _779142) ^ [_1106683, _1106685] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106683, _1106685)) = _1106685), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1106683), _1106685) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106683, _1106685)))], (51241 ^ _779142) ^ [_1815716, _1815718] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815716), _1815718))), 51242 ^ _779142 : [(51243 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815716), _1815718)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815718), _1815716)))], (51249 ^ _779142) ^ [] : [_1815716 = _1815718]]], (11356 ^ _779142) ^ [_974310, _974312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974310), _974312)), 11359 ^ _779142 : [(11366 ^ _779142) ^ [] : [_974312 = _974310, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974312), hAPP(c_Nat_OSuc, _974310))))], (11360 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974312), hAPP(c_Nat_OSuc, _974310))), -(_974312 = _974310)]]], (48707 ^ _779142) ^ [_1761831, _1761833, _1761835, _1761837] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761831), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1761833, _1761835, _1761831, _1761837) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1761833, 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(_1761833)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1761835, _1761837)), 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(_1761833)))), 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(_1761833)))), 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(_1761833)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1761833, 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(_1761833)))), 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(_1761833)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1761833, _1761835, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761831), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761837))), 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(_1761833)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833)))), 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(_1761833)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1761833, 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(_1761833)))), 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(_1761833)))), 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(_1761833))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833)))), 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(_1761833)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833))))), tc_prod(_1761833, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1761833)), hAPP(hAPP(c_COMBB(_1761833, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761833)))), tc_prod(_1761833, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1761833)), c_Product__Type_Ofst(_1761833, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (32045 ^ _779142) ^ [_1359664, _1359666, _1359668, _1359670, _1359672] : [class_Groups_Oab__group__add(_1359664), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359666, _1359664), hAPP(hAPP(c_COMBS(_1359666, _1359664, _1359664), hAPP(hAPP(c_COMBB(_1359664, tc_fun(_1359664, _1359664), _1359666), c_Groups_Ominus__class_Ominus(_1359664)), _1359668)), _1359670)), _1359672) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1359664), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359666, _1359664), _1359668), _1359672)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359666, _1359664), _1359670), _1359672)))], (40366 ^ _779142) ^ [_1568864, _1568866] : [-(c_Transitive__Closure_Ortrancl(_1568864, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568864, _1568864), tc_HOL_Obool)), _1568866), c_Relation_OId(_1568864))) = c_Transitive__Closure_Ortrancl(_1568864, _1568866))], (15577 ^ _779142) ^ [_1052029, _1052031, _1052033] : [class_Int_Onumber__ring(_1052029), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052029), hAPP(c_Int_Onumber__class_Onumber__of(_1052029), _1052031)), hAPP(c_Int_Onumber__class_Onumber__of(_1052029), _1052033)) = hAPP(c_Int_Onumber__class_Onumber__of(_1052029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052031), _1052033)))], (23891 ^ _779142) ^ [_1199798] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199798), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199798))], (49666 ^ _779142) ^ [_1782708, _1782710, _1782712, _1782714, _1782716, _1782718] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782708, _1782710, _1782712, _1782714), _1782716) = hAPP(c_Hilbert__Choice_Oinv__into(_1782708, _1782710, _1782712, _1782714), _1782718), hBOOL(hAPP(hAPP(c_member(_1782710), _1782716), hAPP(c_Set_Oimage(_1782708, _1782710, _1782714), _1782712))), hBOOL(hAPP(hAPP(c_member(_1782710), _1782718), hAPP(c_Set_Oimage(_1782708, _1782710, _1782714), _1782712))), -(_1782716 = _1782718)], (8589 ^ _779142) ^ [_923373, _923375, _923377, _923379] : [class_Groups_Ocancel__semigroup__add(_923373), 8592 ^ _779142 : [(8599 ^ _779142) ^ [] : [_923375 = _923379, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923373), _923375), _923377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923373), _923379), _923377))], (8593 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923373), _923375), _923377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923373), _923379), _923377), -(_923375 = _923379)]]], (45750 ^ _779142) ^ [_1698391, _1698393, _1698395, _1698397] : [-(c_List_Otranspose(_1698391, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698393), tc_List_Olist(_1698391)), hAPP(c_List_Omap(_1698393, _1698391), _1698395)), _1698397)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698393), tc_List_Olist(_1698391)), hAPP(c_List_Omap(_1698393, _1698391), _1698395)), c_List_Otranspose(_1698393, _1698397)))], (4270 ^ _779142) ^ [_843795, _843797, _843799, _843801, _843803, _843805, _843807, _843809] : [-(c_Lazy__Sequence_Oproduct(_843809, _843805, _843801, _843797) = c_Lazy__Sequence_Oproduct(_843807, _843803, _843799, _843795)), _843809 = _843807, _843805 = _843803, _843801 = _843799, _843797 = _843795], (4012 ^ _779142) ^ [_839798, _839800, _839802, _839804, _839806, _839808, _839810, _839812] : [-(c_New__DSequence_Opos__bind(_839812, _839808, _839804, _839800) = c_New__DSequence_Opos__bind(_839810, _839806, _839802, _839798)), _839812 = _839810, _839808 = _839806, _839804 = _839802, _839800 = _839798], (21280 ^ _779142) ^ [_1153265, _1153267] : [c_Nat__Transfer_Ois__nat(_1153265), c_Nat__Transfer_Ois__nat(_1153267), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1153265, _1153267)))], (25590 ^ _779142) ^ [_1228894, _1228896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228894)), c_Int_OBit0(_1228896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228894), _1228896)))], (31905 ^ _779142) ^ [_1354280, _1354282, _1354284, _1354286, _1354288, _1354290] : [-(hAPP(c_Set_Oimage(_1354280, _1354282, _1354284), hAPP(c_Set_Oimage(_1354286, _1354280, _1354288), _1354290)) = hAPP(c_Set_Oimage(_1354286, _1354282, hAPP(hAPP(c_COMBB(_1354280, _1354282, _1354286), _1354284), _1354288)), _1354290))], (46704 ^ _779142) ^ [_1718280, _1718282] : [-(_1718280 = c_List_Olist_ONil(_1718282)), -(c_List_Olast(_1718282, hAPP(c_List_Orev(_1718282), _1718280)) = hAPP(c_List_Ohd(_1718282), _1718280))], (33365 ^ _779142) ^ [_1389759, _1389761, _1389763, _1389765, _1389767, _1389769] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389759, _1389761), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389763), _1389765))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389759, _1389761), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389767), _1389769))), -(_1389761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389763 = _1389767)], (50927 ^ _779142) ^ [_1810226, _1810228] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810226), _1810228)), -(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)))), _1810228, _1810226) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (32129 ^ _779142) ^ [_1362940, _1362942, _1362944] : [-(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)), _1362940)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1362942, _1362944)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362942), _1362940), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362944), _1362940)))], (27728 ^ _779142) ^ [_1268641, _1268643, _1268645, _1268647] : [class_Orderings_Olinorder(_1268641), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268641), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268641), _1268643), _1268645)), _1268647) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268641), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268641), _1268643), _1268647)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268641), _1268645), _1268647)))], (6683 ^ _779142) ^ [_887022, _887024, _887026, _887028] : [c_Finite__Set_Ofolding__one(_887022, _887024, _887026), -(hAPP(_887026, hAPP(hAPP(c_Set_Oinsert(_887022), _887028), c_Orderings_Obot__class_Obot(tc_fun(_887022, tc_HOL_Obool)))) = _887028)], (39916 ^ _779142) ^ [_1557196, _1557198, _1557200, _1557202, _1557204] : [c_Finite__Set_Ofolding__idem(_1557196, _1557198, _1557200, _1557202), -(hAPP(c_Fun_Ocomp(_1557198, _1557198, _1557198, hAPP(_1557200, _1557204)), hAPP(_1557200, _1557204)) = hAPP(_1557200, _1557204))], (46027 ^ _779142) ^ [_1705108, _1705110, _1705112] : [46028 ^ _779142 : [(46031 ^ _779142) ^ [] : [_1705112 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46029 ^ _779142) ^ [] : [-(_1705108 = c_List_Olist_ONil(tc_List_Olist(_1705110)))]], 46035 ^ _779142 : [(46038 ^ _779142) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705110)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1705110)), _1705108), 46034 ^ [_1705108, _1705110, _1705112])) = _1705112], (46036 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46034 ^ [_1705108, _1705110, _1705112]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705110))), _1705108))))]], -(c_List_Otranspose(_1705110, _1705108) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1705110)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705110)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1705110), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705110)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1705110)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1705110), hAPP(hAPP(c_COMBB(tc_List_Olist(_1705110), tc_fun(tc_Nat_Onat, _1705110), tc_Nat_Onat), c_List_Onth(_1705110)), hAPP(c_List_Onth(tc_List_Olist(_1705110)), _1705108))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705110))), _1705108)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1705112)))], (31464 ^ _779142) ^ [_1343473, _1343475, _1343477] : [31466 ^ _779142 : [(31471 ^ _779142) ^ [] : [hBOOL(hAPP(_1343475, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31465 ^ [_1343473, _1343475, _1343477]), _1343473)))], (31469 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1343475, 31465 ^ [_1343473, _1343475, _1343477])))], (31467 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31465 ^ [_1343473, _1343475, _1343477]), _1343473)))]], hBOOL(hAPP(_1343475, _1343477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1343477), _1343473)), -(hBOOL(hAPP(_1343475, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10315 ^ _779142) ^ [_957427, _957429, _957431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957427), _957429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957431), _957429))))], (6968 ^ _779142) ^ [_893392, _893394] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893392, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_893392, tc_HOL_Obool))), _893394) = c_Orderings_Obot__class_Obot(tc_fun(_893392, tc_HOL_Obool)))], (798 ^ _779142) ^ [_791113, _791115, _791117, _791119] : [-(c_Relation_Otrans(_791117, _791113)), c_Relation_Otrans(_791119, _791115), _791119 = _791117, _791115 = _791113], (40109 ^ _779142) ^ [_1561998, _1562000] : [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), _1561998), _1562000)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1561998), _1562000)))], (41957 ^ _779142) ^ [_1612080, _1612082, _1612084] : [-(c_List_Osublist(_1612080, _1612082, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1612084)) = hAPP(hAPP(c_List_Otake(_1612080), _1612084), _1612082))], (24670 ^ _779142) ^ [_1212971, _1212973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212971), _1212973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1212971)), c_Int_OBit1(_1212973))))], (36678 ^ _779142) ^ [_1469553, _1469555, _1469557, _1469559, _1469561] : [-(c_Fun_Oinj__on(_1469553, _1469555, _1469557, hAPP(hAPP(c_Set_Oinsert(_1469553), _1469559), _1469561))), c_Fun_Oinj__on(_1469553, _1469555, _1469557, _1469561), -(hBOOL(hAPP(hAPP(c_member(_1469555), hAPP(_1469557, _1469559)), hAPP(c_Set_Oimage(_1469553, _1469555, _1469557), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469553, tc_HOL_Obool)), _1469561), hAPP(hAPP(c_Set_Oinsert(_1469553), _1469559), c_Orderings_Obot__class_Obot(tc_fun(_1469553, tc_HOL_Obool))))))))], (40526 ^ _779142) ^ [_1572757, _1572759, _1572761, _1572763] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572757, _1572757)), hAPP(hAPP(c_Product__Type_OPair(_1572757, _1572757), _1572759), _1572761)), c_Transitive__Closure_Ortrancl(_1572757, _1572763)))), 40527 ^ _779142 : [(40530 ^ _779142) ^ [] : [-(_1572759 = _1572761), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572757, _1572757)), hAPP(hAPP(c_Product__Type_OPair(_1572757, _1572757), _1572759), _1572761)), c_Transitive__Closure_Otrancl(_1572757, _1572763)))], (40528 ^ _779142) ^ [] : [_1572759 = _1572761]]], (11277 ^ _779142) ^ [_972881, _972883, _972885] : [11278 ^ _779142 : [(11281 ^ _779142) ^ [] : [_972883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11279 ^ _779142) ^ [] : [_972881 = _972885]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972881), _972883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972885), _972883))], (48034 ^ _779142) ^ [_1746942, _1746944, _1746946, _1746948, _1746950] : [-(hAPP(c_New__DSequence_Oneg__bind(_1746942, _1746944, _1746946, _1746948), _1746950) = c_Lazy__Sequence_Ohb__bind(_1746942, _1746944, hAPP(_1746946, _1746950), hAPP(hAPP(c_COMBC(_1746942, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746944))), _1746948), _1746950)))], (3418 ^ _779142) ^ [_830147, _830149, _830151, _830153] : [-(c_Random_Opick(_830153, _830149) = c_Random_Opick(_830151, _830147)), _830153 = _830151, _830149 = _830147], (31206 ^ _779142) ^ [_1338469, _1338471] : [class_Orderings_Olinorder(_1338469), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1338469, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1338469), _1338471)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338469), _1338471))], (44680 ^ _779142) ^ [_1674128, _1674130, _1674132] : [-(hAPP(hAPP(c_List_Ozip(_1674128, _1674130), hAPP(hAPP(c_List_Omap(tc_prod(_1674128, _1674130), _1674128), c_Product__Type_Ofst(_1674128, _1674130)), _1674132)), hAPP(hAPP(c_List_Omap(tc_prod(_1674128, _1674130), _1674130), c_Product__Type_Osnd(_1674128, _1674130)), _1674132)) = _1674132)], (40434 ^ _779142) ^ [_1570571, _1570573] : [-(c_Transitive__Closure_Ortrancl(_1570571, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1570571, _1570571), tc_HOL_Obool)), _1570573), c_Relation_OId(_1570571))) = c_Transitive__Closure_Ortrancl(_1570571, _1570573))], (45049 ^ _779142) ^ [_1682570, _1682572, _1682574, _1682576, _1682578, _1682580, _1682582] : [c_List_Olist__all2(_1682576, _1682572, hAPP(hAPP(c_COMBB(_1682570, tc_fun(_1682572, tc_HOL_Obool), _1682576), _1682574), _1682578), _1682580, _1682582), -(c_List_Olist__all2(_1682570, _1682572, _1682574, hAPP(hAPP(c_List_Omap(_1682576, _1682570), _1682578), _1682580), _1682582))], (43297 ^ _779142) ^ [_1643072, _1643074, _1643076] : [-(c_List_Obutlast(_1643072, hAPP(hAPP(c_List_Oappend(_1643072), _1643074), hAPP(hAPP(c_List_Olist_OCons(_1643072), _1643076), c_List_Olist_ONil(_1643072)))) = _1643074)], (49154 ^ _779142) ^ [_1772841, _1772843] : [-(c_Relation_Oantisym(_1772841, c_Relation_OId__on(_1772841, _1772843)))], (6019 ^ _779142) ^ [_875075, _875077, _875079, _875081] : [_875081 = c_Orderings_Obot__class_Obot(tc_fun(_875075, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_875075, _875077, _875079), _875081) = c_Orderings_Obot__class_Obot(tc_fun(_875077, tc_HOL_Obool)))], (9282 ^ _779142) ^ [_937530, _937532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937530), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937530), _937532))))], (39395 ^ _779142) ^ [_1545330, _1545332, _1545334, _1545336, _1545338, _1545340] : [-(hAPP(c_Set_Ovimage(_1545330, tc_prod(_1545332, _1545334), _1545336), hAPP(hAPP(c_Product__Type_OSigma(_1545332, _1545334), _1545338), hAPP(c_COMBK(tc_fun(_1545334, tc_HOL_Obool), _1545332), _1545340))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545330, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1545330, _1545332, hAPP(c_Fun_Ocomp(tc_prod(_1545332, _1545334), _1545332, _1545330, c_Product__Type_Ofst(_1545332, _1545334)), _1545336)), _1545338)), hAPP(c_Set_Ovimage(_1545330, _1545334, hAPP(c_Fun_Ocomp(tc_prod(_1545332, _1545334), _1545334, _1545330, c_Product__Type_Osnd(_1545332, _1545334)), _1545336)), _1545340)))], (43478 ^ _779142) ^ [_1648073, _1648075] : [hBOOL(hAPP(c_List_Odistinct(_1648073), _1648075)), -(hBOOL(hAPP(c_List_Odistinct(_1648073), hAPP(c_List_Orotate1(_1648073), _1648075))))], (312 ^ _779142) ^ [_783868, _783870, _783872, _783874] : [-(c_Nitpick_Owf_H(_783872, _783868)), c_Nitpick_Owf_H(_783874, _783870), _783874 = _783872, _783870 = _783868], (25148 ^ _779142) ^ [] : [-(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))))))], (32229 ^ _779142) ^ [_1365558, _1365560, _1365562, _1365564, _1365566] : [class_Groups_Ocomm__monoid__mult(_1365558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365560), _1365562)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1365558, _1365560, c_Groups_Otimes__class_Otimes(_1365558)), hAPP(hAPP(c_COMBS(_1365560, _1365558, _1365558), hAPP(hAPP(c_COMBB(_1365558, tc_fun(_1365558, _1365558), _1365560), c_Groups_Otimes__class_Otimes(_1365558)), _1365564)), _1365566)), c_Groups_Oone__class_Oone(_1365558)), _1365562) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365558), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1365558, _1365560, c_Groups_Otimes__class_Otimes(_1365558)), _1365564), c_Groups_Oone__class_Oone(_1365558)), _1365562)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1365558, _1365560, c_Groups_Otimes__class_Otimes(_1365558)), _1365566), c_Groups_Oone__class_Oone(_1365558)), _1365562)))], (29875 ^ _779142) ^ [_1312249, _1312251, _1312253] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312249), _1312251)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312249), _1312253)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312249, tc_HOL_Obool)), _1312251), _1312253) = c_Orderings_Obot__class_Obot(tc_fun(_1312249, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1312249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312249, tc_HOL_Obool)), _1312251), _1312253)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312249), _1312251)), hAPP(c_Finite__Set_Ocard(_1312249), _1312253)))], (1646 ^ _779142) ^ [_802659, _802661] : [-(class_Rings_Olinordered__semidom(_802659)), _802661 = _802659, class_Rings_Olinordered__semidom(_802661)], (26172 ^ _779142) ^ [_1239304, _1239306] : [-(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), _1239304)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1239306))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1239304))) = 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), _1239306)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239304)))], (46494 ^ _779142) ^ [_1713652, _1713654, _1713656, _1713658, _1713660] : [class_Orderings_Olinorder(_1713652), c_Fun_Oinj__on(_1713654, _1713652, _1713656, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713654, tc_HOL_Obool)), hAPP(c_List_Oset(_1713654), _1713658)), hAPP(c_List_Oset(_1713654), _1713660))), c_List_Olinorder__class_Osorted(_1713652, hAPP(hAPP(c_List_Omap(_1713654, _1713652), _1713656), _1713658)), hBOOL(hAPP(c_List_Odistinct(_1713652), hAPP(hAPP(c_List_Omap(_1713654, _1713652), _1713656), _1713658))), c_List_Olinorder__class_Osorted(_1713652, hAPP(hAPP(c_List_Omap(_1713654, _1713652), _1713656), _1713660)), hBOOL(hAPP(c_List_Odistinct(_1713652), hAPP(hAPP(c_List_Omap(_1713654, _1713652), _1713656), _1713660))), hAPP(c_List_Oset(_1713654), _1713658) = hAPP(c_List_Oset(_1713654), _1713660), -(_1713658 = _1713660)], (24630 ^ _779142) ^ [_1212267, _1212269] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1212267), _1212269))))], (50361 ^ _779142) ^ [_1797347, _1797349, _1797351] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797347, _1797347)), hAPP(hAPP(c_Product__Type_OPair(_1797347, _1797347), hAPP(_1797349, hAPP(c_Nat_OSuc, 50362 ^ [_1797347, _1797349, _1797351]))), hAPP(_1797349, 50362 ^ [_1797347, _1797349, _1797351]))), c_Transitive__Closure_Ortrancl(_1797347, _1797351))), c_Wellfounded_Owf(_1797347, c_Transitive__Closure_Otrancl(_1797347, _1797351)), 50370 ^ _779142 : [(50371 ^ _779142) ^ [_1797613] : [-(hAPP(_1797349, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50369 ^ [_1797347, _1797349, _1797351]), _1797613)) = hAPP(_1797349, 50369 ^ [_1797347, _1797349, _1797351]))]]], (1406 ^ _779142) ^ [_799659, _799661] : [-(class_Lattices_Obounded__lattice__bot(_799659)), _799661 = _799659, class_Lattices_Obounded__lattice__bot(_799661)], (23993 ^ _779142) ^ [_1201662, _1201664] : [class_Int_Onumber__ring(_1201662), 23996 ^ _779142 : [(24003 ^ _779142) ^ [] : [c_Int_Oiszero(_1201662, hAPP(c_Int_Onumber__class_Onumber__of(_1201662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201664), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1201662), _1201664) = c_Groups_Ozero__class_Ozero(_1201662))], (23997 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1201662), _1201664) = c_Groups_Ozero__class_Ozero(_1201662), -(c_Int_Oiszero(_1201662, hAPP(c_Int_Onumber__class_Onumber__of(_1201662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201664), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (24944 ^ _779142) ^ [_1217610, _1217612] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1217610)), _1217612) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1217610, _1217612))], (9079 ^ _779142) ^ [_933045, _933047, _933049, _933051, _933053, _933055] : [class_Rings_Oordered__ring(_933045), 9082 ^ _779142 : [(9089 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933045), _933051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933045), _933053), _933047)), _933049)), _933055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933045), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), _933047), _933049)), _933051)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), _933053), _933049)), _933055))))], (9083 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933045), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), _933047), _933049)), _933051)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), _933053), _933049)), _933055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933045), _933051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933045), _933053), _933047)), _933049)), _933055))))]]], (35689 ^ _779142) ^ [_1447813, _1447815, _1447817] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447813), hAPP(hAPP(c_Set_Oinsert(_1447813), _1447815), c_Orderings_Obot__class_Obot(tc_fun(_1447813, tc_HOL_Obool)))), _1447817) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1447813, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447813, _1447813, _1447817), hAPP(hAPP(c_Set_Oinsert(_1447813), _1447815), c_Orderings_Obot__class_Obot(tc_fun(_1447813, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1447813, tc_HOL_Obool), tc_HOL_Obool))))], (44913 ^ _779142) ^ [_1679458, _1679460, _1679462] : [hBOOL(hAPP(c_List_Olistsp(_1679458, _1679460), _1679462)), 44916 ^ _779142 : [(44917 ^ _779142) ^ [_1679547] : [hBOOL(hAPP(hAPP(c_member(_1679458), _1679547), hAPP(c_List_Oset(_1679458), _1679462))), -(hBOOL(hAPP(_1679460, _1679547)))]]], (46901 ^ _779142) ^ [_1722316, _1722318, _1722320, _1722322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722318)), c_List_OtakeWhile(_1722318, _1722320, _1722322)))), -(hAPP(hAPP(c_List_Onth(_1722318), c_List_OtakeWhile(_1722318, _1722320, _1722322)), _1722316) = hAPP(hAPP(c_List_Onth(_1722318), _1722322), _1722316))], (10999 ^ _779142) ^ [_968916, _968918] : [class_Rings_Omult__zero(_968916), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968916), _968918), c_Groups_Ozero__class_Ozero(_968916)) = c_Groups_Ozero__class_Ozero(_968916))], (22382 ^ _779142) ^ [_1172964, _1172966, _1172968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172964)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1172966), _1172968)), 22389 ^ _779142 : [(22390 ^ _779142) ^ [_1173160] : [22392 ^ _779142 : [(22398 ^ _779142) ^ [] : [-(_1173160 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22394 ^ [_1172964, _1172966, _1172968, _1173160]), 22391 ^ [_1172964, _1172966, _1172968, _1173160]))], (22396 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22394 ^ [_1172964, _1172966, _1172968, _1173160]), _1172968)))], (22393 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22391 ^ [_1172964, _1172966, _1172968, _1173160]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1172964))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173160), _1172966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1173160), _1172964)), _1172966)))]]], (23207 ^ _779142) ^ [_1187791, _1187793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187791)), _1187793) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187791), _1187793)))], (13769 ^ _779142) ^ [_1018729, _1018731, _1018733, _1018735] : [class_Fields_Olinordered__field(_1018729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018729), c_Groups_Ozero__class_Ozero(_1018729)), _1018731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018729), _1018733), _1018731)), _1018735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018729), _1018733), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018729), _1018735), _1018731))))], (27226 ^ _779142) ^ [_1259652, _1259654] : [-(_1259652 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1259652, _1259654) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1259652), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1259654)))], (22459 ^ _779142) ^ [_1174373, _1174375] : [22461 ^ _779142 : [(22464 ^ _779142) ^ [] : [hBOOL(hAPP(_1174375, 22460 ^ [_1174373, _1174375]))], (22462 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22460 ^ [_1174373, _1174375]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1174373))))]], 22465 ^ _779142 : [(22466 ^ _779142) ^ [_1174528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174528), _1174373)), -(hBOOL(hAPP(_1174375, _1174528)))]]], (36664 ^ _779142) ^ [_1469135, _1469137, _1469139, _1469141] : [c_Fun_Oinj__on(_1469135, _1469137, _1469139, c_Orderings_Otop__class_Otop(tc_fun(_1469135, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469137, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469135, _1469137, _1469139), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469135, tc_HOL_Obool)), _1469141))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469137, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469135, _1469137, _1469139), _1469141)))))], (46162 ^ _779142) ^ [_1707470] : [class_Orderings_Olinorder(_1707470), -(c_List_Olinorder__class_Osorted(_1707470, c_List_Olist_ONil(_1707470)))], (47236 ^ _779142) ^ [_1729577, _1729579, _1729581, _1729583, _1729585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1729577, _1729579)), hAPP(_1729577, _1729581))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729583, _1729583)), hAPP(hAPP(c_Product__Type_OPair(_1729583, _1729583), _1729579), _1729581)), c_List_Omeasures(_1729583, _1729585))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729583, _1729583)), hAPP(hAPP(c_Product__Type_OPair(_1729583, _1729583), _1729579), _1729581)), c_List_Omeasures(_1729583, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729583, tc_Nat_Onat)), _1729577), _1729585)))))], (43484 ^ _779142) ^ [_1648178, _1648180, _1648182] : [hBOOL(hAPP(c_List_Odistinct(_1648178), _1648180)), -(hBOOL(hAPP(c_List_Odistinct(_1648178), hAPP(hAPP(c_List_Odrop(_1648178), _1648182), _1648180))))], (34925 ^ _779142) ^ [_1427450, _1427452, _1427454, _1427456, _1427458] : [_1427450 = c_Orderings_Obot__class_Obot(tc_fun(_1427452, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427452, tc_fun(_1427454, tc_HOL_Obool)), _1427450), hAPP(hAPP(c_COMBB(tc_fun(_1427454, tc_HOL_Obool), tc_fun(_1427454, tc_HOL_Obool), _1427452), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427454, tc_HOL_Obool)), _1427456)), _1427458)) = c_Orderings_Obot__class_Obot(tc_fun(_1427454, tc_HOL_Obool)))], (45687 ^ _779142) ^ [_1697012, _1697014, _1697016] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1697012), tc_List_Olist(_1697012)), c_List_Opartition(_1697012, _1697014, _1697016)) = hAPP(c_List_Ofilter(_1697012, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1697012, c_fNot), _1697014)), _1697016))], (23451 ^ _779142) ^ [_1192232, _1192234, _1192236] : [class_Groups_Oab__group__add(_1192232), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192232), _1192234), _1192236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192232), _1192234), hAPP(c_Groups_Ouminus__class_Ouminus(_1192232), _1192236)))], (21562 ^ _779142) ^ [_1157884, _1157886] : [21563 ^ _779142 : [(21566 ^ _779142) ^ [] : [_1157886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21564 ^ _779142) ^ [] : [-(_1157884 = 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), _1157884)), _1157886))))], (42222 ^ _779142) ^ [_1619950, _1619952] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1619950), _1619952) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619950, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619952), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52671 ^ _779142) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (19685 ^ _779142) ^ [_1124828, _1124830, _1124832] : [class_Rings_Olinordered__idom(_1124828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124828), c_Groups_Ozero__class_Ozero(_1124828)), _1124830)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124828), hAPP(c_Groups_Oabs__class_Oabs(_1124828), _1124832)), _1124830) = hAPP(c_Groups_Oabs__class_Oabs(_1124828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124828), _1124832), _1124830)))], (30714 ^ _779142) ^ [_1329140, _1329142, _1329144, _1329146, _1329148] : [class_Groups_Ocomm__monoid__mult(_1329140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329142), _1329144)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329142), _1329146)), 30728 ^ _779142 : [(30731 ^ _779142) ^ [] : [hAPP(_1329148, 30727 ^ [_1329140, _1329142, _1329144, _1329146, _1329148]) = c_Groups_Oone__class_Oone(_1329140)], (30729 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329142), 30727 ^ [_1329140, _1329142, _1329144, _1329146, _1329148]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329142, tc_HOL_Obool)), _1329144), _1329146))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1329140, _1329142, c_Groups_Otimes__class_Otimes(_1329140)), _1329148), c_Groups_Oone__class_Oone(_1329140)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329142, tc_HOL_Obool)), _1329144), _1329146)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329140), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1329140, _1329142, c_Groups_Otimes__class_Otimes(_1329140)), _1329148), c_Groups_Oone__class_Oone(_1329140)), _1329144)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1329140, _1329142, c_Groups_Otimes__class_Otimes(_1329140)), _1329148), c_Groups_Oone__class_Oone(_1329140)), _1329146)))], (45851 ^ _779142) ^ [_1701617, _1701619, _1701621] : [-(c_List_Osublist(_1701617, _1701619, _1701621) = hAPP(hAPP(c_List_Omap(tc_prod(_1701617, tc_Nat_Onat), _1701617), c_Product__Type_Ofst(_1701617, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701617, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701617, 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(_1701617, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701617, tc_Nat_Onat))), _1701621)), hAPP(hAPP(c_List_Ozip(_1701617, tc_Nat_Onat), _1701619), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701617)), _1701619))))))], (13429 ^ _779142) ^ [_1012403, _1012405, _1012407, _1012409, _1012411] : [class_Fields_Ofield(_1012403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012405), _1012407)), -(hAPP(_1012409, _1012411) = c_Groups_Ozero__class_Ozero(_1012403)), 13440 ^ _779142 : [(13447 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1012405), _1012411), _1012407))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012405, _1012403), _1012409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012405, tc_HOL_Obool)), _1012407), hAPP(hAPP(c_Set_Oinsert(_1012405), _1012411), c_Orderings_Obot__class_Obot(tc_fun(_1012405, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012405, _1012403), _1012409), _1012407))], (13441 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1012405), _1012411), _1012407)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012405, _1012403), _1012409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012405, tc_HOL_Obool)), _1012407), hAPP(hAPP(c_Set_Oinsert(_1012405), _1012411), c_Orderings_Obot__class_Obot(tc_fun(_1012405, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1012403), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012405, _1012403), _1012409), _1012407)), hAPP(_1012409, _1012411)))]]], (15363 ^ _779142) ^ [_1048270, _1048272, _1048274, _1048276] : [class_Orderings_Olinorder(_1048270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048270), _1048272), _1048274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048270), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048270), _1048276), _1048272)), _1048274)))], (40542 ^ _779142) ^ [_1573095] : [-(c_Relation_Orefl__on(_1573095, c_Orderings_Otop__class_Otop(tc_fun(_1573095, tc_HOL_Obool)), c_Relation_OId(_1573095)))], (17089 ^ _779142) ^ [_1079799, _1079801, _1079803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079799)), _1079799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1079799), _1079803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079801), _1079799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1079803)))], (4802 ^ _779142) ^ [_852273, _852275] : [_852275 = _852273, -(c_Relation_OId(_852275) = c_Relation_OId(_852273))], (48648 ^ _779142) ^ [_1760749, _1760751] : [-(c_Lazy__Sequence_Oappend(_1760749, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760749), _1760751) = _1760751)], (37359 ^ _779142) ^ [_1485576, _1485578] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485576)), 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)), _1485576))), 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, _1485578))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1186 ^ _779142) ^ [_796909, _796911] : [-(class_Rings_Olinordered__semiring__1(_796909)), _796911 = _796909, class_Rings_Olinordered__semiring__1(_796911)], (38446 ^ _779142) ^ [_1520975, _1520977, _1520979, _1520981] : [hBOOL(hAPP(hAPP(c_member(_1520975), _1520977), hAPP(c_Relation_ORange(_1520979, _1520975), _1520981))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1520979, _1520975)), hAPP(hAPP(c_Product__Type_OPair(_1520979, _1520975), 38449 ^ [_1520975, _1520977, _1520979, _1520981]), _1520977)), _1520981)))], (37493 ^ _779142) ^ [_1488699, _1488701, _1488703] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488699), hAPP(c_Set_OCollect(_1488699), hAPP(hAPP(c_COMBS(_1488699, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488699), c_fdisj), _1488701)), _1488703))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488699), hAPP(c_Set_OCollect(_1488699), _1488701))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488699), hAPP(c_Set_OCollect(_1488699), _1488703)))], (24329 ^ _779142) ^ [_1207352, _1207354, _1207356] : [class_Orderings_Oorder(_1207352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207352), _1207354), _1207356)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207352, _1207356), _1207354) = c_Orderings_Obot__class_Obot(tc_fun(_1207352, tc_HOL_Obool)))], (25210 ^ _779142) ^ [_1222237, _1222239] : [class_Int_Onumber__ring(_1222237), class_Rings_Olinordered__idom(_1222237), 25217 ^ _779142 : [(25224 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1222239), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222237), hAPP(c_Int_Onumber__class_Onumber__of(_1222237), _1222239)), c_Groups_Oone__class_Oone(_1222237))))], (25218 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222237), hAPP(c_Int_Onumber__class_Onumber__of(_1222237), _1222239)), c_Groups_Oone__class_Oone(_1222237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1222239), c_Int_OBit1(c_Int_OPls))))]]], (18292 ^ _779142) ^ [_1101160, _1101162, _1101164] : [-(hBOOL(hAPP(_1101160, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101162, _1101164)))), 18295 ^ _779142 : [(18298 ^ _779142) ^ [] : [hBOOL(hAPP(_1101160, _1101162))], (18296 ^ _779142) ^ [] : [-(_1101164 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 18301 ^ _779142 : [(18302 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101164)))], (18308 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 18304 ^ [_1101160, _1101162, _1101164]), _1101164)))], (18312 ^ _779142) ^ [] : [hBOOL(hAPP(_1101160, 18304 ^ [_1101160, _1101162, _1101164]))], (18310 ^ _779142) ^ [] : [-(_1101162 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101164), 18303 ^ [_1101160, _1101162, _1101164])), 18304 ^ [_1101160, _1101162, _1101164]))], (18306 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18304 ^ [_1101160, _1101162, _1101164])))]], 18313 ^ _779142 : [(18314 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101164), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18320 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 18316 ^ [_1101160, _1101162, _1101164]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18324 ^ _779142) ^ [] : [hBOOL(hAPP(_1101160, 18316 ^ [_1101160, _1101162, _1101164]))], (18322 ^ _779142) ^ [] : [-(_1101162 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101164), 18315 ^ [_1101160, _1101162, _1101164])), 18316 ^ [_1101160, _1101162, _1101164]))], (18318 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101164), 18316 ^ [_1101160, _1101162, _1101164])))]]], (47720 ^ _779142) ^ [_1740523, _1740525, _1740527, _1740529] : [c_List_Olist__ex(_1740523, _1740525, hAPP(hAPP(c_List_Olist_OCons(_1740523), _1740527), _1740529)), -(hBOOL(hAPP(_1740525, _1740527))), -(c_List_Olist__ex(_1740523, _1740525, _1740529))], (44704 ^ _779142) ^ [_1674708, _1674710, _1674712, _1674714, _1674716] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674708)), _1674710) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674712)), _1674714), 44707 ^ _779142 : [(44716 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1674708, _1674712), _1674710), _1674714) = _1674716), hAPP(hAPP(c_List_Omap(tc_prod(_1674708, _1674712), _1674708), c_Product__Type_Ofst(_1674708, _1674712)), _1674716) = _1674710, hAPP(hAPP(c_List_Omap(tc_prod(_1674708, _1674712), _1674712), c_Product__Type_Osnd(_1674708, _1674712)), _1674716) = _1674714], (44708 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Ozip(_1674708, _1674712), _1674710), _1674714) = _1674716, 44711 ^ _779142 : [(44714 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674708, _1674712), _1674712), c_Product__Type_Osnd(_1674708, _1674712)), _1674716) = _1674714)], (44712 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674708, _1674712), _1674708), c_Product__Type_Ofst(_1674708, _1674712)), _1674716) = _1674710)]]]]], (29167 ^ _779142) ^ [_1296420, _1296422, _1296424] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296420, tc_HOL_Obool)), _1296422), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296420, tc_HOL_Obool)), _1296422), _1296424)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296420, tc_HOL_Obool)), _1296422), _1296424))], (43822 ^ _779142) ^ [_1655660, _1655662] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655660)), hAPP(c_List_Otl(_1655660), _1655662)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655660)), _1655662)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5669 ^ _779142) ^ [_868602, _868604, _868606, _868608, _868610, _868612] : [_868602 = hAPP(_868604, _868606), hBOOL(hAPP(hAPP(c_member(_868608), _868606), _868610)), -(hBOOL(hAPP(hAPP(c_member(_868612), _868602), hAPP(c_Set_Oimage(_868608, _868612, _868604), _868610))))], (28122 ^ _779142) ^ [_1276124, _1276126, _1276128] : [class_Groups_Olinordered__ab__group__add(_1276124), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1276124), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1276124), _1276126), _1276128)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1276124), hAPP(c_Groups_Ouminus__class_Ouminus(_1276124), _1276126)), hAPP(c_Groups_Ouminus__class_Ouminus(_1276124), _1276128)))], (33779 ^ _779142) ^ [_1397533, _1397535, _1397537] : [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), _1397533), _1397535))), -(hBOOL(hAPP(hAPP(_1397537, _1397533), _1397535))), 33786 ^ _779142 : [(33789 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 33785 ^ [_1397533, _1397535, _1397537]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1397537, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 33784 ^ [_1397533, _1397535, _1397537])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 33785 ^ [_1397533, _1397535, _1397537]))))], (33795 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1397537, 33784 ^ [_1397533, _1397535, _1397537]), 33785 ^ [_1397533, _1397535, _1397537]))], (33787 ^ _779142) ^ [] : [-(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), 33784 ^ [_1397533, _1397535, _1397537]), 33785 ^ [_1397533, _1397535, _1397537]))))]]], (42622 ^ _779142) ^ [_1628853, _1628855, _1628857] : [-(_1628853 = c_List_Olist_ONil(_1628855)), -(c_List_Obutlast(_1628855, hAPP(hAPP(c_List_Olist_OCons(_1628855), _1628857), _1628853)) = hAPP(hAPP(c_List_Olist_OCons(_1628855), _1628857), c_List_Obutlast(_1628855, _1628853)))], (45428 ^ _779142) ^ [_1690744, _1690746, _1690748, _1690750] : [-(c_List_Oremdups(_1690744, hAPP(hAPP(c_List_Omap(_1690746, _1690744), _1690748), c_List_Oremdups(_1690746, _1690750))) = c_List_Oremdups(_1690744, hAPP(hAPP(c_List_Omap(_1690746, _1690744), _1690748), _1690750)))], (45877 ^ _779142) ^ [_1702309, _1702311, _1702313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702309), _1702311)), -(c_List_Oupt(_1702309, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702311), _1702313)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702309, _1702311)), c_List_Oupt(_1702311, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702311), _1702313))))], (26702 ^ _779142) ^ [_1249519, _1249521, _1249523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249519, tc_HOL_Obool)), _1249521), _1249523) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249519, tc_HOL_Obool)), _1249523), _1249521))], (50855 ^ _779142) ^ [_1809143, _1809145, _1809147] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809143, _1809145) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809147), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 50858 ^ _779142 : [(50861 ^ _779142) ^ [] : [-(_1809145 = _1809147)], (50859 ^ _779142) ^ [] : [-(_1809143 = _1809145)]]], (13273 ^ _779142) ^ [_1009296, _1009298, _1009300] : [class_Rings_Olinordered__ring__strict(_1009296), 13276 ^ _779142 : [(13285 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009296), _1009298), _1009298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009296), _1009300), _1009300)) = c_Groups_Ozero__class_Ozero(_1009296)), _1009298 = c_Groups_Ozero__class_Ozero(_1009296), _1009300 = c_Groups_Ozero__class_Ozero(_1009296)], (13277 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009296), _1009298), _1009298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009296), _1009300), _1009300)) = c_Groups_Ozero__class_Ozero(_1009296), 13280 ^ _779142 : [(13283 ^ _779142) ^ [] : [-(_1009300 = c_Groups_Ozero__class_Ozero(_1009296))], (13281 ^ _779142) ^ [] : [-(_1009298 = c_Groups_Ozero__class_Ozero(_1009296))]]]]], (40679 ^ _779142) ^ [_1576288, _1576290, _1576292, _1576294, _1576296] : [-(hAPP(c_Relation_Oconverse(_1576288, _1576290), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576292, tc_fun(tc_prod(_1576288, _1576290), tc_HOL_Obool)), _1576294), _1576296)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576292, tc_fun(tc_prod(_1576290, _1576288), tc_HOL_Obool)), _1576294), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1576288, _1576290), tc_HOL_Obool), tc_fun(tc_prod(_1576290, _1576288), tc_HOL_Obool), _1576292), c_Relation_Oconverse(_1576288, _1576290)), _1576296)))], (24351 ^ _779142) ^ [_1207731, _1207733, _1207735] : [class_Orderings_Oorder(_1207731), 24354 ^ _779142 : [(24361 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207731), _1207733), _1207735))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207731, _1207733), _1207735) = c_Orderings_Obot__class_Obot(tc_fun(_1207731, tc_HOL_Obool)))], (24355 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207731, _1207733), _1207735) = c_Orderings_Obot__class_Obot(tc_fun(_1207731, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207731), _1207733), _1207735))]]], (16667 ^ _779142) ^ [_1072559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072559), 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)), _1072559)), _1072559)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8296 ^ _779142) ^ [_917345, _917347, _917349, _917351, _917353, _917355] : [-(_917345 = _917347), -(hAPP(c_Fun_Ofun__upd(_917349, _917351, _917353, _917347, _917355), _917345) = hAPP(_917353, _917345))], (25342 ^ _779142) ^ [_1224414, _1224416] : [class_Int_Onumber__ring(_1224414), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224414), c_Groups_Oone__class_Oone(_1224414)), hAPP(c_Int_Onumber__class_Onumber__of(_1224414), _1224416)) = hAPP(c_Int_Onumber__class_Onumber__of(_1224414), 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), _1224416))))], (44851 ^ _779142) ^ [_1677633] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1677633), 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, _1677633)) = _1677633)], (39351 ^ _779142) ^ [_1544121, _1544123] : [39353 ^ _779142 : [(39356 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1544123), 39352 ^ [_1544121, _1544123]))], (39354 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39352 ^ [_1544121, _1544123]), _1544121)))]], -(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)), _1544123), _1544121))], (48753 ^ _779142) ^ [_1763343, _1763345, _1763347, _1763349] : [c_Relation_Otrans(_1763343, _1763345), c_Relation_Otrans(_1763347, _1763349), -(c_Relation_Otrans(tc_prod(_1763343, _1763347), c_Wellfounded_Olex__prod(_1763343, _1763347, _1763345, _1763349)))], (10815 ^ _779142) ^ [_965917, _965919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965917), hAPP(c_Nat_OSuc, _965919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965917), _965919))), -(_965917 = _965919)], (32923 ^ _779142) ^ [_1380726, _1380728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1380726, _1380726)), hAPP(hAPP(c_Product__Type_OPair(_1380726, _1380726), 32924 ^ [_1380726, _1380728]), 32924 ^ [_1380726, _1380728])), _1380728)), -(c_Nitpick_Orefl_H(_1380726, _1380728))], (37431 ^ _779142) ^ [_1487313, _1487315, _1487317] : [hBOOL(hAPP(hAPP(c_member(_1487313), _1487315), hAPP(c_Set_OCollect(_1487313), _1487317))), -(hBOOL(hAPP(_1487317, _1487315)))], (4792 ^ _779142) ^ [_852124, _852126, _852128, _852130] : [-(c_Relation_OId__on(_852130, _852126) = c_Relation_OId__on(_852128, _852124)), _852130 = _852128, _852126 = _852124], (33495 ^ _779142) ^ [_1391780, _1391782, _1391784, _1391786] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391780, _1391782), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391784), _1391786))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391780), _1391782), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1391786), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391784)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391784)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1391786), 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), _1391782), _1391786))))))], (49863 ^ _779142) ^ [_1787411, _1787413, _1787415, _1787417, _1787419, _1787421] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1787411, _1787413, _1787415, _1787417), _1787419), _1787421) = hAPP(_1787417, hAPP(hAPP(c_Product__Type_OPair(_1787411, _1787413), _1787419), _1787421)))], (9013 ^ _779142) ^ [_931537, _931539, _931541] : [class_Lattices_Oab__semigroup__idem__mult(_931537), -(_931539 = c_Orderings_Obot__class_Obot(tc_fun(_931537, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_931537), _931539)), -(hAPP(c_Finite__Set_Ofold1(_931537, c_Groups_Otimes__class_Otimes(_931537)), hAPP(hAPP(c_Set_Oinsert(_931537), _931541), _931539)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931537), _931541), hAPP(c_Finite__Set_Ofold1(_931537, c_Groups_Otimes__class_Otimes(_931537)), _931539)))], (45889 ^ _779142) ^ [_1702572, _1702574] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702572), _1702574))), -(c_List_Oupt(_1702572, _1702574) = c_List_Olist_ONil(tc_Nat_Onat))], (32974 ^ _779142) ^ [_1382263, _1382265, _1382267, _1382269, _1382271] : [-(hAPP(c_Nat_Onat_Onat__rec(_1382263, _1382265, _1382267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1382269)), _1382271)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1382263), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1382269))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1382263, _1382263), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1382263, tc_fun(_1382263, _1382263)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1382263, tc_fun(_1382263, _1382263)), tc_Int_Oint), c_If(_1382263)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1382263, _1382265, _1382267), _1382271))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1382263, _1382263), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1382263, _1382263), tc_Int_Oint), _1382267), 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)), _1382271))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1382263, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1382263, _1382265, _1382267)), 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)), _1382271))))))], (3662 ^ _779142) ^ [_833969, _833971, _833973, _833975, _833977, _833979, _833981, _833983] : [-(c_List_Omaps(_833983, _833979, _833975, _833971) = c_List_Omaps(_833981, _833977, _833973, _833969)), _833983 = _833981, _833979 = _833977, _833975 = _833973, _833971 = _833969], (31665 ^ _779142) ^ [_1347624, _1347626, _1347628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1347624), _1347626)), -(c_Random_Ominus__shift(_1347628, _1347624, _1347626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1347628), _1347624)), _1347626))], (25128 ^ _779142) ^ [_1220840, _1220842, _1220844, _1220846] : [class_Groups_Ocomm__monoid__add(_1220840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220842), _1220844)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220840), _1220846), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220842), _1220844)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220840), hAPP(_1220846, _1220842)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220840), _1220846), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1220842)), _1220844))))], (11125 ^ _779142) ^ [_970782] : [-(_970782 = 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)), _970782)))], (35978 ^ _779142) ^ [_1454777, _1454779] : [c_Equiv__Relations_Oequivp(_1454777, _1454779), 35981 ^ _779142 : [(35988 ^ _779142) ^ [_1454970, _1454972] : [hAPP(_1454779, _1454972) = hAPP(_1454779, _1454970), -(hBOOL(hAPP(hAPP(_1454779, _1454972), _1454970)))], (35982 ^ _779142) ^ [_1454871, _1454873] : [hBOOL(hAPP(hAPP(_1454779, _1454873), _1454871)), -(hAPP(_1454779, _1454873) = hAPP(_1454779, _1454871))]]], (32109 ^ _779142) ^ [_1362435, _1362437, _1362439, _1362441, _1362443] : [class_Groups_Ocomm__monoid__add(_1362435), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1362435), _1362437), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362439), _1362441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362443), _1362441))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1362435), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1362435, tc_Nat_Onat), _1362437), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1362441))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1362439, _1362443)))], (12262 ^ _779142) ^ [_990901, _990903, _990905] : [class_Groups_Ocomm__monoid__add(_990901), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_990903, _990901), _990905), c_Orderings_Obot__class_Obot(tc_fun(_990903, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_990901))], (46618 ^ _779142) ^ [_1716396, _1716398, _1716400] : [-(hAPP(c_List_Orev(_1716396), hAPP(c_List_Ofilter(_1716396, _1716398), _1716400)) = hAPP(c_List_Ofilter(_1716396, _1716398), hAPP(c_List_Orev(_1716396), _1716400)))], (36902 ^ _779142) ^ [_1474395, _1474397, _1474399, _1474401, _1474403, _1474405, _1474407] : [c_Typedef_Otype__definition(_1474395, _1474397, _1474399, _1474401, _1474403), hBOOL(hAPP(hAPP(c_member(_1474397), _1474405), _1474403)), hBOOL(hAPP(hAPP(c_member(_1474397), _1474407), _1474403)), 36913 ^ _779142 : [(36920 ^ _779142) ^ [] : [_1474405 = _1474407, -(hAPP(_1474401, _1474405) = hAPP(_1474401, _1474407))], (36914 ^ _779142) ^ [] : [hAPP(_1474401, _1474405) = hAPP(_1474401, _1474407), -(_1474405 = _1474407)]]], (23631 ^ _779142) ^ [_1195321, _1195323] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195321, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195323)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195321, _1195323) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23955 ^ _779142) ^ [] : [-(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))))], (27890 ^ _779142) ^ [_1271623, _1271625, _1271627, _1271629] : [class_Orderings_Olinorder(_1271623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271623), _1271625), _1271627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271623), _1271629), _1271627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271623), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271623), _1271625), _1271629)), _1271627)))], (47432 ^ _779142) ^ [_1734245, _1734247, _1734249, _1734251] : [47434 ^ _779142 : [(47437 ^ _779142) ^ [] : [hBOOL(hAPP(_1734249, 47433 ^ [_1734245, _1734247, _1734249, _1734251]))], (47435 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734245), 47433 ^ [_1734245, _1734247, _1734249, _1734251]), hAPP(c_List_Oset(_1734245), _1734247))))]], -(c_List_OtakeWhile(_1734245, _1734249, hAPP(hAPP(c_List_Oappend(_1734245), _1734247), _1734251)) = hAPP(hAPP(c_List_Oappend(_1734245), _1734247), c_List_OtakeWhile(_1734245, _1734249, _1734251)))], (32077 ^ _779142) ^ [_1360594] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1360594)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1360594)), 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))))], (16206 ^ _779142) ^ [_1063924, _1063926, _1063928] : [class_Orderings_Olinorder(_1063924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063924), _1063926)), -(_1063926 = c_Orderings_Obot__class_Obot(tc_fun(_1063924, tc_HOL_Obool))), 16217 ^ _779142 : [(16227 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063924), hAPP(c_Finite__Set_Ofold1(_1063924, c_Orderings_Oord__class_Omin(_1063924)), _1063926)), _1063928))), 16228 ^ _779142 : [(16229 ^ _779142) ^ [_1064313] : [hBOOL(hAPP(hAPP(c_member(_1063924), _1064313), _1063926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063924), _1064313), _1063928))]]], (16218 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063924), hAPP(c_Finite__Set_Ofold1(_1063924, c_Orderings_Oord__class_Omin(_1063924)), _1063926)), _1063928)), 16222 ^ _779142 : [(16225 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063924), 16221 ^ [_1063924, _1063926, _1063928]), _1063928)))], (16223 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063924), 16221 ^ [_1063924, _1063926, _1063928]), _1063926)))]]]]], (12550 ^ _779142) ^ [_995708, _995710, _995712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995708), _995710)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995710), _995708))), _995712) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _995710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995708), _995712)))], (50921 ^ _779142) ^ [_1810127, _1810129] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810127), _1810129)), -(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)))), _1810129, _1810127) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (27242 ^ _779142) ^ [_1259835, _1259837, _1259839, _1259841] : [27243 ^ _779142 : [(27246 ^ _779142) ^ [] : [hBOOL(hAPP(_1259839, _1259837))], (27244 ^ _779142) ^ [] : [hBOOL(hAPP(_1259835, _1259837))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259841, tc_HOL_Obool)), _1259839), _1259835), _1259837)))], (40636 ^ _779142) ^ [_1575213, _1575215, _1575217, _1575219, _1575221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575213, _1575213)), hAPP(hAPP(c_Product__Type_OPair(_1575213, _1575213), _1575215), _1575217)), c_Transitive__Closure_Ortrancl(_1575213, _1575219))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575213, _1575213), tc_HOL_Obool)), _1575219), hAPP(hAPP(c_Product__Type_OSigma(_1575213, _1575213), _1575221), hAPP(c_COMBK(tc_fun(_1575213, tc_HOL_Obool), _1575213), _1575221)))), -(_1575215 = _1575217), -(hBOOL(hAPP(hAPP(c_member(_1575213), _1575215), _1575221)))], (40344 ^ _779142) ^ [_1568263, _1568265] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1568263, _1568263, _1568263), c_Transitive__Closure_Ortrancl(_1568263, _1568265)), c_Transitive__Closure_Ortrancl(_1568263, _1568265)) = c_Transitive__Closure_Ortrancl(_1568263, _1568265))], (2446 ^ _779142) ^ [_815035, _815037, _815039, _815041] : [-(c_FunDef_Orp__inv__image(_815041, _815037) = c_FunDef_Orp__inv__image(_815039, _815035)), _815041 = _815039, _815037 = _815035], (31242 ^ _779142) ^ [_1339166, _1339168, _1339170] : [class_Orderings_Oorder(_1339166), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339166, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1339166, _1339168, _1339170)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1339166), _1339170)) = c_Orderings_Obot__class_Obot(tc_fun(_1339166, tc_HOL_Obool)))], (5872 ^ _779142) ^ [_872140, _872142, _872144] : [hBOOL(hAPP(hAPP(c_member(_872140), _872142), _872144)), -(hAPP(hAPP(c_Set_Oinsert(_872140), _872142), _872144) = _872144)], (41483 ^ _779142) ^ [_1598507, _1598509] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598507), tc_List_Olist(_1598507)), tc_HOL_Obool)), c_List_Olistrel1(_1598507, c_Transitive__Closure_Ortrancl(_1598507, _1598509))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598507), c_List_Olistrel1(_1598507, _1598509)))))], (20738 ^ _779142) ^ [_1143549, _1143551, _1143553] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1143549), _1143551)), _1143553) = 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), _1143549), _1143553)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143551), _1143553))), 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, _1143549, _1143553)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143551, _1143553))), _1143553)))], (18096 ^ _779142) ^ [_1097852, _1097854, _1097856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097852), _1097854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1097856)), -(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), _1097856)), _1097852)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1097856)), _1097854))))], (48118 ^ _779142) ^ [_1749016, _1749018, _1749020, _1749022, _1749024] : [hBOOL(hAPP(hAPP(_1749020, _1749024), _1749022)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749016, _1749018, _1749020), _1749022), _1749024)))], (29115 ^ _779142) ^ [_1295390, _1295392, _1295394] : [class_Lattices_Osemilattice__inf(_1295390), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295390), _1295392), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295390), _1295392), _1295394)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295390), _1295392), _1295394))], (51165 ^ _779142) ^ [_1814448, _1814450, _1814452, _1814454] : [class_Divides_Osemiring__div(_1814448), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), _1814450), _1814452)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), _1814450), _1814454)), 51176 ^ _779142 : [(51183 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), _1814452), _1814454)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1814448), _1814452), _1814450)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1814448), _1814454), _1814450))))], (51177 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1814448), _1814452), _1814450)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1814448), _1814454), _1814450))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814448), _1814452), _1814454)))]]], (43143 ^ _779142) ^ [_1639887, _1639889, _1639891] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639887)), hAPP(hAPP(c_List_Oappend(_1639887), _1639889), _1639891)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639887)), _1639889)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639887)), _1639891)))], (37235 ^ _779142) ^ [_1482352, _1482354, _1482356, _1482358] : [hAPP(c_Set_Oimage(_1482352, _1482354, _1482356), c_Orderings_Otop__class_Otop(tc_fun(_1482352, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1482354, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1482352, _1482354, _1482356), hAPP(c_Set_Ovimage(_1482352, _1482354, _1482356), _1482358)) = _1482358)], (43217 ^ _779142) ^ [_1641388, _1641390, _1641392] : [_1641388 = hAPP(hAPP(c_List_Oappend(_1641390), _1641388), _1641392), -(_1641392 = c_List_Olist_ONil(_1641390))], (39028 ^ _779142) ^ [_1535833, _1535835, _1535837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535833, _1535833), tc_HOL_Obool)), _1535835), hAPP(hAPP(c_Product__Type_OSigma(_1535833, _1535833), _1535837), hAPP(c_COMBK(tc_fun(_1535833, tc_HOL_Obool), _1535833), _1535837)))), 39034 ^ _779142 : [(39037 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535833, _1535833)), hAPP(hAPP(c_Product__Type_OPair(_1535833, _1535833), 39033 ^ [_1535833, _1535835, _1535837]), 39033 ^ [_1535833, _1535835, _1535837])), _1535835))], (39035 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535833), 39033 ^ [_1535833, _1535835, _1535837]), _1535837)))]], -(c_Relation_Orefl__on(_1535833, _1535837, _1535835))], (8101 ^ _779142) ^ [_912997, _912999, _913001, _913003, _913005] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_912997, _912999, hAPP(hAPP(c_Set_Oinsert(_912997), _913001), _913003)), _913005)), 8106 ^ _779142 : [(8111 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912997), 8104 ^ [_912997, _912999, _913001, _913003, _913005]), 8105 ^ [_912997, _912999, _913001, _913003, _913005]))], (8109 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912997, _912997, _912999, 8104 ^ [_912997, _912999, _913001, _913003, _913005], 8105 ^ [_912997, _912999, _913001, _913003, _913005]), _913005)))], (8107 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_912997), _913001), _913003) = hAPP(hAPP(c_Set_Oinsert(_912997), 8104 ^ [_912997, _912999, _913001, _913003, _913005]), 8105 ^ [_912997, _912999, _913001, _913003, _913005]))]]], (37128 ^ _779142) ^ [_1479701, _1479703, _1479705] : [-(hAPP(c_Finite__Set_Ofold1(_1479701, _1479703), _1479705) = c_HOL_OThe(_1479701, c_Finite__Set_Ofold1Set(_1479701, _1479703, _1479705)))], (5484 ^ _779142) ^ [_862994, _862996] : [_862996 = _862994, -(tc_List_Olist(_862996) = tc_List_Olist(_862994))], (6647 ^ _779142) ^ [_886349, _886351, _886353, _886355] : [-(hBOOL(hAPP(hAPP(c_member(_886349), _886351), _886353))), 6650 ^ _779142 : [(6657 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886349, tc_HOL_Obool)), _886353), _886355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886349, tc_HOL_Obool)), _886353), hAPP(hAPP(c_Set_Oinsert(_886349), _886351), _886355))))], (6651 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886349, tc_HOL_Obool)), _886353), hAPP(hAPP(c_Set_Oinsert(_886349), _886351), _886355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886349, tc_HOL_Obool)), _886353), _886355)))]]], (8308 ^ _779142) ^ [_917465, _917467, _917469, _917471, _917473, _917475] : [-(_917465 = _917467), -(hAPP(c_Fun_Ofun__upd(_917469, _917471, _917473, _917467, _917475), _917465) = hAPP(_917473, _917465))], (12248 ^ _779142) ^ [_990678] : [class_Rings_Olinordered__semidom(_990678), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990678), c_Groups_Ozero__class_Ozero(_990678)), c_Groups_Oone__class_Oone(_990678))))], (27368 ^ _779142) ^ [_1261930, _1261932, _1261934, _1261936] : [hBOOL(hAPP(_1261930, _1261932)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261934, tc_HOL_Obool)), _1261930), _1261936), _1261932)))], (42678 ^ _779142) ^ [_1629750, _1629752] : [-(c_List_Olistrelp(_1629750, _1629752, c_List_Olist_ONil(_1629750), c_List_Olist_ONil(_1629750)))], (45943 ^ _779142) ^ [_1703422, _1703424] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1703422, _1703424))))], (32771 ^ _779142) ^ [_1377588, _1377590, _1377592, _1377594, _1377596, _1377598] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377588, tc_fun(_1377590, tc_HOL_Obool))), _1377592), _1377594), _1377596), _1377598)), 32774 ^ _779142 : [(32777 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1377594, _1377596), _1377598)))], (32775 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1377592, _1377596), _1377598)))]]], (34907 ^ _779142) ^ [_1426972, _1426974, _1426976, _1426978, _1426980] : [-(_1426972 = c_Orderings_Obot__class_Obot(tc_fun(_1426974, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426976, tc_HOL_Obool)), _1426978), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426974, tc_fun(_1426976, tc_HOL_Obool)), _1426972), _1426980)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426974, tc_fun(_1426976, tc_HOL_Obool)), _1426972), hAPP(hAPP(c_COMBB(tc_fun(_1426976, tc_HOL_Obool), tc_fun(_1426976, tc_HOL_Obool), _1426974), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426976, tc_HOL_Obool)), _1426978)), _1426980)))], (52303 ^ _779142) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (6053 ^ _779142) ^ [_875781, _875783] : [-(c_Set_Othe__elem(_875781, hAPP(hAPP(c_Set_Oinsert(_875781), _875783), c_Orderings_Obot__class_Obot(tc_fun(_875781, tc_HOL_Obool)))) = _875783)], (39159 ^ _779142) ^ [_1538926, _1538928] : [c_Wellfounded_Owf(_1538926, _1538928), -(c_Wellfounded_Oacyclic(_1538926, _1538928))], (51951 ^ _779142) ^ [_1827931, _1827933, _1827935, _1827937] : [class_Divides_Osemiring__div(_1827931), -(_1827933 = c_Groups_Ozero__class_Ozero(_1827931)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827931), _1827933), _1827935)), 51962 ^ _779142 : [(51969 ^ _779142) ^ [] : [_1827935 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827931), _1827937), _1827933), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827931), _1827935), _1827933) = _1827937)], (51963 ^ _779142) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827931), _1827935), _1827933) = _1827937, -(_1827935 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827931), _1827937), _1827933))]]], (29187 ^ _779142) ^ [_1296822, _1296824] : [class_Lattices_Obounded__lattice__bot(_1296822), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296822), _1296824), c_Orderings_Obot__class_Obot(_1296822)) = c_Orderings_Obot__class_Obot(_1296822))], (29556 ^ _779142) ^ [_1305134, _1305136, _1305138, _1305140, _1305142] : [class_Orderings_Olinorder(_1305134), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305134, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1305134, _1305136, _1305138)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1305134, _1305140, _1305142)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1305134, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305134), _1305136), _1305140), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305134), _1305138), _1305142)))], (43363 ^ _779142) ^ [_1644759, _1644761, _1644763, _1644765, _1644767] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644761)), _1644763)))), -(hAPP(hAPP(c_List_Olist__update(_1644761, hAPP(hAPP(c_List_Oappend(_1644761), _1644763), _1644765)), _1644759), _1644767) = hAPP(hAPP(c_List_Oappend(_1644761), _1644763), hAPP(hAPP(c_List_Olist__update(_1644761, _1644765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644761)), _1644763))), _1644767)))], (2734 ^ _779142) ^ [_819525, _819527, _819529, _819531, _819533, _819535, _819537, _819539] : [-(c_Product__Type_Oapsnd(_819539, _819535, _819531, _819527) = c_Product__Type_Oapsnd(_819537, _819533, _819529, _819525)), _819539 = _819537, _819535 = _819533, _819531 = _819529, _819527 = _819525], (40600 ^ _779142) ^ [_1574344, _1574346, _1574348, _1574350] : [c_Wellfounded_Oacyclic(_1574344, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574344, _1574344)), hAPP(hAPP(c_Product__Type_OPair(_1574344, _1574344), _1574346), _1574348)), _1574350)), 40603 ^ _779142 : [(40606 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574344, _1574344)), hAPP(hAPP(c_Product__Type_OPair(_1574344, _1574344), _1574348), _1574346)), c_Transitive__Closure_Ortrancl(_1574344, _1574350)))], (40604 ^ _779142) ^ [] : [-(c_Wellfounded_Oacyclic(_1574344, _1574350))]]], (23083 ^ _779142) ^ [_1185404, _1185406, _1185408] : [class_Groups_Ogroup__add(_1185404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185404), hAPP(c_Groups_Ouminus__class_Ouminus(_1185404), _1185406)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185404), _1185406), _1185408)) = _1185408)], (11229 ^ _779142) ^ [_972207] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972207), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4430 ^ _779142) ^ [_846369, _846371] : [_846371 = _846369, -(c_List_Omember(_846371) = c_List_Omember(_846369))], (9217 ^ _779142) ^ [_936274, _936276, _936278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936274), _936276)), _936278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936274), _936278)))], (39279 ^ _779142) ^ [_1541802] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1541802, tc_HOL_Obool) = c_Set_OBall(_1541802))], (5134 ^ _779142) ^ [_857439, _857441, _857443, _857445] : [-(c_List_Oupt(_857445, _857441) = c_List_Oupt(_857443, _857439)), _857445 = _857443, _857441 = _857439], (5679 ^ _779142) ^ [_868795, _868797, _868799, _868801] : [hBOOL(hAPP(hAPP(c_member(_868795), _868797), hAPP(hAPP(c_Set_Oinsert(_868795), _868799), _868801))), -(_868797 = _868799), -(hBOOL(hAPP(hAPP(c_member(_868795), _868797), _868801)))], (28062 ^ _779142) ^ [_1274880, _1274882, _1274884, _1274886] : [class_Groups_Oordered__ab__group__add(_1274880), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274880), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274880), _1274882), _1274884)), _1274886) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274880), _1274882), _1274886)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274880), _1274884), _1274886)))], (890 ^ _779142) ^ [_792431, _792433, _792435, _792437, _792439, _792441, _792443, _792445, _792447, _792449] : [-(c_Fun_Obij__betw(_792447, _792443, _792439, _792435, _792431)), c_Fun_Obij__betw(_792449, _792445, _792441, _792437, _792433), _792449 = _792447, _792445 = _792443, _792441 = _792439, _792437 = _792435, _792433 = _792431], (7014 ^ _779142) ^ [_894400, _894402, _894404, _894406] : [hBOOL(hAPP(hAPP(c_member(_894400), _894402), _894404)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894400, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_894400), _894402), _894406)), _894404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894400, tc_HOL_Obool)), _894406), _894404))], (43155 ^ _779142) ^ [_1640258, _1640260, _1640262] : [-(hAPP(c_List_Oset(_1640258), hAPP(hAPP(c_List_Oappend(_1640258), _1640260), _1640262)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640258, tc_HOL_Obool)), hAPP(c_List_Oset(_1640258), _1640260)), hAPP(c_List_Oset(_1640258), _1640262)))], (44319 ^ _779142) ^ [_1665415, _1665417, _1665419, _1665421, _1665423, _1665425] : [-(hAPP(hAPP(c_List_Ozip(_1665415, _1665417), _1665419), hAPP(hAPP(c_List_Omap(_1665421, _1665417), _1665423), _1665425)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665415, _1665421), tc_prod(_1665415, _1665417)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665415, _1665421, tc_prod(_1665415, _1665417)), hAPP(hAPP(c_COMBC(_1665415, tc_fun(_1665421, _1665417), tc_fun(_1665421, tc_prod(_1665415, _1665417))), hAPP(hAPP(c_COMBB(tc_fun(_1665417, tc_prod(_1665415, _1665417)), tc_fun(tc_fun(_1665421, _1665417), tc_fun(_1665421, tc_prod(_1665415, _1665417))), _1665415), c_COMBB(_1665417, tc_prod(_1665415, _1665417), _1665421)), c_Product__Type_OPair(_1665415, _1665417))), _1665423))), hAPP(hAPP(c_List_Ozip(_1665415, _1665421), _1665419), _1665425)))], (30557 ^ _779142) ^ [_1325804, _1325806, _1325808] : [class_Lattices_Olattice(_1325804), hAPP(_1325806, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325804), 30562 ^ [_1325804, _1325806, _1325808]), 30563 ^ [_1325804, _1325806, _1325808])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325804), hAPP(_1325806, 30562 ^ [_1325804, _1325806, _1325808])), hAPP(_1325806, 30563 ^ [_1325804, _1325806, _1325808])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325804), _1325808)), -(_1325808 = c_Orderings_Obot__class_Obot(tc_fun(_1325804, tc_HOL_Obool))), -(hAPP(_1325806, c_Big__Operators_Olattice__class_OInf__fin(_1325804, _1325808)) = c_Big__Operators_Olattice__class_OInf__fin(_1325804, hAPP(c_Set_Oimage(_1325804, _1325804, _1325806), _1325808)))], (4808 ^ _779142) ^ [_852358, _852360, _852362, _852364] : [-(c_List_Olistrel(_852364, _852360) = c_List_Olistrel(_852362, _852358)), _852364 = _852362, _852360 = _852358], (32601 ^ _779142) ^ [_1374260, _1374262, _1374264, _1374266] : [class_Rings_Ocomm__semiring__1(_1374260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1374260), c_Groups_Oone__class_Oone(_1374260)), c_Groups_Oone__class_Oone(_1374260))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1374260), hAPP(hAPP(c_COMBB(_1374260, _1374260, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1374260), _1374262)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1374260, _1374260), hAPP(hAPP(c_COMBB(_1374260, tc_fun(_1374260, _1374260), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1374260)), c_Nat_Osemiring__1__class_Oof__nat(_1374260))), _1374264))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1374266))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374260), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374260), _1374266)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1374260), _1374262), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1374260), _1374262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374260), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1374266), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1374264)))))], (42750 ^ _779142) ^ [_1631029, _1631031, _1631033] : [-(hBOOL(hAPP(hAPP(c_member(_1631029), _1631031), hAPP(c_List_Oset(_1631029), _1631033)))), -(c_List_Oremove1(_1631029, _1631031, _1631033) = _1631033)], (31521 ^ _779142) ^ [_1344612, _1344614, _1344616, _1344618] : [class_Lattices_Osemilattice__inf(_1344612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344612), _1344614)), 31531 ^ _779142 : [(31534 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344612), _1344616), 31530 ^ [_1344612, _1344614, _1344616, _1344618]))], (31532 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344612), 31530 ^ [_1344612, _1344614, _1344616, _1344618]), _1344614)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1344612), _1344616), _1344618)), hAPP(hAPP(c_Finite__Set_Ofold(_1344612, _1344612, c_Lattices_Osemilattice__inf__class_Oinf(_1344612)), _1344618), _1344614))))], (44849 ^ _779142) ^ [_1677587, _1677589] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1677587), _1677589) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677587)), hAPP(c_Code__Numeral_Onat__of, _1677589))))], (19524 ^ _779142) ^ [_1122445] : [19526 ^ _779142 : [(19529 ^ _779142) ^ [] : [hBOOL(hAPP(_1122445, hAPP(c_Int_Onat, 19525 ^ [_1122445])))], (19527 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19525 ^ [_1122445])))]], 19530 ^ _779142 : [(19531 ^ _779142) ^ [_1122578] : [-(hBOOL(hAPP(_1122445, _1122578)))]]], (34499 ^ _779142) ^ [_1415267, _1415269, _1415271, _1415273] : [_1415267 = c_Orderings_Obot__class_Obot(tc_fun(_1415269, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415269, tc_fun(_1415271, tc_HOL_Obool)), _1415267), hAPP(c_COMBK(tc_fun(_1415271, tc_HOL_Obool), _1415269), _1415273)) = c_Orderings_Obot__class_Obot(tc_fun(_1415271, tc_HOL_Obool)))], (49358 ^ _779142) ^ [_1776874, _1776876, _1776878] : [c_Equiv__Relations_Oequiv(_1776874, _1776876, _1776878), 49361 ^ _779142 : [(49366 ^ _779142) ^ [] : [-(c_Relation_Otrans(_1776874, _1776878))], (49364 ^ _779142) ^ [] : [-(c_Relation_Osym(_1776874, _1776878))], (49362 ^ _779142) ^ [] : [-(c_Relation_Orefl__on(_1776874, _1776876, _1776878))]]], (7402 ^ _779142) ^ [_901682, _901684, _901686] : [class_Orderings_Opreorder(_901682), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901682), _901684), _901686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901682), _901686), _901684))], (39431 ^ _779142) ^ [_1546116, _1546118, _1546120, _1546122, _1546124, _1546126] : [c_Fun_Oinj__on(_1546116, _1546118, _1546120, _1546122), c_Fun_Oinj__on(_1546118, _1546124, _1546126, hAPP(c_Set_Oimage(_1546116, _1546118, _1546120), _1546122)), -(c_Fun_Oinj__on(_1546116, _1546124, hAPP(c_Fun_Ocomp(_1546118, _1546124, _1546116, _1546126), _1546120), _1546122))], (26872 ^ _779142) ^ [_1252887, _1252889, _1252891] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252887, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252887, tc_HOL_Obool)), _1252889), _1252891)), _1252891) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252887, tc_HOL_Obool)), _1252889), _1252891))], (5878 ^ _779142) ^ [_872249, _872251, _872253, _872255] : [hBOOL(hAPP(hAPP(c_member(_872249), _872251), _872253)), -(hBOOL(hAPP(hAPP(c_member(_872249), _872251), hAPP(hAPP(c_Set_Oinsert(_872249), _872255), _872253))))], (41699 ^ _779142) ^ [_1605319, _1605321, _1605323, _1605325, _1605327] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605319), tc_List_Olist(_1605319))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605319), tc_List_Olist(_1605319)), _1605321), hAPP(hAPP(c_List_Olist_OCons(_1605319), _1605323), _1605325))), c_List_Olistrel(_1605319, _1605327))), 41704 ^ _779142 : [(41709 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605319), tc_List_Olist(_1605319))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605319), tc_List_Olist(_1605319)), 41703 ^ [_1605319, _1605321, _1605323, _1605325, _1605327]), _1605325)), c_List_Olistrel(_1605319, _1605327))))], (41707 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605319, _1605319)), hAPP(hAPP(c_Product__Type_OPair(_1605319, _1605319), 41702 ^ [_1605319, _1605321, _1605323, _1605325, _1605327]), _1605323)), _1605327)))], (41705 ^ _779142) ^ [] : [-(_1605321 = hAPP(hAPP(c_List_Olist_OCons(_1605319), 41702 ^ [_1605319, _1605321, _1605323, _1605325, _1605327]), 41703 ^ [_1605319, _1605321, _1605323, _1605325, _1605327]))]]], (46182 ^ _779142) ^ [_1707800, _1707802, _1707804, _1707806] : [class_Orderings_Olinorder(_1707800), 46185 ^ _779142 : [(46194 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707800, hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707802), hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707804), _1707806)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707800), _1707802), _1707804)), c_List_Olinorder__class_Osorted(_1707800, hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707804), _1707806))], (46186 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1707800, hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707802), hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707804), _1707806))), 46189 ^ _779142 : [(46192 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707800, hAPP(hAPP(c_List_Olist_OCons(_1707800), _1707804), _1707806)))], (46190 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707800), _1707802), _1707804)))]]]]], (40546 ^ _779142) ^ [_1573143, _1573145, _1573147, _1573149] : [-(hBOOL(hAPP(hAPP(c_member(_1573143), _1573145), hAPP(c_Relation_ODomain(_1573143, _1573143), _1573147)))), 40549 ^ _779142 : [(40556 ^ _779142) ^ [] : [_1573145 = _1573149, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573143, _1573143)), hAPP(hAPP(c_Product__Type_OPair(_1573143, _1573143), _1573145), _1573149)), c_Transitive__Closure_Ortrancl(_1573143, _1573147))))], (40550 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573143, _1573143)), hAPP(hAPP(c_Product__Type_OPair(_1573143, _1573143), _1573145), _1573149)), c_Transitive__Closure_Ortrancl(_1573143, _1573147))), -(_1573145 = _1573149)]]], (6504 ^ _779142) ^ [_883409, _883411, _883413, _883415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883409, tc_HOL_Obool)), _883411), _883413)), hBOOL(hAPP(hAPP(c_member(_883409), _883415), _883411)), -(hBOOL(hAPP(hAPP(c_member(_883409), _883415), _883413)))], (11153 ^ _779142) ^ [_971079] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971079), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _971079)], (25868 ^ _779142) ^ [] : [-(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)))))], (17601 ^ _779142) ^ [] : [-(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)))], (16579 ^ _779142) ^ [_1070934, _1070936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070936), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070934), _1070936)))], (29417 ^ _779142) ^ [_1301890, _1301892, _1301894, _1301896] : [class_Orderings_Oorder(_1301890), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301890, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301890, _1301892), _1301894)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301890, _1301894), _1301896)) = c_Orderings_Obot__class_Obot(tc_fun(_1301890, tc_HOL_Obool)))], (24205 ^ _779142) ^ [_1205252] : [class_Rings_Osemiring__1(_1205252), -(c_Int_Oiszero(_1205252, c_Groups_Ozero__class_Ozero(_1205252)))], (41911 ^ _779142) ^ [_1611041, _1611043, _1611045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611041, tc_HOL_Obool)), hAPP(c_List_Oset(_1611041), hAPP(hAPP(c_List_Otake(_1611041), _1611043), _1611045))), hAPP(c_List_Oset(_1611041), _1611045))))], (37651 ^ _779142) ^ [_1493090, _1493092, _1493094, _1493096, _1493098] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493090, _1493092), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493090, tc_HOL_Obool)), _1493094), _1493096)), hAPP(c_COMBK(tc_fun(_1493092, tc_HOL_Obool), _1493090), _1493098)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493090, _1493092), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493090, _1493092), _1493094), hAPP(c_COMBK(tc_fun(_1493092, tc_HOL_Obool), _1493090), _1493098))), hAPP(hAPP(c_Product__Type_OSigma(_1493090, _1493092), _1493096), hAPP(c_COMBK(tc_fun(_1493092, tc_HOL_Obool), _1493090), _1493098))))], (32029 ^ _779142) ^ [_1359260, _1359262, _1359264, _1359266, _1359268] : [class_Fields_Ofield__inverse__zero(_1359260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359262), _1359264)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359262, _1359260), hAPP(hAPP(c_COMBS(_1359262, _1359260, _1359260), hAPP(hAPP(c_COMBB(_1359260, tc_fun(_1359260, _1359260), _1359262), c_Rings_Oinverse__class_Odivide(_1359260)), _1359266)), _1359268)), _1359264) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359260), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359262, _1359260), _1359266), _1359264)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359262, _1359260), _1359268), _1359264)))], (21073 ^ _779142) ^ [_1149741] : [21075 ^ _779142 : [(21078 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21074 ^ [_1149741]))], (21076 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21074 ^ [_1149741]), _1149741)))]], -(c_Nat__Transfer_Onat__set(_1149741))], (50887 ^ _779142) ^ [_1809663, _1809665] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809663), _1809665))), -(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), _1809663, _1809665))], (49170 ^ _779142) ^ [_1773091] : [-(c_Relation_Oantisym(_1773091, c_Relation_OId(_1773091)))], (1806 ^ _779142) ^ [_804659, _804661] : [-(class_Groups_Omonoid__add(_804659)), _804661 = _804659, class_Groups_Omonoid__add(_804661)], (4672 ^ _779142) ^ [_850194, _850196, _850198, _850200, _850202, _850204] : [-(c_Relation_OImage(_850204, _850200, _850196) = c_Relation_OImage(_850202, _850198, _850194)), _850204 = _850202, _850200 = _850198, _850196 = _850194], (10887 ^ _779142) ^ [_967089, _967091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967089), _967091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967089), hAPP(c_Nat_OSuc, _967091))))], (36552 ^ _779142) ^ [_1466770, _1466772, _1466774, _1466776, _1466778, _1466780] : [c_Fun_Oinj__on(_1466770, _1466772, _1466774, _1466776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466770, tc_HOL_Obool)), _1466778), _1466776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466770, tc_HOL_Obool)), _1466780), _1466776)), -(hAPP(c_Set_Oimage(_1466770, _1466772, _1466774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466770, tc_HOL_Obool)), _1466778), _1466780)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466772, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466770, _1466772, _1466774), _1466778)), hAPP(c_Set_Oimage(_1466770, _1466772, _1466774), _1466780)))], (17133 ^ _779142) ^ [_1080478, _1080480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1080480)), -(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), _1080478), _1080480))))], (34781 ^ _779142) ^ [_1423831, _1423833, _1423835, _1423837] : [class_Complete__Lattice_Ocomplete__lattice(_1423831), -(_1423833 = c_Orderings_Obot__class_Obot(tc_fun(_1423835, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423835, _1423831), _1423833), hAPP(c_COMBK(_1423831, _1423835), _1423837)) = _1423837)], (29604 ^ _779142) ^ [_1306250, _1306252, _1306254, _1306256, _1306258, _1306260, _1306262, _1306264] : [c_Finite__Set_Ofolding__image__simple(_1306250, _1306252, _1306254, _1306256, _1306258, _1306260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306252), _1306262)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306252), _1306264)), -(hAPP(hAPP(_1306254, hAPP(_1306260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306252, tc_HOL_Obool)), _1306262), _1306264))), hAPP(_1306260, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306252, tc_HOL_Obool)), _1306262), _1306264))) = hAPP(hAPP(_1306254, hAPP(_1306260, _1306262)), hAPP(_1306260, _1306264)))], (40972 ^ _779142) ^ [_1583548, _1583550] : [-(c_Relation_Osingle__valued(_1583548, _1583548, c_Relation_OId__on(_1583548, _1583550)))], (52705 ^ _779142) ^ [] : [hBOOL(c_fFalse)], (13191 ^ _779142) ^ [_1007874, _1007876] : [_1007874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007874), _1007876) = _1007876)], (14549 ^ _779142) ^ [_1032871, _1032873, _1032875, _1032877] : [class_Fields_Olinordered__field(_1032871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032871), _1032873), c_Groups_Ozero__class_Ozero(_1032871))), 14556 ^ _779142 : [(14563 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032871), _1032877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032871), _1032875), _1032873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032871), _1032875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032871), _1032877), _1032873))))], (14557 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032871), _1032875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032871), _1032877), _1032873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032871), _1032877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032871), _1032875), _1032873))))]]], (32261 ^ _779142) ^ [_1366274, _1366276] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366274), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1366276))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366274), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366276))), 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))))], (20518 ^ _779142) ^ [_1139296, _1139298, _1139300] : [-(hBOOL(hAPP(_1139296, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139298), _1139300)))), 20521 ^ _779142 : [(20524 ^ _779142) ^ [] : [hBOOL(hAPP(_1139296, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20522 ^ _779142) ^ [] : [-(_1139300 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 20527 ^ _779142 : [(20528 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139300)))], (20534 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 20530 ^ [_1139296, _1139298, _1139300]), _1139300)))], (20538 ^ _779142) ^ [] : [hBOOL(hAPP(_1139296, 20529 ^ [_1139296, _1139298, _1139300]))], (20536 ^ _779142) ^ [] : [-(_1139298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139300), 20529 ^ [_1139296, _1139298, _1139300])), 20530 ^ [_1139296, _1139298, _1139300]))], (20532 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20530 ^ [_1139296, _1139298, _1139300])))]], 20539 ^ _779142 : [(20540 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20546 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20542 ^ [_1139296, _1139298, _1139300]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20550 ^ _779142) ^ [] : [hBOOL(hAPP(_1139296, 20541 ^ [_1139296, _1139298, _1139300]))], (20548 ^ _779142) ^ [] : [-(_1139298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139300), 20541 ^ [_1139296, _1139298, _1139300])), 20542 ^ [_1139296, _1139298, _1139300]))], (20544 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139300), 20542 ^ [_1139296, _1139298, _1139300])))]]], (32429 ^ _779142) ^ [_1370207, _1370209] : [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(_1370209))), 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)), _1370207))))), -(hAPP(c_Nat_OSuc, _1370207) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370209))], (2892 ^ _779142) ^ [_821960, _821962, _821964, _821966] : [-(c_Nitpick_OAbs__Frac(_821966, _821962) = c_Nitpick_OAbs__Frac(_821964, _821960)), _821966 = _821964, _821962 = _821960], (6271 ^ _779142) ^ [_879642, _879644, _879646, _879648] : [class_Orderings_Oorder(_879642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879642), _879644), _879646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879642), _879648), _879644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879642), _879648), _879646)))], (42876 ^ _779142) ^ [_1633545, _1633547] : [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), _1633545), _1633547))), 42879 ^ _779142 : [(42886 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633545), _1633547))), -(c_List_Oupto(_1633545, _1633547) = c_List_Olist_ONil(tc_Int_Oint))], (42880 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633545), _1633547)), -(c_List_Oupto(_1633545, _1633547) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1633545), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1633545), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1633547)))]]], (46841 ^ _779142) ^ [_1721132, _1721134, _1721136, _1721138] : [hBOOL(hAPP(hAPP(c_member(_1721132), _1721134), hAPP(c_List_Oset(_1721132), c_List_OtakeWhile(_1721132, _1721136, _1721138)))), 46844 ^ _779142 : [(46847 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1721136, _1721134)))], (46845 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721132), _1721134), hAPP(c_List_Oset(_1721132), _1721138))))]]], (3638 ^ _779142) ^ [_833599, _833601, _833603, _833605] : [-(c_List_Oremdups(_833605, _833601) = c_List_Oremdups(_833603, _833599)), _833605 = _833603, _833601 = _833599], (34288 ^ _779142) ^ [_1408727, _1408729, _1408731, _1408733, _1408735, _1408737, _1408739, _1408741] : [hBOOL(hAPP(hAPP(c_member(_1408727), _1408729), _1408731)), hBOOL(hAPP(hAPP(hAPP(_1408733, _1408729), _1408735), _1408737)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408727, tc_fun(_1408739, tc_fun(_1408741, tc_HOL_Obool))), _1408731), _1408733), _1408735), _1408737)))], (34741 ^ _779142) ^ [_1422707, _1422709, _1422711, _1422713, _1422715, _1422717] : [hBOOL(hAPP(hAPP(c_member(_1422707), _1422709), _1422711)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422707, tc_fun(_1422713, tc_HOL_Obool)), _1422711), hAPP(hAPP(c_COMBB(tc_fun(_1422713, tc_HOL_Obool), tc_fun(_1422713, tc_HOL_Obool), _1422707), hAPP(c_Set_Oinsert(_1422713), _1422715)), _1422717)) = hAPP(hAPP(c_Set_Oinsert(_1422713), _1422715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422707, tc_fun(_1422713, tc_HOL_Obool)), _1422711), _1422717)))], (35715 ^ _779142) ^ [_1448554, _1448556, _1448558, _1448560] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1448554, tc_HOL_Obool)), _1448556), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448554), _1448558), _1448560))), 35719 ^ _779142 : [(35722 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1448554), 35718 ^ [_1448554, _1448556, _1448558, _1448560]), _1448558)))], (35720 ^ _779142) ^ [] : [-(_1448556 = hAPP(c_Relation_OImage(_1448554, _1448554, _1448560), hAPP(hAPP(c_Set_Oinsert(_1448554), 35718 ^ [_1448554, _1448556, _1448558, _1448560]), c_Orderings_Obot__class_Obot(tc_fun(_1448554, tc_HOL_Obool)))))]]], (28130 ^ _779142) ^ [_1276306, _1276308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276306), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1276306, tc_HOL_Obool), _1276308))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1276306, tc_HOL_Obool)), _1276308)))], (15223 ^ _779142) ^ [_1045595, _1045597, _1045599] : [class_Orderings_Olinorder(_1045595), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045595), _1045597), _1045599) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045595), _1045599), _1045597))], (9491 ^ _779142) ^ [_940898, _940900, _940902, _940904] : [class_Groups_Ocomm__monoid__mult(_940898), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_940900), _940902))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_940900, _940898), _940904), _940902) = c_Groups_Oone__class_Oone(_940898))], (43790 ^ _779142) ^ [_1654988, _1654990, _1654992] : [-(hAPP(c_List_Orotate1(_1654988), hAPP(c_List_Orotate(_1654988, _1654990), _1654992)) = hAPP(c_List_Orotate(_1654988, _1654990), hAPP(c_List_Orotate1(_1654988), _1654992)))], (8813 ^ _779142) ^ [_927578, _927580, _927582] : [class_Groups_Ogroup__add(_927578), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927578), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_927578), _927580), _927582)), _927582) = _927580)], (21926 ^ _779142) ^ [_1164602, _1164604, _1164606] : [class_Rings_Olinordered__semidom(_1164602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164602), c_Groups_Ozero__class_Ozero(_1164602)), _1164604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164602), c_Groups_Ozero__class_Ozero(_1164602)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164602), _1164604), _1164606))))], (24305 ^ _779142) ^ [_1206894, _1206896] : [class_Int_Onumber__ring(_1206894), -(hAPP(c_Int_Oring__1__class_Oof__int(_1206894), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206896)) = hAPP(c_Int_Onumber__class_Onumber__of(_1206894), _1206896))], (44414 ^ _779142) ^ [_1668435, _1668437, _1668439, _1668441, _1668443] : [c_Fun_Oinj__on(_1668435, _1668437, _1668439, c_Orderings_Otop__class_Otop(tc_fun(_1668435, tc_HOL_Obool))), 44417 ^ _779142 : [(44424 ^ _779142) ^ [] : [_1668441 = _1668443, -(hAPP(hAPP(c_List_Omap(_1668435, _1668437), _1668439), _1668441) = hAPP(hAPP(c_List_Omap(_1668435, _1668437), _1668439), _1668443))], (44418 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Omap(_1668435, _1668437), _1668439), _1668441) = hAPP(hAPP(c_List_Omap(_1668435, _1668437), _1668439), _1668443), -(_1668441 = _1668443)]]], (25314 ^ _779142) ^ [_1223987, _1223989] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1223987)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223989)) = 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)))), _1223987)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223989)))], (33085 ^ _779142) ^ [_1384559, _1384561] : [-(c_Divides_Odivmod__int(_1384559, _1384561) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384559), _1384561)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384559, _1384561)))], (36612 ^ _779142) ^ [_1468090, _1468092, _1468094, _1468096, _1468098] : [c_Fun_Oinj__on(_1468090, _1468092, _1468094, c_Orderings_Otop__class_Otop(tc_fun(_1468090, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1468090, _1468092, _1468094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468090, tc_HOL_Obool)), _1468096), _1468098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468092, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468090, _1468092, _1468094), _1468096)), hAPP(c_Set_Oimage(_1468090, _1468092, _1468094), _1468098)))], (34747 ^ _779142) ^ [_1422912, _1422914, _1422916, _1422918, _1422920] : [hBOOL(hAPP(hAPP(c_member(_1422912), _1422914), _1422916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422918, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422912, tc_fun(_1422918, tc_HOL_Obool)), _1422916), _1422920)), hAPP(_1422920, _1422914))))], (52273 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (44462 ^ _779142) ^ [_1669430, _1669432, _1669434, _1669436, _1669438, _1669440] : [-(hAPP(hAPP(c_List_Omap(_1669430, _1669432), _1669434), hAPP(hAPP(c_List_Omap(_1669436, _1669430), _1669438), _1669440)) = hAPP(hAPP(c_List_Omap(_1669436, _1669432), hAPP(c_Fun_Ocomp(_1669430, _1669432, _1669436, _1669434), _1669438)), _1669440))], (47203 ^ _779142) ^ [_1728668, _1728670, _1728672, _1728674] : [-(c_List_Oconcat(_1728668, hAPP(hAPP(c_List_Omap(_1728670, tc_List_Olist(_1728668)), _1728672), _1728674)) = c_List_Omaps(_1728670, _1728668, _1728672, _1728674))], (25840 ^ _779142) ^ [] : [-(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))))))], (10147 ^ _779142) ^ [_953756, _953758, _953760, _953762] : [class_Rings_Ocomm__semiring__1(_953756), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953756), _953758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953756), _953760), _953762)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953756), _953760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953756), _953758), _953762)))], (16497 ^ _779142) ^ [_1069520, _1069522, _1069524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069520), _1069522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069522), _1069524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069520), _1069524)))], (46015 ^ _779142) ^ [_1704802, _1704804, _1704806, _1704808] : [class_Groups_Ocomm__monoid__add(_1704802), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704802), _1704804), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704806, _1704808))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1704802), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704802), _1704804), c_List_Oupt(_1704806, _1704808))))], (50516 ^ _779142) ^ [_1802595, _1802597, _1802599] : [c_List_Olist__ex(tc_Nat_Onat, _1802595, c_List_Oupt(_1802597, _1802599)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802595), _1802597, _1802599)], (26444 ^ _779142) ^ [_1244264, _1244266, _1244268, _1244270] : [class_Lattices_Osemilattice__sup(_1244264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244264), _1244266), _1244268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244264), _1244266), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1244264), _1244270), _1244268))))], (41511 ^ _779142) ^ [_1599420, _1599422, _1599424, _1599426] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599420), tc_List_Olist(_1599420))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599420), tc_List_Olist(_1599420)), _1599422), _1599424)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1599420), c_List_Olistrel1(_1599420, _1599426)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599420)), _1599422) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599420)), _1599424))], (52365 ^ _779142) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (32709 ^ _779142) ^ [_1376565] : [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), _1376565))), 32712 ^ _779142 : [(32719 ^ _779142) ^ [] : [-(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), _1376565)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1376565)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1376565)), 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), _1376565)))))], (32713 ^ _779142) ^ [] : [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), _1376565))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1376565)) = 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)))]]], (6839 ^ _779142) ^ [_890558, _890560, _890562, _890564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890558, tc_HOL_Obool)), _890560), hAPP(hAPP(c_Set_Oinsert(_890558), _890562), _890564))), 6842 ^ _779142 : [(6849 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890558), _890562), _890560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890558, tc_HOL_Obool)), _890560), _890564)))], (6843 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890558), _890562), _890560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890558, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890558, tc_HOL_Obool)), _890560), hAPP(hAPP(c_Set_Oinsert(_890558), _890562), c_Orderings_Obot__class_Obot(tc_fun(_890558, tc_HOL_Obool))))), _890564)))]]], (25464 ^ _779142) ^ [_1226721] : [c_Int_OBit0(_1226721) = c_Int_OPls, -(_1226721 = c_Int_OPls)], (21374 ^ _779142) ^ [_1154859, _1154861, _1154863] : [class_Orderings_Oorder(_1154859), 21377 ^ _779142 : [(21384 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154859), _1154861), _1154863))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1154859, _1154861, _1154863) = c_Orderings_Obot__class_Obot(tc_fun(_1154859, tc_HOL_Obool)))], (21378 ^ _779142) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1154859, _1154861, _1154863) = c_Orderings_Obot__class_Obot(tc_fun(_1154859, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154859), _1154861), _1154863))]]], (42676 ^ _779142) ^ [_1629705, _1629707, _1629709, _1629711] : [-(c_List_Oremove1(_1629705, _1629707, c_List_Oremove1(_1629705, _1629709, _1629711)) = c_List_Oremove1(_1629705, _1629709, c_List_Oremove1(_1629705, _1629707, _1629711)))], (21330 ^ _779142) ^ [_1154174, _1154176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154174)), -(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), _1154174), _1154176))))], (48124 ^ _779142) ^ [_1749129, _1749131, _1749133, _1749135, _1749137] : [hBOOL(hAPP(hAPP(_1749129, _1749131), _1749133)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749135, _1749137, _1749129), _1749133), _1749131)))], (44321 ^ _779142) ^ [_1665557, _1665559, _1665561, _1665563, _1665565, _1665567, _1665569, _1665571] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665557, _1665559), _1665561), _1665563), hAPP(hAPP(c_List_Ozip(_1665557, _1665559), _1665565), hAPP(hAPP(c_List_Omap(_1665567, _1665559), _1665569), _1665571))) = hAPP(hAPP(c_List_Omap(tc_prod(_1665557, _1665567), _1665561), hAPP(c_Product__Type_Oprod_Oprod__case(_1665557, _1665567, _1665561), hAPP(hAPP(c_COMBB(tc_fun(_1665567, tc_prod(_1665557, _1665559)), tc_fun(_1665567, _1665561), _1665557), hAPP(c_COMBB(tc_prod(_1665557, _1665559), _1665561, _1665567), _1665563)), hAPP(hAPP(c_COMBC(_1665557, tc_fun(_1665567, _1665559), tc_fun(_1665567, tc_prod(_1665557, _1665559))), hAPP(hAPP(c_COMBB(tc_fun(_1665559, tc_prod(_1665557, _1665559)), tc_fun(tc_fun(_1665567, _1665559), tc_fun(_1665567, tc_prod(_1665557, _1665559))), _1665557), c_COMBB(_1665559, tc_prod(_1665557, _1665559), _1665567)), c_Product__Type_OPair(_1665557, _1665559))), _1665569)))), hAPP(hAPP(c_List_Ozip(_1665557, _1665567), _1665565), _1665571)))], (698 ^ _779142) ^ [_789643, _789645, _789647, _789649, _789651, _789653] : [-(c_List_Oall__interval__int(_789651, _789647, _789643)), c_List_Oall__interval__int(_789653, _789649, _789645), _789653 = _789651, _789649 = _789647, _789645 = _789643], (41974 ^ _779142) ^ [_1612498, _1612500, _1612502] : [41976 ^ _779142 : [(41979 ^ _779142) ^ [] : [hBOOL(hAPP(_1612502, hAPP(hAPP(c_List_Onth(_1612498), _1612500), 41975 ^ [_1612498, _1612500, _1612502])))], (41977 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41975 ^ [_1612498, _1612500, _1612502]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612498)), _1612500))))]], 41980 ^ _779142 : [(41981 ^ _779142) ^ [_1612700] : [hBOOL(hAPP(hAPP(c_member(_1612498), _1612700), hAPP(c_List_Oset(_1612498), _1612500))), -(hBOOL(hAPP(_1612502, _1612700)))]]], (8927 ^ _779142) ^ [_929838, _929840, _929842] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929838), _929840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929838, tc_HOL_Obool)), _929842), _929840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_929838), _929842)), hAPP(c_Finite__Set_Ocard(_929838), _929840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929838, tc_HOL_Obool)), _929842), _929840)))], (37187 ^ _779142) ^ [_1481075, _1481077, _1481079, _1481081] : [-(hAPP(c_Set_Ovimage(_1481075, _1481077, _1481079), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1481077, tc_HOL_Obool)), _1481081)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1481075, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481075, _1481077, _1481079), _1481081)))], (15253 ^ _779142) ^ [_1046206, _1046208, _1046210, _1046212] : [class_Orderings_Olinorder(_1046206), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046206), _1046208), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046206), _1046210), _1046212)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046206), _1046210), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046206), _1046208), _1046212)))], (52515 ^ _779142) ^ [_1834773] : [-(class_Nat_Osize(tc_List_Olist(_1834773)))], (41102 ^ _779142) ^ [_1586933, _1586935, _1586937, _1586939, _1586941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586933, _1586933)), hAPP(hAPP(c_Product__Type_OPair(_1586933, _1586933), _1586935), _1586937)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586933, _1586933), tc_HOL_Obool), _1586939), _1586941))), 41107 ^ _779142 : [(41110 ^ _779142) ^ [] : [-(_1586935 = _1586937)], (41108 ^ _779142) ^ [] : [-(_1586939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41113 ^ _779142 : [(41118 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586933, _1586933)), hAPP(hAPP(c_Product__Type_OPair(_1586933, _1586933), 41111 ^ [_1586933, _1586935, _1586937, _1586939, _1586941]), _1586937)), _1586941)))], (41116 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586933, _1586933)), hAPP(hAPP(c_Product__Type_OPair(_1586933, _1586933), _1586935), 41111 ^ [_1586933, _1586935, _1586937, _1586939, _1586941])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586933, _1586933), tc_HOL_Obool), 41112 ^ [_1586933, _1586935, _1586937, _1586939, _1586941]), _1586941))))], (41114 ^ _779142) ^ [] : [-(_1586939 = hAPP(c_Nat_OSuc, 41112 ^ [_1586933, _1586935, _1586937, _1586939, _1586941]))]]], (28340 ^ _779142) ^ [_1279900, _1279902, _1279904, _1279906] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1279900, tc_HOL_Obool)), _1279902), _1279904)), hBOOL(hAPP(hAPP(c_member(_1279900), _1279906), _1279902)), -(hBOOL(hAPP(hAPP(c_member(_1279900), _1279906), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1279900, tc_HOL_Obool), _1279904))))], (7076 ^ _779142) ^ [_895866, _895868, _895870, _895872, _895874, _895876] : [c_Finite__Set_Ofun__left__comm(_895866, _895868, _895870), hBOOL(hAPP(c_Finite__Set_Ofinite(_895866), _895872)), hBOOL(hAPP(hAPP(c_member(_895866), _895874), _895872)), -(hAPP(hAPP(c_Finite__Set_Ofold(_895866, _895868, _895870), _895876), _895872) = hAPP(hAPP(_895870, _895874), hAPP(hAPP(c_Finite__Set_Ofold(_895866, _895868, _895870), _895876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895866, tc_HOL_Obool)), _895872), hAPP(hAPP(c_Set_Oinsert(_895866), _895874), c_Orderings_Obot__class_Obot(tc_fun(_895866, tc_HOL_Obool)))))))], (16713 ^ _779142) ^ [_1073240, _1073242] : [class_Orderings_Olinorder(_1073240), -(c_Big__Operators_Olinorder__class_OMin(_1073240, hAPP(hAPP(c_Set_Oinsert(_1073240), _1073242), c_Orderings_Obot__class_Obot(tc_fun(_1073240, tc_HOL_Obool)))) = _1073242)], (7814 ^ _779142) ^ [_908024, _908026, _908028] : [class_Orderings_Olinorder(_908024), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908024), _908026), _908028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908024), _908028), _908026)))], (45284 ^ _779142) ^ [_1687919, _1687921] : [_1687919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1687921, _1687919, c_List_Olist_ONil(_1687921)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687921)), c_List_Olist_ONil(_1687921)), c_List_Olist_ONil(tc_List_Olist(_1687921))))], (33750 ^ _779142) ^ [_1396935, _1396937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396937), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396935, _1396937) = 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), _1396935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396937)))))], (12900 ^ _779142) ^ [_1002376, _1002378] : [hAPP(c_Finite__Set_Ocard(_1002376), _1002378) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1002378 = c_Orderings_Obot__class_Obot(tc_fun(_1002376, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002376), _1002378))], (36967 ^ _779142) ^ [_1475807, _1475809, _1475811] : [hBOOL(hAPP(hAPP(c_member(_1475807), _1475811), c_Wellfounded_Oacc(_1475807, _1475809))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475807, hAPP(hAPP(c_COMBC(_1475807, tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_fun(_1475807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475807, tc_fun(tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_fun(_1475807, tc_HOL_Obool)), _1475807), c_COMBC(_1475807, tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475807, tc_prod(_1475807, _1475807)), tc_fun(_1475807, tc_fun(tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_HOL_Obool)), _1475807), hAPP(c_COMBB(tc_prod(_1475807, _1475807), tc_fun(tc_fun(tc_prod(_1475807, _1475807), tc_HOL_Obool), tc_HOL_Obool), _1475807), c_member(tc_prod(_1475807, _1475807)))), c_Product__Type_OPair(_1475807, _1475807)))), _1475809)), _1475811)))], (45558 ^ _779142) ^ [_1693317, _1693319, _1693321, _1693323] : [-(hAPP(hAPP(c_List_Omap(_1693317, _1693319), _1693321), c_List_Oconcat(_1693317, _1693323)) = c_List_Oconcat(_1693319, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693317), tc_List_Olist(_1693319)), hAPP(c_List_Omap(_1693317, _1693319), _1693321)), _1693323)))], (49997 ^ _779142) ^ [_1790305, _1790307, _1790309] : [c_Fun_Obij__betw(_1790305, _1790307, _1790309, c_Orderings_Otop__class_Otop(tc_fun(_1790305, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790307, tc_HOL_Obool))), 50000 ^ _779142 : [(50003 ^ _779142) ^ [] : [-(hAPP(c_Set_Oimage(_1790305, _1790307, _1790309), c_Orderings_Otop__class_Otop(tc_fun(_1790305, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790307, tc_HOL_Obool)))], (50001 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1790305, _1790307, _1790309, c_Orderings_Otop__class_Otop(tc_fun(_1790305, tc_HOL_Obool))))]]], (41280 ^ _779142) ^ [_1592094, _1592096] : [-(c_Nitpick_Ouminus__frac(_1592094, _1592096) = c_Nitpick_OAbs__Frac(_1592094, 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(_1592094), _1592096))), hAPP(c_Nitpick_Odenom(_1592094), _1592096))))], (50373 ^ _779142) ^ [_1797672, _1797674, _1797676, _1797678, _1797680] : [50375 ^ _779142 : [(50378 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797676, tc_HOL_Obool)), _1797678), hAPP(_1797680, 50374 ^ [_1797672, _1797674, _1797676, _1797678, _1797680])))], (50376 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797672), 50374 ^ [_1797672, _1797674, _1797676, _1797678, _1797680]), _1797674)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797676, tc_HOL_Obool)), _1797678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797672, tc_fun(_1797676, tc_HOL_Obool)), _1797674), _1797680))))], (27022 ^ _779142) ^ [_1256025, _1256027] : [class_Orderings_Olinorder(_1256025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1256025), _1256027)), -(_1256027 = c_Orderings_Obot__class_Obot(tc_fun(_1256025, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1256025), c_Big__Operators_Olinorder__class_OMax(_1256025, _1256027)), _1256027)))], (33077 ^ _779142) ^ [_1384416, _1384418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1384416), _1384418)), -(c_Divides_Odivmod__nat(_1384416, _1384418) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1384416))], (10309 ^ _779142) ^ [_957330, _957332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957330), _957332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957330), _957332)))], (35395 ^ _779142) ^ [_1439733, _1439735, _1439737, _1439739] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439733), _1439739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439737), _1439735), -(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), _1439733), _1439735)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439737), _1439739))), c_Int_Ointrel)))], (42493 ^ _779142) ^ [_1625926, _1625928] : [hBOOL(hAPP(c_List_Odistinct(_1625926), _1625928)), 42496 ^ _779142 : [(42497 ^ _779142) ^ [_1626058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625926)), _1625928))), 42500 ^ _779142 : [(42501 ^ _779142) ^ [_1626185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625926)), _1625928))), -(_1626058 = _1626185), hAPP(hAPP(c_List_Onth(_1625926), _1625928), _1626058) = hAPP(hAPP(c_List_Onth(_1625926), _1625928), _1626185)]]]]], (40562 ^ _779142) ^ [_1573439, _1573441, _1573443, _1573445] : [hBOOL(hAPP(hAPP(c_member(_1573439), _1573441), c_Wellfounded_Oacc(_1573439, _1573443))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573439, _1573439)), hAPP(hAPP(c_Product__Type_OPair(_1573439, _1573439), _1573445), _1573441)), c_Transitive__Closure_Ortrancl(_1573439, _1573443))), -(hBOOL(hAPP(hAPP(c_member(_1573439), _1573445), c_Wellfounded_Oacc(_1573439, _1573443))))], (24644 ^ _779142) ^ [_1212538, _1212540] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212538, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212538, tc_HOL_Obool)), _1212540)) = _1212540)], (38218 ^ _779142) ^ [_1514467, _1514469] : [-(c_Product__Type_Oapsnd(_1514467, _1514467, _1514469, c_Fun_Oid(_1514467)) = c_Fun_Oid(tc_prod(_1514469, _1514467)))], (19993 ^ _779142) ^ [_1130147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1130147)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1130147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52353 ^ _779142) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (29033 ^ _779142) ^ [_1293711, _1293713, _1293715] : [class_Lattices_Osemilattice__inf(_1293711), 29036 ^ _779142 : [(29043 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293711), _1293713), _1293715) = _1293713, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293711), _1293713), _1293715)))], (29037 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293711), _1293713), _1293715)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293711), _1293713), _1293715) = _1293713)]]], (10241 ^ _779142) ^ [_955950, _955952, _955954, _955956, _955958] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_955950), 10244 ^ _779142 : [(10245 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955952), _955956)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955954), _955958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955952), _955958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955954), _955956)), -(_955952 = _955954), -(_955956 = _955958)], (10255 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955952), _955956)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955954), _955958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955952), _955958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955950), _955954), _955956))), 10258 ^ _779142 : [(10261 ^ _779142) ^ [] : [_955956 = _955958], (10259 ^ _779142) ^ [] : [_955952 = _955954]]]]], (26060 ^ _779142) ^ [_1236937, _1236939, _1236941] : [class_Rings_Oring__1(_1236937), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1236937), hAPP(c_Groups_Ouminus__class_Ouminus(_1236937), _1236939)), 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)))), _1236941)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1236937), _1236939), 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)))), _1236941)))], (15315 ^ _779142) ^ [_1047450, _1047452, _1047454, _1047456] : [class_Orderings_Olinorder(_1047450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047450), _1047452), _1047454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047450), _1047452), _1047456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047450), _1047452), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047450), _1047454), _1047456))))], (52253 ^ _779142) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (28486 ^ _779142) ^ [_1282779, _1282781] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1282779, tc_HOL_Obool)), _1282781)), 28492 ^ _779142 : [(28495 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282779), 28491 ^ [_1282779, _1282781]))], (28493 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1282779, tc_HOL_Obool)), 28491 ^ [_1282779, _1282781]), _1282781)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282779), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1282779, tc_HOL_Obool), _1282781))))], (2290 ^ _779142) ^ [_812573, _812575, _812577, _812579, _812581, _812583, _812585, _812587] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_812587, _812583, _812579, _812575) = c_Nat_Osemiring__1__class_Oof__nat__aux(_812585, _812581, _812577, _812573)), _812587 = _812585, _812583 = _812581, _812579 = _812577, _812575 = _812573], (29181 ^ _779142) ^ [_1296723, _1296725] : [class_Lattices_Obounded__lattice__bot(_1296723), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296723), c_Orderings_Obot__class_Obot(_1296723)), _1296725) = c_Orderings_Obot__class_Obot(_1296723))], (4686 ^ _779142) ^ [_850415, _850417, _850419, _850421, _850423, _850425, _850427, _850429] : [-(c_Wellfounded_Olex__prod(_850429, _850425, _850421, _850417) = c_Wellfounded_Olex__prod(_850427, _850423, _850419, _850415)), _850429 = _850427, _850425 = _850423, _850421 = _850419, _850417 = _850415], (47669 ^ _779142) ^ [_1739628, _1739630] : [c_List_Olist__ex(_1739628, _1739630, c_List_Olist_ONil(_1739628))], (8625 ^ _779142) ^ [_923972, _923974, _923976, _923978] : [class_Groups_Ocancel__semigroup__add(_923972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923972), _923974), _923976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923972), _923978), _923976), -(_923974 = _923978)], (12343 ^ _779142) ^ [_992245, _992247] : [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), _992245), _992247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992247)))], (19467 ^ _779142) ^ [_1121493, _1121495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121493), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19470 ^ _779142 : [(19477 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1121495), _1121493)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19471 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1121495), _1121493)), 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)), _1121495)))]]], (34188 ^ _779142) ^ [_1406597, _1406599, _1406601, _1406603] : [class_Complete__Lattice_Ocomplete__lattice(_1406597), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406599), _1406601)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406599, _1406597), _1406601), _1406603) = hAPP(hAPP(c_Finite__Set_Ofold(_1406599, _1406597, hAPP(hAPP(c_COMBB(_1406597, tc_fun(_1406597, _1406597), _1406599), c_Lattices_Osemilattice__inf__class_Oinf(_1406597)), _1406603)), c_Orderings_Otop__class_Otop(_1406597)), _1406601))], (43718 ^ _779142) ^ [_1653799, _1653801] : [-(_1653799 = c_List_Olist_ONil(_1653801)), -(hBOOL(hAPP(hAPP(c_member(_1653801), hAPP(c_List_Ohd(_1653801), _1653799)), hAPP(c_List_Oset(_1653801), _1653799))))], (8969 ^ _779142) ^ [_930603, _930605, _930607] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930603), _930605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_930603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930603, tc_HOL_Obool)), _930605), hAPP(hAPP(c_Set_Oinsert(_930603), _930607), c_Orderings_Obot__class_Obot(tc_fun(_930603, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_930603), _930605))))], (2210 ^ _779142) ^ [_811365, _811367, _811369, _811371, _811373, _811375] : [-(c_Random_Ominus__shift(_811375, _811371, _811367) = c_Random_Ominus__shift(_811373, _811369, _811365)), _811375 = _811373, _811371 = _811369, _811367 = _811365], (11326 ^ _779142) ^ [_973780, _973782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973780), _973782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973780), hAPP(c_Nat_OSuc, _973782))))], (36274 ^ _779142) ^ [_1461311, _1461313, _1461315, _1461317, _1461319] : [c_Fun_Oinj__on(_1461311, _1461313, _1461315, _1461317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461311, tc_HOL_Obool)), _1461319), _1461317)), -(c_Fun_Oinj__on(_1461311, _1461313, _1461315, _1461319))], (25396 ^ _779142) ^ [_1225544, _1225546] : [_1225544 = _1225546, -(c_Int_OBit0(_1225544) = c_Int_OBit0(_1225546))], (40650 ^ _779142) ^ [_1575487, _1575489, _1575491] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575487, _1575487), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1575487, _1575487), _1575489)), c_Transitive__Closure_Ortrancl(_1575487, _1575489)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575487, _1575487), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575487, _1575487)), hAPP(hAPP(c_Product__Type_OPair(_1575487, _1575487), _1575491), _1575491)), c_Transitive__Closure_Otrancl(_1575487, _1575489)))], (6906 ^ _779142) ^ [_892085, _892087, _892089, _892091] : [hBOOL(hAPP(hAPP(c_member(_892085), _892087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892085, tc_HOL_Obool)), _892089), _892091))), 6909 ^ _779142 : [(6912 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892085), _892087), _892091))], (6910 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_892085), _892087), _892089)))]]], (43502 ^ _779142) ^ [_1648613, _1648615, _1648617, _1648619, _1648621] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1648613, _1648615)), _1648617), hAPP(hAPP(c_List_Ozip(_1648613, _1648615), _1648619), _1648621)) = hAPP(hAPP(c_List_Ozip(_1648613, _1648615), hAPP(hAPP(c_List_Odrop(_1648613), _1648617), _1648619)), hAPP(hAPP(c_List_Odrop(_1648615), _1648617), _1648621)))], (23661 ^ _779142) ^ [_1195843, _1195845, _1195847, _1195849, _1195851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195843, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1195845, _1195843, _1195847), _1195849)), _1195851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1195843, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1195845, tc_HOL_Obool), tc_fun(_1195843, tc_HOL_Obool), c_Set_Oimage(_1195845, _1195843, _1195847)), hAPP(c_Set_OPow(_1195845), _1195849))), hAPP(c_Set_OPow(_1195843), _1195851))))], (51769 ^ _779142) ^ [_1824566, _1824568] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824566), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824568))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824566), _1824568)))], (44861 ^ _779142) ^ [_1677822, _1677824] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1677822, _1677824) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1677822), hAPP(c_Code__Numeral_Onat__of, _1677824))))], (9095 ^ _779142) ^ [_933484, _933486, _933488, _933490, _933492, _933494] : [class_Rings_Oordered__ring(_933484), 9098 ^ _779142 : [(9105 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933484), _933486), _933492)), _933488)), _933490)), _933494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), _933486), _933488)), _933490)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), _933492), _933488)), _933494))))], (9099 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), _933486), _933488)), _933490)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), _933492), _933488)), _933494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933484), _933486), _933492)), _933488)), _933490)), _933494)))]]], (8139 ^ _779142) ^ [_914142, _914144, _914146, _914148, _914150, _914152, _914154] : [c_Finite__Set_Ofun__left__comm(_914142, _914144, _914146), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914142, _914144, _914146, _914148, hAPP(hAPP(c_Set_Oinsert(_914142), _914150), _914152)), _914154)), -(hBOOL(hAPP(hAPP(c_member(_914142), _914150), _914152))), 8151 ^ _779142 : [(8154 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914142, _914144, _914146, _914148, _914152), 8150 ^ [_914142, _914144, _914146, _914148, _914150, _914152, _914154])))], (8152 ^ _779142) ^ [] : [-(_914154 = hAPP(hAPP(_914146, _914150), 8150 ^ [_914142, _914144, _914146, _914148, _914150, _914152, _914154]))]]], (42650 ^ _779142) ^ [_1629294, _1629296] : [-(hAPP(hAPP(c_List_Otake(_1629294), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629296) = c_List_Olist_ONil(_1629294))], (35409 ^ _779142) ^ [_1440525, _1440527, _1440529, _1440531, _1440533, _1440535] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1440525, _1440525)), hAPP(hAPP(c_Product__Type_OPair(_1440525, _1440525), _1440527), _1440529)), hAPP(hAPP(c_Relation_Oinv__image(_1440531, _1440525), _1440533), _1440535))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440531, _1440531)), hAPP(hAPP(c_Product__Type_OPair(_1440531, _1440531), hAPP(_1440535, _1440527)), hAPP(_1440535, _1440529))), _1440533)))], (29562 ^ _779142) ^ [_1305293, _1305295, _1305297, _1305299] : [class_Orderings_Oorder(_1305293), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305293, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1305293, _1305295, _1305297)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305293, _1305297), _1305299)) = c_Orderings_Obot__class_Obot(tc_fun(_1305293, tc_HOL_Obool)))], (3782 ^ _779142) ^ [_835867, _835869, _835871, _835873, _835875, _835877] : [-(c_List_Olinorder__class_Oinsort__key(_835877, _835873, _835869) = c_List_Olinorder__class_Oinsort__key(_835875, _835871, _835867)), _835877 = _835875, _835873 = _835871, _835869 = _835867], (28851 ^ _779142) ^ [_1290171, _1290173, _1290175, _1290177] : [class_Lattices_Odistrib__lattice(_1290171), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290171), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1290171), _1290173), _1290175)), _1290177) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1290171), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290171), _1290173), _1290177)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290171), _1290175), _1290177)))], (24912 ^ _779142) ^ [_1217094] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217094) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1217094))], (780 ^ _779142) ^ [_790844, _790846, _790848, _790850, _790852, _790854] : [-(c_Equiv__Relations_Oequiv(_790852, _790848, _790844)), c_Equiv__Relations_Oequiv(_790854, _790850, _790846), _790854 = _790852, _790850 = _790848, _790846 = _790844], (26916 ^ _779142) ^ [_1253776, _1253778, _1253780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253776, tc_HOL_Obool)), _1253778), _1253780)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253776, tc_HOL_Obool)), _1253778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253776, tc_HOL_Obool)), _1253780), _1253778)) = _1253780)], (11704 ^ _779142) ^ [_980635, _980637, _980639, _980641] : [class_Rings_Oordered__comm__semiring(_980635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980635), _980637), _980639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980635), c_Groups_Ozero__class_Ozero(_980635)), _980641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980635), _980641), _980637)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980635), _980641), _980639))))], (18561 ^ _779142) ^ [_1105983, _1105985] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105983) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105985), -(_1105983 = _1105985)], (39090 ^ _779142) ^ [_1537356] : [-(c_Wellfounded_OwfP(_1537356, hAPP(c_COMBK(tc_fun(_1537356, tc_HOL_Obool), _1537356), hAPP(c_COMBK(tc_HOL_Obool, _1537356), c_fFalse))))], (9989 ^ _779142) ^ [_949967, _949969, _949971, _949973, _949975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949967), _949969)), 9992 ^ _779142 : [(9999 ^ _779142) ^ [] : [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), _949969), _949967)), _949971)), _949973)), _949975)), -(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), _949969), _949971)), _949973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949967), _949971)), _949975))))], (9993 ^ _779142) ^ [] : [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), _949969), _949971)), _949973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949967), _949971)), _949975))), -(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), _949969), _949967)), _949971)), _949973)), _949975)))]]], (17968 ^ _779142) ^ [_1095606, _1095608] : [17969 ^ _779142 : [(17970 ^ _779142) ^ [_1095662] : [_1095608 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095606), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1095662)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095606), _1095608)))], (52405 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (33147 ^ _779142) ^ [_1385736, _1385738] : [-(_1385736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33150 ^ _779142 : [(33157 ^ _779142) ^ [] : [-(_1385738 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1385736, _1385738) = 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, _1385738))), 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)), _1385738)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385736))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385738), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1385736, _1385738)), 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), _1385738))))), c_Divides_Opdivmod(_1385736, _1385738)))))], (33151 ^ _779142) ^ [] : [_1385738 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1385736, _1385738) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385736))]]], (43826 ^ _779142) ^ [_1655765, _1655767, _1655769] : [-(_1655765 = c_List_Olist_ONil(_1655767)), -(hAPP(hAPP(c_List_Otake(_1655767), hAPP(c_Nat_OSuc, _1655769)), _1655765) = hAPP(hAPP(c_List_Olist_OCons(_1655767), hAPP(c_List_Ohd(_1655767), _1655765)), hAPP(hAPP(c_List_Otake(_1655767), _1655769), hAPP(c_List_Otl(_1655767), _1655765))))], (9531 ^ _779142) ^ [_941348, _941350] : [9532 ^ _779142 : [(9535 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941350), _941348))], (9533 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941348), _941350))]], _941348 = _941350], (10641 ^ _779142) ^ [_963035, _963037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963035), _963037))))], (37537 ^ _779142) ^ [_1489856, _1489858, _1489860] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1489856, _1489858), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1489856, _1489858), _1489860), hAPP(c_COMBK(tc_fun(_1489858, tc_HOL_Obool), _1489856), c_Orderings_Otop__class_Otop(tc_fun(_1489858, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1489856, _1489858), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1489856, tc_HOL_Obool)), _1489860)), hAPP(c_COMBK(tc_fun(_1489858, tc_HOL_Obool), _1489856), c_Orderings_Otop__class_Otop(tc_fun(_1489858, tc_HOL_Obool)))))], (11227 ^ _779142) ^ [_972181] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9316 ^ _779142) ^ [_937976, _937978, _937980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937976), _937978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937978), _937980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937976), _937980)))], (43800 ^ _779142) ^ [_1655142, _1655144, _1655146] : [-(hAPP(hAPP(c_List_Otake(_1655142), _1655144), hAPP(c_List_Otl(_1655142), _1655146)) = hAPP(c_List_Otl(_1655142), hAPP(hAPP(c_List_Otake(_1655142), hAPP(c_Nat_OSuc, _1655144)), _1655146)))], (36753 ^ _779142) ^ [_1471237, _1471239, _1471241, _1471243] : [c_Fun_Oinj__on(_1471237, tc_fun(tc_fun(_1471237, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1471237, tc_fun(tc_prod(_1471237, _1471237), tc_HOL_Obool), tc_fun(tc_fun(_1471237, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471237, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1471237, _1471237), tc_HOL_Obool), tc_fun(tc_fun(_1471237, tc_HOL_Obool), tc_HOL_Obool)), _1471237), c_Equiv__Relations_Oquotient(_1471237)), hAPP(hAPP(c_COMBC(_1471237, tc_fun(_1471237, tc_HOL_Obool), tc_fun(_1471237, tc_HOL_Obool)), c_Set_Oinsert(_1471237)), c_Orderings_Obot__class_Obot(tc_fun(_1471237, tc_HOL_Obool))))), _1471239), _1471241), hBOOL(hAPP(hAPP(c_member(_1471237), _1471243), _1471241)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471237, tc_HOL_Obool)), _1471241), hAPP(hAPP(c_Set_Oinsert(_1471237), _1471243), c_Orderings_Obot__class_Obot(tc_fun(_1471237, tc_HOL_Obool))))), _1471239) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1471237, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471237), _1471241), _1471239)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471237), hAPP(hAPP(c_Set_Oinsert(_1471237), _1471243), c_Orderings_Obot__class_Obot(tc_fun(_1471237, tc_HOL_Obool)))), _1471239)))], (43277 ^ _779142) ^ [_1642622, _1642624, _1642626, _1642628] : [hBOOL(hAPP(hAPP(c_member(_1642622), _1642624), hAPP(c_List_Oset(_1642622), _1642626))), -(c_List_Oremove1(_1642622, _1642624, hAPP(hAPP(c_List_Oappend(_1642622), _1642626), _1642628)) = hAPP(hAPP(c_List_Oappend(_1642622), c_List_Oremove1(_1642622, _1642624, _1642626)), _1642628))], (6033 ^ _779142) ^ [_875368, _875370, _875372, _875374] : [_875374 = c_Orderings_Obot__class_Obot(tc_fun(_875370, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_875368, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_875370, _875368, _875372), _875374))], (17875 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43500 ^ _779142) ^ [_1648554, _1648556, _1648558, _1648560] : [-(hAPP(hAPP(c_List_Odrop(_1648554), _1648556), hAPP(hAPP(c_List_Odrop(_1648554), _1648558), _1648560)) = hAPP(hAPP(c_List_Odrop(_1648554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648556), _1648558)), _1648560))], (34971 ^ _779142) ^ [_1428573, _1428575, _1428577, _1428579, _1428581] : [class_Complete__Lattice_Ocomplete__lattice(_1428573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428575, tc_HOL_Obool)), _1428577), _1428579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428573), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428575, _1428573), _1428579), _1428581)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428575, _1428573), _1428577), _1428581))))], (45436 ^ _779142) ^ [_1690911, _1690913, _1690915] : [-(hBOOL(hAPP(hAPP(c_member(_1690911), _1690913), hAPP(c_List_Oset(_1690911), _1690915)))), -(hAPP(c_List_OremoveAll(_1690911, _1690913), _1690915) = _1690915)], (20628 ^ _779142) ^ [_1141427, _1141429] : [-(c_Int_Onat__aux(_1141427, _1141429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1141427)), _1141429))], (42321 ^ _779142) ^ [_1622173, _1622175, _1622177, _1622179] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622173, tc_HOL_Obool)), hAPP(c_List_Oset(_1622173), hAPP(hAPP(c_List_Olist__update(_1622173, _1622175), _1622177), _1622179))), hAPP(hAPP(c_Set_Oinsert(_1622173), _1622179), hAPP(c_List_Oset(_1622173), _1622175)))))], (42541 ^ _779142) ^ [_1627241, _1627243] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627241), _1627243))), -(c_Nitpick_Ocard_H(_1627241, _1627243) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48838 ^ _779142) ^ [_1765184, _1765186, _1765188] : [hBOOL(hAPP(hAPP(c_member(_1765186), _1765184), c_Orderings_Obot__class_Obot(tc_fun(_1765186, tc_HOL_Obool)))), hBOOL(hAPP(_1765188, _1765184))], (5961 ^ _779142) ^ [_873862, _873864, _873866] : [hAPP(hAPP(c_Set_Oinsert(_873862), _873864), c_Orderings_Obot__class_Obot(tc_fun(_873862, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_873862), _873866), c_Orderings_Obot__class_Obot(tc_fun(_873862, tc_HOL_Obool))), -(_873864 = _873866)], (20888 ^ _779142) ^ [_1146426, _1146428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1146426), _1146428)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146428), _1146426) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1146428), _1146426)), _1146426)))], (8352 ^ _779142) ^ [_918315, _918317, _918319, _918321] : [-(hBOOL(hAPP(hAPP(c_member(_918315), _918317), _918319))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918315, tc_Nat_Onat), _918321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918315, tc_HOL_Obool)), _918319), hAPP(hAPP(c_Set_Oinsert(_918315), _918317), c_Orderings_Obot__class_Obot(tc_fun(_918315, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918315, tc_Nat_Onat), _918321), _918319))], (48953 ^ _779142) ^ [_1767653, _1767655, _1767657] : [-(c_List_Olist__ex(_1767653, _1767655, _1767657)), 48954 ^ _779142 : [(48955 ^ _779142) ^ [_1767710] : [hBOOL(hAPP(hAPP(c_member(_1767653), _1767710), hAPP(c_List_Oset(_1767653), _1767657))), hBOOL(hAPP(_1767655, _1767710))]]], (11155 ^ _779142) ^ [_971123, _971125] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971123), _971125) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11158 ^ _779142 : [(11161 ^ _779142) ^ [] : [-(_971125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11159 ^ _779142) ^ [] : [-(_971123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11904 ^ _779142) ^ [_984369, _984371, _984373, _984375] : [class_Rings_Olinordered__ring__strict(_984369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984369), _984371), _984373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984369), _984375), c_Groups_Ozero__class_Ozero(_984369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984369), _984375), _984373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984369), _984375), _984371))))], (1286 ^ _779142) ^ [_798159, _798161] : [-(class_Rings_Ocomm__ring(_798159)), _798161 = _798159, class_Rings_Ocomm__ring(_798161)], (14844 ^ _779142) ^ [_1038485, _1038487, _1038489] : [class_Fields_Olinordered__field__inverse__zero(_1038485), 14850 ^ _779142 : [(14855 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038485), 14849 ^ [_1038485, _1038487, _1038489]), _1038487)), _1038489))], (14853 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038485), 14849 ^ [_1038485, _1038487, _1038489]), c_Groups_Oone__class_Oone(_1038485))))], (14851 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038485), c_Groups_Ozero__class_Ozero(_1038485)), 14849 ^ [_1038485, _1038487, _1038489])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038485), _1038487), _1038489)))], (1136 ^ _779142) ^ [_796284, _796286] : [-(class_Groups_Oordered__ab__group__add__abs(_796284)), _796286 = _796284, class_Groups_Oordered__ab__group__add__abs(_796286)], (34753 ^ _779142) ^ [_1423080, _1423082, _1423084, _1423086] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423080, tc_fun(_1423082, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423080, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1423082, tc_HOL_Obool), tc_fun(_1423082, tc_HOL_Obool), _1423080), hAPP(c_COMBC(_1423082, tc_fun(_1423082, tc_HOL_Obool), tc_HOL_Obool), c_member(_1423082))), _1423084)), _1423086)), -(hBOOL(hAPP(hAPP(c_member(_1423082), _1423086), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423080, tc_fun(_1423082, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423080, tc_HOL_Obool))), _1423084))))], (49172 ^ _779142) ^ [_1773116, _1773118, _1773120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773116, _1773116), tc_HOL_Obool)), _1773118), _1773120)), c_Relation_Oantisym(_1773116, _1773120), -(c_Relation_Oantisym(_1773116, _1773118))], (42377 ^ _779142) ^ [_1623374, _1623376, _1623378, _1623380] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623374), tc_List_Olist(_1623374))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623374), tc_List_Olist(_1623374)), _1623376), _1623378)), c_List_Olistrel1(_1623374, _1623380))), 42382 ^ _779142 : [(42387 ^ _779142) ^ [] : [-(_1623378 = hAPP(hAPP(c_List_Olist__update(_1623374, _1623376), 42381 ^ [_1623374, _1623376, _1623378, _1623380]), 42380 ^ [_1623374, _1623376, _1623378, _1623380]))], (42385 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42381 ^ [_1623374, _1623376, _1623378, _1623380]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623374)), _1623376))))], (42383 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623374, _1623374)), hAPP(hAPP(c_Product__Type_OPair(_1623374, _1623374), hAPP(hAPP(c_List_Onth(_1623374), _1623376), 42381 ^ [_1623374, _1623376, _1623378, _1623380])), 42380 ^ [_1623374, _1623376, _1623378, _1623380])), _1623380)))]]], (24317 ^ _779142) ^ [_1207130] : [class_Rings_Oring__1(_1207130), -(hAPP(c_Int_Oring__1__class_Oof__int(_1207130), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1207130))], (2540 ^ _779142) ^ [_816488, _816490, _816492, _816494, _816496, _816498] : [-(c_Finite__Set_Ofold1Set(_816498, _816494, _816490) = c_Finite__Set_Ofold1Set(_816496, _816492, _816488)), _816498 = _816496, _816494 = _816492, _816490 = _816488], (2628 ^ _779142) ^ [_817856, _817858] : [_817858 = _817856, -(c_Int_Oint__ge__less__than(_817858) = c_Int_Oint__ge__less__than(_817856))], (41012 ^ _779142) ^ [_1584714, _1584716, _1584718, _1584720, _1584722, _1584724] : [c_Relation_Osingle__valued(_1584714, _1584716, _1584718), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584714, _1584716)), hAPP(hAPP(c_Product__Type_OPair(_1584714, _1584716), _1584720), _1584722)), _1584718)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584714, _1584716)), hAPP(hAPP(c_Product__Type_OPair(_1584714, _1584716), _1584720), _1584724)), _1584718)), -(_1584722 = _1584724)], (30345 ^ _779142) ^ [_1321929, _1321931, _1321933] : [class_Lattices_Olattice(_1321929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321929), _1321931)), -(_1321931 = c_Orderings_Obot__class_Obot(tc_fun(_1321929, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1321929, hAPP(hAPP(c_Set_Oinsert(_1321929), _1321933), _1321931)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321929), _1321933), c_Big__Operators_Olattice__class_OInf__fin(_1321929, _1321931)))], (24946 ^ _779142) ^ [_1217648, _1217650] : [class_Int_Onumber__ring(_1217648), -(hAPP(c_Int_Onumber__class_Onumber__of(_1217648), c_Int_OBit1(_1217650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217648), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217648), c_Groups_Oone__class_Oone(_1217648)), hAPP(c_Int_Onumber__class_Onumber__of(_1217648), _1217650))), hAPP(c_Int_Onumber__class_Onumber__of(_1217648), _1217650)))], (47085 ^ _779142) ^ [_1726382, _1726384, _1726386] : [47087 ^ _779142 : [(47090 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1726384, 47086 ^ [_1726382, _1726384, _1726386])))], (47088 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726382), 47086 ^ [_1726382, _1726384, _1726386]), hAPP(c_List_Oset(_1726382), c_List_OdropWhile(_1726382, _1726384, _1726386)))))]], -(c_List_OtakeWhile(_1726382, _1726384, _1726386) = hAPP(c_List_Ofilter(_1726382, _1726384), _1726386))], (22126 ^ _779142) ^ [_1168263, _1168265] : [class_Power_Opower(_1168263), class_Rings_Osemiring__0(_1168263), 22133 ^ _779142 : [(22140 ^ _779142) ^ [] : [-(_1168265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168263), c_Groups_Ozero__class_Ozero(_1168263)), _1168265) = c_Groups_Ozero__class_Ozero(_1168263))], (22134 ^ _779142) ^ [] : [_1168265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168263), c_Groups_Ozero__class_Ozero(_1168263)), _1168265) = c_Groups_Oone__class_Oone(_1168263))]]], (19889 ^ _779142) ^ [_1128364, _1128366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128364), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19892 ^ _779142 : [(19899 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1128366), 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), _1128366), _1128364))))], (19893 ^ _779142) ^ [] : [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), _1128366), _1128364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1128366), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10965 ^ _779142) ^ [_968386, _968388] : [class_Rings_Ocomm__semiring__1(_968386), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968386), c_Groups_Ozero__class_Ozero(_968386)), _968388) = _968388)], (32529 ^ _779142) ^ [_1372571, _1372573] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372571)), hAPP(c_Nat_OSuc, _1372573)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1372571))), 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, _1372573))), 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)), _1372573)))))], (52755 ^ _779142) ^ [_1837612, _1837614] : [hBOOL(hAPP(hAPP(c_fdisj, _1837612), _1837614)), -(hBOOL(_1837612)), -(hBOOL(_1837614))], (46266 ^ _779142) ^ [_1709179, _1709181, _1709183, _1709185, _1709187] : [class_Orderings_Olinorder(_1709179), 46269 ^ _779142 : [(46276 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1709179, hAPP(hAPP(c_List_Omap(_1709181, _1709179), _1709183), _1709187)), -(c_List_Olinorder__class_Osorted(_1709179, hAPP(hAPP(c_List_Omap(_1709181, _1709179), _1709183), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709181, _1709179, _1709183), _1709185), _1709187))))], (46270 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1709179, hAPP(hAPP(c_List_Omap(_1709181, _1709179), _1709183), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709181, _1709179, _1709183), _1709185), _1709187))), -(c_List_Olinorder__class_Osorted(_1709179, hAPP(hAPP(c_List_Omap(_1709181, _1709179), _1709183), _1709187)))]]], (46100 ^ _779142) ^ [_1706580, _1706582] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1706580, _1706582)))], (29745 ^ _779142) ^ [_1309457, _1309459, _1309461, _1309463, _1309465, _1309467, _1309469, _1309471] : [c_Finite__Set_Ofolding__image__simple(_1309457, _1309459, _1309461, _1309463, _1309465, _1309467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309459), _1309469)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309459), _1309471)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309459, tc_HOL_Obool)), _1309469), _1309471) = c_Orderings_Obot__class_Obot(tc_fun(_1309459, tc_HOL_Obool)), -(hAPP(_1309467, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309459, tc_HOL_Obool)), _1309469), _1309471)) = hAPP(hAPP(_1309461, hAPP(_1309467, _1309469)), hAPP(_1309467, _1309471)))], (14129 ^ _779142) ^ [_1025346, _1025348, _1025350, _1025352] : [class_Fields_Olinordered__field(_1025346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025346), _1025348), _1025350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025346), _1025352), c_Groups_Ozero__class_Ozero(_1025346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025346), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025346), _1025350), _1025352)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025346), _1025348), _1025352))))], (42463 ^ _779142) ^ [_1625357, _1625359] : [hAPP(c_Finite__Set_Ocard(_1625357), hAPP(c_List_Oset(_1625357), _1625359)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625357)), _1625359), -(hBOOL(hAPP(c_List_Odistinct(_1625357), _1625359)))], (28785 ^ _779142) ^ [_1288462, _1288464, _1288466, _1288468] : [hBOOL(hAPP(hAPP(c_member(_1288462), _1288464), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288462, tc_HOL_Obool)), _1288466), _1288468))), 28788 ^ _779142 : [(28791 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288462), _1288464), _1288468)))], (28789 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1288462), _1288464), _1288466)))]]], (9853 ^ _779142) ^ [_947019, _947021, _947023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947019), _947021)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947021), _947019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947023), _947019)), _947021))], (22496 ^ _779142) ^ [_1175079, _1175081, _1175083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175079)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1175081), _1175083)), 22503 ^ _779142 : [(22504 ^ _779142) ^ [_1175269] : [22506 ^ _779142 : [(22512 ^ _779142) ^ [] : [-(_1175269 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22508 ^ [_1175079, _1175081, _1175083, _1175269]), 22505 ^ [_1175079, _1175081, _1175083, _1175269]))], (22510 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22508 ^ [_1175079, _1175081, _1175083, _1175269]), _1175083)))], (22507 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22505 ^ [_1175079, _1175081, _1175083, _1175269]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1175079))))]], -(_1175269 = _1175081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175269), _1175079) = _1175081]]], (18591 ^ _779142) ^ [_1106506, _1106508] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106506, _1106508)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106506), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106508)))], (52359 ^ _779142) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (10177 ^ _779142) ^ [_954539, _954541, _954543, _954545] : [class_Rings_Ocomm__semiring__1(_954539), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954539), _954541), _954543)), _954545) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954539), _954541), _954545)), _954543))], (45654 ^ _779142) ^ [_1696405, _1696407, _1696409] : [45656 ^ _779142 : [(45659 ^ _779142) ^ [] : [hBOOL(hAPP(_1696407, 45655 ^ [_1696405, _1696407, _1696409]))], (45657 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696405), 45655 ^ [_1696405, _1696407, _1696409]), hAPP(c_List_Oset(_1696405), _1696409))))]], -(hAPP(c_List_Ofilter(_1696405, _1696407), _1696409) = _1696409)], (43971 ^ _779142) ^ [_1658897, _1658899] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658897), hAPP(c_List_Oset(tc_Nat_Onat), _1658899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658897), 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)), _1658899))))], (32589 ^ _779142) ^ [_1374049, _1374051] : [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), _1374049))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1374051), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1374049))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1374051), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374049))), 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), _1374051))), c_COMBI(tc_Int_Oint))))], (5967 ^ _779142) ^ [_874017, _874019, _874021, _874023, _874025] : [hAPP(hAPP(c_Set_Oinsert(_874017), _874019), hAPP(hAPP(c_Set_Oinsert(_874017), _874021), c_Orderings_Obot__class_Obot(tc_fun(_874017, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_874017), _874023), hAPP(hAPP(c_Set_Oinsert(_874017), _874025), c_Orderings_Obot__class_Obot(tc_fun(_874017, tc_HOL_Obool)))), 5972 ^ _779142 : [(5975 ^ _779142) ^ [] : [-(_874021 = _874025)], (5973 ^ _779142) ^ [] : [-(_874019 = _874023)]], 5976 ^ _779142 : [(5979 ^ _779142) ^ [] : [-(_874021 = _874023)], (5977 ^ _779142) ^ [] : [-(_874019 = _874025)]]], (34370 ^ _779142) ^ [_1411371, _1411373, _1411375, _1411377] : [34372 ^ _779142 : [(34375 ^ _779142) ^ [] : [hAPP(_1411377, 34371 ^ [_1411371, _1411373, _1411375, _1411377]) = c_Orderings_Otop__class_Otop(tc_fun(_1411371, tc_HOL_Obool))], (34373 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411373), 34371 ^ [_1411371, _1411373, _1411375, _1411377]), _1411375)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1411371, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411373, tc_fun(_1411371, tc_HOL_Obool)), _1411375), _1411377))], (33843 ^ _779142) ^ [_1398918, _1398920, _1398922, _1398924] : [-(_1398918 = _1398920), hAPP(c_Product__Type_Ofst(_1398922, _1398924), _1398918) = hAPP(c_Product__Type_Ofst(_1398922, _1398924), _1398920), hAPP(c_Product__Type_Osnd(_1398922, _1398924), _1398918) = hAPP(c_Product__Type_Osnd(_1398922, _1398924), _1398920)], (46652 ^ _779142) ^ [_1717188, _1717190, _1717192] : [hAPP(c_List_Orev(_1717188), _1717190) = hAPP(c_List_Orev(_1717188), _1717192), -(_1717190 = _1717192)], (52469 ^ _779142) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52177 ^ _779142) ^ [_1831496, _1831498] : [class_Lattices_Olattice(_1831496), -(class_Lattices_Olattice(tc_fun(_1831498, _1831496)))], (47201 ^ _779142) ^ [_1728627, _1728629] : [-(c_List_Oinsert(_1728627, _1728629, c_List_Olist_ONil(_1728627)) = hAPP(hAPP(c_List_Olist_OCons(_1728627), _1728629), c_List_Olist_ONil(_1728627)))], (35387 ^ _779142) ^ [_1439483, _1439485, _1439487] : [-(c_Wellfounded_Omlex__prod(_1439483, _1439485, _1439487) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1439483), _1439483), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1439483, c_Wellfounded_Oless__than, _1439487)), hAPP(hAPP(c_COMBS(_1439483, _1439483, tc_prod(tc_Nat_Onat, _1439483)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1439483, tc_prod(tc_Nat_Onat, _1439483)), _1439483), c_Product__Type_OPair(tc_Nat_Onat, _1439483)), _1439485)), c_COMBI(_1439483))))], (49412 ^ _779142) ^ [_1777660, _1777662] : [c_Relation_Osym(_1777660, hAPP(c_Set_OCollect(tc_prod(_1777660, _1777660)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777660, _1777660, tc_HOL_Obool), _1777662))), -(c_Predicate_Osymp(_1777660, _1777662))], (21980 ^ _779142) ^ [_1165460, _1165462, _1165464] : [class_Rings_Olinordered__semidom(_1165460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165460), c_Groups_Oone__class_Oone(_1165460)), _1165462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165460), c_Groups_Oone__class_Oone(_1165460)), hAPP(hAPP(c_Power_Opower__class_Opower(_1165460), _1165462), _1165464))))], (52287 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (37017 ^ _779142) ^ [_1477088, _1477090, _1477092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1477088, _1477088), tc_HOL_Obool)), _1477090), _1477092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477088, tc_HOL_Obool)), c_Wellfounded_Oacc(_1477088, _1477092)), c_Wellfounded_Oacc(_1477088, _1477090))))], (41179 ^ _779142) ^ [_1589243, _1589245, _1589247, _1589249, _1589251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589243, _1589243)), hAPP(hAPP(c_Product__Type_OPair(_1589243, _1589243), _1589245), _1589247)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589243, _1589243), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589249)), _1589251))), 41183 ^ _779142 : [(41186 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589243, _1589243)), hAPP(hAPP(c_Product__Type_OPair(_1589243, _1589243), 41182 ^ [_1589243, _1589245, _1589247, _1589249, _1589251]), _1589247)), _1589251)))], (41184 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589243, _1589243)), hAPP(hAPP(c_Product__Type_OPair(_1589243, _1589243), _1589245), 41182 ^ [_1589243, _1589245, _1589247, _1589249, _1589251])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589243, _1589243), tc_HOL_Obool), _1589249), _1589251))))]]], (25988 ^ _779142) ^ [_1235805, _1235807, _1235809] : [class_Rings_Olinordered__idom(_1235805), 25991 ^ _779142 : [(26000 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235805), hAPP(hAPP(c_Power_Opower__class_Opower(_1235805), _1235807), 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(_1235805), _1235809), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1235805)), _1235807 = c_Groups_Ozero__class_Ozero(_1235805), _1235809 = c_Groups_Ozero__class_Ozero(_1235805)], (25992 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235805), hAPP(hAPP(c_Power_Opower__class_Opower(_1235805), _1235807), 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(_1235805), _1235809), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1235805), 25995 ^ _779142 : [(25998 ^ _779142) ^ [] : [-(_1235809 = c_Groups_Ozero__class_Ozero(_1235805))], (25996 ^ _779142) ^ [] : [-(_1235807 = c_Groups_Ozero__class_Ozero(_1235805))]]]]], (48312 ^ _779142) ^ [_1753149, _1753151, _1753153, _1753155, _1753157] : [-(hAPP(hAPP(c_List_Omap(_1753149, _1753151), _1753153), c_List_Oreplicate(_1753149, _1753155, _1753157)) = c_List_Oreplicate(_1753151, _1753155, hAPP(_1753153, _1753157)))], (1866 ^ _779142) ^ [_805409, _805411] : [-(class_Orderings_Oord(_805409)), _805411 = _805409, class_Orderings_Oord(_805411)], (45959 ^ _779142) ^ [_1703730, _1703732, _1703734, _1703736] : [c_List_Oupt(_1703730, _1703732) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703734), _1703736), 45962 ^ _779142 : [(45967 ^ _779142) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703730), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703732) = _1703736)], (45965 ^ _779142) ^ [] : [-(_1703730 = _1703734)], (45963 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703730), _1703732)))]]], (52593 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (21696 ^ _779142) ^ [_1160226, _1160228] : [21697 ^ _779142 : [(21700 ^ _779142) ^ [] : [_1160226 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21698 ^ _779142) ^ [] : [_1160228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1160226), _1160228) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (32335 ^ _779142) ^ [_1368188, _1368190] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368188), _1368190)), -(hAPP(c_Finite__Set_Ocard(_1368188), _1368190) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1368188, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1368188), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1368190))], (47663 ^ _779142) ^ [_1739456, _1739458, _1739460] : [47664 ^ _779142 : [(47665 ^ _779142) ^ [_1739533, _1739535] : [_1739460 = hAPP(hAPP(c_List_Oappend(_1739456), _1739535), hAPP(hAPP(c_List_Olist_OCons(_1739456), _1739458), _1739533))]], -(hBOOL(hAPP(hAPP(c_member(_1739456), _1739458), hAPP(c_List_Oset(_1739456), _1739460))))], (44998 ^ _779142) ^ [_1681196, _1681198, _1681200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1681196, tc_HOL_Obool)), _1681198), _1681200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1681196), tc_HOL_Obool)), c_List_Olistsp(_1681196, _1681198)), c_List_Olistsp(_1681196, _1681200))))], (35643 ^ _779142) ^ [_1446764, _1446766, _1446768] : [_1446766 = c_Orderings_Obot__class_Obot(tc_fun(_1446764, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446764), _1446766), _1446768) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446764, tc_HOL_Obool), tc_HOL_Obool)))], (49488 ^ _779142) ^ [_1778942, _1778944] : [-(c_Equiv__Relations_Opart__equivp(_1778942, _1778944)), 49491 ^ _779142 : [(49492 ^ _779142) ^ [_1779062] : [hBOOL(hAPP(hAPP(_1778944, _1779062), _1779062))]], 49509 ^ _779142 : [(49512 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778944, 49494 ^ [_1778942, _1778944]), 49494 ^ [_1778942, _1778944])))], (49514 ^ _779142) ^ [] : [-(hAPP(_1778944, 49493 ^ [_1778942, _1778944]) = hAPP(_1778944, 49494 ^ [_1778942, _1778944]))], (49516 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1778944, 49493 ^ [_1778942, _1778944]), 49494 ^ [_1778942, _1778944]))], (49510 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778944, 49493 ^ [_1778942, _1778944]), 49493 ^ [_1778942, _1778944])))]], 49497 ^ _779142 : [(49500 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1778944, 49493 ^ [_1778942, _1778944]), 49493 ^ [_1778942, _1778944])), hBOOL(hAPP(hAPP(_1778944, 49494 ^ [_1778942, _1778944]), 49494 ^ [_1778942, _1778944])), hAPP(_1778944, 49493 ^ [_1778942, _1778944]) = hAPP(_1778944, 49494 ^ [_1778942, _1778944])], (49498 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1778944, 49493 ^ [_1778942, _1778944]), 49494 ^ [_1778942, _1778944])))]]], (29217 ^ _779142) ^ [_1297375, _1297377, _1297379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297375, tc_HOL_Obool)), _1297377), _1297379)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297375, tc_HOL_Obool)), _1297377), _1297379) = _1297377)], (49228 ^ _779142) ^ [_1774325, _1774327] : [c_Relation_Oantisym(_1774325, _1774327), -(c_Relation_Oantisym(_1774325, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774325, _1774325), tc_HOL_Obool)), _1774327), c_Relation_OId(_1774325))))], (10427 ^ _779142) ^ [_959769] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _959769)))], (48096 ^ _779142) ^ [_1748579] : [-(c_Predicate_Oconversep(_1748579, _1748579, c_fequal) = c_fequal)], (37629 ^ _779142) ^ [_1492526, _1492528, _1492530, _1492532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492526), _1492528)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492530), _1492532)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1492526, _1492530)), hAPP(hAPP(c_Product__Type_OSigma(_1492526, _1492530), _1492528), hAPP(c_COMBK(tc_fun(_1492530, tc_HOL_Obool), _1492526), _1492532)))))], (43584 ^ _779142) ^ [_1650527, _1650529, _1650531, _1650533] : [-(_1650527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1650529), _1650527), hAPP(hAPP(c_List_Olist_OCons(_1650529), _1650531), _1650533)) = hAPP(hAPP(c_List_Odrop(_1650529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650527), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1650533))], (32441 ^ _779142) ^ [_1370431] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1370431)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1370431)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370431)), 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)))))], (29001 ^ _779142) ^ [_1293152, _1293154, _1293156, _1293158] : [class_Lattices_Osemilattice__inf(_1293152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293152), _1293154), _1293156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1293152), _1293154), _1293158)), _1293156)))], (48832 ^ _779142) ^ [_1765093, _1765095] : [c_Relation_Otrans(_1765093, _1765095), -(c_Relation_Otrans(_1765093, hAPP(c_Relation_Oconverse(_1765093, _1765093), _1765095)))], (2344 ^ _779142) ^ [_813406, _813408] : [_813408 = _813406, -(c_Int_OBit0(_813408) = c_Int_OBit0(_813406))], (13499 ^ _779142) ^ [_1013883, _1013885] : [class_Rings_Odivision__ring(_1013883), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1013883), c_Groups_Ozero__class_Ozero(_1013883)), _1013885) = c_Groups_Ozero__class_Ozero(_1013883))], (52743 ^ _779142) ^ [_1837438, _1837440] : [hBOOL(_1837438), -(hBOOL(hAPP(hAPP(c_fdisj, _1837438), _1837440)))], (5718 ^ _779142) ^ [_869557, _869559, _869561] : [hBOOL(hAPP(hAPP(c_member(_869557), _869559), hAPP(hAPP(c_Set_Oinsert(_869557), _869561), c_Orderings_Obot__class_Obot(tc_fun(_869557, tc_HOL_Obool))))), -(_869559 = _869561)], (52621 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (5538 ^ _779142) ^ [_863781, _863783, _863785, _863787] : [-(c_COMBK(_863787, _863783) = c_COMBK(_863785, _863781)), _863787 = _863785, _863783 = _863781], (24345 ^ _779142) ^ [_1207620, _1207622] : [class_Rings_Oring__1(_1207620), -(hAPP(c_Int_Oring__1__class_Oof__int(_1207620), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207622)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1207620), hAPP(c_Int_Oring__1__class_Oof__int(_1207620), _1207622)))], (28056 ^ _779142) ^ [_1274721, _1274723, _1274725, _1274727] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1274721), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274721), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274721), _1274723), _1274725)), _1274727) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1274721), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274721), _1274723), _1274727)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274721), _1274725), _1274727)))], (15647 ^ _779142) ^ [_1053471, _1053473, _1053475, _1053477] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053471), hAPP(c_Int_Onumber__class_Onumber__of(_1053471), _1053473)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053471), _1053475), _1053477)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053471), hAPP(c_Int_Onumber__class_Onumber__of(_1053471), _1053473)), _1053475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053471), hAPP(c_Int_Onumber__class_Onumber__of(_1053471), _1053473)), _1053477))), class_Int_Onumber(_1053471), class_Rings_Osemiring(_1053471)], (31835 ^ _779142) ^ [_1352240, _1352242, _1352244, _1352246, _1352248, _1352250] : [-(_1352240 = _1352242), -(hAPP(c_Fun_Ofun__upd(_1352244, _1352246, _1352248, _1352242, _1352250), _1352240) = hAPP(_1352248, _1352240))], (33045 ^ _779142) ^ [_1383814, _1383816, _1383818, _1383820, _1383822, _1383824] : [hAPP(hAPP(c_Product__Type_OPair(_1383814, _1383816), _1383818), _1383820) = hAPP(hAPP(c_Product__Type_OPair(_1383814, _1383816), _1383822), _1383824), 33048 ^ _779142 : [(33051 ^ _779142) ^ [] : [-(_1383820 = _1383824)], (33049 ^ _779142) ^ [] : [-(_1383818 = _1383822)]]], (39973 ^ _779142) ^ [_1558454, _1558456] : [39975 ^ _779142 : [(39978 ^ _779142) ^ [] : [39974 ^ [_1558454, _1558456] = c_Orderings_Obot__class_Obot(tc_fun(_1558454, tc_HOL_Obool))], (39976 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558454, tc_HOL_Obool)), 39974 ^ [_1558454, _1558456]), hAPP(c_Relation_OImage(_1558454, _1558454, _1558456), 39974 ^ [_1558454, _1558456]))))]], -(c_Wellfounded_Owf(_1558454, _1558456))], (43776 ^ _779142) ^ [_1654760, _1654762, _1654764] : [hAPP(c_List_Orotate(_1654760, _1654762), _1654764) = c_List_Olist_ONil(_1654760), -(_1654764 = c_List_Olist_ONil(_1654760))], (47028 ^ _779142) ^ [_1724988, _1724990, _1724992, _1724994, _1724996] : [c_List_OdropWhile(_1724988, _1724990, _1724992) = hAPP(hAPP(c_List_Olist_OCons(_1724988), _1724994), _1724996), 47031 ^ _779142 : [(47034 ^ _779142) ^ [] : [hBOOL(hAPP(_1724990, _1724994))], (47032 ^ _779142) ^ [] : [-(_1724992 = hAPP(hAPP(c_List_Oappend(_1724988), c_List_OtakeWhile(_1724988, _1724990, _1724992)), hAPP(hAPP(c_List_Olist_OCons(_1724988), _1724994), _1724996)))]]], (24235 ^ _779142) ^ [_1205753, _1205755] : [class_Int_Oring__char__0(_1205753), 24238 ^ _779142 : [(24245 ^ _779142) ^ [] : [_1205755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1205753) = hAPP(c_Int_Oring__1__class_Oof__int(_1205753), _1205755))], (24239 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_1205753) = hAPP(c_Int_Oring__1__class_Oof__int(_1205753), _1205755), -(_1205755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (18899 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (48536 ^ _779142) ^ [_1758003, _1758005, _1758007] : [-(c_List_Olist__ex1(_1758003, _1758005, _1758007)), 48537 ^ _779142 : [(48538 ^ _779142) ^ [_1758097] : [hBOOL(hAPP(hAPP(c_member(_1758003), _1758097), hAPP(c_List_Oset(_1758003), _1758007))), hBOOL(hAPP(_1758005, _1758097)), 48546 ^ _779142 : [(48551 ^ _779142) ^ [] : [48545 ^ [_1758003, _1758005, _1758007, _1758097] = _1758097], (48549 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1758005, 48545 ^ [_1758003, _1758005, _1758007, _1758097])))], (48547 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758003), 48545 ^ [_1758003, _1758005, _1758007, _1758097]), hAPP(c_List_Oset(_1758003), _1758007))))]]]]], (52389 ^ _779142) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (17525 ^ _779142) ^ [_1087960, _1087962, _1087964, _1087966] : [class_Divides_Oring__div(_1087960), -(c_Divides_Odiv__class_Omod(_1087960, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087960), _1087962), _1087964), _1087966) = c_Divides_Odiv__class_Omod(_1087960, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087960), _1087962), c_Divides_Odiv__class_Omod(_1087960, _1087964, _1087966)), _1087966))], (4170 ^ _779142) ^ [_842249, _842251, _842253, _842255] : [-(c_List_Ozip(_842255, _842251) = c_List_Ozip(_842253, _842249)), _842255 = _842253, _842251 = _842249], (8755 ^ _779142) ^ [_926465, _926467, _926469, _926471] : [class_Groups_Oordered__cancel__ab__semigroup__add(_926465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926465), _926467), _926469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926465), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926465), _926471), _926467)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926465), _926471), _926469))))], (23667 ^ _779142) ^ [] : [-(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)))], (36312 ^ _779142) ^ [_1462061, _1462063, _1462065, _1462067] : [36314 ^ _779142 : [(36318 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462061), 36316 ^ [_1462061, _1462063, _1462065, _1462067]), _1462067)))], (36320 ^ _779142) ^ [] : [-(hAPP(_1462065, 36313 ^ [_1462061, _1462063, _1462065, _1462067]) = hAPP(_1462065, 36316 ^ [_1462061, _1462063, _1462065, _1462067]))], (36322 ^ _779142) ^ [] : [36313 ^ [_1462061, _1462063, _1462065, _1462067] = 36316 ^ [_1462061, _1462063, _1462065, _1462067]], (36315 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462061), 36313 ^ [_1462061, _1462063, _1462065, _1462067]), _1462067)))]], -(c_Fun_Oinj__on(_1462061, _1462063, _1462065, _1462067))], (26798 ^ _779142) ^ [_1251207, _1251209, _1251211] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1251207), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251207, tc_HOL_Obool)), _1251209), _1251211))), 26801 ^ _779142 : [(26804 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1251207), _1251211)))], (26802 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1251207), _1251209)))]]], (33091 ^ _779142) ^ [_1384719, _1384721, _1384723, _1384725] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1384719, _1384721, _1384723), hAPP(hAPP(c_COMBB(tc_fun(_1384721, tc_prod(_1384719, _1384721)), tc_fun(_1384721, _1384723), _1384719), hAPP(c_COMBB(tc_prod(_1384719, _1384721), _1384723, _1384721), _1384725)), c_Product__Type_OPair(_1384719, _1384721))) = _1384725)], (28839 ^ _779142) ^ [_1289853, _1289855, _1289857, _1289859] : [class_Lattices_Odistrib__lattice(_1289853), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289853), _1289855), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289853), _1289857), _1289859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289853), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289853), _1289855), _1289857)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289853), _1289855), _1289859)))], (20592 ^ _779142) ^ [_1140694, _1140696, _1140698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140694), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20595 ^ _779142 : [(20596 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1140696, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140698), _1140694)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140698, _1140694))), 20599 ^ _779142 : [(20600 ^ _779142) ^ [_1140904, _1140906] : [-(hBOOL(hAPP(hAPP(_1140696, _1140906), _1140904))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140694), _1140904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140904), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1140698 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140694), _1140906)), _1140904)]]], (20614 ^ _779142) ^ [] : [20617 ^ _779142 : [(20620 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20616 ^ [_1140694, _1140696, _1140698]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20622 ^ _779142) ^ [] : [-(_1140698 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140694), 20615 ^ [_1140694, _1140696, _1140698])), 20616 ^ [_1140694, _1140696, _1140698]))], (20624 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1140696, 20615 ^ [_1140694, _1140696, _1140698]), 20616 ^ [_1140694, _1140696, _1140698]))], (20618 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140694), 20616 ^ [_1140694, _1140696, _1140698])))]], -(hBOOL(hAPP(hAPP(_1140696, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140698), _1140694)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140698, _1140694))))]]], (32647 ^ _779142) ^ [_1375422, _1375424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375422)), 32650 ^ _779142 : [(32657 ^ _779142) ^ [] : [-(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), _1375424), _1375422)))), -(c_Divides_OnegDivAlg(_1375424, _1375422) = hAPP(c_Divides_Oadjust(_1375422), c_Divides_OnegDivAlg(_1375424, 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)))), _1375422))))], (32651 ^ _779142) ^ [] : [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), _1375424), _1375422))), -(c_Divides_OnegDivAlg(_1375424, _1375422) = 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), _1375424), _1375422)))]]], (37791 ^ _779142) ^ [_1497000, _1497002, _1497004, _1497006, _1497008] : [class_Groups_Ocomm__monoid__add(_1497000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497002), _1497004)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497002, _1497000), _1497006), hAPP(c_Set_OCollect(_1497002), hAPP(hAPP(c_COMBS(_1497002, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497002), c_fconj), hAPP(hAPP(c_COMBC(_1497002, tc_fun(_1497002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497002)), _1497004))), hAPP(hAPP(c_COMBC(_1497002, tc_fun(_1497002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497002)), _1497008)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497002, _1497000), hAPP(hAPP(c_COMBC(_1497002, _1497000, _1497000), hAPP(hAPP(c_COMBS(_1497002, _1497000, tc_fun(_1497000, _1497000)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1497000, tc_fun(_1497000, _1497000)), _1497002), c_If(_1497000)), hAPP(hAPP(c_COMBC(_1497002, tc_fun(_1497002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497002)), _1497008))), _1497006)), c_Groups_Ozero__class_Ozero(_1497000))), _1497004))], (49818 ^ _779142) ^ [_1786632] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786632), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786632 = hAPP(c_Code__Numeral_Onat__of, 49821 ^ [_1786632]))], (38461 ^ _779142) ^ [_1521363, _1521365, _1521367, _1521369] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521363, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521365, _1521363), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1521365, _1521363), tc_HOL_Obool)), _1521367), _1521369))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521363, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521365, _1521363), _1521367)), hAPP(c_Relation_ORange(_1521365, _1521363), _1521369)))))], (4662 ^ _779142) ^ [_850045, _850047, _850049, _850051] : [-(c_Product__Type_Ofst(_850051, _850047) = c_Product__Type_Ofst(_850049, _850045)), _850051 = _850049, _850047 = _850045], (20732 ^ _779142) ^ [_1143485, _1143487, _1143489] : [-(_1143485 = 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), _1143485), _1143487)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143485), _1143489)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143487), _1143489))], (12254 ^ _779142) ^ [_990773] : [class_Rings_Olinordered__semidom(_990773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990773), c_Groups_Oone__class_Oone(_990773)), c_Groups_Ozero__class_Ozero(_990773)))], (25636 ^ _779142) ^ [_1229699, _1229701] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1229699))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1229701))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229701)))], (33201 ^ _779142) ^ [_1386757, _1386759] : [_1386757 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386757, _1386759) = 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)))], (8655 ^ _779142) ^ [_924529, _924531, _924533, _924535, _924537] : [class_Groups_Oordered__ab__semigroup__add(_924529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924529), _924531), _924533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924529), _924535), _924537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924529), _924531), _924535)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924529), _924533), _924537))))], (23639 ^ _779142) ^ [_1195452, _1195454] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195452), _1195454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1195452), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195454)))], (32239 ^ _779142) ^ [_1365873] : [class_Orderings_Olinorder(_1365873), -(c_Orderings_Oord_Omax(_1365873, hAPP(c_COMBC(_1365873, _1365873, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1365873))) = c_Orderings_Oord__class_Omin(_1365873))], (40582 ^ _779142) ^ [_1573902, _1573904, _1573906, _1573908] : [c_Wellfounded_Owf(_1573902, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573902, _1573902)), hAPP(hAPP(c_Product__Type_OPair(_1573902, _1573902), _1573904), _1573906)), _1573908)), 40585 ^ _779142 : [(40588 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573902, _1573902)), hAPP(hAPP(c_Product__Type_OPair(_1573902, _1573902), _1573906), _1573904)), c_Transitive__Closure_Ortrancl(_1573902, _1573908)))], (40586 ^ _779142) ^ [] : [-(c_Wellfounded_Owf(_1573902, _1573908))]]], (18854 ^ _779142) ^ [_1111123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111123)), 18858 ^ _779142 : [(18861 ^ _779142) ^ [] : [-(_1111123 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18857 ^ [_1111123]))], (18859 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 18857 ^ [_1111123])))]]], (37219 ^ _779142) ^ [_1481963, _1481965, _1481967, _1481969, _1481971] : [hBOOL(hAPP(hAPP(c_member(_1481963), _1481965), hAPP(c_Set_Ovimage(_1481963, _1481967, _1481969), _1481971))), -(hBOOL(hAPP(hAPP(c_member(_1481967), hAPP(_1481969, _1481965)), _1481971)))], (17714 ^ _779142) ^ [_1091234, _1091236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091234)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091234), _1091236)))], (43257 ^ _779142) ^ [_1642081, _1642083, _1642085] : [-(_1642081 = c_List_Olist_ONil(_1642083)), -(c_List_Obutlast(_1642083, hAPP(hAPP(c_List_Oappend(_1642083), _1642085), _1642081)) = hAPP(hAPP(c_List_Oappend(_1642083), _1642085), c_List_Obutlast(_1642083, _1642081)))], (45801 ^ _779142) ^ [_1700148, _1700150] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700148)), c_List_Otranspose__rel(_1700148)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700148)), c_List_Olist_ONil(_1700148)), _1700150))), -(c_List_Otranspose(_1700148, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700148)), c_List_Olist_ONil(_1700148)), _1700150)) = c_List_Otranspose(_1700148, _1700150))], (48158 ^ _779142) ^ [_1750376, _1750378, _1750380] : [-(c_List_Oreplicate(_1750376, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750376)), hAPP(c_List_Ofilter(_1750376, hAPP(c_fequal, _1750378)), _1750380)), _1750378) = hAPP(c_List_Ofilter(_1750376, hAPP(c_fequal, _1750378)), _1750380))], (36688 ^ _779142) ^ [_1469829, _1469831, _1469833, _1469835, _1469837] : [c_Fun_Oinj__on(_1469829, _1469831, _1469833, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469829, tc_HOL_Obool)), _1469835), _1469837)), 36691 ^ _779142 : [(36696 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469831, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469829, _1469831, _1469833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469829, tc_HOL_Obool)), _1469835), _1469837))), hAPP(c_Set_Oimage(_1469829, _1469831, _1469833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469829, tc_HOL_Obool)), _1469837), _1469835))) = c_Orderings_Obot__class_Obot(tc_fun(_1469831, tc_HOL_Obool)))], (36694 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1469829, _1469831, _1469833, _1469837))], (36692 ^ _779142) ^ [] : [-(c_Fun_Oinj__on(_1469829, _1469831, _1469833, _1469835))]]], (40492 ^ _779142) ^ [_1571949, _1571951, _1571953, _1571955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571949, _1571949)), hAPP(hAPP(c_Product__Type_OPair(_1571949, _1571949), _1571951), _1571953)), c_Transitive__Closure_Ortrancl(_1571949, _1571955))), -(_1571951 = _1571953), 40499 ^ _779142 : [(40502 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571949, _1571949)), hAPP(hAPP(c_Product__Type_OPair(_1571949, _1571949), _1571951), _1571953)), c_Transitive__Closure_Otrancl(_1571949, _1571955))))], (40500 ^ _779142) ^ [] : [_1571951 = _1571953]]], (30135 ^ _779142) ^ [_1317264, _1317266, _1317268] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317264), _1317266)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317264), _1317268)), 30145 ^ _779142 : [(30148 ^ _779142) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30146 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317264), 30144 ^ [_1317264, _1317266, _1317268]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317264, tc_HOL_Obool)), _1317266), _1317268))))]], -(hAPP(c_Finite__Set_Ocard(_1317264), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317264, tc_HOL_Obool)), _1317266), _1317268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317264), _1317266)), hAPP(c_Finite__Set_Ocard(_1317264), _1317268)))], (31316 ^ _779142) ^ [_1340656, _1340658, _1340660, _1340662] : [hBOOL(hAPP(hAPP(c_member(_1340656), _1340658), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1340656, tc_HOL_Obool), _1340660))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1340656, tc_HOL_Obool)), _1340662), _1340660)), -(hBOOL(hAPP(hAPP(c_member(_1340656), _1340658), _1340662)))], (45703 ^ _779142) ^ [_1697419, _1697421, _1697423, _1697425] : [-(hBOOL(hAPP(_1697419, _1697421))), -(hAPP(c_List_Ofilter(_1697423, _1697419), hAPP(hAPP(c_List_Olist_OCons(_1697423), _1697421), _1697425)) = hAPP(c_List_Ofilter(_1697423, _1697419), _1697425))], (18652 ^ _779142) ^ [_1107456, _1107458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107456), _1107458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1107456)), _1107458)))], (11378 ^ _779142) ^ [_974654, _974656] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _974654), _974656)), hAPP(c_Nat_OSuc, _974654))))], (40057 ^ _779142) ^ [_1560666, _1560668, _1560670] : [c_Wellfounded_Owf(_1560666, _1560668), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560666, _1560666)), hAPP(hAPP(c_Product__Type_OPair(_1560666, _1560666), hAPP(_1560670, hAPP(c_Nat_OSuc, 40060 ^ [_1560666, _1560668, _1560670]))), hAPP(_1560670, 40060 ^ [_1560666, _1560668, _1560670]))), _1560668))], (19483 ^ _779142) ^ [_1121749, _1121751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121749), 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)), _1121751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1121749), _1121751)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45372 ^ _779142) ^ [_1689760, _1689762] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689760)), c_List_Oremdups(_1689760, _1689762)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689760)), _1689762), -(c_List_Oremdups(_1689760, _1689762) = _1689762)], (27296 ^ _779142) ^ [_1260717, _1260719, _1260721] : [class_Orderings_Oorder(_1260717), 27299 ^ _779142 : [(27306 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260717), _1260719), _1260721))), -(c_Orderings_Obot__class_Obot(tc_fun(_1260717, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1260717, _1260719, _1260721))], (27300 ^ _779142) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1260717, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1260717, _1260719, _1260721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260717), _1260719), _1260721))]]], (18577 ^ _779142) ^ [_1106229, _1106231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106229), _1106231)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106229, _1106231) = _1106229)], (45018 ^ _779142) ^ [_1681735, _1681737, _1681739, _1681741, _1681743] : [c_List_Olist__all2(_1681735, _1681737, _1681739, _1681741, _1681743), 45021 ^ _779142 : [(45024 ^ _779142) ^ [_1681901] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681735, _1681737)), _1681901), hAPP(c_List_Oset(tc_prod(_1681735, _1681737)), hAPP(hAPP(c_List_Ozip(_1681735, _1681737), _1681741), _1681743)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681735, _1681737, tc_HOL_Obool), _1681739), _1681901)))], (45022 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681735)), _1681741) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681737)), _1681743))]]], (37914 ^ _779142) ^ [_1501880] : [-(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)))), _1501880)) = 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), _1501880), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (17407 ^ _779142) ^ [_1085381, _1085383, _1085385, _1085387] : [class_Divides_Osemiring__div(_1085381), -(c_Divides_Odiv__class_Omod(_1085381, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085381), c_Divides_Odiv__class_Omod(_1085381, _1085383, _1085385)), _1085387), _1085385) = c_Divides_Odiv__class_Omod(_1085381, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085381), _1085383), _1085387), _1085385))], (9817 ^ _779142) ^ [_946277, _946279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946277), _946279)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946279), _946277)) = _946277)], (28230 ^ _779142) ^ [_1278056, _1278058, _1278060] : [class_Orderings_Olinorder(_1278056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278056), _1278058)), -(_1278058 = c_Orderings_Obot__class_Obot(tc_fun(_1278056, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278056), _1278060)), -(_1278060 = c_Orderings_Obot__class_Obot(tc_fun(_1278056, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1278056, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278056, tc_HOL_Obool)), _1278058), _1278060)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278056), c_Big__Operators_Olinorder__class_OMax(_1278056, _1278058)), c_Big__Operators_Olinorder__class_OMax(_1278056, _1278060)))], (40777 ^ _779142) ^ [_1578580, _1578582, _1578584] : [c_Equiv__Relations_Oequiv(_1578580, _1578582, _1578584), -(hAPP(hAPP(c_Relation_Orel__comp(_1578580, _1578580, _1578580), hAPP(c_Relation_Oconverse(_1578580, _1578580), _1578584)), _1578584) = _1578584)], (28917 ^ _779142) ^ [_1291659, _1291661, _1291663, _1291665] : [class_Lattices_Osemilattice__inf(_1291659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291659), _1291661), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1291659), _1291663), _1291665))), 28924 ^ _779142 : [(28927 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291659), _1291661), _1291665)))], (28925 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291659), _1291661), _1291663)))]]], (5308 ^ _779142) ^ [_860334, _860336] : [_860336 = _860334, -(c_Groups_Ouminus__class_Ouminus(_860336) = c_Groups_Ouminus__class_Ouminus(_860334))], (24211 ^ _779142) ^ [_1205329] : [class_Rings_Osemiring__1(_1205329), c_Int_Oiszero(_1205329, c_Groups_Oone__class_Oone(_1205329))], (38633 ^ _779142) ^ [_1527121, _1527123] : [c_Wellfounded_Owf(_1527121, _1527123), -(c_Wellfounded_Owf(tc_fun(_1527121, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1527121, _1527123)))], (19383 ^ _779142) ^ [_1119850, _1119852] : [class_Groups_Oordered__ab__group__add__abs(_1119850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119850), hAPP(c_Groups_Oabs__class_Oabs(_1119850), _1119852)), c_Groups_Ozero__class_Ozero(_1119850)))], (41505 ^ _779142) ^ [_1599251, _1599253, _1599255, _1599257] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599251), tc_List_Olist(_1599251))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599251), tc_List_Olist(_1599251)), _1599253), _1599255)), c_List_Olistrel1(_1599251, _1599257))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599251)), _1599253) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599251)), _1599255))], (40105 ^ _779142) ^ [_1561848, _1561850, _1561852, _1561854, _1561856, _1561858, _1561860] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561848, _1561850, _1561852, _1561854), _1561856), _1561858), _1561860) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561850, _1561852, _1561854), _1561858), hAPP(_1561856, _1561860)))], (49144 ^ _779142) ^ [_1772680, _1772682] : [c_Relation_Otrans(_1772680, _1772682), c_Relation_Oantisym(_1772680, _1772682), -(c_Relation_Otrans(_1772680, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1772680, _1772680), tc_HOL_Obool)), _1772682), c_Relation_OId(_1772680))))], (23775 ^ _779142) ^ [_1197902] : [class_Int_Onumber__ring(_1197902), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1197902), c_Groups_Oone__class_Oone(_1197902)) = hAPP(c_Int_Onumber__class_Onumber__of(_1197902), c_Int_OMin))], (10347 ^ _779142) ^ [_958072, _958074, _958076, _958078, _958080] : [class_Groups_Ocomm__monoid__mult(_958072), hBOOL(hAPP(c_Finite__Set_Ofinite(_958074), _958076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958074, tc_HOL_Obool)), _958078), _958076)), 10361 ^ _779142 : [(10364 ^ _779142) ^ [] : [hAPP(_958080, 10360 ^ [_958072, _958074, _958076, _958078, _958080]) = c_Groups_Oone__class_Oone(_958072)], (10362 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_958074), 10360 ^ [_958072, _958074, _958076, _958078, _958080]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958074, tc_HOL_Obool)), _958076), _958078))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_958074, _958072), _958080), _958076) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_958074, _958072), _958080), _958078))], (23029 ^ _779142) ^ [_1184464] : [class_Groups_Ogroup__add(_1184464), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1184464), c_Groups_Ozero__class_Ozero(_1184464)) = c_Groups_Ozero__class_Ozero(_1184464))], (48935 ^ _779142) ^ [_1767321, _1767323, _1767325] : [c_List_Olist__ex(_1767321, _1767325, _1767323), 48939 ^ _779142 : [(48942 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1767325, 48938 ^ [_1767321, _1767323, _1767325])))], (48940 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767321), 48938 ^ [_1767321, _1767323, _1767325]), hAPP(c_List_Oset(_1767321), _1767323))))]]], (47179 ^ _779142) ^ [_1728261, _1728263, _1728265] : [-(hBOOL(hAPP(hAPP(c_member(_1728261), _1728263), hAPP(c_List_Oset(_1728261), _1728265)))), -(c_List_Oinsert(_1728261, _1728263, _1728265) = hAPP(hAPP(c_List_Olist_OCons(_1728261), _1728263), _1728265))], (19579 ^ _779142) ^ [_1123217, _1123219] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1123217, _1123219)), _1123219) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32051 ^ _779142) ^ [_1359865, _1359867, _1359869, _1359871, _1359873] : [-(hAPP(c_Set_Oimage(_1359865, _1359867, hAPP(hAPP(c_COMBB(_1359869, _1359867, _1359865), _1359871), _1359873)), c_Orderings_Otop__class_Otop(tc_fun(_1359865, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1359869, _1359867, _1359871), hAPP(c_Set_Oimage(_1359865, _1359869, _1359873), c_Orderings_Otop__class_Otop(tc_fun(_1359865, tc_HOL_Obool)))))], (16555 ^ _779142) ^ [_1070514, _1070516, _1070518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070514), _1070516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070518), _1070514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070518), _1070516))))], (44785 ^ _779142) ^ [_1676513, _1676515] : [hAPP(c_Code__Numeral_Onat__of, _1676513) = hAPP(c_Code__Numeral_Onat__of, _1676515), -(_1676513 = _1676515)], (41813 ^ _779142) ^ [_1608426, _1608428, _1608430] : [-(_1608426 = _1608428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608430)), _1608426) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608430)), _1608428), 41819 ^ _779142 : [(41822 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Onth(_1608430), _1608426), 41818 ^ [_1608426, _1608428, _1608430]) = hAPP(hAPP(c_List_Onth(_1608430), _1608428), 41818 ^ [_1608426, _1608428, _1608430])], (41820 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41818 ^ [_1608426, _1608428, _1608430]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608430)), _1608426))))]]], (23507 ^ _779142) ^ [_1193159, _1193161, _1193163] : [class_Rings_Odivision__ring(_1193159), -(_1193161 = c_Groups_Ozero__class_Ozero(_1193159)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1193159), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193159), _1193163), _1193161)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193159), _1193163), hAPP(c_Groups_Ouminus__class_Ouminus(_1193159), _1193161)))], (52337 ^ _779142) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (31062 ^ _779142) ^ [] : [-(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))))], (39716 ^ _779142) ^ [_1552480, _1552482, _1552484, _1552486, _1552488, _1552490, _1552492, _1552494, _1552496, _1552498, _1552500] : [c_Finite__Set_Ofolding(_1552480, _1552482, _1552484, _1552486), -(hAPP(c_Fun_Ocomp(_1552488, _1552490, _1552492, _1552494), hAPP(c_Fun_Ocomp(_1552496, _1552488, _1552492, _1552498), _1552500)) = hAPP(c_Fun_Ocomp(_1552496, _1552490, _1552492, hAPP(c_Fun_Ocomp(_1552488, _1552490, _1552496, _1552494), _1552498)), _1552500))], (7020 ^ _779142) ^ [_894549, _894551, _894553, _894555] : [-(hBOOL(hAPP(hAPP(c_member(_894549), _894551), _894553))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894549, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_894549), _894551), _894555)), _894553) = hAPP(hAPP(c_Set_Oinsert(_894549), _894551), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894549, tc_HOL_Obool)), _894555), _894553)))], (40293 ^ _779142) ^ [_1566395, _1566397, _1566399, _1566401] : [-(c_Transitive__Closure_Otrancl(_1566395, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1566395, _1566395)), hAPP(hAPP(c_Product__Type_OPair(_1566395, _1566395), _1566397), _1566399)), _1566401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566395, _1566395), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1566395, _1566401)), hAPP(c_Set_OCollect(tc_prod(_1566395, _1566395)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566395, _1566395, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1566395, tc_fun(_1566395, tc_HOL_Obool), tc_fun(_1566395, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1566395, tc_HOL_Obool), tc_fun(_1566395, tc_HOL_Obool)), _1566395), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1566395)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566395), c_fconj), hAPP(hAPP(c_COMBC(_1566395, tc_fun(tc_prod(_1566395, _1566395), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566395, _1566395), tc_fun(tc_fun(tc_prod(_1566395, _1566395), tc_HOL_Obool), tc_HOL_Obool), _1566395), c_member(tc_prod(_1566395, _1566395))), hAPP(hAPP(c_COMBC(_1566395, _1566395, tc_prod(_1566395, _1566395)), c_Product__Type_OPair(_1566395, _1566395)), _1566397))), c_Transitive__Closure_Ortrancl(_1566395, _1566401))))), hAPP(hAPP(c_COMBC(_1566395, tc_fun(tc_prod(_1566395, _1566395), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566395, _1566395), tc_fun(tc_fun(tc_prod(_1566395, _1566395), tc_HOL_Obool), tc_HOL_Obool), _1566395), c_member(tc_prod(_1566395, _1566395))), hAPP(c_Product__Type_OPair(_1566395, _1566395), _1566399))), c_Transitive__Closure_Ortrancl(_1566395, _1566401)))))))], (20570 ^ _779142) ^ [_1140269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140269)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1140269)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1140269)))], (34981 ^ _779142) ^ [_1428800, _1428802, _1428804, _1428806, _1428808] : [_1428800 = c_Orderings_Obot__class_Obot(tc_fun(_1428802, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428802, tc_fun(_1428804, tc_HOL_Obool)), _1428800), hAPP(hAPP(c_COMBC(_1428802, tc_fun(_1428804, tc_HOL_Obool), tc_fun(_1428804, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428804, tc_HOL_Obool), tc_fun(tc_fun(_1428804, tc_HOL_Obool), tc_fun(_1428804, tc_HOL_Obool)), _1428802), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428804, tc_HOL_Obool))), _1428806)), _1428808)) = c_Orderings_Otop__class_Otop(tc_fun(_1428804, tc_HOL_Obool)))], (44293 ^ _779142) ^ [_1664882, _1664884] : [-(_1664882 = c_List_Olist_ONil(_1664884)), -(c_Random_Oselect__weight(_1664884, hAPP(hAPP(c_List_Omap(_1664884, tc_prod(tc_Code__Numeral_Ocode__numeral, _1664884)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1664884), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1664882)) = c_Random_Oselect(_1664884, _1664882))], (33891 ^ _779142) ^ [_1399972, _1399974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1399972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1399974)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1399972), _1399974) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1399972, _1399974)))], (2822 ^ _779142) ^ [_820893, _820895, _820897, _820899, _820901, _820903] : [-(c_Product__Type_Ointernal__split(_820903, _820899, _820895) = c_Product__Type_Ointernal__split(_820901, _820897, _820893)), _820903 = _820901, _820899 = _820897, _820895 = _820893], (45995 ^ _779142) ^ [_1704365, _1704367, _1704369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704365), _1704367)), _1704369)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1704365, _1704369)), _1704367) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704365), _1704367))], (36810 ^ _779142) ^ [_1472710, _1472712, _1472714, _1472716, _1472718, _1472720] : [c_Fun_Oinj__on(_1472710, _1472712, _1472714, _1472716), hAPP(_1472714, _1472718) = _1472720, hBOOL(hAPP(hAPP(c_member(_1472710), _1472718), _1472716)), -(hAPP(c_Fun_Othe__inv__into(_1472710, _1472712, _1472716, _1472714), _1472720) = _1472718)], (47036 ^ _779142) ^ [_1725169, _1725171, _1725173, _1725175, _1725177] : [-(c_List_OdropWhile(_1725169, _1725171, _1725173) = hAPP(hAPP(c_List_Olist_OCons(_1725169), _1725175), _1725177)), _1725173 = hAPP(hAPP(c_List_Oappend(_1725169), c_List_OtakeWhile(_1725169, _1725171, _1725173)), hAPP(hAPP(c_List_Olist_OCons(_1725169), _1725175), _1725177)), -(hBOOL(hAPP(_1725171, _1725175)))], (32435 ^ _779142) ^ [_1370342] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1370342))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1370342)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7348 ^ _779142) ^ [_900982, _900984, _900986] : [class_Orderings_Olinorder(_900982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900982), _900984), _900986))), 7355 ^ _779142 : [(7362 ^ _779142) ^ [] : [_900986 = _900984, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900982), _900986), _900984))], (7356 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900982), _900986), _900984))), -(_900986 = _900984)]]], (10087 ^ _779142) ^ [_952426, _952428, _952430] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952426), _952428) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952430), _952428), -(_952426 = _952430)], (49847 ^ _779142) ^ [_1787100, _1787102] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1787100), _1787102))), -(c_Quickcheck_Obeyond(_1787100, _1787102) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (26160 ^ _779142) ^ [_1239043, _1239045] : [class_Rings_Oring__1(_1239043), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239043), hAPP(c_Groups_Ouminus__class_Ouminus(_1239043), c_Groups_Oone__class_Oone(_1239043))), 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)))), _1239045)) = c_Groups_Oone__class_Oone(_1239043))], (52473 ^ _779142) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (36636 ^ _779142) ^ [_1468607] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1468607)), c_Int_OInteg)))], (46875 ^ _779142) ^ [_1721809, _1721811, _1721813] : [-(c_List_OtakeWhile(_1721809, _1721811, _1721813) = hAPP(hAPP(c_List_Otake(_1721809), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721809)), c_List_OtakeWhile(_1721809, _1721811, _1721813))), _1721813))], (24437 ^ _779142) ^ [_1209142] : [class_Int_Onumber__ring(_1209142), c_Int_Oiszero(_1209142, hAPP(c_Int_Onumber__class_Onumber__of(_1209142), c_Int_OMin))], (1256 ^ _779142) ^ [_797784, _797786] : [-(class_Rings_Ocomm__ring__1(_797784)), _797786 = _797784, class_Rings_Ocomm__ring__1(_797786)], (39568 ^ _779142) ^ [_1549248, _1549250, _1549252] : [-(hAPP(c_Fun_Ocomp(_1549248, _1549248, _1549250, c_Fun_Oid(_1549248)), _1549252) = _1549252)], (7030 ^ _779142) ^ [_894786, _894788, _894790, _894792] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894786, tc_HOL_Obool)), _894788), hAPP(hAPP(c_Set_Oinsert(_894786), _894790), _894792)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894786, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894786, tc_HOL_Obool)), _894788), _894792)), hAPP(hAPP(c_Set_Oinsert(_894786), _894790), c_Orderings_Obot__class_Obot(tc_fun(_894786, tc_HOL_Obool)))))], (42714 ^ _779142) ^ [_1630371, _1630373] : [_1630373 = c_List_Olist_ONil(_1630371), -(c_Orderings_Obot__class_Obot(tc_fun(_1630371, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630371), _1630373))], (4628 ^ _779142) ^ [_849510, _849512, _849514, _849516, _849518, _849520, _849522, _849524] : [-(c_Random__Sequence_Obind(_849524, _849520, _849516, _849512) = c_Random__Sequence_Obind(_849522, _849518, _849514, _849510)), _849524 = _849522, _849520 = _849518, _849516 = _849514, _849512 = _849510], (41779 ^ _779142) ^ [_1607458, _1607460, _1607462, _1607464] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607458), tc_List_Olist(_1607458))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607458), tc_List_Olist(_1607458)), _1607460), _1607462)), c_List_Olistrel(_1607458, _1607464)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607458)), _1607460) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607458)), _1607462), 41785 ^ _779142 : [(41788 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607458, _1607458)), hAPP(hAPP(c_Product__Type_OPair(_1607458, _1607458), hAPP(hAPP(c_List_Onth(_1607458), _1607460), 41784 ^ [_1607458, _1607460, _1607462, _1607464])), hAPP(hAPP(c_List_Onth(_1607458), _1607462), 41784 ^ [_1607458, _1607460, _1607462, _1607464]))), _1607464))], (41786 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41784 ^ [_1607458, _1607460, _1607462, _1607464]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607458)), _1607460))))]]], (7522 ^ _779142) ^ [_903563, _903565, _903567, _903569] : [class_Orderings_Oorder(_903563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903563), _903565), _903567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903563), _903569), _903565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903563), _903569), _903567)))], (16791 ^ _779142) ^ [_1074512, _1074514] : [class_Orderings_Olinorder(_1074512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074512), _1074514)), -(c_Big__Operators_Olinorder__class_OMin(_1074512, _1074514) = hAPP(c_Finite__Set_Ofold1(_1074512, c_Orderings_Oord__class_Omin(_1074512)), _1074514))], (48160 ^ _779142) ^ [_1750432, _1750434, _1750436] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750432)), c_List_Oreplicate(_1750432, _1750434, _1750436)) = _1750434)], (23865 ^ _779142) ^ [_1199471, _1199473] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199471, _1199473) = 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), _1199471), _1199473) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34546 ^ _779142) ^ [_1416822, _1416824, _1416826, _1416828, _1416830, _1416832] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416822, tc_fun(_1416824, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1416826, _1416822, _1416828), _1416830)), _1416832) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416826, tc_fun(_1416824, tc_HOL_Obool)), _1416830), hAPP(hAPP(c_COMBB(_1416822, tc_fun(_1416824, tc_HOL_Obool), _1416826), _1416832), _1416828)))], (26086 ^ _779142) ^ [_1237474, _1237476, _1237478] : [class_Rings_Olinordered__idom(_1237474), 26089 ^ _779142 : [(26098 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237474), hAPP(hAPP(c_Power_Opower__class_Opower(_1237474), _1237476), 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(_1237474), _1237478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1237474)))), _1237476 = c_Groups_Ozero__class_Ozero(_1237474), _1237478 = c_Groups_Ozero__class_Ozero(_1237474)], (26090 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237474), hAPP(hAPP(c_Power_Opower__class_Opower(_1237474), _1237476), 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(_1237474), _1237478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1237474))), 26093 ^ _779142 : [(26096 ^ _779142) ^ [] : [-(_1237478 = c_Groups_Ozero__class_Ozero(_1237474))], (26094 ^ _779142) ^ [] : [-(_1237476 = c_Groups_Ozero__class_Ozero(_1237474))]]]]], (23651 ^ _779142) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (51229 ^ _779142) ^ [_1815526, _1815528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815526), _1815528)), 51234 ^ _779142 : [(51237 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815528), _1815526))], (51235 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815526), _1815528)))]], -(_1815526 = _1815528)], (28304 ^ _779142) ^ [_1279184, _1279186, _1279188] : [class_Orderings_Olinorder(_1279184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279184), _1279186)), 28311 ^ _779142 : [(28318 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279184, tc_HOL_Obool)), _1279186), hAPP(hAPP(c_Set_Oinsert(_1279184), _1279188), c_Orderings_Obot__class_Obot(tc_fun(_1279184, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1279184, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1279184, hAPP(hAPP(c_Set_Oinsert(_1279184), _1279188), _1279186)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279184), _1279188), c_Big__Operators_Olinorder__class_OMax(_1279184, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279184, tc_HOL_Obool)), _1279186), hAPP(hAPP(c_Set_Oinsert(_1279184), _1279188), c_Orderings_Obot__class_Obot(tc_fun(_1279184, tc_HOL_Obool)))))))], (28312 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279184, tc_HOL_Obool)), _1279186), hAPP(hAPP(c_Set_Oinsert(_1279184), _1279188), c_Orderings_Obot__class_Obot(tc_fun(_1279184, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1279184, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1279184, hAPP(hAPP(c_Set_Oinsert(_1279184), _1279188), _1279186)) = _1279188)]]], (38889 ^ _779142) ^ [_1532439, _1532441] : [-(c_FunDef_Oreduction__pair(_1532439, _1532441)), c_Wellfounded_Owf(_1532439, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool), tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool)), _1532441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532439, _1532439, _1532439), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool), tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool)), _1532441)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool), tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool)), _1532441))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool), tc_fun(tc_prod(_1532439, _1532439), tc_HOL_Obool)), _1532441)))], (33825 ^ _779142) ^ [_1398561, _1398563, _1398565, _1398567] : [hAPP(c_Product__Type_Ofst(_1398561, _1398563), _1398565) = hAPP(c_Product__Type_Ofst(_1398561, _1398563), _1398567), hAPP(c_Product__Type_Osnd(_1398561, _1398563), _1398565) = hAPP(c_Product__Type_Osnd(_1398561, _1398563), _1398567), -(_1398565 = _1398567)], (36808 ^ _779142) ^ [_1472652, _1472654, _1472656] : [-(c_Fun_Oinj__on(tc_prod(_1472652, _1472654), tc_prod(_1472654, _1472652), hAPP(c_Product__Type_Oprod_Oprod__case(_1472652, _1472654, tc_prod(_1472654, _1472652)), hAPP(c_COMBC(_1472654, _1472652, tc_prod(_1472654, _1472652)), c_Product__Type_OPair(_1472654, _1472652))), _1472656))], (23395 ^ _779142) ^ [_1191276, _1191278] : [class_Groups_Ogroup__add(_1191276), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191276), _1191278), hAPP(c_Groups_Ouminus__class_Ouminus(_1191276), _1191278)) = c_Groups_Ozero__class_Ozero(_1191276))], (17551 ^ _779142) ^ [_1088439] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088439), c_Int_OPls) = _1088439)], (41367 ^ _779142) ^ [_1594704, _1594706, _1594708] : [hAPP(hAPP(c_List_Olist_OCons(_1594704), _1594706), _1594708) = _1594708], (37379 ^ _779142) ^ [_1486024] : [-(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)), _1486024)))))], (20093 ^ _779142) ^ [_1131731, _1131733, _1131735] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131731), _1131733)), _1131735) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131731), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131733), _1131735))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131731), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131733, _1131735))), _1131735)))], (11414 ^ _779142) ^ [_975480, _975482] : [class_Groups_Olinordered__ab__group__add(_975480), 11417 ^ _779142 : [(11424 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975480), c_Groups_Ozero__class_Ozero(_975480)), _975482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975480), c_Groups_Ozero__class_Ozero(_975480)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975480), _975482), _975482))))], (11418 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975480), c_Groups_Ozero__class_Ozero(_975480)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975480), _975482), _975482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975480), c_Groups_Ozero__class_Ozero(_975480)), _975482)))]]], (50035 ^ _779142) ^ [_1791085, _1791087, _1791089, _1791091] : [c_Fun_Obij__betw(_1791085, _1791087, _1791089, _1791091, c_Orderings_Otop__class_Otop(tc_fun(_1791087, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1791085, _1791087, _1791089), c_Orderings_Otop__class_Otop(tc_fun(_1791085, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791087, tc_HOL_Obool)))], (18146 ^ _779142) ^ [_1098664, _1098666] : [class_Int_Onumber__ring(_1098664), class_Rings_Olinordered__idom(_1098664), 18153 ^ _779142 : [(18160 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1098666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098664), c_Groups_Ozero__class_Ozero(_1098664)), hAPP(c_Int_Onumber__class_Onumber__of(_1098664), _1098666))))], (18154 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098664), c_Groups_Ozero__class_Ozero(_1098664)), hAPP(c_Int_Onumber__class_Onumber__of(_1098664), _1098666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1098666)))]]], (14793 ^ _779142) ^ [_1037466, _1037468, _1037470, _1037472] : [-(c_Sum__Type_OPlus(_1037466, _1037468, _1037470, _1037472) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1037466, _1037468), tc_HOL_Obool))), _1037470 = c_Orderings_Obot__class_Obot(tc_fun(_1037466, tc_HOL_Obool)), _1037472 = c_Orderings_Obot__class_Obot(tc_fun(_1037468, tc_HOL_Obool))], (36204 ^ _779142) ^ [_1460142, _1460144, _1460146] : [-(c_Fun_Oinj__on(_1460142, _1460144, _1460146, c_Orderings_Obot__class_Obot(tc_fun(_1460142, tc_HOL_Obool))))], (9475 ^ _779142) ^ [_940665, _940667, _940669] : [class_Groups_Ocomm__monoid__mult(_940665), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_940667, _940665), _940669), c_Orderings_Obot__class_Obot(tc_fun(_940667, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_940665))], (16609 ^ _779142) ^ [_1071501, _1071503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071501), _1071503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071501), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1071503)))], (11538 ^ _779142) ^ [_977642, _977644, _977646] : [class_Rings_Olinordered__ring__strict(_977642), 11541 ^ _779142 : [(11556 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977642), _977644), _977646)))), 11557 ^ _779142 : [(11564 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), _977644), c_Groups_Ozero__class_Ozero(_977642))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), _977646), c_Groups_Ozero__class_Ozero(_977642)))], (11558 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), _977644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), _977646))]]], (11542 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977642), _977644), _977646))), 11547 ^ _779142 : [(11550 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), _977646)))], (11548 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), c_Groups_Ozero__class_Ozero(_977642)), _977644)))]], 11551 ^ _779142 : [(11554 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), _977646), c_Groups_Ozero__class_Ozero(_977642))))], (11552 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977642), _977644), c_Groups_Ozero__class_Ozero(_977642))))]]]]], (39084 ^ _779142) ^ [_1537247, _1537249] : [c_Wellfounded_Owf(_1537247, hAPP(c_Set_OCollect(tc_prod(_1537247, _1537247)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537247, _1537247, tc_HOL_Obool), _1537249))), -(c_Wellfounded_OwfP(_1537247, _1537249))], (7100 ^ _779142) ^ [_896466, _896468, _896470, _896472, _896474] : [class_Groups_Ominus(_896466), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896468, _896466)), _896470), _896472), _896474) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896466), hAPP(_896470, _896474)), hAPP(_896472, _896474)))], (29393 ^ _779142) ^ [_1301132, _1301134, _1301136] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301132, tc_HOL_Obool)), _1301134), _1301136) = c_Orderings_Obot__class_Obot(tc_fun(_1301132, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301132, tc_HOL_Obool)), _1301134), _1301136) = _1301134)], (50483 ^ _779142) ^ [_1801984, _1801986, _1801988] : [c_List_Oall__interval__nat(_1801984, _1801986, _1801988), 50486 ^ _779142 : [(50487 ^ _779142) ^ [_1802064] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1802064), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1801986), _1801988))), -(hBOOL(hAPP(_1801984, _1802064)))]]], (24429 ^ _779142) ^ [_1209018] : [class_Int_Onumber__ring(_1209018), -(c_Int_Oiszero(_1209018, hAPP(c_Int_Onumber__class_Onumber__of(_1209018), c_Int_OPls)))], (10201 ^ _779142) ^ [_955111, _955113, _955115] : [class_Rings_Ocomm__semiring__1(_955111), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955111), _955113), _955115) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955111), _955115), _955113))], (9861 ^ _779142) ^ [_947192, _947194] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947192), _947194)), _947194) = _947192)], (4930 ^ _779142) ^ [_854269, _854271] : [_854271 = _854269, -(c_Lattices_Osemilattice__inf__class_Oinf(_854271) = c_Lattices_Osemilattice__inf__class_Oinf(_854269))], (10843 ^ _779142) ^ [_966385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966385)), _966385))], (34841 ^ _779142) ^ [_1425144, _1425146, _1425148, _1425150] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425144, tc_fun(_1425146, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425144, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1425146, tc_HOL_Obool), tc_fun(_1425146, tc_HOL_Obool), _1425144), hAPP(c_COMBC(_1425146, tc_fun(_1425146, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425146))), _1425148)), _1425150)), -(hBOOL(hAPP(hAPP(c_member(_1425146), _1425150), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425144, tc_fun(_1425146, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425144, tc_HOL_Obool))), _1425148))))], (1426 ^ _779142) ^ [_799909, _799911] : [-(class_Lattices_Osemilattice__inf(_799909)), _799911 = _799909, class_Lattices_Osemilattice__inf(_799911)], (47819 ^ _779142) ^ [_1742676] : [class_Nat_Osize(_1742676), -(c_FunDef_Ois__measure(_1742676, c_Nat_Osize__class_Osize(_1742676)))], (50951 ^ _779142) ^ [_1810662, _1810664] : [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)))), _1810662, _1810664) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810662), _1810664)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810664), _1810662)))], (37627 ^ _779142) ^ [_1492425, _1492427, _1492429, _1492431] : [-(hAPP(c_Set_Oimage(tc_prod(_1492425, _1492427), tc_prod(_1492427, _1492425), hAPP(c_Product__Type_Oprod_Oprod__case(_1492425, _1492427, tc_prod(_1492427, _1492425)), hAPP(c_COMBC(_1492427, _1492425, tc_prod(_1492427, _1492425)), c_Product__Type_OPair(_1492427, _1492425)))), hAPP(hAPP(c_Product__Type_OSigma(_1492425, _1492427), _1492429), hAPP(c_COMBK(tc_fun(_1492427, tc_HOL_Obool), _1492425), _1492431))) = hAPP(hAPP(c_Product__Type_OSigma(_1492427, _1492425), _1492431), hAPP(c_COMBK(tc_fun(_1492425, tc_HOL_Obool), _1492427), _1492429)))], (37659 ^ _779142) ^ [_1493455, _1493457] : [-(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), _1493455)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1493457))))))], (47586 ^ _779142) ^ [_1737830, _1737832, _1737834] : [class_Enum_Oenum(_1737830), class_Enum_Oenum(_1737832), 47593 ^ _779142 : [(47600 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737832), hAPP(hAPP(c_COMBB(tc_fun(_1737830, tc_HOL_Obool), tc_HOL_Obool, _1737832), c_Enum_Oenum__class_Oenum__all(_1737830)), hAPP(hAPP(c_COMBB(tc_fun(_1737830, tc_prod(_1737832, _1737830)), tc_fun(_1737830, tc_HOL_Obool), _1737832), hAPP(c_COMBB(tc_prod(_1737832, _1737830), tc_HOL_Obool, _1737830), _1737834)), c_Product__Type_OPair(_1737832, _1737830))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737832, _1737830)), _1737834)))], (47594 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737832, _1737830)), _1737834)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737832), hAPP(hAPP(c_COMBB(tc_fun(_1737830, tc_HOL_Obool), tc_HOL_Obool, _1737832), c_Enum_Oenum__class_Oenum__all(_1737830)), hAPP(hAPP(c_COMBB(tc_fun(_1737830, tc_prod(_1737832, _1737830)), tc_fun(_1737830, tc_HOL_Obool), _1737832), hAPP(c_COMBB(tc_prod(_1737832, _1737830), tc_HOL_Obool, _1737830), _1737834)), c_Product__Type_OPair(_1737832, _1737830))))))]]], (8491 ^ _779142) ^ [_921356, _921358, _921360] : [class_Groups_Oab__semigroup__mult(_921356), -(_921358 = c_Orderings_Obot__class_Obot(tc_fun(_921356, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_921356), _921358)), -(hBOOL(hAPP(hAPP(c_member(_921356), _921360), _921358))), -(hAPP(c_Finite__Set_Ofold1(_921356, c_Groups_Otimes__class_Otimes(_921356)), hAPP(hAPP(c_Set_Oinsert(_921356), _921360), _921358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921356), _921360), hAPP(c_Finite__Set_Ofold1(_921356, c_Groups_Otimes__class_Otimes(_921356)), _921358)))], (22709 ^ _779142) ^ [_1179189, _1179191] : [-(_1179189 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22712 ^ _779142 : [(22719 ^ _779142) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179191, _1179189) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179191), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179189)) = 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), _1179191), _1179189))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22713 ^ _779142) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179191, _1179189) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179191), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179189)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179191), _1179189)))]]], (8955 ^ _779142) ^ [_930353, _930355, _930357, _930359, _930361] : [class_Groups_Ocomm__monoid__mult(_930353), hBOOL(hAPP(c_Finite__Set_Ofinite(_930355), _930357)), -(hBOOL(hAPP(hAPP(c_member(_930355), _930359), _930357))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_930355, _930353), _930361), hAPP(hAPP(c_Set_Oinsert(_930355), _930359), _930357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930353), hAPP(_930361, _930359)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_930355, _930353), _930361), _930357)))], (48378 ^ _779142) ^ [_1754589, _1754591, _1754593, _1754595] : [-(c_Lazy__Sequence_Oappend(_1754589, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754589, _1754591, _1754593), _1754595) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754589, _1754591, c_Lazy__Sequence_Oappend(_1754589, _1754593, _1754595)))], (50184 ^ _779142) ^ [_1793826, _1793828, _1793830, _1793832] : [c_Fun_Obij__betw(_1793826, _1793828, _1793830, c_Orderings_Otop__class_Otop(tc_fun(_1793826, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793828, tc_HOL_Obool))), 50187 ^ _779142 : [(50194 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1793828), _1793832)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1793826), hAPP(c_Set_Ovimage(_1793826, _1793828, _1793830), _1793832))))], (50188 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1793826), hAPP(c_Set_Ovimage(_1793826, _1793828, _1793830), _1793832))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1793828), _1793832)))]]], (40723 ^ _779142) ^ [_1577513, _1577515] : [-(hAPP(c_Relation_Oconverse(_1577513, _1577513), c_Relation_OId__on(_1577513, _1577515)) = c_Relation_OId__on(_1577513, _1577515))], (24031 ^ _779142) ^ [_1202283, _1202285] : [class_Rings_Oring__1(_1202283), 24034 ^ _779142 : [(24041 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202285), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1202283), _1202285) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202283), hAPP(c_Int_Onat, _1202285)))], (24035 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202285), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1202283), _1202285) = hAPP(c_Groups_Ouminus__class_Ouminus(_1202283), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1202283), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1202285)))))]]], (44628 ^ _779142) ^ [_1673186, _1673188] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673186)), hAPP(c_Code__Numeral_Oof__nat, _1673188)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1673186), _1673188)))], (24646 ^ _779142) ^ [_1212579, _1212581] : [class_Rings_Olinordered__idom(_1212579), -(c_Groups_Osgn__class_Osgn(_1212579, c_Groups_Osgn__class_Osgn(_1212579, _1212581)) = c_Groups_Osgn__class_Osgn(_1212579, _1212581))], (20205 ^ _779142) ^ [_1133940, _1133942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133940)), 20208 ^ _779142 : [(20215 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133940), _1133942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1133940)), hAPP(c_Int_Onat, _1133942))))], (20209 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1133940)), hAPP(c_Int_Onat, _1133942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133940), _1133942)))]]], (34258 ^ _779142) ^ [_1408080, _1408082, _1408084, _1408086, _1408088, _1408090] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408080, tc_fun(_1408082, tc_HOL_Obool)), _1408084), _1408086), _1408088)), hBOOL(hAPP(hAPP(c_member(_1408080), _1408090), _1408084)), -(hBOOL(hAPP(hAPP(_1408086, _1408090), _1408088)))], (32125 ^ _779142) ^ [_1362821, _1362823, _1362825] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1362821, tc_Nat_Onat), _1362823), _1362825) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1362821, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1362821), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1362823)), _1362825)))], (42189 ^ _779142) ^ [_1619329, _1619331] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619329, _1619331) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619329, _1619331)))], (9037 ^ _779142) ^ [_932002, _932004, _932006, _932008] : [c_Big__Operators_Osemilattice__big(_932002, _932004, _932006), hBOOL(hAPP(c_Finite__Set_Ofinite(_932002), _932008)), -(hAPP(_932006, _932008) = hAPP(c_Finite__Set_Ofold1(_932002, _932004), _932008))], (32607 ^ _779142) ^ [_1374592, _1374594] : [32608 ^ _779142 : [(32611 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1374594), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32609 ^ _779142) ^ [] : [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), _1374592), _1374594)))]], -(c_Divides_OnegDivAlg(_1374592, _1374594) = 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), _1374592), _1374594)))], (40913 ^ _779142) ^ [_1582291, _1582293, _1582295] : [c_Relation_Osingle__valued(_1582291, _1582291, _1582293), -(c_Relation_Osingle__valued(_1582291, _1582291, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582291, _1582291), tc_HOL_Obool), _1582295), _1582293)))], (9481 ^ _779142) ^ [_940774, _940776, _940778, _940780] : [class_Groups_Ocomm__monoid__mult(_940774), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_940776), _940778))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_940776, _940774), _940780), _940778) = c_Groups_Oone__class_Oone(_940774))], (11572 ^ _779142) ^ [_978232, _978234, _978236] : [class_Rings_Olinordered__ring__strict(_978232), 11575 ^ _779142 : [(11590 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978232), _978234), _978236)), c_Groups_Ozero__class_Ozero(_978232)))), 11591 ^ _779142 : [(11598 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), _978234), c_Groups_Ozero__class_Ozero(_978232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), c_Groups_Ozero__class_Ozero(_978232)), _978236))], (11592 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), c_Groups_Ozero__class_Ozero(_978232)), _978234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), _978236), c_Groups_Ozero__class_Ozero(_978232)))]]], (11576 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978232), _978234), _978236)), c_Groups_Ozero__class_Ozero(_978232))), 11581 ^ _779142 : [(11584 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), _978236), c_Groups_Ozero__class_Ozero(_978232))))], (11582 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), c_Groups_Ozero__class_Ozero(_978232)), _978234)))]], 11585 ^ _779142 : [(11588 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), c_Groups_Ozero__class_Ozero(_978232)), _978236)))], (11586 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978232), _978234), c_Groups_Ozero__class_Ozero(_978232))))]]]]], (33879 ^ _779142) ^ [_1399746, _1399748, _1399750, _1399752, _1399754] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399746, _1399748, _1399750), _1399752), _1399754) = hAPP(hAPP(_1399752, hAPP(c_Product__Type_Ofst(_1399746, _1399748), _1399754)), hAPP(c_Product__Type_Osnd(_1399746, _1399748), _1399754)))], (2666 ^ _779142) ^ [_818463, _818465, _818467, _818469] : [-(c_Predicate_OPowp(_818469, _818465) = c_Predicate_OPowp(_818467, _818463)), _818469 = _818467, _818465 = _818463], (4720 ^ _779142) ^ [_850950, _850952] : [_850952 = _850950, -(c_Set_OBex(_850952) = c_Set_OBex(_850950))], (40097 ^ _779142) ^ [_1561562, _1561564, _1561566, _1561568, _1561570, _1561572, _1561574] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561562, _1561564, _1561566, _1561568), _1561570), _1561572), _1561574) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561564, _1561566, _1561568), _1561572), hAPP(_1561570, _1561574)))], (23153 ^ _779142) ^ [_1186755, _1186757, _1186759] : [class_Groups_Oab__group__add(_1186755), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1186755), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186755), _1186757), _1186759)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186755), _1186759), _1186757))], (38822 ^ _779142) ^ [_1530877, _1530879] : [c_Wellfounded_Owf(_1530877, _1530879), 38826 ^ _779142 : [(38827 ^ _779142) ^ [_1531013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530877, _1530877)), hAPP(hAPP(c_Product__Type_OPair(_1530877, _1530877), hAPP(_1531013, hAPP(c_Nat_OSuc, 38825 ^ [_1530877, _1530879, _1531013]))), hAPP(_1531013, 38825 ^ [_1530877, _1530879, _1531013]))), _1530879))]]], (47841 ^ _779142) ^ [_1743036, _1743038, _1743040] : [47843 ^ _779142 : [(47846 ^ _779142) ^ [] : [hBOOL(hAPP(_1743038, 47842 ^ [_1743036, _1743038, _1743040]))], (47844 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743036), 47842 ^ [_1743036, _1743038, _1743040]), hAPP(c_List_Oset(_1743036), _1743040))))]], -(c_List_Olist__all(_1743036, _1743038, _1743040))], (22020 ^ _779142) ^ [_1166137, _1166139, _1166141] : [class_Power_Opower(_1166137), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1166137), _1166139), hAPP(c_Nat_OSuc, _1166141)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166137), _1166139), hAPP(hAPP(c_Power_Opower__class_Opower(_1166137), _1166139), _1166141)))], (5412 ^ _779142) ^ [_861944, _861946, _861948, _861950, _861952, _861954] : [-(c_Divides_Odiv__class_Omod(_861954, _861950, _861946) = c_Divides_Odiv__class_Omod(_861952, _861948, _861944)), _861954 = _861952, _861950 = _861948, _861946 = _861944], (30830 ^ _779142) ^ [_1331642, _1331644, _1331646] : [class_Orderings_Otop(_1331642), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1331644, _1331642)), _1331646) = c_Orderings_Otop__class_Otop(_1331642))], (24664 ^ _779142) ^ [_1212870, _1212872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1212870)), c_Int_OBit1(_1212872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212870), _1212872)))], (31086 ^ _779142) ^ [_1336240, _1336242, _1336244, _1336246] : [class_Orderings_Olinorder(_1336240), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336240, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1336240, _1336242, _1336244)), hAPP(c_SetInterval_Oord__class_OatLeast(_1336240), _1336246)) = c_SetInterval_Oord__class_OatLeastAtMost(_1336240, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336240), _1336242), _1336246), _1336244))], (16527 ^ _779142) ^ [_1069881, _1069883, _1069885] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069881), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1069883), _1069885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069881), _1069883)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1069881), _1069885)))], (5884 ^ _779142) ^ [_872373, _872375, _872377, _872379] : [-(hBOOL(hAPP(hAPP(c_member(_872373), _872375), _872377))), -(hBOOL(hAPP(hAPP(c_member(_872373), _872375), _872379))), 5891 ^ _779142 : [(5898 ^ _779142) ^ [] : [_872377 = _872379, -(hAPP(hAPP(c_Set_Oinsert(_872373), _872375), _872377) = hAPP(hAPP(c_Set_Oinsert(_872373), _872375), _872379))], (5892 ^ _779142) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_872373), _872375), _872377) = hAPP(hAPP(c_Set_Oinsert(_872373), _872375), _872379), -(_872377 = _872379)]]], (26222 ^ _779142) ^ [_1240281, _1240283] : [class_Rings_Oring__1(_1240281), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240281), hAPP(c_Groups_Ouminus__class_Ouminus(_1240281), c_Groups_Oone__class_Oone(_1240281))), 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)))), _1240283))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1240281), c_Groups_Oone__class_Oone(_1240281)))], (2112 ^ _779142) ^ [_809840, _809842, _809844, _809846, _809848, _809850] : [-(c_Power_Opower_Opower(_809850, _809846, _809842) = c_Power_Opower_Opower(_809848, _809844, _809840)), _809850 = _809848, _809846 = _809844, _809842 = _809840], (42802 ^ _779142) ^ [_1632021, _1632023, _1632025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632021), tc_List_Olist(_1632021))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632021), tc_List_Olist(_1632021)), _1632023), c_List_Olist_ONil(_1632021))), c_List_Olexord(_1632021, _1632025)))], (49520 ^ _779142) ^ [_1779610, _1779612, _1779614, _1779616] : [c_Equiv__Relations_Opart__equivp(_1779610, _1779612), hBOOL(hAPP(hAPP(_1779612, _1779614), _1779616)), -(hBOOL(hAPP(hAPP(_1779612, _1779616), _1779614)))], (1636 ^ _779142) ^ [_802534, _802536] : [-(class_Rings_Olinordered__semiring(_802534)), _802536 = _802534, class_Rings_Olinordered__semiring(_802536)], (18220 ^ _779142) ^ [_1099845, _1099847] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099845), c_Int_OPls))), 18223 ^ _779142 : [(18230 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099847), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099847)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099845), _1099847)))], (18224 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099847), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099847)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099845))]]], (42756 ^ _779142) ^ [_1631082, _1631084, _1631086, _1631088] : [-(hBOOL(hAPP(hAPP(c_member(_1631082), _1631084), hAPP(c_List_Oset(_1631082), _1631086)))), hBOOL(hAPP(hAPP(c_member(_1631082), _1631084), hAPP(c_List_Oset(_1631082), c_List_Oremove1(_1631082, _1631088, _1631086))))], (42289 ^ _779142) ^ [_1621361, _1621363, _1621365, _1621367, _1621369, _1621371] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1621361, _1621363), hAPP(hAPP(c_List_Ozip(_1621361, _1621363), _1621365), _1621367)), _1621369), _1621371) = hAPP(hAPP(c_List_Ozip(_1621361, _1621363), hAPP(hAPP(c_List_Olist__update(_1621361, _1621365), _1621369), hAPP(c_Product__Type_Ofst(_1621361, _1621363), _1621371))), hAPP(hAPP(c_List_Olist__update(_1621363, _1621367), _1621369), hAPP(c_Product__Type_Osnd(_1621361, _1621363), _1621371))))], (28575 ^ _779142) ^ [_1284311, _1284313, _1284315] : [class_Orderings_Olinorder(_1284311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284311), _1284313)), hBOOL(hAPP(hAPP(c_member(_1284311), _1284315), _1284313)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284311), _1284315), c_Big__Operators_Olattice_OSup__fin(_1284311, c_Orderings_Oord__class_Omax(_1284311), _1284313)) = _1284315)], (39316 ^ _779142) ^ [_1543235, _1543237] : [class_Complete__Lattice_Ocomplete__lattice(_1543235), -(c_Complete__Lattice_OSup__class_OSup(_1543235, _1543237) = c_Complete__Lattice_OInf__class_OInf(_1543235, hAPP(c_Set_OCollect(_1543235), hAPP(hAPP(c_COMBB(tc_fun(_1543235, tc_HOL_Obool), tc_HOL_Obool, _1543235), c_HOL_OAll(_1543235)), hAPP(hAPP(c_COMBB(tc_fun(_1543235, tc_HOL_Obool), tc_fun(_1543235, tc_HOL_Obool), _1543235), hAPP(c_COMBS(_1543235, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543235), c_fimplies), hAPP(hAPP(c_COMBC(_1543235, tc_fun(_1543235, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543235)), _1543237)))), hAPP(c_COMBC(_1543235, _1543235, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1543235)))))))], (37417 ^ _779142) ^ [_1487038, _1487040] : [-(hAPP(c_Set_OCollect(_1487038), hAPP(hAPP(c_COMBC(_1487038, tc_fun(_1487038, tc_HOL_Obool), tc_HOL_Obool), c_member(_1487038)), _1487040)) = _1487040)], (26677 ^ _779142) ^ [_1248910, _1248912, _1248914, _1248916] : [26691 ^ _779142 : [(26694 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1248916, 26690 ^ [_1248910, _1248912, _1248914, _1248916])))], (26692 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248910), 26690 ^ [_1248910, _1248912, _1248914, _1248916]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248910, tc_HOL_Obool)), _1248912), _1248914))))]], 26678 ^ _779142 : [(26685 ^ _779142) ^ [_1249119] : [hBOOL(hAPP(hAPP(c_member(_1248910), _1249119), _1248914)), hBOOL(hAPP(_1248916, _1249119))], (26679 ^ _779142) ^ [_1249023] : [hBOOL(hAPP(hAPP(c_member(_1248910), _1249023), _1248912)), hBOOL(hAPP(_1248916, _1249023))]]], (40356 ^ _779142) ^ [_1568582, _1568584] : [-(c_Transitive__Closure_Ortrancl(_1568582, _1568584) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool)), c_Relation_OId(_1568582)), hAPP(hAPP(c_Relation_Orel__comp(_1568582, _1568582, _1568582), c_Transitive__Closure_Ortrancl(_1568582, _1568584)), _1568584)))], (32573 ^ _779142) ^ [_1373771, _1373773, _1373775] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373771), _1373773))), 32576 ^ _779142 : [(32583 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373775), _1373773))), -(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)), _1373771)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1373775), _1373773)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (32577 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373775), _1373773)), -(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)), _1373771)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1373775), _1373773)) = 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))))]]], (3506 ^ _779142) ^ [_831515, _831517, _831519, _831521, _831523, _831525, _831527, _831529, _831531, _831533] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831533, _831529, _831525, _831521, _831517) = c_List_Olinorder__class_Oinsort__insert__key(_831531, _831527, _831523, _831519, _831515)), _831533 = _831531, _831529 = _831527, _831525 = _831523, _831521 = _831519, _831517 = _831515], (35341 ^ _779142) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (21400 ^ _779142) ^ [_1155241, _1155243, _1155245, _1155247, _1155249] : [class_Orderings_Oorder(_1155241), 21403 ^ _779142 : [(21416 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1155241, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1155241, _1155243, _1155245)), c_SetInterval_Oord__class_OatLeastAtMost(_1155241, _1155247, _1155249)))), 21417 ^ _779142 : [(21420 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155247), _1155243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155245), _1155249))], (21418 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155243), _1155245)))]]], (21404 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1155241, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1155241, _1155243, _1155245)), c_SetInterval_Oord__class_OatLeastAtMost(_1155241, _1155247, _1155249))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155243), _1155245)), 21411 ^ _779142 : [(21414 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155245), _1155249)))], (21412 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155241), _1155247), _1155243)))]]]]], (12858 ^ _779142) ^ [_1001600, _1001602, _1001604] : [class_Rings_Olinordered__idom(_1001600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001600), c_Groups_Ozero__class_Ozero(_1001600)), _1001602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001600), c_Groups_Ozero__class_Ozero(_1001600)), _1001604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001600), _1001604), c_Groups_Oone__class_Oone(_1001600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001600), _1001602), _1001604)), _1001602)))], (48790 ^ _779142) ^ [_1764373, _1764375, _1764377, _1764379, _1764381] : [c_Relation_Otrans(_1764373, _1764375), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764373, _1764373)), hAPP(hAPP(c_Product__Type_OPair(_1764373, _1764373), _1764377), _1764379)), _1764375)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764373, _1764373)), hAPP(hAPP(c_Product__Type_OPair(_1764373, _1764373), _1764379), _1764381)), _1764375)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764373, _1764373)), hAPP(hAPP(c_Product__Type_OPair(_1764373, _1764373), _1764377), _1764381)), _1764375)))], (43905 ^ _779142) ^ [_1657394, _1657396, _1657398, _1657400, _1657402] : [c_Finite__Set_Ofun__left__comm__idem(_1657394, _1657396, _1657398), -(hAPP(hAPP(c_Finite__Set_Ofold(_1657394, _1657396, _1657398), _1657400), hAPP(c_List_Oset(_1657394), _1657402)) = hAPP(c_List_Ofoldl(_1657396, _1657394, hAPP(c_COMBC(_1657394, _1657396, _1657396), _1657398), _1657400), _1657402))], (43748 ^ _779142) ^ [_1654198, _1654200, _1654202] : [hBOOL(hAPP(c_List_Odistinct(_1654198), hAPP(c_List_Orotate(_1654198, _1654200), _1654202))), -(hBOOL(hAPP(c_List_Odistinct(_1654198), _1654202)))], (38254 ^ _779142) ^ [_1515128, _1515130, _1515132, _1515134, _1515136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515128, _1515130)), _1515132), hAPP(hAPP(c_Product__Type_OSigma(_1515128, _1515130), _1515134), _1515136))), 38258 ^ _779142 : [(38264 ^ _779142) ^ [] : [-(_1515132 = hAPP(hAPP(c_Product__Type_OPair(_1515128, _1515130), 38257 ^ [_1515128, _1515130, _1515132, _1515134, _1515136]), 38260 ^ [_1515128, _1515130, _1515132, _1515134, _1515136]))], (38262 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515130), 38260 ^ [_1515128, _1515130, _1515132, _1515134, _1515136]), hAPP(_1515136, 38257 ^ [_1515128, _1515130, _1515132, _1515134, _1515136]))))], (38259 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515128), 38257 ^ [_1515128, _1515130, _1515132, _1515134, _1515136]), _1515134)))]]], (19415 ^ _779142) ^ [_1120571, _1120573, _1120575] : [class_Groups_Oordered__ab__group__add__abs(_1120571), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120571), hAPP(c_Groups_Oabs__class_Oabs(_1120571), _1120573)), hAPP(c_Groups_Oabs__class_Oabs(_1120571), _1120575))), hAPP(c_Groups_Oabs__class_Oabs(_1120571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120571), _1120573), _1120575)))))], (43265 ^ _779142) ^ [_1642205, _1642207, _1642209, _1642211] : [-(hAPP(hAPP(c_List_Onth(_1642205), hAPP(hAPP(c_List_Oappend(_1642205), _1642207), _1642209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642205)), _1642207)), _1642211)) = hAPP(hAPP(c_List_Onth(_1642205), _1642209), _1642211))], (26944 ^ _779142) ^ [_1254486, _1254488, _1254490, _1254492, _1254494, _1254496, _1254498, _1254500] : [c_Finite__Set_Ofolding__image__simple__idem(_1254486, _1254488, _1254490, _1254492, _1254494, _1254496), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254488), _1254498)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254488), _1254500)), -(hAPP(_1254496, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254488, tc_HOL_Obool)), _1254498), _1254500)) = hAPP(hAPP(_1254490, hAPP(_1254496, _1254498)), hAPP(_1254496, _1254500)))], (37831 ^ _779142) ^ [_1498834, _1498836, _1498838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1498834), _1498836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498834, _1498834), tc_HOL_Obool)), _1498838), hAPP(hAPP(c_Product__Type_OSigma(_1498834, _1498834), _1498836), hAPP(c_COMBK(tc_fun(_1498834, tc_HOL_Obool), _1498834), _1498836)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1498834, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1498834), _1498836), _1498838))))], (26166 ^ _779142) ^ [_1239167, _1239169] : [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), _1239167))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1239169))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1239167))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239169)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239167)))], (45004 ^ _779142) ^ [_1681349, _1681351, _1681353] : [hBOOL(hAPP(c_List_Olistsp(_1681349, hAPP(hAPP(c_COMBC(_1681349, tc_fun(_1681349, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681349)), _1681351)), _1681353)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681349)), _1681353), c_List_Olists(_1681349, _1681351))))], (6027 ^ _779142) ^ [_875257, _875259, _875261, _875263] : [c_Orderings_Obot__class_Obot(tc_fun(_875257, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_875259, _875257, _875261), _875263), -(_875263 = c_Orderings_Obot__class_Obot(tc_fun(_875259, tc_HOL_Obool)))], (30960 ^ _779142) ^ [_1333838, _1333840] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333838), _1333840)), 30963 ^ _779142 : [(30970 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333838), c_Orderings_Otop__class_Otop(tc_fun(_1333838, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333838), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1333838, tc_HOL_Obool)), _1333840))))], (30964 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333838), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1333838, tc_HOL_Obool)), _1333840))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333838), c_Orderings_Otop__class_Otop(tc_fun(_1333838, tc_HOL_Obool)))))]]], (37173 ^ _779142) ^ [_1480787, _1480789, _1480791] : [-(hAPP(c_Set_Ovimage(_1480787, _1480789, _1480791), c_Orderings_Otop__class_Otop(tc_fun(_1480789, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1480787, tc_HOL_Obool)))], (37077 ^ _779142) ^ [_1478582] : [-(c_Nitpick_Ozero__frac(_1478582) = c_Nitpick_OAbs__Frac(_1478582, 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))))], (48314 ^ _779142) ^ [_1753221, _1753223, _1753225, _1753227] : [hBOOL(hAPP(hAPP(c_member(_1753221), _1753223), hAPP(c_List_Oset(_1753221), c_List_Oreplicate(_1753221, _1753225, _1753227)))), 48317 ^ _779142 : [(48320 ^ _779142) ^ [] : [_1753225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48318 ^ _779142) ^ [] : [-(_1753223 = _1753227)]]], (11308 ^ _779142) ^ [_973462, _973464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973462), _973464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973462)), _973464)))], (23625 ^ _779142) ^ [_1195231, _1195233] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195231), _1195233) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195231, _1195233) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (16355 ^ _779142) ^ [_1066799] : [class_Orderings_Oord(_1066799), -(c_Orderings_Oord__class_Omin(_1066799) = c_Orderings_Oord_Omin(_1066799, c_Orderings_Oord__class_Oless__eq(_1066799)))], (31979 ^ _779142) ^ [_1357553, _1357555, _1357557, _1357559, _1357561, _1357563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1357553, _1357555)), hAPP(hAPP(c_Product__Type_OPair(_1357553, _1357555), _1357561), _1357563)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool)), _1357557), _1357559))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357553, tc_fun(_1357555, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1357553, tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_fun(_1357555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1357555, tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_fun(_1357555, tc_HOL_Obool)), _1357553), c_COMBC(_1357555, tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1357555, tc_prod(_1357553, _1357555)), tc_fun(_1357555, tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), _1357553), hAPP(c_COMBB(tc_prod(_1357553, _1357555), tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool), _1357555), c_member(tc_prod(_1357553, _1357555)))), c_Product__Type_OPair(_1357553, _1357555)))), _1357557)), hAPP(hAPP(c_COMBC(_1357553, tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_fun(_1357555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1357555, tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_fun(_1357555, tc_HOL_Obool)), _1357553), c_COMBC(_1357555, tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1357555, tc_prod(_1357553, _1357555)), tc_fun(_1357555, tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool)), _1357553), hAPP(c_COMBB(tc_prod(_1357553, _1357555), tc_fun(tc_fun(tc_prod(_1357553, _1357555), tc_HOL_Obool), tc_HOL_Obool), _1357555), c_member(tc_prod(_1357553, _1357555)))), c_Product__Type_OPair(_1357553, _1357555)))), _1357559)), _1357561), _1357563)))], (45793 ^ _779142) ^ [_1699463, _1699465] : [-(c_List_Oconcat(tc_List_Olist(_1699463), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699463), tc_List_Olist(tc_List_Olist(_1699463))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699463)), _1699463, c_List_Olist_ONil(tc_List_Olist(_1699463)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699463), tc_List_Olist(tc_List_Olist(_1699463))), _1699463), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699463), tc_List_Olist(tc_List_Olist(_1699463)), tc_List_Olist(tc_List_Olist(_1699463))), c_List_Olist_OCons(tc_List_Olist(_1699463))), c_List_Olist_ONil(tc_List_Olist(_1699463)))))), _1699465)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699463), tc_List_Olist(_1699463)), c_List_Otl(_1699463)), hAPP(c_List_Ofilter(tc_List_Olist(_1699463), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699463)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699463), tc_List_Olist(_1699463), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699463)))), _1699465)))], (9251 ^ _779142) ^ [_936921, _936923, _936925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936921), _936923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936923), _936925))))], (5080 ^ _779142) ^ [_856622, _856624, _856626, _856628] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856628, _856624) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856626, _856622)), _856628 = _856626, _856624 = _856622], (14607 ^ _779142) ^ [_1033992, _1033994, _1033996, _1033998] : [class_Fields_Olinordered__field(_1033992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033992), _1033994), _1033996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033992), _1033998), c_Groups_Ozero__class_Ozero(_1033992))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033992), c_Groups_Ozero__class_Ozero(_1033992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033992), _1033994), _1033996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033992), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033992), _1033998), _1033994)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033992), _1033998), _1033996))))], (38266 ^ _779142) ^ [_1515430, _1515432, _1515434, _1515436, _1515438, _1515440] : [hAPP(c_Set_Oimage(_1515430, _1515432, _1515434), c_Orderings_Otop__class_Otop(tc_fun(_1515430, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1515432, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515436, _1515438, _1515440), c_Orderings_Otop__class_Otop(tc_fun(_1515436, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1515438, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1515430, _1515436), tc_prod(_1515432, _1515438), c_Product__Type_Omap__pair(_1515430, _1515432, _1515436, _1515438, _1515434, _1515440)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1515430, _1515436), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1515432, _1515438), tc_HOL_Obool)))], (4524 ^ _779142) ^ [_847830, _847832, _847834, _847836, _847838, _847840, _847842, _847844] : [-(c_Product__Type_Oscomp(_847844, _847840, _847836, _847832) = c_Product__Type_Oscomp(_847842, _847838, _847834, _847830)), _847844 = _847842, _847840 = _847838, _847836 = _847834, _847832 = _847830], (24716 ^ _779142) ^ [_1213827] : [c_Int_OBit1(_1213827) = c_Int_OMin, -(_1213827 = c_Int_OMin)], (31853 ^ _779142) ^ [_1352524, _1352526, _1352528, _1352530, _1352532] : [class_Groups_Ocomm__monoid__mult(_1352524), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352526, _1352524), hAPP(hAPP(c_COMBS(_1352526, _1352524, _1352524), hAPP(hAPP(c_COMBB(_1352524, tc_fun(_1352524, _1352524), _1352526), c_Groups_Otimes__class_Otimes(_1352524)), _1352528)), _1352530)), _1352532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352524), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352526, _1352524), _1352528), _1352532)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352526, _1352524), _1352530), _1352532)))], (1626 ^ _779142) ^ [_802409, _802411] : [-(class_Groups_Ocancel__semigroup__add(_802409)), _802411 = _802409, class_Groups_Ocancel__semigroup__add(_802411)], (29839 ^ _779142) ^ [_1311459, _1311461, _1311463, _1311465, _1311467] : [class_Groups_Ocomm__monoid__mult(_1311459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311461), _1311463)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311461), _1311465)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311461, tc_HOL_Obool)), _1311463), _1311465) = c_Orderings_Obot__class_Obot(tc_fun(_1311461, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311461, _1311459), _1311467), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311461, tc_HOL_Obool)), _1311463), _1311465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311459), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311461, _1311459), _1311467), _1311463)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1311461, _1311459), _1311467), _1311465)))], (33863 ^ _779142) ^ [_1399315, _1399317, _1399319, _1399321] : [-(hAPP(c_Product__Type_Ofst(_1399315, _1399317), hAPP(hAPP(c_Product__Type_OPair(_1399315, _1399317), _1399319), _1399321)) = _1399319)], (28737 ^ _779142) ^ [_1287450, _1287452, _1287454] : [class_Orderings_Olinorder(_1287450), hAPP(_1287452, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287450), 28742 ^ [_1287450, _1287452, _1287454]), 28743 ^ [_1287450, _1287452, _1287454])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287450), hAPP(_1287452, 28742 ^ [_1287450, _1287452, _1287454])), hAPP(_1287452, 28743 ^ [_1287450, _1287452, _1287454])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287450), _1287454)), -(_1287454 = c_Orderings_Obot__class_Obot(tc_fun(_1287450, tc_HOL_Obool))), -(hAPP(_1287452, c_Big__Operators_Olinorder__class_OMax(_1287450, _1287454)) = c_Big__Operators_Olinorder__class_OMax(_1287450, hAPP(c_Set_Oimage(_1287450, _1287450, _1287452), _1287454)))], (7688 ^ _779142) ^ [_906248, _906250, _906252] : [class_Orderings_Oorder(_906248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906248), _906250), _906252)), -(_906250 = _906252), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906248), _906250), _906252)))], (14327 ^ _779142) ^ [_1028732, _1028734, _1028736, _1028738, _1028740] : [class_Fields_Olinordered__field(_1028732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028732), c_Groups_Ozero__class_Ozero(_1028732)), _1028734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028732), _1028734), _1028736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028732), c_Groups_Ozero__class_Ozero(_1028732)), _1028738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028732), _1028738), _1028740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028732), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028732), _1028734), _1028740)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028732), _1028736), _1028738))))], (34993 ^ _779142) ^ [_1429152, _1429154, _1429156, _1429158, _1429160] : [_1429152 = c_Orderings_Obot__class_Obot(tc_fun(_1429154, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429154, tc_fun(_1429156, tc_HOL_Obool)), _1429152), hAPP(hAPP(c_COMBB(tc_fun(_1429156, tc_HOL_Obool), tc_fun(_1429156, tc_HOL_Obool), _1429154), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429156, tc_HOL_Obool)), _1429158)), _1429160)) = c_Orderings_Otop__class_Otop(tc_fun(_1429156, tc_HOL_Obool)))], (52617 ^ _779142) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (9667 ^ _779142) ^ [_943601, _943603] : [9668 ^ _779142 : [(9671 ^ _779142) ^ [] : [_943601 = _943603], (9669 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943601), _943603))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943601), _943603)))], (5844 ^ _779142) ^ [_871746, _871748] : [hBOOL(hAPP(hAPP(c_member(_871746), _871748), c_Orderings_Obot__class_Obot(tc_fun(_871746, tc_HOL_Obool))))], (38508 ^ _779142) ^ [_1524469, _1524471, _1524473, _1524475, _1524477, _1524479, _1524481, _1524483] : [hBOOL(hAPP(hAPP(_1524469, _1524471), _1524473)), hBOOL(hAPP(hAPP(_1524475, _1524473), _1524477)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1524479, _1524481, _1524483, _1524469, _1524475), _1524471), _1524477)))], (49686 ^ _779142) ^ [_1783169, _1783171, _1783173] : [hAPP(_1783173, hAPP(c_Hilbert__Choice_Oinv__into(_1783169, _1783171, c_Orderings_Otop__class_Otop(tc_fun(_1783169, tc_HOL_Obool)), _1783173), 49687 ^ [_1783169, _1783171, _1783173])) = 49687 ^ [_1783169, _1783171, _1783173], -(hAPP(c_Set_Oimage(_1783169, _1783171, _1783173), c_Orderings_Otop__class_Otop(tc_fun(_1783169, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783171, tc_HOL_Obool)))], (45488 ^ _779142) ^ [_1691928, _1691930, _1691932, _1691934] : [class_Orderings_Olinorder(_1691928), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691930)), c_List_Olinorder__class_Osort__key(_1691930, _1691928, _1691932, _1691934)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691930)), _1691934))], (32976 ^ _779142) ^ [_1382415, _1382417, _1382419, _1382421, _1382423] : [hBOOL(hAPP(hAPP(_1382415, _1382417), _1382419)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382421, _1382423, tc_HOL_Obool), _1382415), hAPP(hAPP(c_Product__Type_OPair(_1382421, _1382423), _1382417), _1382419))))], (45772 ^ _779142) ^ [_1698978, _1698980] : [c_List_Otranspose(_1698978, _1698980) = c_List_Olist_ONil(tc_List_Olist(_1698978)), 45775 ^ _779142 : [(45776 ^ _779142) ^ [_1699073] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698978)), _1699073), hAPP(c_List_Oset(tc_List_Olist(_1698978)), _1698980))), -(_1699073 = c_List_Olist_ONil(_1698978))]]], (51657 ^ _779142) ^ [_1822519, _1822521] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1822521), _1822519))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822519), _1822521)))], (49981 ^ _779142) ^ [_1789913, _1789915, _1789917, _1789919] : [c_Fun_Obij__betw(_1789913, _1789915, _1789917, c_Orderings_Otop__class_Otop(tc_fun(_1789913, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789915, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1789913, _1789915, _1789917), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789913, tc_HOL_Obool)), _1789919)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789915, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1789913, _1789915, _1789917), _1789919)))], (42606 ^ _779142) ^ [_1628576] : [-(hBOOL(hAPP(c_List_Odistinct(_1628576), c_List_Olist_ONil(_1628576))))], (27520 ^ _779142) ^ [_1264839, _1264841, _1264843] : [class_Lattices_Olattice(_1264839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264839), _1264841)), hBOOL(hAPP(hAPP(c_member(_1264839), _1264843), _1264841)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264839), _1264843), c_Big__Operators_Olattice__class_OSup__fin(_1264839, _1264841)) = c_Big__Operators_Olattice__class_OSup__fin(_1264839, _1264841))], (42291 ^ _779142) ^ [_1621450, _1621452, _1621454, _1621456, _1621458, _1621460] : [-(_1621450 = _1621452), -(hAPP(hAPP(c_List_Olist__update(_1621454, hAPP(hAPP(c_List_Olist__update(_1621454, _1621456), _1621450), _1621458)), _1621452), _1621460) = hAPP(hAPP(c_List_Olist__update(_1621454, hAPP(hAPP(c_List_Olist__update(_1621454, _1621456), _1621452), _1621460)), _1621450), _1621458))], (47962 ^ _779142) ^ [_1745380, _1745382] : [c_List_Olist__ex1(_1745380, _1745382, c_List_Olist_ONil(_1745380))], (23951 ^ _779142) ^ [_1200968] : [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, _1200968)))))], (46678 ^ _779142) ^ [_1717633, _1717635] : [class_Groups_Ocomm__monoid__add(_1717633), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717633), hAPP(c_List_Orev(_1717633), _1717635)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717633), _1717635))], (38477 ^ _779142) ^ [_1522290, _1522292, _1522294, _1522296] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522290, _1522292, hAPP(hAPP(c_COMBC(_1522290, tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_fun(_1522292, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522292, tc_fun(tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_fun(_1522292, tc_HOL_Obool)), _1522290), c_COMBC(_1522292, tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522292, tc_prod(_1522290, _1522292)), tc_fun(_1522292, tc_fun(tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_HOL_Obool)), _1522290), hAPP(c_COMBB(tc_prod(_1522290, _1522292), tc_fun(tc_fun(tc_prod(_1522290, _1522292), tc_HOL_Obool), tc_HOL_Obool), _1522292), c_member(tc_prod(_1522290, _1522292)))), c_Product__Type_OPair(_1522290, _1522292)))), _1522294)), _1522296)), -(hBOOL(hAPP(hAPP(c_member(_1522292), _1522296), hAPP(c_Relation_ORange(_1522290, _1522292), _1522294))))], (28198 ^ _779142) ^ [_1277507, _1277509, _1277511] : [class_Orderings_Olinorder(_1277507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277507), _1277509)), -(_1277511 = c_Orderings_Obot__class_Obot(tc_fun(_1277507, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277507, tc_HOL_Obool)), _1277511), _1277509)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277507), c_Big__Operators_Olinorder__class_OMax(_1277507, _1277511)), c_Big__Operators_Olinorder__class_OMax(_1277507, _1277509)) = c_Big__Operators_Olinorder__class_OMax(_1277507, _1277509))], (50005 ^ _779142) ^ [_1790480, _1790482, _1790484] : [-(c_Fun_Obij__betw(_1790480, _1790482, _1790484, c_Orderings_Otop__class_Otop(tc_fun(_1790480, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790482, tc_HOL_Obool)))), c_Fun_Oinj__on(_1790480, _1790482, _1790484, c_Orderings_Otop__class_Otop(tc_fun(_1790480, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1790480, _1790482, _1790484), c_Orderings_Otop__class_Otop(tc_fun(_1790480, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790482, tc_HOL_Obool))], (35760 ^ _779142) ^ [_1449434, _1449436, _1449438, _1449440, _1449442] : [c_Equiv__Relations_Oequiv(_1449434, _1449436, _1449438), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449434, _1449434)), hAPP(hAPP(c_Product__Type_OPair(_1449434, _1449434), _1449440), _1449442)), _1449438)), -(hAPP(c_Relation_OImage(_1449434, _1449434, _1449438), hAPP(hAPP(c_Set_Oinsert(_1449434), _1449440), c_Orderings_Obot__class_Obot(tc_fun(_1449434, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449434, _1449434, _1449438), hAPP(hAPP(c_Set_Oinsert(_1449434), _1449442), c_Orderings_Obot__class_Obot(tc_fun(_1449434, tc_HOL_Obool)))))], (22292 ^ _779142) ^ [_1171275, _1171277, _1171279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171275)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1171277), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1171279)), 22299 ^ _779142 : [(22300 ^ _779142) ^ [_1171483] : [22302 ^ _779142 : [(22308 ^ _779142) ^ [] : [-(_1171483 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22304 ^ [_1171275, _1171277, _1171279, _1171483]), 22301 ^ [_1171275, _1171277, _1171279, _1171483]))], (22306 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22304 ^ [_1171275, _1171277, _1171279, _1171483]), _1171279)))], (22303 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22301 ^ [_1171275, _1171277, _1171279, _1171483]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1171275))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171277), _1171483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1171483), _1171275))))]]], (1216 ^ _779142) ^ [_797284, _797286] : [-(class_Rings_Olinordered__ring(_797284)), _797286 = _797284, class_Rings_Olinordered__ring(_797286)], (45993 ^ _779142) ^ [_1704333] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1704333) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704333)))], (35691 ^ _779142) ^ [_1447900, _1447902, _1447904, _1447906, _1447908, _1447910] : [c_Equiv__Relations_Oequiv(_1447900, _1447902, _1447904), hBOOL(hAPP(hAPP(c_member(_1447900), _1447906), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447900, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447900, _1447900, _1447904), hAPP(hAPP(c_Set_Oinsert(_1447900), _1447908), c_Orderings_Obot__class_Obot(tc_fun(_1447900, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1447900, _1447900, _1447904), hAPP(hAPP(c_Set_Oinsert(_1447900), _1447910), c_Orderings_Obot__class_Obot(tc_fun(_1447900, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447900, _1447900)), hAPP(hAPP(c_Product__Type_OPair(_1447900, _1447900), _1447908), _1447910)), _1447904)))], (48589 ^ _779142) ^ [_1759441, _1759443, _1759445] : [-(c_FunDef_OTHE__default(_1759443, _1759445, _1759441) = c_HOL_OThe(_1759443, _1759441)), 48590 ^ _779142 : [(48591 ^ _779142) ^ [_1759505] : [hBOOL(hAPP(_1759441, _1759505)), 48595 ^ _779142 : [(48598 ^ _779142) ^ [] : [48594 ^ [_1759441, _1759443, _1759445, _1759505] = _1759505], (48596 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1759441, 48594 ^ [_1759441, _1759443, _1759445, _1759505])))]]]]], (35389 ^ _779142) ^ [_1439586, _1439588, _1439590, _1439592] : [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), _1439586), _1439588)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439590), _1439592))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439586), _1439592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439590), _1439588))], (37860 ^ _779142) ^ [_1499728, _1499730, _1499732, _1499734] : [-(c_Fun_Oinj__on(_1499728, tc_prod(_1499730, _1499728), 37858 ^ [_1499728, _1499730, _1499732, _1499734], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499730, tc_fun(_1499728, tc_HOL_Obool)), _1499732), _1499734)))], (17537 ^ _779142) ^ [_1088200, _1088202, _1088204] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088200), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1088202, _1088204)), _1088204) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088200), _1088202), _1088204))], (49016 ^ _779142) ^ [_1770515, _1770517] : [c_Predicate_Otransp(_1770515, _1770517), -(c_Relation_Otrans(_1770515, hAPP(c_Set_OCollect(tc_prod(_1770515, _1770515)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770515, _1770515, tc_HOL_Obool), _1770517))))], (52167 ^ _779142) ^ [_1831367, _1831369] : [-(class_Finite__Set_Ofinite(tc_fun(_1831367, _1831369))), class_Finite__Set_Ofinite(_1831367), class_Finite__Set_Ofinite(_1831369)], (49839 ^ _779142) ^ [_1786967, _1786969, _1786971, _1786973] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786967, _1786969, _1786971, _1786973, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1786969)) = _1786971)], (3970 ^ _779142) ^ [_839111, _839113, _839115, _839117, _839119, _839121, _839123, _839125] : [-(c_New__Random__Sequence_Oneg__map(_839125, _839121, _839117, _839113) = c_New__Random__Sequence_Oneg__map(_839123, _839119, _839115, _839111)), _839125 = _839123, _839121 = _839119, _839117 = _839115, _839113 = _839111], (31349 ^ _779142) ^ [_1341287, _1341289, _1341291] : [class_Complete__Lattice_Ocomplete__lattice(_1341287), class_Orderings_Olinorder(_1341287), 31356 ^ _779142 : [(31366 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341287), c_Complete__Lattice_OInf__class_OInf(_1341287, _1341289)), _1341291))), 31367 ^ _779142 : [(31368 ^ _779142) ^ [_1341593] : [hBOOL(hAPP(hAPP(c_member(_1341287), _1341593), _1341289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341287), _1341593), _1341291))]]], (31357 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341287), c_Complete__Lattice_OInf__class_OInf(_1341287, _1341289)), _1341291)), 31361 ^ _779142 : [(31364 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341287), 31360 ^ [_1341287, _1341289, _1341291]), _1341291)))], (31362 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341287), 31360 ^ [_1341287, _1341289, _1341291]), _1341289)))]]]]], (34881 ^ _779142) ^ [_1426352, _1426354, _1426356, _1426358, _1426360] : [-(_1426352 = c_Orderings_Obot__class_Obot(tc_fun(_1426354, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1426356), _1426358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426354, tc_fun(_1426356, tc_HOL_Obool)), _1426352), _1426360)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426354, tc_fun(_1426356, tc_HOL_Obool)), _1426352), hAPP(hAPP(c_COMBB(tc_fun(_1426356, tc_HOL_Obool), tc_fun(_1426356, tc_HOL_Obool), _1426354), hAPP(c_Set_Oinsert(_1426356), _1426358)), _1426360)))], (36880 ^ _779142) ^ [_1474031, _1474033, _1474035, _1474037, _1474039, _1474041, _1474043] : [c_Typedef_Otype__definition(_1474031, _1474033, _1474035, _1474037, _1474039), 36883 ^ _779142 : [(36890 ^ _779142) ^ [] : [_1474041 = _1474043, -(hAPP(_1474035, _1474041) = hAPP(_1474035, _1474043))], (36884 ^ _779142) ^ [] : [hAPP(_1474035, _1474041) = hAPP(_1474035, _1474043), -(_1474041 = _1474043)]]], (9304 ^ _779142) ^ [_937843, _937845] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937843), _937845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937845), _937843)))], (1366 ^ _779142) ^ [_799159, _799161] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799159)), _799161 = _799159, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799161)], (33095 ^ _779142) ^ [_1384893, _1384895, _1384897, _1384899] : [-(hAPP(c_Nat_Onat_Onat__rec(_1384893, _1384895, _1384897), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384899)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1384893), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1384899))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1384893, _1384893), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1384893, tc_fun(_1384893, _1384893)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1384893, tc_fun(_1384893, _1384893)), tc_Int_Oint), c_If(_1384893)), c_Nat__Numeral_Oneg)), _1384895)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1384893, _1384893), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1384893, _1384893), tc_Int_Oint), _1384897), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1384893, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1384893, _1384895, _1384897)), c_Int_Onat)))))], (52661 ^ _779142) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (17831 ^ _779142) ^ [_1093342, _1093344, _1093346] : [class_Rings_Olinordered__semidom(_1093342), 17834 ^ _779142 : [(17841 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093344), _1093346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093342), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093342), _1093344)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093342), _1093346))))], (17835 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093342), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093342), _1093344)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093342), _1093346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093344), _1093346)))]]], (41373 ^ _779142) ^ [_1594871, _1594873, _1594875, _1594877, _1594879, _1594881] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594871), tc_List_Olist(_1594871))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594871), tc_List_Olist(_1594871)), hAPP(hAPP(c_List_Olist_OCons(_1594871), _1594873), _1594875)), hAPP(hAPP(c_List_Olist_OCons(_1594871), _1594877), _1594879))), c_List_Olex(_1594871, _1594881))), 41378 ^ _779142 : [(41381 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594871)), _1594875) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594871)), _1594879))], (41379 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594871, _1594871)), hAPP(hAPP(c_Product__Type_OPair(_1594871, _1594871), _1594873), _1594877)), _1594881)))]], 41382 ^ _779142 : [(41385 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594871), tc_List_Olist(_1594871))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594871), tc_List_Olist(_1594871)), _1594875), _1594879)), c_List_Olex(_1594871, _1594881))))], (41383 ^ _779142) ^ [] : [-(_1594873 = _1594877)]]], (594 ^ _779142) ^ [_788065, _788067] : [-(c_List_Onat__list(_788065)), _788067 = _788065, c_List_Onat__list(_788067)], (39494 ^ _779142) ^ [_1547434, _1547436] : [39495 ^ _779142 : [(39496 ^ _779142) ^ [_1547480] : [hBOOL(hAPP(_1547434, _1547480))]], -(hBOOL(hAPP(_1547434, c_Hilbert__Choice_OEps(_1547436, _1547434))))], (826 ^ _779142) ^ [_791499, _791501, _791503, _791505] : [-(c_Predicate_Osymp(_791503, _791499)), c_Predicate_Osymp(_791505, _791501), _791505 = _791503, _791501 = _791499], (37485 ^ _779142) ^ [_1488504, _1488506, _1488508] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488504), hAPP(c_Set_OCollect(_1488504), hAPP(hAPP(c_COMBS(_1488504, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488504), c_fdisj), _1488506)), _1488508)))), 37488 ^ _779142 : [(37491 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488504), hAPP(c_Set_OCollect(_1488504), _1488508))))], (37489 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488504), hAPP(c_Set_OCollect(_1488504), _1488506))))]]], (36254 ^ _779142) ^ [_1460973, _1460975, _1460977, _1460979, _1460981, _1460983] : [c_Fun_Oinj__on(_1460973, _1460975, _1460977, _1460979), hAPP(_1460977, _1460981) = hAPP(_1460977, _1460983), hBOOL(hAPP(hAPP(c_member(_1460973), _1460981), _1460979)), hBOOL(hAPP(hAPP(c_member(_1460973), _1460983), _1460979)), -(_1460981 = _1460983)], (33006 ^ _779142) ^ [_1383124, _1383126, _1383128] : [-(hAPP(c_Nat_Onat_Onat__rec(_1383124, _1383126, _1383128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1383126)], (42608 ^ _779142) ^ [_1628605, _1628607, _1628609] : [hBOOL(hAPP(c_List_Odistinct(_1628605), _1628607)), -(hBOOL(hAPP(c_List_Odistinct(_1628605), c_List_Oremove1(_1628605, _1628609, _1628607))))], (25624 ^ _779142) ^ [_1229527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229527)))], (11139 ^ _779142) ^ [_970933, _970935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970933), _970935)), _970935 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17419 ^ _779142) ^ [_1085651, _1085653, _1085655, _1085657] : [class_Divides_Osemiring__div(_1085651), -(c_Divides_Odiv__class_Omod(_1085651, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085651), _1085653), _1085655), _1085657) = c_Divides_Odiv__class_Omod(_1085651, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085651), c_Divides_Odiv__class_Omod(_1085651, _1085653, _1085657)), c_Divides_Odiv__class_Omod(_1085651, _1085655, _1085657)), _1085657))], (7784 ^ _779142) ^ [_907601, _907603, _907605] : [class_Orderings_Olinorder(_907601), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907601), _907603), _907605))), 7791 ^ _779142 : [(7798 ^ _779142) ^ [] : [_907603 = _907605, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907601), _907603), _907605)))], (7792 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907601), _907603), _907605)), -(_907603 = _907605)]]], (49530 ^ _779142) ^ [_1779767, _1779769, _1779771, _1779773, _1779775] : [c_Equiv__Relations_Opart__equivp(_1779767, _1779769), hBOOL(hAPP(hAPP(_1779769, _1779771), _1779773)), hBOOL(hAPP(hAPP(_1779769, _1779773), _1779775)), -(hBOOL(hAPP(hAPP(_1779769, _1779771), _1779775)))], (10235 ^ _779142) ^ [_955791, _955793, _955795, _955797] : [class_Rings_Ocomm__semiring__1(_955791), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955791), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955791), _955793), _955795)), _955797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955791), _955793), _955797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955791), _955795), _955797)))], (28869 ^ _779142) ^ [_1290552, _1290554, _1290556, _1290558] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290552, tc_HOL_Obool)), _1290554), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290552, tc_HOL_Obool)), _1290556), _1290558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290552, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290552, tc_HOL_Obool)), _1290554), _1290556)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290552, tc_HOL_Obool)), _1290554), _1290558)))], (25686 ^ _779142) ^ [_1230551, _1230553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1230551)), c_Int_OBit1(_1230553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230551), _1230553)))], (1906 ^ _779142) ^ [_805909, _805911] : [-(class_Int_Onumber(_805909)), _805911 = _805909, class_Int_Onumber(_805911)], (41959 ^ _779142) ^ [_1612122, _1612124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1612122), hAPP(c_List_Oset(_1612122), _1612124))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612122)), _1612124))))], (28184 ^ _779142) ^ [_1277299, _1277301, _1277303] : [class_Orderings_Olinorder(_1277299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277299), _1277301)), -(_1277301 = c_Orderings_Obot__class_Obot(tc_fun(_1277299, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1277299, hAPP(hAPP(c_Set_Oinsert(_1277299), _1277303), _1277301)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277299), _1277303), c_Big__Operators_Olinorder__class_OMax(_1277299, _1277301)))], (35131 ^ _779142) ^ [_1432691, _1432693, _1432695, _1432697, _1432699, _1432701] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432691, tc_fun(_1432693, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432695, tc_fun(_1432691, tc_HOL_Obool)), _1432697), _1432699)), _1432701) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432695, tc_fun(_1432693, tc_HOL_Obool)), _1432697), hAPP(hAPP(c_COMBC(_1432695, tc_fun(_1432691, tc_fun(_1432693, tc_HOL_Obool)), tc_fun(_1432693, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432691, tc_HOL_Obool), tc_fun(tc_fun(_1432691, tc_fun(_1432693, tc_HOL_Obool)), tc_fun(_1432693, tc_HOL_Obool)), _1432695), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432691, tc_fun(_1432693, tc_HOL_Obool))), _1432699)), _1432701)))], (19713 ^ _779142) ^ [_1125424, _1125426, _1125428, _1125430, _1125432] : [class_Groups_Oordered__ab__group__add__abs(_1125424), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125424), hAPP(c_Groups_Oabs__class_Oabs(_1125424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125424), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125424), _1125426), _1125428)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125424), _1125430), _1125432)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125424), hAPP(c_Groups_Oabs__class_Oabs(_1125424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125424), _1125426), _1125430))), hAPP(c_Groups_Oabs__class_Oabs(_1125424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125424), _1125428), _1125432))))))], (38663 ^ _779142) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (9127 ^ _779142) ^ [_934320, _934322, _934324, _934326, _934328, _934330] : [class_Rings_Oring(_934320), 9130 ^ _779142 : [(9137 ^ _779142) ^ [] : [_934326 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934320), _934328), _934322)), _934324)), _934330), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), _934322), _934324)), _934326) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), _934328), _934324)), _934330))], (9131 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), _934322), _934324)), _934326) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), _934328), _934324)), _934330), -(_934326 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934320), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934320), _934328), _934322)), _934324)), _934330))]]], (48388 ^ _779142) ^ [_1754779, _1754781, _1754783, _1754785, _1754787] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1754779, _1754781, _1754783) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754779, _1754785, _1754787)), _1754781 = _1754785, _1754783 = _1754787], (19637 ^ _779142) ^ [_1124128, _1124130, _1124132] : [class_Divides_Osemiring__div(_1124128), -(_1124130 = c_Groups_Ozero__class_Ozero(_1124128)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124128), _1124130), _1124132)), _1124130) = _1124132)], (32751 ^ _779142) ^ [_1377227, _1377229, _1377231, _1377233, _1377235, _1377237] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377227, tc_fun(_1377229, tc_HOL_Obool))), _1377231), _1377233), _1377235), _1377237)), -(hBOOL(hAPP(hAPP(_1377231, _1377235), _1377237))), -(hBOOL(hAPP(hAPP(_1377233, _1377235), _1377237)))], (31148 ^ _779142) ^ [_1337493, _1337495] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1337493, tc_HOL_Obool)), _1337495)))], (18440 ^ _779142) ^ [_1103827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103827), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103827)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35252 ^ _779142) ^ [_1435933] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1435933)), -(_1435933 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), _1435933)), c_FunDef_Omax__strict)))], (25022 ^ _779142) ^ [_1219118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1219118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1219118))))], (20167 ^ _779142) ^ [_1133304, _1133306, _1133308] : [class_Divides_Osemiring__div(_1133304), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133304), c_Divides_Odiv__class_Omod(_1133304, _1133306, _1133308)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133304), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133304), _1133306), _1133308)), _1133308)) = _1133306)], (19221 ^ _779142) ^ [_1117109, _1117111] : [class_Groups_Oordered__ab__group__add__abs(_1117109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117109), _1117111), hAPP(c_Groups_Oabs__class_Oabs(_1117109), _1117111))))], (11338 ^ _779142) ^ [_973999, _974001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973999), _974001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973999)), _974001)))], (33423 ^ _779142) ^ [_1390687, _1390689, _1390691] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390687, _1390687), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390689), _1390691))), -(_1390687 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1390689 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34629 ^ _779142) ^ [_1419711, _1419713, _1419715, _1419717, _1419719, _1419721] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419711, tc_fun(_1419713, tc_fun(_1419715, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1419711, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_fun(_1419713, tc_fun(_1419715, tc_HOL_Obool)), _1419711), hAPP(c_COMBC(_1419713, tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_fun(_1419715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419715, tc_fun(tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_fun(_1419715, tc_HOL_Obool)), _1419713), c_COMBC(_1419715, tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419715, tc_prod(_1419713, _1419715)), tc_fun(_1419715, tc_fun(tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_HOL_Obool)), _1419713), hAPP(c_COMBB(tc_prod(_1419713, _1419715), tc_fun(tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool), tc_HOL_Obool), _1419715), c_member(tc_prod(_1419713, _1419715)))), c_Product__Type_OPair(_1419713, _1419715))))), _1419717)), _1419719), _1419721)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419713, _1419715)), hAPP(hAPP(c_Product__Type_OPair(_1419713, _1419715), _1419719), _1419721)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419711, tc_fun(tc_prod(_1419713, _1419715), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1419711, tc_HOL_Obool))), _1419717))))], (20 ^ _779142) ^ [_779402, _779404] : [-(v_wt(_779402)), _779404 = _779402, v_wt(_779404)], (42415 ^ _779142) ^ [_1624403, _1624405, _1624407] : [hBOOL(hAPP(c_List_Odistinct(_1624403), _1624405)), -(hBOOL(hAPP(c_List_Odistinct(_1624403), hAPP(hAPP(c_List_Otake(_1624403), _1624407), _1624405))))], (36332 ^ _779142) ^ [_1462566, _1462568, _1462570, _1462572, _1462574] : [c_Fun_Oinj__on(_1462566, _1462568, _1462570, c_Orderings_Otop__class_Otop(tc_fun(_1462566, tc_HOL_Obool))), hAPP(_1462570, _1462572) = hAPP(_1462570, _1462574), -(_1462572 = _1462574)], (52483 ^ _779142) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (34350 ^ _779142) ^ [_1410641, _1410643, _1410645, _1410647] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1410641, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410643, tc_fun(_1410641, tc_HOL_Obool)), _1410645), _1410647)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410643, tc_fun(_1410641, tc_HOL_Obool)), _1410645), hAPP(hAPP(c_COMBB(tc_fun(_1410641, tc_HOL_Obool), tc_fun(_1410641, tc_HOL_Obool), _1410643), c_Groups_Ouminus__class_Ouminus(tc_fun(_1410641, tc_HOL_Obool))), _1410647)))], (34552 ^ _779142) ^ [_1417060, _1417062, _1417064, _1417066, _1417068, _1417070] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417060, tc_fun(_1417062, tc_HOL_Obool)), _1417064), hAPP(hAPP(c_COMBB(_1417066, tc_fun(_1417062, tc_HOL_Obool), _1417060), _1417068), _1417070)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417066, tc_fun(_1417062, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1417060, _1417066, _1417070), _1417064)), _1417068))], (21744 ^ _779142) ^ [_1161014, _1161016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161014), hAPP(c_Nat_OSuc, _1161016))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161014, hAPP(c_Nat_OSuc, _1161016)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161016)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161014, _1161016)))], (31745 ^ _779142) ^ [_1349098, _1349100, _1349102] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1349098), _1349100), _1349102) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1349098), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1349098, tc_Int_Oint), _1349100), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1349102))), class_Groups_Ocomm__monoid__add(_1349098), class_Groups_Ocomm__monoid__mult(_1349098)], (35023 ^ _779142) ^ [_1429964, _1429966, _1429968, _1429970, _1429972] : [-(_1429964 = c_Orderings_Obot__class_Obot(tc_fun(_1429966, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429966, tc_fun(_1429968, tc_HOL_Obool)), _1429964), hAPP(hAPP(c_COMBC(_1429966, tc_fun(_1429968, tc_HOL_Obool), tc_fun(_1429968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429968, tc_HOL_Obool), tc_fun(tc_fun(_1429968, tc_HOL_Obool), tc_fun(_1429968, tc_HOL_Obool)), _1429966), c_Groups_Ominus__class_Ominus(tc_fun(_1429968, tc_HOL_Obool))), _1429970)), _1429972)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429968, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429966, tc_fun(_1429968, tc_HOL_Obool)), _1429964), _1429970)), _1429972))], (9903 ^ _779142) ^ [_948148, _948150, _948152, _948154] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_948148), _948150)), hBOOL(hAPP(hAPP(c_member(_948148), _948152), _948150)), -(hBOOL(hAPP(hAPP(c_member(_948148), _948152), _948154))), -(hAPP(c_Finite__Set_Ocard(_948148), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_948148, tc_HOL_Obool)), _948150), hAPP(hAPP(c_Set_Oinsert(_948148), _948152), _948154))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_948148), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_948148, tc_HOL_Obool)), _948150), _948154))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2092 ^ _779142) ^ [_809542, _809544, _809546, _809548] : [-(c_Nat__Transfer_Otsub(_809548, _809544) = c_Nat__Transfer_Otsub(_809546, _809542)), _809548 = _809546, _809544 = _809542], (11960 ^ _779142) ^ [_985445, _985447, _985449, _985451] : [class_Rings_Olinordered__semiring__strict(_985445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985445), _985447), _985449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985445), c_Groups_Ozero__class_Ozero(_985445)), _985451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985445), _985447), _985451)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985445), _985449), _985451))))], (27156 ^ _779142) ^ [_1258301, _1258303] : [class_Orderings_Olinorder(_1258301), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258301, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1258301), _1258303)), hAPP(hAPP(c_Set_Oinsert(_1258301), _1258303), c_Orderings_Obot__class_Obot(tc_fun(_1258301, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1258301), _1258303))], (25432 ^ _779142) ^ [_1226193, _1226195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226193), _1226195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1226193)), c_Int_OBit0(_1226195))))], (26010 ^ _779142) ^ [_1236180, _1236182] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1236180), hAPP(c_Int_Onumber__class_Onumber__of(_1236180), _1236182)), 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(_1236180), hAPP(c_Int_Onumber__class_Onumber__of(_1236180), _1236182)), hAPP(c_Int_Onumber__class_Onumber__of(_1236180), _1236182))), class_Groups_Omonoid__mult(_1236180), class_Int_Onumber(_1236180)], (8288 ^ _779142) ^ [_917187, _917189, _917191, _917193, _917195] : [-(hAPP(c_Fun_Ofun__upd(_917187, _917189, _917191, _917193, _917195), _917193) = _917195)], (37739 ^ _779142) ^ [_1495909, _1495911, _1495913, _1495915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1495909, _1495911)), hAPP(hAPP(c_Product__Type_OSigma(_1495909, _1495911), _1495913), hAPP(c_COMBK(tc_fun(_1495911, tc_HOL_Obool), _1495909), _1495915)))), -(_1495913 = c_Orderings_Obot__class_Obot(tc_fun(_1495909, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1495911), _1495915)))], (23597 ^ _779142) ^ [_1194729, _1194731, _1194733] : [class_Rings_Olinordered__idom(_1194729), -(hAPP(c_Groups_Oabs__class_Oabs(_1194729), hAPP(hAPP(c_Power_Opower__class_Opower(_1194729), hAPP(c_Groups_Ouminus__class_Ouminus(_1194729), _1194731)), _1194733)) = hAPP(c_Groups_Oabs__class_Oabs(_1194729), hAPP(hAPP(c_Power_Opower__class_Opower(_1194729), _1194731), _1194733)))], (35852 ^ _779142) ^ [_1451424, _1451426, _1451428, _1451430, _1451432] : [hAPP(c_Relation_OImage(_1451424, _1451424, _1451426), hAPP(hAPP(c_Set_Oinsert(_1451424), _1451428), c_Orderings_Obot__class_Obot(tc_fun(_1451424, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451424, _1451424, _1451426), hAPP(hAPP(c_Set_Oinsert(_1451424), _1451430), c_Orderings_Obot__class_Obot(tc_fun(_1451424, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1451424, _1451432, _1451426), hBOOL(hAPP(hAPP(c_member(_1451424), _1451430), _1451432)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451424, _1451424)), hAPP(hAPP(c_Product__Type_OPair(_1451424, _1451424), _1451428), _1451430)), _1451426)))], (45883 ^ _779142) ^ [_1702461, _1702463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702461), _1702463)), -(c_List_Oupt(_1702461, _1702463) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702461), c_List_Oupt(hAPP(c_Nat_OSuc, _1702461), _1702463)))], (39127 ^ _779142) ^ [_1537967, _1537969] : [c_Wellfounded_OwfP(_1537967, hAPP(hAPP(c_COMBC(_1537967, tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_fun(_1537967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537967, tc_fun(tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_fun(_1537967, tc_HOL_Obool)), _1537967), c_COMBC(_1537967, tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537967, tc_prod(_1537967, _1537967)), tc_fun(_1537967, tc_fun(tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_HOL_Obool)), _1537967), hAPP(c_COMBB(tc_prod(_1537967, _1537967), tc_fun(tc_fun(tc_prod(_1537967, _1537967), tc_HOL_Obool), tc_HOL_Obool), _1537967), c_member(tc_prod(_1537967, _1537967)))), c_Product__Type_OPair(_1537967, _1537967)))), _1537969)), -(c_Wellfounded_Owf(_1537967, _1537969))], (40911 ^ _779142) ^ [_1582220, _1582222, _1582224] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582220, _1582220, _1582220), _1582222), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582220, _1582220), tc_HOL_Obool), _1582224), _1582222)) = hAPP(hAPP(c_Relation_Orel__comp(_1582220, _1582220, _1582220), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582220, _1582220), tc_HOL_Obool), _1582224), _1582222)), _1582222))], (52321 ^ _779142) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (30956 ^ _779142) ^ [_1333756] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1333756, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1333756, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1333756, tc_HOL_Obool)))], (38244 ^ _779142) ^ [_1514935, _1514937, _1514939, _1514941] : [class_Groups_Ocomm__monoid__mult(_1514935), c_Fun_Oinj__on(_1514937, _1514935, _1514939, _1514941), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514937, _1514935), _1514939), _1514941) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514935, _1514935), c_Fun_Oid(_1514935)), hAPP(c_Set_Oimage(_1514937, _1514935, _1514939), _1514941)))], (27120 ^ _779142) ^ [_1257665, _1257667, _1257669] : [class_Orderings_Olinorder(_1257665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257665), _1257667)), -(_1257667 = c_Orderings_Obot__class_Obot(tc_fun(_1257665, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257665), _1257669)), -(_1257669 = c_Orderings_Obot__class_Obot(tc_fun(_1257665, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1257665, c_Orderings_Oord__class_Omin(_1257665), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257665, tc_HOL_Obool)), _1257667), _1257669)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1257665), c_Big__Operators_Olattice_OInf__fin(_1257665, c_Orderings_Oord__class_Omin(_1257665), _1257667)), c_Big__Operators_Olattice_OInf__fin(_1257665, c_Orderings_Oord__class_Omin(_1257665), _1257669)))], (19303 ^ _779142) ^ [_1118615] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1118615)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1118615))], (49715 ^ _779142) ^ [_1783896, _1783898, _1783900, _1783902, _1783904] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783896, _1783898, _1783900, _1783902), _1783904) = c_Hilbert__Choice_OEps(_1783896, hAPP(hAPP(c_COMBS(_1783896, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1783896), c_fconj), hAPP(hAPP(c_COMBC(_1783896, tc_fun(_1783896, tc_HOL_Obool), tc_HOL_Obool), c_member(_1783896)), _1783900))), hAPP(hAPP(c_COMBC(_1783896, _1783898, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783898, tc_fun(_1783898, tc_HOL_Obool), _1783896), c_fequal), _1783902)), _1783904))))], (5859 ^ _779142) ^ [_871973, _871975] : [-(hBOOL(hAPP(hAPP(c_member(_871973), 5860 ^ [_871973, _871975]), _871975))), -(_871975 = c_Orderings_Obot__class_Obot(tc_fun(_871973, tc_HOL_Obool)))], (24694 ^ _779142) ^ [_1213417, _1213419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213417), _1213419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1213417)), c_Int_OBit1(_1213419))))], (47124 ^ _779142) ^ [_1727215, _1727217] : [class_Orderings_Olinorder(_1727215), 47127 ^ _779142 : [(47148 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727215, _1727217)), 47149 ^ _779142 : [(47152 ^ _779142) ^ [_1727775, _1727777] : [_1727217 = hAPP(hAPP(c_List_Olist_OCons(_1727215), _1727775), _1727777), 47158 ^ _779142 : [(47161 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727215), _1727775), 47157 ^ [_1727215, _1727217, _1727775, _1727777]))], (47159 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727215), 47157 ^ [_1727215, _1727217, _1727775, _1727777]), hAPP(c_List_Oset(_1727215), _1727777))))]], c_List_Olinorder__class_Osorted(_1727215, _1727777)], (47150 ^ _779142) ^ [] : [_1727217 = c_List_Olist_ONil(_1727215)]]], (47128 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1727215, _1727217), -(_1727217 = c_List_Olist_ONil(_1727215)), 47137 ^ _779142 : [(47140 ^ _779142) ^ [_1727549] : [hBOOL(hAPP(hAPP(c_member(_1727215), _1727549), hAPP(c_List_Oset(_1727215), 47135 ^ [_1727215, _1727217]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727215), 47136 ^ [_1727215, _1727217]), _1727549)))], (47146 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727215, 47135 ^ [_1727215, _1727217]))], (47138 ^ _779142) ^ [] : [-(_1727217 = hAPP(hAPP(c_List_Olist_OCons(_1727215), 47136 ^ [_1727215, _1727217]), 47135 ^ [_1727215, _1727217]))]]]]], (26130 ^ _779142) ^ [_1238245, _1238247, _1238249] : [class_Rings_Olinordered__idom(_1238245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1238245), hAPP(hAPP(c_Power_Opower__class_Opower(_1238245), _1238247), 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(_1238245), _1238249), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1238245)))], (11151 ^ _779142) ^ [_971053] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971053) = _971053)], (52627 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (19395 ^ _779142) ^ [_1120107, _1120109, _1120111, _1120113, _1120115] : [class_Rings_Olinordered__idom(_1120107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120107), hAPP(c_Groups_Oabs__class_Oabs(_1120107), _1120109)), _1120111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120107), hAPP(c_Groups_Oabs__class_Oabs(_1120107), _1120113)), _1120115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120107), hAPP(c_Groups_Oabs__class_Oabs(_1120107), _1120109)), hAPP(c_Groups_Oabs__class_Oabs(_1120107), _1120113))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120107), _1120111), _1120115))))], (37111 ^ _779142) ^ [_1479228] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1479228), c_Int_OInteg)), -(_1479228 = hAPP(c_Int_ORep__Integ, 37114 ^ [_1479228]))], (48662 ^ _779142) ^ [_1761016, _1761018, _1761020] : [c_List_Oall__interval__int(_1761016, _1761018, _1761020), -(c_List_Olist__all(tc_Int_Oint, _1761016, c_List_Oupto(_1761018, _1761020)))], (15589 ^ _779142) ^ [_1052333, _1052335, _1052337] : [class_Int_Onumber__ring(_1052333), -(hAPP(c_Int_Onumber__class_Onumber__of(_1052333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052335), _1052337)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052333), hAPP(c_Int_Onumber__class_Onumber__of(_1052333), _1052335)), hAPP(c_Int_Onumber__class_Onumber__of(_1052333), _1052337)))], (23209 ^ _779142) ^ [_1187834, _1187836] : [-(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, _1187834, _1187836)), _1187836) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187834), _1187836))], (45055 ^ _779142) ^ [_1682745, _1682747, _1682749, _1682751, _1682753, _1682755, _1682757] : [c_List_Olist__all2(_1682745, _1682747, _1682749, _1682751, hAPP(hAPP(c_List_Omap(_1682753, _1682747), _1682755), _1682757)), -(c_List_Olist__all2(_1682745, _1682753, hAPP(hAPP(c_COMBC(_1682745, tc_fun(_1682753, _1682747), tc_fun(_1682753, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682747, tc_HOL_Obool), tc_fun(tc_fun(_1682753, _1682747), tc_fun(_1682753, tc_HOL_Obool)), _1682745), c_COMBB(_1682747, tc_HOL_Obool, _1682753)), _1682749)), _1682755), _1682751, _1682757))], (26396 ^ _779142) ^ [_1243444, _1243446, _1243448, _1243450] : [class_Lattices_Osemilattice__sup(_1243444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243444), _1243446), _1243448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243444), _1243450), _1243448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243444), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1243444), _1243446), _1243450)), _1243448)))], (13543 ^ _779142) ^ [_1014768, _1014770, _1014772, _1014774] : [class_Rings_Odivision__ring(_1014768), -(_1014770 = c_Groups_Ozero__class_Ozero(_1014768)), _1014772 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014768), _1014774), _1014770), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014768), _1014772), _1014770) = _1014774)], (50329 ^ _779142) ^ [_1796759, _1796761, _1796763, _1796765] : [c_Equiv__Relations_Oequivp(_1796759, _1796761), 50335 ^ _779142 : [(50338 ^ _779142) ^ [] : [hBOOL(hAPP(_1796765, 50334 ^ [_1796759, _1796761, _1796763, _1796765]))], (50336 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1796763, 50334 ^ [_1796759, _1796761, _1796763, _1796765])))]], 50341 ^ _779142 : [(50342 ^ _779142) ^ [_1797018] : [hBOOL(hAPP(_1796763, _1797018))]], 50344 ^ _779142 : [(50347 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1796765, 50343 ^ [_1796759, _1796761, _1796763, _1796765])))], (50345 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796759), 50343 ^ [_1796759, _1796761, _1796763, _1796765]), c_Quotient_ORespects(_1796759, _1796761))))]]], (5368 ^ _779142) ^ [_861252, _861254, _861256, _861258, _861260, _861262] : [-(c_SetInterval_Oord_OgreaterThan(_861262, _861258, _861254) = c_SetInterval_Oord_OgreaterThan(_861260, _861256, _861252)), _861262 = _861260, _861258 = _861256, _861254 = _861252], (44063 ^ _779142) ^ [_1660972, _1660974, _1660976, _1660978, _1660980] : [class_Orderings_Olinorder(_1660972), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660974, _1660972, _1660976), _1660978), _1660980) = c_List_Olist_ONil(_1660974)], (52633 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (36326 ^ _779142) ^ [_1462453, _1462455, _1462457, _1462459, _1462461] : [c_Fun_Oinj__on(_1462453, _1462455, _1462457, _1462459), -(c_Fun_Oinj__on(_1462453, _1462455, _1462457, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462453, tc_HOL_Obool)), _1462459), _1462461)))], (35474 ^ _779142) ^ [_1442152, _1442154, _1442156, _1442158, _1442160] : [-(hAPP(c_Relation_OImage(_1442152, _1442154, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1442152, _1442154), tc_HOL_Obool)), _1442156), _1442158)), _1442160) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442154, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442152, _1442154, _1442156), _1442160)), hAPP(c_Relation_OImage(_1442152, _1442154, _1442158), _1442160)))], (38324 ^ _779142) ^ [_1517040, _1517042, _1517044, _1517046, _1517048, _1517050, _1517052, _1517054] : [c_Fun_Oinj__on(_1517040, _1517042, _1517044, _1517046), c_Fun_Oinj__on(_1517048, _1517050, _1517052, _1517054), -(c_Fun_Oinj__on(tc_prod(_1517040, _1517048), tc_prod(_1517042, _1517050), c_Product__Type_Omap__pair(_1517040, _1517042, _1517048, _1517050, _1517044, _1517052), hAPP(hAPP(c_Product__Type_OSigma(_1517040, _1517048), _1517046), hAPP(c_COMBK(tc_fun(_1517048, tc_HOL_Obool), _1517040), _1517054))))], (39500 ^ _779142) ^ [_1547538, _1547540, _1547542, _1547544, _1547546, _1547548, _1547550] : [-(hAPP(c_Product__Type_Oapsnd(_1547538, _1547540, _1547542, _1547544), hAPP(c_Product__Type_Oapsnd(_1547546, _1547538, _1547542, _1547548), _1547550)) = hAPP(c_Product__Type_Oapsnd(_1547546, _1547540, _1547542, hAPP(c_Fun_Ocomp(_1547538, _1547540, _1547546, _1547544), _1547548)), _1547550))], (19783 ^ _779142) ^ [_1126691, _1126693] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126691), _1126693) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19784 ^ _779142 : [(19793 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126691), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126693), _1126691))], (19787 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126691), _1126693))], (19785 ^ _779142) ^ [] : [_1126693 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (43941 ^ _779142) ^ [_1658156, _1658158, _1658160] : [class_Orderings_Olinorder(_1658156), -(c_Big__Operators_Olinorder__class_OMax(_1658156, hAPP(c_List_Oset(_1658156), hAPP(hAPP(c_List_Olist_OCons(_1658156), _1658158), _1658160))) = hAPP(c_List_Ofoldl(_1658156, _1658156, c_Orderings_Oord__class_Omax(_1658156), _1658158), _1658160))], (9352 ^ _779142) ^ [_938602, _938604, _938606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938602), _938604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938602), _938606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938604), _938606))))], (45494 ^ _779142) ^ [_1692045, _1692047, _1692049, _1692051] : [class_Orderings_Olinorder(_1692045), -(hAPP(c_List_Oset(_1692047), c_List_Olinorder__class_Osort__key(_1692047, _1692045, _1692049, _1692051)) = hAPP(c_List_Oset(_1692047), _1692051))], (13022 ^ _779142) ^ [_1004678, _1004680, _1004682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004678)), 13025 ^ _779142 : [(13032 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004680), _1004682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004678), _1004680)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004678), _1004682))))], (13026 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004678), _1004680)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004678), _1004682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004680), _1004682)))]]], (28358 ^ _779142) ^ [_1280312, _1280314, _1280316] : [class_Complete__Lattice_Ocomplete__lattice(_1280312), -(c_Complete__Lattice_OSup__class_OSup(_1280312, hAPP(hAPP(c_Set_Oinsert(_1280312), _1280314), _1280316)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280312), _1280314), c_Complete__Lattice_OSup__class_OSup(_1280312, _1280316)))], (30359 ^ _779142) ^ [_1322137, _1322139, _1322141] : [class_Lattices_Olattice(_1322137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322137), _1322139)), -(_1322141 = c_Orderings_Obot__class_Obot(tc_fun(_1322137, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322137, tc_HOL_Obool)), _1322141), _1322139)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322137), c_Big__Operators_Olattice__class_OInf__fin(_1322137, _1322141)), c_Big__Operators_Olattice__class_OInf__fin(_1322137, _1322139)) = c_Big__Operators_Olattice__class_OInf__fin(_1322137, _1322139))], (48721 ^ _779142) ^ [_1762423, _1762425, _1762427, _1762429, _1762431, _1762433, _1762435] : [hBOOL(hAPP(hAPP(_1762423, hAPP(c_Product__Type_Osnd(_1762425, _1762427), _1762429)), hAPP(c_Product__Type_Ofst(_1762425, _1762427), _1762429))), 48728 ^ _779142 : [(48731 ^ _779142) ^ [] : [hBOOL(hAPP(_1762431, hAPP(hAPP(_1762433, 48726 ^ [_1762423, _1762425, _1762427, _1762429, _1762431, _1762433, _1762435]), 48727 ^ [_1762423, _1762425, _1762427, _1762429, _1762431, _1762433, _1762435])))], (48729 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1762423, 48727 ^ [_1762423, _1762425, _1762427, _1762429, _1762431, _1762433, _1762435]), 48726 ^ [_1762423, _1762425, _1762427, _1762429, _1762431, _1762433, _1762435])))]], -(hBOOL(hAPP(_1762431, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1762425, _1762427, _1762435), _1762433), _1762429))))], (6855 ^ _779142) ^ [_890890, _890892, _890894, _890896] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890890, tc_HOL_Obool)), _890892), hAPP(hAPP(c_Set_Oinsert(_890890), _890894), _890896)))), 6858 ^ _779142 : [(6861 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890890, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890890, tc_HOL_Obool)), _890892), hAPP(hAPP(c_Set_Oinsert(_890890), _890894), c_Orderings_Obot__class_Obot(tc_fun(_890890, tc_HOL_Obool))))), _890896))], (6859 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890890), _890894), _890892)))]], 6862 ^ _779142 : [(6865 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890890, tc_HOL_Obool)), _890892), _890896))], (6863 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890890), _890894), _890892))]]], (34641 ^ _779142) ^ [_1420683, _1420685, _1420687, _1420689, _1420691] : [class_Complete__Lattice_Ocomplete__lattice(_1420683), 34644 ^ _779142 : [(34645 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420683), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420685, _1420683), _1420687), _1420689)), _1420691)), 34648 ^ _779142 : [(34649 ^ _779142) ^ [_1420864] : [hBOOL(hAPP(hAPP(c_member(_1420685), _1420864), _1420687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420683), hAPP(_1420689, _1420864)), _1420691)))]]], (34655 ^ _779142) ^ [] : [34657 ^ _779142 : [(34660 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420683), hAPP(_1420689, 34656 ^ [_1420683, _1420685, _1420687, _1420689, _1420691])), _1420691))], (34658 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420685), 34656 ^ [_1420683, _1420685, _1420687, _1420689, _1420691]), _1420687)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420683), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420685, _1420683), _1420687), _1420689)), _1420691)))]]], (37381 ^ _779142) ^ [_1486055] : [-(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)), _1486055)))))], (28356 ^ _779142) ^ [_1280238, _1280240, _1280242] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280238, tc_HOL_Obool)), _1280240), _1280242) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1280238, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1280238, tc_HOL_Obool)), _1280240), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1280238, tc_HOL_Obool)), _1280242), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1280238, tc_HOL_Obool), tc_HOL_Obool))))))], (22420 ^ _779142) ^ [_1173634, _1173636] : [22428 ^ _779142 : [(22431 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1173636, 22427 ^ [_1173634, _1173636])))], (22429 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22427 ^ [_1173634, _1173636]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1173634))))]], 22421 ^ _779142 : [(22422 ^ _779142) ^ [_1173703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173703), _1173634)), hBOOL(hAPP(_1173636, _1173703))]]], (40976 ^ _779142) ^ [_1583641, _1583643, _1583645, _1583647] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583641, _1583641), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1583643), _1583645)), _1583647) = hAPP(hAPP(c_Relation_Orel__comp(_1583641, _1583641, _1583641), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583641, _1583641), tc_HOL_Obool), _1583643), _1583647)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583641, _1583641), tc_HOL_Obool), _1583645), _1583647)))], (42413 ^ _779142) ^ [_1624373, _1624375] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1624373, _1624375))))], (49895 ^ _779142) ^ [_1788075, _1788077, _1788079] : [c_Fun_Obij__betw(_1788075, _1788077, _1788079, c_Orderings_Otop__class_Otop(tc_fun(_1788075, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788077, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788077, _1788075, c_Orderings_Otop__class_Otop(tc_fun(_1788077, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1788075, _1788077, c_Orderings_Otop__class_Otop(tc_fun(_1788075, tc_HOL_Obool)), _1788079)) = _1788079)], (12830 ^ _779142) ^ [_1001062, _1001064, _1001066, _1001068] : [class_Rings_Olinordered__semiring__strict(_1001062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001062), _1001064), _1001066)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001062), _1001068), _1001066))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001062), c_Groups_Ozero__class_Ozero(_1001062)), _1001066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001062), _1001064), _1001068)))], (45171 ^ _779142) ^ [_1685143, _1685145, _1685147] : [-(c_Enum_Oproduct(_1685143, _1685145, c_List_Olist_ONil(_1685143), _1685147) = c_List_Olist_ONil(tc_prod(_1685143, _1685145)))], (48166 ^ _779142) ^ [_1750594, _1750596, _1750598] : [-(c_List_Oreplicate(_1750594, hAPP(c_Nat_OSuc, _1750596), _1750598) = hAPP(hAPP(c_List_Olist_OCons(_1750594), _1750598), c_List_Oreplicate(_1750594, _1750596, _1750598)))], (31801 ^ _779142) ^ [_1351504, _1351506, _1351508, _1351510] : [class_Groups_Oab__group__add(_1351504), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351506, _1351504), hAPP(hAPP(c_COMBB(_1351504, _1351504, _1351506), c_Groups_Ouminus__class_Ouminus(_1351504)), _1351508)), _1351510) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351504), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351506, _1351504), _1351508), _1351510)))], (44217 ^ _779142) ^ [_1663469, _1663471] : [-(_1663469 = c_List_Olist_ONil(_1663471)), -(hBOOL(hAPP(hAPP(c_member(_1663471), c_List_Olast(_1663471, _1663469)), hAPP(c_List_Oset(_1663471), _1663469))))], (45246 ^ _779142) ^ [_1686914, _1686916, _1686918, _1686920] : [hBOOL(hAPP(c_List_Odistinct(_1686914), _1686916)), hBOOL(hAPP(c_List_Odistinct(_1686918), _1686920)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1686914, _1686918)), c_Enum_Oproduct(_1686914, _1686918, _1686916, _1686920))))], (50721 ^ _779142) ^ [_1806226, _1806228, _1806230, _1806232] : [class_Rings_Ocomm__semiring__1(_1806226), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806226), _1806228), _1806230)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806226), _1806228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806226), _1806232), _1806230))))], (47606 ^ _779142) ^ [_1738269, _1738271, _1738273, _1738275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738271)), _1738273))), 47612 ^ _779142 : [(47615 ^ _779142) ^ [] : [hBOOL(hAPP(_1738275, 47611 ^ [_1738269, _1738271, _1738273, _1738275]))], (47613 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738271), 47611 ^ [_1738269, _1738271, _1738273, _1738275]), hAPP(c_List_Oset(_1738271), _1738273))))]], -(hBOOL(hAPP(_1738275, hAPP(hAPP(c_List_Onth(_1738271), _1738273), _1738269))))], (37958 ^ _779142) ^ [_1503136, _1503138, _1503140, _1503142] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503136), _1503138)), 37964 ^ _779142 : [(37967 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503140), hAPP(_1503142, 37963 ^ [_1503136, _1503138, _1503140, _1503142])))], (37965 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503136), 37963 ^ [_1503136, _1503138, _1503140, _1503142]), _1503138)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1503136, _1503140)), hAPP(hAPP(c_Product__Type_OSigma(_1503136, _1503140), _1503138), _1503142)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503136, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1503140, tc_HOL_Obool), tc_Nat_Onat, _1503136), c_Finite__Set_Ocard(_1503140)), _1503142)), _1503138))], (43712 ^ _779142) ^ [_1653745, _1653747, _1653749] : [-(_1653745 = c_List_Olist_ONil(_1653747)), -(hAPP(c_List_Ohd(_1653747), hAPP(hAPP(c_List_Oappend(_1653747), _1653745), _1653749)) = hAPP(c_List_Ohd(_1653747), _1653745))], (18887 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (32807 ^ _779142) ^ [_1378324, _1378326, _1378328, _1378330, _1378332, _1378334] : [hBOOL(hAPP(hAPP(_1378324, _1378326), _1378328)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1378330, tc_fun(_1378332, tc_HOL_Obool))), _1378334), _1378324), _1378326), _1378328)))], (18788 ^ _779142) ^ [_1109973, _1109975] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109973))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109973)), _1109975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1109975))], (9963 ^ _779142) ^ [_949389, _949391, _949393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949389), _949391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949393), _949389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949389), _949393)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949391), _949393))))], (43441 ^ _779142) ^ [_1647072, _1647074, _1647076, _1647078, _1647080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647072), tc_List_Olist(_1647072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647072), tc_List_Olist(_1647072)), hAPP(hAPP(c_List_Oappend(_1647072), _1647074), _1647076)), hAPP(hAPP(c_List_Oappend(_1647072), _1647074), _1647078))), c_List_Olexord(_1647072, _1647080))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647072, _1647072)), hAPP(hAPP(c_Product__Type_OPair(_1647072, _1647072), 43446 ^ [_1647072, _1647074, _1647076, _1647078, _1647080]), 43446 ^ [_1647072, _1647074, _1647076, _1647078, _1647080])), _1647080))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647072), tc_List_Olist(_1647072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647072), tc_List_Olist(_1647072)), _1647076), _1647078)), c_List_Olexord(_1647072, _1647080))))], (24513 ^ _779142) ^ [_1210372, _1210374] : [class_Rings_Oring__1(_1210372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210374)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210372), hAPP(c_Int_Onat, _1210374)) = hAPP(c_Int_Oring__1__class_Oof__int(_1210372), _1210374))], (46066 ^ _779142) ^ [_1706074, _1706076] : [class_Orderings_Olinorder(_1706074), -(c_List_Olinorder__class_Osorted(_1706074, hAPP(hAPP(c_List_Olist_OCons(_1706074), _1706076), c_List_Olist_ONil(_1706074))))], (4446 ^ _779142) ^ [_846603, _846605, _846607, _846609] : [-(c_HOL_OThe(_846609, _846605) = c_HOL_OThe(_846607, _846603)), _846609 = _846607, _846605 = _846603], (13203 ^ _779142) ^ [_1008016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1008016)), -(_1008016 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008016), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (8320 ^ _779142) ^ [_917622, _917624, _917626, _917628] : [-(c_Nitpick_Ofold__graph_H(_917622, _917624, _917626, _917628, c_Orderings_Obot__class_Obot(tc_fun(_917622, tc_HOL_Obool)), _917628))], (19585 ^ _779142) ^ [_1123305, _1123307] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123305), _1123307)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1123305) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (47193 ^ _779142) ^ [_1728467, _1728469, _1728471] : [hBOOL(hAPP(hAPP(c_member(_1728467), _1728469), hAPP(c_List_Oset(_1728467), _1728471))), -(c_List_Oinsert(_1728467, _1728469, _1728471) = _1728471)], (40827 ^ _779142) ^ [_1580019, _1580021, _1580023] : [c_Relation_Orefl__on(_1580019, _1580021, _1580023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580019, _1580019), tc_HOL_Obool)), _1580023), hAPP(hAPP(c_Relation_Orel__comp(_1580019, _1580019, _1580019), hAPP(c_Relation_Oconverse(_1580019, _1580019), _1580023)), _1580023))))], (42421 ^ _779142) ^ [_1624514, _1624516, _1624518] : [hBOOL(hAPP(c_List_Odistinct(_1624514), _1624516)), -(hBOOL(hAPP(c_List_Odistinct(_1624514), c_List_Osublist(_1624514, _1624516, _1624518))))], (50979 ^ _779142) ^ [_1811147, _1811149] : [50980 ^ _779142 : [(50983 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811149), _1811147))], (50981 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811147), _1811149)))]], -(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)))), _1811147, _1811149))], (3274 ^ _779142) ^ [_827903, _827905, _827907, _827909, _827911, _827913, _827915, _827917] : [-(c_Enum_Oproduct(_827917, _827913, _827909, _827905) = c_Enum_Oproduct(_827915, _827911, _827907, _827903)), _827917 = _827915, _827913 = _827911, _827909 = _827907, _827905 = _827903], (50565 ^ _779142) ^ [_1803526, _1803528] : [class_Rings_Ocomm__semiring__1(_1803526), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803526), _1803528), c_Groups_Ozero__class_Ozero(_1803526))))], (42652 ^ _779142) ^ [_1629347, _1629349, _1629351] : [hAPP(hAPP(c_List_Otake(_1629347), _1629349), _1629351) = c_List_Olist_ONil(_1629347), -(_1629349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1629351 = c_List_Olist_ONil(_1629347))], (37122 ^ _779142) ^ [_1479517, _1479519, _1479521, _1479523, _1479525] : [-(hAPP(c_Fun_Othe__inv__into(_1479517, _1479519, _1479521, _1479523), _1479525) = c_HOL_OThe(_1479517, hAPP(hAPP(c_COMBS(_1479517, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1479517), c_fconj), hAPP(hAPP(c_COMBC(_1479517, tc_fun(_1479517, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479517)), _1479521))), hAPP(hAPP(c_COMBC(_1479517, _1479519, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1479519, tc_fun(_1479519, tc_HOL_Obool), _1479517), c_fequal), _1479523)), _1479525))))], (4610 ^ _779142) ^ [_849209, _849211, _849213, _849215, _849217, _849219, _849221, _849223] : [-(c_Random__Sequence_Omap(_849223, _849219, _849215, _849211) = c_Random__Sequence_Omap(_849221, _849217, _849213, _849209)), _849223 = _849221, _849219 = _849217, _849215 = _849213, _849211 = _849209], (2136 ^ _779142) ^ [_810210, _810212, _810214, _810216] : [-(c_SMT_Oz3mod(_810216, _810212) = c_SMT_Oz3mod(_810214, _810210)), _810216 = _810214, _810212 = _810210], (28815 ^ _779142) ^ [_1289169, _1289171, _1289173, _1289175] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289169, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289169, tc_HOL_Obool)), _1289171), _1289173)), _1289175) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289169, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289169, tc_HOL_Obool)), _1289171), _1289175)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289169, tc_HOL_Obool)), _1289173), _1289175)))], (34198 ^ _779142) ^ [_1406812, _1406814, _1406816, _1406818] : [class_Complete__Lattice_Ocomplete__lattice(_1406812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406814), _1406816)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406814, _1406812), _1406816), _1406818) = hAPP(hAPP(c_Finite__Set_Ofold(_1406814, _1406812, hAPP(hAPP(c_COMBB(_1406812, tc_fun(_1406812, _1406812), _1406814), c_Lattices_Osemilattice__sup__class_Osup(_1406812)), _1406818)), c_Orderings_Obot__class_Obot(_1406812)), _1406816))], (42978 ^ _779142) ^ [_1636232, _1636234, _1636236, _1636238, _1636240] : [hAPP(hAPP(c_List_Olist_OCons(_1636232), _1636234), _1636236) = hAPP(hAPP(c_List_Oappend(_1636232), _1636238), _1636240), 42983 ^ _779142 : [(42986 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636232), _1636234), _1636236) = _1636240)], (42984 ^ _779142) ^ [] : [-(_1636238 = c_List_Olist_ONil(_1636232))]], 42988 ^ _779142 : [(42991 ^ _779142) ^ [] : [-(_1636236 = hAPP(hAPP(c_List_Oappend(_1636232), 42987 ^ [_1636232, _1636234, _1636236, _1636238, _1636240]), _1636240))], (42989 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636232), _1636234), 42987 ^ [_1636232, _1636234, _1636236, _1636238, _1636240]) = _1636238)]]], (42297 ^ _779142) ^ [_1621530, _1621532, _1621534, _1621536, _1621538] : [-(hAPP(hAPP(c_List_Olist__update(_1621530, hAPP(hAPP(c_List_Olist__update(_1621530, _1621532), _1621534), _1621536)), _1621534), _1621538) = hAPP(hAPP(c_List_Olist__update(_1621530, _1621532), _1621534), _1621538))], (25748 ^ _779142) ^ [_1231671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1231671)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231671), c_Int_OMin)))], (33760 ^ _779142) ^ [_1397116, _1397118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1397118), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397116, _1397118) = 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), _1397116), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1397118)))))], (37279 ^ _779142) ^ [_1483458, _1483460, _1483462, _1483464] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483458), _1483460)), c_Fun_Oinj__on(_1483462, _1483458, _1483464, c_Orderings_Otop__class_Otop(tc_fun(_1483462, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1483462), hAPP(c_Set_Ovimage(_1483462, _1483458, _1483464), _1483460))))], (45173 ^ _779142) ^ [_1685182, _1685184, _1685186, _1685188, _1685190, _1685192] : [c_List_Olist__all2(_1685182, _1685184, _1685186, _1685188, _1685190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685192), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685184)), _1685190))), -(hBOOL(hAPP(hAPP(_1685186, hAPP(hAPP(c_List_Onth(_1685182), _1685188), _1685192)), hAPP(hAPP(c_List_Onth(_1685184), _1685190), _1685192))))], (298 ^ _779142) ^ [_783675, _783677, _783679, _783681] : [-(c_FunDef_Oreduction__pair(_783679, _783675)), c_FunDef_Oreduction__pair(_783681, _783677), _783681 = _783679, _783677 = _783675], (39642 ^ _779142) ^ [_1550831, _1550833, _1550835, _1550837, _1550839, _1550841, _1550843] : [c_Fun_Oinj__on(_1550831, _1550833, _1550835, hAPP(c_Set_Oimage(_1550837, _1550831, _1550839), _1550841)), c_Fun_Oinj__on(_1550837, _1550831, _1550839, _1550841), hBOOL(hAPP(hAPP(c_member(_1550833), _1550843), hAPP(c_Set_Oimage(_1550831, _1550833, _1550835), hAPP(c_Set_Oimage(_1550837, _1550831, _1550839), _1550841)))), -(hAPP(c_Fun_Othe__inv__into(_1550837, _1550833, _1550841, hAPP(c_Fun_Ocomp(_1550831, _1550833, _1550837, _1550835), _1550839)), _1550843) = hAPP(hAPP(c_Fun_Ocomp(_1550831, _1550837, _1550833, c_Fun_Othe__inv__into(_1550837, _1550831, _1550841, _1550839)), c_Fun_Othe__inv__into(_1550831, _1550833, hAPP(c_Set_Oimage(_1550837, _1550831, _1550839), _1550841), _1550835)), _1550843))], (25482 ^ _779142) ^ [_1226990, _1226992] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1226990)), c_Int_OBit0(_1226992)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226990), _1226992)))], (43040 ^ _779142) ^ [_1637536, _1637538, _1637540, _1637542, _1637544, _1637546] : [hAPP(hAPP(c_List_Olist_OCons(_1637536), _1637538), _1637540) = _1637542, _1637544 = hAPP(hAPP(c_List_Oappend(_1637536), _1637540), _1637546), -(hAPP(hAPP(c_List_Olist_OCons(_1637536), _1637538), _1637544) = hAPP(hAPP(c_List_Oappend(_1637536), _1637542), _1637546))], (24299 ^ _779142) ^ [_1206759, _1206761, _1206763] : [class_Rings_Oring__1(_1206759), -(hAPP(c_Int_Oring__1__class_Oof__int(_1206759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1206761), _1206763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206759), hAPP(c_Int_Oring__1__class_Oof__int(_1206759), _1206761)), hAPP(c_Int_Oring__1__class_Oof__int(_1206759), _1206763)))], (10425 ^ _779142) ^ [_959741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959741), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44205 ^ _779142) ^ [_1663312, _1663314, _1663316] : [_1663312 = c_List_Olist_ONil(_1663314), -(c_List_Olast(_1663314, hAPP(hAPP(c_List_Oappend(_1663314), _1663316), _1663312)) = c_List_Olast(_1663314, _1663316))], (25270 ^ _779142) ^ [_1223161, _1223163] : [class_Int_Onumber__ring(_1223161), class_Rings_Olinordered__idom(_1223161), 25277 ^ _779142 : [(25284 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223163), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223161), hAPP(c_Int_Onumber__class_Onumber__of(_1223161), _1223163)), c_Groups_Oone__class_Oone(_1223161))))], (25278 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223161), hAPP(c_Int_Onumber__class_Onumber__of(_1223161), _1223163)), c_Groups_Oone__class_Oone(_1223161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223163), c_Int_OBit1(c_Int_OPls))))]]], (34176 ^ _779142) ^ [_1406316, _1406318, _1406320, _1406322, _1406324, _1406326, _1406328] : [-(hAPP(c_Product__Type_Oapfst(_1406316, _1406318, _1406320, _1406322), hAPP(c_Product__Type_Oapsnd(_1406324, _1406320, _1406316, _1406326), _1406328)) = hAPP(hAPP(c_Product__Type_OPair(_1406318, _1406320), hAPP(_1406322, hAPP(c_Product__Type_Ofst(_1406316, _1406324), _1406328))), hAPP(_1406326, hAPP(c_Product__Type_Osnd(_1406316, _1406324), _1406328))))], (6996 ^ _779142) ^ [_893937, _893939, _893941, _893943, _893945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893937, tc_HOL_Obool)), _893939), _893941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893937, tc_HOL_Obool)), _893943), _893945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893937, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893937, tc_HOL_Obool)), _893939), _893945)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893937, tc_HOL_Obool)), _893941), _893943))))], (26724 ^ _779142) ^ [_1249885, _1249887, _1249889] : [class_Lattices_Obounded__lattice__bot(_1249885), 26727 ^ _779142 : [(26736 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1249885), _1249887), _1249889) = c_Orderings_Obot__class_Obot(_1249885)), _1249887 = c_Orderings_Obot__class_Obot(_1249885), _1249889 = c_Orderings_Obot__class_Obot(_1249885)], (26728 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1249885), _1249887), _1249889) = c_Orderings_Obot__class_Obot(_1249885), 26731 ^ _779142 : [(26734 ^ _779142) ^ [] : [-(_1249889 = c_Orderings_Obot__class_Obot(_1249885))], (26732 ^ _779142) ^ [] : [-(_1249887 = c_Orderings_Obot__class_Obot(_1249885))]]]]], (46738 ^ _779142) ^ [_1719060, _1719062, _1719064, _1719066] : [class_Orderings_Olinorder(_1719060), c_List_Olinorder__class_Osorted(_1719060, hAPP(c_List_Orev(_1719060), _1719062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719064), _1719066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719066), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719060)), _1719062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719060), hAPP(hAPP(c_List_Onth(_1719060), _1719062), _1719066)), hAPP(hAPP(c_List_Onth(_1719060), _1719062), _1719064))))], (49022 ^ _779142) ^ [_1770618, _1770620] : [c_Relation_Otrans(_1770618, hAPP(c_Set_OCollect(tc_prod(_1770618, _1770618)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770618, _1770618, tc_HOL_Obool), _1770620))), -(c_Predicate_Otransp(_1770618, _1770620))], (23877 ^ _779142) ^ [_1199629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199629), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1199629) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199629))], (2938 ^ _779142) ^ [_822649, _822651] : [_822651 = _822649, -(c_Nitpick_ORep__Frac(_822651) = c_Nitpick_ORep__Frac(_822649))], (2390 ^ _779142) ^ [_814087, _814089, _814091, _814093, _814095, _814097, _814099, _814101, _814103, _814105] : [-(c_Product__Type_Oprod_Oprod__size(_814105, _814101, _814097, _814093, _814089) = c_Product__Type_Oprod_Oprod__size(_814103, _814099, _814095, _814091, _814087)), _814105 = _814103, _814101 = _814099, _814097 = _814095, _814093 = _814091, _814089 = _814087], (25426 ^ _779142) ^ [_1226092, _1226094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1226092)), c_Int_OBit0(_1226094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226092), _1226094)))], (37993 ^ _779142) ^ [_1504590, _1504592, _1504594] : [class_Orderings_Olinorder(_1504590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504590), _1504592)), -(_1504592 = c_Orderings_Obot__class_Obot(tc_fun(_1504590, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1504590), _1504594), c_Big__Operators_Olattice_OInf__fin(_1504590, c_Orderings_Oord__class_Omin(_1504590), _1504592)) = c_Big__Operators_Olattice_OInf__fin(_1504590, c_Orderings_Oord__class_Omin(_1504590), hAPP(c_Set_OCollect(_1504590), hAPP(hAPP(c_COMBB(tc_fun(_1504590, tc_HOL_Obool), tc_HOL_Obool, _1504590), c_HOL_OEx(_1504590)), hAPP(hAPP(c_COMBC(_1504590, tc_fun(_1504590, tc_HOL_Obool), tc_fun(_1504590, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504590, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1504590, tc_HOL_Obool), tc_fun(_1504590, tc_HOL_Obool)), _1504590), c_COMBS(_1504590, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504590, tc_HOL_Obool), tc_fun(_1504590, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1504590), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504590), c_fconj)), hAPP(hAPP(c_COMBC(_1504590, tc_fun(_1504590, _1504590), tc_fun(_1504590, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504590, tc_HOL_Obool), tc_fun(tc_fun(_1504590, _1504590), tc_fun(_1504590, tc_HOL_Obool)), _1504590), c_COMBB(_1504590, tc_HOL_Obool, _1504590)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1504590), _1504594))))), hAPP(hAPP(c_COMBC(_1504590, tc_fun(_1504590, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504590)), _1504592))))))], (38436 ^ _779142) ^ [_1520723, _1520725, _1520727, _1520729] : [-(hAPP(c_Relation_ORange(_1520723, _1520725), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520723, _1520725), tc_HOL_Obool)), _1520727), _1520729)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520725, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1520723, _1520725), _1520727)), hAPP(c_Relation_ORange(_1520723, _1520725), _1520729)))], (26228 ^ _779142) ^ [_1240412, _1240414] : [class_Int_Onumber__ring(_1240412), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240412), hAPP(c_Int_Onumber__class_Onumber__of(_1240412), 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)))), _1240414)) = c_Groups_Oone__class_Oone(_1240412))], (50029 ^ _779142) ^ [_1790946, _1790948, _1790950] : [c_Fun_Obij__betw(_1790946, _1790948, _1790950, c_Orderings_Otop__class_Otop(tc_fun(_1790946, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790948, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1790946, _1790948, _1790950), c_Orderings_Otop__class_Otop(tc_fun(_1790946, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790948, tc_HOL_Obool)))], (51589 ^ _779142) ^ [_1821344, _1821346, _1821348] : [class_Rings_Olinordered__idom(_1821344), 51592 ^ _779142 : [(51599 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821344), _1821346), _1821348)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821344), hAPP(c_Groups_Oabs__class_Oabs(_1821344), _1821346)), _1821348)))], (51593 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821344), hAPP(c_Groups_Oabs__class_Oabs(_1821344), _1821346)), _1821348)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821344), _1821346), _1821348)))]]], (32819 ^ _779142) ^ [_1378590, _1378592, _1378594, _1378596, _1378598, _1378600] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378590, tc_fun(_1378592, tc_HOL_Obool))), _1378594), _1378596), _1378598), _1378600)), -(hBOOL(hAPP(hAPP(_1378594, _1378598), _1378600)))], (34314 ^ _779142) ^ [_1409448, _1409450, _1409452, _1409454] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1409448, tc_HOL_Obool), tc_fun(_1409450, tc_HOL_Obool)), _1409452), hAPP(hAPP(c_COMBC(tc_fun(_1409448, tc_HOL_Obool), tc_fun(_1409448, tc_fun(_1409450, tc_HOL_Obool)), tc_fun(_1409450, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409448, tc_fun(_1409450, tc_HOL_Obool))), _1409454)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409448, tc_fun(_1409450, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1409448, tc_HOL_Obool), _1409452)), _1409454))], (19307 ^ _779142) ^ [_1118676, _1118678] : [class_Divides_Osemiring__div(_1118676), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1118676), _1118678), c_Groups_Ozero__class_Ozero(_1118676)) = c_Groups_Ozero__class_Ozero(_1118676))], (24562 ^ _779142) ^ [_1211184, _1211186] : [class_Int_Onumber__ring(_1211184), 24565 ^ _779142 : [(24572 ^ _779142) ^ [] : [c_Int_Oiszero(_1211184, hAPP(c_Int_Onumber__class_Onumber__of(_1211184), 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), _1211186)))), -(c_Groups_Oone__class_Oone(_1211184) = hAPP(c_Int_Onumber__class_Onumber__of(_1211184), _1211186))], (24566 ^ _779142) ^ [] : [c_Groups_Oone__class_Oone(_1211184) = hAPP(c_Int_Onumber__class_Onumber__of(_1211184), _1211186), -(c_Int_Oiszero(_1211184, hAPP(c_Int_Onumber__class_Onumber__of(_1211184), 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), _1211186)))))]]], (35043 ^ _779142) ^ [_1430468, _1430470, _1430472, _1430474, _1430476] : [class_Complete__Lattice_Ocomplete__lattice(_1430468), hBOOL(hAPP(hAPP(c_member(_1430470), _1430472), _1430474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430468), hAPP(_1430476, _1430472)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430470, _1430468), _1430474), _1430476))))], (51005 ^ _779142) ^ [_1811631] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811631), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1811631 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (604 ^ _779142) ^ [_788190, _788192, _788194, _788196, _788198, _788200, _788202, _788204, _788206, _788208] : [-(c_List_Olist__all2(_788206, _788202, _788198, _788194, _788190)), c_List_Olist__all2(_788208, _788204, _788200, _788196, _788192), _788208 = _788206, _788204 = _788202, _788200 = _788198, _788196 = _788194, _788192 = _788190], (20991 ^ _779142) ^ [_1148240, _1148242] : [c_Nat__Transfer_Onat__set(_1148240), c_Nat__Transfer_Onat__set(_1148242), 20998 ^ _779142 : [(21005 ^ _779142) ^ [] : [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), _1148240)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1148240), _1148242)))], (20999 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1148240), _1148242)), -(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), _1148240)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148242))))]]], (43496 ^ _779142) ^ [_1648454, _1648456, _1648458, _1648460] : [-(hAPP(hAPP(c_List_Otake(_1648454), _1648456), hAPP(hAPP(c_List_Odrop(_1648454), _1648458), _1648460)) = hAPP(hAPP(c_List_Odrop(_1648454), _1648458), hAPP(hAPP(c_List_Otake(_1648454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648456), _1648458)), _1648460)))], (23429 ^ _779142) ^ [_1191847, _1191849, _1191851] : [class_Groups_Ogroup__add(_1191847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191847), _1191849), _1191851) = c_Groups_Ozero__class_Ozero(_1191847), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1191847), _1191849) = _1191851)], (37922 ^ _779142) ^ [_1502136] : [-(c_Int_Oint__ge__less__than2(_1502136) = 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), _1502136)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (7290 ^ _779142) ^ [_900343, _900345, _900347] : [class_Orderings_Olinorder(_900343), 7293 ^ _779142 : [(7294 ^ _779142) ^ [] : [-(_900345 = _900347), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900343), _900345), _900347))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900343), _900347), _900345)))], (7304 ^ _779142) ^ [] : [7305 ^ _779142 : [(7308 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900343), _900347), _900345))], (7306 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900343), _900345), _900347))]], _900345 = _900347]]], (50899 ^ _779142) ^ [_1809818, _1809820] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809818), _1809820))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809818, _1809820) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (50731 ^ _779142) ^ [_1806405, _1806407, _1806409, _1806411] : [class_Rings_Ocomm__semiring__1(_1806405), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806405), _1806407), _1806409)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806405), _1806407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806405), _1806409), _1806411))))], (48032 ^ _779142) ^ [_1746831, _1746833, _1746835, _1746837, _1746839, _1746841, _1746843] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746831, _1746833, _1746835, _1746837, _1746839, _1746841, _1746843) = c_New__DSequence_Opos__decr__bind(_1746831, _1746833, hAPP(hAPP(hAPP(_1746835, _1746839), _1746841), _1746843), hAPP(hAPP(c_COMBC(_1746831, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746833))), hAPP(hAPP(c_COMBC(_1746831, 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(_1746833)))), hAPP(hAPP(c_COMBC(_1746831, 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(_1746833))))), _1746837), _1746839)), _1746841)), _1746843)))], (38400 ^ _779142) ^ [_1519734, _1519736, _1519738, _1519740] : [hAPP(hAPP(c_Relation_Orel__comp(_1519734, _1519734, _1519734), _1519736), _1519738) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519734, _1519734), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519734, _1519734, _1519734), _1519740), _1519738) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519734, _1519734), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1519734, _1519734, _1519734), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519734, _1519734), tc_HOL_Obool)), _1519736), _1519740)), _1519738) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519734, _1519734), tc_HOL_Obool)))], (38653 ^ _779142) ^ [_1527416, _1527418] : [-(hAPP(c_Relation_ODomain(_1527416, _1527416), c_Relation_OId__on(_1527416, _1527418)) = _1527418)], (52385 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (29269 ^ _779142) ^ [_1298580, _1298582, _1298584] : [29271 ^ _779142 : [(29277 ^ _779142) ^ [] : [-(29270 ^ [_1298580, _1298582, _1298584] = 29273 ^ [_1298580, _1298582, _1298584])], (29275 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298580), 29273 ^ [_1298580, _1298582, _1298584]), _1298584)))], (29272 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298580), 29270 ^ [_1298580, _1298582, _1298584]), _1298582)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298580, tc_HOL_Obool)), _1298582), _1298584) = c_Orderings_Obot__class_Obot(tc_fun(_1298580, tc_HOL_Obool)))], (15353 ^ _779142) ^ [_1048109, _1048111, _1048113] : [class_Orderings_Olinorder(_1048109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048109), _1048111), _1048113)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048109), _1048111), _1048113) = _1048111)], (37079 ^ _779142) ^ [_1478609, _1478611, _1478613, _1478615] : [-(_1478609 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1478611, tc_HOL_Obool), tc_HOL_Obool))), 37085 ^ _779142 : [(37088 ^ _779142) ^ [] : [c_Fun_Oinj__on(_1478611, _1478613, _1478615, 37084 ^ [_1478609, _1478611, _1478613, _1478615])], (37086 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1478611, tc_HOL_Obool)), 37084 ^ [_1478609, _1478611, _1478613, _1478615]), _1478609)))]], -(c_Fun_Oinj__on(_1478611, _1478613, _1478615, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478611, tc_HOL_Obool), _1478609)))], (32059 ^ _779142) ^ [_1360104, _1360106, _1360108, _1360110, _1360112] : [class_Groups_Ocomm__monoid__add(_1360104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360106), _1360108)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360106, _1360104), hAPP(hAPP(c_COMBS(_1360106, _1360104, _1360104), hAPP(hAPP(c_COMBB(_1360104, tc_fun(_1360104, _1360104), _1360106), c_Groups_Oplus__class_Oplus(_1360104)), _1360110)), _1360112)), _1360108) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360104), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360106, _1360104), _1360110), _1360108)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360106, _1360104), _1360112), _1360108)))], (29729 ^ _779142) ^ [_1309005, _1309007, _1309009] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309005), _1309007)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309005), _1309009)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1309005), _1309007)), hAPP(c_Finite__Set_Ocard(_1309005), _1309009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1309005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309005, tc_HOL_Obool)), _1309007), _1309009))), hAPP(c_Finite__Set_Ocard(_1309005), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309005, tc_HOL_Obool)), _1309007), _1309009))))], (13237 ^ _779142) ^ [_1008632, _1008634, _1008636] : [class_Rings_Olinordered__ring(_1008632), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008632), c_Groups_Ozero__class_Ozero(_1008632)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008632), _1008634), _1008634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008632), _1008636), _1008636)))))], (2412 ^ _779142) ^ [_814476, _814478, _814480, _814482, _814484, _814486, _814488, _814490, _814492, _814494] : [-(c_Product__Type_Oprod_Oprod__rec(_814494, _814490, _814486, _814482, _814478) = c_Product__Type_Oprod_Oprod__rec(_814492, _814488, _814484, _814480, _814476)), _814494 = _814492, _814490 = _814488, _814486 = _814484, _814482 = _814480, _814478 = _814476], (21946 ^ _779142) ^ [_1164968, _1164970, _1164972] : [class_Power_Opower(_1164968), class_Rings_Omult__zero(_1164968), class_Rings_Ono__zero__divisors(_1164968), class_Rings_Ozero__neq__one(_1164968), 21961 ^ _779142 : [(21970 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1164968), _1164970), _1164972) = c_Groups_Ozero__class_Ozero(_1164968)), _1164970 = c_Groups_Ozero__class_Ozero(_1164968), -(_1164972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21962 ^ _779142) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1164968), _1164970), _1164972) = c_Groups_Ozero__class_Ozero(_1164968), 21965 ^ _779142 : [(21968 ^ _779142) ^ [] : [_1164972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21966 ^ _779142) ^ [] : [-(_1164970 = c_Groups_Ozero__class_Ozero(_1164968))]]]]], (45819 ^ _779142) ^ [_1700703, _1700705] : [-(c_List_Ofoldr(tc_List_Olist(_1700703), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700703)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700703))), c_List_Otranspose(_1700703, _1700705), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700703))), hAPP(c_List_Ofilter(tc_List_Olist(_1700703), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700703)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700703), tc_List_Olist(_1700703), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700703)))), _1700705)))], (45342 ^ _779142) ^ [_1689235, _1689237] : [-(hBOOL(hAPP(c_List_Odistinct(_1689235), c_List_Oremdups(_1689235, _1689237))))], (31026 ^ _779142) ^ [_1335005, _1335007] : [class_Lattices_Oboolean__algebra(_1335005), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1335005), _1335007), hAPP(c_Groups_Ouminus__class_Ouminus(_1335005), _1335007)) = c_Orderings_Otop__class_Otop(_1335005))], (10083 ^ _779142) ^ [_952294, _952296, _952298] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952296), _952298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952294), _952296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952294), _952298)))], (19627 ^ _779142) ^ [_1124000, _1124002, _1124004] : [class_Divides_Osemiring__div(_1124000), -(_1124002 = c_Groups_Ozero__class_Ozero(_1124000)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124000), _1124004), _1124002)), _1124002) = _1124004)], (37447 ^ _779142) ^ [_1487737, _1487739, _1487741, _1487743] : [-(hAPP(c_Set_OCollect(tc_prod(_1487737, _1487739)), hAPP(c_Product__Type_Oprod_Oprod__case(_1487737, _1487739, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1487737, tc_fun(_1487739, tc_HOL_Obool), tc_fun(_1487739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1487739, tc_HOL_Obool), tc_fun(_1487739, tc_HOL_Obool)), _1487737), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1487739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487737), c_fconj), _1487741))), _1487743))) = hAPP(hAPP(c_Product__Type_OSigma(_1487737, _1487739), hAPP(c_Set_OCollect(_1487737), _1487741)), hAPP(c_COMBK(tc_fun(_1487739, tc_HOL_Obool), _1487737), hAPP(c_Set_OCollect(_1487739), _1487743))))], (21244 ^ _779142) ^ [_1152741, _1152743, _1152745] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1152741), _1152743)), _1152745) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1152741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152743), _1152745)))], (18452 ^ _779142) ^ [_1103979, _1103981, _1103983, _1103985, _1103987] : [class_Groups_Oordered__ab__semigroup__add(_1103979), class_Rings_Osemiring__1(_1103979), 18462 ^ _779142 : [(18465 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103979), hAPP(_1103985, 18461 ^ [_1103979, _1103981, _1103983, _1103985, _1103987])), _1103987))], (18463 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1103981), 18461 ^ [_1103979, _1103981, _1103983, _1103985, _1103987]), _1103983)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103979), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1103981, _1103979), _1103985), _1103983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103979), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103979), hAPP(c_Finite__Set_Ocard(_1103981), _1103983))), _1103987))))], (25312 ^ _779142) ^ [_1223942, _1223944] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223942, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1223944)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223942, 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)))), _1223944)))], (38184 ^ _779142) ^ [_1513411, _1513413, _1513415, _1513417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513411), _1513413)), 38190 ^ _779142 : [(38193 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513415), hAPP(_1513417, 38189 ^ [_1513411, _1513413, _1513415, _1513417])))], (38191 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513411), 38189 ^ [_1513411, _1513413, _1513415, _1513417]), _1513413)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1513411, _1513415)), hAPP(hAPP(c_Product__Type_OSigma(_1513411, _1513415), _1513413), _1513417))))], (43385 ^ _779142) ^ [_1645320, _1645322, _1645324, _1645326, _1645328, _1645330, _1645332] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645320, _1645320)), hAPP(hAPP(c_Product__Type_OPair(_1645320, _1645320), _1645322), _1645324)), _1645326)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645320), tc_List_Olist(_1645320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645320), tc_List_Olist(_1645320)), hAPP(hAPP(c_List_Oappend(_1645320), _1645328), hAPP(hAPP(c_List_Olist_OCons(_1645320), _1645322), _1645330))), hAPP(hAPP(c_List_Oappend(_1645320), _1645328), hAPP(hAPP(c_List_Olist_OCons(_1645320), _1645324), _1645332)))), c_List_Olexord(_1645320, _1645326))))], (29055 ^ _779142) ^ [_1294074, _1294076, _1294078] : [class_Lattices_Olattice(_1294074), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294074), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294074), _1294076), _1294078)), _1294078)))], (25860 ^ _779142) ^ [_1233579] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233579), 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), _1233579), _1233579))], (48188 ^ _779142) ^ [_1750959, _1750961, _1750963, _1750965] : [48190 ^ _779142 : [(48193 ^ _779142) ^ [] : [hBOOL(hAPP(_1750965, 48189 ^ [_1750959, _1750961, _1750963, _1750965]))], (48191 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750959), 48189 ^ [_1750959, _1750961, _1750963, _1750965]), hAPP(c_List_Oset(_1750959), c_List_Oreplicate(_1750959, _1750961, _1750963)))))]], -(hBOOL(hAPP(_1750965, _1750963))), -(_1750961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37243 ^ _779142) ^ [_1482580, _1482582, _1482584, _1482586, _1482588] : [hBOOL(hAPP(hAPP(c_member(_1482580), _1482582), hAPP(c_Set_Ovimage(_1482580, _1482584, _1482586), hAPP(hAPP(c_Set_Oinsert(_1482584), _1482588), c_Orderings_Obot__class_Obot(tc_fun(_1482584, tc_HOL_Obool)))))), -(hAPP(_1482586, _1482582) = _1482588)], (27270 ^ _779142) ^ [_1260335, _1260337, _1260339] : [class_Orderings_Oorder(_1260335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260335), _1260337), _1260339)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1260335, _1260339, _1260337) = c_Orderings_Obot__class_Obot(tc_fun(_1260335, tc_HOL_Obool)))], (45626 ^ _779142) ^ [_1695771, _1695773, _1695775] : [-(hAPP(c_List_Ofilter(_1695771, _1695773), c_List_Oconcat(_1695771, _1695775)) = c_List_Oconcat(_1695771, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695771), tc_List_Olist(_1695771)), c_List_Ofilter(_1695771, _1695773)), _1695775)))], (8214 ^ _779142) ^ [_915629, _915631, _915633, _915635, _915637] : [class_Groups_Oab__group__add(_915629), hBOOL(hAPP(c_Finite__Set_Ofinite(_915631), _915633)), 8221 ^ _779142 : [(8228 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915631), _915635), _915633))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_915631, _915629), _915637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915631, tc_HOL_Obool)), _915633), hAPP(hAPP(c_Set_Oinsert(_915631), _915635), c_Orderings_Obot__class_Obot(tc_fun(_915631, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_915631, _915629), _915637), _915633))], (8222 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_915631), _915635), _915633)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_915631, _915629), _915637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915631, tc_HOL_Obool)), _915633), hAPP(hAPP(c_Set_Oinsert(_915631), _915635), c_Orderings_Obot__class_Obot(tc_fun(_915631, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915629), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_915631, _915629), _915637), _915633)), hAPP(_915637, _915635)))]]], (14363 ^ _779142) ^ [_1029410, _1029412, _1029414] : [class_Fields_Olinordered__field(_1029410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029410), c_Groups_Ozero__class_Ozero(_1029410)), _1029412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029410), c_Groups_Ozero__class_Ozero(_1029410)), _1029414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029410), c_Groups_Ozero__class_Ozero(_1029410)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029410), _1029412), _1029414))))], (24053 ^ _779142) ^ [_1202601, _1202603] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1202601), _1202603))))], (19451 ^ _779142) ^ [_1121234, _1121236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121234)), 19454 ^ _779142 : [(19461 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121236), 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), _1121236), _1121234)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19455 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1121236), _1121234)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121236), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10513 ^ _779142) ^ [_961112] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _961112)], (45282 ^ _779142) ^ [_1687865, _1687867] : [-(c_Enum_On__lists(_1687865, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1687867) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687865)), c_List_Olist_ONil(_1687865)), c_List_Olist_ONil(tc_List_Olist(_1687865))))], (3988 ^ _779142) ^ [_839412, _839414, _839416, _839418, _839420, _839422, _839424, _839426] : [-(c_New__Random__Sequence_Oneg__bind(_839426, _839422, _839418, _839414) = c_New__Random__Sequence_Oneg__bind(_839424, _839420, _839416, _839412)), _839426 = _839424, _839422 = _839420, _839418 = _839416, _839414 = _839412], (11199 ^ _779142) ^ [_971755, _971757] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971755), _971757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971757), _971755) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_971755 = _971757)], (47252 ^ _779142) ^ [_1730068, _1730070, _1730072, _1730074, _1730076] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730068, _1730068)), hAPP(hAPP(c_Product__Type_OPair(_1730068, _1730068), _1730070), _1730072)), c_List_Omeasures(_1730068, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730068, tc_Nat_Onat)), _1730074), _1730076)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730074, _1730070)), hAPP(_1730074, _1730072)))), 47259 ^ _779142 : [(47262 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730068, _1730068)), hAPP(hAPP(c_Product__Type_OPair(_1730068, _1730068), _1730070), _1730072)), c_List_Omeasures(_1730068, _1730076))))], (47260 ^ _779142) ^ [] : [-(hAPP(_1730074, _1730070) = hAPP(_1730074, _1730072))]]], (38595 ^ _779142) ^ [_1526454] : [-(c_Wellfounded_Owf(_1526454, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526454, _1526454), tc_HOL_Obool))))], (10429 ^ _779142) ^ [_959794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _959794))))], (22668 ^ _779142) ^ [_1178420, _1178422, _1178424, _1178426] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1178420, _1178422, _1178424), _1178426), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1178422)], (10661 ^ _779142) ^ [_963368, _963370] : [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), _963368), _963370))), 10664 ^ _779142 : [(10667 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963370)))], (10665 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963368)))]]], (17787 ^ _779142) ^ [_1092565, _1092567] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092565)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092567)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1092565), _1092567)))], (42780 ^ _779142) ^ [_1631537, _1631539, _1631541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631537, tc_HOL_Obool)), hAPP(c_List_Oset(_1631537), c_List_Oremove1(_1631537, _1631539, _1631541))), hAPP(c_List_Oset(_1631537), _1631541))))], (37571 ^ _779142) ^ [_1490939, _1490941, _1490943] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490939, tc_HOL_Obool)), _1490941), _1490943) = hAPP(c_Set_OCollect(_1490939), hAPP(hAPP(c_COMBS(_1490939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490939), c_fconj), hAPP(hAPP(c_COMBC(_1490939, tc_fun(_1490939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490939)), _1490941))), hAPP(hAPP(c_COMBC(_1490939, tc_fun(_1490939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490939)), _1490943))))], (40681 ^ _779142) ^ [_1576404, _1576406, _1576408, _1576410, _1576412] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576404, _1576406)), hAPP(hAPP(c_Product__Type_OPair(_1576404, _1576406), _1576408), _1576410)), hAPP(c_Relation_Oconverse(_1576406, _1576404), _1576412))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576406, _1576404)), hAPP(hAPP(c_Product__Type_OPair(_1576406, _1576404), _1576410), _1576408)), _1576412)))], (44468 ^ _779142) ^ [_1669637, _1669639, _1669641, _1669643, _1669645] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669637), tc_List_Olist(_1669639), tc_List_Olist(_1669641), hAPP(c_List_Omap(_1669637, _1669639), _1669643)), hAPP(c_List_Omap(_1669641, _1669637), _1669645)) = hAPP(c_List_Omap(_1669641, _1669639), hAPP(c_Fun_Ocomp(_1669637, _1669639, _1669641, _1669643), _1669645)))], (34480 ^ _779142) ^ [_1414793, _1414795, _1414797, _1414799] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414793, tc_fun(_1414795, tc_HOL_Obool)), _1414797), _1414799) = c_Orderings_Obot__class_Obot(tc_fun(_1414795, tc_HOL_Obool)), 34483 ^ _779142 : [(34484 ^ _779142) ^ [_1414909] : [hBOOL(hAPP(hAPP(c_member(_1414793), _1414909), _1414797)), -(hAPP(_1414799, _1414909) = c_Orderings_Obot__class_Obot(tc_fun(_1414795, tc_HOL_Obool)))]]], (31719 ^ _779142) ^ [_1348515, _1348517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348515), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1348517)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1348515)) = 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), _1348517), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1348515)))), 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)))], (7980 ^ _779142) ^ [_910558, _910560, _910562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910558, tc_HOL_Obool)), _910560), _910562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910558, tc_HOL_Obool)), _910560), _910562)))], (41451 ^ _779142) ^ [_1597558, _1597560, _1597562, _1597564] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597558), tc_List_Olist(_1597558))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597558), tc_List_Olist(_1597558)), _1597560), _1597562)), c_List_Olex(_1597558, _1597564)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597558), tc_List_Olist(_1597558))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597558), tc_List_Olist(_1597558)), _1597560), _1597562)), c_List_Olexord(_1597558, _1597564))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597558)), _1597560) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597558)), _1597562)], (44440 ^ _779142) ^ [_1668919, _1668921] : [-(hAPP(hAPP(c_List_Omap(_1668919, _1668919), c_COMBI(_1668919)), _1668921) = _1668921)], (42106 ^ _779142) ^ [_1617158, _1617160, _1617162] : [_1617158 = _1617160, 42109 ^ _779142 : [(42112 ^ _779142) ^ [_1617314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617162, _1617162)), _1617314), hAPP(c_List_Oset(tc_prod(_1617162, _1617162)), hAPP(hAPP(c_List_Ozip(_1617162, _1617162), _1617158), _1617160)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617162, _1617162, tc_HOL_Obool), c_fequal), _1617314)))], (42110 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617162)), _1617158) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617162)), _1617160))]]], (14924 ^ _779142) ^ [_1040013, _1040015, _1040017] : [class_Rings_Oring__1(_1040013), hBOOL(hAPP(hAPP(c_member(_1040013), _1040015), c_Int_Oring__1__class_OInts(_1040013))), hBOOL(hAPP(hAPP(c_member(_1040013), _1040017), c_Int_Oring__1__class_OInts(_1040013))), -(hBOOL(hAPP(hAPP(c_member(_1040013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040013), _1040015), _1040017)), c_Int_Oring__1__class_OInts(_1040013))))], (41487 ^ _779142) ^ [_1598610, _1598612, _1598614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool)), _1598612), _1598614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598610), tc_List_Olist(_1598610)), tc_HOL_Obool)), c_List_Olistrel1(_1598610, _1598612)), c_List_Olistrel1(_1598610, _1598614))))], (49328 ^ _779142) ^ [_1776391, _1776393] : [hAPP(c_Relation_Oconverse(_1776391, _1776391), _1776393) = _1776393, -(c_Relation_Osym(_1776391, _1776393))], (50563 ^ _779142) ^ [_1803498] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803498), _1803498)))], (22584 ^ _779142) ^ [_1176817] : [class_Power_Opower(_1176817), -(c_Power_Opower__class_Opower(_1176817) = c_Power_Opower_Opower(_1176817, c_Groups_Oone__class_Oone(_1176817), c_Groups_Otimes__class_Otimes(_1176817)))], (9869 ^ _779142) ^ [_947368, _947370, _947372] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947368), _947370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947368), _947372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947370), _947372))], (41323 ^ _779142) ^ [_1593009, _1593011, _1593013] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593009)), _1593011) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593009)), _1593013)), _1593011 = _1593013], (5432 ^ _779142) ^ [_862250, _862252, _862254, _862256] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862256, _862252) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862254, _862250)), _862256 = _862254, _862252 = _862250], (20037 ^ _779142) ^ [_1130819, _1130821, _1130823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130819)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1130823), _1130819)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130821), _1130823)), _1130819))], (4828 ^ _779142) ^ [_852656, _852658, _852660, _852662] : [-(c_Relation_Oinv__image(_852662, _852658) = c_Relation_Oinv__image(_852660, _852656)), _852662 = _852660, _852658 = _852656], (33405 ^ _779142) ^ [_1390417, _1390419] : [-(_1390417 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390419, _1390417), c_Divides_Odivmod__int(_1390419, _1390417))))], (35525 ^ _779142) ^ [_1443572, _1443574, _1443576] : [class_Rings_Oring__1(_1443572), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443572), 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), _1443574), _1443576)), 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(_1443572), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443572), _1443574)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443572), _1443576)))], (52451 ^ _779142) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (40693 ^ _779142) ^ [_1576744, _1576746, _1576748, _1576750, _1576752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576744, _1576746)), hAPP(hAPP(c_Product__Type_OPair(_1576744, _1576746), _1576748), _1576750)), _1576752)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576746, _1576744)), hAPP(hAPP(c_Product__Type_OPair(_1576746, _1576744), _1576750), _1576748)), hAPP(c_Relation_Oconverse(_1576744, _1576746), _1576752))))], (3124 ^ _779142) ^ [_825550, _825552, _825554, _825556] : [-(c_Big__Operators_Olinorder__class_OMax(_825556, _825552) = c_Big__Operators_Olinorder__class_OMax(_825554, _825550)), _825556 = _825554, _825552 = _825550], (9575 ^ _779142) ^ [_942010, _942012, _942014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942010), _942012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942010), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942012), _942014))))], (7176 ^ _779142) ^ [_897987, _897989, _897991, _897993, _897995, _897997] : [c_Finite__Set_Ofun__left__comm__idem(_897987, _897989, _897991), hBOOL(hAPP(c_Finite__Set_Ofinite(_897987), _897993)), -(hAPP(hAPP(c_Finite__Set_Ofold(_897987, _897989, _897991), _897995), hAPP(hAPP(c_Set_Oinsert(_897987), _897997), _897993)) = hAPP(hAPP(c_Finite__Set_Ofold(_897987, _897989, _897991), hAPP(hAPP(_897991, _897997), _897995)), _897993))], (37691 ^ _779142) ^ [_1494303, _1494305, _1494307, _1494309, _1494311, _1494313] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494303, _1494305)), hAPP(hAPP(c_Product__Type_OPair(_1494303, _1494305), _1494307), _1494309)), hAPP(hAPP(c_Product__Type_OSigma(_1494303, _1494305), _1494311), _1494313)))), hBOOL(hAPP(hAPP(c_member(_1494303), _1494307), _1494311)), hBOOL(hAPP(hAPP(c_member(_1494305), _1494309), hAPP(_1494313, _1494307)))], (15028 ^ _779142) ^ [_1041962, _1041964, _1041966] : [class_Fields_Olinordered__field(_1041962), 15034 ^ _779142 : [(15037 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041962), _1041964), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041962), _1041966), 15033 ^ [_1041962, _1041964, _1041966])))], (15035 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041962), c_Groups_Ozero__class_Ozero(_1041962)), 15033 ^ [_1041962, _1041964, _1041966])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041962), _1041964), _1041966)))], (24926 ^ _779142) ^ [_1217331, _1217333] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217331), _1217333)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217333), _1217331))], (25768 ^ _779142) ^ [_1232023, _1232025] : [class_Int_Onumber__ring(_1232023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232023), c_Groups_Oone__class_Oone(_1232023)), c_Groups_Oone__class_Oone(_1232023))), hAPP(c_Int_Onumber__class_Onumber__of(_1232023), _1232025)) = hAPP(c_Int_Onumber__class_Onumber__of(_1232023), c_Int_OBit0(_1232025)))], (34947 ^ _779142) ^ [_1428082, _1428084, _1428086, _1428088] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428082, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428084, tc_fun(_1428082, tc_HOL_Obool), _1428086), _1428088)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428084, tc_fun(_1428082, tc_HOL_Obool)), _1428088), _1428086))], (19967 ^ _779142) ^ [_1129709, _1129711] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1129709)), hAPP(c_Int_Onat, _1129711)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129709), _1129711))], (25156 ^ _779142) ^ [_1221330, _1221332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221330), _1221332)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221330), hAPP(c_Nat_OSuc, _1221332)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1221332), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221330), _1221332)))], (2762 ^ _779142) ^ [_819975, _819977, _819979, _819981, _819983, _819985, _819987, _819989] : [-(c_Random_Oiterate(_819989, _819985, _819981, _819977) = c_Random_Oiterate(_819987, _819983, _819979, _819975)), _819989 = _819987, _819985 = _819983, _819981 = _819979, _819977 = _819975], (13113 ^ _779142) ^ [_1006389, _1006391, _1006393] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006389), _1006391)), 13116 ^ _779142 : [(13123 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1006389), _1006393), _1006391))), -(hAPP(c_Finite__Set_Ocard(_1006389), hAPP(hAPP(c_Set_Oinsert(_1006389), _1006393), _1006391)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1006389), _1006391)))], (13117 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1006389), _1006393), _1006391)), -(hAPP(c_Finite__Set_Ocard(_1006389), hAPP(hAPP(c_Set_Oinsert(_1006389), _1006393), _1006391)) = hAPP(c_Finite__Set_Ocard(_1006389), _1006391))]]], (33097 ^ _779142) ^ [] : [-(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)))))], (45665 ^ _779142) ^ [_1696649, _1696651, _1696653, _1696655] : [-(hAPP(c_List_Ofilter(_1696649, _1696651), hAPP(c_List_Ofilter(_1696649, _1696653), _1696655)) = hAPP(c_List_Ofilter(_1696649, hAPP(hAPP(c_COMBS(_1696649, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696649), c_fconj), _1696653)), _1696651)), _1696655))], (6145 ^ _779142) ^ [_877413, _877415, _877417, _877419, _877421, _877423, _877425, _877427] : [c_Finite__Set_Ofolding__image__simple__idem(_877413, _877415, _877417, _877419, _877421, _877423), hBOOL(hAPP(c_Finite__Set_Ofinite(_877415), _877425)), hBOOL(hAPP(hAPP(c_member(_877415), _877427), _877425)), -(hAPP(hAPP(_877417, hAPP(_877421, _877427)), hAPP(_877423, _877425)) = hAPP(_877423, _877425))], (24904 ^ _779142) ^ [_1216976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1216976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1216976))))], (9003 ^ _779142) ^ [_931268, _931270, _931272, _931274, _931276] : [class_Groups_Ocomm__monoid__mult(_931268), hBOOL(hAPP(c_Finite__Set_Ofinite(_931270), _931272)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_931270, _931268), _931274), hAPP(hAPP(c_Set_Oinsert(_931270), _931276), _931272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931268), hAPP(_931274, _931276)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_931270, _931268), _931274), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931270, tc_HOL_Obool)), _931272), hAPP(hAPP(c_Set_Oinsert(_931270), _931276), c_Orderings_Obot__class_Obot(tc_fun(_931270, tc_HOL_Obool)))))))], (9063 ^ _779142) ^ [_932606, _932608, _932610, _932612, _932614, _932616] : [class_Rings_Oordered__ring(_932606), 9066 ^ _779142 : [(9073 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932606), _932608), _932614)), _932610)), _932612)), _932616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), _932608), _932610)), _932612)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), _932614), _932610)), _932616))))], (9067 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), _932608), _932610)), _932612)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), _932614), _932610)), _932616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932606), _932608), _932614)), _932610)), _932612)), _932616)))]]], (18632 ^ _779142) ^ [_1107133, _1107135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107133), _1107135)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107133, _1107135) = _1107133)], (46009 ^ _779142) ^ [_1704659, _1704661, _1704663, _1704665] : [class_Groups_Ocomm__monoid__add(_1704659), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704659), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704659), _1704661), c_List_Oupt(_1704663, _1704665))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704659), _1704661), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704663, _1704665))))], (7422 ^ _779142) ^ [_901988, _901990, _901992] : [class_Orderings_Oorder(_901988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901988), _901990), _901992)), _901992 = _901990], (37910 ^ _779142) ^ [_1501479] : [-(c_Wellfounded_Ofinite__psubset(_1501479) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1501479, tc_HOL_Obool), tc_fun(_1501479, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1501479, tc_HOL_Obool), tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1501479, tc_HOL_Obool), tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1501479, tc_HOL_Obool)), c_COMBS(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501479, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1501479, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1501479, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1501479, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1501479)))))], (1576 ^ _779142) ^ [_801784, _801786] : [-(class_Groups_Oordered__ab__semigroup__add(_801784)), _801786 = _801784, class_Groups_Oordered__ab__semigroup__add(_801786)], (34170 ^ _779142) ^ [_1406144, _1406146, _1406148, _1406150, _1406152] : [-(hAPP(c_Product__Type_Ofst(_1406144, _1406146), hAPP(c_Product__Type_Oapfst(_1406148, _1406144, _1406146, _1406150), _1406152)) = hAPP(_1406150, hAPP(c_Product__Type_Ofst(_1406148, _1406146), _1406152)))], (47016 ^ _779142) ^ [_1724725, _1724727, _1724729, _1724731, _1724733] : [-(c_List_OdropWhile(_1724725, _1724727, hAPP(hAPP(c_List_Omap(_1724729, _1724725), _1724731), _1724733)) = hAPP(hAPP(c_List_Omap(_1724729, _1724725), _1724731), c_List_OdropWhile(_1724729, hAPP(c_Fun_Ocomp(_1724725, tc_HOL_Obool, _1724729, _1724727), _1724731), _1724733)))], (21082 ^ _779142) ^ [_1149889] : [-(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)), _1149889)))], (25644 ^ _779142) ^ [_1229859] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229859))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1229859)))))], (45925 ^ _779142) ^ [_1703078] : [-(c_List_Oupt(_1703078, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (43530 ^ _779142) ^ [_1649231, _1649233] : [-(hAPP(hAPP(c_List_Odrop(_1649231), _1649233), c_List_Olist_ONil(_1649231)) = c_List_Olist_ONil(_1649231))], (34122 ^ _779142) ^ [_1404942, _1404944, _1404946, _1404948, _1404950] : [class_Groups_Oordered__ab__group__add(_1404942), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404944), _1404946)), 34132 ^ _779142 : [(34135 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404942), c_Groups_Ozero__class_Ozero(_1404942)), hAPP(_1404948, 34131 ^ [_1404942, _1404944, _1404946, _1404948, _1404950])))], (34133 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404944), 34131 ^ [_1404942, _1404944, _1404946, _1404948, _1404950]), _1404946)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404944, _1404942), _1404948), _1404946) = c_Groups_Ozero__class_Ozero(_1404942), hBOOL(hAPP(hAPP(c_member(_1404944), _1404950), _1404946)), -(hAPP(_1404948, _1404950) = c_Groups_Ozero__class_Ozero(_1404942))], (21906 ^ _779142) ^ [_1164242, _1164244] : [class_Groups_Omonoid__mult(_1164242), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164242), _1164244), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1164244)], (42946 ^ _779142) ^ [_1635288, _1635290, _1635292, _1635294, _1635296] : [_1635288 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635290, _1635292, _1635294), _1635288), _1635296) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635292), _1635290), c_List_Olist_ONil(_1635292)), _1635296))], (16507 ^ _779142) ^ [_1069683, _1069685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069683), _1069685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1069685), _1069683)), -(_1069683 = _1069685)], (25536 ^ _779142) ^ [_1227934, _1227936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227934), _1227936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1227934)), c_Int_OBit1(_1227936))))], (48456 ^ _779142) ^ [_1756247, _1756249, _1756251, _1756253, _1756255] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756247, _1756249, _1756251, _1756253, _1756255) = c_Option_Ooption_Ooption__case(_1756247, tc_prod(_1756249, tc_Lazy__Sequence_Olazy__sequence(_1756249)), _1756251, hAPP(c_Product__Type_Oprod_Oprod__case(_1756249, tc_Lazy__Sequence_Olazy__sequence(_1756249), _1756247), _1756253), hAPP(c_Lazy__Sequence_Oyield(_1756249), _1756255)))], (25826 ^ _779142) ^ [] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (25844 ^ _779142) ^ [_1233298] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1233298), 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, _1233298)))], (29538 ^ _779142) ^ [_1304753, _1304755, _1304757, _1304759] : [class_Orderings_Oorder(_1304753), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304753, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1304753, _1304755, _1304757)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1304753, _1304757, _1304759)) = c_Orderings_Obot__class_Obot(tc_fun(_1304753, tc_HOL_Obool)))], (12816 ^ _779142) ^ [_1000793, _1000795, _1000797, _1000799] : [class_Rings_Olinordered__semiring__strict(_1000793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000793), _1000795), _1000797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000793), _1000795), _1000799))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000793), c_Groups_Ozero__class_Ozero(_1000793)), _1000795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000793), _1000797), _1000799)))], (19137 ^ _779142) ^ [_1115498] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115498)))), -(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), _1115498)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115498))))], (45043 ^ _779142) ^ [_1682431, _1682433, _1682435, _1682437, _1682439, _1682441, _1682443] : [c_List_Olist__all2(_1682431, _1682433, _1682435, hAPP(hAPP(c_List_Omap(_1682437, _1682431), _1682439), _1682441), _1682443), -(c_List_Olist__all2(_1682437, _1682433, hAPP(hAPP(c_COMBB(_1682431, tc_fun(_1682433, tc_HOL_Obool), _1682437), _1682435), _1682439), _1682441, _1682443))], (8605 ^ _779142) ^ [_923638, _923640, _923642, _923644] : [class_Groups_Ocancel__semigroup__add(_923638), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923638), _923640), _923642) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923638), _923640), _923644), -(_923642 = _923644)], (25296 ^ _779142) ^ [_1223596, _1223598] : [class_Int_Onumber__ring(_1223596), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223596), hAPP(c_Int_Onumber__class_Onumber__of(_1223596), _1223598)), c_Groups_Oone__class_Oone(_1223596)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223598), c_Int_OBit1(c_Int_OPls))))], (4202 ^ _779142) ^ [_842717, _842719, _842721, _842723] : [-(c_List_Oconcat(_842723, _842719) = c_List_Oconcat(_842721, _842717)), _842723 = _842721, _842719 = _842717], (51565 ^ _779142) ^ [_1820949, _1820951] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820949), _1820951)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820951), _1820949))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820951), _1820949)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820949), _1820951)))], (10477 ^ _779142) ^ [_960540, _960542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960540), hAPP(c_Nat_OSuc, _960542)))), 10478 ^ _779142 : [(10481 ^ _779142) ^ [_960628] : [_960540 = hAPP(c_Nat_OSuc, _960628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960628), _960542))], (10479 ^ _779142) ^ [] : [_960540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51881 ^ _779142) ^ [_1826613, _1826615, _1826617, _1826619] : [class_Rings_Ocomm__semiring__1(_1826613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826615), _1826617)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826613), hAPP(hAPP(c_Power_Opower__class_Opower(_1826613), _1826619), _1826615)), hAPP(hAPP(c_Power_Opower__class_Opower(_1826613), _1826619), _1826617))))], (37904 ^ _779142) ^ [_1501272, _1501274] : [-(hAPP(c_Set_OPow(_1501272), _1501274) = hAPP(c_Set_OCollect(tc_fun(_1501272, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1501272, tc_HOL_Obool), tc_fun(_1501272, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1501272, tc_HOL_Obool))), _1501274)))], (26894 ^ _779142) ^ [_1253301, _1253303, _1253305] : [-(hAPP(hAPP(c_Set_Oinsert(_1253301), _1253303), _1253305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253301, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1253301), _1253303), c_Orderings_Obot__class_Obot(tc_fun(_1253301, tc_HOL_Obool)))), _1253305))], (43816 ^ _779142) ^ [_1655545, _1655547, _1655549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655545)), _1655547)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1655545, _1655549), _1655547) = _1655547)], (2488 ^ _779142) ^ [_815652, _815654, _815656, _815658] : [-(c_Set_Othe__elem(_815658, _815654) = c_Set_Othe__elem(_815656, _815652)), _815658 = _815656, _815654 = _815652], (43510 ^ _779142) ^ [_1648828, _1648830, _1648832, _1648834] : [hBOOL(hAPP(hAPP(c_member(_1648828), _1648830), hAPP(c_List_Oset(_1648828), hAPP(hAPP(c_List_Odrop(_1648828), _1648832), _1648834)))), -(hBOOL(hAPP(hAPP(c_member(_1648828), _1648830), hAPP(c_List_Oset(_1648828), _1648834))))], (37773 ^ _779142) ^ [_1496650, _1496652, _1496654, _1496656] : [_1496650 = c_Orderings_Obot__class_Obot(tc_fun(_1496652, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1496652, _1496654), _1496654, c_Product__Type_Osnd(_1496652, _1496654)), hAPP(hAPP(c_Product__Type_OSigma(_1496652, _1496654), _1496650), hAPP(c_COMBK(tc_fun(_1496654, tc_HOL_Obool), _1496652), _1496656))) = c_Orderings_Obot__class_Obot(tc_fun(_1496654, tc_HOL_Obool)))], (18370 ^ _779142) ^ [_1102655, _1102657, _1102659, _1102661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102657), _1102659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102659), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102657), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1102661, _1102655))), _1102659)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40763 ^ _779142) ^ [_1578333, _1578335, _1578337] : [c_Relation_Orefl__on(_1578333, _1578335, _1578337), -(c_Relation_Orefl__on(_1578333, _1578335, hAPP(c_Relation_Oconverse(_1578333, _1578333), _1578337)))], (10977 ^ _779142) ^ [_968576, _968578, _968580] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_968576), 10980 ^ _779142 : [(10987 ^ _779142) ^ [] : [_968580 = c_Groups_Ozero__class_Ozero(_968576), -(_968578 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968576), _968578), _968580))], (10981 ^ _779142) ^ [] : [_968578 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968576), _968578), _968580), -(_968580 = c_Groups_Ozero__class_Ozero(_968576))]]], (42854 ^ _779142) ^ [_1633108, _1633110] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633108)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633110)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633108), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633110)) = c_List_Olist_ONil(tc_Int_Oint))], (43331 ^ _779142) ^ [_1644038, _1644040, _1644042] : [-(hBOOL(hAPP(c_List_Odistinct(_1644038), hAPP(hAPP(c_List_Oappend(_1644038), _1644040), _1644042)))), hBOOL(hAPP(c_List_Odistinct(_1644038), _1644040)), hBOOL(hAPP(c_List_Odistinct(_1644038), _1644042)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644038, tc_HOL_Obool)), hAPP(c_List_Oset(_1644038), _1644040)), hAPP(c_List_Oset(_1644038), _1644042)) = c_Orderings_Obot__class_Obot(tc_fun(_1644038, tc_HOL_Obool))], (6243 ^ _779142) ^ [_879188, _879190, _879192] : [_879188 = _879190, 6246 ^ _779142 : [(6249 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879192, tc_HOL_Obool)), _879190), _879188)))], (6247 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879192, tc_HOL_Obool)), _879188), _879190)))]]], (20898 ^ _779142) ^ [_1146611, _1146613, _1146615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146611)), 20901 ^ _779142 : [(20902 ^ _779142) ^ [] : [-(_1146613 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146615), _1146611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146611), _1146613)), _1146615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146611), hAPP(c_Nat_OSuc, _1146613))))], (20912 ^ _779142) ^ [] : [_1146613 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146615), _1146611), 20915 ^ _779142 : [(20918 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146611), hAPP(c_Nat_OSuc, _1146613)))))], (20916 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146611), _1146613)), _1146615)))]]]]], (20101 ^ _779142) ^ [_1131973, _1131975] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131973), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131975), _1131973)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1131975), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131975, _1131973)))], (28024 ^ _779142) ^ [_1273978, _1273980, _1273982] : [class_Orderings_Olinorder(_1273978), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273978), _1273980), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273978), _1273980), _1273982)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273978), _1273980), _1273982))], (45010 ^ _779142) ^ [_1681488, _1681490, _1681492] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681488)), _1681492), c_List_Olists(_1681488, _1681490))), -(hBOOL(hAPP(c_List_Olistsp(_1681488, hAPP(hAPP(c_COMBC(_1681488, tc_fun(_1681488, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681488)), _1681490)), _1681492)))], (48737 ^ _779142) ^ [_1762946, _1762948, _1762950, _1762952, _1762954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762946), tc_List_Olist(_1762946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762946), tc_List_Olist(_1762946)), _1762948), _1762950)), c_List_Olexord(_1762946, _1762952))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762946), tc_List_Olist(_1762946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762946), tc_List_Olist(_1762946)), _1762950), _1762954)), c_List_Olexord(_1762946, _1762952))), c_Relation_Otrans(_1762946, _1762952), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762946), tc_List_Olist(_1762946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762946), tc_List_Olist(_1762946)), _1762948), _1762954)), c_List_Olexord(_1762946, _1762952))))], (20390 ^ _779142) ^ [_1136961, _1136963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136961), _1136963)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1136963), _1136961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1136963)), hAPP(c_Int_Onat, _1136961)))], (35535 ^ _779142) ^ [_1443874] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1443874)) = _1443874)], (50232 ^ _779142) ^ [_1794919, _1794921] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1794919), _1794921)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1794919, 50235 ^ [_1794919, _1794921], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1794919), _1794921)), _1794921))], (25960 ^ _779142) ^ [_1235362, _1235364] : [class_Rings_Olinordered__idom(_1235362), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235362), c_Groups_Ozero__class_Ozero(_1235362)), hAPP(hAPP(c_Power_Opower__class_Opower(_1235362), _1235364), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (4456 ^ _779142) ^ [_846752, _846754, _846756, _846758, _846760, _846762] : [-(c_FunDef_OTHE__default(_846762, _846758, _846754) = c_FunDef_OTHE__default(_846760, _846756, _846752)), _846762 = _846760, _846758 = _846756, _846754 = _846752], (44175 ^ _779142) ^ [_1662918, _1662920, _1662922] : [-(_1662918 = c_List_Olist_ONil(_1662920)), -(c_List_Olast(_1662920, hAPP(hAPP(c_List_Olist_OCons(_1662920), _1662922), _1662918)) = c_List_Olast(_1662920, _1662918))], (45500 ^ _779142) ^ [_1692154, _1692156, _1692158, _1692160] : [class_Orderings_Olinorder(_1692154), 45503 ^ _779142 : [(45510 ^ _779142) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692156), _1692160)), -(hBOOL(hAPP(c_List_Odistinct(_1692156), c_List_Olinorder__class_Osort__key(_1692156, _1692154, _1692158, _1692160))))], (45504 ^ _779142) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692156), c_List_Olinorder__class_Osort__key(_1692156, _1692154, _1692158, _1692160))), -(hBOOL(hAPP(c_List_Odistinct(_1692156), _1692160)))]]], (42672 ^ _779142) ^ [_1629639, _1629641] : [-(c_List_Osublist(_1629639, c_List_Olist_ONil(_1629639), _1629641) = c_List_Olist_ONil(_1629639))], (26846 ^ _779142) ^ [_1252254, _1252256, _1252258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252254, tc_HOL_Obool)), _1252256), _1252258)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252254, tc_HOL_Obool)), _1252256), _1252258) = _1252258)], (43804 ^ _779142) ^ [_1655248, _1655250, _1655252] : [-(hAPP(hAPP(c_List_Odrop(_1655248), hAPP(c_Nat_OSuc, _1655250)), _1655252) = hAPP(hAPP(c_List_Odrop(_1655248), _1655250), hAPP(c_List_Otl(_1655248), _1655252)))], (46832 ^ _779142) ^ [_1720944, _1720946, _1720948] : [46834 ^ _779142 : [(46837 ^ _779142) ^ [] : [hBOOL(hAPP(_1720946, 46833 ^ [_1720944, _1720946, _1720948]))], (46835 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720944), 46833 ^ [_1720944, _1720946, _1720948]), hAPP(c_List_Oset(_1720944), _1720948))))]], -(c_List_OtakeWhile(_1720944, _1720946, _1720948) = _1720948)], (40789 ^ _779142) ^ [_1578828, _1578830] : [-(c_Relation_Ototal__on(_1578828, c_Orderings_Obot__class_Obot(tc_fun(_1578828, tc_HOL_Obool)), _1578830))], (44962 ^ _779142) ^ [_1680519, _1680521, _1680523, _1680525] : [hBOOL(hAPP(c_List_Olistsp(_1680519, _1680521), hAPP(hAPP(c_List_Olist_OCons(_1680519), _1680523), _1680525))), 44965 ^ _779142 : [(44968 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680519, _1680521), _1680525)))], (44966 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1680521, _1680523)))]]], (23671 ^ _779142) ^ [_1196088] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196088)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1196088), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1196088)))], (44355 ^ _779142) ^ [_1666662, _1666664, _1666666, _1666668, _1666670, _1666672] : [-(hAPP(hAPP(c_List_Omap(_1666662, _1666664), _1666666), hAPP(hAPP(c_List_Olist__update(_1666662, _1666668), _1666670), _1666672)) = hAPP(hAPP(c_List_Olist__update(_1666664, hAPP(hAPP(c_List_Omap(_1666662, _1666664), _1666666), _1666668)), _1666670), hAPP(_1666666, _1666672)))], (1706 ^ _779142) ^ [_803409, _803411] : [-(class_Groups_Ocomm__monoid__add(_803409)), _803411 = _803409, class_Groups_Ocomm__monoid__add(_803411)], (36598 ^ _779142) ^ [_1467755, _1467757, _1467759, _1467761, _1467763, _1467765] : [c_Fun_Oinj__on(_1467755, _1467757, _1467759, _1467761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467755, tc_HOL_Obool)), _1467763), _1467761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467755, tc_HOL_Obool)), _1467765), _1467761)), -(hAPP(c_Set_Oimage(_1467755, _1467757, _1467759), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467755, tc_HOL_Obool)), _1467763), _1467765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467757, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467755, _1467757, _1467759), _1467763)), hAPP(c_Set_Oimage(_1467755, _1467757, _1467759), _1467765)))], (52339 ^ _779142) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (33855 ^ _779142) ^ [_1399151, _1399153, _1399155, _1399157, _1399159] : [-(hAPP(c_Product__Type_Ofst(_1399151, _1399153), hAPP(c_Product__Type_Oapsnd(_1399155, _1399153, _1399151, _1399157), _1399159)) = hAPP(c_Product__Type_Ofst(_1399151, _1399155), _1399159))], (43880 ^ _779142) ^ [_1656957, _1656959] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656957), _1656959) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43883 ^ _779142 : [(43886 ^ _779142) ^ [_1657071] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1657071), hAPP(c_List_Oset(tc_Nat_Onat), _1656959))), -(_1657071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43884 ^ _779142) ^ [] : [-(_1656957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37451 ^ _779142) ^ [_1487912, _1487914] : [c_Orderings_Obot__class_Obot(tc_fun(_1487912, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1487912), _1487914), 37454 ^ _779142 : [(37455 ^ _779142) ^ [_1487997] : [hBOOL(hAPP(_1487914, _1487997))]]], (25302 ^ _779142) ^ [_1223723, _1223725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1223723)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1223725)), _1223723) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223723), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (522 ^ _779142) ^ [_786957, _786959] : [-(class_Lattices_Oab__semigroup__idem__mult(_786957)), _786959 = _786957, class_Lattices_Oab__semigroup__idem__mult(_786959)], (1032 ^ _779142) ^ [_794698, _794700, _794702, _794704, _794706, _794708] : [-(c_List_Olist__ex(_794706, _794702, _794698)), c_List_Olist__ex(_794708, _794704, _794700), _794708 = _794706, _794704 = _794702, _794700 = _794698], (49544 ^ _779142) ^ [_1779996, _1779998] : [c_Equiv__Relations_Oequivp(_1779996, _1779998), -(c_Equiv__Relations_Opart__equivp(_1779996, _1779998))], (31901 ^ _779142) ^ [_1354188, _1354190, _1354192] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354188, tc_Nat_Onat), _1354190), _1354192)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354188, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1354188), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1354190)), _1354192))], (24311 ^ _779142) ^ [_1206995, _1206997, _1206999] : [class_Rings_Oring__1(_1206995), -(hAPP(c_Int_Oring__1__class_Oof__int(_1206995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206997), _1206999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206995), hAPP(c_Int_Oring__1__class_Oof__int(_1206995), _1206997)), hAPP(c_Int_Oring__1__class_Oof__int(_1206995), _1206999)))], (39409 ^ _779142) ^ [_1545685, _1545687, _1545689, _1545691, _1545693, _1545695] : [c_Fun_Oinj__on(_1545685, _1545687, hAPP(c_Fun_Ocomp(_1545689, _1545687, _1545685, _1545691), _1545693), _1545695), -(c_Fun_Oinj__on(_1545685, _1545689, _1545693, _1545695))], (18446 ^ _779142) ^ [_1103924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103924), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103924)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1103924)))], (26142 ^ _779142) ^ [_1238604, _1238606, _1238608] : [class_Rings_Olinordered__idom(_1238604), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238604), c_Groups_Ozero__class_Ozero(_1238604)), hAPP(hAPP(c_Power_Opower__class_Opower(_1238604), _1238606), 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)))), _1238608)))))], (7154 ^ _779142) ^ [_897462, _897464, _897466] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897462), _897464)), hBOOL(hAPP(_897466, _897464)), 7165 ^ _779142 : [(7168 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897462), 7163 ^ [_897462, _897464, _897466]), 7164 ^ [_897462, _897464, _897466])))], (7170 ^ _779142) ^ [] : [-(hBOOL(hAPP(_897466, 7164 ^ [_897462, _897464, _897466])))], (7172 ^ _779142) ^ [] : [hBOOL(hAPP(_897466, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897462, tc_HOL_Obool)), 7164 ^ [_897462, _897464, _897466]), hAPP(hAPP(c_Set_Oinsert(_897462), 7163 ^ [_897462, _897464, _897466]), c_Orderings_Obot__class_Obot(tc_fun(_897462, tc_HOL_Obool))))))], (7166 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_897462), 7164 ^ [_897462, _897464, _897466])))]], -(hBOOL(hAPP(_897466, c_Orderings_Obot__class_Obot(tc_fun(_897462, tc_HOL_Obool)))))], (31412 ^ _779142) ^ [_1342514] : [class_Complete__Lattice_Ocomplete__lattice(_1342514), -(c_Complete__Lattice_OInf__class_OInf(_1342514, c_Orderings_Obot__class_Obot(tc_fun(_1342514, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1342514))], (35296 ^ _779142) ^ [_1436742] : [-(hAPP(c_Int_Onat, _1436742) = 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, _1436742)), 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)))))))], (52235 ^ _779142) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (26696 ^ _779142) ^ [_1249313, _1249315, _1249317, _1249319] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249313, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249313, tc_HOL_Obool)), _1249315), _1249317)), _1249319) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249313, tc_HOL_Obool)), _1249315), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249313, tc_HOL_Obool)), _1249317), _1249319)))], (15617 ^ _779142) ^ [_1052962, _1052964] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1052962)), hAPP(c_Nat_OSuc, _1052964)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1052962), _1052964)))], (42145 ^ _779142) ^ [_1618199, _1618201, _1618203, _1618205, _1618207, _1618209] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618199, _1618201)), hAPP(hAPP(c_Product__Type_OPair(_1618199, _1618201), _1618203), _1618205)), hAPP(c_List_Oset(tc_prod(_1618199, _1618201)), hAPP(hAPP(c_List_Ozip(_1618199, _1618201), _1618207), _1618209)))), -(hBOOL(hAPP(hAPP(c_member(_1618199), _1618203), hAPP(c_List_Oset(_1618199), _1618207))))], (7494 ^ _779142) ^ [_903111, _903113, _903115, _903117] : [class_Orderings_Oorder(_903111), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903111), _903113), _903115)), _903113 = _903117, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903111), _903117), _903115)))], (35726 ^ _779142) ^ [_1448800, _1448802, _1448804] : [c_Equiv__Relations_Oequiv(_1448800, _1448802, _1448804), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1448800, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448800), _1448802), _1448804)) = _1448802)], (48272 ^ _779142) ^ [_1752521, _1752523, _1752525, _1752527] : [hBOOL(hAPP(_1752521, _1752523)), -(hAPP(c_List_Ofilter(_1752525, _1752521), c_List_Oreplicate(_1752525, _1752527, _1752523)) = c_List_Oreplicate(_1752525, _1752527, _1752523))], (37575 ^ _779142) ^ [_1491147, _1491149, _1491151, _1491153, _1491155] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491147, _1491149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491147, tc_HOL_Obool)), _1491151), _1491153)), hAPP(c_COMBK(tc_fun(_1491149, tc_HOL_Obool), _1491147), _1491155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491147, _1491149), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491147, _1491149), _1491151), hAPP(c_COMBK(tc_fun(_1491149, tc_HOL_Obool), _1491147), _1491155))), hAPP(hAPP(c_Product__Type_OSigma(_1491147, _1491149), _1491153), hAPP(c_COMBK(tc_fun(_1491149, tc_HOL_Obool), _1491147), _1491155))))], (18917 ^ _779142) ^ [_1111960] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1111960) = c_Int_Opred(_1111960))], (2682 ^ _779142) ^ [_818697, _818699] : [_818699 = _818697, -(c_HOL_OAll(_818699) = c_HOL_OAll(_818697))], (11402 ^ _779142) ^ [_975212, _975214, _975216] : [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, _975212)), _975214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _975212)), _975216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975214), _975216)))], (6966 ^ _779142) ^ [_893351, _893353] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893351, tc_HOL_Obool)), _893353), c_Orderings_Obot__class_Obot(tc_fun(_893351, tc_HOL_Obool))) = _893353)], (40735 ^ _779142) ^ [_1577793, _1577795, _1577797] : [c_Relation_Ototal__on(_1577793, _1577795, _1577797), -(c_Relation_Ototal__on(_1577793, _1577795, hAPP(c_Relation_Oconverse(_1577793, _1577793), _1577797)))], (22564 ^ _779142) ^ [_1176409, _1176411, _1176413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176409)), 22567 ^ _779142 : [(22568 ^ _779142) ^ [_1176543] : [22570 ^ _779142 : [(22576 ^ _779142) ^ [] : [-(_1176543 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22572 ^ [_1176409, _1176411, _1176413, _1176543]), 22569 ^ [_1176409, _1176411, _1176413, _1176543]))], (22574 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22572 ^ [_1176409, _1176411, _1176413, _1176543]), _1176411)))], (22571 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22569 ^ [_1176409, _1176411, _1176413, _1176543]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1176409))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176413), _1176543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176543), _1176409))))]]], (38502 ^ _779142) ^ [_1523828, _1523830, _1523832, _1523834, _1523836, _1523838, _1523840] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523828, _1523832)), hAPP(hAPP(c_Product__Type_OPair(_1523828, _1523832), _1523838), _1523840)), hAPP(hAPP(c_Relation_Orel__comp(_1523828, _1523830, _1523832), _1523834), _1523836))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1523828, _1523830, _1523832, hAPP(hAPP(c_COMBC(_1523828, tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_fun(_1523830, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523830, tc_fun(tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_fun(_1523830, tc_HOL_Obool)), _1523828), c_COMBC(_1523830, tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523830, tc_prod(_1523828, _1523830)), tc_fun(_1523830, tc_fun(tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_HOL_Obool)), _1523828), hAPP(c_COMBB(tc_prod(_1523828, _1523830), tc_fun(tc_fun(tc_prod(_1523828, _1523830), tc_HOL_Obool), tc_HOL_Obool), _1523830), c_member(tc_prod(_1523828, _1523830)))), c_Product__Type_OPair(_1523828, _1523830)))), _1523834), hAPP(hAPP(c_COMBC(_1523830, tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_fun(_1523832, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523832, tc_fun(tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_fun(_1523832, tc_HOL_Obool)), _1523830), c_COMBC(_1523832, tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523832, tc_prod(_1523830, _1523832)), tc_fun(_1523832, tc_fun(tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_HOL_Obool)), _1523830), hAPP(c_COMBB(tc_prod(_1523830, _1523832), tc_fun(tc_fun(tc_prod(_1523830, _1523832), tc_HOL_Obool), tc_HOL_Obool), _1523832), c_member(tc_prod(_1523830, _1523832)))), c_Product__Type_OPair(_1523830, _1523832)))), _1523836)), _1523838), _1523840)))], (43508 ^ _779142) ^ [_1648788, _1648790] : [-(hAPP(c_List_Oset(_1648788), hAPP(c_List_Orotate1(_1648788), _1648790)) = hAPP(c_List_Oset(_1648788), _1648790))], (30880 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14059 ^ _779142) ^ [_1024057, _1024059, _1024061] : [class_Fields_Olinordered__field(_1024057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024057), c_Groups_Ozero__class_Ozero(_1024057)), _1024059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024057), c_Groups_Ozero__class_Ozero(_1024057)), _1024061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024057), c_Groups_Ozero__class_Ozero(_1024057)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024057), _1024059), _1024061))))], (32377 ^ _779142) ^ [_1368956] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1368956) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1368956), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (42259 ^ _779142) ^ [_1620762, _1620764, _1620766, _1620768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620762)), _1620764)), _1620766)), -(hAPP(hAPP(c_List_Olist__update(_1620762, _1620764), _1620766), _1620768) = _1620764)], (24447 ^ _779142) ^ [_1209301, _1209303] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1209301), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1209303) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1209301, _1209303))], (42367 ^ _779142) ^ [_1623109, _1623111] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623109)), c_List_Obutlast(_1623109, _1623111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623109)), _1623111)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7052 ^ _779142) ^ [_895405, _895407, _895409] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_895405, _895407, c_Orderings_Obot__class_Obot(tc_fun(_895405, tc_HOL_Obool))), _895409))], (27502 ^ _779142) ^ [_1264540, _1264542] : [_1264540 = _1264542, -(c_Code__Numeral_OSuc__code__numeral(_1264540) = c_Code__Numeral_OSuc__code__numeral(_1264542))], (22190 ^ _779142) ^ [_1169366, _1169368, _1169370, _1169372] : [class_Rings_Olinordered__semidom(_1169366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169368), _1169370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169366), c_Groups_Oone__class_Oone(_1169366)), _1169372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169366), hAPP(hAPP(c_Power_Opower__class_Opower(_1169366), _1169372), _1169368)), hAPP(hAPP(c_Power_Opower__class_Opower(_1169366), _1169372), _1169370))))], (27438 ^ _779142) ^ [_1263325, _1263327, _1263329] : [class_Orderings_Olinorder(_1263325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263325), _1263327), _1263329)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263325, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1263325, _1263327, _1263329)), hAPP(hAPP(c_Set_Oinsert(_1263325), _1263329), c_Orderings_Obot__class_Obot(tc_fun(_1263325, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1263325, _1263327, _1263329))], (15475 ^ _779142) ^ [_1050185, _1050187, _1050189, _1050191] : [class_Orderings_Olinorder(_1050185), 15478 ^ _779142 : [(15487 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1050185), _1050189), _1050191)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), _1050189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), _1050191))], (15479 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1050185), _1050189), _1050191))), 15482 ^ _779142 : [(15485 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), _1050191)))], (15483 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050185), _1050187), _1050189)))]]]]], (47930 ^ _779142) ^ [_1744766, _1744768, _1744770, _1744772] : [c_List_Olist__ex1(_1744766, _1744768, hAPP(hAPP(c_List_Olist_OCons(_1744766), _1744770), _1744772)), 47933 ^ _779142 : [(47940 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1744768, _1744770))), -(c_List_Olist__ex1(_1744766, _1744768, _1744772))], (47934 ^ _779142) ^ [] : [hBOOL(hAPP(_1744768, _1744770)), -(c_List_Olist__all(_1744766, hAPP(hAPP(c_COMBS(_1744766, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744766), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744766), c_fNot), _1744768))), hAPP(c_fequal, _1744770)), _1744772))]]], (45530 ^ _779142) ^ [_1692714, _1692716] : [45532 ^ _779142 : [(45535 ^ _779142) ^ [] : [45531 ^ [_1692714, _1692716] = c_List_Olist_ONil(_1692714)], (45533 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692714)), 45531 ^ [_1692714, _1692716]), hAPP(c_List_Oset(tc_List_Olist(_1692714)), _1692716))))]], -(c_List_Olist_ONil(_1692714) = c_List_Oconcat(_1692714, _1692716))], (52415 ^ _779142) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (16175 ^ _779142) ^ [_1063346, _1063348, _1063350] : [class_Orderings_Olinorder(_1063346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063346), _1063348)), -(_1063348 = c_Orderings_Obot__class_Obot(tc_fun(_1063346, tc_HOL_Obool))), 16186 ^ _779142 : [(16187 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063346), _1063350), hAPP(c_Finite__Set_Ofold1(_1063346, c_Orderings_Oord__class_Omin(_1063346)), _1063348))), 16190 ^ _779142 : [(16191 ^ _779142) ^ [_1063639] : [hBOOL(hAPP(hAPP(c_member(_1063346), _1063639), _1063348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063346), _1063350), _1063639)))]]], (16197 ^ _779142) ^ [] : [16199 ^ _779142 : [(16202 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063346), _1063350), 16198 ^ [_1063346, _1063348, _1063350]))], (16200 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063346), 16198 ^ [_1063346, _1063348, _1063350]), _1063348)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063346), _1063350), hAPP(c_Finite__Set_Ofold1(_1063346, c_Orderings_Oord__class_Omin(_1063346)), _1063348))))]]], (4988 ^ _779142) ^ [_855182, _855184, _855186, _855188, _855190, _855192, _855194, _855196] : [-(c_Hilbert__Choice_Oinv__into(_855196, _855192, _855188, _855184) = c_Hilbert__Choice_Oinv__into(_855194, _855190, _855186, _855182)), _855196 = _855194, _855192 = _855190, _855188 = _855186, _855184 = _855182], (12511 ^ _779142) ^ [_995085, _995087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995085), _995087)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995085), _995087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50065 ^ _779142) ^ [_1791641, _1791643, _1791645, _1791647, _1791649] : [c_Fun_Obij__betw(_1791641, _1791643, _1791645, _1791647, _1791649), -(c_Fun_Oinj__on(_1791641, _1791643, _1791645, _1791647))], (51379 ^ _779142) ^ [_1817903, _1817905] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817903), _1817905)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817905), _1817903)), -(_1817903 = _1817905)], (19091 ^ _779142) ^ [_1114655] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1114655)), 19095 ^ _779142 : [(19096 ^ _779142) ^ [_1114735] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1114735), _1114655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114735), 19094 ^ [_1114655])))]]], (34861 ^ _779142) ^ [_1425856, _1425858, _1425860, _1425862, _1425864] : [_1425856 = c_Orderings_Obot__class_Obot(tc_fun(_1425858, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425858, tc_fun(_1425860, tc_HOL_Obool)), _1425856), hAPP(hAPP(c_COMBB(tc_fun(_1425860, tc_HOL_Obool), tc_fun(_1425860, tc_HOL_Obool), _1425858), hAPP(c_Set_Oinsert(_1425860), _1425862)), _1425864)) = c_Orderings_Obot__class_Obot(tc_fun(_1425860, tc_HOL_Obool)))], (3562 ^ _779142) ^ [_832423, _832425, _832427, _832429] : [-(c_List_Olist__update(_832429, _832425) = c_List_Olist__update(_832427, _832423)), _832429 = _832427, _832425 = _832423], (43770 ^ _779142) ^ [_1654596, _1654598, _1654600] : [-(c_List_Orotate(_1654596, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654598), _1654600)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1654596), tc_List_Olist(_1654596), tc_List_Olist(_1654596), c_List_Orotate(_1654596, _1654598)), c_List_Orotate(_1654596, _1654600)))], (37437 ^ _779142) ^ [_1487420, _1487422, _1487424] : [hBOOL(hAPP(hAPP(c_member(_1487420), _1487422), hAPP(c_Set_OCollect(_1487420), _1487424))), -(hBOOL(hAPP(_1487424, _1487422)))], (6938 ^ _779142) ^ [_892733, _892735, _892737, _892739] : [hBOOL(hAPP(hAPP(c_member(_892733), _892735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892733, tc_HOL_Obool)), _892737), _892739))), -(hBOOL(hAPP(hAPP(c_member(_892733), _892735), _892737)))], (46112 ^ _779142) ^ [_1706755, _1706757, _1706759] : [class_Orderings_Olinorder(_1706755), c_List_Olinorder__class_Osorted(_1706755, _1706757), -(c_List_Olinorder__class_Osorted(_1706755, c_List_Oremove1(_1706755, _1706759, _1706757)))], (46676 ^ _779142) ^ [_1717598, _1717600] : [-(hAPP(c_List_Orev(_1717598), hAPP(c_List_Orev(_1717598), _1717600)) = _1717600)], (20582 ^ _779142) ^ [_1140527, _1140529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140527), _1140529)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140527), _1140529) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (11181 ^ _779142) ^ [_971503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971503), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_971503 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17742 ^ _779142) ^ [_1091787, _1091789] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091787)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091789)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091787), _1091789)))], (9675 ^ _779142) ^ [_943738, _943740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943738), _943740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943738), _943740)))], (36780 ^ _779142) ^ [] : [-(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))], (44845 ^ _779142) ^ [_1677516, _1677518] : [-(c_Code__Numeral_Onat__of__aux(_1677516, _1677518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677516)), _1677518))], (18646 ^ _779142) ^ [_1107326, _1107328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107326), _1107328)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1107328, _1107326) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1107328), _1107326), _1107326))], (47738 ^ _779142) ^ [_1740800, _1740802, _1740804] : [hBOOL(hAPP(hAPP(c_member(_1740800), _1740802), hAPP(c_List_Oset(_1740800), _1740804))), 47743 ^ _779142 : [(47746 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740800), _1740802), hAPP(c_List_Oset(_1740800), 47741 ^ [_1740800, _1740802, _1740804])))], (47744 ^ _779142) ^ [] : [-(_1740804 = hAPP(hAPP(c_List_Oappend(_1740800), 47741 ^ [_1740800, _1740802, _1740804]), hAPP(hAPP(c_List_Olist_OCons(_1740800), _1740802), 47742 ^ [_1740800, _1740802, _1740804])))]]], (52777 ^ _779142) ^ [_1837833, _1837835] : [hBOOL(hAPP(hAPP(c_fimplies, _1837833), _1837835)), hBOOL(_1837833), -(hBOOL(_1837835))], (21238 ^ _779142) ^ [_1152602, _1152604, _1152606, _1152608] : [class_Rings_Ocomm__semiring__1(_1152602), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1152602), hAPP(hAPP(c_Power_Opower__class_Opower(_1152602), _1152604), _1152606)), _1152608) = hAPP(hAPP(c_Power_Opower__class_Opower(_1152602), _1152604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152606), _1152608)))], (10583 ^ _779142) ^ [_962163, _962165] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962163), _962165) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10584 ^ _779142 : [(10591 ^ _779142) ^ [] : [_962163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _962165 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10585 ^ _779142) ^ [] : [_962163 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (35976 ^ _779142) ^ [_1454739] : [-(c_Equiv__Relations_Oequivp(_1454739, c_fequal))], (47048 ^ _779142) ^ [_1725433, _1725435, _1725437, _1725439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725433), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725435)), c_List_OdropWhile(_1725435, _1725437, _1725439)))), -(hAPP(hAPP(c_List_Onth(_1725435), c_List_OdropWhile(_1725435, _1725437, _1725439)), _1725433) = hAPP(hAPP(c_List_Onth(_1725435), _1725439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725433), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725435)), c_List_OtakeWhile(_1725435, _1725437, _1725439)))))], (34037 ^ _779142) ^ [_1402806] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1402806)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1402806)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18863 ^ _779142) ^ [_1111253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111253)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1111253) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1111253), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9229 ^ _779142) ^ [_936496, _936498, _936500, _936502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936496), _936498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936500), _936502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936496), _936500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936498), _936502))))], (36624 ^ _779142) ^ [_1468403, _1468405, _1468407, _1468409, _1468411, _1468413] : [c_Fun_Oinj__on(_1468403, _1468405, _1468407, _1468409), -(hBOOL(hAPP(hAPP(c_member(_1468405), _1468411), hAPP(c_Set_Oimage(_1468403, _1468405, _1468407), _1468409)))), -(c_Fun_Oinj__on(_1468403, _1468405, c_Fun_Ofun__upd(_1468403, _1468405, _1468407, _1468413, _1468411), _1468409))], (35533 ^ _779142) ^ [_1443749, _1443751, _1443753, _1443755] : [-(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), _1443749), _1443751)), 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), _1443753), _1443755)), 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), _1443749), _1443753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443751), _1443755))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443749), _1443755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443751), _1443753)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37205 ^ _779142) ^ [_1481595, _1481597, _1481599, _1481601, _1481603, _1481605] : [-(hAPP(c_Set_Ovimage(_1481595, _1481597, _1481599), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481601, tc_fun(_1481597, tc_HOL_Obool)), _1481603), _1481605)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481601, tc_fun(_1481595, tc_HOL_Obool)), _1481603), hAPP(hAPP(c_COMBB(tc_fun(_1481597, tc_HOL_Obool), tc_fun(_1481595, tc_HOL_Obool), _1481601), c_Set_Ovimage(_1481595, _1481597, _1481599)), _1481605)))], (39215 ^ _779142) ^ [_1539678, _1539680, _1539682, _1539684] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539678), _1539680))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539682), hAPP(c_Set_Oimage(_1539678, _1539682, _1539684), _1539680))), 39223 ^ _779142 : [(39226 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539678), hAPP(c_Set_OCollect(_1539678), hAPP(hAPP(c_COMBS(_1539678, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539678), c_fconj), hAPP(hAPP(c_COMBC(_1539678, tc_fun(_1539678, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539678)), _1539680))), hAPP(hAPP(c_COMBC(_1539678, _1539682, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1539682, tc_fun(_1539682, tc_HOL_Obool), _1539678), c_fequal), _1539684)), hAPP(_1539684, 39222 ^ [_1539678, _1539680, _1539682, _1539684]))))))], (39224 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539678), 39222 ^ [_1539678, _1539680, _1539682, _1539684]), _1539680)))]]], (23769 ^ _779142) ^ [_1197805] : [class_Int_Onumber__ring(_1197805), -(hAPP(c_Int_Onumber__class_Onumber__of(_1197805), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1197805), c_Groups_Oone__class_Oone(_1197805)))], (18328 ^ _779142) ^ [_1101872, _1101874, _1101876, _1101878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101874), _1101876)), -(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), _1101876), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101878, _1101872))), _1101874))))], (49350 ^ _779142) ^ [_1776730, _1776732] : [-(c_Relation_Osym(_1776730, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776730, _1776730), tc_HOL_Obool)), _1776732), hAPP(c_Relation_Oconverse(_1776730, _1776730), _1776732))))], (30539 ^ _779142) ^ [_1325361, _1325363, _1325365, _1325367, _1325369] : [class_Groups_Ocomm__monoid__mult(_1325361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325363), _1325365)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325363), _1325367)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325363, tc_HOL_Obool)), _1325365), _1325367) = c_Orderings_Obot__class_Obot(tc_fun(_1325363, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1325361, _1325363, c_Groups_Otimes__class_Otimes(_1325361)), _1325369), c_Groups_Oone__class_Oone(_1325361)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325363, tc_HOL_Obool)), _1325365), _1325367)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325361), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1325361, _1325363, c_Groups_Otimes__class_Otimes(_1325361)), _1325369), c_Groups_Oone__class_Oone(_1325361)), _1325365)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1325361, _1325363, c_Groups_Otimes__class_Otimes(_1325361)), _1325369), c_Groups_Oone__class_Oone(_1325361)), _1325367)))], (48018 ^ _779142) ^ [_1746537, _1746539, _1746541, _1746543, _1746545] : [_1746537 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746539, _1746541, _1746543, _1746545), _1746537) = c_Lazy__Sequence_Oempty(_1746541))], (39092 ^ _779142) ^ [_1537409, _1537411] : [c_Wellfounded_OwfP(_1537409, _1537411), 39095 ^ _779142 : [(39096 ^ _779142) ^ [_1537473] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1537409, _1537411), _1537473)))]]], (8635 ^ _779142) ^ [_924139, _924141, _924143, _924145] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_924139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924139), _924141), _924143)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924139), _924141), _924145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924139), _924143), _924145)))], (50530 ^ _779142) ^ [_1802779, _1802781, _1802783, _1802785, _1802787, _1802789, _1802791, _1802793] : [c_Finite__Set_Ofolding__image(_1802779, _1802781, _1802783, _1802785, _1802787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802781), _1802789)), 50540 ^ _779142 : [(50543 ^ _779142) ^ [] : [hAPP(_1802791, 50539 ^ [_1802779, _1802781, _1802783, _1802785, _1802787, _1802789, _1802791, _1802793]) = hAPP(_1802793, 50539 ^ [_1802779, _1802781, _1802783, _1802785, _1802787, _1802789, _1802791, _1802793])], (50541 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802781), 50539 ^ [_1802779, _1802781, _1802783, _1802785, _1802787, _1802789, _1802791, _1802793]), _1802789)))]], -(hAPP(hAPP(_1802787, _1802791), _1802789) = hAPP(hAPP(_1802787, _1802793), _1802789))], (19357 ^ _779142) ^ [_1119480, _1119482] : [class_Groups_Oordered__ab__group__add__abs(_1119480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119480), c_Groups_Ozero__class_Ozero(_1119480)), _1119482)), -(hAPP(c_Groups_Oabs__class_Oabs(_1119480), _1119482) = _1119482)], (41094 ^ _779142) ^ [_1586722, _1586724, _1586726, _1586728, _1586730] : [c_Relation_Osingle__valued(_1586722, _1586724, hAPP(c_Relation_Oconverse(_1586724, _1586722), _1586726)), -(hAPP(c_Relation_OImage(_1586724, _1586722, _1586726), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586724, tc_HOL_Obool)), _1586728), _1586730)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586722, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586724, _1586722, _1586726), _1586728)), hAPP(c_Relation_OImage(_1586724, _1586722, _1586726), _1586730)))], (48850 ^ _779142) ^ [_1765377, _1765379, _1765381, _1765383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765377), _1765379)), 48853 ^ _779142 : [(48854 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765381), hAPP(c_Set_OCollect(_1765381), hAPP(hAPP(c_COMBB(tc_fun(_1765377, tc_HOL_Obool), tc_HOL_Obool, _1765381), c_HOL_OEx(_1765377)), hAPP(hAPP(c_COMBB(tc_fun(_1765377, tc_HOL_Obool), tc_fun(_1765377, tc_HOL_Obool), _1765381), hAPP(c_COMBS(_1765377, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765377), c_fconj), hAPP(hAPP(c_COMBC(_1765377, tc_fun(_1765377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765377)), _1765379)))), _1765383))))), 48857 ^ _779142 : [(48858 ^ _779142) ^ [_1765685] : [hBOOL(hAPP(hAPP(c_member(_1765377), _1765685), _1765379)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765381), hAPP(c_Set_OCollect(_1765381), hAPP(hAPP(c_COMBC(_1765381, _1765377, tc_HOL_Obool), _1765383), _1765685)))))]]], (48864 ^ _779142) ^ [] : [48866 ^ _779142 : [(48869 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765381), hAPP(c_Set_OCollect(_1765381), hAPP(hAPP(c_COMBC(_1765381, _1765377, tc_HOL_Obool), _1765383), 48865 ^ [_1765377, _1765379, _1765381, _1765383]))))], (48867 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765377), 48865 ^ [_1765377, _1765379, _1765381, _1765383]), _1765379)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765381), hAPP(c_Set_OCollect(_1765381), hAPP(hAPP(c_COMBB(tc_fun(_1765377, tc_HOL_Obool), tc_HOL_Obool, _1765381), c_HOL_OEx(_1765377)), hAPP(hAPP(c_COMBB(tc_fun(_1765377, tc_HOL_Obool), tc_fun(_1765377, tc_HOL_Obool), _1765381), hAPP(c_COMBS(_1765377, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765377), c_fconj), hAPP(hAPP(c_COMBC(_1765377, tc_fun(_1765377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765377)), _1765379)))), _1765383))))))]]], (4726 ^ _779142) ^ [_851035, _851037] : [_851037 = _851035, -(c_List_Oset(_851037) = c_List_Oset(_851035))], (25310 ^ _779142) ^ [_1223897, _1223899] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1223897))), _1223899) = 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)))), _1223897), _1223899))], (25092 ^ _779142) ^ [_1220168, _1220170] : [class_Rings_Olinordered__idom(_1220168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220168), c_Groups_Osgn__class_Osgn(_1220168, _1220170)), hAPP(c_Groups_Oabs__class_Oabs(_1220168), _1220170)) = _1220170)], (43145 ^ _779142) ^ [_1639949, _1639951, _1639953, _1639955, _1639957, _1639959] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639949)), _1639951) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639953)), _1639955), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639949)), _1639957) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639953)), _1639959), -(hAPP(hAPP(c_List_Ozip(_1639949, _1639953), hAPP(hAPP(c_List_Oappend(_1639949), _1639951), _1639957)), hAPP(hAPP(c_List_Oappend(_1639953), _1639955), _1639959)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1639949, _1639953)), hAPP(hAPP(c_List_Ozip(_1639949, _1639953), _1639951), _1639955)), hAPP(hAPP(c_List_Ozip(_1639949, _1639953), _1639957), _1639959)))], (42892 ^ _779142) ^ [_1633795, _1633797, _1633799] : [-(_1633795 = c_List_Olist_ONil(_1633797)), -(hBOOL(hAPP(hAPP(c_member(_1633797), hAPP(c_Product__Type_Ofst(_1633797, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633797, _1633795), _1633799))), hAPP(c_List_Oset(_1633797), _1633795))))], (17689 ^ _779142) ^ [_1090771, _1090773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090771)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090771), _1090773)))], (36516 ^ _779142) ^ [_1466039, _1466041] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466039), c_Orderings_Otop__class_Otop(tc_fun(_1466039, tc_HOL_Obool)))), c_Fun_Oinj__on(_1466039, _1466039, _1466041, c_Orderings_Otop__class_Otop(tc_fun(_1466039, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1466039, _1466039, _1466041), c_Orderings_Otop__class_Otop(tc_fun(_1466039, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466039, tc_HOL_Obool)))], (9284 ^ _779142) ^ [_937566, _937568] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937568), _937566))))], (37383 ^ _779142) ^ [_1486086, _1486088, _1486090, _1486092, _1486094, _1486096] : [hBOOL(hAPP(hAPP(c_member(_1486086), _1486088), _1486090)), hBOOL(hAPP(hAPP(c_member(_1486092), _1486094), hAPP(_1486096, _1486088))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486086, _1486092)), hAPP(hAPP(c_Product__Type_OPair(_1486086, _1486092), _1486088), _1486094)), hAPP(hAPP(c_Product__Type_OSigma(_1486086, _1486092), _1486090), _1486096))))], (52791 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))], (6879 ^ _779142) ^ [_891509, _891511, _891513, _891515, _891517] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891509), _891511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891509, tc_HOL_Obool)), _891511), hAPP(c_Set_Oimage(_891513, _891509, _891515), _891517))), 6887 ^ _779142 : [(6892 ^ _779142) ^ [] : [-(_891511 = hAPP(c_Set_Oimage(_891513, _891509, _891515), 6886 ^ [_891509, _891511, _891513, _891515, _891517]))], (6890 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891513), 6886 ^ [_891509, _891511, _891513, _891515, _891517])))], (6888 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891513, tc_HOL_Obool)), 6886 ^ [_891509, _891511, _891513, _891515, _891517]), _891517)))]]], (41499 ^ _779142) ^ [_1598996, _1598998, _1599000, _1599002, _1599004] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598996), tc_List_Olist(_1598996))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598996), tc_List_Olist(_1598996)), _1598998), _1599000)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598996), c_List_Olistrel1(_1598996, _1599002)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598996), tc_List_Olist(_1598996))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598996), tc_List_Olist(_1598996)), hAPP(hAPP(c_List_Olist_OCons(_1598996), _1599004), _1598998)), hAPP(hAPP(c_List_Olist_OCons(_1598996), _1599004), _1599000))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598996), c_List_Olistrel1(_1598996, _1599002)))))], (33700 ^ _779142) ^ [_1395911, _1395913, _1395915, _1395917, _1395919] : [hAPP(c_Product__Type_Osnd(_1395911, _1395913), hAPP(hAPP(c_Product__Type_OPair(_1395911, _1395913), _1395915), _1395917)) = _1395919, -(_1395917 = _1395919)], (9973 ^ _779142) ^ [_949576, _949578, _949580, _949582, _949584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949576), _949578)), 9976 ^ _779142 : [(9983 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949582), 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), _949578), _949576)), _949580)), _949584))), -(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), _949576), _949580)), _949582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949578), _949580)), _949584))))], (9977 ^ _779142) ^ [] : [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), _949576), _949580)), _949582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949578), _949580)), _949584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949582), 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), _949578), _949576)), _949580)), _949584))))]]], (21266 ^ _779142) ^ [_1153087] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1153087)))], (45129 ^ _779142) ^ [_1684440, _1684442, _1684444] : [_1684440 = _1684442, -(c_List_Olist__all2(_1684444, _1684444, c_fequal, _1684440, _1684442))], (44169 ^ _779142) ^ [_1662817, _1662819, _1662821] : [_1662817 = c_List_Olist_ONil(_1662819), -(c_List_Olast(_1662819, hAPP(hAPP(c_List_Olist_OCons(_1662819), _1662821), _1662817)) = _1662821)], (31967 ^ _779142) ^ [_1356664, _1356666, _1356668, _1356670] : [hBOOL(hAPP(hAPP(c_member(_1356664), _1356670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356664, tc_HOL_Obool)), _1356666), _1356668))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356664, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1356664, tc_fun(_1356664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356664)), _1356666)), hAPP(hAPP(c_COMBC(_1356664, tc_fun(_1356664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356664)), _1356668)), _1356670)))], (38483 ^ _779142) ^ [_1522641, _1522643, _1522645, _1522647] : [hBOOL(hAPP(hAPP(c_member(_1522643), _1522647), hAPP(c_Relation_ORange(_1522641, _1522643), _1522645))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522641, _1522643, hAPP(hAPP(c_COMBC(_1522641, tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_fun(_1522643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522643, tc_fun(tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_fun(_1522643, tc_HOL_Obool)), _1522641), c_COMBC(_1522643, tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522643, tc_prod(_1522641, _1522643)), tc_fun(_1522643, tc_fun(tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_HOL_Obool)), _1522641), hAPP(c_COMBB(tc_prod(_1522641, _1522643), tc_fun(tc_fun(tc_prod(_1522641, _1522643), tc_HOL_Obool), tc_HOL_Obool), _1522643), c_member(tc_prod(_1522641, _1522643)))), c_Product__Type_OPair(_1522641, _1522643)))), _1522645)), _1522647)))], (1676 ^ _779142) ^ [_803034, _803036] : [-(class_Groups_Oab__semigroup__add(_803034)), _803036 = _803034, class_Groups_Oab__semigroup__add(_803036)], (26454 ^ _779142) ^ [_1244443, _1244445, _1244447, _1244449] : [class_Lattices_Osemilattice__sup(_1244443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244443), _1244445), _1244447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244443), _1244445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1244443), _1244447), _1244449))))], (50265 ^ _779142) ^ [_1795526, _1795528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795526), _1795528)), -(c_Fun_Obij__betw(_1795526, tc_Nat_Onat, 50268 ^ [_1795526, _1795528], _1795528, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795526), _1795528))))], (45689 ^ _779142) ^ [_1697067, _1697069, _1697071] : [-(c_List_Opartition(_1697067, _1697069, _1697071) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697067), tc_List_Olist(_1697067)), hAPP(c_List_Ofilter(_1697067, _1697069), _1697071)), hAPP(c_List_Ofilter(_1697067, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1697067, c_fNot), _1697069)), _1697071)))], (37505 ^ _779142) ^ [_1489018] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1489018, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1489018), hAPP(c_COMBK(tc_HOL_Obool, _1489018), c_fTrue)))], (42596 ^ _779142) ^ [_1628425, _1628427] : [-(_1628425 = c_List_Olist_ONil(_1628427)), hBOOL(hAPP(c_List_Odistinct(_1628427), _1628425)), -(hBOOL(hAPP(c_List_Odistinct(_1628427), c_List_Obutlast(_1628427, _1628425))))], (1816 ^ _779142) ^ [_804784, _804786] : [-(class_Rings_Osemiring__1(_804784)), _804786 = _804784, class_Rings_Osemiring__1(_804786)], (40590 ^ _779142) ^ [_1574097, _1574099, _1574101, _1574103] : [-(c_Wellfounded_Owf(_1574097, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574097, _1574097)), hAPP(hAPP(c_Product__Type_OPair(_1574097, _1574097), _1574099), _1574101)), _1574103))), c_Wellfounded_Owf(_1574097, _1574103), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574097, _1574097)), hAPP(hAPP(c_Product__Type_OPair(_1574097, _1574097), _1574101), _1574099)), c_Transitive__Closure_Ortrancl(_1574097, _1574103))))], (18732 ^ _779142) ^ [_1108896, _1108898, _1108900] : [hBOOL(hAPP(_1108896, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1108898, _1108900))), 18735 ^ _779142 : [(18742 ^ _779142) ^ [] : [-(_1108900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 18745 ^ _779142 : [(18746 ^ _779142) ^ [_1109144, _1109146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109144), _1108900)), _1108898 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108900), _1109146)), _1109144), -(hBOOL(hAPP(_1108896, _1109144)))]]], (18736 ^ _779142) ^ [] : [_1108900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1108896, _1108898)))]]], (17769 ^ _779142) ^ [_1092287, _1092289] : [class_Rings_Olinordered__semidom(_1092287), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092287), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092287), _1092289)), c_Groups_Ozero__class_Ozero(_1092287)))], (10851 ^ _779142) ^ [_966470, _966472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966472)), _966470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966470), _966472))], (22670 ^ _779142) ^ [_1178459, _1178461, _1178463, _1178465, _1178467] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1178459, _1178461, _1178463), _1178465), hAPP(c_Nat_OSuc, _1178467)) = hAPP(hAPP(_1178463, _1178465), hAPP(hAPP(c_Power_Opower_Opower(_1178459, _1178461, _1178463), _1178465), _1178467)))], (4900 ^ _779142) ^ [_853798, _853800] : [_853800 = _853798, -(c_Set_OCollect(_853800) = c_Set_OCollect(_853798))], (34901 ^ _779142) ^ [_1426839, _1426841, _1426843, _1426845, _1426847] : [_1426839 = c_Orderings_Obot__class_Obot(tc_fun(_1426841, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426843, tc_HOL_Obool)), _1426845), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426841, tc_fun(_1426843, tc_HOL_Obool)), _1426839), _1426847)) = _1426845)], (51663 ^ _779142) ^ [_1822624, _1822626] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822624), _1822626)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822624), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1822626), _1822624))))], (41567 ^ _779142) ^ [_1601245, _1601247, _1601249, _1601251] : [41570 ^ _779142 : [(41575 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601245, _1601245)), hAPP(hAPP(c_Product__Type_OPair(_1601245, _1601245), 41569 ^ [_1601245, _1601247, _1601249, _1601251]), 41568 ^ [_1601245, _1601247, _1601249, _1601251])), _1601247))], (41573 ^ _779142) ^ [] : [41568 ^ [_1601245, _1601247, _1601249, _1601251] = 41569 ^ [_1601245, _1601247, _1601249, _1601251]], (41571 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601245, _1601245)), hAPP(hAPP(c_Product__Type_OPair(_1601245, _1601245), 41568 ^ [_1601245, _1601247, _1601249, _1601251]), 41569 ^ [_1601245, _1601247, _1601249, _1601251])), _1601247))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601245), tc_List_Olist(_1601245))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601245), tc_List_Olist(_1601245)), _1601249), _1601251)), c_List_Olexord(_1601245, _1601247)))), -(_1601249 = _1601251), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601245), tc_List_Olist(_1601245))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601245), tc_List_Olist(_1601245)), _1601251), _1601249)), c_List_Olexord(_1601245, _1601247))))], (31538 ^ _779142) ^ [_1344976, _1344978, _1344980] : [31540 ^ _779142 : [(31543 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344976, tc_HOL_Obool)), 31539 ^ [_1344976, _1344978, _1344980]), _1344980))], (31541 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1344976, tc_HOL_Obool)), 31539 ^ [_1344976, _1344978, _1344980]), _1344978)))]], -(_1344978 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1344976, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344976, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1344976, tc_HOL_Obool), _1344978)), _1344980)))], (45807 ^ _779142) ^ [_1700307, _1700309, _1700311, _1700313] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1700307, tc_Nat_Onat), _1700307), c_Product__Type_Ofst(_1700307, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700307, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700307, tc_Nat_Onat)), _1700309), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1700307, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1700307, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1700307, tc_Nat_Onat), _1700311), _1700313))) = hAPP(hAPP(c_List_Omap(tc_prod(_1700307, tc_Nat_Onat), _1700307), c_Product__Type_Ofst(_1700307, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700307, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700307, tc_Nat_Onat)), _1700309), c_Product__Type_Osnd(_1700307, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1700307, tc_Nat_Onat), _1700311), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1700313)))))], (3104 ^ _779142) ^ [_825252, _825254, _825256, _825258] : [-(c_Big__Operators_Olattice__class_OInf__fin(_825258, _825254) = c_Big__Operators_Olattice__class_OInf__fin(_825256, _825252)), _825258 = _825256, _825254 = _825252], (31961 ^ _779142) ^ [_1356465, _1356467, _1356469, _1356471] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356465, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1356465, tc_fun(_1356465, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356465)), _1356467)), hAPP(hAPP(c_COMBC(_1356465, tc_fun(_1356465, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356465)), _1356469)), _1356471)), -(hBOOL(hAPP(hAPP(c_member(_1356465), _1356471), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356465, tc_HOL_Obool)), _1356467), _1356469))))], (18951 ^ _779142) ^ [_1112417, _1112419] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112417), _1112419) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18956 ^ _779142 : [(18959 ^ _779142) ^ [] : [-(_1112419 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18957 ^ _779142) ^ [] : [-(_1112417 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18960 ^ _779142 : [(18963 ^ _779142) ^ [] : [-(_1112419 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18961 ^ _779142) ^ [] : [-(_1112417 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (24892 ^ _779142) ^ [_1216780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216780), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1216780)), c_Int_OMin)))], (48164 ^ _779142) ^ [_1750525, _1750527, _1750529, _1750531] : [-(hAPP(hAPP(c_List_Oappend(_1750525), c_List_Oreplicate(_1750525, _1750527, _1750529)), hAPP(hAPP(c_List_Olist_OCons(_1750525), _1750529), _1750531)) = hAPP(hAPP(c_List_Olist_OCons(_1750525), _1750529), hAPP(hAPP(c_List_Oappend(_1750525), c_List_Oreplicate(_1750525, _1750527, _1750529)), _1750531)))], (9811 ^ _779142) ^ [_946166, _946168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946166), _946168)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946168), _946166)) = _946168)], (5500 ^ _779142) ^ [_863228, _863230] : [_863230 = _863228, -(tc_Option_Ooption(_863230) = tc_Option_Ooption(_863228))], (20410 ^ _779142) ^ [_1137317, _1137319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137319)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1137317, _1137319)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1137317), hAPP(c_Int_Onat, _1137319)))], (12369 ^ _779142) ^ [_992570, _992572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _992572), _992570)), _992572)))], (24423 ^ _779142) ^ [_1208925] : [class_Int_Onumber__ring(_1208925), -(hAPP(c_Int_Oring__1__class_Oof__int(_1208925), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1208925), c_Int_OMin))], (23217 ^ _779142) ^ [_1188004, _1188006] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188004), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1188006)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1188004)), _1188006))], (32853 ^ _779142) ^ [_1379277, _1379279] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379277), hAPP(c_Nat_OSuc, _1379279)) = 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), _1379277), _1379279)))], (1116 ^ _779142) ^ [_796034, _796036] : [-(class_Lattices_Obounded__lattice(_796034)), _796036 = _796034, class_Lattices_Obounded__lattice(_796036)], (39728 ^ _779142) ^ [_1552788, _1552790, _1552792, _1552794, _1552796, _1552798, _1552800, _1552802] : [c_Finite__Set_Ofolding(_1552788, _1552790, _1552792, _1552794), -(hAPP(c_Fun_Ocomp(_1552790, _1552790, _1552796, hAPP(_1552792, _1552798)), hAPP(c_Fun_Ocomp(_1552790, _1552790, _1552796, hAPP(_1552792, _1552800)), _1552802)) = hAPP(c_Fun_Ocomp(_1552790, _1552790, _1552796, hAPP(_1552792, _1552800)), hAPP(c_Fun_Ocomp(_1552790, _1552790, _1552796, hAPP(_1552792, _1552798)), _1552802)))], (46917 ^ _779142) ^ [_1722665, _1722667, _1722669, _1722671, _1722673] : [class_Orderings_Olinorder(_1722665), c_List_Olinorder__class_Osorted(_1722665, hAPP(c_List_Orev(_1722665), hAPP(hAPP(c_List_Omap(_1722667, _1722665), _1722669), _1722671))), -(hAPP(c_List_Ofilter(_1722667, hAPP(hAPP(c_COMBB(_1722665, tc_HOL_Obool, _1722667), hAPP(c_Orderings_Oord__class_Oless(_1722665), _1722673)), _1722669)), _1722671) = c_List_OtakeWhile(_1722667, hAPP(hAPP(c_COMBB(_1722665, tc_HOL_Obool, _1722667), hAPP(c_Orderings_Oord__class_Oless(_1722665), _1722673)), _1722669), _1722671))], (44261 ^ _779142) ^ [_1664237, _1664239, _1664241] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664237)), _1664239), c_List_Olists(_1664237, _1664241))), -(_1664239 = c_List_Olist_ONil(_1664237)), 44270 ^ _779142 : [(44275 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664237)), 44269 ^ [_1664237, _1664239, _1664241]), c_List_Olists(_1664237, _1664241))))], (44273 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664237), 44268 ^ [_1664237, _1664239, _1664241]), _1664241)))], (44271 ^ _779142) ^ [] : [-(_1664239 = hAPP(hAPP(c_List_Olist_OCons(_1664237), 44268 ^ [_1664237, _1664239, _1664241]), 44269 ^ [_1664237, _1664239, _1664241]))]]], (47532 ^ _779142) ^ [_1736934, _1736936, _1736938, _1736940] : [class_Orderings_Oorder(_1736934), class_Enum_Oenum(_1736936), 47539 ^ _779142 : [(47546 ^ _779142) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736936), hAPP(hAPP(c_COMBS(_1736936, _1736934, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736934, tc_fun(_1736934, tc_HOL_Obool), _1736936), c_Orderings_Oord__class_Oless__eq(_1736934)), _1736938)), _1736940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736936, _1736934)), _1736938), _1736940)))], (47540 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736936, _1736934)), _1736938), _1736940)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736936), hAPP(hAPP(c_COMBS(_1736936, _1736934, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736934, tc_fun(_1736934, tc_HOL_Obool), _1736936), c_Orderings_Oord__class_Oless__eq(_1736934)), _1736938)), _1736940))))]]], (15099 ^ _779142) ^ [_1043416, _1043418, _1043420, _1043422] : [class_Fields_Olinordered__field__inverse__zero(_1043416), class_Int_Onumber(_1043416), 15106 ^ _779142 : [(15107 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1043416), _1043418), _1043420)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422))), 15110 ^ _779142 : [(15117 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), _1043420))), 15120 ^ _779142 : [(15127 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), _1043420), c_Groups_Ozero__class_Ozero(_1043416)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422))))], (15121 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), _1043420), c_Groups_Ozero__class_Ozero(_1043416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)), _1043420)), _1043418)))]]], (15111 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), _1043420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), _1043418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)), _1043420))))]]], (15133 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1043416), _1043418), _1043420)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)))), 15136 ^ _779142 : [(15139 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), _1043418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)), _1043420)))], (15137 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), _1043420)))]], 15140 ^ _779142 : [(15143 ^ _779142) ^ [] : [15144 ^ _779142 : [(15147 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)), _1043420)), _1043418))], (15145 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), _1043420), c_Groups_Ozero__class_Ozero(_1043416))))]], 15148 ^ _779142 : [(15151 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043422)))], (15149 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), _1043420), c_Groups_Ozero__class_Ozero(_1043416)))]]], (15141 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), c_Groups_Ozero__class_Ozero(_1043416)), _1043420))]]]]], (44349 ^ _779142) ^ [_1666553, _1666555, _1666557, _1666559] : [_1666559 = c_List_Olist_ONil(_1666553), -(hAPP(hAPP(c_List_Omap(_1666553, _1666555), _1666557), _1666559) = c_List_Olist_ONil(_1666555))], (21570 ^ _779142) ^ [_1158029, _1158031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158029), _1158031)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1158031, _1158029) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (23829 ^ _779142) ^ [_1198900, _1198902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198900)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1198902)))), 23832 ^ _779142 : [(23835 ^ _779142) ^ [] : [-(_1198902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23833 ^ _779142) ^ [] : [-(_1198900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43391 ^ _779142) ^ [_1645569, _1645571, _1645573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645569), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645571)), _1645573))), -(hAPP(hAPP(c_List_Otake(_1645571), hAPP(c_Nat_OSuc, _1645569)), _1645573) = hAPP(hAPP(c_List_Oappend(_1645571), hAPP(hAPP(c_List_Otake(_1645571), _1645569), _1645573)), hAPP(hAPP(c_List_Olist_OCons(_1645571), hAPP(hAPP(c_List_Onth(_1645571), _1645573), _1645569)), c_List_Olist_ONil(_1645571))))], (21456 ^ _779142) ^ [_1156197, _1156199, _1156201] : [class_Orderings_Oorder(_1156197), _1156199 = _1156201, -(c_SetInterval_Oord__class_OatLeastAtMost(_1156197, _1156199, _1156201) = hAPP(hAPP(c_Set_Oinsert(_1156197), _1156199), c_Orderings_Obot__class_Obot(tc_fun(_1156197, tc_HOL_Obool))))], (214 ^ _779142) ^ [_782437, _782439, _782441, _782443, _782445, _782447, _782449, _782451, _782453, _782455, _782457, _782459] : [-(c_Finite__Set_Ofolding__image__simple(_782457, _782453, _782449, _782445, _782441, _782437)), c_Finite__Set_Ofolding__image__simple(_782459, _782455, _782451, _782447, _782443, _782439), _782459 = _782457, _782455 = _782453, _782451 = _782449, _782447 = _782445, _782443 = _782441, _782439 = _782437], (3552 ^ _779142) ^ [_832274, _832276, _832278, _832280] : [-(c_List_Orotate(_832280, _832276) = c_List_Orotate(_832278, _832274)), _832280 = _832278, _832276 = _832274], (9027 ^ _779142) ^ [_931807, _931809, _931811] : [class_Lattices_Oab__semigroup__idem__mult(_931807), hBOOL(hAPP(c_Finite__Set_Ofinite(_931807), _931809)), -(hAPP(c_Finite__Set_Ofold1(_931807, c_Groups_Otimes__class_Otimes(_931807)), hAPP(hAPP(c_Set_Oinsert(_931807), _931811), _931809)) = hAPP(hAPP(c_Finite__Set_Ofold(_931807, _931807, c_Groups_Otimes__class_Otimes(_931807)), _931811), _931809))], (32251 ^ _779142) ^ [_1366075, _1366077, _1366079, _1366081] : [class_Groups_Ocomm__monoid__mult(_1366075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366077), _1366079)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366077, _1366075), hAPP(c_COMBK(_1366075, _1366077), _1366081)), _1366079) = hAPP(hAPP(c_Power_Opower__class_Opower(_1366075), _1366081), hAPP(c_Finite__Set_Ocard(_1366077), _1366079)))], (28589 ^ _779142) ^ [_1284546, _1284548, _1284550] : [class_Orderings_Olinorder(_1284546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284546), _1284548)), -(_1284548 = c_Orderings_Obot__class_Obot(tc_fun(_1284546, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284546), _1284550)), -(_1284550 = c_Orderings_Obot__class_Obot(tc_fun(_1284546, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1284546, c_Orderings_Oord__class_Omax(_1284546), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284546, tc_HOL_Obool)), _1284548), _1284550)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1284546), c_Big__Operators_Olattice_OSup__fin(_1284546, c_Orderings_Oord__class_Omax(_1284546), _1284548)), c_Big__Operators_Olattice_OSup__fin(_1284546, c_Orderings_Oord__class_Omax(_1284546), _1284550)))], (88 ^ _779142) ^ [_780466, _780468] : [-(class_Rings_Odivision__ring(_780466)), _780468 = _780466, class_Rings_Odivision__ring(_780468)], (46634 ^ _779142) ^ [_1716801, _1716803, _1716805, _1716807, _1716809] : [c_List_Olist__all2(_1716801, _1716803, _1716805, _1716807, hAPP(c_List_Orev(_1716803), _1716809)), -(c_List_Olist__all2(_1716801, _1716803, _1716805, hAPP(c_List_Orev(_1716801), _1716807), _1716809))], (42960 ^ _779142) ^ [_1635816, _1635818, _1635820, _1635822, _1635824] : [hAPP(hAPP(c_List_Oappend(_1635816), _1635818), hAPP(hAPP(c_List_Olist_OCons(_1635816), _1635820), c_List_Olist_ONil(_1635816))) = hAPP(hAPP(c_List_Oappend(_1635816), _1635822), hAPP(hAPP(c_List_Olist_OCons(_1635816), _1635824), c_List_Olist_ONil(_1635816))), 42963 ^ _779142 : [(42966 ^ _779142) ^ [] : [-(_1635820 = _1635824)], (42964 ^ _779142) ^ [] : [-(_1635818 = _1635822)]]], (40155 ^ _779142) ^ [_1563224, _1563226] : [-(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)))), _1563224)) = 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)))), _1563226))), 40157 ^ _779142 : [(40160 ^ _779142) ^ [] : [40161 ^ _779142 : [(40164 ^ _779142) ^ [] : [hBOOL(hAPP(_1563226, 40156 ^ [_1563224, _1563226]))], (40162 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1563224, 40156 ^ [_1563224, _1563226])))]], 40165 ^ _779142 : [(40168 ^ _779142) ^ [] : [hBOOL(hAPP(_1563224, 40156 ^ [_1563224, _1563226]))], (40166 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1563226, 40156 ^ [_1563224, _1563226])))]]], (40158 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 40156 ^ [_1563224, _1563226])))]]], (41679 ^ _779142) ^ [_1604927, _1604929, _1604931, _1604933, _1604935, _1604937] : [-(c_List_Olistrelp(_1604927, _1604929, hAPP(hAPP(c_List_Olist_OCons(_1604927), _1604931), _1604933), hAPP(hAPP(c_List_Olist_OCons(_1604927), _1604935), _1604937))), hBOOL(hAPP(hAPP(_1604929, _1604931), _1604935)), c_List_Olistrelp(_1604927, _1604929, _1604933, _1604937)], (10971 ^ _779142) ^ [_968481, _968483] : [class_Rings_Ocomm__semiring__1(_968481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968481), _968483), c_Groups_Ozero__class_Ozero(_968481)) = _968483)], (36936 ^ _779142) ^ [_1474985, _1474987, _1474989, _1474991, _1474993] : [class_Groups_Ocomm__monoid__add(_1474985), class_Groups_Ocomm__monoid__mult(_1474985), _1474987 = _1474989, c_Nat__Transfer_Onat__set(_1474989), 36954 ^ _779142 : [(36957 ^ _779142) ^ [] : [hAPP(_1474991, 36953 ^ [_1474985, _1474987, _1474989, _1474991, _1474993]) = hAPP(_1474993, 36953 ^ [_1474985, _1474987, _1474989, _1474991, _1474993])], (36955 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36953 ^ [_1474985, _1474987, _1474989, _1474991, _1474993])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1474985), _1474991), _1474987) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1474985), _1474993), _1474989))], (49406 ^ _779142) ^ [_1777557, _1777559] : [c_Predicate_Osymp(_1777557, _1777559), -(c_Relation_Osym(_1777557, hAPP(c_Set_OCollect(tc_prod(_1777557, _1777557)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777557, _1777557, tc_HOL_Obool), _1777559))))], (5667 ^ _779142) ^ [_868570] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_868570), c_Orderings_Obot__class_Obot(tc_fun(_868570, tc_HOL_Obool)))))], (992 ^ _779142) ^ [_794076, _794078, _794080, _794082, _794084, _794086, _794088, _794090] : [-(c_Equiv__Relations_Ocongruent(_794088, _794084, _794080, _794076)), c_Equiv__Relations_Ocongruent(_794090, _794086, _794082, _794078), _794090 = _794088, _794086 = _794084, _794082 = _794080, _794078 = _794076], (30836 ^ _779142) ^ [_1331739, _1331741] : [-(c_Sum__Type_OPlus(_1331739, _1331741, c_Orderings_Otop__class_Otop(tc_fun(_1331739, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1331741, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1331739, _1331741), tc_HOL_Obool)))], (52219 ^ _779142) ^ [_1832049, _1832051] : [-(class_Enum_Oenum(tc_fun(_1832049, _1832051))), class_Enum_Oenum(_1832049), class_Enum_Oenum(_1832051)], (45317 ^ _779142) ^ [_1688609, _1688611, _1688613, _1688615] : [45319 ^ _779142 : [(45322 ^ _779142) ^ [] : [hBOOL(hAPP(_1688613, hAPP(hAPP(c_List_Onth(_1688609), _1688611), 45318 ^ [_1688609, _1688611, _1688613, _1688615])))], (45320 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45318 ^ [_1688609, _1688611, _1688613, _1688615]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688609)), _1688611))))]], hBOOL(hAPP(hAPP(c_member(_1688609), _1688615), hAPP(c_List_Oset(_1688609), _1688611))), -(hBOOL(hAPP(_1688613, _1688615)))], (20812 ^ _779142) ^ [_1144993, _1144995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144993)), 20815 ^ _779142 : [(20822 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144995), _1144993))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144995), _1144993) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144995), _1144993)), _1144993)))], (20816 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144995), _1144993)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144995), _1144993) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25630 ^ _779142) ^ [_1229610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229610))))], (47454 ^ _779142) ^ [_1734822, _1734824, _1734826, _1734828, _1734830] : [hAPP(c_List_Ofilter(_1734822, _1734824), _1734826) = hAPP(hAPP(c_List_Olist_OCons(_1734822), _1734828), _1734830), 47459 ^ _779142 : [(47468 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1734824, _1734828)))], (47470 ^ _779142) ^ [] : [-(_1734830 = hAPP(c_List_Ofilter(_1734822, _1734824), 47458 ^ [_1734822, _1734824, _1734826, _1734828, _1734830]))], (47462 ^ _779142) ^ [_1735136] : [hBOOL(hAPP(hAPP(c_member(_1734822), _1735136), hAPP(c_List_Oset(_1734822), 47457 ^ [_1734822, _1734824, _1734826, _1734828, _1734830]))), hBOOL(hAPP(_1734824, _1735136))], (47460 ^ _779142) ^ [] : [-(_1734826 = hAPP(hAPP(c_List_Oappend(_1734822), 47457 ^ [_1734822, _1734824, _1734826, _1734828, _1734830]), hAPP(hAPP(c_List_Olist_OCons(_1734822), _1734828), 47458 ^ [_1734822, _1734824, _1734826, _1734828, _1734830])))]]], (26878 ^ _779142) ^ [_1253087, _1253089] : [c_Nat__Transfer_Onat__set(_1253087), c_Nat__Transfer_Onat__set(_1253089), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1253087), _1253089)))], (28929 ^ _779142) ^ [_1291882, _1291884, _1291886, _1291888, _1291890] : [class_Lattices_Osemilattice__inf(_1291882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291882), _1291884), _1291886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291882), _1291888), _1291890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291882), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1291882), _1291884), _1291888)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1291882), _1291886), _1291890))))], (25118 ^ _779142) ^ [_1220651, _1220653, _1220655] : [class_Groups_Ocomm__monoid__add(_1220651), hAPP(_1220653, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1220651), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220651), _1220653), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1220655)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220651), _1220653), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220655)))], (36016 ^ _779142) ^ [_1455493, _1455495, _1455497, _1455499] : [c_Equiv__Relations_Oequivp(_1455493, _1455495), hBOOL(hAPP(hAPP(_1455495, _1455497), _1455499)), -(hBOOL(hAPP(hAPP(_1455495, _1455499), _1455497)))], (15595 ^ _779142) ^ [_1052468, _1052470, _1052472] : [class_Int_Onumber__ring(_1052468), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052468), hAPP(c_Int_Onumber__class_Onumber__of(_1052468), _1052470)), hAPP(c_Int_Onumber__class_Onumber__of(_1052468), _1052472)) = hAPP(c_Int_Onumber__class_Onumber__of(_1052468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052470), _1052472)))], (20420 ^ _779142) ^ [_1137488, _1137490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137490)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1137488)), hAPP(c_Int_Onat, _1137490)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1137488, _1137490)))], (40787 ^ _779142) ^ [_1578783, _1578785, _1578787] : [-(hAPP(c_Relation_ORange(_1578783, _1578785), _1578787) = hAPP(c_Relation_ODomain(_1578785, _1578783), hAPP(c_Relation_Oconverse(_1578783, _1578785), _1578787)))], (13511 ^ _779142) ^ [_1014141, _1014143, _1014145, _1014147] : [class_Rings_Odivision__ring(_1014141), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014141), _1014143), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014141), _1014145), _1014147)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014141), _1014143), _1014145)), _1014147))], (34829 ^ _779142) ^ [_1424868, _1424870, _1424872, _1424874, _1424876] : [-(_1424868 = c_Orderings_Obot__class_Obot(tc_fun(_1424870, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424872, tc_HOL_Obool)), _1424874), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424870, tc_fun(_1424872, tc_HOL_Obool)), _1424868), _1424876)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424870, tc_fun(_1424872, tc_HOL_Obool)), _1424868), hAPP(hAPP(c_COMBB(tc_fun(_1424872, tc_HOL_Obool), tc_fun(_1424872, tc_HOL_Obool), _1424870), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424872, tc_HOL_Obool)), _1424874)), _1424876)))], (34505 ^ _779142) ^ [_1415404, _1415406, _1415408, _1415410] : [-(_1415404 = c_Orderings_Obot__class_Obot(tc_fun(_1415406, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415406, tc_fun(_1415408, tc_HOL_Obool)), _1415404), hAPP(c_COMBK(tc_fun(_1415408, tc_HOL_Obool), _1415406), _1415410)) = _1415410)], (36526 ^ _779142) ^ [_1466234, _1466236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466234), c_Orderings_Otop__class_Otop(tc_fun(_1466234, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1466234, _1466234, _1466236), c_Orderings_Otop__class_Otop(tc_fun(_1466234, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466234, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1466234, _1466234, _1466236, c_Orderings_Otop__class_Otop(tc_fun(_1466234, tc_HOL_Obool))))], (10743 ^ _779142) ^ [_964767, _964769] : [10744 ^ _779142 : [(10747 ^ _779142) ^ [] : [_964767 = _964769], (10745 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964767), _964769))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964767), hAPP(c_Nat_OSuc, _964769))))], (30790 ^ _779142) ^ [_1330871, _1330873] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1330871, _1330873)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1330871, _1330873), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330871), c_Orderings_Otop__class_Otop(tc_fun(_1330871, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330873), c_Orderings_Otop__class_Otop(tc_fun(_1330873, tc_HOL_Obool))))], (3620 ^ _779142) ^ [_833344, _833346] : [_833346 = _833344, -(c_List_Oreturn__list(_833346) = c_List_Oreturn__list(_833344))], (51127 ^ _779142) ^ [_1813793, _1813795, _1813797, _1813799] : [class_Divides_Osemiring__div(_1813793), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813793), _1813795), _1813797)), -(c_Divides_Odiv__class_Omod(_1813793, c_Divides_Odiv__class_Omod(_1813793, _1813799, _1813797), _1813795) = c_Divides_Odiv__class_Omod(_1813793, _1813799, _1813795))], (10105 ^ _779142) ^ [_952747, _952749, _952751] : [_952749 = _952751, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952747), _952749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952747), _952751))], (47758 ^ _779142) ^ [_1741356, _1741358, _1741360] : [hBOOL(hAPP(hAPP(c_member(_1741356), _1741358), hAPP(c_List_Oset(_1741356), _1741360))), 47763 ^ _779142 : [(47766 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1741356), _1741358), hAPP(c_List_Oset(_1741356), 47762 ^ [_1741356, _1741358, _1741360])))], (47764 ^ _779142) ^ [] : [-(_1741360 = hAPP(hAPP(c_List_Oappend(_1741356), 47761 ^ [_1741356, _1741358, _1741360]), hAPP(hAPP(c_List_Olist_OCons(_1741356), _1741358), 47762 ^ [_1741356, _1741358, _1741360])))]]], (43698 ^ _779142) ^ [_1653524, _1653526, _1653528] : [-(hAPP(c_List_Ohd(_1653524), hAPP(hAPP(c_List_Olist_OCons(_1653524), _1653526), _1653528)) = _1653526)], (17905 ^ _779142) ^ [_1094569] : [_1094569 = 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), _1094569)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47381 ^ _779142) ^ [_1733112, _1733114, _1733116, _1733118] : [47383 ^ _779142 : [(47386 ^ _779142) ^ [] : [hBOOL(hAPP(_1733116, 47382 ^ [_1733112, _1733114, _1733116, _1733118]))], (47384 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733112), 47382 ^ [_1733112, _1733114, _1733116, _1733118]), hAPP(c_List_Oset(_1733112), _1733114))))]], -(c_List_OdropWhile(_1733112, _1733116, hAPP(hAPP(c_List_Oappend(_1733112), _1733114), _1733118)) = c_List_OdropWhile(_1733112, _1733116, _1733118))], (21754 ^ _779142) ^ [_1161233, _1161235] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1161233)), _1161235) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161233), _1161235)))], (37120 ^ _779142) ^ [_1479411, _1479413, _1479415, _1479417] : [-(c_HOL_OThe(tc_prod(_1479411, _1479413), hAPP(c_Product__Type_Oprod_Oprod__case(_1479411, _1479413, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1479411, tc_fun(_1479413, tc_HOL_Obool), tc_fun(_1479413, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1479413, tc_HOL_Obool), tc_fun(_1479413, tc_HOL_Obool)), _1479411), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1479413)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1479411), c_fconj), hAPP(c_fequal, _1479415)))), hAPP(c_fequal, _1479417)))) = hAPP(hAPP(c_Product__Type_OPair(_1479411, _1479413), _1479415), _1479417))], (39982 ^ _779142) ^ [_1558651, _1558653, _1558655, _1558657, _1558659, _1558661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558651, tc_HOL_Obool)), _1558653), _1558655)), 39988 ^ _779142 : [(39991 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558657, tc_HOL_Obool)), hAPP(_1558659, 39987 ^ [_1558651, _1558653, _1558655, _1558657, _1558659, _1558661])), hAPP(_1558661, 39987 ^ [_1558651, _1558653, _1558655, _1558657, _1558659, _1558661])))], (39989 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558651), 39987 ^ [_1558651, _1558653, _1558655, _1558657, _1558659, _1558661]), _1558653)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1558651, _1558657), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1558651, _1558657), _1558653), _1558659)), hAPP(hAPP(c_Product__Type_OSigma(_1558651, _1558657), _1558655), _1558661))))], (37371 ^ _779142) ^ [_1485813, _1485815, _1485817] : [37372 ^ _779142 : [(37375 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485813), hAPP(c_Set_OCollect(_1485813), _1485817)))], (37373 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485813), hAPP(c_Set_OCollect(_1485813), _1485815)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1485813), hAPP(c_Set_OCollect(_1485813), hAPP(hAPP(c_COMBS(_1485813, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1485813), c_fconj), _1485815)), _1485817)))))], (45570 ^ _779142) ^ [_1693626, _1693628, _1693630] : [-(c_List_Oconcat(_1693626, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1693626)), _1693628), _1693630)) = hAPP(hAPP(c_List_Oappend(_1693626), c_List_Oconcat(_1693626, _1693628)), c_List_Oconcat(_1693626, _1693630)))], (43009 ^ _779142) ^ [_1636896, _1636898, _1636900, _1636902, _1636904] : [hAPP(hAPP(c_List_Oappend(_1636896), _1636898), _1636900) = hAPP(hAPP(c_List_Olist_OCons(_1636896), _1636902), _1636904), 43014 ^ _779142 : [(43017 ^ _779142) ^ [] : [-(_1636900 = hAPP(hAPP(c_List_Olist_OCons(_1636896), _1636902), _1636904))], (43015 ^ _779142) ^ [] : [-(_1636898 = c_List_Olist_ONil(_1636896))]], 43019 ^ _779142 : [(43022 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1636896), 43018 ^ [_1636896, _1636898, _1636900, _1636902, _1636904]), _1636900) = _1636904)], (43020 ^ _779142) ^ [] : [-(_1636898 = hAPP(hAPP(c_List_Olist_OCons(_1636896), _1636902), 43018 ^ [_1636896, _1636898, _1636900, _1636902, _1636904]))]]], (35067 ^ _779142) ^ [_1431154, _1431156, _1431158, _1431160, _1431162] : [class_Complete__Lattice_Ocomplete__lattice(_1431154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431156), _1431158)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1431154), _1431160), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1431156, _1431154), _1431158), _1431162)) = hAPP(hAPP(c_Finite__Set_Ofold(_1431156, _1431154, hAPP(hAPP(c_COMBB(_1431154, tc_fun(_1431154, _1431154), _1431156), c_Lattices_Osemilattice__sup__class_Osup(_1431154)), _1431162)), _1431160), _1431158))], (6007 ^ _779142) ^ [_874830, _874832, _874834] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_874830), _874834)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_874830), hAPP(hAPP(c_Set_Oinsert(_874830), _874832), _874834))))], (28527 ^ _779142) ^ [_1283483, _1283485] : [class_Orderings_Olinorder(_1283483), -(c_Big__Operators_Olattice_OSup__fin(_1283483, c_Orderings_Oord__class_Omax(_1283483), hAPP(hAPP(c_Set_Oinsert(_1283483), _1283485), c_Orderings_Obot__class_Obot(tc_fun(_1283483, tc_HOL_Obool)))) = _1283485)], (2076 ^ _779142) ^ [_809308, _809310] : [_809310 = _809308, -(c_Nat_Osemiring__1__class_ONats(_809310) = c_Nat_Osemiring__1__class_ONats(_809308))], (35401 ^ _779142) ^ [_1439886, _1439888, _1439890, _1439892] : [c_FunDef_Oreduction__pair(_1439886, _1439888), -(c_FunDef_Oreduction__pair(_1439890, hAPP(hAPP(c_FunDef_Orp__inv__image(_1439886, _1439890), _1439888), _1439892)))], (26594 ^ _779142) ^ [_1247183, _1247185, _1247187] : [class_Lattices_Olattice(_1247183), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247183), _1247185), _1247187) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247183), _1247187), _1247185))], (41349 ^ _779142) ^ [_1594377, _1594379, _1594381, _1594383, _1594385] : [hAPP(hAPP(c_List_Olist_OCons(_1594377), _1594379), _1594381) = hAPP(hAPP(c_List_Olist_OCons(_1594377), _1594383), _1594385), 41352 ^ _779142 : [(41355 ^ _779142) ^ [] : [-(_1594381 = _1594385)], (41353 ^ _779142) ^ [] : [-(_1594379 = _1594383)]]], (31168 ^ _779142) ^ [_1337798, _1337800, _1337802] : [class_Orderings_Oord(_1337798), 31171 ^ _779142 : [(31178 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337798), _1337802), _1337800)), -(hBOOL(hAPP(hAPP(c_member(_1337798), _1337800), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337798), _1337802))))], (31172 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1337798), _1337800), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337798), _1337802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337798), _1337802), _1337800)))]]], (1146 ^ _779142) ^ [_796409, _796411] : [-(class_Groups_Olinordered__ab__group__add(_796409)), _796411 = _796409, class_Groups_Olinordered__ab__group__add(_796411)], (30936 ^ _779142) ^ [_1333345, _1333347, _1333349, _1333351, _1333353] : [_1333345 = hAPP(_1333347, _1333349), -(hBOOL(hAPP(hAPP(c_member(_1333351), _1333345), hAPP(c_Set_Oimage(_1333353, _1333351, _1333347), c_Orderings_Otop__class_Otop(tc_fun(_1333353, tc_HOL_Obool))))))], (52443 ^ _779142) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (4142 ^ _779142) ^ [_841845, _841847] : [_841847 = _841845, -(c_List_Odrop(_841847) = c_List_Odrop(_841845))], (22316 ^ _779142) ^ [_1171759, _1171761, _1171763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171759)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1171761), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1171763)), 22323 ^ _779142 : [(22324 ^ _779142) ^ [_1171967] : [22326 ^ _779142 : [(22332 ^ _779142) ^ [] : [-(_1171967 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 22328 ^ [_1171759, _1171761, _1171763, _1171967]), 22325 ^ [_1171759, _1171761, _1171763, _1171967]))], (22330 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22328 ^ [_1171759, _1171761, _1171763, _1171967]), _1171763)))], (22327 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22325 ^ [_1171759, _1171761, _1171763, _1171967]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1171759))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171967), _1171761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1171967), _1171759)), _1171761)))]]], (52681 ^ _779142) ^ [_1836543] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1836543)))], (37419 ^ _779142) ^ [_1487101, _1487103, _1487105] : [hBOOL(hAPP(hAPP(c_member(_1487101), _1487103), hAPP(c_Set_OCollect(_1487101), _1487105))), -(hBOOL(hAPP(_1487105, _1487103)))], (20099 ^ _779142) ^ [_1131926, _1131928] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131926, _1131928) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1131926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131926), _1131928)), _1131928)))], (18897 ^ _779142) ^ [_1111733] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111733)))], (51151 ^ _779142) ^ [_1814207, _1814209, _1814211, _1814213] : [class_Divides_Osemiring__div(_1814207), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814207), _1814209), c_Divides_Odiv__class_Omod(_1814207, _1814211, _1814213))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814207), _1814209), _1814213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814207), _1814209), _1814211)))], (49987 ^ _779142) ^ [_1790080, _1790082, _1790084] : [c_Fun_Oinj__on(_1790080, _1790082, _1790084, c_Orderings_Otop__class_Otop(tc_fun(_1790080, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1790080, _1790082, _1790084), c_Orderings_Otop__class_Otop(tc_fun(_1790080, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790082, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1790080, _1790082, _1790084, c_Orderings_Otop__class_Otop(tc_fun(_1790080, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790082, tc_HOL_Obool))))], (15539 ^ _779142) ^ [_1051245, _1051247, _1051249] : [class_Int_Onumber__ring(_1051245), class_Rings_Olinordered__idom(_1051245), 15546 ^ _779142 : [(15553 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051247), _1051249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051245), hAPP(c_Int_Onumber__class_Onumber__of(_1051245), _1051247)), hAPP(c_Int_Onumber__class_Onumber__of(_1051245), _1051249))))], (15547 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051245), hAPP(c_Int_Onumber__class_Onumber__of(_1051245), _1051247)), hAPP(c_Int_Onumber__class_Onumber__of(_1051245), _1051249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051247), _1051249)))]]], (15191 ^ _779142) ^ [_1045021, _1045023, _1045025] : [class_Int_Onumber(_1045021), class_Orderings_Oord(_1045021), 15198 ^ _779142 : [(15205 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045021), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045023)), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045025)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045021), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045023)), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045025)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045025))], (15199 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045021), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045023)), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045025))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045021), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045023)), hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045025)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045021), _1045023))]]], (23347 ^ _779142) ^ [_1190460, _1190462] : [class_Groups_Oordered__ab__group__add(_1190460), 23350 ^ _779142 : [(23357 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190460), c_Groups_Ozero__class_Ozero(_1190460)), _1190462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190460), hAPP(c_Groups_Ouminus__class_Ouminus(_1190460), _1190462)), c_Groups_Ozero__class_Ozero(_1190460))))], (23351 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190460), hAPP(c_Groups_Ouminus__class_Ouminus(_1190460), _1190462)), c_Groups_Ozero__class_Ozero(_1190460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190460), c_Groups_Ozero__class_Ozero(_1190460)), _1190462)))]]], (47797 ^ _779142) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (25790 ^ _779142) ^ [_1232436, _1232438] : [class_Int_Onumber__ring(_1232436), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232436), _1232438), hAPP(c_Int_Onumber__class_Onumber__of(_1232436), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232436), _1232438), _1232438))], (18919 ^ _779142) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (2240 ^ _779142) ^ [_811820, _811822, _811824, _811826] : [-(c_Orderings_Oord_Omax(_811826, _811822) = c_Orderings_Oord_Omax(_811824, _811820)), _811826 = _811824, _811822 = _811820], (21176 ^ _779142) ^ [_1151299, _1151301, _1151303] : [21178 ^ _779142 : [(21181 ^ _779142) ^ [] : [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(_1151301, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21177 ^ [_1151299, _1151301, _1151303]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1151301, 21177 ^ [_1151299, _1151301, _1151303])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21179 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21177 ^ [_1151299, _1151301, _1151303]), _1151299)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1151301, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1151303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151303), hAPP(_1151301, _1151299))), 21191 ^ _779142 : [(21194 ^ _779142) ^ [] : [-(hAPP(_1151301, 21190 ^ [_1151299, _1151301, _1151303]) = _1151303)], (21192 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21190 ^ [_1151299, _1151301, _1151303]), _1151299)))]]], (24153 ^ _779142) ^ [_1204427, _1204429, _1204431, _1204433, _1204435] : [class_Orderings_Olinorder(_1204427), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204427, _1204429), _1204431) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204427, _1204433), _1204435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204427), _1204429), _1204431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204427), _1204433), _1204435)), -(_1204429 = _1204433)], (22680 ^ _779142) ^ [_1178682] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1178682)) = 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), _1178682))))], (33871 ^ _779142) ^ [_1399514, _1399516] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1399514), _1399516) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1399514, _1399516)))], (16085 ^ _779142) ^ [_1061714, _1061716, _1061718, _1061720] : [class_Orderings_Olinorder(_1061714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061714), _1061716)), hBOOL(hAPP(hAPP(c_member(_1061714), _1061718), _1061716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061714), hAPP(hAPP(c_Finite__Set_Ofold(_1061714, _1061714, c_Orderings_Oord__class_Omin(_1061714)), _1061720), _1061716)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1061714), _1061718), _1061720))))], (25560 ^ _779142) ^ [_1228359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1228359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1228359))))], (18434 ^ _779142) ^ [_1103766] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103766), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103766)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1103766)))], (1546 ^ _779142) ^ [_801409, _801411] : [-(class_Rings_Olinordered__comm__semiring__strict(_801409)), _801411 = _801409, class_Rings_Olinordered__comm__semiring__strict(_801411)], (18913 ^ _779142) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (22733 ^ _779142) ^ [_1179620] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1179620))))], (49164 ^ _779142) ^ [_1773000, _1773002] : [c_Relation_Oantisym(_1773000, _1773002), -(c_Relation_Oantisym(_1773000, hAPP(c_Relation_Oconverse(_1773000, _1773000), _1773002)))], (2152 ^ _779142) ^ [_810444, _810446] : [_810446 = _810444, -(c_Int_Osucc(_810446) = c_Int_Osucc(_810444))], (24121 ^ _779142) ^ [_1203914] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203914)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203914))], (6589 ^ _779142) ^ [_885112, _885114, _885116, _885118, _885120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885112, tc_HOL_Obool)), _885114), hAPP(c_Set_Oimage(_885116, _885112, _885118), _885120)))), 6590 ^ _779142 : [(6591 ^ _779142) ^ [_885192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885116, tc_HOL_Obool)), _885192), _885120)), _885114 = hAPP(c_Set_Oimage(_885116, _885112, _885118), _885192)]]], (33399 ^ _779142) ^ [_1390304, _1390306, _1390308] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390304), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390306)), _1390308)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390304, _1390306), hAPP(c_Divides_OnegateSnd, _1390308))))], (19581 ^ _779142) ^ [_1123250] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1123250), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5959 ^ _779142) ^ [_873830] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_873830), c_Orderings_Obot__class_Obot(tc_fun(_873830, tc_HOL_Obool)))))], (48262 ^ _779142) ^ [_1752275, _1752277, _1752279, _1752281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752275), _1752277)), -(hAPP(hAPP(c_List_Onth(_1752279), c_List_Oreplicate(_1752279, _1752277, _1752281)), _1752275) = _1752281)], (18941 ^ _779142) ^ [_1112260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112260), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1112260)))], (40669 ^ _779142) ^ [_1576095, _1576097, _1576099] : [c_Relation_Ototal__on(_1576095, _1576097, _1576099), -(c_Relation_Ototal__on(_1576095, _1576097, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576095, _1576095), tc_HOL_Obool)), _1576099), c_Relation_OId(_1576095))))], (11344 ^ _779142) ^ [_974104, _974106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974104), _974106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974104), hAPP(c_Nat_OSuc, _974106))))], (41717 ^ _779142) ^ [_1605953] : [-(c_List_Olists(_1605953, c_Orderings_Otop__class_Otop(tc_fun(_1605953, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1605953), tc_HOL_Obool)))], (38665 ^ _779142) ^ [_1527585, _1527587, _1527589] : [c_Wellfounded_Owf(_1527585, _1527587), -(c_Wellfounded_Owf(_1527585, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527585, _1527585), tc_HOL_Obool)), _1527589), _1527587)))], (38302 ^ _779142) ^ [_1516369, _1516371, _1516373, _1516375, _1516377, _1516379, _1516381] : [-(hAPP(c_Product__Type_Osnd(_1516369, _1516371), hAPP(c_Product__Type_Omap__pair(_1516373, _1516369, _1516375, _1516371, _1516377, _1516379), _1516381)) = hAPP(_1516379, hAPP(c_Product__Type_Osnd(_1516373, _1516375), _1516381)))], (9923 ^ _779142) ^ [_948587, _948589, _948591, _948593, _948595] : [class_Rings_Osemiring(_948587), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948587), _948589), _948591)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948587), _948593), _948591)), _948595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948587), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948587), _948589), _948593)), _948591)), _948595))], (42403 ^ _779142) ^ [_1624155, _1624157, _1624159, _1624161] : [hBOOL(hAPP(c_List_Odistinct(_1624155), _1624157)), -(hBOOL(hAPP(hAPP(c_member(_1624155), _1624159), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1624155, tc_HOL_Obool)), hAPP(c_List_Oset(_1624155), _1624157)), hAPP(hAPP(c_Set_Oinsert(_1624155), hAPP(hAPP(c_List_Onth(_1624155), _1624157), _1624161)), c_Orderings_Obot__class_Obot(tc_fun(_1624155, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1624155), hAPP(hAPP(c_List_Olist__update(_1624155, _1624157), _1624161), _1624159))))], (17744 ^ _779142) ^ [_1091848, _1091850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091848), _1091850)), -(_1091850 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091848), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 17747 ^ [_1091848, _1091850])))], (19929 ^ _779142) ^ [_1129030, _1129032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129030), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129032), _1129030)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129030), _1129032) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9957 ^ _779142) ^ [_949264, _949266, _949268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949264), _949268)), _949266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949264), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949266), _949268))))], (12064 ^ _779142) ^ [_987370, _987372, _987374] : [class_Rings_Olinordered__semiring__strict(_987370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987370), c_Groups_Ozero__class_Ozero(_987370)), _987372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987370), _987374), c_Groups_Ozero__class_Ozero(_987370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987370), _987372), _987374)), c_Groups_Ozero__class_Ozero(_987370))))], (29299 ^ _779142) ^ [_1299035, _1299037, _1299039, _1299041] : [class_Lattices_Olattice(_1299035), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299035), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299035), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299035), _1299037), _1299039)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299035), _1299037), _1299041))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299035), _1299037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299035), _1299039), _1299041)))))], (44746 ^ _779142) ^ [_1675475, _1675477, _1675479, _1675481] : [class_Groups_Ocomm__monoid__add(_1675475), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675475), _1675477), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675479, _1675481))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1675475), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675475), _1675477), c_List_Oupto(_1675479, _1675481))))], (40711 ^ _779142) ^ [_1577186, _1577188] : [c_Wellfounded_Oacyclic(_1577186, _1577188), -(c_Wellfounded_Oacyclic(_1577186, hAPP(c_Relation_Oconverse(_1577186, _1577186), _1577188)))], (45663 ^ _779142) ^ [_1696597, _1696599, _1696601] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696597)), hAPP(c_List_Ofilter(_1696597, _1696599), _1696601))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696597)), _1696601))))], (49901 ^ _779142) ^ [_1788220, _1788222, _1788224, _1788226, _1788228] : [c_Fun_Obij__betw(_1788220, _1788222, _1788224, c_Orderings_Otop__class_Otop(tc_fun(_1788220, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788222, tc_HOL_Obool))), c_Fun_Obij__betw(_1788226, _1788220, _1788228, c_Orderings_Otop__class_Otop(tc_fun(_1788226, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788220, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788226, _1788222, c_Orderings_Otop__class_Otop(tc_fun(_1788226, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1788220, _1788222, _1788226, _1788224), _1788228)) = hAPP(c_Fun_Ocomp(_1788220, _1788226, _1788222, c_Hilbert__Choice_Oinv__into(_1788226, _1788220, c_Orderings_Otop__class_Otop(tc_fun(_1788226, tc_HOL_Obool)), _1788228)), c_Hilbert__Choice_Oinv__into(_1788220, _1788222, c_Orderings_Otop__class_Otop(tc_fun(_1788220, tc_HOL_Obool)), _1788224)))], (40456 ^ _779142) ^ [_1571013, _1571015, _1571017] : [_1571015 = _1571017, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571013, _1571013)), hAPP(hAPP(c_Product__Type_OPair(_1571013, _1571013), _1571015), _1571017)), c_Relation_OId(_1571013))))], (42900 ^ _779142) ^ [_1633909, _1633911, _1633913, _1633915, _1633917] : [-(hAPP(hAPP(c_List_Ozip(_1633909, _1633911), hAPP(hAPP(c_List_Olist_OCons(_1633909), _1633913), _1633915)), _1633917) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633909, _1633911)), _1633911, c_List_Olist_ONil(tc_prod(_1633909, _1633911)), hAPP(hAPP(c_COMBC(_1633911, tc_fun(tc_List_Olist(_1633911), tc_List_Olist(tc_prod(_1633909, _1633911))), tc_fun(tc_List_Olist(_1633911), tc_List_Olist(tc_prod(_1633909, _1633911)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633909, _1633911)), tc_List_Olist(tc_prod(_1633909, _1633911))), tc_fun(tc_fun(tc_List_Olist(_1633911), tc_List_Olist(tc_prod(_1633909, _1633911))), tc_fun(tc_List_Olist(_1633911), tc_List_Olist(tc_prod(_1633909, _1633911)))), _1633911), c_COMBB(tc_List_Olist(tc_prod(_1633909, _1633911)), tc_List_Olist(tc_prod(_1633909, _1633911)), tc_List_Olist(_1633911))), hAPP(hAPP(c_COMBB(tc_prod(_1633909, _1633911), tc_fun(tc_List_Olist(tc_prod(_1633909, _1633911)), tc_List_Olist(tc_prod(_1633909, _1633911))), _1633911), c_List_Olist_OCons(tc_prod(_1633909, _1633911))), hAPP(c_Product__Type_OPair(_1633909, _1633911), _1633913)))), hAPP(c_List_Ozip(_1633909, _1633911), _1633915))), _1633917))], (6099 ^ _779142) ^ [_876467, _876469, _876471, _876473, _876475, _876477, _876479, _876481] : [c_Finite__Set_Ofolding__image__simple(_876467, _876469, _876471, _876473, _876475, _876477), hBOOL(hAPP(c_Finite__Set_Ofinite(_876469), _876479)), -(hBOOL(hAPP(hAPP(c_member(_876469), _876481), _876479))), -(hAPP(_876477, hAPP(hAPP(c_Set_Oinsert(_876469), _876481), _876479)) = hAPP(hAPP(_876471, hAPP(_876475, _876481)), hAPP(_876477, _876479)))], (39736 ^ _779142) ^ [_1553044, _1553046, _1553048, _1553050, _1553052, _1553054] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1553044, _1553046), _1553044, tc_prod(_1553048, _1553050), c_Product__Type_Ofst(_1553044, _1553046)), c_Product__Type_Omap__pair(_1553048, _1553044, _1553050, _1553046, _1553052, _1553054)) = hAPP(c_Fun_Ocomp(_1553048, _1553044, tc_prod(_1553048, _1553050), _1553052), c_Product__Type_Ofst(_1553048, _1553050)))], (18208 ^ _779142) ^ [_1099633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1099633)), -(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), _1099633))))], (9945 ^ _779142) ^ [_949074, _949076] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949074), _949076))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949076), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949074), _949076)) = _949074)], (21738 ^ _779142) ^ [_1160891, _1160893] : [hAPP(_1160891, 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), _1160891), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160893)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1160891), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1160893)))], (46822 ^ _779142) ^ [_1720748, _1720750, _1720752] : [c_List_OtakeWhile(_1720748, _1720750, _1720752) = _1720752, 46825 ^ _779142 : [(46826 ^ _779142) ^ [_1720835] : [hBOOL(hAPP(hAPP(c_member(_1720748), _1720835), hAPP(c_List_Oset(_1720748), _1720752))), -(hBOOL(hAPP(_1720750, _1720835)))]]], (51631 ^ _779142) ^ [_1822087] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822087), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1822087 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19367 ^ _779142) ^ [_1119635, _1119637] : [class_Groups_Oordered__ab__group__add__abs(_1119635), 19370 ^ _779142 : [(19377 ^ _779142) ^ [] : [-(_1119637 = c_Groups_Ozero__class_Ozero(_1119635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119635), c_Groups_Ozero__class_Ozero(_1119635)), hAPP(c_Groups_Oabs__class_Oabs(_1119635), _1119637))))], (19371 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119635), c_Groups_Ozero__class_Ozero(_1119635)), hAPP(c_Groups_Oabs__class_Oabs(_1119635), _1119637))), _1119637 = c_Groups_Ozero__class_Ozero(_1119635)]]], (14635 ^ _779142) ^ [_1034529, _1034531, _1034533, _1034535] : [class_Fields_Ofield(_1034529), -(_1034531 = c_Groups_Ozero__class_Ozero(_1034529)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034529), _1034533), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034529), _1034535), _1034531)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034529), _1034531), _1034533)), _1034535)), _1034531))], (42511 ^ _779142) ^ [_1626386, _1626388] : [42513 ^ _779142 : [(42517 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42515 ^ [_1626386, _1626388]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626386)), _1626388))))], (42519 ^ _779142) ^ [] : [42512 ^ [_1626386, _1626388] = 42515 ^ [_1626386, _1626388]], (42521 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1626386), _1626388), 42512 ^ [_1626386, _1626388]) = hAPP(hAPP(c_List_Onth(_1626386), _1626388), 42515 ^ [_1626386, _1626388]))], (42514 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42512 ^ [_1626386, _1626388]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626386)), _1626388))))]], -(hBOOL(hAPP(c_List_Odistinct(_1626386), _1626388)))], (29109 ^ _779142) ^ [_1295247, _1295249, _1295251, _1295253] : [class_Lattices_Osemilattice__inf(_1295247), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295247), _1295249), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295247), _1295251), _1295253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295247), _1295251), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295247), _1295249), _1295253)))], (43760 ^ _779142) ^ [_1654410, _1654412] : [hBOOL(hAPP(c_List_Odistinct(_1654410), _1654412)), -(hBOOL(hAPP(c_List_Odistinct(_1654410), hAPP(c_List_Otl(_1654410), _1654412))))], (23195 ^ _779142) ^ [_1187587, _1187589] : [class_Groups_Oordered__ab__group__add__abs(_1187587), -(hAPP(c_Groups_Oabs__class_Oabs(_1187587), hAPP(c_Groups_Ouminus__class_Ouminus(_1187587), _1187589)) = hAPP(c_Groups_Oabs__class_Oabs(_1187587), _1187589))], (13557 ^ _779142) ^ [_1014998, _1015000, _1015002, _1015004] : [class_Rings_Odivision__ring(_1014998), -(_1015000 = c_Groups_Ozero__class_Ozero(_1014998)), 13564 ^ _779142 : [(13571 ^ _779142) ^ [] : [_1015002 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014998), _1015004), _1015000), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014998), _1015002), _1015000) = _1015004)], (13565 ^ _779142) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014998), _1015002), _1015000) = _1015004, -(_1015002 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014998), _1015004), _1015000))]]], (1156 ^ _779142) ^ [_796534, _796536] : [-(class_Rings_Oring__1__no__zero__divisors(_796534)), _796536 = _796534, class_Rings_Oring__1__no__zero__divisors(_796536)], (3226 ^ _779142) ^ [_827201, _827203] : [_827203 = _827201, -(c_Random_Orange(_827203) = c_Random_Orange(_827201))], (11111 ^ _779142) ^ [_970575] : [class_Rings_Ozero__neq__one(_970575), c_Groups_Oone__class_Oone(_970575) = c_Groups_Ozero__class_Ozero(_970575)], (13817 ^ _779142) ^ [_1019648, _1019650, _1019652, _1019654] : [class_Fields_Olinordered__field(_1019648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019648), c_Groups_Ozero__class_Ozero(_1019648)), _1019650)), 13824 ^ _779142 : [(13831 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019648), _1019652), _1019650)), _1019654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019648), _1019652), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019648), _1019654), _1019650))))], (13825 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019648), _1019652), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019648), _1019654), _1019650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019648), _1019652), _1019650)), _1019654)))]]], (7032 ^ _779142) ^ [_894890, _894892, _894894, _894896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894890, tc_HOL_Obool)), _894892), hAPP(hAPP(c_Set_Oinsert(_894890), _894894), _894896)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_894890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894890, tc_HOL_Obool)), _894892), _894896))))], (32079 ^ _779142) ^ [_1360649, _1360651, _1360653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360649, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1360649, tc_fun(_1360649, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360649)), _1360651)), hAPP(hAPP(c_COMBC(_1360649, tc_fun(_1360649, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360649)), _1360653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360649, tc_HOL_Obool)), _1360651), _1360653)))], (36572 ^ _779142) ^ [_1467288, _1467290, _1467292, _1467294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467288), _1467290)), 36575 ^ _779142 : [(36582 ^ _779142) ^ [] : [hAPP(c_Finite__Set_Ocard(_1467292), hAPP(c_Set_Oimage(_1467288, _1467292, _1467294), _1467290)) = hAPP(c_Finite__Set_Ocard(_1467288), _1467290), -(c_Fun_Oinj__on(_1467288, _1467292, _1467294, _1467290))], (36576 ^ _779142) ^ [] : [c_Fun_Oinj__on(_1467288, _1467292, _1467294, _1467290), -(hAPP(c_Finite__Set_Ocard(_1467292), hAPP(c_Set_Oimage(_1467288, _1467292, _1467294), _1467290)) = hAPP(c_Finite__Set_Ocard(_1467288), _1467290))]]], (52355 ^ _779142) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (26876 ^ _779142) ^ [_1253007, _1253009, _1253011] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1253007, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1253007, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1253007), _1253009)), hAPP(c_Set_OPow(_1253007), _1253011))), hAPP(c_Set_OPow(_1253007), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253007, tc_HOL_Obool)), _1253009), _1253011)))))], (48483 ^ _779142) ^ [_1756921, _1756923] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756921), c_List_Olist_ONil(_1756921)), _1756923))], (39816 ^ _779142) ^ [_1554890, _1554892, _1554894, _1554896, _1554898, _1554900, _1554902] : [c_Finite__Set_Ofolding__image(_1554890, _1554892, _1554894, _1554896, _1554898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554892), _1554900)), -(hAPP(hAPP(_1554898, _1554902), _1554900) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1554890, _1554892, _1554894), _1554902), _1554896), _1554900))], (11350 ^ _779142) ^ [_974207, _974209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974207), _974209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974207)), _974209)))], (24928 ^ _779142) ^ [_1217371] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1217371)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217371))))], (15615 ^ _779142) ^ [_1052936] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052936) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45460 ^ _779142) ^ [_1691285, _1691287] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691285)), c_List_Oremdups(_1691285, _1691287)) = hAPP(c_Finite__Set_Ocard(_1691285), hAPP(c_List_Oset(_1691285), _1691287)))], (46873 ^ _779142) ^ [_1721776, _1721778] : [-(c_List_OtakeWhile(_1721776, _1721778, c_List_Olist_ONil(_1721776)) = c_List_Olist_ONil(_1721776))], (7466 ^ _779142) ^ [_902673, _902675, _902677, _902679] : [class_Orderings_Oorder(_902673), _902675 = _902677, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902673), _902679), _902677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902673), _902679), _902675)))], (32103 ^ _779142) ^ [_1362234, _1362236, _1362238, _1362240, _1362242] : [class_Groups_Ocomm__monoid__add(_1362234), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362236, _1362234), hAPP(hAPP(c_COMBS(_1362236, _1362234, _1362234), hAPP(hAPP(c_COMBB(_1362234, tc_fun(_1362234, _1362234), _1362236), c_Groups_Oplus__class_Oplus(_1362234)), _1362238)), _1362240)), _1362242) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362234), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362236, _1362234), _1362238), _1362242)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362236, _1362234), _1362240), _1362242)))], (30890 ^ _779142) ^ [_1332630, _1332632] : [class_Lattices_Obounded__lattice__top(_1332630), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332630), _1332632), c_Orderings_Otop__class_Otop(_1332630)) = c_Orderings_Otop__class_Otop(_1332630))], (32085 ^ _779142) ^ [_1360824, _1360826, _1360828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360824, tc_HOL_Obool)), _1360826), _1360828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360824, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1360824, tc_fun(_1360824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360824)), _1360826)), hAPP(hAPP(c_COMBC(_1360824, tc_fun(_1360824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360824)), _1360828))))], (52393 ^ _779142) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (25808 ^ _779142) ^ [_1232757, _1232759] : [class_Rings_Oring__1__no__zero__divisors(_1232757), 25811 ^ _779142 : [(25818 ^ _779142) ^ [] : [_1232759 = c_Groups_Ozero__class_Ozero(_1232757), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1232757), _1232759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1232757))], (25812 ^ _779142) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1232757), _1232759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1232757), -(_1232759 = c_Groups_Ozero__class_Ozero(_1232757))]]], (35059 ^ _779142) ^ [] : [-(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)))], (40783 ^ _779142) ^ [_1578693, _1578695, _1578697] : [-(hAPP(c_Relation_ORange(_1578693, _1578695), hAPP(c_Relation_Oconverse(_1578695, _1578693), _1578697)) = hAPP(c_Relation_ODomain(_1578695, _1578693), _1578697))], (48644 ^ _779142) ^ [_1760684] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760684)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760684)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48356 ^ _779142) ^ [_1753931, _1753933] : [class_Lazy__Sequence_Osmall__lazy(_1753931), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753931), _1753933) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1753931), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1753931)), c_List_Olist_ONil(_1753931)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753931))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1753933)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1753931, tc_List_Olist(_1753931)), tc_List_Olist(_1753931), c_Lazy__Sequence_Oproduct(_1753931, tc_List_Olist(_1753931), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753931, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753933), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753933), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1753931, tc_List_Olist(_1753931), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753931))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1753931), tc_List_Olist(_1753931)), tc_fun(tc_List_Olist(_1753931), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753931))), _1753931), hAPP(c_COMBB(tc_List_Olist(_1753931), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753931)), tc_List_Olist(_1753931)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1753931)))), c_List_Olist_OCons(_1753931))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1753931)))))], (2652 ^ _779142) ^ [_818242, _818244, _818246, _818248, _818250, _818252] : [-(c_FunDef_Oin__rel(_818252, _818248, _818244) = c_FunDef_Oin__rel(_818250, _818246, _818242)), _818252 = _818250, _818248 = _818246, _818244 = _818242], (17463 ^ _779142) ^ [_1086565, _1086567, _1086569, _1086571] : [class_Divides_Osemiring__div(_1086565), -(c_Divides_Odiv__class_Omod(_1086565, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086565), c_Divides_Odiv__class_Omod(_1086565, _1086567, _1086569)), _1086571), _1086569) = c_Divides_Odiv__class_Omod(_1086565, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086565), _1086567), _1086571), _1086569))], (10619 ^ _779142) ^ [_962676, _962678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962676), hAPP(c_Nat_OSuc, _962678))), _962676)))], (46776 ^ _779142) ^ [_1719711, _1719713] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719711), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719711))), _1719713))), 46779 ^ _779142 : [(46786 ^ _779142) ^ [] : [-(_1719713 = c_List_Olist_ONil(tc_List_Olist(_1719711))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719711))), c_List_Otranspose(_1719711, _1719713)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719711)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719711)), _1719713), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46780 ^ _779142) ^ [] : [_1719713 = c_List_Olist_ONil(tc_List_Olist(_1719711)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719711))), c_List_Otranspose(_1719711, _1719713)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7038 ^ _779142) ^ [_895043, _895045, _895047, _895049] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895043, tc_HOL_Obool)), _895045), _895049))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_895043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895043, tc_HOL_Obool)), _895045), hAPP(hAPP(c_Set_Oinsert(_895043), _895047), _895049)))))], (37150 ^ _779142) ^ [_1480302, _1480304, _1480306, _1480308, _1480310, _1480312] : [-(_1480302 = c_Orderings_Obot__class_Obot(tc_fun(_1480304, tc_HOL_Obool))), 37156 ^ _779142 : [(37159 ^ _779142) ^ [] : [c_Fun_Oinj__on(_1480306, _1480308, _1480310, hAPP(_1480312, 37155 ^ [_1480302, _1480304, _1480306, _1480308, _1480310, _1480312]))], (37157 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480304), 37155 ^ [_1480302, _1480304, _1480306, _1480308, _1480310, _1480312]), _1480302)))]], -(c_Fun_Oinj__on(_1480306, _1480308, _1480310, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480304, tc_fun(_1480306, tc_HOL_Obool)), _1480302), _1480312)))], (34955 ^ _779142) ^ [] : [-(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)))], (47282 ^ _779142) ^ [_1730841, _1730843, _1730845, _1730847, _1730849, _1730851, _1730853, _1730855] : [47284 ^ _779142 : [(47287 ^ _779142) ^ [] : [hAPP(c_Fun_Ocomp(_1730845, _1730845, _1730847, hAPP(_1730849, 47283 ^ [_1730841, _1730843, _1730845, _1730847, _1730849, _1730851, _1730853, _1730855])), _1730851) = hAPP(c_Fun_Ocomp(_1730847, _1730845, _1730847, _1730851), hAPP(_1730853, 47283 ^ [_1730841, _1730843, _1730845, _1730847, _1730849, _1730851, _1730853, _1730855]))], (47285 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730841), 47283 ^ [_1730841, _1730843, _1730845, _1730847, _1730849, _1730851, _1730853, _1730855]), hAPP(c_List_Oset(_1730841), _1730843))))]], -(hAPP(c_List_Ofoldl(_1730845, _1730841, hAPP(c_COMBC(_1730841, _1730845, _1730845), _1730849), hAPP(_1730851, _1730855)), _1730843) = hAPP(_1730851, hAPP(c_List_Ofoldl(_1730847, _1730841, hAPP(c_COMBC(_1730841, _1730847, _1730847), _1730853), _1730855), _1730843)))], (32964 ^ _779142) ^ [_1382052, _1382054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1382052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1382052), _1382054)), -(c_Divides_Odivmod__nat(_1382054, _1382052) = 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), _1382054), _1382052)), _1382052))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1382054), _1382052), _1382052)))], (34823 ^ _779142) ^ [_1424735, _1424737, _1424739, _1424741, _1424743] : [_1424735 = c_Orderings_Obot__class_Obot(tc_fun(_1424737, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424739, tc_HOL_Obool)), _1424741), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424737, tc_fun(_1424739, tc_HOL_Obool)), _1424735), _1424743)) = _1424741)], (34318 ^ _779142) ^ [_1409589, _1409591, _1409593, _1409595, _1409597] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409589, tc_fun(_1409591, tc_HOL_Obool)), _1409593), hAPP(hAPP(c_COMBB(tc_fun(_1409591, tc_HOL_Obool), tc_fun(_1409591, tc_HOL_Obool), _1409589), hAPP(c_Set_Oinsert(_1409591), _1409595)), _1409597)) = hAPP(hAPP(c_Set_Oinsert(_1409591), _1409595), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409589, tc_fun(_1409591, tc_HOL_Obool)), _1409593), _1409597)))], (37395 ^ _779142) ^ [_1486377, _1486379, _1486381, _1486383, _1486385] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486377, _1486379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486377, tc_HOL_Obool)), _1486381), _1486383)), _1486385) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486377, _1486379), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486377, _1486379), _1486381), _1486385)), hAPP(hAPP(c_Product__Type_OSigma(_1486377, _1486379), _1486383), _1486385)))], (39738 ^ _779142) ^ [_1553115, _1553117, _1553119, _1553121, _1553123, _1553125] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1553115, _1553117), _1553117, tc_prod(_1553119, _1553121), c_Product__Type_Osnd(_1553115, _1553117)), c_Product__Type_Omap__pair(_1553119, _1553115, _1553121, _1553117, _1553123, _1553125)) = hAPP(c_Fun_Ocomp(_1553121, _1553117, tc_prod(_1553119, _1553121), _1553125), c_Product__Type_Osnd(_1553119, _1553121)))], (32405 ^ _779142) ^ [_1369535, _1369537, _1369539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369535), _1369537)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369535, tc_HOL_Obool)), _1369539), _1369537) = hAPP(hAPP(c_Finite__Set_Ofold(_1369535, tc_fun(_1369535, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1369535, tc_HOL_Obool), tc_fun(tc_fun(_1369535, tc_HOL_Obool), tc_fun(_1369535, tc_HOL_Obool)), _1369535), hAPP(c_COMBC(tc_fun(_1369535, tc_HOL_Obool), tc_fun(_1369535, tc_HOL_Obool), tc_fun(_1369535, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1369535, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1369535, tc_fun(_1369535, tc_HOL_Obool), tc_fun(_1369535, tc_HOL_Obool)), c_Set_Oinsert(_1369535)), c_Orderings_Obot__class_Obot(tc_fun(_1369535, tc_HOL_Obool))))), _1369539), _1369537))], (35099 ^ _779142) ^ [_1431891, _1431893, _1431895, _1431897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1431891), _1431893)), 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)), _1431895), _1431891)), 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)), _1431897), _1431893)), 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)), _1431895), _1431897)), _1431893)), c_FunDef_Omax__strict)))], (35653 ^ _779142) ^ [_1447020, _1447022, _1447024] : [-(hAPP(c_Relation_OImage(_1447020, _1447020, c_Relation_OId__on(_1447020, _1447022)), _1447024) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447020, tc_HOL_Obool)), _1447022), _1447024))], (23211 ^ _779142) ^ [_1187877, _1187879] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187877), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187879)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187877, _1187879)))], (10123 ^ _779142) ^ [_953150, _953152, _953154, _953156, _953158] : [class_Rings_Ocomm__semiring__1(_953150), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), _953152), _953154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), _953156), _953158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), _953152), _953156)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953150), _953154), _953158)))], (52241 ^ _779142) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (31757 ^ _779142) ^ [_1349334, _1349336, _1349338, _1349340, _1349342, _1349344] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349334, tc_fun(_1349336, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1349334, tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_fun(_1349336, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349336, tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_fun(_1349336, tc_HOL_Obool)), _1349334), c_COMBC(_1349336, tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349336, tc_prod(_1349334, _1349336)), tc_fun(_1349336, tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), _1349334), hAPP(c_COMBB(tc_prod(_1349334, _1349336), tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool), _1349336), c_member(tc_prod(_1349334, _1349336)))), c_Product__Type_OPair(_1349334, _1349336)))), _1349338)), hAPP(hAPP(c_COMBC(_1349334, tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_fun(_1349336, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349336, tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_fun(_1349336, tc_HOL_Obool)), _1349334), c_COMBC(_1349336, tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1349336, tc_prod(_1349334, _1349336)), tc_fun(_1349336, tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool)), _1349334), hAPP(c_COMBB(tc_prod(_1349334, _1349336), tc_fun(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool), tc_HOL_Obool), _1349336), c_member(tc_prod(_1349334, _1349336)))), c_Product__Type_OPair(_1349334, _1349336)))), _1349340)), _1349342), _1349344)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1349334, _1349336)), hAPP(hAPP(c_Product__Type_OPair(_1349334, _1349336), _1349342), _1349344)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1349334, _1349336), tc_HOL_Obool)), _1349338), _1349340))))], (25572 ^ _779142) ^ [_1228555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228555), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1228555)), c_Int_OPls)))], (38366 ^ _779142) ^ [_1518591, _1518593, _1518595, _1518597] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518591, _1518593, _1518595), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518591, _1518593), tc_HOL_Obool))), _1518597) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518591, _1518595), tc_HOL_Obool)))], (16453 ^ _779142) ^ [_1068812, _1068814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068812), _1068814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068812)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068814))))], (7560 ^ _779142) ^ [_904091, _904093, _904095, _904097, _904099] : [c_Finite__Set_Ofun__left__comm__idem(_904091, _904093, _904095), -(hAPP(hAPP(_904095, _904097), hAPP(hAPP(_904095, _904097), _904099)) = hAPP(hAPP(_904095, _904097), _904099))], (8615 ^ _779142) ^ [_923805, _923807, _923809, _923811] : [class_Groups_Ocancel__ab__semigroup__add(_923805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923805), _923807), _923809) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923805), _923807), _923811), -(_923809 = _923811)], (28170 ^ _779142) ^ [_1277032, _1277034, _1277036, _1277038] : [class_Orderings_Olinorder(_1277032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277032), _1277034)), hBOOL(hAPP(hAPP(c_member(_1277032), _1277036), _1277034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277032), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1277032), _1277036), _1277038)), hAPP(hAPP(c_Finite__Set_Ofold(_1277032, _1277032, c_Orderings_Oord__class_Omax(_1277032)), _1277038), _1277034))))], (42238 ^ _779142) ^ [_1620198, _1620200, _1620202, _1620204] : [42240 ^ _779142 : [(42243 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1620202, 42239 ^ [_1620198, _1620200, _1620202, _1620204])), hAPP(_1620204, 42239 ^ [_1620198, _1620200, _1620202, _1620204])))], (42241 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620198), 42239 ^ [_1620198, _1620200, _1620202, _1620204]), hAPP(c_List_Oset(_1620198), _1620200))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1620198, _1620202, _1620200)), c_List_Olist_Olist__size(_1620198, _1620204, _1620200))))], (19143 ^ _779142) ^ [_1115565, _1115567] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115565))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115565), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115567)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1068 ^ _779142) ^ [_795236, _795238, _795240, _795242, _795244, _795246, _795248, _795250, _795252, _795254] : [-(c_Finite__Set_Ofolding__image(_795252, _795248, _795244, _795240, _795236)), c_Finite__Set_Ofolding__image(_795254, _795250, _795246, _795242, _795238), _795254 = _795252, _795250 = _795248, _795246 = _795244, _795242 = _795240, _795238 = _795236], (31262 ^ _779142) ^ [_1339546, _1339548, _1339550, _1339552] : [class_Groups_Ocomm__monoid__mult(_1339546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339548), _1339550)), 31272 ^ _779142 : [(31275 ^ _779142) ^ [] : [hAPP(_1339552, 31271 ^ [_1339546, _1339548, _1339550, _1339552]) = c_Groups_Oone__class_Oone(_1339546)], (31273 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339548), 31271 ^ [_1339546, _1339548, _1339550, _1339552]), _1339550)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1339546, _1339548, c_Groups_Otimes__class_Otimes(_1339546)), _1339552), c_Groups_Oone__class_Oone(_1339546)), _1339550) = c_Groups_Oone__class_Oone(_1339546))], (37918 ^ _779142) ^ [_1501962, _1501964, _1501966, _1501968] : [-(c_Nitpick_Oprod(_1501962, _1501964, _1501966, _1501968) = hAPP(c_Set_OCollect(tc_prod(_1501962, _1501964)), hAPP(c_Product__Type_Oprod_Oprod__case(_1501962, _1501964, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1501962, tc_fun(_1501964, tc_HOL_Obool), tc_fun(_1501964, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1501964, tc_HOL_Obool), tc_fun(_1501964, tc_HOL_Obool)), _1501962), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1501964)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501962), c_fconj), hAPP(hAPP(c_COMBC(_1501962, tc_fun(_1501962, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501962)), _1501966)))), hAPP(hAPP(c_COMBC(_1501964, tc_fun(_1501964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501964)), _1501968)))))], (25372 ^ _779142) ^ [_1225057, _1225059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225057)), -(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)))), _1225059))), 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)))), _1225057)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1225059), _1225057))], (46564 ^ _779142) ^ [_1715284, _1715286] : [c_List_Olist_ONil(_1715284) = hAPP(c_List_Orev(_1715284), _1715286), -(_1715286 = c_List_Olist_ONil(_1715284))], (51277 ^ _779142) ^ [_1816315, _1816317] : [-(_1816315 = _1816317), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816315), _1816317)), 51284 ^ _779142 : [(51287 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816317), _1816315))], (51285 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816315), _1816317)))]]], (4710 ^ _779142) ^ [_850801, _850803, _850805, _850807] : [-(c_List_Olexord(_850807, _850803) = c_List_Olexord(_850805, _850801)), _850807 = _850805, _850803 = _850801], (24123 ^ _779142) ^ [_1203946, _1203948, _1203950, _1203952, _1203954] : [class_Orderings_Olinorder(_1203946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203946), _1203948), _1203950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203946), _1203952), _1203954)), 24134 ^ _779142 : [(24143 ^ _779142) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203946, _1203948), _1203950) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203946, _1203952), _1203954)), _1203948 = _1203952, _1203950 = _1203954], (24135 ^ _779142) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203946, _1203948), _1203950) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203946, _1203952), _1203954), 24138 ^ _779142 : [(24141 ^ _779142) ^ [] : [-(_1203950 = _1203954)], (24139 ^ _779142) ^ [] : [-(_1203948 = _1203952)]]]]], (37912 ^ _779142) ^ [_1501639, _1501641, _1501643, _1501645] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1501639, _1501641), _1501643), _1501645) = hAPP(c_Set_OCollect(tc_prod(_1501641, _1501641)), hAPP(c_Product__Type_Oprod_Oprod__case(_1501641, _1501641, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1501641, tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_fun(_1501641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501641, tc_fun(tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_fun(_1501641, tc_HOL_Obool)), _1501641), c_COMBC(_1501641, tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501641, tc_prod(_1501639, _1501639)), tc_fun(_1501641, tc_fun(tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_HOL_Obool)), _1501641), hAPP(c_COMBB(tc_prod(_1501639, _1501639), tc_fun(tc_fun(tc_prod(_1501639, _1501639), tc_HOL_Obool), tc_HOL_Obool), _1501641), c_member(tc_prod(_1501639, _1501639)))), hAPP(hAPP(c_COMBC(_1501641, tc_fun(_1501641, _1501639), tc_fun(_1501641, tc_prod(_1501639, _1501639))), hAPP(hAPP(c_COMBB(tc_fun(_1501639, tc_prod(_1501639, _1501639)), tc_fun(tc_fun(_1501641, _1501639), tc_fun(_1501641, tc_prod(_1501639, _1501639))), _1501641), c_COMBB(_1501639, tc_prod(_1501639, _1501639), _1501641)), hAPP(hAPP(c_COMBB(_1501639, tc_fun(_1501639, tc_prod(_1501639, _1501639)), _1501641), c_Product__Type_OPair(_1501639, _1501639)), _1501645))), _1501645)))), _1501643))))], (16767 ^ _779142) ^ [_1074114, _1074116, _1074118] : [class_Orderings_Olinorder(_1074114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074114), _1074116)), hBOOL(hAPP(hAPP(c_member(_1074114), _1074118), _1074116)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074114), _1074118), c_Big__Operators_Olinorder__class_OMin(_1074114, _1074116)) = c_Big__Operators_Olinorder__class_OMin(_1074114, _1074116))], (30423 ^ _779142) ^ [_1323171, _1323173, _1323175] : [class_Lattices_Olattice(_1323171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323171), _1323173)), -(hBOOL(hAPP(hAPP(c_member(_1323171), _1323175), _1323173))), -(_1323173 = c_Orderings_Obot__class_Obot(tc_fun(_1323171, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1323171, hAPP(hAPP(c_Set_Oinsert(_1323171), _1323175), _1323173)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323171), _1323175), c_Big__Operators_Olattice__class_OInf__fin(_1323171, _1323173)))], (10893 ^ _779142) ^ [_967192, _967194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967192), hAPP(c_Nat_OSuc, _967194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967192), _967194))), -(_967192 = hAPP(c_Nat_OSuc, _967194))], (52263 ^ _779142) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11532 ^ _779142) ^ [_977533, _977535] : [class_Rings_Olinordered__ring(_977533), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977533), c_Groups_Ozero__class_Ozero(_977533)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977533), _977535), _977535))))], (20764 ^ _779142) ^ [_1144068, _1144070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144068)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144070), _1144068)), _1144068) = _1144070)], (33805 ^ _779142) ^ [_1398139, _1398141, _1398143] : [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), _1398139), _1398141))), -(hBOOL(hAPP(hAPP(_1398143, _1398139), _1398141))), 33812 ^ _779142 : [(33815 ^ _779142) ^ [] : [-(33811 ^ [_1398139, _1398141, _1398143] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1398143, 33811 ^ [_1398139, _1398141, _1398143]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 33810 ^ [_1398139, _1398141, _1398143], 33811 ^ [_1398139, _1398141, _1398143]))))], (33821 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1398143, 33810 ^ [_1398139, _1398141, _1398143]), 33811 ^ [_1398139, _1398141, _1398143]))], (33813 ^ _779142) ^ [] : [-(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), 33810 ^ [_1398139, _1398141, _1398143]), 33811 ^ [_1398139, _1398141, _1398143]))))]]], (44035 ^ _779142) ^ [_1660407] : [class_Orderings_Olinorder(_1660407), -(c_Finite__Set_Ofun__left__comm(_1660407, tc_List_Olist(_1660407), c_List_Olinorder__class_Oinsort__key(_1660407, _1660407, c_COMBI(_1660407))))], (42232 ^ _779142) ^ [_1620119] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1620119)), -(c_List_Onat__list(_1620119))], (13453 ^ _779142) ^ [_1012943, _1012945] : [-(hBOOL(hAPP(_1012943, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1012943, _1012945)), 13461 ^ _779142 : [(13464 ^ _779142) ^ [_1013181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1013181), 13460 ^ [_1012943, _1012945])), hBOOL(hAPP(_1012943, _1013181))], (13470 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1012943, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13460 ^ [_1012943, _1012945]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13462 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13460 ^ [_1012943, _1012945]), _1012945)))]]], (32515 ^ _779142) ^ [_1372203, _1372205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372203)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372205))), -(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(_1372205))), 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), _1372203)), c_Int_Onat))))))], (8084 ^ _779142) ^ [_912589, _912591, _912593, _912595, _912597, _912599, _912601] : [c_Finite__Set_Ofun__left__comm(_912589, _912591, _912593), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912589, _912591, _912593, _912595, _912597), _912599)), hBOOL(hAPP(hAPP(c_member(_912589), _912601), _912597)), 8096 ^ _779142 : [(8099 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912589, _912591, _912593, _912595, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912589, tc_HOL_Obool)), _912597), hAPP(hAPP(c_Set_Oinsert(_912589), _912601), c_Orderings_Obot__class_Obot(tc_fun(_912589, tc_HOL_Obool))))), 8095 ^ [_912589, _912591, _912593, _912595, _912597, _912599, _912601])))], (8097 ^ _779142) ^ [] : [-(_912599 = hAPP(hAPP(_912593, _912601), 8095 ^ [_912589, _912591, _912593, _912595, _912597, _912599, _912601]))]]], (34464 ^ _779142) ^ [_1413871, _1413873, _1413875, _1413877, _1413879] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413871, tc_fun(_1413873, tc_HOL_Obool)), _1413875), hAPP(hAPP(c_COMBB(tc_fun(_1413873, tc_HOL_Obool), tc_fun(_1413873, tc_HOL_Obool), _1413871), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413873, tc_HOL_Obool)), _1413877)), _1413879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413873, tc_HOL_Obool)), _1413877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413871, tc_fun(_1413873, tc_HOL_Obool)), _1413875), _1413879)))], (20678 ^ _779142) ^ [_1142448, _1142450, _1142452, _1142454, _1142456] : [-(hBOOL(hAPP(hAPP(c_member(_1142448), _1142450), c_SetInterval_Oord_OgreaterThanLessThan(_1142448, _1142452, _1142454, _1142456)))), hBOOL(hAPP(hAPP(_1142452, _1142454), _1142450)), hBOOL(hAPP(hAPP(_1142452, _1142450), _1142456))], (44626 ^ _779142) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (28775 ^ _779142) ^ [_1288291, _1288293, _1288295, _1288297] : [hBOOL(hAPP(_1288291, _1288293)), hBOOL(hAPP(_1288295, _1288293)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288297, tc_HOL_Obool)), _1288291), _1288295), _1288293)))], (52409 ^ _779142) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12556 ^ _779142) ^ [_995857, _995859, _995861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995857), _995859)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995861), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995859), _995857))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995861), _995857)), hAPP(c_Nat_OSuc, _995859)))], (49975 ^ _779142) ^ [_1789788, _1789790, _1789792, _1789794, _1789796] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789788, _1789790, tc_HOL_Obool, _1789792), _1789794), _1789796)), -(hBOOL(hAPP(_1789792, hAPP(hAPP(c_Product__Type_OPair(_1789788, _1789790), _1789794), _1789796))))], (10045 ^ _779142) ^ [_951341, _951343, _951345, _951347, _951349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951341), _951343)), 10048 ^ _779142 : [(10055 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951347), 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), _951343), _951341)), _951345)), _951349))), -(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), _951341), _951345)), _951347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951343), _951345)), _951349))))], (10049 ^ _779142) ^ [] : [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), _951341), _951345)), _951347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951343), _951345)), _951349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951347), 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), _951343), _951341)), _951345)), _951349))))]]], (8248 ^ _779142) ^ [_916424, _916426, _916428, _916430] : [-(c_Fun_Ofun__upd(_916424, _916426, _916428, _916430, hAPP(_916428, _916430)) = _916428)], (15497 ^ _779142) ^ [_1050565, _1050567, _1050569, _1050571] : [class_Orderings_Olinorder(_1050565), 15500 ^ _779142 : [(15501 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1050565), _1050567), _1050569)), _1050571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), _1050567), _1050571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), _1050569), _1050571)))], (15511 ^ _779142) ^ [] : [15512 ^ _779142 : [(15515 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), _1050569), _1050571))], (15513 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), _1050567), _1050571))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050565), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1050565), _1050567), _1050569)), _1050571)))]]], (38782 ^ _779142) ^ [_1530005, _1530007] : [-(hAPP(c_Relation_ODomain(_1530005, _1530007), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530005, _1530007), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1530005, tc_HOL_Obool)))], (25506 ^ _779142) ^ [_1227438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1227438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1227438)))], (44582 ^ _779142) ^ [_1672167, _1672169, _1672171, _1672173, _1672175] : [class_Groups_Ocomm__monoid__add(_1672167), hBOOL(hAPP(hAPP(c_member(_1672169), _1672171), hAPP(c_List_Oset(_1672169), _1672173))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672167), hAPP(hAPP(c_List_Omap(_1672169, _1672167), _1672175), _1672173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672167), hAPP(_1672175, _1672171)), hAPP(c_List_Omonoid__add__class_Olistsum(_1672167), hAPP(hAPP(c_List_Omap(_1672169, _1672167), _1672175), c_List_Oremove1(_1672169, _1672171, _1672173)))))], (26030 ^ _779142) ^ [] : [-(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))))], (40677 ^ _779142) ^ [_1576255] : [-(hAPP(c_Relation_Oconverse(_1576255, _1576255), c_Relation_OId(_1576255)) = c_Relation_OId(_1576255))], (49322 ^ _779142) ^ [_1776306, _1776308] : [c_Relation_Osym(_1776306, _1776308), -(hAPP(c_Relation_Oconverse(_1776306, _1776306), _1776308) = _1776308)], (50504 ^ _779142) ^ [_1802401, _1802403, _1802405] : [c_List_Olist__all(tc_Nat_Onat, _1802401, c_List_Oupt(_1802403, _1802405)), -(c_List_Oall__interval__nat(_1802401, _1802403, _1802405))], (52345 ^ _779142) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (44877 ^ _779142) ^ [_1678118, _1678120, _1678122, _1678124, _1678126] : [c_List_Opartition(_1678118, _1678120, _1678122) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678118), tc_List_Olist(_1678118)), _1678124), _1678126), 44880 ^ _779142 : [(44887 ^ _779142) ^ [_1678380] : [hBOOL(hAPP(hAPP(c_member(_1678118), _1678380), hAPP(c_List_Oset(_1678118), _1678126))), hBOOL(hAPP(_1678120, _1678380))], (44881 ^ _779142) ^ [_1678271] : [hBOOL(hAPP(hAPP(c_member(_1678118), _1678271), hAPP(c_List_Oset(_1678118), _1678124))), -(hBOOL(hAPP(_1678120, _1678271)))]]], (27512 ^ _779142) ^ [_1264695, _1264697] : [class_Lattices_Olattice(_1264695), -(c_Big__Operators_Olattice__class_OSup__fin(_1264695, hAPP(hAPP(c_Set_Oinsert(_1264695), _1264697), c_Orderings_Obot__class_Obot(tc_fun(_1264695, tc_HOL_Obool)))) = _1264697)], (42732 ^ _779142) ^ [_1630710, _1630712, _1630714, _1630716] : [hAPP(hAPP(c_List_Olist__update(_1630710, _1630712), _1630714), _1630716) = c_List_Olist_ONil(_1630710), -(_1630712 = c_List_Olist_ONil(_1630710))], (42057 ^ _779142) ^ [_1614386, _1614388] : [-(c_List_Olists(_1614386, _1614388) = hAPP(c_Set_OCollect(tc_List_Olist(_1614386)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614386), tc_fun(_1614386, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614386, tc_HOL_Obool), tc_fun(tc_fun(_1614386, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614386)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614386, tc_HOL_Obool))), c_List_Oset(_1614386))), _1614388)))], (48056 ^ _779142) ^ [_1747632, _1747634, _1747636] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747632)), c_List_Osplice(_1747632, _1747634, _1747636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747632)), _1747634)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747632)), _1747636)))], (39325 ^ _779142) ^ [_1543502] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39321 ^ [_1543502]), c_Int_OInteg)))], (3482 ^ _779142) ^ [_831129, _831131] : [_831131 = _831129, -(c_SetInterval_Oord__class_OatMost(_831131) = c_SetInterval_Oord__class_OatMost(_831129))], (10959 ^ _779142) ^ [_968291, _968293] : [class_Groups_Omonoid__add(_968291), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968291), c_Groups_Ozero__class_Ozero(_968291)), _968293) = _968293)], (30487 ^ _779142) ^ [_1324355, _1324357, _1324359] : [class_Lattices_Olattice(_1324355), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324355), _1324357)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324355), _1324359)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324355, tc_HOL_Obool)), _1324357), _1324359) = c_Orderings_Obot__class_Obot(tc_fun(_1324355, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324355), c_Big__Operators_Olattice__class_OInf__fin(_1324355, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324355, tc_HOL_Obool)), _1324357), _1324359))), c_Big__Operators_Olattice__class_OInf__fin(_1324355, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324355, tc_HOL_Obool)), _1324357), _1324359))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324355), c_Big__Operators_Olattice__class_OInf__fin(_1324355, _1324357)), c_Big__Operators_Olattice__class_OInf__fin(_1324355, _1324359)))], (41844 ^ _779142) ^ [_1609104, _1609106, _1609108, _1609110] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609104) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1609106), hAPP(hAPP(c_List_Olist_OCons(_1609106), _1609108), _1609110)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609104)) = _1609108)], (39149 ^ _779142) ^ [_1538767, _1538769, _1538771] : [c_Wellfounded_Oacyclic(_1538767, _1538769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538767, _1538767), tc_HOL_Obool)), _1538771), _1538769)), -(c_Wellfounded_Oacyclic(_1538767, _1538771))], (18981 ^ _779142) ^ [_1112827, _1112829] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112827), _1112829) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1112827 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1112827 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (23013 ^ _779142) ^ [_1184232, _1184234] : [class_Groups_Ogroup__add(_1184232), 23016 ^ _779142 : [(23023 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_1184232) = _1184234, -(c_Groups_Ozero__class_Ozero(_1184232) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184232), _1184234))], (23017 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(_1184232) = hAPP(c_Groups_Ouminus__class_Ouminus(_1184232), _1184234), -(c_Groups_Ozero__class_Ozero(_1184232) = _1184234)]]], (34919 ^ _779142) ^ [_1427305, _1427307, _1427309, _1427311, _1427313] : [-(_1427305 = c_Orderings_Obot__class_Obot(tc_fun(_1427307, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427307, tc_fun(_1427309, tc_HOL_Obool)), _1427305), hAPP(hAPP(c_COMBC(_1427307, tc_fun(_1427309, tc_HOL_Obool), tc_fun(_1427309, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1427309, tc_HOL_Obool), tc_fun(tc_fun(_1427309, tc_HOL_Obool), tc_fun(_1427309, tc_HOL_Obool)), _1427307), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427309, tc_HOL_Obool))), _1427311)), _1427313)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427309, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427307, tc_fun(_1427309, tc_HOL_Obool)), _1427305), _1427311)), _1427313))], (44223 ^ _779142) ^ [_1663522, _1663524, _1663526] : [-(c_List_Olast(_1663522, hAPP(hAPP(c_List_Oappend(_1663522), _1663524), hAPP(hAPP(c_List_Olist_OCons(_1663522), _1663526), c_List_Olist_ONil(_1663522)))) = _1663526)], (11844 ^ _779142) ^ [_983293, _983295] : [class_Groups_Olinordered__ab__group__add(_983293), 11847 ^ _779142 : [(11854 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983293), c_Groups_Ozero__class_Ozero(_983293)), _983295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983293), c_Groups_Ozero__class_Ozero(_983293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983293), _983295), _983295))))], (11848 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983293), c_Groups_Ozero__class_Ozero(_983293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983293), _983295), _983295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983293), c_Groups_Ozero__class_Ozero(_983293)), _983295)))]]], (43175 ^ _779142) ^ [_1640650, _1640652, _1640654] : [hAPP(hAPP(c_List_Oappend(_1640650), _1640652), _1640654) = _1640652, -(_1640654 = c_List_Olist_ONil(_1640650))], (51073 ^ _779142) ^ [_1812759, _1812761, _1812763, _1812765] : [class_Divides_Osemiring__div(_1812759), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812759), _1812761), _1812763)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812759), _1812761), _1812765)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1812759), _1812763), _1812765)), _1812761) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1812759), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812759), _1812763), _1812761)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812759), _1812765), _1812761)))], (44101 ^ _779142) ^ [_1661652, _1661654, _1661656] : [class_Orderings_Olinorder(_1661652), -(hBOOL(hAPP(hAPP(c_member(_1661652), _1661654), hAPP(c_List_Oset(_1661652), _1661656)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661652, _1661652, c_COMBI(_1661652), _1661654, _1661656) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661652, _1661652, c_COMBI(_1661652)), _1661654), _1661656))], (45218 ^ _779142) ^ [_1686316, _1686318, _1686320, _1686322, _1686324, _1686326, _1686328, _1686330] : [c_List_Olist__all2(_1686316, _1686318, _1686320, _1686322, _1686324), hBOOL(hAPP(hAPP(_1686320, _1686326), _1686328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686330), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686318)), _1686324))), -(c_List_Olist__all2(_1686316, _1686318, _1686320, hAPP(hAPP(c_List_Olist__update(_1686316, _1686322), _1686330), _1686326), hAPP(hAPP(c_List_Olist__update(_1686318, _1686324), _1686330), _1686328)))], (35679 ^ _779142) ^ [_1447618, _1447620, _1447622, _1447624] : [_1447618 = _1447620, hBOOL(hAPP(hAPP(c_member(_1447622), _1447618), _1447624)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447622, _1447622)), hAPP(hAPP(c_Product__Type_OPair(_1447622, _1447622), _1447618), _1447620)), c_Relation_OId__on(_1447622, _1447624))))], (34039 ^ _779142) ^ [_1402844, _1402846, _1402848, _1402850, _1402852, _1402854] : [-(c_Product__Type_Oprod_Oprod__rec(_1402844, _1402846, _1402848, _1402850, hAPP(hAPP(c_Product__Type_OPair(_1402844, _1402846), _1402852), _1402854)) = hAPP(hAPP(_1402850, _1402852), _1402854))], (5506 ^ _779142) ^ [_863313, _863315, _863317, _863319] : [-(tc_Nitpick_Opair__box(_863319, _863315) = tc_Nitpick_Opair__box(_863317, _863313)), _863319 = _863317, _863315 = _863313], (21752 ^ _779142) ^ [_1161190, _1161192] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1161190), _1161192)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1161190)), _1161192))], (37335 ^ _779142) ^ [_1484795, _1484797, _1484799, _1484801, _1484803, _1484805] : [-(hBOOL(hAPP(hAPP(c_member(_1484795), _1484797), _1484799))), 37338 ^ _779142 : [(37345 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484795), _1484801), _1484799))), -(hAPP(c_Set_Ovimage(_1484803, _1484795, hAPP(hAPP(c_COMBC(_1484803, _1484795, _1484795), hAPP(hAPP(c_COMBC(_1484803, _1484795, tc_fun(_1484795, _1484795)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484795, tc_fun(_1484795, _1484795)), _1484803), c_If(_1484795)), hAPP(hAPP(c_COMBC(_1484803, tc_fun(_1484803, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484803)), _1484805))), _1484797)), _1484801)), _1484799) = c_Orderings_Obot__class_Obot(tc_fun(_1484803, tc_HOL_Obool)))], (37339 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484795), _1484801), _1484799)), -(hAPP(c_Set_Ovimage(_1484803, _1484795, hAPP(hAPP(c_COMBC(_1484803, _1484795, _1484795), hAPP(hAPP(c_COMBC(_1484803, _1484795, tc_fun(_1484795, _1484795)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484795, tc_fun(_1484795, _1484795)), _1484803), c_If(_1484795)), hAPP(hAPP(c_COMBC(_1484803, tc_fun(_1484803, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484803)), _1484805))), _1484797)), _1484801)), _1484799) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484803, tc_HOL_Obool)), _1484805))]]], (37233 ^ _779142) ^ [_1482299, _1482301, _1482303, _1482305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482299, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1482301, _1482299, _1482303), hAPP(c_Set_Ovimage(_1482301, _1482299, _1482303), _1482305))), _1482305)))], (13667 ^ _779142) ^ [_1016816, _1016818] : [class_Rings_Odivision__ring__inverse__zero(_1016816), 13670 ^ _779142 : [(13677 ^ _779142) ^ [] : [-(_1016818 = c_Groups_Ozero__class_Ozero(_1016816)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016816), _1016818), _1016818) = c_Groups_Oone__class_Oone(_1016816))], (13671 ^ _779142) ^ [] : [_1016818 = c_Groups_Ozero__class_Ozero(_1016816), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016816), _1016818), _1016818) = c_Groups_Ozero__class_Ozero(_1016816))]]], (40959 ^ _779142) ^ [_1583225, _1583227, _1583229] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583225, _1583225)), _1583227), c_Transitive__Closure_Ortrancl(_1583225, _1583229))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583225, _1583225)), _1583227), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583225, _1583225), tc_HOL_Obool), 40962 ^ [_1583225, _1583227, _1583229]), _1583229))))], (35511 ^ _779142) ^ [_1443193, _1443195, _1443197, _1443199, _1443201] : [hBOOL(hAPP(hAPP(c_member(_1443193), _1443195), hAPP(c_Relation_OImage(_1443197, _1443193, _1443199), hAPP(hAPP(c_Set_Oinsert(_1443197), _1443201), c_Orderings_Obot__class_Obot(tc_fun(_1443197, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443197, _1443193)), hAPP(hAPP(c_Product__Type_OPair(_1443197, _1443193), _1443201), _1443195)), _1443199)))], (43157 ^ _779142) ^ [_1640319, _1640321, _1640323] : [_1640319 = _1640321, -(_1640319 = hAPP(hAPP(c_List_Oappend(_1640323), c_List_Olist_ONil(_1640323)), _1640321))], (48268 ^ _779142) ^ [_1752390, _1752392, _1752394, _1752396] : [-(hAPP(hAPP(c_List_Oappend(_1752390), c_List_Oreplicate(_1752390, _1752392, _1752394)), c_List_Oreplicate(_1752390, _1752396, _1752394)) = hAPP(hAPP(c_List_Oappend(_1752390), c_List_Oreplicate(_1752390, _1752396, _1752394)), c_List_Oreplicate(_1752390, _1752392, _1752394)))], (42822 ^ _779142) ^ [_1632501, _1632503, _1632505] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632501)), -(c_List_Osublist(_1632503, hAPP(hAPP(c_List_Olist_OCons(_1632503), _1632505), c_List_Olist_ONil(_1632503)), _1632501) = hAPP(hAPP(c_List_Olist_OCons(_1632503), _1632505), c_List_Olist_ONil(_1632503)))], (37779 ^ _779142) ^ [_1496807, _1496809, _1496811, _1496813] : [-(_1496807 = c_Orderings_Obot__class_Obot(tc_fun(_1496809, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1496809, _1496811), _1496811, c_Product__Type_Osnd(_1496809, _1496811)), hAPP(hAPP(c_Product__Type_OSigma(_1496809, _1496811), _1496807), hAPP(c_COMBK(tc_fun(_1496811, tc_HOL_Obool), _1496809), _1496813))) = _1496813)], (42738 ^ _779142) ^ [_1630813, _1630815, _1630817, _1630819] : [_1630815 = c_List_Olist_ONil(_1630813), -(hAPP(hAPP(c_List_Olist__update(_1630813, _1630815), _1630817), _1630819) = c_List_Olist_ONil(_1630813))], (46855 ^ _779142) ^ [_1721508, _1721510, _1721512, _1721514, _1721516] : [-(hBOOL(hAPP(_1721508, _1721510))), -(c_List_OtakeWhile(_1721512, _1721508, hAPP(hAPP(c_List_Oappend(_1721512), _1721514), hAPP(hAPP(c_List_Olist_OCons(_1721512), _1721510), _1721516))) = c_List_OtakeWhile(_1721512, _1721508, _1721514))], (46594 ^ _779142) ^ [_1715818, _1715820, _1715822] : [_1715820 = hAPP(hAPP(c_List_Olist_OCons(_1715818), _1715822), c_List_Olist_ONil(_1715818)), -(hAPP(c_List_Orev(_1715818), _1715820) = hAPP(hAPP(c_List_Olist_OCons(_1715818), _1715822), c_List_Olist_ONil(_1715818)))], (46895 ^ _779142) ^ [_1722148, _1722150, _1722152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722148)), c_List_OtakeWhile(_1722148, _1722150, _1722152))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722148)), _1722152))), hBOOL(hAPP(_1722150, hAPP(hAPP(c_List_Onth(_1722148), _1722152), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722148)), c_List_OtakeWhile(_1722148, _1722150, _1722152)))))], (29253 ^ _779142) ^ [_1298202, _1298204] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298202, tc_HOL_Obool)), _1298204), c_Orderings_Obot__class_Obot(tc_fun(_1298202, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1298202, tc_HOL_Obool)))], (3114 ^ _779142) ^ [_825401, _825403, _825405, _825407] : [-(c_Big__Operators_Olinorder__class_OMin(_825407, _825403) = c_Big__Operators_Olinorder__class_OMin(_825405, _825401)), _825407 = _825405, _825403 = _825401], (5999 ^ _779142) ^ [_874665, _874667, _874669] : [c_Orderings_Obot__class_Obot(tc_fun(_874665, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_874665), _874667), _874669)], (20085 ^ _779142) ^ [_1131573, _1131575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1131573)), _1131575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1131573), hAPP(c_Int_Onat, _1131575))))], (32521 ^ _779142) ^ [_1372348, _1372350] : [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(_1372350))), 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), _1372348)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1372348)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372350))))], (39600 ^ _779142) ^ [_1549884, _1549886, _1549888, _1549890, _1549892, _1549894] : [class_Groups_Ocomm__monoid__mult(_1549884), c_Fun_Oinj__on(_1549886, _1549888, _1549890, _1549892), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549888, _1549884), _1549894), hAPP(c_Set_Oimage(_1549886, _1549888, _1549890), _1549892)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549886, _1549884), hAPP(c_Fun_Ocomp(_1549888, _1549884, _1549886, _1549894), _1549890)), _1549892))], (33185 ^ _779142) ^ [_1386501, _1386503] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1386501), _1386503)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1386501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1386503)))], (2260 ^ _779142) ^ [_812118, _812120, _812122, _812124] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_812124, _812120) = c_Code__Numeral_Odiv__mod__code__numeral(_812122, _812118)), _812124 = _812122, _812120 = _812118], (37703 ^ _779142) ^ [_1494613, _1494615, _1494617, _1494619, _1494621, _1494623] : [hBOOL(hAPP(hAPP(c_member(_1494613), _1494615), _1494617)), 37706 ^ _779142 : [(37713 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494619, tc_HOL_Obool)), _1494621), _1494623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494619, _1494613), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494619, _1494613), _1494621), hAPP(c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494619), _1494617))), hAPP(hAPP(c_Product__Type_OSigma(_1494619, _1494613), _1494623), hAPP(c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494619), _1494617)))))], (37707 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494619, _1494613), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494619, _1494613), _1494621), hAPP(c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494619), _1494617))), hAPP(hAPP(c_Product__Type_OSigma(_1494619, _1494613), _1494623), hAPP(c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494619), _1494617)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494619, tc_HOL_Obool)), _1494621), _1494623)))]]], (1756 ^ _779142) ^ [_804034, _804036] : [-(class_Nat_Osemiring__char__0(_804034)), _804036 = _804034, class_Nat_Osemiring__char__0(_804036)], (17673 ^ _779142) ^ [_1090457] : [-(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), _1090457))))], (45442 ^ _779142) ^ [_1690967, _1690969, _1690971] : [hBOOL(hAPP(c_List_Odistinct(_1690967), _1690969)), -(c_List_Oremove1(_1690967, _1690971, _1690969) = hAPP(c_List_OremoveAll(_1690967, _1690971), _1690969))], (41529 ^ _779142) ^ [_1600111, _1600113, _1600115, _1600117, _1600119, _1600121] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600111), tc_List_Olist(_1600111))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600111), tc_List_Olist(_1600111)), hAPP(hAPP(c_List_Olist_OCons(_1600111), _1600113), _1600115)), hAPP(hAPP(c_List_Olist_OCons(_1600111), _1600117), _1600119))), c_List_Olistrel1(_1600111, _1600121))), 41534 ^ _779142 : [(41537 ^ _779142) ^ [] : [-(_1600115 = _1600119)], (41535 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600111, _1600111)), hAPP(hAPP(c_Product__Type_OPair(_1600111, _1600111), _1600113), _1600117)), _1600121)))]], 41538 ^ _779142 : [(41541 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600111), tc_List_Olist(_1600111))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600111), tc_List_Olist(_1600111)), _1600115), _1600119)), c_List_Olistrel1(_1600111, _1600121))))], (41539 ^ _779142) ^ [] : [-(_1600113 = _1600117)]]], (45378 ^ _779142) ^ [_1689873, _1689875] : [c_List_Oremdups(_1689873, _1689875) = _1689875, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689873)), c_List_Oremdups(_1689873, _1689875)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689873)), _1689875))], (29429 ^ _779142) ^ [_1302187, _1302189, _1302191] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302187, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1302187, tc_HOL_Obool), _1302189)), _1302191) = c_Orderings_Obot__class_Obot(tc_fun(_1302187, tc_HOL_Obool)), 29432 ^ _779142 : [(29433 ^ _779142) ^ [_1302322] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1302187, tc_HOL_Obool)), _1302322), _1302189)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302187, tc_HOL_Obool)), _1302322), _1302191) = c_Orderings_Obot__class_Obot(tc_fun(_1302187, tc_HOL_Obool)))]]], (43472 ^ _779142) ^ [_1647974, _1647976] : [hBOOL(hAPP(c_List_Odistinct(_1647974), hAPP(c_List_Orotate1(_1647974), _1647976))), -(hBOOL(hAPP(c_List_Odistinct(_1647974), _1647976)))], (40342 ^ _779142) ^ [_1568212, _1568214] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1568212, _1568212, _1568212), _1568214), c_Transitive__Closure_Ortrancl(_1568212, _1568214)) = hAPP(hAPP(c_Relation_Orel__comp(_1568212, _1568212, _1568212), c_Transitive__Closure_Ortrancl(_1568212, _1568214)), _1568214))], (52403 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (2812 ^ _779142) ^ [_820744, _820746, _820748, _820750] : [-(c_Nitpick_Oint__lcm(_820750, _820746) = c_Nitpick_Oint__lcm(_820748, _820744)), _820750 = _820748, _820746 = _820744], (9681 ^ _779142) ^ [_943835, _943837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943835), _943837)), -(_943835 = _943837), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943835), _943837)))], (2146 ^ _779142) ^ [_810359, _810361] : [_810361 = _810359, -(c_Int_Oring__1__class_OInts(_810361) = c_Int_Oring__1__class_OInts(_810359))], (19855 ^ _779142) ^ [_1127805, _1127807, _1127809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127807), _1127809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127805), _1127809)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127805), _1127807))))], (52489 ^ _779142) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (33283 ^ _779142) ^ [_1388376, _1388378, _1388380, _1388382] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1388376, _1388378), _1388380)), hBOOL(hAPP(hAPP(_1388378, _1388382), _1388380)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1388376, _1388378), _1388382)))], (22743 ^ _779142) ^ [_1179837, _1179839] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1179837, tc_HOL_Obool)), _1179839), hAPP(c_Set_OPow(_1179837), _1179839))))], (10805 ^ _779142) ^ [_965748, _965750, _965752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965748), _965750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965750), _965752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965748)), _965752)))], (34589 ^ _779142) ^ [_1417956, _1417958, _1417960, _1417962, _1417964] : [34591 ^ _779142 : [(34594 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1417956), _1417958), hAPP(_1417964, 34590 ^ [_1417956, _1417958, _1417960, _1417962, _1417964])))], (34592 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417960), 34590 ^ [_1417956, _1417958, _1417960, _1417962, _1417964]), _1417962)))]], -(hBOOL(hAPP(hAPP(c_member(_1417956), _1417958), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417960, tc_fun(_1417956, tc_HOL_Obool)), _1417962), _1417964))))], (46616 ^ _779142) ^ [_1716339, _1716341, _1716343, _1716345] : [-(hAPP(c_List_Orev(_1716339), hAPP(hAPP(c_List_Omap(_1716341, _1716339), _1716343), _1716345)) = hAPP(hAPP(c_List_Omap(_1716341, _1716339), _1716343), hAPP(c_List_Orev(_1716341), _1716345)))], (31889 ^ _779142) ^ [_1353832, _1353834, _1353836, _1353838] : [class_Groups_Oordered__ab__group__add__abs(_1353832), -(hAPP(c_Groups_Oabs__class_Oabs(_1353832), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353834, _1353832), hAPP(hAPP(c_COMBB(_1353832, _1353832, _1353834), c_Groups_Oabs__class_Oabs(_1353832)), _1353836)), _1353838)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353834, _1353832), hAPP(hAPP(c_COMBB(_1353832, _1353832, _1353834), c_Groups_Oabs__class_Oabs(_1353832)), _1353836)), _1353838))], (24251 ^ _779142) ^ [_1205979, _1205981] : [class_Int_Oring__char__0(_1205979), 24254 ^ _779142 : [(24261 ^ _779142) ^ [] : [_1205981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1205979), _1205981) = c_Groups_Ozero__class_Ozero(_1205979))], (24255 ^ _779142) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1205979), _1205981) = c_Groups_Ozero__class_Ozero(_1205979), -(_1205981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (20436 ^ _779142) ^ [_1137758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1137758)), -(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, _1137758))))], (43850 ^ _779142) ^ [_1656277, _1656279, _1656281, _1656283] : [-(hAPP(c_List_Ofoldl(_1656277, _1656279, _1656281, _1656283), c_List_Olist_ONil(_1656279)) = _1656283)], (44760 ^ _779142) ^ [_1675899, _1675901] : [-(c_Random_Oselect(_1675899, _1675901) = 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(_1675899, 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(_1675899)), _1675901)))), hAPP(hAPP(c_COMBB(_1675899, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675899, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675899, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1675899, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1675899), _1675901)), c_Code__Numeral_Onat__of))))], (31296 ^ _779142) ^ [_1340251, _1340253] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1340251), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1340251, tc_HOL_Obool), _1340253)))), 31297 ^ _779142 : [(31298 ^ _779142) ^ [_1340315] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1340251, tc_HOL_Obool)), _1340315), _1340253)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340251), _1340315))]]], (48042 ^ _779142) ^ [_1747194, _1747196, _1747198, _1747200, _1747202] : [-(hAPP(c_New__DSequence_Opos__bind(_1747194, _1747196, _1747198, _1747200), _1747202) = hAPP(c_Lazy__Sequence_Obind(_1747194, _1747196, hAPP(_1747198, _1747202)), hAPP(hAPP(c_COMBC(_1747194, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747196)), _1747200), _1747202)))], (45141 ^ _779142) ^ [_1684608, _1684610, _1684612, _1684614, _1684616] : [c_List_Olist__all2(_1684608, _1684610, _1684612, _1684614, _1684616), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684608)), _1684614) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684610)), _1684616))], (11231 ^ _779142) ^ [_972251, _972253] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972251), _972253) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_972251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_972253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41314 ^ _779142) ^ [_1592742, _1592744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41315 ^ [_1592742, _1592744]), hAPP(_1592742, 41315 ^ [_1592742, _1592744]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1592742)), _1592744)))))], (7736 ^ _779142) ^ [_906850, _906852, _906854] : [class_Orderings_Opreorder(_906850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906850), _906852), _906854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906850), _906852), _906854)))], (41961 ^ _779142) ^ [_1612187, _1612189, _1612191] : [41963 ^ _779142 : [(41966 ^ _779142) ^ [] : [hBOOL(hAPP(_1612191, 41962 ^ [_1612187, _1612189, _1612191]))], (41964 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612187), 41962 ^ [_1612187, _1612189, _1612191]), hAPP(c_List_Oset(_1612187), _1612189))))]], 41967 ^ _779142 : [(41968 ^ _779142) ^ [_1612371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612371), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612187)), _1612189))), -(hBOOL(hAPP(_1612191, hAPP(hAPP(c_List_Onth(_1612187), _1612189), _1612371))))]]], (40301 ^ _779142) ^ [_1567084, _1567086, _1567088, _1567090] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567084, _1567084)), hAPP(hAPP(c_Product__Type_OPair(_1567084, _1567084), _1567088), _1567090)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool)), _1567086), c_Relation_OId(_1567084)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567084, tc_fun(_1567084, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1567084, tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_fun(_1567084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567084, tc_fun(tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_fun(_1567084, tc_HOL_Obool)), _1567084), c_COMBC(_1567084, tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567084, tc_prod(_1567084, _1567084)), tc_fun(_1567084, tc_fun(tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_HOL_Obool)), _1567084), hAPP(c_COMBB(tc_prod(_1567084, _1567084), tc_fun(tc_fun(tc_prod(_1567084, _1567084), tc_HOL_Obool), tc_HOL_Obool), _1567084), c_member(tc_prod(_1567084, _1567084)))), c_Product__Type_OPair(_1567084, _1567084)))), _1567086)), c_fequal), _1567088), _1567090)))], (41915 ^ _779142) ^ [_1611147, _1611149, _1611151, _1611153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611147), _1611149)), -(hAPP(hAPP(c_List_Onth(_1611151), hAPP(hAPP(c_List_Otake(_1611151), _1611149), _1611153)), _1611147) = hAPP(hAPP(c_List_Onth(_1611151), _1611153), _1611147))], (10911 ^ _779142) ^ [_967462, _967464, _967466] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967462)), _967464)), hAPP(c_Nat_OSuc, _967466)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967462), _967464)), _967466))], (19657 ^ _779142) ^ [_1124418, _1124420, _1124422, _1124424] : [class_Divides_Osemiring__div(_1124418), -(_1124420 = c_Groups_Ozero__class_Ozero(_1124418)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124418), _1124420), _1124422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124418), _1124420), _1124424)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124418), _1124422), _1124424))], (50323 ^ _779142) ^ [_1796658, _1796660, _1796662] : [hBOOL(hAPP(hAPP(_1796660, _1796662), _1796662)), -(hBOOL(hAPP(c_Quotient_ORespects(_1796658, _1796660), _1796662)))], (18722 ^ _779142) ^ [_1108673, _1108675, _1108677, _1108679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108675), _1108677)), -(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), _1108677), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1108679, _1108673))), _1108675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108677), _1108673))))], (46080 ^ _779142) ^ [_1706286, _1706288, _1706290] : [class_Orderings_Olinorder(_1706286), c_List_Olinorder__class_Osorted(_1706286, _1706288), -(c_List_Olinorder__class_Osorted(_1706286, c_List_Olinorder__class_Oinsort__insert__key(_1706286, _1706286, c_COMBI(_1706286), _1706290, _1706288)))], (52441 ^ _779142) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (2886 ^ _779142) ^ [_821875, _821877] : [_821877 = _821875, -(c_Nitpick_Ofrac(_821877) = c_Nitpick_Ofrac(_821875))], (23331 ^ _779142) ^ [_1190192, _1190194] : [class_Groups_Olinordered__ab__group__add(_1190192), 23334 ^ _779142 : [(23341 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190192), c_Groups_Ozero__class_Ozero(_1190192)), _1190194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190192), hAPP(c_Groups_Ouminus__class_Ouminus(_1190192), _1190194)), _1190194)))], (23335 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190192), hAPP(c_Groups_Ouminus__class_Ouminus(_1190192), _1190194)), _1190194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190192), c_Groups_Ozero__class_Ozero(_1190192)), _1190194)))]]], (51479 ^ _779142) ^ [_1819528, _1819530] : [_1819528 = _1819530, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819528), _1819530)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819530), _1819528)))], (46971 ^ _779142) ^ [_1723902, _1723904, _1723906] : [c_List_OdropWhile(_1723902, _1723904, _1723906) = c_List_Olist_ONil(_1723902), 46974 ^ _779142 : [(46975 ^ _779142) ^ [_1723993] : [hBOOL(hAPP(hAPP(c_member(_1723902), _1723993), hAPP(c_List_Oset(_1723902), _1723906))), -(hBOOL(hAPP(_1723904, _1723993)))]]], (37301 ^ _779142) ^ [_1483902, _1483904, _1483906, _1483908] : [-(hBOOL(hAPP(hAPP(c_member(_1483902), _1483904), _1483906))), -(hAPP(c_Set_Ovimage(_1483908, _1483902, hAPP(c_COMBK(_1483902, _1483908), _1483904)), _1483906) = c_Orderings_Obot__class_Obot(tc_fun(_1483908, tc_HOL_Obool)))], (44897 ^ _779142) ^ [_1678967, _1678969, _1678971, _1678973] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678967)), _1678969), c_List_Olists(_1678967, _1678971))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1678967)), _1678969), c_List_Olists(_1678967, _1678973))), -(hBOOL(hAPP(c_List_Olistsp(_1678967, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678967, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1678967, tc_fun(_1678967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1678967)), _1678971)), hAPP(hAPP(c_COMBC(_1678967, tc_fun(_1678967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1678967)), _1678973))), _1678969)))], (47901 ^ _779142) ^ [_1744159, _1744161, _1744163] : [c_List_Olist__all(_1744159, _1744163, _1744161), 47904 ^ _779142 : [(47905 ^ _779142) ^ [_1744240] : [hBOOL(hAPP(hAPP(c_member(_1744159), _1744240), hAPP(c_List_Oset(_1744159), _1744161))), -(hBOOL(hAPP(_1744163, _1744240)))]]], (45825 ^ _779142) ^ [_1701006, _1701008, _1701010, _1701012, _1701014, _1701016] : [-(c_List_Ofoldr(_1701006, _1701008, _1701010, hAPP(hAPP(c_List_Olist_OCons(_1701006), _1701012), _1701014), _1701016) = hAPP(hAPP(_1701010, _1701012), c_List_Ofoldr(_1701006, _1701008, _1701010, _1701014, _1701016)))], (30946 ^ _779142) ^ [_1333569, _1333571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333569), c_Orderings_Otop__class_Otop(tc_fun(_1333569, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1333569), _1333571) = hAPP(c_Finite__Set_Ocard(_1333569), c_Orderings_Otop__class_Otop(tc_fun(_1333569, tc_HOL_Obool))), -(_1333571 = c_Orderings_Otop__class_Otop(tc_fun(_1333569, tc_HOL_Obool)))], (32115 ^ _779142) ^ [_1362618, _1362620, _1362622, _1362624] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1362618), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1362620, tc_Nat_Onat), _1362622), _1362624)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1362620, _1362618), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1362618, _1362620), c_Nat_Osemiring__1__class_Oof__nat(_1362618)), _1362622)), _1362624)), class_Groups_Ocomm__monoid__mult(_1362618), class_Rings_Osemiring__1(_1362618)], (26178 ^ _779142) ^ [_1239393] : [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, _1239393, 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, _1239393, 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))], (41850 ^ _779142) ^ [_1609223, _1609225, _1609227, _1609229] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609223) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1609225), hAPP(hAPP(c_List_Olist_OCons(_1609225), _1609227), _1609229)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609223)) = hAPP(hAPP(c_List_Onth(_1609225), _1609229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609223)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (14952 ^ _779142) ^ [_1040523] : [class_Rings_Oring__1(_1040523), -(hBOOL(hAPP(hAPP(c_member(_1040523), c_Groups_Oone__class_Oone(_1040523)), c_Int_Oring__1__class_OInts(_1040523))))], (52507 ^ _779142) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (23253 ^ _779142) ^ [_1188797, _1188799, _1188801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1188797, tc_HOL_Obool)), _1188799), _1188801)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1188797, tc_HOL_Obool)), _1188799), hAPP(c_Set_OPow(_1188797), _1188801))))], (36068 ^ _779142) ^ [_1456467, _1456469, _1456471, _1456473, _1456475, _1456477] : [c_Equiv__Relations_Ocongruent(_1456467, _1456469, _1456471, _1456473), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456467, _1456467)), hAPP(hAPP(c_Product__Type_OPair(_1456467, _1456467), _1456475), _1456477)), _1456471)), -(hAPP(_1456473, _1456475) = hAPP(_1456473, _1456477))], (50144 ^ _779142) ^ [_1792993, _1792995, _1792997] : [_1792995 = _1792997, -(c_Fun_Obij__betw(_1792993, _1792993, c_Fun_Oid(_1792993), _1792995, _1792997))], (34468 ^ _779142) ^ [_1414070, _1414072, _1414074, _1414076, _1414078] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414070, tc_fun(_1414072, tc_HOL_Obool)), _1414074), hAPP(hAPP(c_COMBS(_1414070, tc_fun(_1414072, tc_HOL_Obool), tc_fun(_1414072, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414072, tc_HOL_Obool), tc_fun(tc_fun(_1414072, tc_HOL_Obool), tc_fun(_1414072, tc_HOL_Obool)), _1414070), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414072, tc_HOL_Obool))), _1414076)), _1414078)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414072, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414070, tc_fun(_1414072, tc_HOL_Obool)), _1414074), _1414076)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414070, tc_fun(_1414072, tc_HOL_Obool)), _1414074), _1414078)))], (5576 ^ _779142) ^ [_864372, _864374, _864376, _864378, _864380, _864382] : [-(c_COMBS(_864382, _864378, _864374) = c_COMBS(_864380, _864376, _864372)), _864382 = _864380, _864378 = _864376, _864374 = _864372], (39610 ^ _779142) ^ [_1550097, _1550099, _1550101, _1550103] : [-(c_Hilbert__Choice_OEps(tc_prod(_1550097, _1550099), hAPP(c_Product__Type_Oprod_Oprod__case(_1550097, _1550099, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1550097, tc_fun(_1550099, tc_HOL_Obool), tc_fun(_1550099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1550099, tc_HOL_Obool), tc_fun(_1550099, tc_HOL_Obool)), _1550097), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1550099)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550097), c_fconj), hAPP(c_fequal, _1550101)))), hAPP(c_fequal, _1550103)))) = hAPP(hAPP(c_Product__Type_OPair(_1550097, _1550099), _1550101), _1550103))], (43169 ^ _779142) ^ [_1640531, _1640533, _1640535] : [_1640533 = c_List_Olist_ONil(_1640531), -(hAPP(hAPP(c_List_Oappend(_1640531), _1640533), _1640535) = _1640535)], (52061 ^ _779142) ^ [_1829850, _1829852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829850)), 52064 ^ _779142 : [(52071 ^ _779142) ^ [] : [_1829852 = 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), _1829850), _1829852)), _1829850)))], (52065 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829850), _1829852)), _1829850)), -(_1829852 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (52093 ^ _779142) ^ [_1830338, _1830340, _1830342, _1830344] : [class_Orderings_Oorder(_1830338), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1830338, 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)))), _1830340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1830338), hAPP(_1830340, _1830342)), hAPP(_1830340, _1830344)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830342), _1830344)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830344), _1830342)))], (38597 ^ _779142) ^ [_1526485, _1526487, _1526489, _1526491] : [c_Wellfounded_Owf(_1526485, _1526487), -(c_Wellfounded_Owf(_1526489, hAPP(hAPP(c_Relation_Oinv__image(_1526485, _1526489), _1526487), _1526491)))], (26774 ^ _779142) ^ [_1250741, _1250743, _1250745] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250741, tc_HOL_Obool)), _1250743), _1250745) = c_Orderings_Obot__class_Obot(tc_fun(_1250741, tc_HOL_Obool))), _1250743 = c_Orderings_Obot__class_Obot(tc_fun(_1250741, tc_HOL_Obool)), _1250745 = c_Orderings_Obot__class_Obot(tc_fun(_1250741, tc_HOL_Obool))], (27610 ^ _779142) ^ [_1266318, _1266320, _1266322] : [class_Lattices_Olattice(_1266318), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266318), _1266320)), -(hBOOL(hAPP(hAPP(c_member(_1266318), _1266322), _1266320))), -(_1266320 = c_Orderings_Obot__class_Obot(tc_fun(_1266318, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1266318, hAPP(hAPP(c_Set_Oinsert(_1266318), _1266322), _1266320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266318), _1266322), c_Big__Operators_Olattice__class_OSup__fin(_1266318, _1266320)))], (35329 ^ _779142) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (43558 ^ _779142) ^ [_1649919, _1649921, _1649923, _1649925] : [hAPP(hAPP(c_List_Oappend(_1649919), _1649921), _1649923) = _1649925, 43561 ^ _779142 : [(43564 ^ _779142) ^ [] : [-(_1649923 = hAPP(hAPP(c_List_Odrop(_1649919), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649919)), _1649921)), _1649925))], (43562 ^ _779142) ^ [] : [-(_1649921 = hAPP(hAPP(c_List_Otake(_1649919), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649919)), _1649921)), _1649925))]]], (10607 ^ _779142) ^ [_962515, _962517] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962515), _962517) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _962515 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962517 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28000 ^ _779142) ^ [_1273544, _1273546] : [class_Orderings_Olinorder(_1273544), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273544), _1273546), _1273546) = _1273546)], (8113 ^ _779142) ^ [_913388, _913390, _913392, _913394, _913396] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_913388, _913390, hAPP(hAPP(c_Set_Oinsert(_913388), _913392), _913394)), _913396))), 8114 ^ _779142 : [(8115 ^ _779142) ^ [_913492, _913494] : [hAPP(hAPP(c_Set_Oinsert(_913388), _913392), _913394) = hAPP(hAPP(c_Set_Oinsert(_913388), _913494), _913492), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_913388, _913388, _913390, _913494, _913492), _913396)), -(hBOOL(hAPP(hAPP(c_member(_913388), _913494), _913492)))]]], (16597 ^ _779142) ^ [_1071270, _1071272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071270), _1071272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071270), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1071272), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (19869 ^ _779142) ^ [_1128044, _1128046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1128044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128046), 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), _1128044), _1128046)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21768 ^ _779142) ^ [_1161542, _1161544, _1161546, _1161548] : [class_Groups_Ocomm__monoid__add(_1161542), 21771 ^ _779142 : [(21778 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161544)), _1161546))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1161542), _1161548), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161546, hAPP(c_Nat_OSuc, _1161544))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161542), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1161542), _1161548), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161546, _1161544))), hAPP(_1161548, hAPP(c_Nat_OSuc, _1161544))))], (21772 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161544)), _1161546)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1161542), _1161548), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161546, hAPP(c_Nat_OSuc, _1161544))) = c_Groups_Ozero__class_Ozero(_1161542))]]], (39469 ^ _779142) ^ [_1546916, _1546918, _1546920, _1546922, _1546924, _1546926] : [-(hAPP(c_Set_Ovimage(_1546916, _1546918, hAPP(c_Fun_Ocomp(_1546920, _1546918, _1546916, _1546922), _1546924)), _1546926) = hAPP(c_Set_Ovimage(_1546916, _1546920, _1546924), hAPP(c_Set_Ovimage(_1546920, _1546918, _1546922), _1546926)))], (1746 ^ _779142) ^ [_803909, _803911] : [-(class_Rings_Ocomm__semiring(_803909)), _803911 = _803909, class_Rings_Ocomm__semiring(_803911)], (48106 ^ _779142) ^ [_1748772, _1748774, _1748776, _1748778, _1748780] : [hBOOL(hAPP(hAPP(_1748776, _1748780), _1748778)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748772, _1748774, _1748776), _1748778), _1748780)))], (23957 ^ _779142) ^ [_1201057, _1201059] : [class_Orderings_Oorder(_1201057), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201057, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1201057), _1201059), c_Orderings_Obot__class_Obot(tc_fun(_1201057, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1201057), _1201059)) = hAPP(hAPP(c_Set_Oinsert(_1201057), _1201059), c_Orderings_Obot__class_Obot(tc_fun(_1201057, tc_HOL_Obool))))], (48963 ^ _779142) ^ [_1767849, _1767851, _1767853, _1767855] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767849, tc_fun(_1767851, tc_HOL_Obool)), _1767853), _1767855) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767851, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767849, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767851, tc_HOL_Obool)), c_HOL_OEx(_1767849)), hAPP(hAPP(c_COMBB(tc_fun(_1767849, tc_HOL_Obool), tc_fun(_1767849, tc_HOL_Obool), tc_fun(_1767851, tc_HOL_Obool)), hAPP(c_COMBS(_1767849, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767849), c_fconj), hAPP(hAPP(c_COMBC(_1767849, tc_fun(_1767849, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767849)), _1767853)))), hAPP(hAPP(c_COMBC(tc_fun(_1767851, tc_HOL_Obool), tc_fun(_1767849, tc_fun(_1767851, tc_HOL_Obool)), tc_fun(_1767849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767851, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767849, tc_fun(_1767851, tc_HOL_Obool)), tc_fun(_1767849, tc_HOL_Obool)), tc_fun(_1767851, tc_HOL_Obool)), c_COMBB(tc_fun(_1767851, tc_HOL_Obool), tc_HOL_Obool, _1767849)), c_fequal)), _1767855))))))], (17799 ^ _779142) ^ [_1092804, _1092806] : [class_Int_Onumber__ring(_1092804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092804), hAPP(c_Int_Onumber__class_Onumber__of(_1092804), c_Int_OPls)), _1092806) = _1092806)], (13729 ^ _779142) ^ [_1017967, _1017969, _1017971, _1017973] : [class_Fields_Olinordered__field(_1017967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017967), _1017969), c_Groups_Ozero__class_Ozero(_1017967))), 13736 ^ _779142 : [(13743 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017967), _1017973), _1017969)), _1017971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017967), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017967), _1017971), _1017969)), _1017973)))], (13737 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017967), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017967), _1017971), _1017969)), _1017973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017967), _1017973), _1017969)), _1017971)))]]], (1786 ^ _779142) ^ [_804409, _804411] : [-(class_Orderings_Olinorder(_804409)), _804411 = _804409, class_Orderings_Olinorder(_804411)], (21252 ^ _779142) ^ [_1152883, _1152885, _1152887] : [-(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, _1152883, _1152885)), _1152887), _1152885) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1152883), _1152887), _1152885))], (30194 ^ _779142) ^ [_1318599, _1318601, _1318603, _1318605, _1318607] : [class_Groups_Ocomm__monoid__mult(_1318599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318601), _1318603)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318601), _1318605)), 30208 ^ _779142 : [(30211 ^ _779142) ^ [] : [hAPP(_1318607, 30207 ^ [_1318599, _1318601, _1318603, _1318605, _1318607]) = c_Groups_Oone__class_Oone(_1318599)], (30209 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318601), 30207 ^ [_1318599, _1318601, _1318603, _1318605, _1318607]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318601, tc_HOL_Obool)), _1318603), _1318605))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318601, _1318599), _1318607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318601, tc_HOL_Obool)), _1318603), _1318605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318599), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318601, _1318599), _1318607), _1318603)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318601, _1318599), _1318607), _1318605)))], (45738 ^ _779142) ^ [_1698016, _1698018, _1698020] : [-(c_List_Oremdups(_1698016, hAPP(c_List_Ofilter(_1698016, _1698018), _1698020)) = hAPP(c_List_Ofilter(_1698016, _1698018), c_List_Oremdups(_1698016, _1698020)))], (49717 ^ _779142) ^ [_1783996, _1783998, _1784000, _1784002, _1784004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783996, tc_HOL_Obool)), _1783998), hAPP(c_Set_Oimage(_1784000, _1783996, _1784002), _1784004))), -(c_Fun_Oinj__on(_1783996, _1784000, c_Hilbert__Choice_Oinv__into(_1784000, _1783996, _1784004, _1784002), _1783998))], (49418 ^ _779142) ^ [_1777784, _1777786] : [c_Equiv__Relations_Opart__equivp(_1777784, _1777786), 49422 ^ _779142 : [(49427 ^ _779142) ^ [] : [-(c_Predicate_Otransp(_1777784, _1777786))], (49425 ^ _779142) ^ [] : [-(c_Predicate_Osymp(_1777784, _1777786))], (49423 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1777786, 49421 ^ [_1777784, _1777786]), 49421 ^ [_1777784, _1777786])))]]], (10669 ^ _779142) ^ [_963491, _963493] : [-(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), _963491), _963493)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _963493))], (39471 ^ _779142) ^ [_1546978, _1546980, _1546982, _1546984, _1546986, _1546988, _1546990] : [-(hAPP(c_Product__Type_Oapfst(_1546978, _1546980, _1546982, _1546984), hAPP(c_Product__Type_Oapfst(_1546986, _1546978, _1546982, _1546988), _1546990)) = hAPP(c_Product__Type_Oapfst(_1546986, _1546980, _1546982, hAPP(c_Fun_Ocomp(_1546978, _1546980, _1546986, _1546984), _1546988)), _1546990))], (8557 ^ _779142) ^ [_922732, _922734, _922736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922732), _922734)), hBOOL(hAPP(hAPP(c_member(_922732), _922736), _922734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_922732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922732, tc_HOL_Obool)), _922734), hAPP(hAPP(c_Set_Oinsert(_922732), _922736), c_Orderings_Obot__class_Obot(tc_fun(_922732, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_922732), _922734))))], (22406 ^ _779142) ^ [_1173445, _1173447] : [_1173445 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1173447, _1173445) = _1173447)], (42686 ^ _779142) ^ [_1629898] : [class_Groups_Omonoid__add(_1629898), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629898), c_List_Olist_ONil(_1629898)) = c_Groups_Ozero__class_Ozero(_1629898))], (21576 ^ _779142) ^ [_1158118, _1158120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158118), _1158120))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1158120, _1158118) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1158120), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1158120), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1158118)))], (33207 ^ _779142) ^ [_1386835, _1386837] : [-(_1386835 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33210 ^ _779142 : [(33217 ^ _779142) ^ [] : [-(_1386837 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1386835, _1386837) = 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, _1386837))), 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, _1386835)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1386837))), c_Divides_Opdivmod(_1386835, _1386837)), 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), _1386837))))), c_Divides_Opdivmod(_1386835, _1386837)))))], (33211 ^ _779142) ^ [] : [_1386837 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386835, _1386837) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386835))]]], (21116 ^ _779142) ^ [_1150369] : [c_Nat__Transfer_Onat__set(_1150369), -(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), _1150369)) = _1150369)], (43892 ^ _779142) ^ [_1657168, _1657170] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657168), _1657170) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43898 ^ _779142 : [(43901 ^ _779142) ^ [] : [43897 ^ [_1657168, _1657170] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43899 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43897 ^ [_1657168, _1657170]), hAPP(c_List_Oset(tc_Nat_Onat), _1657170))))]]], (38346 ^ _779142) ^ [_1518048, _1518050, _1518052] : [-(hAPP(c_Relation_ORange(_1518048, _1518050), hAPP(c_Set_OCollect(tc_prod(_1518048, _1518050)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518048, _1518050, tc_HOL_Obool), _1518052))) = hAPP(c_Set_OCollect(_1518050), hAPP(hAPP(c_COMBB(tc_fun(_1518048, tc_HOL_Obool), tc_HOL_Obool, _1518050), c_HOL_OEx(_1518048)), hAPP(c_COMBC(_1518048, _1518050, tc_HOL_Obool), _1518052))))], (18485 ^ _779142) ^ [_1104667] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1104667)), -(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)), _1104667))))], (18903 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (52335 ^ _779142) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (47960 ^ _779142) ^ [] : [-(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)))], (16445 ^ _779142) ^ [_1068646, _1068648] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068646)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1068648)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068646), _1068648)))], (11332 ^ _779142) ^ [_973900, _973902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973900)), _973902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973900), _973902)))], (10171 ^ _779142) ^ [_954362, _954364, _954366, _954368, _954370] : [class_Rings_Ocomm__semiring__1(_954362), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), _954364), _954366)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), _954368), _954370)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), _954364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), _954366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954362), _954368), _954370))))], (1656 ^ _779142) ^ [_802784, _802786] : [-(class_Groups_Oab__semigroup__mult(_802784)), _802786 = _802784, class_Groups_Oab__semigroup__mult(_802786)], (23673 ^ _779142) ^ [_1196126] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1196126)) = hAPP(c_Nat_OSuc, _1196126))], (51531 ^ _779142) ^ [_1820376, _1820378] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820376), _1820378)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820378), _1820376))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820378), _1820376)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820376), _1820378)))], (43299 ^ _779142) ^ [_1643120, _1643122, _1643124, _1643126, _1643128, _1643130] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643120), tc_List_Olist(_1643120))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643120), tc_List_Olist(_1643120)), hAPP(hAPP(c_List_Oappend(_1643120), _1643122), _1643128)), hAPP(hAPP(c_List_Oappend(_1643120), _1643124), _1643130))), c_List_Olistrel1(_1643120, _1643126)))), 43300 ^ _779142 : [(43307 ^ _779142) ^ [] : [_1643122 = _1643124, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643120), tc_List_Olist(_1643120))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643120), tc_List_Olist(_1643120)), _1643128), _1643130)), c_List_Olistrel1(_1643120, _1643126)))], (43301 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643120), tc_List_Olist(_1643120))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643120), tc_List_Olist(_1643120)), _1643122), _1643124)), c_List_Olistrel1(_1643120, _1643126))), _1643128 = _1643130]]], (37573 ^ _779142) ^ [_1491032, _1491034, _1491036, _1491038, _1491040] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491032, _1491034), _1491036), hAPP(hAPP(c_COMBS(_1491032, tc_fun(_1491034, tc_HOL_Obool), tc_fun(_1491034, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491034, tc_HOL_Obool), tc_fun(tc_fun(_1491034, tc_HOL_Obool), tc_fun(_1491034, tc_HOL_Obool)), _1491032), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491034, tc_HOL_Obool))), _1491038)), _1491040)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491032, _1491034), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491032, _1491034), _1491036), _1491038)), hAPP(hAPP(c_Product__Type_OSigma(_1491032, _1491034), _1491036), _1491040)))], (5206 ^ _779142) ^ [_858565, _858567, _858569, _858571, _858573, _858575, _858577, _858579, _858581, _858583] : [-(c_New__DSequence_Opos__map(_858583, _858579, _858575, _858571, _858567) = c_New__DSequence_Opos__map(_858581, _858577, _858573, _858569, _858565)), _858583 = _858581, _858579 = _858577, _858575 = _858573, _858571 = _858569, _858567 = _858565], (42118 ^ _779142) ^ [_1617469, _1617471, _1617473] : [-(_1617469 = _1617471), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617473)), _1617469) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617473)), _1617471), 42124 ^ _779142 : [(42127 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617473, _1617473, tc_HOL_Obool), c_fequal), 42123 ^ [_1617469, _1617471, _1617473]))], (42125 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617473, _1617473)), 42123 ^ [_1617469, _1617471, _1617473]), hAPP(c_List_Oset(tc_prod(_1617473, _1617473)), hAPP(hAPP(c_List_Ozip(_1617473, _1617473), _1617469), _1617471)))))]]], (27480 ^ _779142) ^ [] : [-(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))], (24497 ^ _779142) ^ [_1210110, _1210112] : [class_Rings_Olinordered__idom(_1210110), 24500 ^ _779142 : [(24507 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210110), hAPP(c_Int_Oring__1__class_Oof__int(_1210110), _1210112)), c_Groups_Ozero__class_Ozero(_1210110))))], (24501 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210110), hAPP(c_Int_Oring__1__class_Oof__int(_1210110), _1210112)), c_Groups_Ozero__class_Ozero(_1210110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15217 ^ _779142) ^ [_1045504, _1045506] : [class_Orderings_Olinorder(_1045504), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045504), _1045506), _1045506) = _1045506)], (1386 ^ _779142) ^ [_799409, _799411] : [-(class_Complete__Lattice_Ocomplete__lattice(_799409)), _799411 = _799409, class_Complete__Lattice_Ocomplete__lattice(_799411)], (7962 ^ _779142) ^ [_910271, _910273, _910275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910271, tc_HOL_Obool)), _910273), _910275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_910271, tc_HOL_Obool)), _910273), _910275))), -(_910273 = _910275)], (25142 ^ _779142) ^ [_1221109, _1221111] : [class_Groups_Omonoid__mult(_1221109), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221109), _1221111), 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(_1221109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221109), _1221111), _1221111)), _1221111))], (41074 ^ _779142) ^ [_1586261, _1586263] : [-(c_Transitive__Closure_Ortrancl(_1586261, _1586263) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1586261, _1586261), 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(_1586261, _1586261), tc_HOL_Obool), tc_fun(tc_prod(_1586261, _1586261), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1586261, _1586261), tc_HOL_Obool)), _1586263)))], (43532 ^ _779142) ^ [_1649268, _1649270, _1649272, _1649274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1649268), _1649270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649272, tc_HOL_Obool)), hAPP(c_List_Oset(_1649272), hAPP(hAPP(c_List_Odrop(_1649272), _1649270), _1649274))), hAPP(c_List_Oset(_1649272), hAPP(hAPP(c_List_Odrop(_1649272), _1649268), _1649274)))))], (6445 ^ _779142) ^ [_882367, _882369, _882371] : [class_Orderings_Olinorder(_882367), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882367), _882369), _882371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882367), _882371), _882369)))], (13155 ^ _779142) ^ [_1007227, _1007229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1007227), _1007229))), 13158 ^ _779142 : [(13161 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007227), _1007229)))], (13159 ^ _779142) ^ [] : [_1007229 = c_Orderings_Obot__class_Obot(tc_fun(_1007227, tc_HOL_Obool))]]], (8262 ^ _779142) ^ [_916730, _916732] : [class_Lattices_Oab__semigroup__idem__mult(_916730), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916730), _916732), _916732) = _916732)], (16815 ^ _779142) ^ [_1074889, _1074891, _1074893] : [class_Orderings_Olinorder(_1074889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074889), _1074891)), -(_1074893 = c_Orderings_Obot__class_Obot(tc_fun(_1074889, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1074889, tc_HOL_Obool)), _1074893), _1074891)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074889), c_Big__Operators_Olattice_OInf__fin(_1074889, c_Orderings_Oord__class_Omin(_1074889), _1074893)), c_Big__Operators_Olattice_OInf__fin(_1074889, c_Orderings_Oord__class_Omin(_1074889), _1074891)) = c_Big__Operators_Olattice_OInf__fin(_1074889, c_Orderings_Oord__class_Omin(_1074889), _1074891))], (11394 ^ _779142) ^ [_975025, _975027] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975025), hAPP(c_Nat_OSuc, _975027)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _975025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975025), _975027)))], (4370 ^ _779142) ^ [_845419, _845421, _845423, _845425, _845427, _845429, _845431, _845433, _845435, _845437] : [-(c_Option_Ooption_Ooption__case(_845437, _845433, _845429, _845425, _845421) = c_Option_Ooption_Ooption__case(_845435, _845431, _845427, _845423, _845419)), _845437 = _845435, _845433 = _845431, _845429 = _845427, _845425 = _845423, _845421 = _845419], (8889 ^ _779142) ^ [_929092, _929094, _929096] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929092), _929094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929092, tc_HOL_Obool)), _929096), _929094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_929092), _929096)), hAPP(c_Finite__Set_Ocard(_929092), _929094))))], (42720 ^ _779142) ^ [_1630489, _1630491] : [hAPP(c_List_Oset(_1630489), _1630491) = c_Orderings_Obot__class_Obot(tc_fun(_1630489, tc_HOL_Obool)), -(_1630491 = c_List_Olist_ONil(_1630489))], (36185 ^ _779142) ^ [_1459594, _1459596, _1459598] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1459594, _1459594)), _1459596), c_Relation_OId__on(_1459594, _1459598))), 36189 ^ _779142 : [(36192 ^ _779142) ^ [] : [-(_1459596 = hAPP(hAPP(c_Product__Type_OPair(_1459594, _1459594), 36188 ^ [_1459594, _1459596, _1459598]), 36188 ^ [_1459594, _1459596, _1459598]))], (36190 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459594), 36188 ^ [_1459594, _1459596, _1459598]), _1459598)))]]], (39397 ^ _779142) ^ [_1545444, _1545446, _1545448] : [-(c_Hilbert__Choice_OEps(tc_prod(_1545444, _1545446), hAPP(c_Product__Type_Oprod_Oprod__case(_1545444, _1545446, tc_HOL_Obool), _1545448)) = c_Hilbert__Choice_OEps(tc_prod(_1545444, _1545446), hAPP(hAPP(c_COMBS(tc_prod(_1545444, _1545446), _1545446, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1545444, tc_fun(_1545446, tc_HOL_Obool), tc_prod(_1545444, _1545446)), _1545448), c_Product__Type_Ofst(_1545444, _1545446))), c_Product__Type_Osnd(_1545444, _1545446))))], (42864 ^ _779142) ^ [_1633330, _1633332, _1633334] : [hBOOL(hAPP(hAPP(c_member(_1633330), _1633332), hAPP(c_List_Oset(_1633330), _1633334))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633330)), c_List_Oremove1(_1633330, _1633332, _1633334)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633330)), _1633334)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (52683 ^ _779142) ^ [_1836567, _1836569] : [-(hAPP(c_COMBI(_1836567), _1836569) = _1836569)], (22026 ^ _779142) ^ [_1166268, _1166270, _1166272] : [class_Groups_Omonoid__mult(_1166268), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1166268), _1166270), hAPP(c_Nat_OSuc, _1166272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166268), hAPP(hAPP(c_Power_Opower__class_Opower(_1166268), _1166270), _1166272)), _1166270))], (37483 ^ _779142) ^ [_1488456, _1488458] : [-(hAPP(c_Set_OCollect(_1488456), _1488458) = _1488458)], (32797 ^ _779142) ^ [_1378133, _1378135, _1378137, _1378139, _1378141, _1378143] : [hBOOL(hAPP(hAPP(_1378133, _1378135), _1378137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1378139, tc_fun(_1378141, tc_HOL_Obool))), _1378133), _1378143)), -(hBOOL(hAPP(hAPP(_1378143, _1378135), _1378137)))], (36272 ^ _779142) ^ [_1461282, _1461284] : [-(c_Fun_Oinj__on(_1461282, _1461282, c_COMBI(_1461282), _1461284))], (17549 ^ _779142) ^ [_1088413] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1088413) = _1088413)], (33063 ^ _779142) ^ [_1384140, _1384142, _1384144, _1384146, _1384148, _1384150] : [hAPP(hAPP(c_Product__Type_OPair(_1384140, _1384142), _1384144), _1384146) = hAPP(hAPP(c_Product__Type_OPair(_1384140, _1384142), _1384148), _1384150), 33066 ^ _779142 : [(33069 ^ _779142) ^ [] : [-(_1384146 = _1384150)], (33067 ^ _779142) ^ [] : [-(_1384144 = _1384148)]]], (6663 ^ _779142) ^ [_886657, _886659, _886661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886657, tc_HOL_Obool)), _886659), hAPP(hAPP(c_Set_Oinsert(_886657), _886661), c_Orderings_Obot__class_Obot(tc_fun(_886657, tc_HOL_Obool))))), -(_886659 = c_Orderings_Obot__class_Obot(tc_fun(_886657, tc_HOL_Obool))), -(_886659 = hAPP(hAPP(c_Set_Oinsert(_886657), _886661), c_Orderings_Obot__class_Obot(tc_fun(_886657, tc_HOL_Obool))))], (27162 ^ _779142) ^ [_1258444, _1258446, _1258448] : [class_Orderings_Olinorder(_1258444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258444), _1258446), _1258448)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258444, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1258444), _1258446)), c_SetInterval_Oord__class_OatLeastAtMost(_1258444, _1258446, _1258448)) = hAPP(c_SetInterval_Oord__class_OatMost(_1258444), _1258448))], (3264 ^ _779142) ^ [_827754, _827756, _827758, _827760] : [-(c_List_Olists(_827760, _827756) = c_List_Olists(_827758, _827754)), _827760 = _827758, _827756 = _827754], (39043 ^ _779142) ^ [_1536198, _1536200] : [-(c_List_Olex(_1536198, _1536200) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1536198), tc_List_Olist(_1536198)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1536198, _1536200)))], (12361 ^ _779142) ^ [_992496] : [-(hAPP(c_Finite__Set_Ocard(_992496), c_Orderings_Obot__class_Obot(tc_fun(_992496, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40909 ^ _779142) ^ [_1582194] : [-(c_Relation_Osingle__valued(_1582194, _1582194, c_Relation_OId(_1582194)))], (32903 ^ _779142) ^ [_1380271, _1380273, _1380275, _1380277, _1380279] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1380271, _1380273, _1380275), _1380277), _1380279)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1380271, _1380273)), hAPP(hAPP(c_Product__Type_OPair(_1380271, _1380273), _1380277), _1380279)), _1380275)))], (27390 ^ _779142) ^ [_1262345, _1262347, _1262349] : [class_Groups_Oordered__ab__group__add(_1262345), -(hAPP(c_Set_Oimage(_1262345, _1262345, c_Groups_Ouminus__class_Ouminus(_1262345)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1262345, _1262347), _1262349)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1262345, hAPP(c_Groups_Ouminus__class_Ouminus(_1262345), _1262349), hAPP(c_Groups_Ouminus__class_Ouminus(_1262345), _1262347)))], (50863 ^ _779142) ^ [_1809266, _1809268, _1809270] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809266, _1809268) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809270), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1809266 = _1809268, _1809268 = _1809270], (408 ^ _779142) ^ [_785278, _785280, _785282, _785284, _785286, _785288] : [-(c_Relation_Ototal__on(_785286, _785282, _785278)), c_Relation_Ototal__on(_785288, _785284, _785280), _785288 = _785286, _785284 = _785282, _785280 = _785278], (5776 ^ _779142) ^ [_870601, _870603, _870605, _870607] : [_870601 = _870603, 5779 ^ _779142 : [(5786 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870605), _870607), _870603)), -(hBOOL(hAPP(hAPP(c_member(_870605), _870607), _870601)))], (5780 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870605), _870607), _870601)), -(hBOOL(hAPP(hAPP(c_member(_870605), _870607), _870603)))]]], (45855 ^ _779142) ^ [_1701925, _1701927] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701925, _1701927)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701925), _1701927))], (19591 ^ _779142) ^ [_1123406] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123406)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1123406))], (33527 ^ _779142) ^ [_1392469, _1392471, _1392473, _1392475, _1392477] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1392469, _1392471), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1392473), _1392475))), -(_1392471 = 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), _1392477), _1392469), _1392471), 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), _1392477), _1392473)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1392477), _1392475)), _1392471))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1392477), _1392475), _1392471)))))], (7824 ^ _779142) ^ [_908144, _908146, _908148] : [class_Orderings_Oorder(_908144), 7827 ^ _779142 : [(7828 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908144), _908146), _908148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908144), _908146), _908148))), -(_908146 = _908148)], (7838 ^ _779142) ^ [] : [7839 ^ _779142 : [(7842 ^ _779142) ^ [] : [_908146 = _908148], (7840 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908144), _908146), _908148))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908144), _908146), _908148)))]]], (5866 ^ _779142) ^ [_872024, _872026] : [_872026 = c_Orderings_Obot__class_Obot(tc_fun(_872024, tc_HOL_Obool)), 5869 ^ _779142 : [(5870 ^ _779142) ^ [_872104] : [hBOOL(hAPP(hAPP(c_member(_872024), _872104), _872026))]]], (24770 ^ _779142) ^ [_1214624, _1214626] : [24772 ^ _779142 : [(24775 ^ _779142) ^ [] : [hBOOL(hAPP(_1214626, 24771 ^ [_1214624, _1214626]))], (24773 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24771 ^ [_1214624, _1214626]), _1214624)))]], 24776 ^ _779142 : [(24777 ^ _779142) ^ [_1214774] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1214774), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214624))), -(hBOOL(hAPP(_1214626, _1214774)))]]], (40721 ^ _779142) ^ [_1577438, _1577440, _1577442, _1577444] : [-(hAPP(c_Relation_Oconverse(_1577438, _1577440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577438, _1577440), tc_HOL_Obool)), _1577442), _1577444)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577440, _1577438), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1577438, _1577440), _1577442)), hAPP(c_Relation_Oconverse(_1577438, _1577440), _1577444)))], (15383 ^ _779142) ^ [_1048628, _1048630, _1048632, _1048634] : [class_Orderings_Olinorder(_1048628), 15386 ^ _779142 : [(15395 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048628), _1048632), _1048634)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), _1048632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), _1048634))], (15387 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048628), _1048632), _1048634))), 15390 ^ _779142 : [(15393 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), _1048634)))], (15391 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048628), _1048630), _1048632)))]]]]], (2850 ^ _779142) ^ [_821335, _821337, _821339, _821341, _821343, _821345] : [-(c_Nitpick_Oof__frac(_821345, _821341, _821337) = c_Nitpick_Oof__frac(_821343, _821339, _821335)), _821345 = _821343, _821341 = _821339, _821337 = _821335], (41197 ^ _779142) ^ [_1589867, _1589869, _1589871, _1589873] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589867, _1589867)), hAPP(hAPP(c_Product__Type_OPair(_1589867, _1589867), _1589869), _1589871)), c_Transitive__Closure_Otrancl(_1589867, _1589873))), 41201 ^ _779142 : [(41204 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589867, _1589867)), hAPP(hAPP(c_Product__Type_OPair(_1589867, _1589867), 41200 ^ [_1589867, _1589869, _1589871, _1589873]), _1589871)), c_Transitive__Closure_Ortrancl(_1589867, _1589873))))], (41202 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589867, _1589867)), hAPP(hAPP(c_Product__Type_OPair(_1589867, _1589867), _1589869), 41200 ^ [_1589867, _1589869, _1589871, _1589873])), _1589873)))]]], (21312 ^ _779142) ^ [_1153793, _1153795, _1153797] : [class_Rings_Ocomm__semiring__1(_1153793), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1153793), _1153795), hAPP(c_Nat_OSuc, _1153797)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153793), _1153795), hAPP(hAPP(c_Power_Opower__class_Opower(_1153793), _1153795), _1153797)))], (37118 ^ _779142) ^ [_1479333, _1479335, _1479337] : [-(c_HOL_OThe(tc_prod(_1479333, _1479335), _1479337) = c_HOL_OThe(tc_prod(_1479333, _1479335), hAPP(c_Product__Type_Oprod_Oprod__case(_1479333, _1479335, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1479335, tc_prod(_1479333, _1479335)), tc_fun(_1479335, tc_HOL_Obool), _1479333), hAPP(c_COMBB(tc_prod(_1479333, _1479335), tc_HOL_Obool, _1479335), _1479337)), c_Product__Type_OPair(_1479333, _1479335)))))], (33941 ^ _779142) ^ [_1400938, _1400940, _1400942, _1400944, _1400946] : [hBOOL(hAPP(hAPP(_1400938, _1400940), _1400942)), -(hBOOL(hAPP(hAPP(_1400938, hAPP(c_Product__Type_Osnd(_1400944, _1400946), hAPP(hAPP(c_Product__Type_OPair(_1400944, _1400946), _1400942), _1400940))), hAPP(c_Product__Type_Ofst(_1400944, _1400946), hAPP(hAPP(c_Product__Type_OPair(_1400944, _1400946), _1400942), _1400940)))))], (33927 ^ _779142) ^ [_1400624, _1400626, _1400628, _1400630, _1400632] : [-(c_Product__Type_Oprod_Oprod__size(_1400624, _1400626, _1400628, _1400630, _1400632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1400628, hAPP(c_Product__Type_Ofst(_1400624, _1400626), _1400632))), hAPP(_1400630, hAPP(c_Product__Type_Osnd(_1400624, _1400626), _1400632)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27412 ^ _779142) ^ [_1262810, _1262812] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1262810, _1262812)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262812), _1262810)))], (48650 ^ _779142) ^ [_1760795, _1760797, _1760799] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760795, _1760797, _1760799) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760795)], (23439 ^ _779142) ^ [_1192008, _1192010] : [class_Groups_Ogroup__add(_1192008), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192008), c_Groups_Ozero__class_Ozero(_1192008)), _1192010) = hAPP(c_Groups_Ouminus__class_Ouminus(_1192008), _1192010))], (16643 ^ _779142) ^ [_1072143, _1072145, _1072147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072143), _1072145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072147), _1072143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072147), _1072145))))], (9729 ^ _779142) ^ [_944636, _944638, _944640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944636), _944638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944636), _944640)), 9736 ^ _779142 : [(9743 ^ _779142) ^ [] : [_944638 = _944640, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944638), _944636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944640), _944636))], (9737 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944638), _944636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _944640), _944636), -(_944638 = _944640)]]], (34474 ^ _779142) ^ [_1414371, _1414373, _1414375, _1414377, _1414379] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414371, tc_fun(_1414373, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414371, tc_HOL_Obool)), _1414375), _1414377)), _1414379) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414373, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414371, tc_fun(_1414373, tc_HOL_Obool)), _1414375), _1414379)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414371, tc_fun(_1414373, tc_HOL_Obool)), _1414377), _1414379)))], (48170 ^ _779142) ^ [_1750680, _1750682, _1750684, _1750686] : [-(hAPP(hAPP(c_List_Odrop(_1750680), _1750682), c_List_Oreplicate(_1750680, _1750684, _1750686)) = c_List_Oreplicate(_1750680, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750684), _1750682), _1750686))], (264 ^ _779142) ^ [_783232, _783234] : [-(class_Fields_Ofield(_783232)), _783234 = _783232, class_Fields_Ofield(_783234)], (12802 ^ _779142) ^ [_1000524, _1000526, _1000528, _1000530] : [class_Rings_Olinordered__semiring(_1000524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000524), _1000526), _1000528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000524), _1000526), _1000530))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000524), c_Groups_Ozero__class_Ozero(_1000524)), _1000526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000524), _1000528), _1000530)))], (33680 ^ _779142) ^ [_1395411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395411)), 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), _1395411)) = 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), _1395411))))))], (38655 ^ _779142) ^ [_1527450] : [-(c_Wellfounded_Owf(tc_fun(_1527450, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1527450)))], (24443 ^ _779142) ^ [_1209226] : [-(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)), _1209226)) = hAPP(c_Int_Onat, _1209226))], (20067 ^ _779142) ^ [_1131324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131324)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1131324)) = _1131324)], (46204 ^ _779142) ^ [_1708186, _1708188] : [class_Orderings_Olinorder(_1708186), c_List_Olinorder__class_Osorted(_1708186, _1708188), -(c_List_Olinorder__class_Osorted(_1708186, c_List_Oremdups(_1708186, _1708188)))], (9939 ^ _779142) ^ [_948967, _948969, _948971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948967), _948969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948967), _948971)), _948969)))], (48844 ^ _779142) ^ [_1765290, _1765292] : [c_Relation_Otrans(_1765290, _1765292), -(c_Relation_Otrans(tc_List_Olist(_1765290), c_List_Olistrel(_1765290, _1765292)))], (13991 ^ _779142) ^ [_1022877, _1022879, _1022881] : [class_Fields_Olinordered__field__inverse__zero(_1022877), 13994 ^ _779142 : [(14009 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022877), _1022879), _1022881)))), 14010 ^ _779142 : [(14017 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), _1022879), c_Groups_Ozero__class_Ozero(_1022877))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), _1022881), c_Groups_Ozero__class_Ozero(_1022877)))], (14011 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), _1022879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), _1022881))]]], (13995 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022877), _1022879), _1022881))), 14000 ^ _779142 : [(14003 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), _1022881)))], (14001 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), c_Groups_Ozero__class_Ozero(_1022877)), _1022879)))]], 14004 ^ _779142 : [(14007 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), _1022881), c_Groups_Ozero__class_Ozero(_1022877))))], (14005 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022877), _1022879), c_Groups_Ozero__class_Ozero(_1022877))))]]]]], (41659 ^ _779142) ^ [_1604354, _1604356, _1604358, _1604360, _1604362] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604354), tc_List_Olist(_1604354))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604354), tc_List_Olist(_1604354)), hAPP(hAPP(c_List_Olist_OCons(_1604354), _1604356), _1604358)), _1604360)), c_List_Olistrel(_1604354, _1604362))), 41664 ^ _779142 : [(41669 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604354), tc_List_Olist(_1604354))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604354), tc_List_Olist(_1604354)), _1604358), 41663 ^ [_1604354, _1604356, _1604358, _1604360, _1604362])), c_List_Olistrel(_1604354, _1604362))))], (41667 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604354, _1604354)), hAPP(hAPP(c_Product__Type_OPair(_1604354, _1604354), _1604356), 41662 ^ [_1604354, _1604356, _1604358, _1604360, _1604362])), _1604362)))], (41665 ^ _779142) ^ [] : [-(_1604360 = hAPP(hAPP(c_List_Olist_OCons(_1604354), 41662 ^ [_1604354, _1604356, _1604358, _1604360, _1604362]), 41663 ^ [_1604354, _1604356, _1604358, _1604360, _1604362]))]]], (24898 ^ _779142) ^ [_1216893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1216893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1216893)))], (46606 ^ _779142) ^ [_1716092, _1716094, _1716096] : [_1716096 = hAPP(hAPP(c_List_Olist_OCons(_1716092), _1716094), c_List_Olist_ONil(_1716092)), -(hAPP(hAPP(c_List_Olist_OCons(_1716092), _1716094), c_List_Olist_ONil(_1716092)) = hAPP(c_List_Orev(_1716092), _1716096))], (19437 ^ _779142) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (41250 ^ _779142) ^ [_1591307, _1591309, _1591311, _1591313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591307, _1591309)), _1591311), hAPP(c_Relation_Oconverse(_1591309, _1591307), _1591313))), 41255 ^ _779142 : [(41258 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591309, _1591307)), hAPP(hAPP(c_Product__Type_OPair(_1591309, _1591307), 41253 ^ [_1591307, _1591309, _1591311, _1591313]), 41254 ^ [_1591307, _1591309, _1591311, _1591313])), _1591313)))], (41256 ^ _779142) ^ [] : [-(_1591311 = hAPP(hAPP(c_Product__Type_OPair(_1591307, _1591309), 41254 ^ [_1591307, _1591309, _1591311, _1591313]), 41253 ^ [_1591307, _1591309, _1591311, _1591313]))]]], (33053 ^ _779142) ^ [_1383957, _1383959, _1383961, _1383963, _1383965, _1383967] : [-(hAPP(hAPP(c_Product__Type_OPair(_1383957, _1383959), _1383961), _1383963) = hAPP(hAPP(c_Product__Type_OPair(_1383957, _1383959), _1383965), _1383967)), _1383961 = _1383965, _1383963 = _1383967], (27448 ^ _779142) ^ [_1263534] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1263534)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1263534)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49723 ^ _779142) ^ [_1784127, _1784129, _1784131, _1784133, _1784135] : [c_Fun_Oinj__on(_1784127, _1784129, _1784131, _1784133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784127, tc_HOL_Obool)), _1784135), _1784133)), -(hAPP(c_Set_Oimage(_1784129, _1784127, c_Hilbert__Choice_Oinv__into(_1784127, _1784129, _1784133, _1784131)), hAPP(c_Set_Oimage(_1784127, _1784129, _1784131), _1784135)) = _1784135)], (48376 ^ _779142) ^ [_1754538, _1754540, _1754542] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754538)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754538, _1754540, _1754542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754538)), _1754542)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10263 ^ _779142) ^ [_956368, _956370, _956372, _956374] : [class_Rings_Ocomm__semiring__1(_956368), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956368), _956370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956368), _956372), _956374)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956368), _956370), _956372)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956368), _956370), _956374)))], (51465 ^ _779142) ^ [_1819298, _1819300] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819298), _1819300)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819300), _1819298))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819300), _1819298)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819298), _1819300)))], (38214 ^ _779142) ^ [_1514408, _1514410] : [-(c_Fun_Oinj__on(_1514408, _1514408, c_Fun_Oid(_1514408), _1514410))], (10165 ^ _779142) ^ [_954185, _954187, _954189, _954191, _954193] : [class_Rings_Ocomm__semiring__1(_954185), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), _954187), _954189)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), _954191), _954193)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), _954191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954185), _954187), _954189)), _954193)))], (26788 ^ _779142) ^ [_1251010, _1251012, _1251014] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1251010), _1251012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251010), _1251014)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1251010), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251010, tc_HOL_Obool)), _1251012), _1251014))))], (22038 ^ _779142) ^ [_1166494, _1166496, _1166498, _1166500] : [class_Groups_Omonoid__mult(_1166494), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1166494), _1166496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1166498), _1166500)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166494), hAPP(hAPP(c_Power_Opower__class_Opower(_1166494), _1166496), _1166498)), hAPP(hAPP(c_Power_Opower__class_Opower(_1166494), _1166496), _1166500)))], (25888 ^ _779142) ^ [_1234070] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1234070))), 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), _1234070), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (1356 ^ _779142) ^ [_799034, _799036] : [-(class_Rings_Oidom(_799034)), _799036 = _799034, class_Rings_Oidom(_799036)], (16653 ^ _779142) ^ [_1072324] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072324), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1072324)], (40941 ^ _779142) ^ [_1582826, _1582828, _1582830, _1582832, _1582834] : [c_Relation_Osingle__valued(_1582826, _1582828, _1582830), c_Relation_Osingle__valued(_1582828, _1582832, _1582834), -(c_Relation_Osingle__valued(_1582826, _1582832, hAPP(hAPP(c_Relation_Orel__comp(_1582826, _1582828, _1582832), _1582830), _1582834)))], (8689 ^ _779142) ^ [_925190, _925192, _925194, _925196] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925190), 8692 ^ _779142 : [(8699 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925190), _925194), _925196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925190), _925192), _925194)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925190), _925192), _925196))))], (8693 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925190), _925192), _925194)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925190), _925192), _925196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925190), _925194), _925196)))]]], (46628 ^ _779142) ^ [_1716690, _1716692, _1716694, _1716696, _1716698] : [c_List_Olist__all2(_1716690, _1716692, _1716694, hAPP(c_List_Orev(_1716690), _1716696), _1716698), -(c_List_Olist__all2(_1716690, _1716692, _1716694, _1716696, hAPP(c_List_Orev(_1716692), _1716698)))], (18589 ^ _779142) ^ [_1106464, _1106466] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106464), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1106466)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106464, _1106466)))], (47714 ^ _779142) ^ [_1740407, _1740409, _1740411] : [c_List_Olist__ex(_1740407, _1740409, _1740411), -(c_List_Olist__ex(_1740407, _1740409, hAPP(c_List_Orev(_1740407), _1740411)))], (21900 ^ _779142) ^ [_1164113, _1164115, _1164117] : [class_Rings_Olinordered__idom(_1164113), -(hAPP(c_Groups_Oabs__class_Oabs(_1164113), hAPP(hAPP(c_Power_Opower__class_Opower(_1164113), _1164115), _1164117)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1164113), hAPP(c_Groups_Oabs__class_Oabs(_1164113), _1164115)), _1164117))], (33347 ^ _779142) ^ [_1389575, _1389577] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389575, _1389577), c_Divides_Odivmod__nat(_1389575, _1389577))))], (47862 ^ _779142) ^ [_1743470, _1743472, _1743474] : [c_List_Olist__all(_1743470, _1743472, hAPP(c_List_Orev(_1743470), _1743474)), -(c_List_Olist__all(_1743470, _1743472, _1743474))], (42862 ^ _779142) ^ [_1633243, _1633245] : [-(c_List_Oset__Cons(_1633243, _1633245, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633243)), c_List_Olist_ONil(_1633243)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633243), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1633243, tc_List_Olist(_1633243), hAPP(hAPP(c_COMBC(_1633243, tc_List_Olist(_1633243), tc_List_Olist(_1633243)), c_List_Olist_OCons(_1633243)), c_List_Olist_ONil(_1633243))), _1633245))], (52669 ^ _779142) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52447 ^ _779142) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (27974 ^ _779142) ^ [_1273095, _1273097, _1273099, _1273101] : [class_Orderings_Olinorder(_1273095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273095), _1273097), _1273099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273095), _1273097), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273095), _1273099), _1273101))))], (23189 ^ _779142) ^ [_1187458, _1187460, _1187462] : [class_Fields_Ofield__inverse__zero(_1187458), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187458), _1187460), _1187462)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187458), _1187460), hAPP(c_Groups_Ouminus__class_Ouminus(_1187458), _1187462)))], (39722 ^ _779142) ^ [_1552643, _1552645, _1552647, _1552649, _1552651, _1552653] : [c_Finite__Set_Ofolding(_1552643, _1552645, _1552647, _1552649), -(hAPP(c_Fun_Ocomp(_1552645, _1552645, _1552645, hAPP(_1552647, _1552651)), hAPP(_1552647, _1552653)) = hAPP(c_Fun_Ocomp(_1552645, _1552645, _1552645, hAPP(_1552647, _1552653)), hAPP(_1552647, _1552651)))], (31212 ^ _779142) ^ [_1338580, _1338582, _1338584] : [class_Orderings_Oorder(_1338580), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338580, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1338580, _1338582, _1338584)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338580), _1338584)) = c_Orderings_Obot__class_Obot(tc_fun(_1338580, tc_HOL_Obool)))], (21766 ^ _779142) ^ [_1161501, _1161503] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1161501, _1161503)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161503)), _1161501))], (17879 ^ _779142) ^ [_1094127, _1094129, _1094131] : [class_Rings_Osemiring__1(_1094127), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1094129), _1094131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094127), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094127), _1094129)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094127), _1094131)))], (20754 ^ _779142) ^ [_1143887, _1143889, _1143891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1143887), _1143889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143891), _1143889)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143891), _1143887))))], (10281 ^ _779142) ^ [_956717, _956719, _956721, _956723, _956725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956717), _956719)), 10284 ^ _779142 : [(10291 ^ _779142) ^ [] : [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), _956719), _956717)), _956721)), _956723)), _956725)), -(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), _956719), _956721)), _956723)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956717), _956721)), _956725))))], (10285 ^ _779142) ^ [] : [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), _956719), _956721)), _956723)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956717), _956721)), _956725))), -(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), _956719), _956717)), _956721)), _956723)), _956725)))]]], (21390 ^ _779142) ^ [_1155078, _1155080, _1155082] : [class_Orderings_Oorder(_1155078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155078), _1155080), _1155082)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1155078, _1155082, _1155080) = c_Orderings_Obot__class_Obot(tc_fun(_1155078, tc_HOL_Obool)))], (35631 ^ _779142) ^ [_1446506, _1446508, _1446510] : [_1446508 = c_Orderings_Obot__class_Obot(tc_fun(_1446506, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446506, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446506), _1446508), _1446510))], (9362 ^ _779142) ^ [_938814, _938816] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938814), _938816) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 9365 ^ _779142 : [(9368 ^ _779142) ^ [] : [-(_938816 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9366 ^ _779142) ^ [] : [-(_938814 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (42547 ^ _779142) ^ [_1627286, _1627288, _1627290, _1627292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627286), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627288)), _1627290))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627286), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627288)), _1627292))), 42557 ^ _779142 : [(42560 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Onth(_1627288), _1627290), 42556 ^ [_1627286, _1627288, _1627290, _1627292]) = hAPP(hAPP(c_List_Onth(_1627288), _1627292), 42556 ^ [_1627286, _1627288, _1627290, _1627292])], (42558 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42556 ^ [_1627286, _1627288, _1627290, _1627292]), _1627286)))]], -(hAPP(hAPP(c_List_Otake(_1627288), _1627286), _1627290) = hAPP(hAPP(c_List_Otake(_1627288), _1627286), _1627292))], (40372 ^ _779142) ^ [_1569025, _1569027, _1569029] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569025, _1569025), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569025, _1569025), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569025, _1569027)), c_Transitive__Closure_Ortrancl(_1569025, _1569029))), c_Transitive__Closure_Ortrancl(_1569025, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569025, _1569025), tc_HOL_Obool)), _1569027), _1569029)))))], (17625 ^ _779142) ^ [_1089639, _1089641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1089641, _1089639)), _1089639)))], (28440 ^ _779142) ^ [_1281871, _1281873] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1281871, tc_HOL_Obool), tc_HOL_Obool)), _1281873), hAPP(c_Set_OPow(_1281871), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1281871, tc_HOL_Obool), _1281873)))))], (20073 ^ _779142) ^ [_1131409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131409))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1131409)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22997 ^ _779142) ^ [_1184006, _1184008] : [class_Groups_Olinordered__ab__group__add(_1184006), 23000 ^ _779142 : [(23007 ^ _779142) ^ [] : [_1184008 = c_Groups_Ozero__class_Ozero(_1184006), -(_1184008 = hAPP(c_Groups_Ouminus__class_Ouminus(_1184006), _1184008))], (23001 ^ _779142) ^ [] : [_1184008 = hAPP(c_Groups_Ouminus__class_Ouminus(_1184006), _1184008), -(_1184008 = c_Groups_Ozero__class_Ozero(_1184006))]]], (43492 ^ _779142) ^ [_1648338, _1648340, _1648342] : [-(c_List_Obutlast(_1648338, hAPP(hAPP(c_List_Odrop(_1648338), _1648340), _1648342)) = hAPP(hAPP(c_List_Odrop(_1648338), _1648340), c_List_Obutlast(_1648338, _1648342)))], (15699 ^ _779142) ^ [_1054715, _1054717, _1054719, _1054721] : [class_Fields_Ofield__inverse__zero(_1054715), class_Int_Onumber(_1054715), 15706 ^ _779142 : [(15707 ^ _779142) ^ [] : [_1054717 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1054715), _1054719), hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721)), 15710 ^ _779142 : [(15717 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721) = c_Groups_Ozero__class_Ozero(_1054715), -(_1054717 = c_Groups_Ozero__class_Ozero(_1054715))], (15711 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721) = c_Groups_Ozero__class_Ozero(_1054715)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054715), _1054717), hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721)) = _1054719)]]], (15723 ^ _779142) ^ [] : [-(_1054717 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1054715), _1054719), hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721))), 15726 ^ _779142 : [(15729 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054715), _1054717), hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721)) = _1054719], (15727 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721) = c_Groups_Ozero__class_Ozero(_1054715)]], 15730 ^ _779142 : [(15733 ^ _779142) ^ [] : [_1054717 = c_Groups_Ozero__class_Ozero(_1054715)], (15731 ^ _779142) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1054715), _1054721) = c_Groups_Ozero__class_Ozero(_1054715))]]]]], (9871 ^ _779142) ^ [_947419, _947421, _947423] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947419), _947421)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947423), _947421)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947419), _947423))], (44843 ^ _779142) ^ [_1677487] : [-(hAPP(c_Code__Numeral_Onat__of, _1677487) = c_Code__Numeral_Onat__of__aux(_1677487, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37126 ^ _779142) ^ [_1479667, _1479669] : [-(c_Divides_Odivmod__nat(_1479667, _1479669) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1479667, _1479669)))], (39399 ^ _779142) ^ [_1545525, _1545527, _1545529] : [39400 ^ _779142 : [(39401 ^ _779142) ^ [_1545579] : [hBOOL(hAPP(_1545525, _1545579))]], _1545527 = c_Hilbert__Choice_OEps(_1545529, _1545525), -(hBOOL(hAPP(_1545525, _1545527)))], (13080 ^ _779142) ^ [_1005795, _1005797, _1005799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1005795), _1005797)), 13083 ^ _779142 : [(13084 ^ _779142) ^ [] : [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(_1005795, tc_Nat_Onat), _1005799), _1005797))), 13087 ^ _779142 : [(13088 ^ _779142) ^ [_1005963] : [hBOOL(hAPP(hAPP(c_member(_1005795), _1005963), _1005797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1005799, _1005963))))]]], (13094 ^ _779142) ^ [] : [13096 ^ _779142 : [(13099 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1005799, 13095 ^ [_1005795, _1005797, _1005799])))], (13097 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1005795), 13095 ^ [_1005795, _1005797, _1005799]), _1005797)))]], -(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(_1005795, tc_Nat_Onat), _1005799), _1005797))))]]], (11830 ^ _779142) ^ [_983040, _983042, _983044, _983046] : [class_Rings_Olinordered__semidom(_983040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983040), c_Groups_Ozero__class_Ozero(_983040)), _983042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983040), _983044), _983046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983040), _983044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983040), _983042), _983046))))], (36800 ^ _779142) ^ [_1472553] : [class_Nat_Osemiring__char__0(_1472553), -(c_Fun_Oinj__on(tc_Nat_Onat, _1472553, c_Nat_Osemiring__1__class_Oof__nat(_1472553), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (12876 ^ _779142) ^ [_1001923, _1001925, _1001927] : [class_Rings_Olinordered__idom(_1001923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001923), c_Groups_Ozero__class_Ozero(_1001923)), _1001925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001923), c_Groups_Ozero__class_Ozero(_1001923)), _1001927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001923), _1001927), c_Groups_Oone__class_Oone(_1001923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001923), _1001927), _1001925)), _1001925)))], (45370 ^ _779142) ^ [_1689707, _1689709] : [-(hAPP(c_List_Oset(_1689707), c_List_Oremdups(_1689707, _1689709)) = hAPP(c_List_Oset(_1689707), _1689709))], (28673 ^ _779142) ^ [_1286061, _1286063, _1286065] : [class_Orderings_Olinorder(_1286061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286061), _1286063)), hBOOL(hAPP(hAPP(c_member(_1286061), _1286065), _1286063)), 28684 ^ _779142 : [(28691 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286061, tc_HOL_Obool)), _1286063), hAPP(hAPP(c_Set_Oinsert(_1286061), _1286065), c_Orderings_Obot__class_Obot(tc_fun(_1286061, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1286061, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1286061, c_Orderings_Oord__class_Omax(_1286061), _1286063) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286061), _1286065), c_Big__Operators_Olattice_OSup__fin(_1286061, c_Orderings_Oord__class_Omax(_1286061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286061, tc_HOL_Obool)), _1286063), hAPP(hAPP(c_Set_Oinsert(_1286061), _1286065), c_Orderings_Obot__class_Obot(tc_fun(_1286061, tc_HOL_Obool)))))))], (28685 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286061, tc_HOL_Obool)), _1286063), hAPP(hAPP(c_Set_Oinsert(_1286061), _1286065), c_Orderings_Obot__class_Obot(tc_fun(_1286061, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1286061, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1286061, c_Orderings_Oord__class_Omax(_1286061), _1286063) = _1286065)]]], (52527 ^ _779142) ^ [_1834926, _1834928] : [-(class_Enum_Oenum(tc_sum(_1834926, _1834928))), class_Enum_Oenum(_1834926), class_Enum_Oenum(_1834928)], (20237 ^ _779142) ^ [_1134406, _1134408] : [-(_1134406 = hAPP(c_Int_Onat, _1134408)), 20240 ^ _779142 : [(20243 ^ _779142) ^ [] : [_1134408 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134406)], (20241 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134408)))]], 20244 ^ _779142 : [(20247 ^ _779142) ^ [] : [_1134406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20245 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134408))]]], (49612 ^ _779142) ^ [_1781657] : [-(c_Hilbert__Choice_Oinv__into(_1781657, _1781657, c_Orderings_Otop__class_Otop(tc_fun(_1781657, tc_HOL_Obool)), c_Fun_Oid(_1781657)) = c_Fun_Oid(_1781657))], (15259 ^ _779142) ^ [_1046349, _1046351, _1046353, _1046355] : [class_Orderings_Olinorder(_1046349), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046349), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046349), _1046351), _1046353)), _1046355) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046349), _1046351), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046349), _1046353), _1046355)))], (35310 ^ _779142) ^ [_1436971] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436971)), -(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))), _1436971)), c_FunDef_Omax__weak)))], (29085 ^ _779142) ^ [_1294675, _1294677, _1294679, _1294681] : [class_Lattices_Olattice(_1294675), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294675), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294675), _1294677), _1294679)), _1294681) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294675), _1294677), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294675), _1294679), _1294681)))], (18509 ^ _779142) ^ [_1105049, _1105051] : [_1105049 = _1105051, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105049) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105051))], (36162 ^ _779142) ^ [_1459065, _1459067, _1459069, _1459071, _1459073, _1459075, _1459077] : [c_Equiv__Relations_Oequiv(_1459065, _1459067, _1459069), c_Equiv__Relations_Ocongruent(_1459065, tc_fun(_1459071, tc_HOL_Obool), _1459069, _1459073), hBOOL(hAPP(hAPP(c_member(tc_fun(_1459065, tc_HOL_Obool)), _1459075), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1459065), _1459067), _1459069))), 36176 ^ _779142 : [(36179 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1459071, tc_HOL_Obool)), hAPP(_1459073, 36175 ^ [_1459065, _1459067, _1459069, _1459071, _1459073, _1459075, _1459077])), _1459077))], (36177 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459065), 36175 ^ [_1459065, _1459067, _1459069, _1459071, _1459073, _1459075, _1459077]), _1459067)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1459071, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459065, tc_fun(_1459071, tc_HOL_Obool)), _1459075), _1459073)), _1459077)))], (30505 ^ _779142) ^ [_1324703, _1324705, _1324707] : [class_Lattices_Olattice(_1324703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324703), _1324705)), -(hBOOL(hAPP(hAPP(c_member(_1324703), _1324707), _1324705))), -(c_Big__Operators_Olattice__class_OInf__fin(_1324703, hAPP(hAPP(c_Set_Oinsert(_1324703), _1324707), _1324705)) = hAPP(hAPP(c_Finite__Set_Ofold(_1324703, _1324703, c_Lattices_Osemilattice__inf__class_Oinf(_1324703)), _1324707), _1324705))], (23987 ^ _779142) ^ [_1201612, _1201614] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201612))), -(c_SMT_Oz3mod(_1201614, _1201612) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201614, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201612)))], (43666 ^ _779142) ^ [_1652609, _1652611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652609)), _1652611)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1652609), _1652611) = _1652611)], (12022 ^ _779142) ^ [_986605, _986607, _986609] : [class_Rings_Olinordered__semiring__strict(_986605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986605), c_Groups_Ozero__class_Ozero(_986605)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986605), _986607), _986609))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986605), c_Groups_Ozero__class_Ozero(_986605)), _986609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986605), c_Groups_Ozero__class_Ozero(_986605)), _986607)))], (44446 ^ _779142) ^ [_1669073, _1669075, _1669077, _1669079] : [-(hAPP(c_List_Oset(_1669073), hAPP(hAPP(c_List_Omap(_1669075, _1669073), _1669077), _1669079)) = hAPP(c_Set_Oimage(_1669075, _1669073, _1669077), hAPP(c_List_Oset(_1669075), _1669079)))], (29691 ^ _779142) ^ [_1308026, _1308028, _1308030, _1308032, _1308034] : [class_Groups_Ocomm__monoid__mult(_1308026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308028), _1308030)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308028), _1308032)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308026), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308028, _1308026), _1308034), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308028, tc_HOL_Obool)), _1308030), _1308032))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308028, _1308026), _1308034), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308028, tc_HOL_Obool)), _1308030), _1308032))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308026), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308028, _1308026), _1308034), _1308030)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308028, _1308026), _1308034), _1308032)))], (25084 ^ _779142) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (17974 ^ _779142) ^ [_1095732] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1095732)) = 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), _1095732)))], (51499 ^ _779142) ^ [_1819834, _1819836, _1819838] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819834), _1819836)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819836), _1819834))), _1819836 = _1819838, 51510 ^ _779142 : [(51513 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819838), _1819834))], (51511 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819834), _1819838)))]]], (45766 ^ _779142) ^ [_1698808, _1698810, _1698812] : [hBOOL(hAPP(c_List_Odistinct(_1698808), _1698810)), -(hAPP(c_List_Ofilter(_1698808, hAPP(hAPP(c_COMBC(_1698808, tc_fun(_1698808, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698808)), hAPP(c_List_Oset(_1698808), c_List_Osublist(_1698808, _1698810, _1698812)))), _1698810) = c_List_Osublist(_1698808, _1698810, _1698812))], (35194 ^ _779142) ^ [_1434516, _1434518, _1434520, _1434522, _1434524, _1434526, _1434528] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434516, tc_fun(_1434518, tc_fun(_1434520, tc_HOL_Obool))), _1434522), _1434524), _1434526), _1434528)), 35198 ^ _779142 : [(35201 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1434524, 35197 ^ [_1434516, _1434518, _1434520, _1434522, _1434524, _1434526, _1434528]), _1434526), _1434528)))], (35199 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434516), 35197 ^ [_1434516, _1434518, _1434520, _1434522, _1434524, _1434526, _1434528]), _1434522)))]]], (41737 ^ _779142) ^ [_1606345, _1606347, _1606349, _1606351] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606345)), hAPP(hAPP(c_List_Olist_OCons(_1606345), _1606347), _1606349)), c_List_Olists(_1606345, _1606351))), 41740 ^ _779142 : [(41743 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606345)), _1606349), c_List_Olists(_1606345, _1606351))))], (41741 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606345), _1606347), _1606351)))]]], (31434 ^ _779142) ^ [_1342975, _1342977, _1342979] : [class_Complete__Lattice_Ocomplete__lattice(_1342975), -(c_Complete__Lattice_OInf__class_OInf(_1342975, hAPP(hAPP(c_Set_Oinsert(_1342975), _1342977), hAPP(hAPP(c_Set_Oinsert(_1342975), _1342979), c_Orderings_Obot__class_Obot(tc_fun(_1342975, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1342975), _1342977), _1342979))], (20718 ^ _779142) ^ [_1143236] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143236), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1143236)], (29411 ^ _779142) ^ [_1301662, _1301664, _1301666] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301662, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301662, tc_HOL_Obool)), _1301664), _1301666)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301662, tc_HOL_Obool)), _1301664), _1301666)) = _1301664)], (28639 ^ _779142) ^ [_1285353, _1285355, _1285357] : [class_Orderings_Olinorder(_1285353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285353), _1285355)), 28646 ^ _779142 : [(28653 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285353, tc_HOL_Obool)), _1285355), hAPP(hAPP(c_Set_Oinsert(_1285353), _1285357), c_Orderings_Obot__class_Obot(tc_fun(_1285353, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1285353, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1285353, c_Orderings_Oord__class_Omax(_1285353), hAPP(hAPP(c_Set_Oinsert(_1285353), _1285357), _1285355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285353), _1285357), c_Big__Operators_Olattice_OSup__fin(_1285353, c_Orderings_Oord__class_Omax(_1285353), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285353, tc_HOL_Obool)), _1285355), hAPP(hAPP(c_Set_Oinsert(_1285353), _1285357), c_Orderings_Obot__class_Obot(tc_fun(_1285353, tc_HOL_Obool)))))))], (28647 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285353, tc_HOL_Obool)), _1285355), hAPP(hAPP(c_Set_Oinsert(_1285353), _1285357), c_Orderings_Obot__class_Obot(tc_fun(_1285353, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1285353, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1285353, c_Orderings_Oord__class_Omax(_1285353), hAPP(hAPP(c_Set_Oinsert(_1285353), _1285357), _1285355)) = _1285357)]]], (2014 ^ _779142) ^ [_808229, _808231, _808233, _808235, _808237, _808239, _808241, _808243, _808245, _808247] : [-(c_Nitpick_Opair__box_Opair__box__rec(_808247, _808243, _808239, _808235, _808231) = c_Nitpick_Opair__box_Opair__box__rec(_808245, _808241, _808237, _808233, _808229)), _808247 = _808245, _808243 = _808241, _808239 = _808237, _808235 = _808233, _808231 = _808229], (22342 ^ _779142) ^ [_1172286, _1172288, _1172290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172286)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1172288), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1172290)), 22352 ^ _779142 : [(22358 ^ _779142) ^ [] : [-(_1172288 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 22354 ^ [_1172286, _1172288, _1172290]), 22351 ^ [_1172286, _1172288, _1172290]))], (22356 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22354 ^ [_1172286, _1172288, _1172290]), _1172290)))], (22353 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22351 ^ [_1172286, _1172288, _1172290]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1172286))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1172288), _1172286) = _1172288)], (10779 ^ _779142) ^ [_965373, _965375] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965373), _965375))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965373), hAPP(c_Nat_OSuc, _965375))), -(_965375 = _965373)], (46464 ^ _779142) ^ [_1712928, _1712930] : [class_Orderings_Olinorder(_1712928), 46467 ^ _779142 : [(46468 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1712928, _1712930), 46471 ^ _779142 : [(46472 ^ _779142) ^ [_1713099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713099), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712928)), _1712930))), 46475 ^ _779142 : [(46476 ^ _779142) ^ [_1713216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713216), _1713099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712928), hAPP(hAPP(c_List_Onth(_1712928), _1712930), _1713216)), hAPP(hAPP(c_List_Onth(_1712928), _1712930), _1713099))))]]]]], (46482 ^ _779142) ^ [] : [46484 ^ _779142 : [(46490 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712928), hAPP(hAPP(c_List_Onth(_1712928), _1712930), 46486 ^ [_1712928, _1712930])), hAPP(hAPP(c_List_Onth(_1712928), _1712930), 46483 ^ [_1712928, _1712930])))], (46488 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46486 ^ [_1712928, _1712930]), 46483 ^ [_1712928, _1712930])))], (46485 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46483 ^ [_1712928, _1712930]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712928)), _1712930))))]], -(c_List_Olinorder__class_Osorted(_1712928, _1712930))]]], (16733 ^ _779142) ^ [_1073594, _1073596, _1073598] : [class_Orderings_Olinorder(_1073594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073594), _1073596)), hBOOL(hAPP(hAPP(c_member(_1073594), _1073598), _1073596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073594), c_Big__Operators_Olinorder__class_OMin(_1073594, _1073596)), _1073598)))], (50071 ^ _779142) ^ [_1791734, _1791736, _1791738] : [c_Fun_Obij__betw(_1791734, _1791736, _1791738, c_Orderings_Otop__class_Otop(tc_fun(_1791734, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1791736, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1791734, _1791736, _1791738, c_Orderings_Otop__class_Otop(tc_fun(_1791734, tc_HOL_Obool))))], (34949 ^ _779142) ^ [_1428139, _1428141, _1428143, _1428145] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428139, tc_fun(_1428141, tc_HOL_Obool)), _1428143), _1428145) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428141, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428139, tc_fun(_1428141, tc_HOL_Obool), _1428145), _1428143)))], (11073 ^ _779142) ^ [_969998, _970000] : [class_Groups_Ogroup__add(_969998), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969998), _970000), _970000) = c_Groups_Ozero__class_Ozero(_969998))], (44396 ^ _779142) ^ [_1667876, _1667878, _1667880, _1667882, _1667884] : [class_Rings_Osemiring__0(_1667876), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667876), hAPP(hAPP(c_List_Omap(_1667878, _1667876), hAPP(hAPP(c_COMBC(_1667878, _1667876, _1667876), hAPP(hAPP(c_COMBB(_1667876, tc_fun(_1667876, _1667876), _1667878), c_Groups_Otimes__class_Otimes(_1667876)), _1667880)), _1667882)), _1667884)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667876), hAPP(c_List_Omonoid__add__class_Olistsum(_1667876), hAPP(hAPP(c_List_Omap(_1667878, _1667876), _1667880), _1667884))), _1667882))], (10446 ^ _779142) ^ [_960065] : [10447 ^ _779142 : [(10448 ^ _779142) ^ [_960107] : [_960065 = hAPP(c_Nat_OSuc, _960107)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960065)))], (51097 ^ _779142) ^ [_1813255, _1813257, _1813259] : [class_Divides_Oring__div(_1813255), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813255), _1813257), _1813259)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813255), hAPP(c_Groups_Ouminus__class_Ouminus(_1813255), _1813259)), _1813257) = hAPP(c_Groups_Ouminus__class_Ouminus(_1813255), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813255), _1813259), _1813257)))], (38971 ^ _779142) ^ [_1534343, _1534345] : [c_Relation_Orefl__on(_1534343, c_Orderings_Otop__class_Otop(tc_fun(_1534343, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1534343, _1534343)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534343, _1534343, tc_HOL_Obool), _1534345))), -(c_Predicate_Oreflp(_1534343, _1534345))], (43267 ^ _779142) ^ [_1642271, _1642273, _1642275, _1642277] : [-(hAPP(hAPP(c_List_Otake(_1642271), _1642273), hAPP(hAPP(c_List_Oappend(_1642271), _1642275), _1642277)) = hAPP(hAPP(c_List_Oappend(_1642271), hAPP(hAPP(c_List_Otake(_1642271), _1642273), _1642275)), hAPP(hAPP(c_List_Otake(_1642271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1642273), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642271)), _1642275))), _1642277)))], (41565 ^ _779142) ^ [_1601122, _1601124, _1601126, _1601128] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1601122), tc_List_Olist(_1601122), c_List_Olistrel(_1601122, _1601124)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601122)), hAPP(hAPP(c_List_Olist_OCons(_1601122), _1601126), _1601128)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601122), tc_HOL_Obool)))) = c_List_Oset__Cons(_1601122, hAPP(c_Relation_OImage(_1601122, _1601122, _1601124), hAPP(hAPP(c_Set_Oinsert(_1601122), _1601126), c_Orderings_Obot__class_Obot(tc_fun(_1601122, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1601122), tc_List_Olist(_1601122), c_List_Olistrel(_1601122, _1601124)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601122)), _1601128), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601122), tc_HOL_Obool))))))], (48477 ^ _779142) ^ [_1756790, _1756792, _1756794] : [hBOOL(hAPP(hAPP(c_member(_1756790), _1756794), hAPP(c_List_Oset(_1756790), _1756792))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756790), _1756792), _1756794)))], (44500 ^ _779142) ^ [_1670347, _1670349, _1670351, _1670353, _1670355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670347), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670349)), _1670351))), -(hAPP(hAPP(c_List_Onth(_1670353), hAPP(hAPP(c_List_Omap(_1670349, _1670353), _1670355), _1670351)), _1670347) = hAPP(_1670355, hAPP(hAPP(c_List_Onth(_1670349), _1670351), _1670347)))], (8721 ^ _779142) ^ [_925804, _925806, _925808, _925810] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925804), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925804), _925806), _925808)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925804), _925806), _925810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925804), _925808), _925810)))], (19265 ^ _779142) ^ [_1117859, _1117861, _1117863] : [class_Rings_Olinordered__idom(_1117859), -(hAPP(c_Groups_Oabs__class_Oabs(_1117859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117859), _1117861), _1117863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117859), hAPP(c_Groups_Oabs__class_Oabs(_1117859), _1117861)), hAPP(c_Groups_Oabs__class_Oabs(_1117859), _1117863)))], (11285 ^ _779142) ^ [_973024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _973024)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973024), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _973024)], (42762 ^ _779142) ^ [_1631205, _1631207, _1631209, _1631211] : [-(_1631205 = _1631207), 42765 ^ _779142 : [(42772 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1631209), _1631205), hAPP(c_List_Oset(_1631209), _1631211))), -(hBOOL(hAPP(hAPP(c_member(_1631209), _1631205), hAPP(c_List_Oset(_1631209), c_List_Oremove1(_1631209, _1631207, _1631211)))))], (42766 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1631209), _1631205), hAPP(c_List_Oset(_1631209), c_List_Oremove1(_1631209, _1631207, _1631211)))), -(hBOOL(hAPP(hAPP(c_member(_1631209), _1631205), hAPP(c_List_Oset(_1631209), _1631211))))]]], (23035 ^ _779142) ^ [_1184555, _1184557, _1184559] : [class_Groups_Oordered__ab__group__add(_1184555), 23038 ^ _779142 : [(23045 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184555), _1184559), hAPP(c_Groups_Ouminus__class_Ouminus(_1184555), _1184557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184555), _1184557), hAPP(c_Groups_Ouminus__class_Ouminus(_1184555), _1184559))))], (23039 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184555), _1184557), hAPP(c_Groups_Ouminus__class_Ouminus(_1184555), _1184559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184555), _1184559), hAPP(c_Groups_Ouminus__class_Ouminus(_1184555), _1184557))))]]], (6013 ^ _779142) ^ [_874964, _874966, _874968, _874970] : [hAPP(c_Set_Oimage(_874964, _874966, _874968), _874970) = c_Orderings_Obot__class_Obot(tc_fun(_874966, tc_HOL_Obool)), -(_874970 = c_Orderings_Obot__class_Obot(tc_fun(_874964, tc_HOL_Obool)))], (39864 ^ _779142) ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917] : [class_Groups_Ocomm__monoid__add(_1555907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555909), _1555911)), 39874 ^ _779142 : [(39875 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555909), 39873 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917]), _1555911)))], (39880 ^ _779142) ^ [] : [39873 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917] = 39876 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917]], (39884 ^ _779142) ^ [] : [hAPP(_1555915, hAPP(_1555913, 39873 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917])) = c_Groups_Ozero__class_Ozero(_1555907)], (39882 ^ _779142) ^ [] : [-(hAPP(_1555913, 39873 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917]) = hAPP(_1555913, 39876 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917]))], (39878 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555909), 39876 ^ [_1555907, _1555909, _1555911, _1555913, _1555915, _1555917]), _1555911)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555917, _1555907), _1555915), hAPP(c_Set_Oimage(_1555909, _1555917, _1555913), _1555911)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555909, _1555907), hAPP(c_Fun_Ocomp(_1555917, _1555907, _1555909, _1555915), _1555913)), _1555911))], (52279 ^ _779142) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (25734 ^ _779142) ^ [_1231428, _1231430] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1231428)), _1231430) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231428), _1231430))), _1231430))], (11137 ^ _779142) ^ [_970905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970905), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41100 ^ _779142) ^ [_1586905] : [-(c_Nat_Ofunpow(_1586905) = c_Nat_Ocompow(_1586905, _1586905))], (40974 ^ _779142) ^ [_1583577, _1583579, _1583581] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583577, _1583577), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583579)), _1583581) = hAPP(hAPP(c_Relation_Orel__comp(_1583577, _1583577, _1583577), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583577, _1583577), tc_HOL_Obool), _1583579), _1583581)), _1583581))], (40797 ^ _779142) ^ [_1579040, _1579042, _1579044, _1579046] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579040, _1579040)), hAPP(hAPP(c_Product__Type_OPair(_1579040, _1579040), _1579042), _1579044)), c_Transitive__Closure_Ortrancl(_1579040, hAPP(c_Relation_Oconverse(_1579040, _1579040), _1579046)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579040, _1579040)), hAPP(hAPP(c_Product__Type_OPair(_1579040, _1579040), _1579044), _1579042)), c_Transitive__Closure_Ortrancl(_1579040, _1579046))))], (8127 ^ _779142) ^ [_913749, _913751, _913753, _913755, _913757] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_913749, _913751, hAPP(hAPP(c_Set_Oinsert(_913749), _913753), _913755)), _913757)), 8132 ^ _779142 : [(8137 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913749), 8130 ^ [_913749, _913751, _913753, _913755, _913757]), 8131 ^ [_913749, _913751, _913753, _913755, _913757]))], (8135 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_913749, _913749, _913751, 8130 ^ [_913749, _913751, _913753, _913755, _913757], 8131 ^ [_913749, _913751, _913753, _913755, _913757]), _913757)))], (8133 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_913749), _913753), _913755) = hAPP(hAPP(c_Set_Oinsert(_913749), 8130 ^ [_913749, _913751, _913753, _913755, _913757]), 8131 ^ [_913749, _913751, _913753, _913755, _913757]))]]], (27740 ^ _779142) ^ [_1268959, _1268961, _1268963, _1268965] : [class_Orderings_Olinorder(_1268959), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268959), _1268961), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268959), _1268963), _1268965)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268959), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268959), _1268961), _1268963)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1268959), _1268961), _1268965)))], (8336 ^ _779142) ^ [_917856, _917858, _917860, _917862] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917856), _917858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917856, tc_HOL_Obool)), _917858), _917860)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_917856, tc_Nat_Onat), _917862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917856, tc_HOL_Obool)), _917860), _917858)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_917856, tc_Nat_Onat), _917862), _917860)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_917856, tc_Nat_Onat), _917862), _917858)))], (8899 ^ _779142) ^ [_929283, _929285, _929287] : [-(hAPP(c_Finite__Set_Ofold1(_929283, _929285), hAPP(hAPP(c_Set_Oinsert(_929283), _929287), c_Orderings_Obot__class_Obot(tc_fun(_929283, tc_HOL_Obool)))) = _929287)], (20079 ^ _779142) ^ [_1131468, _1131470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1131468), hAPP(c_Int_Onat, _1131470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1131468)), _1131470)))], (33835 ^ _779142) ^ [_1398767, _1398769, _1398771, _1398773] : [_1398767 = _1398769, 33838 ^ _779142 : [(33841 ^ _779142) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1398771, _1398773), _1398767) = hAPP(c_Product__Type_Osnd(_1398771, _1398773), _1398769))], (33839 ^ _779142) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1398771, _1398773), _1398767) = hAPP(c_Product__Type_Ofst(_1398771, _1398773), _1398769))]]], (41595 ^ _779142) ^ [_1602003, _1602005] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602003), tc_List_Olist(_1602003)), tc_HOL_Obool)), c_List_Olistrel(_1602003, _1602005)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602003), c_List_Olistrel1(_1602003, _1602005)))))], (5655 ^ _779142) ^ [_868348, _868350, _868352, _868354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868348), _868350)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868352), hAPP(c_Set_Oimage(_868348, _868352, _868354), _868350))))], (8819 ^ _779142) ^ [_927687, _927689, _927691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927687), _927689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_927687), _927689)), hAPP(c_Finite__Set_Ocard(_927687), hAPP(hAPP(c_Set_Oinsert(_927687), _927691), _927689)))))], (36806 ^ _779142) ^ [] : [-(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))))], (41473 ^ _779142) ^ [_1598266, _1598268, _1598270, _1598272] : [hBOOL(hAPP(hAPP(c_member(_1598266), _1598268), c_Wellfounded_Oacc(_1598266, _1598270))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598266)), _1598272), c_Wellfounded_Oacc(tc_List_Olist(_1598266), c_List_Olistrel1(_1598266, _1598270)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598266)), hAPP(hAPP(c_List_Olist_OCons(_1598266), _1598268), _1598272)), c_Wellfounded_Oacc(tc_List_Olist(_1598266), c_List_Olistrel1(_1598266, _1598270)))))], (34322 ^ _779142) ^ [_1409757, _1409759, _1409761, _1409763, _1409765, _1409767] : [class_Complete__Lattice_Ocomplete__lattice(_1409757), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409759, _1409757), _1409761), hAPP(hAPP(c_COMBB(tc_fun(_1409763, _1409757), _1409757, _1409759), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409763, _1409757), _1409765)), _1409767)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409763, _1409757), _1409765), hAPP(hAPP(c_COMBB(tc_fun(_1409759, _1409757), _1409757, _1409763), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409759, _1409757), _1409761)), hAPP(c_COMBC(_1409759, _1409763, _1409757), _1409767))))], (23725 ^ _779142) ^ [_1197047, _1197049, _1197051] : [class_Orderings_Oord(_1197047), 23728 ^ _779142 : [(23735 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197047), _1197049), _1197051)), -(hBOOL(hAPP(hAPP(c_member(_1197047), _1197049), hAPP(c_SetInterval_Oord__class_OatMost(_1197047), _1197051))))], (23729 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1197047), _1197049), hAPP(c_SetInterval_Oord__class_OatMost(_1197047), _1197051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197047), _1197049), _1197051)))]]], (6709 ^ _779142) ^ [_887623, _887625, _887627, _887629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887623), _887625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887623, tc_HOL_Obool)), _887625), _887627)), hBOOL(hAPP(_887629, c_Orderings_Obot__class_Obot(tc_fun(_887623, tc_HOL_Obool)))), 6724 ^ _779142 : [(6725 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_887623), 6723 ^ [_887623, _887625, _887627, _887629])))], (6729 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887623), 6722 ^ [_887623, _887625, _887627, _887629]), 6723 ^ [_887623, _887625, _887627, _887629]))], (6733 ^ _779142) ^ [] : [hBOOL(hAPP(_887629, hAPP(hAPP(c_Set_Oinsert(_887623), 6722 ^ [_887623, _887625, _887627, _887629]), 6723 ^ [_887623, _887625, _887627, _887629])))], (6731 ^ _779142) ^ [] : [-(hBOOL(hAPP(_887629, 6723 ^ [_887623, _887625, _887627, _887629])))], (6727 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887623), 6722 ^ [_887623, _887625, _887627, _887629]), _887627)))]], -(hBOOL(hAPP(_887629, _887625)))], (6211 ^ _779142) ^ [_878618, _878620, _878622] : [-(_878618 = _878620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878622, tc_HOL_Obool)), _878618), _878620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878622, tc_HOL_Obool)), _878620), _878618))], (37511 ^ _779142) ^ [_1489177, _1489179, _1489181, _1489183, _1489185, _1489187] : [class_Groups_Ocomm__monoid__add(_1489177), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489179, _1489177), hAPP(hAPP(c_COMBC(_1489179, tc_fun(_1489181, tc_HOL_Obool), _1489177), hAPP(hAPP(c_COMBB(tc_fun(_1489181, _1489177), tc_fun(tc_fun(_1489181, tc_HOL_Obool), _1489177), _1489179), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489181, _1489177)), _1489183)), _1489185)), _1489187) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1489179, _1489181), _1489177), hAPP(c_Product__Type_Oprod_Oprod__case(_1489179, _1489181, _1489177), _1489183)), hAPP(hAPP(c_Product__Type_OSigma(_1489179, _1489181), _1489187), hAPP(c_COMBK(tc_fun(_1489181, tc_HOL_Obool), _1489179), _1489185))))], (46718 ^ _779142) ^ [_1718424, _1718426] : [-(hAPP(c_List_Orev(_1718424), _1718426) = hAPP(c_List_Ofoldl(tc_List_Olist(_1718424), _1718424, hAPP(c_COMBC(_1718424, tc_List_Olist(_1718424), tc_List_Olist(_1718424)), c_List_Olist_OCons(_1718424)), c_List_Olist_ONil(_1718424)), _1718426))], (37639 ^ _779142) ^ [_1492729, _1492731] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492729, tc_HOL_Obool)), _1492731) = hAPP(c_Set_OCollect(_1492729), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492729), c_fNot), hAPP(hAPP(c_COMBC(_1492729, tc_fun(_1492729, tc_HOL_Obool), tc_HOL_Obool), c_member(_1492729)), _1492731))))], (24323 ^ _779142) ^ [_1207217, _1207219, _1207221] : [class_Rings_Oring__1(_1207217), -(hAPP(c_Int_Oring__1__class_Oof__int(_1207217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1207219), _1207221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207217), hAPP(c_Int_Oring__1__class_Oof__int(_1207217), _1207219)), hAPP(c_Int_Oring__1__class_Oof__int(_1207217), _1207221)))], (29508 ^ _779142) ^ [_1304034, _1304036, _1304038, _1304040] : [class_Orderings_Oorder(_1304034), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304034, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304034, _1304036), _1304038)), c_SetInterval_Oord__class_OatLeastAtMost(_1304034, _1304038, _1304040)) = c_Orderings_Obot__class_Obot(tc_fun(_1304034, tc_HOL_Obool)))], (8022 ^ _779142) ^ [_911373, _911375, _911377, _911379, _911381] : [c_Finite__Set_Ofun__left__comm(_911373, _911375, _911377), hBOOL(hAPP(c_Finite__Set_Ofinite(_911373), _911379)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911373, _911375, _911377, _911381, _911379), hAPP(hAPP(c_Finite__Set_Ofold(_911373, _911375, _911377), _911381), _911379))))], (12632 ^ _779142) ^ [_997277, _997279, _997281] : [class_Groups_Oordered__comm__monoid__add(_997277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997277), _997279), c_Groups_Ozero__class_Ozero(_997277))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997277), _997281), c_Groups_Ozero__class_Ozero(_997277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997277), _997279), _997281)), c_Groups_Ozero__class_Ozero(_997277))))], (37577 ^ _779142) ^ [_1491257, _1491259, _1491261, _1491263, _1491265] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491257, _1491259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491257, tc_HOL_Obool)), _1491261), _1491263)), _1491265) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491257, _1491259), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491257, _1491259), _1491261), _1491265)), hAPP(hAPP(c_Product__Type_OSigma(_1491257, _1491259), _1491263), _1491265)))], (10229 ^ _779142) ^ [_955632, _955634, _955636, _955638] : [class_Rings_Ocomm__semiring__1(_955632), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955632), _955634), _955636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955632), _955638), _955636)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955632), _955634), _955638)), _955636))], (35828 ^ _779142) ^ [_1450876, _1450878, _1450880, _1450882, _1450884] : [c_Equiv__Relations_Oequiv(_1450876, _1450878, _1450880), hBOOL(hAPP(hAPP(c_member(_1450876), _1450882), _1450878)), hBOOL(hAPP(hAPP(c_member(_1450876), _1450884), _1450878)), 35839 ^ _779142 : [(35846 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450876, _1450876)), hAPP(hAPP(c_Product__Type_OPair(_1450876, _1450876), _1450882), _1450884)), _1450880)), -(hAPP(c_Relation_OImage(_1450876, _1450876, _1450880), hAPP(hAPP(c_Set_Oinsert(_1450876), _1450882), c_Orderings_Obot__class_Obot(tc_fun(_1450876, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450876, _1450876, _1450880), hAPP(hAPP(c_Set_Oinsert(_1450876), _1450884), c_Orderings_Obot__class_Obot(tc_fun(_1450876, tc_HOL_Obool)))))], (35840 ^ _779142) ^ [] : [hAPP(c_Relation_OImage(_1450876, _1450876, _1450880), hAPP(hAPP(c_Set_Oinsert(_1450876), _1450882), c_Orderings_Obot__class_Obot(tc_fun(_1450876, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450876, _1450876, _1450880), hAPP(hAPP(c_Set_Oinsert(_1450876), _1450884), c_Orderings_Obot__class_Obot(tc_fun(_1450876, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450876, _1450876)), hAPP(hAPP(c_Product__Type_OPair(_1450876, _1450876), _1450882), _1450884)), _1450880)))]]], (11061 ^ _779142) ^ [_969804, _969806] : [class_Rings_Ocomm__semiring__1(_969804), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969804), _969806), c_Groups_Ozero__class_Ozero(_969804)) = c_Groups_Ozero__class_Ozero(_969804))], (9613 ^ _779142) ^ [_942727, _942729, _942731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942727), _942729)), _942731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942727), _942731)))], (1246 ^ _779142) ^ [_797659, _797661] : [-(class_Rings_Oordered__ring(_797659)), _797661 = _797659, class_Rings_Oordered__ring(_797661)], (35651 ^ _779142) ^ [_1446981] : [-(c_Relation_OId__on(_1446981, c_Orderings_Obot__class_Obot(tc_fun(_1446981, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1446981, _1446981), tc_HOL_Obool)))], (17720 ^ _779142) ^ [_1091339, _1091341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091339), _1091341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091339)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091341))))], (19085 ^ _779142) ^ [_1114546] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114546) = 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(_1114546)))))], (38671 ^ _779142) ^ [_1527692, _1527694, _1527696] : [c_Wellfounded_Owf(_1527692, _1527694), -(c_Wellfounded_Owf(_1527692, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527692, _1527692), tc_HOL_Obool)), _1527694), _1527696)))], (18674 ^ _779142) ^ [_1107839] : [-(c_Int_Osucc(_1107839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1107839), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33341 ^ _779142) ^ [_1389480, _1389482, _1389484] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389480, _1389482), _1389484)), -(c_Divides_Odivmod__nat(_1389480, _1389482) = _1389484)], (16903 ^ _779142) ^ [_1076425, _1076427, _1076429] : [class_Orderings_Olinorder(_1076425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076425), _1076427)), -(hBOOL(hAPP(hAPP(c_member(_1076425), _1076429), _1076427))), -(_1076427 = c_Orderings_Obot__class_Obot(tc_fun(_1076425, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1076425, c_Orderings_Oord__class_Omin(_1076425), hAPP(hAPP(c_Set_Oinsert(_1076425), _1076429), _1076427)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1076425), _1076429), c_Big__Operators_Olattice_OInf__fin(_1076425, c_Orderings_Oord__class_Omin(_1076425), _1076427)))], (27200 ^ _779142) ^ [_1259140, _1259142, _1259144] : [class_Orderings_Olinorder(_1259140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259140), _1259142), _1259144)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259140, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259140, _1259142), _1259144)), hAPP(hAPP(c_Set_Oinsert(_1259140), _1259144), c_Orderings_Obot__class_Obot(tc_fun(_1259140, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1259140, _1259142, _1259144))], (14655 ^ _779142) ^ [_1034885, _1034887, _1034889, _1034891] : [class_Fields_Ofield(_1034885), -(_1034887 = c_Groups_Ozero__class_Ozero(_1034885)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034885), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034885), _1034889), _1034887)), _1034891) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034885), _1034889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034885), _1034887), _1034891))), _1034887))], (39139 ^ _779142) ^ [_1538591, _1538593] : [c_Wellfounded_OwfP(_1538591, _1538593), -(c_Wellfounded_Oacyclic(_1538591, hAPP(c_Set_OCollect(tc_prod(_1538591, _1538591)), hAPP(c_Product__Type_Oprod_Oprod__case(_1538591, _1538591, tc_HOL_Obool), _1538593))))], (26340 ^ _779142) ^ [_1242349, _1242351, _1242353, _1242355] : [hBOOL(hAPP(hAPP(c_member(_1242349), _1242351), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242349, tc_HOL_Obool)), _1242353), _1242355))), -(hBOOL(hAPP(hAPP(c_member(_1242349), _1242351), _1242353))), -(hBOOL(hAPP(hAPP(c_member(_1242349), _1242351), _1242355)))], (10763 ^ _779142) ^ [_965140, _965142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965140), _965142))), 10766 ^ _779142 : [(10773 ^ _779142) ^ [] : [_965140 = _965142, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965140), hAPP(c_Nat_OSuc, _965142))))], (10767 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965140), hAPP(c_Nat_OSuc, _965142))), -(_965140 = _965142)]]], (48342 ^ _779142) ^ [_1753761, _1753763, _1753765] : [-(_1753761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753763), c_List_Oreplicate(_1753763, _1753761, _1753765)) = hAPP(hAPP(c_Set_Oinsert(_1753763), _1753765), c_Orderings_Obot__class_Obot(tc_fun(_1753763, tc_HOL_Obool))))], (29520 ^ _779142) ^ [_1304324, _1304326, _1304328, _1304330, _1304332] : [class_Orderings_Olinorder(_1304324), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304324, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304324, _1304326), _1304328)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304324, _1304330), _1304332)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304324, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1304324), _1304326), _1304330)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1304324), _1304328), _1304332)))], (27688 ^ _779142) ^ [_1267872, _1267874, _1267876, _1267878] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1267872, _1267874, _1267876, c_Code__Numeral_OSuc__code__numeral(_1267878)) = hAPP(_1267876, _1267878))], (30021 ^ _779142) ^ [_1315053, _1315055, _1315057] : [class_Orderings_Olinorder(_1315053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315053), _1315055)), -(_1315055 = c_Orderings_Obot__class_Obot(tc_fun(_1315053, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315053), _1315057)), -(_1315057 = c_Orderings_Obot__class_Obot(tc_fun(_1315053, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315053, tc_HOL_Obool)), _1315055), _1315057) = c_Orderings_Obot__class_Obot(tc_fun(_1315053, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1315053, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315053, tc_HOL_Obool)), _1315055), _1315057)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1315053), c_Big__Operators_Olinorder__class_OMax(_1315053, _1315055)), c_Big__Operators_Olinorder__class_OMax(_1315053, _1315057)))], (6629 ^ _779142) ^ [_885968, _885970, _885972, _885974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885968, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885968), _885970), _885972)), _885974)), 6632 ^ _779142 : [(6635 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885968, tc_HOL_Obool)), _885972), _885974)))], (6633 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885968), _885970), _885974)))]]], (34799 ^ _779142) ^ [_1424234, _1424236, _1424238, _1424240] : [_1424234 = c_Orderings_Obot__class_Obot(tc_fun(_1424236, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424236, tc_fun(_1424238, tc_HOL_Obool)), _1424234), hAPP(c_COMBK(tc_fun(_1424238, tc_HOL_Obool), _1424236), _1424240)) = c_Orderings_Otop__class_Otop(tc_fun(_1424238, tc_HOL_Obool)))], (33071 ^ _779142) ^ [_1384291, _1384293, _1384295, _1384297, _1384299, _1384301] : [_1384291 = _1384293, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384295, _1384297, _1384299), _1384301), _1384291) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1384295, _1384297, _1384299), _1384301), _1384293))], (42920 ^ _779142) ^ [_1634686, _1634688, _1634690] : [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), _1634686), _1634688))), -(hBOOL(hAPP(hAPP(_1634690, _1634686), _1634688))), 42927 ^ _779142 : [(42930 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42925 ^ [_1634686, _1634688, _1634690]), 42926 ^ [_1634686, _1634688, _1634690])), -(hBOOL(hAPP(hAPP(_1634690, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42925 ^ [_1634686, _1634688, _1634690]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42926 ^ [_1634686, _1634688, _1634690])))], (42936 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1634690, 42925 ^ [_1634686, _1634688, _1634690]), 42926 ^ [_1634686, _1634688, _1634690]))], (42928 ^ _779142) ^ [] : [-(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), 42925 ^ [_1634686, _1634688, _1634690]), 42926 ^ [_1634686, _1634688, _1634690]))))]]], (20963 ^ _779142) ^ [_1147829, _1147831] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147829)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147829)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147831)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147829)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147831))))], (48362 ^ _779142) ^ [_1754292, _1754294] : [-(c_Predicate_Opred__comp(_1754292, _1754292, _1754292, c_fequal, c_Predicate_Opred__comp(_1754292, _1754292, _1754292, _1754294, c_fequal)) = _1754294)], (6383 ^ _779142) ^ [_881410, _881412, _881414] : [class_Orderings_Oorder(_881410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881410), _881412), _881414)), 6390 ^ _779142 : [(6397 ^ _779142) ^ [] : [_881414 = _881412, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881410), _881414), _881412)))], (6391 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881410), _881414), _881412)), -(_881414 = _881412)]]], (42311 ^ _779142) ^ [_1621940, _1621942, _1621944, _1621946, _1621948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621940, tc_HOL_Obool)), hAPP(c_List_Oset(_1621940), _1621942)), _1621944)), hBOOL(hAPP(hAPP(c_member(_1621940), _1621946), _1621944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621940, tc_HOL_Obool)), hAPP(c_List_Oset(_1621940), hAPP(hAPP(c_List_Olist__update(_1621940, _1621942), _1621948), _1621946))), _1621944)))], (32127 ^ _779142) ^ [_1362879, _1362881, _1362883] : [-(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)), _1362879)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1362881), _1362883)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362881), _1362879)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1362883), _1362879)))], (29179 ^ _779142) ^ [_1296656, _1296658, _1296660] : [-(hAPP(c_Set_OPow(_1296656), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296656, tc_HOL_Obool)), _1296658), _1296660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1296656, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1296656), _1296658)), hAPP(c_Set_OPow(_1296656), _1296660)))], (18016 ^ _779142) ^ [_1096463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096463), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096463) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32629 ^ _779142) ^ [_1374943, _1374945, _1374947] : [-(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), _1374943)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1374945))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1374947))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1374947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1374943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1374943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1374947), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1374945)))))], (45193 ^ _779142) ^ [_1685640, _1685642, _1685644, _1685646, _1685648] : [c_List_Olist__all2(_1685640, _1685642, _1685644, _1685646, _1685648), 45196 ^ _779142 : [(45199 ^ _779142) ^ [_1685803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685803), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685640)), _1685646))), -(hBOOL(hAPP(hAPP(_1685644, hAPP(hAPP(c_List_Onth(_1685640), _1685646), _1685803)), hAPP(hAPP(c_List_Onth(_1685642), _1685648), _1685803))))], (45197 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685640)), _1685646) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685642)), _1685648))]]], (42038 ^ _779142) ^ [_1613962, _1613964, _1613966] : [hBOOL(hAPP(hAPP(c_member(_1613962), _1613964), hAPP(c_List_Oset(_1613962), _1613966))), 42042 ^ _779142 : [(42045 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613962), _1613966), 42041 ^ [_1613962, _1613964, _1613966]) = _1613964)], (42043 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42041 ^ [_1613962, _1613964, _1613966]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613962)), _1613966))))]]], (51579 ^ _779142) ^ [_1821179, _1821181, _1821183] : [class_Rings_Olinordered__idom(_1821179), hAPP(c_Groups_Oabs__class_Oabs(_1821179), _1821181) = hAPP(c_Groups_Oabs__class_Oabs(_1821179), _1821183), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821179), _1821181), _1821183)))], (24632 ^ _779142) ^ [_1212318, _1212320, _1212322] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212318, tc_HOL_Obool)), _1212320) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1212318, tc_HOL_Obool)), _1212322), -(_1212320 = _1212322)], (2568 ^ _779142) ^ [_816930, _816932] : [_816932 = _816930, -(c_Equiv__Relations_Oquotient(_816932) = c_Equiv__Relations_Oquotient(_816930))], (13295 ^ _779142) ^ [_1009671, _1009673] : [class_Rings_Olinordered__idom(_1009671), 13298 ^ _779142 : [(13305 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009671), _1009673), c_Groups_Ozero__class_Ozero(_1009671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009671), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009671), _1009673), _1009673)), c_Groups_Ozero__class_Ozero(_1009671))))], (13299 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009671), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009671), _1009673), _1009673)), c_Groups_Ozero__class_Ozero(_1009671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009671), _1009673), c_Groups_Ozero__class_Ozero(_1009671))))]]], (48400 ^ _779142) ^ [_1755000, _1755002, _1755004, _1755006] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755000, _1755002), c_Lazy__Sequence_Olazy__sequence_OInsert(_1755000, _1755004, _1755006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1755002, _1755004)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755000, _1755002), _1755006))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37551 ^ _779142) ^ [_1490455, _1490457, _1490459] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490455, tc_HOL_Obool)), _1490457), _1490459) = hAPP(c_Set_OCollect(_1490455), hAPP(hAPP(c_COMBS(_1490455, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490455), c_fdisj), hAPP(hAPP(c_COMBC(_1490455, tc_fun(_1490455, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490455)), _1490457))), hAPP(hAPP(c_COMBC(_1490455, tc_fun(_1490455, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490455)), _1490459))))], (36862 ^ _779142) ^ [_1473694, _1473696, _1473698, _1473700, _1473702] : [c_Typedef_Otype__definition(_1473694, _1473696, _1473698, _1473700, _1473702), -(hAPP(c_Set_Oimage(_1473694, _1473696, _1473698), c_Orderings_Otop__class_Otop(tc_fun(_1473694, tc_HOL_Obool))) = _1473702)], (30735 ^ _779142) ^ [_1329683, _1329685] : [class_Orderings_Oorder(_1329683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329683, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1329683), _1329685)), hAPP(c_SetInterval_Oord__class_OatLeast(_1329683), _1329685)) = hAPP(hAPP(c_Set_Oinsert(_1329683), _1329685), c_Orderings_Obot__class_Obot(tc_fun(_1329683, tc_HOL_Obool))))], (41801 ^ _779142) ^ [_1608139, _1608141, _1608143] : [_1608139 = _1608141, 41804 ^ _779142 : [(41807 ^ _779142) ^ [_1608287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1608287), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608143)), _1608139))), -(hAPP(hAPP(c_List_Onth(_1608143), _1608139), _1608287) = hAPP(hAPP(c_List_Onth(_1608143), _1608141), _1608287))], (41805 ^ _779142) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608143)), _1608139) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608143)), _1608141))]]], (34853 ^ _779142) ^ [_1425588, _1425590, _1425592, _1425594, _1425596] : [hBOOL(hAPP(hAPP(c_member(_1425588), _1425590), _1425592)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425594, tc_HOL_Obool)), hAPP(_1425596, _1425590)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425588, tc_fun(_1425594, tc_HOL_Obool)), _1425592), _1425596)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425588, tc_fun(_1425594, tc_HOL_Obool)), _1425592), _1425596))], (9414 ^ _779142) ^ [_939582, _939584] : [class_Groups_Ocomm__monoid__mult(_939582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939582), c_Groups_Oone__class_Oone(_939582)), _939584) = _939584)], (30896 ^ _779142) ^ [_1332729, _1332731] : [class_Lattices_Obounded__lattice__top(_1332729), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332729), c_Orderings_Otop__class_Otop(_1332729)), _1332731) = c_Orderings_Otop__class_Otop(_1332729))], (31841 ^ _779142) ^ [_1352298, _1352300, _1352302, _1352304, _1352306] : [c_Finite__Set_Ofun__left__comm__idem(_1352298, _1352300, _1352302), -(c_Finite__Set_Ofun__left__comm__idem(_1352304, _1352300, hAPP(hAPP(c_COMBB(_1352298, tc_fun(_1352300, _1352300), _1352304), _1352302), _1352306)))], (2950 ^ _779142) ^ [_822819, _822821, _822823, _822825] : [-(c_List_Olenlex(_822825, _822821) = c_List_Olenlex(_822823, _822819)), _822825 = _822823, _822821 = _822819], (47968 ^ _779142) ^ [_1745462, _1745464, _1745466] : [c_List_Olist__ex1(_1745462, _1745464, _1745466), 47972 ^ _779142 : [(47977 ^ _779142) ^ [_1745708] : [-(_1745708 = 47971 ^ [_1745462, _1745464, _1745466]), hBOOL(hAPP(hAPP(c_member(_1745462), _1745708), hAPP(c_List_Oset(_1745462), _1745466))), hBOOL(hAPP(_1745464, _1745708))], (47975 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1745464, 47971 ^ [_1745462, _1745464, _1745466])))], (47973 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745462), 47971 ^ [_1745462, _1745464, _1745466]), hAPP(c_List_Oset(_1745462), _1745466))))]]], (38364 ^ _779142) ^ [_1518557, _1518559] : [-(hAPP(c_Relation_ORange(_1518557, _1518557), c_Relation_OId__on(_1518557, _1518559)) = _1518559)], (34867 ^ _779142) ^ [_1426019, _1426021, _1426023, _1426025, _1426027] : [-(_1426019 = c_Orderings_Obot__class_Obot(tc_fun(_1426021, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426021, tc_fun(_1426023, tc_HOL_Obool)), _1426019), hAPP(hAPP(c_COMBB(tc_fun(_1426023, tc_HOL_Obool), tc_fun(_1426023, tc_HOL_Obool), _1426021), hAPP(c_Set_Oinsert(_1426023), _1426025)), _1426027)) = hAPP(hAPP(c_Set_Oinsert(_1426023), _1426025), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426021, tc_fun(_1426023, tc_HOL_Obool)), _1426019), _1426027)))], (38021 ^ _779142) ^ [_1505586, _1505588, _1505590, _1505592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505586), hAPP(c_Set_OCollect(_1505586), _1505588))), 38024 ^ _779142 : [(38025 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505590), hAPP(c_Set_OCollect(_1505590), hAPP(hAPP(c_COMBB(tc_fun(_1505586, tc_HOL_Obool), tc_HOL_Obool, _1505590), c_HOL_OEx(_1505586)), hAPP(hAPP(c_COMBB(tc_fun(_1505586, tc_HOL_Obool), tc_fun(_1505586, tc_HOL_Obool), _1505590), hAPP(c_COMBS(_1505586, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505586), c_fconj), _1505588))), _1505592))))), 38028 ^ _779142 : [(38029 ^ _779142) ^ [_1505869] : [hBOOL(hAPP(_1505588, _1505869)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505590), hAPP(c_Set_OCollect(_1505590), hAPP(hAPP(c_COMBC(_1505590, _1505586, tc_HOL_Obool), _1505592), _1505869)))))]]], (38035 ^ _779142) ^ [] : [38037 ^ _779142 : [(38040 ^ _779142) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505590), hAPP(c_Set_OCollect(_1505590), hAPP(hAPP(c_COMBC(_1505590, _1505586, tc_HOL_Obool), _1505592), 38036 ^ [_1505586, _1505588, _1505590, _1505592]))))], (38038 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1505588, 38036 ^ [_1505586, _1505588, _1505590, _1505592])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505590), hAPP(c_Set_OCollect(_1505590), hAPP(hAPP(c_COMBB(tc_fun(_1505586, tc_HOL_Obool), tc_HOL_Obool, _1505590), c_HOL_OEx(_1505586)), hAPP(hAPP(c_COMBB(tc_fun(_1505586, tc_HOL_Obool), tc_fun(_1505586, tc_HOL_Obool), _1505590), hAPP(c_COMBS(_1505586, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505586), c_fconj), _1505588))), _1505592))))))]]], (38758 ^ _779142) ^ [_1529351, _1529353, _1529355] : [c_Wellfounded_Owf(_1529351, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529351, _1529351), tc_HOL_Obool)), _1529353), _1529355)), -(c_Wellfounded_Owf(_1529351, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529351, _1529351), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529351, _1529351), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529351, _1529351, _1529351), _1529353), _1529353)), hAPP(hAPP(c_Relation_Orel__comp(_1529351, _1529351, _1529351), _1529355), _1529353))), _1529355)))], (11209 ^ _779142) ^ [_971926, _971928, _971930] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971926), _971928) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971926), _971930), -(_971926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_971928 = _971930)], (44323 ^ _779142) ^ [_1665738, _1665740, _1665742, _1665744, _1665746, _1665748, _1665750, _1665752] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665738, _1665740), _1665742), _1665744), hAPP(hAPP(c_List_Ozip(_1665738, _1665740), hAPP(hAPP(c_List_Omap(_1665746, _1665738), _1665748), _1665750)), _1665752)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665746, _1665740), _1665742), hAPP(c_Product__Type_Oprod_Oprod__case(_1665746, _1665740, _1665742), hAPP(hAPP(c_COMBB(tc_fun(_1665740, tc_prod(_1665738, _1665740)), tc_fun(_1665740, _1665742), _1665746), hAPP(c_COMBB(tc_prod(_1665738, _1665740), _1665742, _1665740), _1665744)), hAPP(hAPP(c_COMBB(_1665738, tc_fun(_1665740, tc_prod(_1665738, _1665740)), _1665746), c_Product__Type_OPair(_1665738, _1665740)), _1665748)))), hAPP(hAPP(c_List_Ozip(_1665746, _1665740), _1665750), _1665752)))], (45562 ^ _779142) ^ [_1693433, _1693435] : [-(hAPP(c_List_Oset(_1693433), c_List_Oconcat(_1693433, _1693435)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1693433), tc_fun(_1693433, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1693433)), _1693435)), c_List_Oset(_1693433)))], (48084 ^ _779142) ^ [_1748369, _1748371, _1748373] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748369, _1748369, hAPP(hAPP(c_COMBB(tc_fun(_1748369, tc_HOL_Obool), tc_fun(_1748369, tc_HOL_Obool), _1748369), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748369), c_fNot)), c_fequal)), _1748371), _1748373)), _1748371 = _1748373], (37445 ^ _779142) ^ [_1487612, _1487614, _1487616, _1487618] : [-(hAPP(c_Set_OCollect(tc_prod(_1487612, _1487614)), hAPP(c_Product__Type_Oprod_Oprod__case(_1487612, _1487614, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1487612, tc_fun(_1487614, tc_HOL_Obool), tc_fun(_1487614, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1487614, tc_HOL_Obool), tc_fun(_1487614, tc_HOL_Obool)), _1487612), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1487614)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487612), c_fconj), _1487616))), _1487618))) = hAPP(hAPP(c_Product__Type_OSigma(_1487612, _1487614), hAPP(c_Set_OCollect(_1487612), _1487616)), hAPP(hAPP(c_COMBB(tc_fun(_1487614, tc_HOL_Obool), tc_fun(_1487614, tc_HOL_Obool), _1487612), c_Set_OCollect(_1487614)), _1487618)))], (5110 ^ _779142) ^ [_857069, _857071, _857073, _857075, _857077, _857079] : [-(c_Lazy__Sequence_Oappend(_857079, _857075, _857071) = c_Lazy__Sequence_Oappend(_857077, _857073, _857069)), _857079 = _857077, _857075 = _857073, _857071 = _857069], (25892 ^ _779142) ^ [_1234166] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1234166), _1234166)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1234166)], (23591 ^ _779142) ^ [_1194598, _1194600, _1194602] : [class_Groups_Oordered__ab__group__add(_1194598), -(hAPP(c_Set_Oimage(_1194598, _1194598, c_Groups_Ouminus__class_Ouminus(_1194598)), c_SetInterval_Oord__class_OatLeastAtMost(_1194598, _1194600, _1194602)) = c_SetInterval_Oord__class_OatLeastAtMost(_1194598, hAPP(c_Groups_Ouminus__class_Ouminus(_1194598), _1194602), hAPP(c_Groups_Ouminus__class_Ouminus(_1194598), _1194600)))], (1476 ^ _779142) ^ [_800534, _800536] : [-(class_Orderings_Obot(_800534)), _800536 = _800534, class_Orderings_Obot(_800536)], (23235 ^ _779142) ^ [_1188380, _1188382, _1188384] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1188380, tc_HOL_Obool)), _1188382), hAPP(c_Set_OPow(_1188380), _1188384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1188380, tc_HOL_Obool)), _1188382), _1188384)))], (1766 ^ _779142) ^ [_804159, _804161] : [-(class_Rings_Ozero__neq__one(_804159)), _804161 = _804159, class_Rings_Ozero__neq__one(_804161)], (33537 ^ _779142) ^ [_1392691, _1392693] : [-(c_Divides_Odivmod__int__rel(_1392691, _1392693) = 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, _1392691))), 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), _1392693)))))), 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)), _1392693))), 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)), _1392693))))), 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)), _1392693)))), 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), _1392693))), 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))))))))], (6556 ^ _779142) ^ [_884380, _884382, _884384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884380, tc_HOL_Obool)), _884382), _884384)), hBOOL(hAPP(c_Finite__Set_Ofinite(_884380), _884384)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_884380), _884382)))], (8523 ^ _779142) ^ [_921980, _921982, _921984, _921986, _921988] : [class_Groups_Ocomm__monoid__add(_921980), hBOOL(hAPP(c_Finite__Set_Ofinite(_921982), _921984)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921982, _921980), _921986), hAPP(hAPP(c_Set_Oinsert(_921982), _921988), _921984)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921980), hAPP(_921986, _921988)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921982, _921980), _921986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921982, tc_HOL_Obool)), _921984), hAPP(hAPP(c_Set_Oinsert(_921982), _921988), c_Orderings_Obot__class_Obot(tc_fun(_921982, tc_HOL_Obool)))))))], (45384 ^ _779142) ^ [_1689992, _1689994] : [-(c_List_Oremdups(_1689992, c_List_Oremdups(_1689992, _1689994)) = c_List_Oremdups(_1689992, _1689994))], (33000 ^ _779142) ^ [_1382995, _1382997, _1382999, _1383001, _1383003] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382995, _1382997, tc_HOL_Obool), _1382999), hAPP(hAPP(c_Product__Type_OPair(_1382995, _1382997), _1383001), _1383003))), -(hBOOL(hAPP(hAPP(_1382999, _1383001), _1383003)))], (43774 ^ _779142) ^ [_1654699, _1654701, _1654703] : [-(hAPP(c_List_Oset(_1654699), hAPP(c_List_Orotate(_1654699, _1654701), _1654703)) = hAPP(c_List_Oset(_1654699), _1654703))], (28054 ^ _779142) ^ [_1274675, _1274677] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1274675)), hAPP(c_Nat_OSuc, _1274677)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1274675), _1274677)))], (31640 ^ _779142) ^ [_1347217, _1347219] : [-(c_Random_Olog(_1347217, _1347219) = 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(_1347217, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1347219), _1347217)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1347217), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1347219), _1347217)))], (26588 ^ _779142) ^ [_1247074, _1247076, _1247078] : [class_Lattices_Osemilattice__sup(_1247074), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247074), _1247076), _1247078) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247074), _1247078), _1247076))], (48090 ^ _779142) ^ [_1748507, _1748509, _1748511] : [-(_1748509 = _1748511), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748507, _1748507, hAPP(hAPP(c_COMBB(tc_fun(_1748507, tc_HOL_Obool), tc_fun(_1748507, tc_HOL_Obool), _1748507), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748507), c_fNot)), c_fequal)), _1748509), _1748511)))], (10111 ^ _779142) ^ [_952852, _952854, _952856] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952852), _952854)), _952856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952854), _952856)))], (16423 ^ _779142) ^ [_1068130, _1068132, _1068134] : [class_Orderings_Olinorder(_1068130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068130), _1068132)), 16430 ^ _779142 : [(16437 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068130, tc_HOL_Obool)), _1068132), hAPP(hAPP(c_Set_Oinsert(_1068130), _1068134), c_Orderings_Obot__class_Obot(tc_fun(_1068130, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068130, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1068130, hAPP(hAPP(c_Set_Oinsert(_1068130), _1068134), _1068132)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068130), _1068134), c_Big__Operators_Olinorder__class_OMin(_1068130, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068130, tc_HOL_Obool)), _1068132), hAPP(hAPP(c_Set_Oinsert(_1068130), _1068134), c_Orderings_Obot__class_Obot(tc_fun(_1068130, tc_HOL_Obool)))))))], (16431 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068130, tc_HOL_Obool)), _1068132), hAPP(hAPP(c_Set_Oinsert(_1068130), _1068134), c_Orderings_Obot__class_Obot(tc_fun(_1068130, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068130, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1068130, hAPP(hAPP(c_Set_Oinsert(_1068130), _1068134), _1068132)) = _1068134)]]], (40663 ^ _779142) ^ [_1575984, _1575986, _1575988] : [c_Relation_Ototal__on(_1575984, _1575986, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575984, _1575984), tc_HOL_Obool)), _1575988), c_Relation_OId(_1575984))), -(c_Relation_Ototal__on(_1575984, _1575986, _1575988))], (52131 ^ _779142) ^ [_1830893, _1830895] : [class_Lattices_Obounded__lattice(_1830893), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1830895, _1830893)))], (5949 ^ _779142) ^ [_873612, _873614, _873616, _873618, _873620] : [-(hBOOL(hAPP(hAPP(c_member(_873612), _873614), hAPP(c_Set_Oimage(_873616, _873612, _873618), _873620)))), 5950 ^ _779142 : [(5951 ^ _779142) ^ [_873682] : [hBOOL(hAPP(hAPP(c_member(_873616), _873682), _873620)), _873614 = hAPP(_873618, _873682)]]], (44199 ^ _779142) ^ [_1663246, _1663248, _1663250] : [-(_1663246 = c_List_Olist_ONil(_1663248)), -(c_List_Olast(_1663248, hAPP(hAPP(c_List_Oappend(_1663248), _1663250), _1663246)) = c_List_Olast(_1663248, _1663246))], (32813 ^ _779142) ^ [_1378457, _1378459, _1378461, _1378463, _1378465, _1378467] : [hBOOL(hAPP(hAPP(_1378457, _1378459), _1378461)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1378463, tc_fun(_1378465, tc_HOL_Obool))), _1378457), _1378467), _1378459), _1378461)))], (48820 ^ _779142) ^ [_1764906, _1764908] : [c_Relation_Otrans(_1764906, _1764908), -(c_Relation_Otrans(tc_List_Olist(_1764906), c_List_Olexord(_1764906, _1764908)))], (42828 ^ _779142) ^ [_1632626, _1632628, _1632630] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632626))), -(c_List_Osublist(_1632628, hAPP(hAPP(c_List_Olist_OCons(_1632628), _1632630), c_List_Olist_ONil(_1632628)), _1632626) = c_List_Olist_ONil(_1632628))], (49889 ^ _779142) ^ [_1787924, _1787926, _1787928] : [c_Fun_Obij__betw(_1787924, _1787926, _1787928, c_Orderings_Otop__class_Otop(tc_fun(_1787924, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787926, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1787926, _1787924, c_Hilbert__Choice_Oinv__into(_1787924, _1787926, c_Orderings_Otop__class_Otop(tc_fun(_1787924, tc_HOL_Obool)), _1787928), c_Orderings_Otop__class_Otop(tc_fun(_1787926, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787924, tc_HOL_Obool))))], (26936 ^ _779142) ^ [_1254314, _1254316, _1254318] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1254314, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254314, tc_HOL_Obool)), _1254316), _1254318)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254314, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1254314, tc_HOL_Obool)), _1254316)), _1254318))], (52275 ^ _779142) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (15241 ^ _779142) ^ [_1045938, _1045940, _1045942] : [class_Orderings_Olinorder(_1045938), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045938), _1045940), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045938), _1045940), _1045942)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045938), _1045940), _1045942))], (18428 ^ _779142) ^ [_1103669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103669), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103669)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (48136 ^ _779142) ^ [_1749351, _1749353, _1749355, _1749357, _1749359] : [-(c_Predicate_Oconversep(_1749351, _1749353, c_Predicate_Opred__comp(_1749351, _1749355, _1749353, _1749357, _1749359)) = c_Predicate_Opred__comp(_1749353, _1749355, _1749351, c_Predicate_Oconversep(_1749355, _1749353, _1749359), c_Predicate_Oconversep(_1749351, _1749355, _1749357)))], (34805 ^ _779142) ^ [_1424371, _1424373, _1424375, _1424377] : [-(_1424371 = c_Orderings_Obot__class_Obot(tc_fun(_1424373, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424373, tc_fun(_1424375, tc_HOL_Obool)), _1424371), hAPP(c_COMBK(tc_fun(_1424375, tc_HOL_Obool), _1424373), _1424377)) = _1424377)], (28444 ^ _779142) ^ [_1281990, _1281992, _1281994] : [class_Complete__Lattice_Ocomplete__lattice(_1281990), hBOOL(hAPP(hAPP(c_member(_1281990), _1281992), _1281994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281990), _1281992), c_Complete__Lattice_OSup__class_OSup(_1281990, _1281994))))], (45352 ^ _779142) ^ [_1689416, _1689418] : [hBOOL(hAPP(c_List_Odistinct(_1689416), _1689418)), -(c_List_Oremdups(_1689416, _1689418) = _1689418)], (19833 ^ _779142) ^ [_1127477, _1127479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127477)), 19836 ^ _779142 : [(19845 ^ _779142) ^ [] : [-(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), _1127477), _1127479)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127479), _1127477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127479))], (19837 ^ _779142) ^ [] : [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), _1127477), _1127479))), 19840 ^ _779142 : [(19843 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127479)))], (19841 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127479), _1127477)))]]]]], (42576 ^ _779142) ^ [_1628004, _1628006, _1628008, _1628010] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628004) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1628006), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628004)), hAPP(hAPP(c_List_Olist_OCons(_1628006), _1628008), _1628010)) = hAPP(hAPP(c_List_Olist_OCons(_1628006), _1628008), hAPP(hAPP(c_List_Otake(_1628006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628004)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1628010)))], (33981 ^ _779142) ^ [_1401692, _1401694, _1401696] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1401692, _1401694), _1401696))), _1401692 = 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), _1401696)), _1401694)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401696)), 33988 ^ _779142 : [(33991 ^ _779142) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1401696) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33989 ^ _779142) ^ [] : [-(_1401694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 33992 ^ _779142 : [(33995 ^ _779142) ^ [] : [33996 ^ _779142 : [(33999 ^ _779142) ^ [] : [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), _1401696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401696)), _1401694))], (33997 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401694)))]], 34004 ^ _779142 : [(34007 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401694), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401696)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34005 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401694))]]], (33993 ^ _779142) ^ [] : [_1401694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51489 ^ _779142) ^ [_1819681, _1819683] : [_1819683 = _1819681, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819681), _1819683)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819683), _1819681)))], (38224 ^ _779142) ^ [_1514571, _1514573] : [-(hAPP(c_Set_Ovimage(_1514571, _1514571, c_Fun_Oid(_1514571)), _1514573) = _1514573)], (21628 ^ _779142) ^ [_1159035, _1159037, _1159039, _1159041] : [class_Rings_Olinordered__semidom(_1159035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159035), c_Groups_Oone__class_Oone(_1159035)), _1159037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159035), hAPP(hAPP(c_Power_Opower__class_Opower(_1159035), _1159037), _1159039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1159035), _1159037), _1159041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159039), _1159041)))], (32787 ^ _779142) ^ [_1377942, _1377944, _1377946, _1377948, _1377950, _1377952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377942, tc_fun(_1377944, tc_HOL_Obool))), _1377946), _1377948)), hBOOL(hAPP(hAPP(_1377946, _1377950), _1377952)), -(hBOOL(hAPP(hAPP(_1377948, _1377950), _1377952)))], (52491 ^ _779142) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (840 ^ _779142) ^ [_791692, _791694, _791696, _791698] : [-(c_Predicate_Otransp(_791696, _791692)), c_Predicate_Otransp(_791698, _791694), _791698 = _791696, _791694 = _791692], (23401 ^ _779142) ^ [_1191381, _1191383, _1191385] : [class_Groups_Ogroup__add(_1191381), 23404 ^ _779142 : [(23411 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191381), _1191383), _1191385) = c_Groups_Ozero__class_Ozero(_1191381), -(_1191383 = hAPP(c_Groups_Ouminus__class_Ouminus(_1191381), _1191385))], (23405 ^ _779142) ^ [] : [_1191383 = hAPP(c_Groups_Ouminus__class_Ouminus(_1191381), _1191385), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191381), _1191383), _1191385) = c_Groups_Ozero__class_Ozero(_1191381))]]], (2598 ^ _779142) ^ [_817401, _817403, _817405, _817407] : [-(c_Wellfounded_Omin__ext(_817407, _817403) = c_Wellfounded_Omin__ext(_817405, _817401)), _817407 = _817405, _817403 = _817401], (18537 ^ _779142) ^ [_1105521, _1105523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1105521), _1105523)), -(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)), _1105521)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1105523))))], (38699 ^ _779142) ^ [_1528218, _1528220, _1528222, _1528224] : [c_Wellfounded_Owf(_1528218, _1528220), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528218, _1528218)), hAPP(hAPP(c_Product__Type_OPair(_1528218, _1528218), _1528222), _1528224)), _1528220)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528218, _1528218)), hAPP(hAPP(c_Product__Type_OPair(_1528218, _1528218), _1528224), _1528222)), _1528220))], (34067 ^ _779142) ^ [] : [-(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))], (22204 ^ _779142) ^ [_1169631, _1169633, _1169635] : [class_Rings_Olinordered__idom(_1169631), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169631), c_Groups_Ozero__class_Ozero(_1169631)), hAPP(hAPP(c_Power_Opower__class_Opower(_1169631), hAPP(c_Groups_Oabs__class_Oabs(_1169631), _1169633)), _1169635))))], (47636 ^ _779142) ^ [_1738889, _1738891, _1738893] : [c_List_Olist__ex(_1738889, _1738891, _1738893), 47640 ^ _779142 : [(47643 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1738891, hAPP(hAPP(c_List_Onth(_1738889), _1738893), 47639 ^ [_1738889, _1738891, _1738893]))))], (47641 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47639 ^ [_1738889, _1738891, _1738893]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738889)), _1738893))))]]], (26294 ^ _779142) ^ [_1241514, _1241516] : [class_Groups_Olinordered__ab__group__add(_1241514), hBOOL(hAPP(c_Finite__Set_Ofinite(_1241514), _1241516)), -(_1241516 = c_Orderings_Obot__class_Obot(tc_fun(_1241514, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1241514), c_Big__Operators_Olinorder__class_OMin(_1241514, _1241516)) = c_Big__Operators_Olinorder__class_OMax(_1241514, hAPP(c_Set_Oimage(_1241514, _1241514, c_Groups_Ouminus__class_Ouminus(_1241514)), _1241516)))], (6689 ^ _779142) ^ [_887137, _887139, _887141, _887143] : [c_Finite__Set_Ofolding__one(_887137, _887139, _887141), hBOOL(hAPP(c_Finite__Set_Ofinite(_887137), _887143)), -(_887143 = c_Orderings_Obot__class_Obot(tc_fun(_887137, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_887137), hAPP(hAPP(_887139, 6702 ^ [_887137, _887139, _887141, _887143]), 6703 ^ [_887137, _887139, _887141, _887143])), hAPP(hAPP(c_Set_Oinsert(_887137), 6702 ^ [_887137, _887139, _887141, _887143]), hAPP(hAPP(c_Set_Oinsert(_887137), 6703 ^ [_887137, _887139, _887141, _887143]), c_Orderings_Obot__class_Obot(tc_fun(_887137, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_887137), hAPP(_887141, _887143)), _887143)))], (46810 ^ _779142) ^ [_1720541, _1720543, _1720545] : [class_Orderings_Olinorder(_1720541), c_List_Olinorder__class_Osorted(_1720541, _1720543), -(c_List_Olinorder__class_Osorted(_1720541, c_List_OtakeWhile(_1720541, _1720545, _1720543)))], (50807 ^ _779142) ^ [_1807899, _1807901, _1807903, _1807905] : [class_Rings_Ocomm__ring(_1807899), class_Rings_Odvd(_1807899), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807899), _1807901), _1807903)), 50818 ^ _779142 : [(50825 ^ _779142) ^ [_1808325, _1808327] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807899), _1807901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1807899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1807899), _1808327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807899), _1808325), _1807903))), _1807905))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807899), _1807901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1807899), _1808327), _1807905))))], (50819 ^ _779142) ^ [_1808152, _1808154] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807899), _1807901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1807899), _1808154), _1807905))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807899), _1807901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1807899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1807899), _1808154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807899), _1808152), _1807903))), _1807905))))]]], (48633 ^ _779142) ^ [_1760444, _1760446] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760444)), _1760446)), 48637 ^ _779142 : [(48638 ^ _779142) ^ [_1760545] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760444)), _1760545), _1760446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760444)), _1760545)), 48636 ^ [_1760444, _1760446])))]]], (46304 ^ _779142) ^ [_1709951, _1709953, _1709955] : [class_Orderings_Olinorder(_1709951), 46307 ^ _779142 : [(46320 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709951, hAPP(hAPP(c_List_Olist_OCons(_1709951), _1709953), _1709955))), c_List_Olinorder__class_Osorted(_1709951, _1709955), 46326 ^ _779142 : [(46329 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709951), _1709953), 46325 ^ [_1709951, _1709953, _1709955]))], (46327 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709951), 46325 ^ [_1709951, _1709953, _1709955]), hAPP(c_List_Oset(_1709951), _1709955))))]]], (46308 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1709951, hAPP(hAPP(c_List_Olist_OCons(_1709951), _1709953), _1709955)), 46311 ^ _779142 : [(46314 ^ _779142) ^ [_1710137] : [hBOOL(hAPP(hAPP(c_member(_1709951), _1710137), hAPP(c_List_Oset(_1709951), _1709955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709951), _1709953), _1710137)))], (46312 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709951, _1709955))]]]]], (40199 ^ _779142) ^ [_1564026, _1564028] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564026, _1564026), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564026, _1564028)), hAPP(hAPP(c_Product__Type_OSigma(_1564026, _1564026), hAPP(c_Relation_OField(_1564026), _1564028)), hAPP(c_COMBK(tc_fun(_1564026, tc_HOL_Obool), _1564026), hAPP(c_Relation_OField(_1564026), _1564028))))))], (35573 ^ _779142) ^ [_1445061, _1445063] : [c_Relation_Oirrefl(_1445061, _1445063), 35576 ^ _779142 : [(35577 ^ _779142) ^ [_1445143] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1445061, _1445061)), hAPP(hAPP(c_Product__Type_OPair(_1445061, _1445061), _1445143), _1445143)), _1445063))]]], (33179 ^ _779142) ^ [_1386390, _1386392, _1386394, _1386396] : [class_Rings_Osemiring__1(_1386390), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1386390, _1386392, hAPP(c_Nat_OSuc, _1386394), _1386396) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1386390, _1386392, _1386394, hAPP(_1386392, _1386396)))], (29281 ^ _779142) ^ [_1298741, _1298743, _1298745] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298741, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1298741, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1298741, tc_HOL_Obool), tc_HOL_Obool)), _1298743), _1298745))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298741, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1298741, tc_HOL_Obool), _1298743)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1298741, tc_HOL_Obool), _1298745)))))], (17775 ^ _779142) ^ [_1092391] : [class_Int_Onumber__ring(_1092391), -(hAPP(c_Int_Onumber__class_Onumber__of(_1092391), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1092391))], (34635 ^ _779142) ^ [_1420194, _1420196, _1420198, _1420200, _1420202, _1420204] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1420196, _1420198)), hAPP(hAPP(c_Product__Type_OPair(_1420196, _1420198), _1420202), _1420204)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420194, tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1420194, tc_HOL_Obool))), _1420200))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420194, tc_fun(_1420196, tc_fun(_1420198, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1420194, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_fun(_1420196, tc_fun(_1420198, tc_HOL_Obool)), _1420194), hAPP(c_COMBC(_1420196, tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_fun(_1420198, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1420198, tc_fun(tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_fun(_1420198, tc_HOL_Obool)), _1420196), c_COMBC(_1420198, tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1420198, tc_prod(_1420196, _1420198)), tc_fun(_1420198, tc_fun(tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_HOL_Obool)), _1420196), hAPP(c_COMBB(tc_prod(_1420196, _1420198), tc_fun(tc_fun(tc_prod(_1420196, _1420198), tc_HOL_Obool), tc_HOL_Obool), _1420198), c_member(tc_prod(_1420196, _1420198)))), c_Product__Type_OPair(_1420196, _1420198))))), _1420200)), _1420202), _1420204)))], (26502 ^ _779142) ^ [_1245258, _1245260, _1245262] : [class_Lattices_Osemilattice__sup(_1245258), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245258), _1245260), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245258), _1245262), _1245260))))], (50166 ^ _779142) ^ [_1793427, _1793429, _1793431, _1793433, _1793435, _1793437, _1793439] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793427, tc_HOL_Obool)), _1793429), _1793431) = c_Orderings_Obot__class_Obot(tc_fun(_1793427, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793433, tc_HOL_Obool)), _1793435), _1793437) = c_Orderings_Obot__class_Obot(tc_fun(_1793433, tc_HOL_Obool)), c_Fun_Obij__betw(_1793427, _1793433, _1793439, _1793429, _1793435), c_Fun_Obij__betw(_1793427, _1793433, _1793439, _1793431, _1793437), -(c_Fun_Obij__betw(_1793427, _1793433, _1793439, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793427, tc_HOL_Obool)), _1793429), _1793431), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793433, tc_HOL_Obool)), _1793435), _1793437)))], (33010 ^ _779142) ^ [_1383210] : [-(c_Divides_Odivmod__nat(_1383210, 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)), _1383210))], (30047 ^ _779142) ^ [_1315530, _1315532, _1315534] : [class_Orderings_Olinorder(_1315530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315530), _1315532)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315530), _1315534)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315530, tc_HOL_Obool)), _1315532), _1315534) = c_Orderings_Obot__class_Obot(tc_fun(_1315530, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315530), c_Big__Operators_Olattice_OInf__fin(_1315530, c_Orderings_Oord__class_Omin(_1315530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315530, tc_HOL_Obool)), _1315532), _1315534))), c_Big__Operators_Olattice_OInf__fin(_1315530, c_Orderings_Oord__class_Omin(_1315530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315530, tc_HOL_Obool)), _1315532), _1315534))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315530), c_Big__Operators_Olattice_OInf__fin(_1315530, c_Orderings_Oord__class_Omin(_1315530), _1315532)), c_Big__Operators_Olattice_OInf__fin(_1315530, c_Orderings_Oord__class_Omin(_1315530), _1315534)))], (30577 ^ _779142) ^ [_1326207, _1326209, _1326211] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1326207, tc_HOL_Obool)), _1326209)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326207), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1326207, tc_HOL_Obool), _1326209))), 30587 ^ _779142 : [(30590 ^ _779142) ^ [] : [hAPP(c_Finite__Set_Ocard(_1326207), 30586 ^ [_1326207, _1326209, _1326211]) = _1326211], (30588 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1326207, tc_HOL_Obool)), 30586 ^ [_1326207, _1326209, _1326211]), _1326209)))]], 30594 ^ _779142 : [(30598 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1326207, tc_HOL_Obool)), 30596 ^ [_1326207, _1326209, _1326211]), _1326209)))], (30600 ^ _779142) ^ [] : [30593 ^ [_1326207, _1326209, _1326211] = 30596 ^ [_1326207, _1326209, _1326211]], (30602 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326207, tc_HOL_Obool)), 30593 ^ [_1326207, _1326209, _1326211]), 30596 ^ [_1326207, _1326209, _1326211]) = c_Orderings_Obot__class_Obot(tc_fun(_1326207, tc_HOL_Obool))], (30595 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1326207, tc_HOL_Obool)), 30593 ^ [_1326207, _1326209, _1326211]), _1326209)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1326211), hAPP(c_Finite__Set_Ocard(tc_fun(_1326207, tc_HOL_Obool)), _1326209)) = hAPP(c_Finite__Set_Ocard(_1326207), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1326207, tc_HOL_Obool), _1326209)))], (19583 ^ _779142) ^ [_1123276] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1123276, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1123276)], (25098 ^ _779142) ^ [_1220275, _1220277] : [class_Rings_Olinordered__idom(_1220275), -(hAPP(c_Groups_Oabs__class_Oabs(_1220275), _1220277) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220275), _1220277), c_Groups_Osgn__class_Osgn(_1220275, _1220277)))], (7054 ^ _779142) ^ [_895443, _895445, _895447] : [hBOOL(hAPP(hAPP(c_member(_895443), _895445), _895447)), -(hAPP(hAPP(c_Set_Oinsert(_895443), _895445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895443, tc_HOL_Obool)), _895447), hAPP(hAPP(c_Set_Oinsert(_895443), _895445), c_Orderings_Obot__class_Obot(tc_fun(_895443, tc_HOL_Obool))))) = _895447)], (45837 ^ _779142) ^ [_1701304, _1701306] : [class_Groups_Omonoid__add(_1701304), -(hAPP(c_List_Ofoldl(_1701304, _1701304, c_Groups_Oplus__class_Oplus(_1701304), c_Groups_Ozero__class_Ozero(_1701304)), _1701306) = c_List_Ofoldr(_1701304, _1701304, c_Groups_Oplus__class_Oplus(_1701304), _1701306, c_Groups_Ozero__class_Ozero(_1701304)))], (9426 ^ _779142) ^ [_939772, _939774, _939776] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_939772), _939774)), 9429 ^ _779142 : [(9430 ^ _779142) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_939772, tc_Nat_Onat), _939776), _939774) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 9433 ^ _779142 : [(9434 ^ _779142) ^ [_939934] : [hBOOL(hAPP(hAPP(c_member(_939772), _939934), _939774)), -(hAPP(_939776, _939934) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (9440 ^ _779142) ^ [] : [9442 ^ _779142 : [(9445 ^ _779142) ^ [] : [hAPP(_939776, 9441 ^ [_939772, _939774, _939776]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (9443 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939772), 9441 ^ [_939772, _939774, _939776]), _939774)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_939772, tc_Nat_Onat), _939776), _939774) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (50553 ^ _779142) ^ [_1803317, _1803319, _1803321] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803317), _1803319)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803317), _1803321))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1803317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803319), _1803321)))], (37023 ^ _779142) ^ [_1477225, _1477227, _1477229, _1477231] : [hBOOL(hAPP(hAPP(c_member(_1477225), _1477227), c_Wellfounded_Oacc(_1477225, _1477229))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1477225, _1477225)), hAPP(hAPP(c_Product__Type_OPair(_1477225, _1477225), _1477231), _1477227)), _1477229)), -(hBOOL(hAPP(hAPP(c_member(_1477225), _1477231), c_Wellfounded_Oacc(_1477225, _1477229))))], (30109 ^ _779142) ^ [_1316769, _1316771, _1316773] : [class_Orderings_Olinorder(_1316769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316769), _1316771)), -(_1316771 = c_Orderings_Obot__class_Obot(tc_fun(_1316769, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316769), _1316773)), -(_1316773 = c_Orderings_Obot__class_Obot(tc_fun(_1316769, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316769, tc_HOL_Obool)), _1316771), _1316773) = c_Orderings_Obot__class_Obot(tc_fun(_1316769, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1316769, c_Orderings_Oord__class_Omax(_1316769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316769, tc_HOL_Obool)), _1316771), _1316773)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316769), c_Big__Operators_Olattice_OSup__fin(_1316769, c_Orderings_Oord__class_Omax(_1316769), _1316771)), c_Big__Operators_Olattice_OSup__fin(_1316769, c_Orderings_Oord__class_Omax(_1316769), _1316773)))], (23125 ^ _779142) ^ [_1186307, _1186309, _1186311] : [class_Rings_Oring(_1186307), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186307), hAPP(c_Groups_Ouminus__class_Ouminus(_1186307), _1186309)), hAPP(c_Groups_Ouminus__class_Ouminus(_1186307), _1186311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186307), _1186309), _1186311))], (31122 ^ _779142) ^ [_1336960, _1336962, _1336964] : [class_Orderings_Olinorder(_1336960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336960), _1336962), _1336964)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336960, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1336960, _1336962, _1336964)), hAPP(c_SetInterval_Oord__class_OatLeast(_1336960), _1336964)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1336960), _1336962))], (45693 ^ _779142) ^ [_1697200] : [-(c_List_Otranspose(_1697200, c_List_Olist_ONil(tc_List_Olist(_1697200))) = c_List_Olist_ONil(tc_List_Olist(_1697200)))], (25878 ^ _779142) ^ [_1233898, _1233900] : [class_Rings_Olinordered__idom(_1233898), -(hAPP(c_Groups_Oabs__class_Oabs(_1233898), hAPP(hAPP(c_Power_Opower__class_Opower(_1233898), _1233900), 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(_1233898), _1233900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (24217 ^ _779142) ^ [_1205422, _1205424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205422, tc_HOL_Obool)), _1205424), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205422, tc_HOL_Obool)), _1205424))), -(_1205424 = c_Orderings_Obot__class_Obot(tc_fun(_1205422, tc_HOL_Obool)))], (29097 ^ _779142) ^ [_1294961, _1294963, _1294965, _1294967] : [class_Lattices_Osemilattice__inf(_1294961), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294961), _1294963), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294961), _1294965), _1294967)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294961), _1294965), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294961), _1294963), _1294967)))], (52439 ^ _779142) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (45853 ^ _779142) ^ [_1701720, _1701722, _1701724, _1701726] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701720, tc_Nat_Onat), _1701720), c_Product__Type_Ofst(_1701720, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701720, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701720, 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(_1701720, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701720, tc_Nat_Onat))), _1701722)), hAPP(hAPP(c_List_Ozip(_1701720, tc_Nat_Onat), _1701724), c_List_Oupt(_1701726, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701726), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701720)), _1701724)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701720, tc_Nat_Onat), _1701720), c_Product__Type_Ofst(_1701720, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701720, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701720, 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(_1701720, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701720, 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(_1701720, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701720, tc_Nat_Onat))), _1701726))), _1701722)), hAPP(hAPP(c_List_Ozip(_1701720, tc_Nat_Onat), _1701724), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701720)), _1701724))))))], (50753 ^ _779142) ^ [_1806798, _1806800, _1806802, _1806804, _1806806] : [class_Divides_Osemiring__div(_1806798), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806798), _1806800), _1806802)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806798), _1806804), _1806806)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806798), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806798), _1806802), _1806800)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806798), _1806806), _1806804)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806798), _1806802), _1806806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806798), _1806800), _1806804)))], (47827 ^ _779142) ^ [_1742778, _1742780] : [-(c_FunDef_Ois__measure(_1742778, _1742780))], (48225 ^ _779142) ^ [_1751681, _1751683, _1751685, _1751687] : [48233 ^ _779142 : [(48236 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1751687, 48232 ^ [_1751681, _1751683, _1751685, _1751687])))], (48234 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751681), 48232 ^ [_1751681, _1751683, _1751685, _1751687]), hAPP(c_List_Oset(_1751681), c_List_Oreplicate(_1751681, _1751683, _1751685)))))]], hBOOL(hAPP(_1751687, _1751685)), -(_1751683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17988 ^ _779142) ^ [_1096017, _1096019] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1096017), _1096019), hAPP(c_Int_Onumber__class_Onumber__of(_1096017), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1096017)), class_Fields_Ofield__inverse__zero(_1096017), class_Int_Onumber__ring(_1096017)], (26350 ^ _779142) ^ [_1242503, _1242505, _1242507, _1242509] : [26351 ^ _779142 : [(26354 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1242503), _1242505), _1242509))], (26352 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1242503), _1242505), _1242507))]], -(hBOOL(hAPP(hAPP(c_member(_1242503), _1242505), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242503, tc_HOL_Obool)), _1242507), _1242509))))], (37249 ^ _779142) ^ [_1482719, _1482721, _1482723, _1482725, _1482727] : [hAPP(_1482725, _1482721) = _1482727, -(hBOOL(hAPP(hAPP(c_member(_1482719), _1482721), hAPP(c_Set_Ovimage(_1482719, _1482723, _1482725), hAPP(hAPP(c_Set_Oinsert(_1482723), _1482727), c_Orderings_Obot__class_Obot(tc_fun(_1482723, tc_HOL_Obool)))))))], (3572 ^ _779142) ^ [_832572, _832574, _832576, _832578, _832580, _832582, _832584, _832586, _832588, _832590] : [-(c_List_Ofoldr(_832590, _832586, _832582, _832578, _832574) = c_List_Ofoldr(_832588, _832584, _832580, _832576, _832572)), _832590 = _832588, _832586 = _832584, _832582 = _832580, _832578 = _832576, _832574 = _832572], (31787 ^ _779142) ^ [_1351216, _1351218, _1351220] : [class_Groups_Ocomm__monoid__add(_1351216), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351218, _1351216), hAPP(c_COMBK(_1351216, _1351218), c_Groups_Ozero__class_Ozero(_1351216))), _1351220) = c_Groups_Ozero__class_Ozero(_1351216))], (20642 ^ _779142) ^ [_1141709, _1141711, _1141713, _1141715, _1141717, _1141719] : [-(hBOOL(hAPP(hAPP(c_member(_1141709), _1141711), c_SetInterval_Oord_OgreaterThanAtMost(_1141709, _1141713, _1141715, _1141717, _1141719)))), hBOOL(hAPP(hAPP(_1141715, _1141717), _1141711)), hBOOL(hAPP(hAPP(_1141713, _1141711), _1141719))], (20632 ^ _779142) ^ [_1141482, _1141484] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1141482, _1141484)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1141484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141482), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45296 ^ _779142) ^ [_1688082, _1688084, _1688086] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1688082))), c_Enum_On__lists(_1688082, _1688084, _1688086)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688082)), _1688086)), _1688084))], (22833 ^ _779142) ^ [_1181275, _1181277] : [class_Groups_Ogroup__add(_1181275), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181275), hAPP(c_Groups_Ouminus__class_Ouminus(_1181275), _1181277)) = _1181277)], (46562 ^ _779142) ^ [_1715237] : [-(hAPP(c_List_Orev(_1715237), c_List_Olist_ONil(_1715237)) = c_List_Olist_ONil(_1715237))], (2836 ^ _779142) ^ [_821114, _821116, _821118, _821120, _821122, _821124] : [-(c_Nitpick_Otimes__frac(_821124, _821120, _821116) = c_Nitpick_Otimes__frac(_821122, _821118, _821114)), _821124 = _821122, _821120 = _821118, _821116 = _821114], (14785 ^ _779142) ^ [_1037317, _1037319, _1037321, _1037323] : [c_Sum__Type_OPlus(_1037317, _1037319, _1037321, _1037323) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1037317, _1037319), tc_HOL_Obool)), 14788 ^ _779142 : [(14791 ^ _779142) ^ [] : [-(_1037323 = c_Orderings_Obot__class_Obot(tc_fun(_1037319, tc_HOL_Obool)))], (14789 ^ _779142) ^ [] : [-(_1037321 = c_Orderings_Obot__class_Obot(tc_fun(_1037317, tc_HOL_Obool)))]]], (5100 ^ _779142) ^ [_856920, _856922, _856924, _856926] : [-(c_Product__Type_OPair(_856926, _856922) = c_Product__Type_OPair(_856924, _856920)), _856926 = _856924, _856922 = _856920], (47250 ^ _779142) ^ [_1729947, _1729949] : [-(c_List_Omeasures(_1729947, _1729949) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1729947), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1729947, tc_List_Olist(tc_fun(_1729947, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729947, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1729947, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1729947), c_List_Omap(tc_fun(_1729947, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1729947, tc_Nat_Onat), _1729947, tc_Nat_Onat), c_COMBI(tc_fun(_1729947, tc_Nat_Onat))))), _1729949)))], (37267 ^ _779142) ^ [_1483149, _1483151, _1483153, _1483155, _1483157] : [hAPP(c_Set_Oimage(_1483149, _1483151, _1483153), c_Orderings_Otop__class_Otop(tc_fun(_1483149, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1483151, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483149, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1483149, _1483151, _1483153), _1483155)), _1483157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483151, tc_HOL_Obool)), _1483155), hAPP(c_Set_Oimage(_1483149, _1483151, _1483153), _1483157))))], (32857 ^ _779142) ^ [_1379367, _1379369] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379367)), _1379369) = 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), _1379367)), _1379369))], (1736 ^ _779142) ^ [_803784, _803786] : [-(class_Divides_Osemiring__div(_803784)), _803786 = _803784, class_Divides_Osemiring__div(_803786)], (7206 ^ _779142) ^ [_898610, _898612, _898614, _898616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898610, tc_HOL_Obool)), _898612), hAPP(hAPP(c_Set_Oinsert(_898610), _898614), _898616))), 7209 ^ _779142 : [(7216 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898610), _898614), _898616))), 7219 ^ _779142 : [(7226 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898610), _898614), _898612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898610, tc_HOL_Obool)), _898612), _898616)))], (7220 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898610), _898614), _898612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898610, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898610, tc_HOL_Obool)), _898612), hAPP(hAPP(c_Set_Oinsert(_898610), _898614), c_Orderings_Obot__class_Obot(tc_fun(_898610, tc_HOL_Obool))))), _898616)))]]], (7210 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898610), _898614), _898616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898610, tc_HOL_Obool)), _898612), _898616)))]]], (41893 ^ _779142) ^ [_1610526, _1610528, _1610530] : [-(hAPP(c_List_Oset(_1610526), c_List_Osublist(_1610526, _1610528, _1610530)) = hAPP(c_Set_OCollect(_1610526), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1610526), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1610526, 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)), _1610526), 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)), _1610526), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1610526, tc_fun(tc_Nat_Onat, _1610526), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610526, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1610526), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1610526), c_COMBB(_1610526, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1610526), _1610528))))), 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(_1610526)), _1610528)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1610530))))))], (25796 ^ _779142) ^ [_1232553] : [class_Int_Onumber__ring(_1232553), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232553), c_Groups_Oone__class_Oone(_1232553)), c_Groups_Oone__class_Oone(_1232553)) = hAPP(c_Int_Onumber__class_Onumber__of(_1232553), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (44960 ^ _779142) ^ [_1680438, _1680440, _1680442] : [-(c_List_Olistsp(_1680438, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680438, tc_HOL_Obool)), _1680440), _1680442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1680438), tc_HOL_Obool)), c_List_Olistsp(_1680438, _1680440)), c_List_Olistsp(_1680438, _1680442)))], (10679 ^ _779142) ^ [_963646, _963648, _963650] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_963646), _963648)), 10682 ^ _779142 : [(10702 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_963646, tc_Nat_Onat), _963650), _963648) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10703 ^ _779142 : [(10704 ^ _779142) ^ [_964127] : [hBOOL(hAPP(hAPP(c_member(_963646), _964127), _963648)), hAPP(_963650, _964127) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10712 ^ _779142 : [(10717 ^ _779142) ^ [] : [hAPP(_963650, 10711 ^ [_963646, _963648, _963650, _964127]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10715 ^ _779142) ^ [] : [_964127 = 10711 ^ [_963646, _963648, _963650, _964127]], (10713 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_963646), 10711 ^ [_963646, _963648, _963650, _964127]), _963648)))]]]]], (10683 ^ _779142) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_963646, tc_Nat_Onat), _963650), _963648) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10687 ^ _779142 : [(10692 ^ _779142) ^ [_963966] : [hBOOL(hAPP(hAPP(c_member(_963646), _963966), _963648)), -(10686 ^ [_963646, _963648, _963650] = _963966), -(hAPP(_963650, _963966) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10690 ^ _779142) ^ [] : [-(hAPP(_963650, 10686 ^ [_963646, _963648, _963650]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10688 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_963646), 10686 ^ [_963646, _963648, _963650]), _963648)))]]]]], (31142 ^ _779142) ^ [_1337350, _1337352] : [class_Orderings_Olinorder(_1337350), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337350, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1337350), _1337352), c_Orderings_Obot__class_Obot(tc_fun(_1337350, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1337350), _1337352)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1337350), _1337352))], (37092 ^ _779142) ^ [_1478870] : [-(c_Nitpick_Oone__frac(_1478870) = c_Nitpick_OAbs__Frac(_1478870, 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))))], (4508 ^ _779142) ^ [_847596, _847598, _847600, _847602] : [-(c_List_Oupto(_847602, _847598) = c_List_Oupto(_847600, _847596)), _847602 = _847600, _847598 = _847596], (9569 ^ _779142) ^ [_941922, _941924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941922), _941924)), _941922 = _941924], (5532 ^ _779142) ^ [_863696, _863698] : [_863698 = _863696, -(c_COMBI(_863698) = c_COMBI(_863696))], (38873 ^ _779142) ^ [_1531957] : [class_Orderings_Owellorder(_1531957), -(c_Wellfounded_Owf(_1531957, hAPP(c_Set_OCollect(tc_prod(_1531957, _1531957)), hAPP(c_Product__Type_Oprod_Oprod__case(_1531957, _1531957, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1531957)))))], (9875 ^ _779142) ^ [_947527, _947529, _947531] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947529), _947531)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947527), _947529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947527), _947531)))], (49739 ^ _779142) ^ [_1784479, _1784481, _1784483, _1784485, _1784487, _1784489, _1784491] : [c_Fun_Oinj__on(_1784479, _1784481, _1784483, hAPP(c_Set_Oimage(_1784485, _1784479, _1784487), _1784489)), c_Fun_Oinj__on(_1784485, _1784479, _1784487, _1784489), hBOOL(hAPP(hAPP(c_member(_1784481), _1784491), hAPP(c_Set_Oimage(_1784479, _1784481, _1784483), hAPP(c_Set_Oimage(_1784485, _1784479, _1784487), _1784489)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784485, _1784481, _1784489, hAPP(c_Fun_Ocomp(_1784479, _1784481, _1784485, _1784483), _1784487)), _1784491) = hAPP(hAPP(c_Fun_Ocomp(_1784479, _1784485, _1784481, c_Hilbert__Choice_Oinv__into(_1784485, _1784479, _1784489, _1784487)), c_Hilbert__Choice_Oinv__into(_1784479, _1784481, hAPP(c_Set_Oimage(_1784485, _1784479, _1784487), _1784489), _1784483)), _1784491))], (2224 ^ _779142) ^ [_811586, _811588, _811590, _811592] : [-(c_Random_Oinc__shift(_811592, _811588) = c_Random_Oinc__shift(_811590, _811586)), _811592 = _811590, _811588 = _811586], (52411 ^ _779142) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (5314 ^ _779142) ^ [_860419, _860421] : [_860421 = _860419, -(c_Groups_Oabs__class_Oabs(_860421) = c_Groups_Oabs__class_Oabs(_860419))], (42628 ^ _779142) ^ [_1628932, _1628934, _1628936, _1628938] : [_1628932 = _1628934, -(c_List_Oremove1(_1628936, _1628932, hAPP(hAPP(c_List_Olist_OCons(_1628936), _1628934), _1628938)) = _1628938)], (17117 ^ _779142) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (25908 ^ _779142) ^ [_1234442, _1234444] : [class_Fields_Olinordered__field__inverse__zero(_1234442), class_Int_Onumber__ring(_1234442), 25915 ^ _779142 : [(25922 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234442), c_Groups_Ozero__class_Ozero(_1234442)), _1234444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234442), c_Groups_Ozero__class_Ozero(_1234442)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234442), _1234444), hAPP(c_Int_Onumber__class_Onumber__of(_1234442), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25916 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234442), c_Groups_Ozero__class_Ozero(_1234442)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234442), _1234444), hAPP(c_Int_Onumber__class_Onumber__of(_1234442), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234442), c_Groups_Ozero__class_Ozero(_1234442)), _1234444)))]]], (32285 ^ _779142) ^ [_1366828, _1366830] : [-(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)), _1366828)), 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), _1366830), _1366828))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1366828), _1366830))], (1306 ^ _779142) ^ [_798409, _798411] : [-(class_Int_Onumber__ring(_798409)), _798411 = _798409, class_Int_Onumber__ring(_798411)], (37803 ^ _779142) ^ [_1497562, _1497564, _1497566, _1497568, _1497570, _1497572] : [class_Groups_Ocomm__monoid__add(_1497562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497564), _1497566)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497564, _1497562), _1497568), _1497566) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497570, _1497562), hAPP(hAPP(c_COMBB(tc_fun(_1497564, tc_HOL_Obool), _1497562, _1497570), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497564, _1497562), _1497568)), hAPP(hAPP(c_COMBB(tc_fun(_1497564, tc_HOL_Obool), tc_fun(_1497564, tc_HOL_Obool), _1497570), c_Set_OCollect(_1497564)), hAPP(hAPP(c_COMBB(tc_fun(_1497564, tc_HOL_Obool), tc_fun(_1497564, tc_HOL_Obool), _1497570), hAPP(c_COMBS(_1497564, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497564), c_fconj), hAPP(hAPP(c_COMBC(_1497564, tc_fun(_1497564, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497564)), _1497566)))), hAPP(c_COMBC(_1497564, _1497570, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1497570, tc_fun(_1497570, tc_HOL_Obool), _1497564), c_fequal), _1497572)))))), hAPP(c_Set_Oimage(_1497564, _1497570, _1497572), _1497566)))], (26582 ^ _779142) ^ [_1246949, _1246951, _1246953] : [class_Lattices_Osemilattice__sup(_1246949), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246949), _1246951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246949), _1246951), _1246953)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246949), _1246951), _1246953))], (23267 ^ _779142) ^ [_1189108, _1189110] : [class_Groups_Olinordered__ab__group__add(_1189108), 23270 ^ _779142 : [(23277 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189108), c_Groups_Ozero__class_Ozero(_1189108)), _1189110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189108), hAPP(c_Groups_Ouminus__class_Ouminus(_1189108), _1189110)), _1189110)))], (23271 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189108), hAPP(c_Groups_Ouminus__class_Ouminus(_1189108), _1189110)), _1189110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189108), c_Groups_Ozero__class_Ozero(_1189108)), _1189110)))]]], (31865 ^ _779142) ^ [_1352874, _1352876, _1352878, _1352880, _1352882, _1352884] : [class_Groups_Ocomm__monoid__add(_1352874), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352876, _1352874), hAPP(hAPP(c_COMBC(_1352876, tc_fun(_1352878, tc_HOL_Obool), _1352874), hAPP(hAPP(c_COMBB(tc_fun(_1352878, _1352874), tc_fun(tc_fun(_1352878, tc_HOL_Obool), _1352874), _1352876), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352878, _1352874)), _1352880)), _1352882)), _1352884) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352878, _1352874), hAPP(hAPP(c_COMBC(_1352878, tc_fun(_1352876, tc_HOL_Obool), _1352874), hAPP(hAPP(c_COMBB(tc_fun(_1352876, _1352874), tc_fun(tc_fun(_1352876, tc_HOL_Obool), _1352874), _1352878), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352876, _1352874)), hAPP(c_COMBC(_1352876, _1352878, _1352874), _1352880))), _1352884)), _1352882))], (4838 ^ _779142) ^ [_852805, _852807] : [_852807 = _852805, -(c_HOL_OEx(_852807) = c_HOL_OEx(_852805))], (28957 ^ _779142) ^ [_1292402, _1292404, _1292406, _1292408] : [class_Lattices_Osemilattice__inf(_1292402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292402), _1292404), _1292406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292402), _1292404), _1292408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292402), _1292404), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1292402), _1292406), _1292408))))], (26606 ^ _779142) ^ [_1247401, _1247403] : [class_Lattices_Osemilattice__sup(_1247401), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1247401), _1247403), _1247403) = _1247403)], (14910 ^ _779142) ^ [_1039758, _1039760, _1039762] : [class_Rings_Oring__1(_1039758), hBOOL(hAPP(hAPP(c_member(_1039758), _1039760), c_Int_Oring__1__class_OInts(_1039758))), hBOOL(hAPP(hAPP(c_member(_1039758), _1039762), c_Int_Oring__1__class_OInts(_1039758))), -(hBOOL(hAPP(hAPP(c_member(_1039758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039758), _1039760), _1039762)), c_Int_Oring__1__class_OInts(_1039758))))], (3318 ^ _779142) ^ [_828587, _828589, _828591, _828593] : [-(c_Enum_Osublists(_828593, _828589) = c_Enum_Osublists(_828591, _828587)), _828593 = _828591, _828589 = _828587], (19647 ^ _779142) ^ [_1124256, _1124258, _1124260, _1124262] : [class_Divides_Osemiring__div(_1124256), -(_1124258 = c_Groups_Ozero__class_Ozero(_1124256)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124256), _1124260), _1124258)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124256), _1124262), _1124258)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1124256), _1124260), _1124262))], (11988 ^ _779142) ^ [_985969, _985971, _985973] : [class_Rings_Olinordered__semiring__strict(_985969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985969), _985971), c_Groups_Ozero__class_Ozero(_985969))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985969), c_Groups_Ozero__class_Ozero(_985969)), _985973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985969), _985971), _985973)), c_Groups_Ozero__class_Ozero(_985969))))], (19023 ^ _779142) ^ [_1113420, _1113422] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113420) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1113422)), 19026 ^ _779142 : [(19029 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113422)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19027 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113420))))]], 19030 ^ _779142 : [(19033 ^ _779142) ^ [] : [19034 ^ _779142 : [(19037 ^ _779142) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113420) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19035 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113422))))]], 19038 ^ _779142 : [(19041 ^ _779142) ^ [] : [_1113420 = _1113422], (19039 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113422)))]]], (19031 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1113420)))]]], (45394 ^ _779142) ^ [_1690158, _1690160] : [_1690160 = c_List_Olist_ONil(_1690158), -(c_List_Olist_ONil(_1690158) = c_List_Oremdups(_1690158, _1690160))], (17381 ^ _779142) ^ [_1084920, _1084922] : [class_Divides_Osemiring__div(_1084920), -(c_Divides_Odiv__class_Omod(_1084920, _1084922, c_Groups_Ozero__class_Ozero(_1084920)) = _1084922)], (20179 ^ _779142) ^ [_1133534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1133534))))], (37052 ^ _779142) ^ [_1477951, _1477953, _1477955, _1477957] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477951), _1477953)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477951), _1477955)), -(_1477955 = c_Orderings_Obot__class_Obot(tc_fun(_1477951, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1477951, tc_HOL_Obool), tc_fun(_1477951, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1477951, tc_HOL_Obool), tc_fun(_1477951, tc_HOL_Obool)), _1477953), _1477955)), c_Wellfounded_Omax__ext(_1477951, _1477957)))), 37066 ^ _779142 : [(37069 ^ _779142) ^ [_1478356] : [hBOOL(hAPP(hAPP(c_member(_1477951), _1478356), _1477955)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1477951, _1477951)), hAPP(hAPP(c_Product__Type_OPair(_1477951, _1477951), 37065 ^ [_1477951, _1477953, _1477955, _1477957]), _1478356)), _1477957))], (37067 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477951), 37065 ^ [_1477951, _1477953, _1477955, _1477957]), _1477953)))]]], (25604 ^ _779142) ^ [_1229145, _1229147] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1229145)), c_Int_OBit1(_1229147)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1229145), _1229147)))], (47018 ^ _779142) ^ [_1724790, _1724792, _1724794, _1724796, _1724798] : [hBOOL(hAPP(hAPP(c_member(_1724790), _1724792), hAPP(c_List_Oset(_1724790), _1724794))), -(hBOOL(hAPP(_1724796, _1724792))), -(c_List_OdropWhile(_1724790, _1724796, hAPP(hAPP(c_List_Oappend(_1724790), _1724794), _1724798)) = hAPP(hAPP(c_List_Oappend(_1724790), c_List_OdropWhile(_1724790, _1724796, _1724794)), _1724798))], (18710 ^ _779142) ^ [_1108475] : [class_Rings_Osemiring__1(_1108475), -(hBOOL(hAPP(hAPP(c_member(_1108475), c_Groups_Oone__class_Oone(_1108475)), c_Nat_Osemiring__1__class_ONats(_1108475))))], (9789 ^ _779142) ^ [_945740, _945742, _945744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945740), _945742)), 9792 ^ _779142 : [(9799 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945744), _945740)), _945742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945742), _945740))))], (9793 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945742), _945740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945744), _945740)), _945742)))]]], (32367 ^ _779142) ^ [_1368775, _1368777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368775), 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)), _1368777)), -(c_Divides_OnegDivAlg(_1368775, _1368777) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368775), _1368777)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368775, _1368777)))], (20340 ^ _779142) ^ [_1136082, _1136084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136084)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1136082), _1136084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1136082)), hAPP(c_Int_Onat, _1136084)))], (43870 ^ _779142) ^ [_1656719, _1656721, _1656723, _1656725, _1656727, _1656729] : [-(hAPP(c_List_Ofoldl(_1656719, _1656721, _1656723, _1656725), hAPP(hAPP(c_List_Olist_OCons(_1656721), _1656727), _1656729)) = hAPP(c_List_Ofoldl(_1656719, _1656721, _1656723, hAPP(hAPP(_1656723, _1656725), _1656727)), _1656729))], (40070 ^ _779142) ^ [_1560990, _1560992, _1560994, _1560996, _1560998] : [-(_1560990 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1560992, _1560994, _1560990, _1560996), _1560998) = hAPP(hAPP(c_Product__Type_Oscomp(_1560994, _1560992, _1560994, tc_prod(_1560992, _1560994)), hAPP(_1560996, _1560998)), c_Random_Oiterate(_1560992, _1560994, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1560990), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1560996)))], (39360 ^ _779142) ^ [_1544296, _1544298, _1544300] : [c_Wellfounded_OwfP(_1544296, hAPP(_1544298, 39361 ^ [_1544296, _1544298, _1544300])), 39368 ^ _779142 : [(39371 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544296, tc_HOL_Obool)), c_Predicate_ODomainP(_1544296, _1544296, hAPP(_1544298, 39366 ^ [_1544296, _1544298, _1544300]))), c_Predicate_ORangeP(_1544296, _1544296, hAPP(_1544298, 39367 ^ [_1544296, _1544298, _1544300]))) = c_Orderings_Obot__class_Obot(tc_fun(_1544296, tc_HOL_Obool))], (39369 ^ _779142) ^ [] : [hAPP(_1544298, 39366 ^ [_1544296, _1544298, _1544300]) = hAPP(_1544298, 39367 ^ [_1544296, _1544298, _1544300])]], -(c_Wellfounded_OwfP(_1544296, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1544300, tc_fun(_1544296, tc_fun(_1544296, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1544300, tc_HOL_Obool))), _1544298)))], (47671 ^ _779142) ^ [_1739677, _1739679, _1739681, _1739683] : [c_List_Olist__ex(_1739677, _1739679, hAPP(hAPP(c_List_Oappend(_1739677), _1739681), _1739683)), -(c_List_Olist__ex(_1739677, _1739679, _1739681)), -(c_List_Olist__ex(_1739677, _1739679, _1739683))], (23603 ^ _779142) ^ [_1194868] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194868)), _1194868) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19801 ^ _779142) ^ [_1126986, _1126988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126986)), 19804 ^ _779142 : [(19811 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126988)), -(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), _1126988), _1126986))))], (19805 ^ _779142) ^ [] : [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), _1126988), _1126986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126988)))]]], (45400 ^ _779142) ^ [_1690251, _1690253] : [-(hAPP(c_List_OremoveAll(_1690251, _1690253), c_List_Olist_ONil(_1690251)) = c_List_Olist_ONil(_1690251))], (34218 ^ _779142) ^ [_1407244, _1407246, _1407248, _1407250, _1407252, _1407254] : [hBOOL(hAPP(hAPP(c_member(_1407244), _1407246), _1407248)), hBOOL(hAPP(hAPP(_1407250, _1407246), _1407252)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407244, tc_fun(_1407254, tc_HOL_Obool)), _1407248), _1407250), _1407252)))], (5846 ^ _779142) ^ [_871798, _871800] : [5847 ^ _779142 : [(5848 ^ _779142) ^ [_871851] : [hBOOL(hAPP(hAPP(c_member(_871798), _871851), _871800))]], _871800 = c_Orderings_Obot__class_Obot(tc_fun(_871798, tc_HOL_Obool))], (48810 ^ _779142) ^ [_1764770, _1764772] : [-(c_Relation_Otrans(_1764770, c_Transitive__Closure_Otrancl(_1764770, _1764772)))], (30700 ^ _779142) ^ [_1328715, _1328717, _1328719, _1328721, _1328723] : [class_Groups_Ocomm__monoid__mult(_1328715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328717), _1328719)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328717), _1328721)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328715), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328715, _1328717, c_Groups_Otimes__class_Otimes(_1328715)), _1328723), c_Groups_Oone__class_Oone(_1328715)), _1328719)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328715, _1328717, c_Groups_Otimes__class_Otimes(_1328715)), _1328723), c_Groups_Oone__class_Oone(_1328715)), _1328721)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328715), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328715, _1328717, c_Groups_Otimes__class_Otimes(_1328715)), _1328723), c_Groups_Oone__class_Oone(_1328715)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328717, tc_HOL_Obool)), _1328719), _1328721))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1328715, _1328717, c_Groups_Otimes__class_Otimes(_1328715)), _1328723), c_Groups_Oone__class_Oone(_1328715)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328717, tc_HOL_Obool)), _1328719), _1328721))))], (30806 ^ _779142) ^ [_1331159, _1331161] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331159, tc_HOL_Obool)), _1331161), c_Orderings_Otop__class_Otop(tc_fun(_1331159, tc_HOL_Obool)))))], (29317 ^ _779142) ^ [_1299486, _1299488] : [class_Lattices_Oboolean__algebra(_1299486), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299486), hAPP(c_Groups_Ouminus__class_Ouminus(_1299486), _1299488)), _1299488) = c_Orderings_Obot__class_Obot(_1299486))], (12294 ^ _779142) ^ [_991367, _991369, _991371, _991373] : [class_Rings_Ocomm__semiring__1(_991367), hBOOL(hAPP(c_Finite__Set_Ofinite(_991369), _991371)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_991369, _991367), _991373), _991371) = c_Groups_Ozero__class_Ozero(_991367)), 12303 ^ _779142 : [(12304 ^ _779142) ^ [_991548] : [hBOOL(hAPP(hAPP(c_member(_991369), _991548), _991371)), hAPP(_991373, _991548) = c_Groups_Ozero__class_Ozero(_991367)]]], (52373 ^ _779142) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (44740 ^ _779142) ^ [_1675332, _1675334, _1675336, _1675338] : [class_Groups_Ocomm__monoid__add(_1675332), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675332), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675332), _1675334), c_List_Oupto(_1675336, _1675338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675332), _1675334), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675336, _1675338))))], (31883 ^ _779142) ^ [_1353669, _1353671, _1353673, _1353675, _1353677] : [class_Rings_Osemiring__0(_1353669), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353669), _1353671), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353673, _1353669), _1353675), _1353677)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353673, _1353669), hAPP(hAPP(c_COMBB(_1353669, _1353669, _1353673), hAPP(c_Groups_Otimes__class_Otimes(_1353669), _1353671)), _1353675)), _1353677))], (16659 ^ _779142) ^ [] : [-(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))))], (29127 ^ _779142) ^ [_1295640, _1295642, _1295644] : [class_Lattices_Osemilattice__inf(_1295640), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295640), _1295642), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295640), _1295642), _1295644)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295640), _1295642), _1295644))], (13505 ^ _779142) ^ [_1013982, _1013984, _1013986, _1013988] : [class_Rings_Odivision__ring(_1013982), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1013982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013982), _1013984), _1013986)), _1013988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013982), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1013982), _1013984), _1013988)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1013982), _1013986), _1013988)))], (32491 ^ _779142) ^ [_1371617, _1371619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1371617)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371619))), -(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(_1371619))), 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), _1371617)), c_Int_Onat))))))], (48674 ^ _779142) ^ [_1761215, _1761217, _1761219] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761215), _1761217, _1761219)), -(c_List_Olist__ex(tc_Int_Oint, _1761215, c_List_Oupto(_1761217, _1761219)))], (38007 ^ _779142) ^ [_1505088, _1505090, _1505092] : [class_Orderings_Olinorder(_1505088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505088), _1505090)), -(_1505090 = c_Orderings_Obot__class_Obot(tc_fun(_1505088, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1505088), _1505092), c_Big__Operators_Olattice_OSup__fin(_1505088, c_Orderings_Oord__class_Omax(_1505088), _1505090)) = c_Big__Operators_Olattice_OSup__fin(_1505088, c_Orderings_Oord__class_Omax(_1505088), hAPP(c_Set_OCollect(_1505088), hAPP(hAPP(c_COMBB(tc_fun(_1505088, tc_HOL_Obool), tc_HOL_Obool, _1505088), c_HOL_OEx(_1505088)), hAPP(hAPP(c_COMBC(_1505088, tc_fun(_1505088, tc_HOL_Obool), tc_fun(_1505088, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505088, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1505088, tc_HOL_Obool), tc_fun(_1505088, tc_HOL_Obool)), _1505088), c_COMBS(_1505088, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505088, tc_HOL_Obool), tc_fun(_1505088, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1505088), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505088), c_fconj)), hAPP(hAPP(c_COMBC(_1505088, tc_fun(_1505088, _1505088), tc_fun(_1505088, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505088, tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505088), tc_fun(_1505088, tc_HOL_Obool)), _1505088), c_COMBB(_1505088, tc_HOL_Obool, _1505088)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1505088), _1505092))))), hAPP(hAPP(c_COMBC(_1505088, tc_fun(_1505088, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505088)), _1505090))))))], (25676 ^ _779142) ^ [_1230331] : [-(c_Int_Osucc(c_Int_OBit1(_1230331)) = c_Int_OBit0(c_Int_Osucc(_1230331)))], (7546 ^ _779142) ^ [_903956, _903958, _903960] : [class_Orderings_Olinorder(_903956), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903956), _903958), _903960))), -(_903958 = _903960), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903956), _903960), _903958)))], (9179 ^ _779142) ^ [_935535, _935537, _935539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_935535), _935537)), hBOOL(hAPP(hAPP(c_member(_935535), _935539), _935537)), -(hAPP(c_Finite__Set_Ocard(_935535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935535, tc_HOL_Obool)), _935537), hAPP(hAPP(c_Set_Oinsert(_935535), _935539), c_Orderings_Obot__class_Obot(tc_fun(_935535, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_935535), _935537)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (51975 ^ _779142) ^ [_1828329, _1828331, _1828333] : [class_Divides_Osemiring__div(_1828329), class_Int_Onumber(_1828329), 51982 ^ _779142 : [(51989 ^ _779142) ^ [] : [c_Divides_Odiv__class_Omod(_1828329, hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828333), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828331)) = c_Groups_Ozero__class_Ozero(_1828329), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828329), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828331)), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828333))))], (51983 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828329), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828331)), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828333))), -(c_Divides_Odiv__class_Omod(_1828329, hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828333), hAPP(c_Int_Onumber__class_Onumber__of(_1828329), _1828331)) = c_Groups_Ozero__class_Ozero(_1828329))]]], (40769 ^ _779142) ^ [_1578430, _1578432] : [-(c_Transitive__Closure_Otrancl(_1578430, hAPP(c_Relation_Oconverse(_1578430, _1578430), _1578432)) = hAPP(c_Relation_Oconverse(_1578430, _1578430), c_Transitive__Closure_Otrancl(_1578430, _1578432)))], (2864 ^ _779142) ^ [_821556, _821558] : [_821558 = _821556, -(c_Rings_Oinverse__class_Odivide(_821558) = c_Rings_Oinverse__class_Odivide(_821556))], (22881 ^ _779142) ^ [_1182058, _1182060, _1182062] : [class_Groups_Oordered__ab__group__add(_1182058), 22884 ^ _779142 : [(22891 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182058), _1182062), hAPP(c_Groups_Ouminus__class_Ouminus(_1182058), _1182060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182058), _1182060), hAPP(c_Groups_Ouminus__class_Ouminus(_1182058), _1182062))))], (22885 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182058), _1182060), hAPP(c_Groups_Ouminus__class_Ouminus(_1182058), _1182062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182058), _1182062), hAPP(c_Groups_Ouminus__class_Ouminus(_1182058), _1182060))))]]], (21888 ^ _779142) ^ [_1163815, _1163817, _1163819, _1163821] : [class_Groups_Omonoid__mult(_1163815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163815), _1163817), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163819), _1163821)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163815), hAPP(hAPP(c_Power_Opower__class_Opower(_1163815), _1163817), _1163819)), _1163821))], (21870 ^ _779142) ^ [_1163432, _1163434, _1163436, _1163438] : [class_Groups_Ocomm__monoid__mult(_1163432), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163432), _1163434), _1163436)), _1163438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163432), hAPP(hAPP(c_Power_Opower__class_Opower(_1163432), _1163434), _1163438)), hAPP(hAPP(c_Power_Opower__class_Opower(_1163432), _1163436), _1163438)))], (49680 ^ _779142) ^ [_1783019, _1783021, _1783023] : [hAPP(c_Set_Oimage(_1783019, _1783021, _1783023), c_Orderings_Otop__class_Otop(tc_fun(_1783019, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783021, tc_HOL_Obool)), 49683 ^ _779142 : [(49684 ^ _779142) ^ [_1783130] : [-(hAPP(_1783023, hAPP(c_Hilbert__Choice_Oinv__into(_1783019, _1783021, c_Orderings_Otop__class_Otop(tc_fun(_1783019, tc_HOL_Obool)), _1783023), _1783130)) = _1783130)]]], (52597 ^ _779142) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (41343 ^ _779142) ^ [_1594217, _1594219, _1594221, _1594223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594217)), _1594219)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594217)), _1594221))), _1594219 = hAPP(hAPP(c_List_Olist_OCons(_1594217), _1594223), _1594221)], (42329 ^ _779142) ^ [_1622378, _1622380, _1622382, _1622384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622378), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622380)), _1622382))), 42332 ^ _779142 : [(42339 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Onth(_1622380), _1622382), _1622378) = _1622384, -(hAPP(hAPP(c_List_Olist__update(_1622380, _1622382), _1622378), _1622384) = _1622382)], (42333 ^ _779142) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1622380, _1622382), _1622378), _1622384) = _1622382, -(hAPP(hAPP(c_List_Onth(_1622380), _1622382), _1622378) = _1622384)]]], (12409 ^ _779142) ^ [_993259, _993261, _993263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993259), _993261)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993259), _993263))), 12412 ^ _779142 : [(12415 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993261), _993263)))], (12413 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993259)))]]], (1396 ^ _779142) ^ [_799534, _799536] : [-(class_Lattices_Obounded__lattice__top(_799534)), _799536 = _799534, class_Lattices_Obounded__lattice__top(_799536)], (17847 ^ _779142) ^ [] : [-(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))], (48044 ^ _779142) ^ [_1747255, _1747257, _1747259, _1747261] : [-(c_New__Random__Sequence_Oneg__map(_1747255, _1747257, _1747259, _1747261) = c_New__Random__Sequence_Oneg__bind(_1747255, _1747257, _1747261, hAPP(c_Fun_Ocomp(_1747257, 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(_1747257)))))), _1747255, c_New__Random__Sequence_Oneg__single(_1747257)), _1747259)))], (45941 ^ _779142) ^ [_1703377, _1703379, _1703381] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1703377), c_List_Oupt(_1703379, _1703381)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703379), _1703377), _1703381))], (10505 ^ _779142) ^ [_960979, _960981] : [hAPP(c_Nat_OSuc, _960979) = hAPP(c_Nat_OSuc, _960981), -(_960979 = _960981)], (6113 ^ _779142) ^ [_876711, _876713, _876715, _876717, _876719, _876721, _876723, _876725] : [c_Finite__Set_Ofolding__image__simple__idem(_876711, _876713, _876715, _876717, _876719, _876721), hBOOL(hAPP(c_Finite__Set_Ofinite(_876713), _876723)), -(hAPP(_876721, hAPP(hAPP(c_Set_Oinsert(_876713), _876725), _876723)) = hAPP(hAPP(_876715, hAPP(_876719, _876725)), hAPP(_876721, _876723)))], (34532 ^ _779142) ^ [_1416010, _1416012, _1416014, _1416016, _1416018] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416010, tc_fun(_1416012, tc_HOL_Obool)), _1416014), hAPP(hAPP(c_COMBB(tc_fun(_1416012, tc_HOL_Obool), tc_fun(_1416012, tc_HOL_Obool), _1416010), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416012, tc_HOL_Obool)), _1416016)), _1416018)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416012, tc_HOL_Obool)), _1416016), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416010, tc_fun(_1416012, tc_HOL_Obool)), _1416014), _1416018)))], (32217 ^ _779142) ^ [_1365242, _1365244, _1365246, _1365248] : [class_Rings_Osemiring__1(_1365242), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365244, _1365242), hAPP(c_COMBK(_1365242, _1365244), _1365246)), _1365248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365242), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1365242), hAPP(c_Finite__Set_Ocard(_1365244), _1365248))), _1365246))], (38304 ^ _779142) ^ [_1516429, _1516431, _1516433] : [-(hAPP(c_Product__Type_Omap__pair(_1516429, _1516429, _1516431, _1516431, c_COMBI(_1516429), c_COMBI(_1516431)), _1516433) = _1516433)], (25354 ^ _779142) ^ [_1224677, _1224679] : [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), _1224677))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1224679)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1224677))) = 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), _1224679), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1224677)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30413 ^ _779142) ^ [_1322986, _1322988, _1322990] : [class_Lattices_Olattice(_1322986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322986), _1322988)), -(c_Big__Operators_Olattice__class_OInf__fin(_1322986, hAPP(hAPP(c_Set_Oinsert(_1322986), _1322990), _1322988)) = hAPP(hAPP(c_Finite__Set_Ofold(_1322986, _1322986, c_Lattices_Osemilattice__inf__class_Oinf(_1322986)), _1322990), _1322988))], (10085 ^ _779142) ^ [_952351, _952353, _952355] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952351), _952353)), _952355) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952351), _952355)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952353), _952355)))], (23095 ^ _779142) ^ [_1185642, _1185644, _1185646] : [class_Groups_Ogroup__add(_1185642), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1185642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185642), _1185644), _1185646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185642), hAPP(c_Groups_Ouminus__class_Ouminus(_1185642), _1185646)), hAPP(c_Groups_Ouminus__class_Ouminus(_1185642), _1185644)))], (28454 ^ _779142) ^ [_1282155] : [class_Complete__Lattice_Ocomplete__lattice(_1282155), -(c_Complete__Lattice_OSup__class_OSup(_1282155, c_Orderings_Obot__class_Obot(tc_fun(_1282155, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1282155))], (26576 ^ _779142) ^ [_1246824, _1246826, _1246828] : [class_Lattices_Olattice(_1246824), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246824), _1246826), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246824), _1246826), _1246828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1246824), _1246826), _1246828))], (9805 ^ _779142) ^ [_946029, _946031, _946033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946029), _946031)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _946031), _946029)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946033), _946031)), _946029))], (26514 ^ _779142) ^ [_1245472, _1245474, _1245476] : [class_Lattices_Osemilattice__sup(_1245472), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245472), _1245474), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245472), _1245474), _1245476))))], (10625 ^ _779142) ^ [_962785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962785)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962785), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _962785)], (38465 ^ _779142) ^ [_1521527, _1521529, _1521531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521527, _1521527), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521527, _1521527, _1521527), _1521529), _1521531)), _1521529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1521527, _1521529)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1521527, _1521531)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1521527, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1521527, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1521527, tc_HOL_Obool), tc_fun(_1521527, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1521527, _1521529))))], (25494 ^ _779142) ^ [_1227230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1227230)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227230), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34835 ^ _779142) ^ [_1424976, _1424978, _1424980, _1424982, _1424984] : [hBOOL(hAPP(hAPP(c_member(_1424976), _1424978), _1424980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424982, tc_HOL_Obool)), hAPP(_1424984, _1424978)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424976, tc_fun(_1424982, tc_HOL_Obool)), _1424980), _1424984))))], (52301 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52551 ^ _779142) ^ [_1835232] : [-(class_Nat_Osize(tc_Option_Ooption(_1835232)))], (20576 ^ _779142) ^ [_1140372, _1140374, _1140376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140372)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140374, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140376), _1140372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140376), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140374), _1140376), _1140372))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140374, _1140376)))], (12465 ^ _779142) ^ [_994303, _994305, _994307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _994303)), 12468 ^ _779142 : [(12475 ^ _779142) ^ [] : [_994305 = _994307, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994303), _994305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994303), _994307))], (12469 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994303), _994305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994303), _994307), -(_994305 = _994307)]]], (7008 ^ _779142) ^ [_894230, _894232, _894234, _894236] : [hBOOL(hAPP(hAPP(c_member(_894230), _894232), _894234)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894230, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_894230), _894232), _894236)), _894234) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894230, tc_HOL_Obool)), _894236), _894234))], (17443 ^ _779142) ^ [_1086173, _1086175, _1086177] : [class_Divides_Osemiring__div(_1086173), -(c_Divides_Odiv__class_Omod(_1086173, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086173), _1086175), _1086177), _1086177) = c_Divides_Odiv__class_Omod(_1086173, _1086175, _1086177))], (5460 ^ _779142) ^ [_862654, _862656] : [_862656 = _862654, -(c_Groups_Otimes__class_Otimes(_862656) = c_Groups_Otimes__class_Otimes(_862654))], (7334 ^ _779142) ^ [_900851, _900853, _900855] : [class_Orderings_Olinorder(_900851), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900851), _900853), _900855))), -(_900853 = _900855), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900851), _900855), _900853)))], (44007 ^ _779142) ^ [_1659753, _1659755, _1659757, _1659759, _1659761, _1659763] : [class_Orderings_Olinorder(_1659753), 44010 ^ _779142 : [(44017 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659753), hAPP(_1659755, _1659757)), hAPP(_1659755, _1659759)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659761, _1659753, _1659755), _1659757), hAPP(hAPP(c_List_Olist_OCons(_1659761), _1659759), _1659763)) = hAPP(hAPP(c_List_Olist_OCons(_1659761), _1659759), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659761, _1659753, _1659755), _1659757), _1659763)))], (44011 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659753), hAPP(_1659755, _1659757)), hAPP(_1659755, _1659759))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659761, _1659753, _1659755), _1659757), hAPP(hAPP(c_List_Olist_OCons(_1659761), _1659759), _1659763)) = hAPP(hAPP(c_List_Olist_OCons(_1659761), _1659757), hAPP(hAPP(c_List_Olist_OCons(_1659761), _1659759), _1659763)))]]], (25608 ^ _779142) ^ [_1229221, _1229223] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1229221)), c_Int_OBit0(_1229223)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229221), _1229223)))], (4974 ^ _779142) ^ [_854961, _854963, _854965, _854967, _854969, _854971] : [-(c_Set_Ovimage(_854971, _854967, _854963) = c_Set_Ovimage(_854969, _854965, _854961)), _854971 = _854969, _854967 = _854965, _854963 = _854961], (2360 ^ _779142) ^ [_813640, _813642, _813644, _813646] : [-(c_Divides_Odivmod__int(_813646, _813642) = c_Divides_Odivmod__int(_813644, _813640)), _813646 = _813644, _813642 = _813640], (43050 ^ _779142) ^ [_1637745, _1637747, _1637749, _1637751] : [-(hAPP(hAPP(c_List_Oappend(_1637745), hAPP(hAPP(c_List_Olist_OCons(_1637745), _1637747), _1637749)), _1637751) = hAPP(hAPP(c_List_Olist_OCons(_1637745), _1637747), hAPP(hAPP(c_List_Oappend(_1637745), _1637749), _1637751)))], (35246 ^ _779142) ^ [_1435888] : [-(_1435888 = 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)), _1435888), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (38232 ^ _779142) ^ [_1514699, _1514701] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1514699, _1514701, tc_prod(_1514699, _1514701)), c_Product__Type_OPair(_1514699, _1514701)) = c_Fun_Oid(tc_prod(_1514699, _1514701)))], (21246 ^ _779142) ^ [_1152792, _1152794] : [class_Rings_Ocomm__semiring__1(_1152792), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1152792), _1152794), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1152794)], (6221 ^ _779142) ^ [_878793, _878795, _878797] : [_878793 = _878795, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878797, tc_HOL_Obool)), _878793), _878795)))], (38216 ^ _779142) ^ [_1514437, _1514439] : [-(hAPP(c_Fun_Oid(_1514437), _1514439) = _1514439)], (24449 ^ _779142) ^ [_1209342, _1209344] : [class_Rings_Olinordered__idom(_1209342), 24452 ^ _779142 : [(24459 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209342), c_Groups_Ozero__class_Ozero(_1209342)), hAPP(c_Int_Oring__1__class_Oof__int(_1209342), _1209344))))], (24453 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209342), c_Groups_Ozero__class_Ozero(_1209342)), hAPP(c_Int_Oring__1__class_Oof__int(_1209342), _1209344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209344)))]]], (20251 ^ _779142) ^ [_1134645, _1134647] : [hAPP(c_Int_Onat, _1134645) = _1134647, 20254 ^ _779142 : [(20261 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134645))), -(_1134647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20255 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1134645)), -(_1134645 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134647))]]], (27994 ^ _779142) ^ [_1273453, _1273455] : [class_Orderings_Olinorder(_1273453), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273453), _1273455), _1273455) = _1273455)], (42860 ^ _779142) ^ [_1633166, _1633168] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1633166), tc_List_Olist(_1633166), c_List_Olistrel(_1633166, _1633168)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633166)), c_List_Olist_ONil(_1633166)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633166), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633166)), c_List_Olist_ONil(_1633166)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633166), tc_HOL_Obool))))], (5246 ^ _779142) ^ [_859255, _859257, _859259, _859261, _859263, _859265, _859267, _859269] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_859269, _859265, _859261, _859257) = c_SetInterval_Oord_OgreaterThanLessThan(_859267, _859263, _859259, _859255)), _859269 = _859267, _859265 = _859263, _859261 = _859259, _859257 = _859255], (9346 ^ _779142) ^ [_938479, _938481, _938483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938479), _938481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938483), _938479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938483), _938481))))], (28943 ^ _779142) ^ [_1292153, _1292155, _1292157, _1292159] : [class_Lattices_Osemilattice__inf(_1292153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292153), _1292155), _1292157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292153), _1292155), _1292159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292153), _1292155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1292153), _1292157), _1292159))))], (48060 ^ _779142) ^ [_1747761, _1747763] : [-(c_List_Osplice(_1747761, _1747763, c_List_Olist_ONil(_1747761)) = _1747763)], (46570 ^ _779142) ^ [_1715375, _1715377] : [_1715377 = c_List_Olist_ONil(_1715375), -(c_List_Olist_ONil(_1715375) = hAPP(c_List_Orev(_1715375), _1715377))], (16637 ^ _779142) ^ [_1072032, _1072034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1072032), _1072034)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072032), _1072034)))], (52401 ^ _779142) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (29568 ^ _779142) ^ [_1305424, _1305426, _1305428, _1305430, _1305432] : [class_Orderings_Olinorder(_1305424), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305424, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1305424, _1305426, _1305428)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1305424, _1305430, _1305432)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1305424, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305424), _1305426), _1305430), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305424), _1305428), _1305432)))], (52137 ^ _779142) ^ [_1830972, _1830974] : [class_Lattices_Olattice(_1830972), -(class_Lattices_Osemilattice__sup(tc_fun(_1830974, _1830972)))], (34316 ^ _779142) ^ [_1409538, _1409540] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1409538, tc_HOL_Obool), _1409540) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1409538, tc_HOL_Obool), tc_fun(_1409538, tc_HOL_Obool)), _1409540), c_COMBI(tc_fun(_1409538, tc_HOL_Obool))))], (32725 ^ _779142) ^ [_1376834, _1376836] : [32726 ^ _779142 : [(32729 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1376836), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32727 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376834), _1376836))]], -(c_Divides_OposDivAlg(_1376834, _1376836) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376834))], (50522 ^ _779142) ^ [_1802685, _1802687, _1802689] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802685), _1802687, _1802689)), -(c_List_Olist__ex(tc_Nat_Onat, _1802685, c_List_Oupt(_1802687, _1802689)))], (12455 ^ _779142) ^ [_994122, _994124, _994126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994122), _994124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _994126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994126), _994122)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994126), _994124))))], (34458 ^ _779142) ^ [_1413763, _1413765, _1413767, _1413769, _1413771] : [-(_1413763 = c_Orderings_Obot__class_Obot(tc_fun(_1413765, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413767, tc_HOL_Obool)), _1413769), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413765, tc_fun(_1413767, tc_HOL_Obool)), _1413763), _1413771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413765, tc_fun(_1413767, tc_HOL_Obool)), _1413763), hAPP(hAPP(c_COMBB(tc_fun(_1413767, tc_HOL_Obool), tc_fun(_1413767, tc_HOL_Obool), _1413765), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1413767, tc_HOL_Obool)), _1413769)), _1413771)))], (14679 ^ _779142) ^ [_1035310, _1035312, _1035314, _1035316, _1035318] : [class_Fields_Ofield(_1035310), -(_1035312 = c_Groups_Ozero__class_Ozero(_1035310)), -(_1035314 = c_Groups_Ozero__class_Ozero(_1035310)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035310), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035310), _1035316), _1035312)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035310), _1035318), _1035314)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035310), _1035316), _1035314)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035310), _1035318), _1035312))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035310), _1035312), _1035314)))], (40320 ^ _779142) ^ [_1567704, _1567706, _1567708] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567704, _1567704)), hAPP(hAPP(c_Product__Type_OPair(_1567704, _1567704), _1567706), _1567706)), c_Transitive__Closure_Ortrancl(_1567704, _1567708))))], (35322 ^ _779142) ^ [_1437136, _1437138, _1437140, _1437142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437136, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437136, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35323 ^ [_1437136, _1437138, _1437140, _1437142])), _1437138)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437136, 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), 35323 ^ [_1437136, _1437138, _1437140, _1437142]), _1437140))), _1437142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437136, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437136, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1437138)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437136, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1437142))))], (23203 ^ _779142) ^ [_1187710, _1187712] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187710), _1187712)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187710)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187712)))], (39069 ^ _779142) ^ [_1536736, _1536738, _1536740, _1536742] : [39071 ^ _779142 : [(39074 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1536738, hAPP(_1536740, 39070 ^ [_1536736, _1536738, _1536740, _1536742]))), hAPP(_1536738, 39070 ^ [_1536736, _1536738, _1536740, _1536742])))], (39072 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1536736, 39070 ^ [_1536736, _1536738, _1536740, _1536742])))]], -(c_Wellfounded_Owf(_1536742, hAPP(c_Set_OCollect(tc_prod(_1536742, _1536742)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536742, _1536742, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1536742, tc_HOL_Obool), tc_fun(_1536742, tc_HOL_Obool), _1536742), hAPP(c_COMBS(_1536742, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536742), c_fconj), _1536736))), hAPP(hAPP(c_COMBC(_1536742, tc_fun(_1536742, _1536742), tc_fun(_1536742, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536742, tc_HOL_Obool), tc_fun(tc_fun(_1536742, _1536742), tc_fun(_1536742, tc_HOL_Obool)), _1536742), c_COMBB(_1536742, tc_HOL_Obool, _1536742)), c_fequal)), _1536740))))))], (42273 ^ _779142) ^ [_1621007, _1621009, _1621011, _1621013] : [_1621007 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621009)), _1621011)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1621009, hAPP(hAPP(c_List_Olist__update(_1621009, _1621011), _1621007), _1621013)) = c_List_Obutlast(_1621009, _1621011))], (45935 ^ _779142) ^ [_1703278, _1703280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703278), _1703280)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1703278, _1703280)) = _1703278)], (45578 ^ _779142) ^ [_1693827, _1693829, _1693831] : [45580 ^ _779142 : [(45583 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693827), tc_List_Olist(_1693827), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693827), tc_fun(tc_List_Olist(_1693827), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693827), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693827), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693827), tc_HOL_Obool)), tc_List_Olist(_1693827)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693827))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693827)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693827))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693827)))), 45579 ^ [_1693827, _1693829, _1693831]))], (45581 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693827), tc_List_Olist(_1693827))), 45579 ^ [_1693827, _1693829, _1693831]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693827), tc_List_Olist(_1693827))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693827), tc_List_Olist(_1693827)), _1693829), _1693831)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693827))), _1693829) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693827))), _1693831), 45588 ^ _779142 : [(45595 ^ _779142) ^ [] : [_1693829 = _1693831, -(c_List_Oconcat(_1693827, _1693829) = c_List_Oconcat(_1693827, _1693831))], (45589 ^ _779142) ^ [] : [c_List_Oconcat(_1693827, _1693829) = c_List_Oconcat(_1693827, _1693831), -(_1693829 = _1693831)]]], (11446 ^ _779142) ^ [_976046, _976048, _976050] : [class_Groups_Oordered__comm__monoid__add(_976046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976046), c_Groups_Ozero__class_Ozero(_976046)), _976048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976046), c_Groups_Ozero__class_Ozero(_976046)), _976050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976046), c_Groups_Ozero__class_Ozero(_976046)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976046), _976048), _976050))))], (23299 ^ _779142) ^ [_1189650, _1189652] : [class_Groups_Olinordered__ab__group__add(_1189650), 23302 ^ _779142 : [(23309 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189650), _1189652), c_Groups_Ozero__class_Ozero(_1189650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189650), _1189652), hAPP(c_Groups_Ouminus__class_Ouminus(_1189650), _1189652))))], (23303 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189650), _1189652), hAPP(c_Groups_Ouminus__class_Ouminus(_1189650), _1189652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189650), _1189652), c_Groups_Ozero__class_Ozero(_1189650))))]]], (47173 ^ _779142) ^ [_1728201, _1728203, _1728205] : [-(hBOOL(hAPP(hAPP(c_member(_1728201), _1728203), hAPP(c_List_Oset(_1728201), _1728205)))), -(c_List_Oinsert(_1728201, _1728203, _1728205) = hAPP(hAPP(c_List_Olist_OCons(_1728201), _1728203), _1728205))], (45730 ^ _779142) ^ [_1697886, _1697888, _1697890, _1697892, _1697894] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697886)), hAPP(c_List_Ofilter(_1697886, _1697888), hAPP(hAPP(c_List_Omap(_1697890, _1697886), _1697892), _1697894))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), hAPP(c_List_Ofilter(_1697890, hAPP(c_Fun_Ocomp(_1697886, tc_HOL_Obool, _1697890, _1697888), _1697892)), _1697894)))], (40064 ^ _779142) ^ [_1560885, _1560887, _1560889, _1560891, _1560893] : [_1560885 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1560887, _1560889, _1560885, _1560891), _1560893) = hAPP(c_Product__Type_OPair(_1560887, _1560889), _1560893))], (7260 ^ _779142) ^ [_899811, _899813, _899815, _899817, _899819, _899821, _899823] : [c_Finite__Set_Ofun__left__comm(_899811, _899813, _899815), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899811, _899813, _899815, _899817, _899819), _899821)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899811, _899813, _899815, _899817, _899819), _899823)), -(_899823 = _899821)], (42191 ^ _779142) ^ [_1619376] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619376) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42194 ^ _779142 : [(42195 ^ _779142) ^ [_1619451] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1619451), hAPP(c_List_Oset(tc_Nat_Onat), _1619376))), -(_1619451 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5792 ^ _779142) ^ [_870880, _870882, _870884] : [hBOOL(hAPP(hAPP(c_member(_870880), _870882), _870884)), -(hBOOL(hAPP(_870884, _870882)))], (45462 ^ _779142) ^ [_1691330, _1691332, _1691334, _1691336, _1691338] : [c_Fun_Oinj__on(_1691330, _1691332, _1691334, c_Orderings_Otop__class_Otop(tc_fun(_1691330, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1691330, _1691332), _1691334), hAPP(c_List_OremoveAll(_1691330, _1691336), _1691338)) = hAPP(c_List_OremoveAll(_1691332, hAPP(_1691334, _1691336)), hAPP(hAPP(c_List_Omap(_1691330, _1691332), _1691334), _1691338)))], (32779 ^ _779142) ^ [_1377779, _1377781, _1377783, _1377785] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1377779, tc_fun(_1377781, tc_HOL_Obool))), _1377783), _1377785))], (36796 ^ _779142) ^ [_1472498, _1472500] : [-(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)), _1472498), _1472500))], (43648 ^ _779142) ^ [_1652184, _1652186, _1652188, _1652190] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652184) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1652186), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652184)), hAPP(hAPP(c_List_Olist_OCons(_1652186), _1652188), _1652190)) = hAPP(hAPP(c_List_Olist_OCons(_1652186), _1652188), _1652190))], (25872 ^ _779142) ^ [_1233781, _1233783] : [class_Rings_Olinordered__idom(_1233781), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233781), hAPP(c_Groups_Oabs__class_Oabs(_1233781), _1233783)), 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(_1233781), _1233783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26196 ^ _779142) ^ [_1239676, _1239678, _1239680] : [class_Int_Onumber__ring(_1239676), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239676), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1239676), _1239678), _1239680)), 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(_1239676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239676), hAPP(hAPP(c_Power_Opower__class_Opower(_1239676), _1239678), 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(_1239676), _1239680), 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(_1239676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239676), hAPP(c_Int_Onumber__class_Onumber__of(_1239676), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1239678)), _1239680)))], (15613 ^ _779142) ^ [_1052907] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1052907), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38152 ^ _779142) ^ [_1511017, _1511019, _1511021] : [class_Orderings_Olinorder(_1511017), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511017), _1511019)), -(_1511019 = c_Orderings_Obot__class_Obot(tc_fun(_1511017, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511017), _1511021)), -(_1511021 = c_Orderings_Obot__class_Obot(tc_fun(_1511017, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1511017), c_Big__Operators_Olattice_OSup__fin(_1511017, c_Orderings_Oord__class_Omax(_1511017), _1511019)), c_Big__Operators_Olattice_OSup__fin(_1511017, c_Orderings_Oord__class_Omax(_1511017), _1511021)) = c_Big__Operators_Olattice_OSup__fin(_1511017, c_Orderings_Oord__class_Omax(_1511017), hAPP(c_Set_OCollect(_1511017), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_HOL_Obool), tc_HOL_Obool, _1511017), c_HOL_OEx(_1511017)), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool)), tc_fun(_1511017, tc_HOL_Obool), _1511017), hAPP(c_COMBB(tc_fun(_1511017, tc_HOL_Obool), tc_HOL_Obool, _1511017), c_HOL_OEx(_1511017))), hAPP(hAPP(c_COMBC(_1511017, tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool)), tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_fun(tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool))), tc_fun(tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool)), tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool))), _1511017), c_COMBS(_1511017, tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_fun(_1511017, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1511017, tc_fun(tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool))), _1511017), hAPP(c_COMBB(tc_fun(_1511017, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool)), _1511017), c_COMBS(_1511017, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool)), tc_fun(_1511017, tc_fun(_1511017, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1511017), hAPP(c_COMBB(tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511017), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511017), c_fconj))), hAPP(hAPP(c_COMBC(_1511017, tc_fun(_1511017, tc_fun(_1511017, _1511017)), tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511017, _1511017), tc_fun(_1511017, tc_HOL_Obool)), tc_fun(tc_fun(_1511017, tc_fun(_1511017, _1511017)), tc_fun(_1511017, tc_fun(_1511017, tc_HOL_Obool))), _1511017), c_COMBB(tc_fun(_1511017, _1511017), tc_fun(_1511017, tc_HOL_Obool), _1511017)), hAPP(hAPP(c_COMBB(tc_fun(_1511017, tc_HOL_Obool), tc_fun(tc_fun(_1511017, _1511017), tc_fun(_1511017, tc_HOL_Obool)), _1511017), c_COMBB(_1511017, tc_HOL_Obool, _1511017)), c_fequal))), c_Orderings_Oord__class_Omin(_1511017)))))), hAPP(hAPP(c_COMBC(_1511017, tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1511017, tc_HOL_Obool), tc_fun(_1511017, tc_HOL_Obool)), _1511017), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1511017)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511017), c_fconj), hAPP(hAPP(c_COMBC(_1511017, tc_fun(_1511017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511017)), _1511019)))), hAPP(hAPP(c_COMBC(_1511017, tc_fun(_1511017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511017)), _1511021))))))))], (490 ^ _779142) ^ [_786479, _786481] : [-(c_Nat__Transfer_Onat__set(_786479)), _786481 = _786479, c_Nat__Transfer_Onat__set(_786481)], (50305 ^ _779142) ^ [_1796329, _1796331, _1796333] : [hBOOL(hAPP(hAPP(c_member(_1796329), _1796331), c_Quotient_ORespects(_1796329, _1796333))), -(hBOOL(hAPP(hAPP(_1796333, _1796331), _1796331)))], (13837 ^ _779142) ^ [_1020029, _1020031, _1020033, _1020035] : [class_Fields_Olinordered__field__inverse__zero(_1020029), 13840 ^ _779142 : [(13841 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020029), _1020031), _1020033)), _1020035)), 13844 ^ _779142 : [(13851 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020033))), 13854 ^ _779142 : [(13861 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), _1020033), c_Groups_Ozero__class_Ozero(_1020029)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020035)))], (13855 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), _1020033), c_Groups_Ozero__class_Ozero(_1020029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020029), _1020035), _1020033)), _1020031)))]]], (13845 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), _1020031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020029), _1020035), _1020033))))]]], (13867 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020029), _1020031), _1020033)), _1020035))), 13870 ^ _779142 : [(13873 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), _1020031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020029), _1020035), _1020033)))], (13871 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020033)))]], 13874 ^ _779142 : [(13877 ^ _779142) ^ [] : [13878 ^ _779142 : [(13881 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020029), _1020035), _1020033)), _1020031))], (13879 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), _1020033), c_Groups_Ozero__class_Ozero(_1020029))))]], 13882 ^ _779142 : [(13885 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020035))], (13883 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), _1020033), c_Groups_Ozero__class_Ozero(_1020029)))]]], (13875 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020029), c_Groups_Ozero__class_Ozero(_1020029)), _1020033))]]]]], (52707 ^ _779142) ^ [] : [-(hBOOL(c_fTrue))], (25438 ^ _779142) ^ [_1226315, _1226317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1226315)), c_Int_OBit0(_1226317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226315), _1226317)))], (17851 ^ _779142) ^ [_1093655, _1093657, _1093659] : [class_Rings_Olinordered__semidom(_1093655), 17854 ^ _779142 : [(17861 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1093657), _1093659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093655), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093655), _1093657)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093655), _1093659))))], (17855 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093655), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093655), _1093657)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093655), _1093659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1093657), _1093659)))]]], (16861 ^ _779142) ^ [_1075718, _1075720, _1075722] : [class_Orderings_Olinorder(_1075718), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075718), _1075720)), -(_1075720 = c_Orderings_Obot__class_Obot(tc_fun(_1075718, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1075718, hAPP(hAPP(c_Set_Oinsert(_1075718), _1075722), _1075720)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075718), _1075722), c_Big__Operators_Olinorder__class_OMin(_1075718, _1075720)))], (31092 ^ _779142) ^ [_1336383, _1336385, _1336387] : [class_Orderings_Oorder(_1336383), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336383, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1336383, _1336385, _1336387)), hAPP(c_SetInterval_Oord__class_OatLeast(_1336383), _1336387)) = c_Orderings_Obot__class_Obot(tc_fun(_1336383, tc_HOL_Obool)))], (36284 ^ _779142) ^ [_1461480, _1461482, _1461484, _1461486, _1461488] : [c_Fun_Oinj__on(_1461480, _1461482, _1461484, _1461486), c_Fun_Oinj__on(_1461480, _1461482, _1461484, _1461488), -(c_Fun_Oinj__on(_1461480, _1461482, _1461484, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461480, tc_HOL_Obool)), _1461486), _1461488)))], (27546 ^ _779142) ^ [_1265262, _1265264, _1265266] : [class_Lattices_Olattice(_1265262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265262), _1265264)), -(_1265264 = c_Orderings_Obot__class_Obot(tc_fun(_1265262, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1265262, hAPP(hAPP(c_Set_Oinsert(_1265262), _1265266), _1265264)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265262), _1265266), c_Big__Operators_Olattice__class_OSup__fin(_1265262, _1265264)))], (22789 ^ _779142) ^ [_1180581, _1180583, _1180585] : [class_Groups_Ogroup__add(_1180581), 22792 ^ _779142 : [(22799 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1180581), _1180585) = _1180583, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1180581), _1180583) = _1180585)], (22793 ^ _779142) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1180581), _1180583) = _1180585, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1180581), _1180585) = _1180583)]]], (19759 ^ _779142) ^ [_1126352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126352), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1126352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15373 ^ _779142) ^ [_1048449, _1048451, _1048453, _1048455] : [class_Orderings_Olinorder(_1048449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048449), _1048451), _1048453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048449), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048449), _1048451), _1048455)), _1048453)))], (21614 ^ _779142) ^ [_1158794, _1158796, _1158798] : [class_Rings_Olinordered__semidom(_1158794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158794), c_Groups_Oone__class_Oone(_1158794)), _1158796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158794), c_Groups_Oone__class_Oone(_1158794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1158794), _1158796), _1158798))))], (46060 ^ _779142) ^ [_1705997] : [class_Orderings_Olinorder(_1705997), -(c_List_Olinorder__class_Osorted(_1705997, c_List_Olist_ONil(_1705997)))], (10789 ^ _779142) ^ [_965521, _965523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965521), _965523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965521), hAPP(c_Nat_OSuc, _965523))))], (45123 ^ _779142) ^ [_1684293, _1684295, _1684297, _1684299, _1684301, _1684303] : [c_List_Olist__all2(_1684293, _1684295, _1684297, _1684299, _1684301), -(c_List_Olist__all2(_1684293, _1684295, _1684297, hAPP(hAPP(c_List_Otake(_1684293), _1684303), _1684299), hAPP(hAPP(c_List_Otake(_1684295), _1684303), _1684301)))], (27510 ^ _779142) ^ [_1264670] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1264670)], (34931 ^ _779142) ^ [_1427619, _1427621, _1427623, _1427625, _1427627] : [-(_1427619 = c_Orderings_Obot__class_Obot(tc_fun(_1427621, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427621, tc_fun(_1427623, tc_HOL_Obool)), _1427619), hAPP(hAPP(c_COMBB(tc_fun(_1427623, tc_HOL_Obool), tc_fun(_1427623, tc_HOL_Obool), _1427621), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427623, tc_HOL_Obool)), _1427625)), _1427627)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427623, tc_HOL_Obool)), _1427625), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427621, tc_fun(_1427623, tc_HOL_Obool)), _1427619), _1427627)))], (35407 ^ _779142) ^ [_1439985, _1439987] : [-(c_FunDef_Orp__inv__image(_1439985, _1439987) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))))), tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))), tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)), tc_fun(tc_fun(_1439987, _1439985), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool)), c_COMBS(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)), tc_fun(tc_fun(_1439987, _1439985), tc_fun(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), tc_fun(tc_prod(_1439985, _1439985), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool))), tc_fun(_1439987, _1439985)), c_Product__Type_OPair(tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool), tc_fun(tc_prod(_1439987, _1439987), tc_HOL_Obool)))), c_Relation_Oinv__image(_1439985, _1439987))))), c_Relation_Oinv__image(_1439985, _1439987))))], (25086 ^ _779142) ^ [_1220099] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1220099)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1220099)))], (52637 ^ _779142) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (50510 ^ _779142) ^ [_1802486, _1802488, _1802490] : [c_List_Oall__interval__nat(_1802486, _1802488, _1802490), -(c_List_Olist__all(tc_Nat_Onat, _1802486, c_List_Oupt(_1802488, _1802490)))], (25638 ^ _779142) ^ [_1229764] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1229764)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229764))))], (39007 ^ _779142) ^ [_1535495, _1535497, _1535499, _1535501] : [hBOOL(hAPP(c_Predicate_ODomainP(_1535495, _1535497, _1535499), _1535501)), -(hBOOL(hAPP(hAPP(_1535499, _1535501), 39010 ^ [_1535495, _1535497, _1535499, _1535501])))], (37549 ^ _779142) ^ [_1490370, _1490372, _1490374] : [-(hAPP(hAPP(c_Set_Oinsert(_1490370), _1490372), _1490374) = hAPP(c_Set_OCollect(_1490370), hAPP(hAPP(c_COMBS(_1490370, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490370), c_fdisj), hAPP(hAPP(c_COMBC(_1490370, _1490370, tc_HOL_Obool), c_fequal), _1490372))), hAPP(hAPP(c_COMBC(_1490370, tc_fun(_1490370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490370)), _1490374))))], (30377 ^ _779142) ^ [_1322451, _1322453, _1322455] : [class_Lattices_Olattice(_1322451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322451), _1322453)), -(_1322453 = c_Orderings_Obot__class_Obot(tc_fun(_1322451, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322451), _1322455)), -(_1322455 = c_Orderings_Obot__class_Obot(tc_fun(_1322451, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1322451, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322451, tc_HOL_Obool)), _1322453), _1322455)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322451), c_Big__Operators_Olattice__class_OInf__fin(_1322451, _1322453)), c_Big__Operators_Olattice__class_OInf__fin(_1322451, _1322455)))], (47825 ^ _779142) ^ [_1742753, _1742755] : [-(c_FunDef_Ois__measure(_1742753, _1742755))], (40180 ^ _779142) ^ [_1563661, _1563663] : [c_Wellfounded_Oacyclic(_1563661, _1563663), 40183 ^ _779142 : [(40184 ^ _779142) ^ [_1563746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563661, _1563661)), hAPP(hAPP(c_Product__Type_OPair(_1563661, _1563661), _1563746), _1563746)), c_Transitive__Closure_Otrancl(_1563661, _1563663)))]]], (3302 ^ _779142) ^ [_828353, _828355] : [_828355 = _828353, -(c_Set_OPow(_828355) = c_Set_OPow(_828353))], (30065 ^ _779142) ^ [_1315902, _1315904, _1315906] : [class_Orderings_Olinorder(_1315902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315902), _1315904)), -(_1315904 = c_Orderings_Obot__class_Obot(tc_fun(_1315902, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315902), _1315906)), -(_1315906 = c_Orderings_Obot__class_Obot(tc_fun(_1315902, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315902, tc_HOL_Obool)), _1315904), _1315906) = c_Orderings_Obot__class_Obot(tc_fun(_1315902, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1315902, c_Orderings_Oord__class_Omin(_1315902), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315902, tc_HOL_Obool)), _1315904), _1315906)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315902), c_Big__Operators_Olattice_OInf__fin(_1315902, c_Orderings_Oord__class_Omin(_1315902), _1315904)), c_Big__Operators_Olattice_OInf__fin(_1315902, c_Orderings_Oord__class_Omin(_1315902), _1315906)))], (19879 ^ _779142) ^ [_1128209, _1128211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1128209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128209), _1128211)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128209), _1128211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45272 ^ _779142) ^ [_1687582, _1687584, _1687586] : [-(hAPP(c_List_Oset(tc_List_Olist(_1687582)), c_Enum_On__lists(_1687582, _1687584, _1687586)) = hAPP(c_Set_OCollect(tc_List_Olist(_1687582)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687582), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687582)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687582), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687582)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1687582)))), _1687584))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687582), tc_fun(_1687582, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687582, tc_HOL_Obool), tc_fun(tc_fun(_1687582, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687582)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687582, tc_HOL_Obool))), c_List_Oset(_1687582))), hAPP(c_List_Oset(_1687582), _1687586)))))], (33881 ^ _779142) ^ [_1399805, _1399807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399805), 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)), _1399807)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1399805), _1399807) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1399805, _1399807)))], (52397 ^ _779142) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (43596 ^ _779142) ^ [_1650800, _1650802, _1650804, _1650806, _1650808] : [hAPP(hAPP(c_List_Oappend(_1650800), _1650802), _1650804) = hAPP(hAPP(c_List_Oappend(_1650800), _1650806), _1650808), 43599 ^ _779142 : [(43608 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650802)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650806)))), 43611 ^ _779142 : [(43614 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650800), hAPP(hAPP(c_List_Odrop(_1650800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650806)), _1650802)), _1650804) = _1650808)], (43612 ^ _779142) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650806)), _1650802) = _1650806)]]], (43600 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650802)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650806))), 43603 ^ _779142 : [(43606 ^ _779142) ^ [] : [-(_1650804 = hAPP(hAPP(c_List_Oappend(_1650800), hAPP(hAPP(c_List_Odrop(_1650800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650802)), _1650806)), _1650808))], (43604 ^ _779142) ^ [] : [-(_1650802 = hAPP(hAPP(c_List_Otake(_1650800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650800)), _1650802)), _1650806))]]]]], (20043 ^ _779142) ^ [_1130950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130950)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1130950)) = _1130950)], (34540 ^ _779142) ^ [_1416420, _1416422, _1416424, _1416426, _1416428] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416420, tc_HOL_Obool)), _1416422), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416424, tc_fun(_1416420, tc_HOL_Obool)), _1416426), _1416428)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416424, tc_fun(_1416420, tc_HOL_Obool)), _1416426), hAPP(hAPP(c_COMBB(tc_fun(_1416420, tc_HOL_Obool), tc_fun(_1416420, tc_HOL_Obool), _1416424), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416420, tc_HOL_Obool)), _1416422)), _1416428)))], (44893 ^ _779142) ^ [_1678500, _1678502] : [-(c_List_Opartition(_1678500, _1678502, c_List_Olist_ONil(_1678500)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678500), tc_List_Olist(_1678500)), c_List_Olist_ONil(_1678500)), c_List_Olist_ONil(_1678500)))], (39826 ^ _779142) ^ [_1555091, _1555093, _1555095, _1555097, _1555099, _1555101] : [c_Finite__Set_Ofolding(_1555091, _1555093, _1555095, _1555097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555091), _1555099)), -(hBOOL(hAPP(hAPP(c_member(_1555091), _1555101), _1555099))), -(hAPP(_1555097, hAPP(hAPP(c_Set_Oinsert(_1555091), _1555101), _1555099)) = hAPP(c_Fun_Ocomp(_1555093, _1555093, _1555093, hAPP(_1555097, _1555099)), hAPP(_1555095, _1555101)))], (50873 ^ _779142) ^ [_1809423] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809423, _1809423) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809423), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (40891 ^ _779142) ^ [_1581581, _1581583, _1581585] : [-(hAPP(c_Relation_Oconverse(_1581581, _1581583), _1581585) = hAPP(c_Set_OCollect(tc_prod(_1581583, _1581581)), hAPP(c_Product__Type_Oprod_Oprod__case(_1581583, _1581581, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581583, tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_fun(_1581581, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581581, tc_fun(tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_fun(_1581581, tc_HOL_Obool)), _1581583), c_COMBC(_1581581, tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581581, tc_prod(_1581581, _1581583)), tc_fun(_1581581, tc_fun(tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_HOL_Obool)), _1581583), hAPP(c_COMBB(tc_prod(_1581581, _1581583), tc_fun(tc_fun(tc_prod(_1581581, _1581583), tc_HOL_Obool), tc_HOL_Obool), _1581581), c_member(tc_prod(_1581581, _1581583)))), hAPP(c_COMBC(_1581581, _1581583, tc_prod(_1581581, _1581583)), c_Product__Type_OPair(_1581581, _1581583))))), _1581585))))], (27508 ^ _779142) ^ [_1264636] : [c_Code__Numeral_OSuc__code__numeral(_1264636) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (37457 ^ _779142) ^ [_1488020, _1488022] : [-(hBOOL(hAPP(_1488022, 37458 ^ [_1488020, _1488022]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1488020, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1488020), _1488022))], (23655 ^ _779142) ^ [_1195712, _1195714, _1195716] : [class_Groups_Oordered__ab__group__add(_1195712), -(hAPP(c_Set_Oimage(_1195712, _1195712, c_Groups_Ouminus__class_Ouminus(_1195712)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1195712, _1195714, _1195716)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1195712, hAPP(c_Groups_Ouminus__class_Ouminus(_1195712), _1195716), hAPP(c_Groups_Ouminus__class_Ouminus(_1195712), _1195714)))], (47379 ^ _779142) ^ [_1733067, _1733069, _1733071, _1733073] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1733067, _1733069, _1733071, _1733073) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1733067, _1733069), _1733071), _1733073)))], (38639 ^ _779142) ^ [_1527210, _1527212, _1527214] : [c_Wellfounded_Owf(_1527210, _1527212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527210, _1527210), tc_HOL_Obool)), _1527214), _1527212)), -(c_Wellfounded_Owf(_1527210, _1527214))], (42151 ^ _779142) ^ [_1618401, _1618403, _1618405, _1618407] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618401, _1618401)), hAPP(hAPP(c_Product__Type_OPair(_1618401, _1618401), _1618403), _1618405)), hAPP(c_List_Oset(tc_prod(_1618401, _1618401)), hAPP(hAPP(c_List_Ozip(_1618401, _1618401), _1618407), _1618407)))), 42154 ^ _779142 : [(42157 ^ _779142) ^ [] : [-(_1618403 = _1618405)], (42155 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618401), _1618403), hAPP(c_List_Oset(_1618401), _1618407))))]]], (39772 ^ _779142) ^ [_1553990, _1553992, _1553994, _1553996, _1553998, _1554000] : [c_Finite__Set_Ofolding(_1553990, _1553992, _1553994, _1553996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553990), _1553998)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553990), _1554000)), -(hAPP(c_Fun_Ocomp(_1553992, _1553992, _1553992, hAPP(_1553996, _1554000)), hAPP(_1553996, _1553998)) = hAPP(c_Fun_Ocomp(_1553992, _1553992, _1553992, hAPP(_1553996, _1553998)), hAPP(_1553996, _1554000)))], (32003 ^ _779142) ^ [_1358562, _1358564, _1358566, _1358568] : [-(hAPP(c_Finite__Set_Ofold__image(_1358562, _1358564, _1358566), _1358568) = c_Finite__Set_Ofold(_1358564, _1358562, hAPP(hAPP(c_COMBB(_1358562, tc_fun(_1358562, _1358562), _1358564), _1358566), _1358568)))], (33706 ^ _779142) ^ [_1396051, _1396053, _1396055, _1396057, _1396059, _1396061] : [hAPP(c_Product__Type_Oapsnd(_1396051, _1396053, _1396055, _1396057), _1396059) = hAPP(c_Product__Type_Oapsnd(_1396051, _1396053, _1396055, _1396061), _1396059), -(hAPP(_1396057, hAPP(c_Product__Type_Osnd(_1396055, _1396051), _1396059)) = hAPP(_1396061, hAPP(c_Product__Type_Osnd(_1396055, _1396051), _1396059)))], (23893 ^ _779142) ^ [_1199830, _1199832, _1199834] : [class_Orderings_Olinorder(_1199830), 23896 ^ _779142 : [(23903 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199830), _1199832), _1199834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1199830, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1199830), _1199832)), hAPP(c_SetInterval_Oord__class_OlessThan(_1199830), _1199834))))], (23897 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1199830, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1199830), _1199832)), hAPP(c_SetInterval_Oord__class_OlessThan(_1199830), _1199834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199830), _1199832), _1199834)))]]], (12391 ^ _779142) ^ [_992963, _992965] : [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), _992963), _992965))), 12394 ^ _779142 : [(12397 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992965)))], (12395 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992963)))]]], (38829 ^ _779142) ^ [_1531080, _1531082] : [38831 ^ _779142 : [(38832 ^ _779142) ^ [_1531105] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531080, _1531080)), hAPP(hAPP(c_Product__Type_OPair(_1531080, _1531080), hAPP(38830 ^ [_1531080, _1531082], hAPP(c_Nat_OSuc, _1531105))), hAPP(38830 ^ [_1531080, _1531082], _1531105))), _1531082)))]], -(c_Wellfounded_Owf(_1531080, _1531082))], (44023 ^ _779142) ^ [_1660135, _1660137, _1660139, _1660141, _1660143] : [class_Orderings_Olinorder(_1660135), -(hAPP(c_List_Oset(_1660137), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660137, _1660135, _1660139), _1660141), _1660143)) = hAPP(hAPP(c_Set_Oinsert(_1660137), _1660141), hAPP(c_List_Oset(_1660137), _1660143)))], (28533 ^ _779142) ^ [_1283596, _1283598] : [class_Orderings_Olinorder(_1283596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283596), _1283598)), -(c_Big__Operators_Olattice_OSup__fin(_1283596, c_Orderings_Oord__class_Omax(_1283596), _1283598) = hAPP(c_Finite__Set_Ofold1(_1283596, c_Orderings_Oord__class_Omax(_1283596)), _1283598))], (28372 ^ _779142) ^ [_1280558, _1280560] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1280558, tc_HOL_Obool), hAPP(c_Set_OPow(_1280558), _1280560)) = _1280560)], (39628 ^ _779142) ^ [_1550556, _1550558, _1550560, _1550562, _1550564] : [class_Groups_Ocomm__monoid__mult(_1550556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550558), _1550560)), c_Fun_Oinj__on(_1550558, _1550558, _1550562, _1550560), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1550558, _1550556), _1550564), hAPP(c_Set_Oimage(_1550558, _1550558, _1550562), _1550560)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1550558, _1550556), hAPP(c_Fun_Ocomp(_1550558, _1550556, _1550558, _1550564), _1550562)), _1550560))], (34248 ^ _779142) ^ [_1407879, _1407881, _1407883, _1407885, _1407887, _1407889] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407879, tc_fun(_1407881, tc_HOL_Obool)), _1407883), _1407885), _1407887)), -(hBOOL(hAPP(hAPP(_1407885, _1407889), _1407887))), hBOOL(hAPP(hAPP(c_member(_1407879), _1407889), _1407883))], (33873 ^ _779142) ^ [_1399551, _1399553] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399551, _1399553) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1399551, _1399553)))], (20660 ^ _779142) ^ [_1142082, _1142084, _1142086, _1142088, _1142090, _1142092] : [-(hBOOL(hAPP(hAPP(c_member(_1142082), _1142084), c_SetInterval_Oord_OatLeastLessThan(_1142082, _1142086, _1142088, _1142090, _1142092)))), hBOOL(hAPP(hAPP(_1142086, _1142090), _1142084)), hBOOL(hAPP(hAPP(_1142088, _1142084), _1142092))], (26958 ^ _779142) ^ [_1254779, _1254781] : [c_Nat__Transfer_Onat__set(_1254779), c_Nat__Transfer_Onat__set(_1254781), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1254779), _1254781) = 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), _1254779)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1254781))))], (38388 ^ _779142) ^ [_1519329, _1519331, _1519333, _1519335, _1519337, _1519339, _1519341] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519329, _1519331, _1519333), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519335, tc_fun(tc_prod(_1519329, _1519331), tc_HOL_Obool)), _1519337), _1519339)), _1519341) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519335, tc_fun(tc_prod(_1519329, _1519333), tc_HOL_Obool)), _1519337), hAPP(hAPP(c_COMBC(_1519335, tc_fun(tc_prod(_1519331, _1519333), tc_HOL_Obool), tc_fun(tc_prod(_1519329, _1519333), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519329, _1519331), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1519331, _1519333), tc_HOL_Obool), tc_fun(tc_prod(_1519329, _1519333), tc_HOL_Obool)), _1519335), c_Relation_Orel__comp(_1519329, _1519331, _1519333)), _1519339)), _1519341)))], (32091 ^ _779142) ^ [_1361026, _1361028, _1361030, _1361032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1361026, tc_fun(_1361028, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1361026, tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_fun(_1361028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361028, tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_fun(_1361028, tc_HOL_Obool)), _1361026), c_COMBC(_1361028, tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361028, tc_prod(_1361026, _1361028)), tc_fun(_1361028, tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), _1361026), hAPP(c_COMBB(tc_prod(_1361026, _1361028), tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool), _1361028), c_member(tc_prod(_1361026, _1361028)))), c_Product__Type_OPair(_1361026, _1361028)))), _1361030)), hAPP(hAPP(c_COMBC(_1361026, tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_fun(_1361028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361028, tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_fun(_1361028, tc_HOL_Obool)), _1361026), c_COMBC(_1361028, tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361028, tc_prod(_1361026, _1361028)), tc_fun(_1361028, tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool)), _1361026), hAPP(c_COMBB(tc_prod(_1361026, _1361028), tc_fun(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool), tc_HOL_Obool), _1361028), c_member(tc_prod(_1361026, _1361028)))), c_Product__Type_OPair(_1361026, _1361028)))), _1361032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1361026, _1361028), tc_HOL_Obool)), _1361030), _1361032)))], (31406 ^ _779142) ^ [_1342407, _1342409] : [class_Complete__Lattice_Ocomplete__lattice(_1342407), -(c_Complete__Lattice_OInf__class_OInf(_1342407, hAPP(hAPP(c_Set_Oinsert(_1342407), _1342409), c_Orderings_Obot__class_Obot(tc_fun(_1342407, tc_HOL_Obool)))) = _1342409)], (10533 ^ _779142) ^ [_961443] : [_961443 = hAPP(c_Nat_OSuc, _961443)], (32595 ^ _779142) ^ [_1374206, _1374208] : [-(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), _1374206)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1374208), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1374206))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (12399 ^ _779142) ^ [_993086, _993088] : [-(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), _993086), _993088)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993088))], (35950 ^ _779142) ^ [_1453775, _1453777, _1453779, _1453781, _1453783, _1453785] : [c_Equiv__Relations_Oequiv(_1453775, _1453777, _1453779), c_Equiv__Relations_Ocongruent(_1453775, tc_fun(_1453781, tc_HOL_Obool), _1453779, _1453783), hBOOL(hAPP(hAPP(c_member(_1453775), _1453785), _1453777)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453775, tc_fun(_1453781, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453775, _1453775, _1453779), hAPP(hAPP(c_Set_Oinsert(_1453775), _1453785), c_Orderings_Obot__class_Obot(tc_fun(_1453775, tc_HOL_Obool))))), _1453783) = hAPP(_1453783, _1453785))], (454 ^ _779142) ^ [_785941, _785943, _785945, _785947, _785949, _785951] : [-(c_Nitpick_Oless__frac(_785949, _785945, _785941)), c_Nitpick_Oless__frac(_785951, _785947, _785943), _785951 = _785949, _785947 = _785945, _785943 = _785941], (17131 ^ _779142) ^ [] : [-(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))))], (35596 ^ _779142) ^ [_1445500, _1445502, _1445504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445500, _1445500), tc_HOL_Obool)), _1445502), _1445504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1445500, tc_HOL_Obool)), hAPP(c_Relation_OField(_1445500), _1445502)), hAPP(c_Relation_OField(_1445500), _1445504))))], (18620 ^ _779142) ^ [_1106961, _1106963] : [18621 ^ _779142 : [(18622 ^ _779142) ^ [_1107010] : [_1106961 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106963), _1107010)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106961, _1106963) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20720 ^ _779142) ^ [_1143265, _1143267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143265), _1143267)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143265), _1143267) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39425 ^ _779142) ^ [_1545993, _1545995, _1545997, _1545999, _1546001, _1546003] : [c_Fun_Oinj__on(_1545993, _1545995, hAPP(c_Fun_Ocomp(_1545997, _1545995, _1545993, _1545999), _1546001), _1546003), -(c_Fun_Oinj__on(_1545997, _1545995, _1545999, hAPP(c_Set_Oimage(_1545993, _1545997, _1546001), _1546003)))], (4566 ^ _779142) ^ [_848517, _848519, _848521, _848523, _848525, _848527, _848529, _848531] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848531, _848527, _848523, _848519) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848529, _848525, _848521, _848517)), _848531 = _848529, _848527 = _848525, _848523 = _848521, _848519 = _848517], (10875 ^ _779142) ^ [_966873, _966875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966873)), hAPP(c_Nat_OSuc, _966875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966873), _966875)))], (8010 ^ _779142) ^ [_911155, _911157, _911159, _911161, _911163] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911155, _911157, _911159, _911161, c_Orderings_Obot__class_Obot(tc_fun(_911155, tc_HOL_Obool))), _911163)), -(_911163 = _911161)], (16631 ^ _779142) ^ [_1071927, _1071929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071927), _1071929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1071927), _1071929)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22340 ^ _779142) ^ [_1172243, _1172245] : [-(c_Nitpick_Onat__lcm(_1172243, _1172245) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172243), _1172245)), c_Nitpick_Onat__gcd(_1172243, _1172245)))], (28160 ^ _779142) ^ [_1276875, _1276877] : [class_Orderings_Olinorder(_1276875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276875), _1276877)), -(c_Big__Operators_Olinorder__class_OMax(_1276875, _1276877) = hAPP(c_Finite__Set_Ofold1(_1276875, c_Orderings_Oord__class_Omax(_1276875)), _1276877))], (25530 ^ _779142) ^ [_1227833, _1227835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1227833)), c_Int_OBit1(_1227835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227833), _1227835)))], (18126 ^ _779142) ^ [_1098350, _1098352] : [class_Int_Onumber__ring(_1098350), class_Rings_Olinordered__idom(_1098350), 18133 ^ _779142 : [(18140 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098352), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098350), hAPP(c_Int_Onumber__class_Onumber__of(_1098350), _1098352)), c_Groups_Ozero__class_Ozero(_1098350))))], (18134 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098350), hAPP(c_Int_Onumber__class_Onumber__of(_1098350), _1098352)), c_Groups_Ozero__class_Ozero(_1098350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098352), c_Int_OPls)))]]], (13421 ^ _779142) ^ [_1012303, _1012305, _1012307, _1012309] : [13422 ^ _779142 : [(13425 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012307), _1012309)))], (13423 ^ _779142) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012303), _1012305)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1012303, _1012307)), c_Sum__Type_OPlus(_1012303, _1012307, _1012305, _1012309)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51857 ^ _779142) ^ [_1826160, _1826162, _1826164, _1826166] : [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), _1826160, _1826162)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826164, _1826166))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826160), _1826162)), 51864 ^ _779142 : [(51867 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826162), _1826166)))], (51865 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826164), _1826160)))]]], (44464 ^ _779142) ^ [_1669498, _1669500, _1669502, _1669504, _1669506, _1669508] : [-(hAPP(hAPP(c_List_Omap(_1669498, _1669500), _1669502), hAPP(hAPP(c_List_Omap(_1669504, _1669498), _1669506), _1669508)) = hAPP(hAPP(c_List_Omap(_1669504, _1669500), hAPP(c_Fun_Ocomp(_1669498, _1669500, _1669504, _1669502), _1669506)), _1669508))], (36078 ^ _779142) ^ [_1456666, _1456668, _1456670, _1456672, _1456674, _1456676, _1456678, _1456680, _1456682] : [c_Equiv__Relations_Oequiv(_1456666, _1456668, _1456670), c_Equiv__Relations_Oequiv(_1456672, _1456674, _1456676), c_Equiv__Relations_Ocongruent2(_1456666, _1456672, tc_fun(_1456678, tc_HOL_Obool), _1456670, _1456676, _1456680), hBOOL(hAPP(hAPP(c_member(_1456672), _1456682), _1456674)), -(c_Equiv__Relations_Ocongruent(_1456666, tc_fun(_1456678, tc_HOL_Obool), _1456670, hAPP(hAPP(c_COMBB(tc_fun(_1456672, tc_fun(_1456678, tc_HOL_Obool)), tc_fun(_1456678, tc_HOL_Obool), _1456666), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456672, tc_fun(_1456678, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1456672, _1456672, _1456676), hAPP(hAPP(c_Set_Oinsert(_1456672), _1456682), c_Orderings_Obot__class_Obot(tc_fun(_1456672, tc_HOL_Obool)))))), _1456680)))], (17513 ^ _779142) ^ [_1087682, _1087684, _1087686, _1087688] : [class_Divides_Oring__div(_1087682), -(c_Divides_Odiv__class_Omod(_1087682, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087682), _1087684), _1087686), _1087688) = c_Divides_Odiv__class_Omod(_1087682, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1087682), c_Divides_Odiv__class_Omod(_1087682, _1087684, _1087688)), c_Divides_Odiv__class_Omod(_1087682, _1087686, _1087688)), _1087688))], (41294 ^ _779142) ^ [_1592408, _1592410, _1592412] : [c_Nitpick_Oless__eq__frac(_1592408, _1592410, _1592412), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592408), c_Nitpick_Oplus__frac(_1592408, _1592410, c_Nitpick_Ouminus__frac(_1592408, _1592412)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28833 ^ _779142) ^ [_1289694, _1289696, _1289698, _1289700] : [class_Lattices_Odistrib__lattice(_1289694), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289694), _1289696), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289694), _1289698), _1289700)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289694), _1289696), _1289698)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1289694), _1289696), _1289700)))], (37843 ^ _779142) ^ [_1499170, _1499172, _1499174, _1499176, _1499178, _1499180] : [class_Groups_Ocomm__monoid__add(_1499170), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499172), _1499174)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499172, _1499170), hAPP(hAPP(c_COMBS(_1499172, _1499170, _1499170), hAPP(hAPP(c_COMBS(_1499172, _1499170, tc_fun(_1499170, _1499170)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1499170, tc_fun(_1499170, _1499170)), _1499172), c_If(_1499170)), _1499176)), _1499178)), _1499180)), _1499174) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1499170), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499172, _1499170), _1499178), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499172, tc_HOL_Obool)), _1499174), hAPP(c_Set_OCollect(_1499172), _1499176)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499172, _1499170), _1499180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499172, tc_HOL_Obool)), _1499174), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499172, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1499172), _1499176))))))], (44554 ^ _779142) ^ [_1671549, _1671551, _1671553] : [c_Fun_Oinj__on(tc_List_Olist(_1671549), tc_List_Olist(_1671551), hAPP(c_List_Omap(_1671549, _1671551), _1671553), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671549), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671549, _1671551, _1671553, c_Orderings_Otop__class_Otop(tc_fun(_1671549, tc_HOL_Obool))))], (29586 ^ _779142) ^ [_1305869, _1305871, _1305873] : [class_Orderings_Oorder(_1305869), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305869, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305869), _1305871)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1305869, _1305871, _1305873)) = c_Orderings_Obot__class_Obot(tc_fun(_1305869, tc_HOL_Obool)))], (18895 ^ _779142) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35592 ^ _779142) ^ [_1445396, _1445398] : [-(hAPP(c_Relation_OField(_1445396), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1445396, _1445396), tc_HOL_Obool), _1445398)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1445396, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1445396, _1445396), tc_HOL_Obool), tc_fun(_1445396, tc_HOL_Obool), c_Relation_OField(_1445396)), _1445398)))], (10569 ^ _779142) ^ [_961979, _961981] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961979), _961981) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10574 ^ _779142 : [(10577 ^ _779142) ^ [] : [-(_961981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10575 ^ _779142) ^ [] : [-(_961979 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10578 ^ _779142 : [(10581 ^ _779142) ^ [] : [-(_961981 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10579 ^ _779142) ^ [] : [-(_961979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27496 ^ _779142) ^ [_1264459, _1264461] : [c_Code__Numeral_OSuc__code__numeral(_1264459) = c_Code__Numeral_OSuc__code__numeral(_1264461), -(_1264459 = _1264461)], (48112 ^ _779142) ^ [_1748909, _1748911, _1748913, _1748915, _1748917] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748909, _1748911, _1748913), _1748915), _1748917)), -(hBOOL(hAPP(hAPP(_1748913, _1748917), _1748915)))], (43464 ^ _779142) ^ [_1647785, _1647787, _1647789] : [-(hAPP(hAPP(c_List_Odrop(_1647785), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647785), _1647787), _1647789)) = _1647789)], (8008 ^ _779142) ^ [_911113, _911115, _911117, _911119] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911113, _911115, _911117, _911119, c_Orderings_Obot__class_Obot(tc_fun(_911113, tc_HOL_Obool))), _911119)))], (6815 ^ _779142) ^ [_890052, _890054, _890056, _890058, _890060, _890062, _890064, _890066] : [c_Finite__Set_Ofolding__image__simple(_890052, _890054, _890056, _890058, _890060, _890062), hBOOL(hAPP(c_Finite__Set_Ofinite(_890054), _890064)), -(hAPP(_890062, hAPP(hAPP(c_Set_Oinsert(_890054), _890066), _890064)) = hAPP(hAPP(_890056, hAPP(_890060, _890066)), hAPP(_890062, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890054, tc_HOL_Obool)), _890064), hAPP(hAPP(c_Set_Oinsert(_890054), _890066), c_Orderings_Obot__class_Obot(tc_fun(_890054, tc_HOL_Obool)))))))], (10881 ^ _779142) ^ [_966978, _966980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966978), _966980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966978)), hAPP(c_Nat_OSuc, _966980))))], (44402 ^ _779142) ^ [_1668079, _1668081, _1668083] : [class_Groups_Omonoid__add(_1668079), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668079), hAPP(hAPP(c_List_Omap(_1668081, _1668079), hAPP(c_COMBK(_1668079, _1668081), c_Groups_Ozero__class_Ozero(_1668079))), _1668083)) = c_Groups_Ozero__class_Ozero(_1668079))], (28817 ^ _779142) ^ [_1289253, _1289255, _1289257, _1289259] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289253, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289253, tc_HOL_Obool)), _1289255), _1289257)), _1289259) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289253, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289253, tc_HOL_Obool)), _1289255), _1289259)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289253, tc_HOL_Obool)), _1289257), _1289259)))], (6574 ^ _779142) ^ [_884731, _884733, _884735, _884737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884731, tc_HOL_Obool)), _884733), _884735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884731, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_884731), _884737), _884733)), hAPP(hAPP(c_Set_Oinsert(_884731), _884737), _884735))))], (6737 ^ _779142) ^ [_888288, _888290, _888292, _888294, _888296] : [c_Finite__Set_Ofolding__one__idem(_888288, _888290, _888292), hAPP(_888294, hAPP(hAPP(_888290, 6742 ^ [_888288, _888290, _888292, _888294, _888296]), 6743 ^ [_888288, _888290, _888292, _888294, _888296])) = hAPP(hAPP(_888290, hAPP(_888294, 6742 ^ [_888288, _888290, _888292, _888294, _888296])), hAPP(_888294, 6743 ^ [_888288, _888290, _888292, _888294, _888296])), hBOOL(hAPP(c_Finite__Set_Ofinite(_888288), _888296)), -(_888296 = c_Orderings_Obot__class_Obot(tc_fun(_888288, tc_HOL_Obool))), -(hAPP(_888294, hAPP(_888292, _888296)) = hAPP(_888292, hAPP(c_Set_Oimage(_888288, _888288, _888294), _888296)))], (38929 ^ _779142) ^ [_1533341, _1533343, _1533345, _1533347] : [c_FunDef_Oreduction__pair(_1533341, _1533343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool)), _1533345), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool), tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool)), _1533343))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool)), _1533347), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool), tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool)), _1533343))), c_Wellfounded_Owf(_1533341, _1533347), -(c_Wellfounded_Owf(_1533341, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533341, _1533341), tc_HOL_Obool)), _1533345), _1533347)))], (35033 ^ _779142) ^ [_1430277, _1430279, _1430281, _1430283, _1430285] : [class_Complete__Lattice_Ocomplete__lattice(_1430277), hBOOL(hAPP(hAPP(c_member(_1430279), _1430281), _1430283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430277), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430279, _1430277), _1430283), _1430285)), hAPP(_1430285, _1430281))))], (32615 ^ _779142) ^ [_1374751, _1374753] : [-(c_Divides_OnegDivAlg(_1374751, _1374753) = hAPP(c_Divides_Oadjust(_1374753), c_Divides_OnegDivAlg(_1374751, 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)))), _1374753)))), -(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), _1374751), _1374753)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1374753), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6944 ^ _779142) ^ [_892885, _892887, _892889, _892891] : [hBOOL(hAPP(hAPP(c_member(_892885), _892887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892885, tc_HOL_Obool)), _892889), _892891))), 6947 ^ _779142 : [(6950 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892885), _892887), _892891))], (6948 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_892885), _892887), _892889)))]]], (39323 ^ _779142) ^ [_1543474] : [-(_1543474 = hAPP(c_Int_OAbs__Integ, 39321 ^ [_1543474]))], (170 ^ _779142) ^ [_781723, _781725, _781727, _781729, _781731, _781733] : [-(c_Finite__Set_Ofolding__one(_781731, _781727, _781723)), c_Finite__Set_Ofolding__one(_781733, _781729, _781725), _781733 = _781731, _781729 = _781727, _781725 = _781723], (10159 ^ _779142) ^ [_954008, _954010, _954012, _954014, _954016] : [class_Rings_Ocomm__semiring__1(_954008), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), _954010), _954012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), _954014), _954016)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), _954010), _954014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954008), _954012), _954016)))], (48144 ^ _779142) ^ [_1749813, _1749815, _1749817, _1749819, _1749821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749815, _1749813)), hAPP(hAPP(c_Product__Type_OPair(_1749815, _1749813), _1749819), _1749821)), hAPP(c_Relation_Oconverse(_1749813, _1749815), _1749817))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749813, _1749815, hAPP(hAPP(c_COMBC(_1749813, tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_fun(_1749815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749815, tc_fun(tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_fun(_1749815, tc_HOL_Obool)), _1749813), c_COMBC(_1749815, tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749815, tc_prod(_1749813, _1749815)), tc_fun(_1749815, tc_fun(tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_HOL_Obool)), _1749813), hAPP(c_COMBB(tc_prod(_1749813, _1749815), tc_fun(tc_fun(tc_prod(_1749813, _1749815), tc_HOL_Obool), tc_HOL_Obool), _1749815), c_member(tc_prod(_1749813, _1749815)))), c_Product__Type_OPair(_1749813, _1749815)))), _1749817)), _1749819), _1749821)))], (31110 ^ _779142) ^ [_1336756] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1336756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1336756)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1336756), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (12146 ^ _779142) ^ [_988867, _988869, _988871, _988873] : [class_Rings_Olinordered__ring__strict(_988867), 12149 ^ _779142 : [(12164 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988867), _988869), _988871)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988867), _988873), _988871)))), 12165 ^ _779142 : [(12172 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988871), c_Groups_Ozero__class_Ozero(_988867))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988873), _988869))], (12166 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), c_Groups_Ozero__class_Ozero(_988867)), _988871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988869), _988873))]]], (12150 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988867), _988869), _988871)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988867), _988873), _988871))), 12155 ^ _779142 : [(12158 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988869), _988873)))], (12156 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), c_Groups_Ozero__class_Ozero(_988867)), _988871)))]], 12159 ^ _779142 : [(12162 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988873), _988869)))], (12160 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988867), _988871), c_Groups_Ozero__class_Ozero(_988867))))]]]]], (52565 ^ _779142) ^ [_1835412, _1835414] : [-(class_Finite__Set_Ofinite(tc_prod(_1835412, _1835414))), class_Finite__Set_Ofinite(_1835412), class_Finite__Set_Ofinite(_1835414)], (17143 ^ _779142) ^ [_1080631, _1080633] : [class_Orderings_Olinorder(_1080631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080631), _1080633)), -(_1080633 = c_Orderings_Obot__class_Obot(tc_fun(_1080631, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1080631), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1080631), 17156 ^ [_1080631, _1080633]), 17157 ^ [_1080631, _1080633])), hAPP(hAPP(c_Set_Oinsert(_1080631), 17156 ^ [_1080631, _1080633]), hAPP(hAPP(c_Set_Oinsert(_1080631), 17157 ^ [_1080631, _1080633]), c_Orderings_Obot__class_Obot(tc_fun(_1080631, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1080631), c_Big__Operators_Olattice_OInf__fin(_1080631, c_Orderings_Oord__class_Omin(_1080631), _1080633)), _1080633)))], (42224 ^ _779142) ^ [_1619993, _1619995] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1619993, _1619995) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619993), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1619995)))], (51669 ^ _779142) ^ [_1822756, _1822758, _1822760, _1822762] : [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), _1822756, _1822758)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822760, _1822762))), 51672 ^ _779142 : [(51673 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822756), _1822758)), 51676 ^ _779142 : [(51681 ^ _779142) ^ [] : [51682 ^ _779142 : [(51685 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822756), _1822760))], (51683 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822760), _1822756)))]], 51686 ^ _779142 : [(51689 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822762), _1822758))], (51687 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822758), _1822762)))]]], (51679 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822758), _1822762)))], (51677 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822760), _1822756)))]]], (51691 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822760), _1822762)))]]], (8855 ^ _779142) ^ [_928389, _928391, _928393] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_928389), _928391)), -(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(_928389), _928393)), hAPP(c_Finite__Set_Ocard(_928389), _928391))), hAPP(c_Finite__Set_Ocard(_928389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928389, tc_HOL_Obool)), _928393), _928391)))))], (1316 ^ _779142) ^ [_798534, _798536] : [-(class_Groups_Osgn__if(_798534)), _798536 = _798534, class_Groups_Osgn__if(_798536)], (13711 ^ _779142) ^ [_1017608, _1017610, _1017612, _1017614] : [class_Fields_Olinordered__field(_1017608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017608), _1017610), _1017612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017608), c_Groups_Ozero__class_Ozero(_1017608)), _1017614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017608), c_Groups_Ozero__class_Ozero(_1017608)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017608), _1017612), _1017610))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017608), _1017614), _1017612)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017608), _1017614), _1017610))))], (20742 ^ _779142) ^ [_1143678, _1143680] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1143678)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1143680)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143678), _1143680)))], (916 ^ _779142) ^ [_792876, _792878, _792880, _792882, _792884, _792886] : [-(c_Relation_Orefl__on(_792884, _792880, _792876)), c_Relation_Orefl__on(_792886, _792882, _792878), _792886 = _792884, _792882 = _792880, _792878 = _792876], (52641 ^ _779142) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (17867 ^ _779142) ^ [_1093932, _1093934, _1093936] : [class_Rings_Osemiring__1(_1093932), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1093934), _1093936)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093932), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093932), _1093934)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1093932), _1093936)))], (46722 ^ _779142) ^ [_1718545, _1718547, _1718549] : [-(hAPP(c_List_Orev(_1718545), hAPP(hAPP(c_List_Odrop(_1718545), _1718547), _1718549)) = hAPP(hAPP(c_List_Otake(_1718545), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718545)), _1718549)), _1718547)), hAPP(c_List_Orev(_1718545), _1718549)))], (22751 ^ _779142) ^ [_1179988, _1179990] : [class_Int_Onumber__ring(_1179988), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1179988), hAPP(c_Int_Onumber__class_Onumber__of(_1179988), _1179990)) = hAPP(c_Int_Onumber__class_Onumber__of(_1179988), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179990)))], (35135 ^ _779142) ^ [_1432929, _1432931, _1432933, _1432935, _1432937, _1432939] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432929, tc_fun(_1432931, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432933, tc_fun(_1432929, tc_HOL_Obool)), _1432935), _1432937)), _1432939) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432933, tc_fun(_1432931, tc_HOL_Obool)), _1432935), hAPP(hAPP(c_COMBC(_1432933, tc_fun(_1432929, tc_fun(_1432931, tc_HOL_Obool)), tc_fun(_1432931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432929, tc_HOL_Obool), tc_fun(tc_fun(_1432929, tc_fun(_1432931, tc_HOL_Obool)), tc_fun(_1432931, tc_HOL_Obool)), _1432933), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432929, tc_fun(_1432931, tc_HOL_Obool))), _1432937)), _1432939)))], (1796 ^ _779142) ^ [_804534, _804536] : [-(class_Groups_Omonoid__mult(_804534)), _804536 = _804534, class_Groups_Omonoid__mult(_804536)], (11095 ^ _779142) ^ [_970334, _970336, _970338] : [class_Groups_Ogroup__add(_970334), 11098 ^ _779142 : [(11105 ^ _779142) ^ [] : [_970336 = _970338, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970334), _970336), _970338) = c_Groups_Ozero__class_Ozero(_970334))], (11099 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970334), _970336), _970338) = c_Groups_Ozero__class_Ozero(_970334), -(_970336 = _970338)]]], (7868 ^ _779142) ^ [_908799, _908801, _908803] : [class_Orderings_Oorder(_908799), 7871 ^ _779142 : [(7880 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908799), _908801), _908803))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908799), _908801), _908803)), -(_908801 = _908803)], (7872 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908799), _908801), _908803)), 7875 ^ _779142 : [(7878 ^ _779142) ^ [] : [_908801 = _908803], (7876 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908799), _908801), _908803)))]]]]], (17393 ^ _779142) ^ [_1085098, _1085100, _1085102, _1085104, _1085106, _1085108] : [class_Divides_Osemiring__div(_1085098), c_Divides_Odiv__class_Omod(_1085098, _1085100, _1085102) = c_Divides_Odiv__class_Omod(_1085098, _1085104, _1085102), c_Divides_Odiv__class_Omod(_1085098, _1085106, _1085102) = c_Divides_Odiv__class_Omod(_1085098, _1085108, _1085102), -(c_Divides_Odiv__class_Omod(_1085098, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085098), _1085100), _1085106), _1085102) = c_Divides_Odiv__class_Omod(_1085098, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085098), _1085104), _1085108), _1085102))], (6227 ^ _779142) ^ [_878892, _878894, _878896] : [_878892 = _878894, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878896, tc_HOL_Obool)), _878894), _878892)))], (41264 ^ _779142) ^ [_1591726, _1591728, _1591730, _1591732, _1591734, _1591736] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1591726, _1591728, _1591730), _1591732), hAPP(hAPP(c_Product__Type_OPair(_1591726, _1591728), _1591734), _1591736)) = hAPP(hAPP(_1591732, _1591734), _1591736))], (33631 ^ _779142) ^ [_1394477, _1394479, _1394481] : [33633 ^ _779142 : [(33636 ^ _779142) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1394481, 33632 ^ [_1394477, _1394479, _1394481]))], (33634 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394477), 33632 ^ [_1394477, _1394479, _1394481]), _1394479)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394477, tc_Int_Oint), _1394481), _1394479) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394477, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1394477), c_Int_Onat), _1394481)), _1394479)))], (46710 ^ _779142) ^ [_1718327, _1718329] : [-(_1718327 = c_List_Olist_ONil(_1718329)), -(hAPP(c_List_Ohd(_1718329), hAPP(c_List_Orev(_1718329), _1718327)) = c_List_Olast(_1718329, _1718327))], (41725 ^ _779142) ^ [_1606126, _1606128, _1606130] : [c_Equiv__Relations_Oequiv(_1606126, _1606128, _1606130), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1606126), c_List_Olists(_1606126, _1606128), c_List_Olistrel(_1606126, _1606130)))], (18587 ^ _779142) ^ [_1106411, _1106413, _1106415] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106411), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1106413, _1106415)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106411), _1106413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106411), _1106415)))], (37547 ^ _779142) ^ [_1490285, _1490287, _1490289] : [-(hAPP(hAPP(c_Set_Oinsert(_1490285), _1490287), _1490289) = hAPP(c_Set_OCollect(_1490285), hAPP(hAPP(c_COMBS(_1490285, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490285), c_fdisj), hAPP(hAPP(c_COMBC(_1490285, _1490285, tc_HOL_Obool), c_fequal), _1490287))), hAPP(hAPP(c_COMBC(_1490285, tc_fun(_1490285, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490285)), _1490289))))], (33349 ^ _779142) ^ [_1389604] : [-(_1389604 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1389604), 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)))))], (23851 ^ _779142) ^ [_1199252, _1199254] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199252)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199254)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199252), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199254))))], (5934 ^ _779142) ^ [_873273, _873275, _873277, _873279, _873281] : [hBOOL(hAPP(hAPP(c_member(_873273), _873275), _873277)), -(hBOOL(hAPP(hAPP(c_member(_873279), hAPP(_873281, _873275)), hAPP(c_Set_Oimage(_873273, _873279, _873281), _873277))))], (29763 ^ _779142) ^ [_1309846, _1309848, _1309850, _1309852, _1309854] : [c_Finite__Set_Ofolding__one(_1309846, _1309848, _1309850), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309846), _1309852)), -(_1309852 = c_Orderings_Obot__class_Obot(tc_fun(_1309846, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309846), _1309854)), -(_1309854 = c_Orderings_Obot__class_Obot(tc_fun(_1309846, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309846, tc_HOL_Obool)), _1309852), _1309854) = c_Orderings_Obot__class_Obot(tc_fun(_1309846, tc_HOL_Obool)), -(hAPP(_1309850, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309846, tc_HOL_Obool)), _1309852), _1309854)) = hAPP(hAPP(_1309848, hAPP(_1309850, _1309852)), hAPP(_1309850, _1309854)))], (32631 ^ _779142) ^ [_1375024, _1375026, _1375028] : [class_Int_Onumber__ring(_1375024), 32634 ^ _779142 : [(32641 ^ _779142) ^ [] : [-(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), _1375026)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1375024), hAPP(c_Int_Onumber__class_Onumber__of(_1375024), _1375028)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1375026))) = c_Groups_Oone__class_Oone(_1375024))], (32635 ^ _779142) ^ [] : [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), _1375026))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1375024), hAPP(c_Int_Onumber__class_Onumber__of(_1375024), _1375028)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1375026))) = hAPP(hAPP(c_HOL_OLet(_1375024, _1375024), hAPP(hAPP(c_Power_Opower__class_Opower(_1375024), hAPP(c_Int_Onumber__class_Onumber__of(_1375024), _1375028)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375026))), hAPP(hAPP(c_COMBS(_1375024, _1375024, _1375024), hAPP(hAPP(c_COMBB(_1375024, tc_fun(_1375024, _1375024), _1375024), c_Groups_Otimes__class_Otimes(_1375024)), hAPP(c_Groups_Otimes__class_Otimes(_1375024), hAPP(c_Int_Onumber__class_Onumber__of(_1375024), _1375028)))), c_COMBI(_1375024))))]]], (41010 ^ _779142) ^ [_1584644, _1584646, _1584648, _1584650] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584644, _1584644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1584646), _1584648)), _1584650) = hAPP(c_Fun_Ocomp(_1584644, _1584644, _1584644, hAPP(hAPP(c_Nat_Ocompow(_1584644, _1584644), _1584646), _1584650)), hAPP(hAPP(c_Nat_Ocompow(_1584644, _1584644), _1584648), _1584650)))], (10061 ^ _779142) ^ [_951732, _951734, _951736, _951738, _951740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951732), _951734)), 10064 ^ _779142 : [(10071 ^ _779142) ^ [] : [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), _951734), _951732)), _951736)), _951738) = _951740, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951734), _951736)), _951738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951732), _951736)), _951740))], (10065 ^ _779142) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951734), _951736)), _951738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951732), _951736)), _951740), -(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), _951734), _951732)), _951736)), _951738) = _951740)]]], (6173 ^ _779142) ^ [_877937, _877939] : [class_Orderings_Opreorder(_877937), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877937), _877939), _877939)))], (40380 ^ _779142) ^ [_1569251, _1569253, _1569255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569251, _1569251), tc_HOL_Obool)), _1569253), _1569255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569251, _1569251), tc_HOL_Obool)), _1569255), c_Transitive__Closure_Ortrancl(_1569251, _1569253))), -(c_Transitive__Closure_Ortrancl(_1569251, _1569255) = c_Transitive__Closure_Ortrancl(_1569251, _1569253))], (1992 ^ _779142) ^ [_807840, _807842, _807844, _807846, _807848, _807850, _807852, _807854, _807856, _807858] : [-(c_Nitpick_Opair__box_Opair__box__size(_807858, _807854, _807850, _807846, _807842) = c_Nitpick_Opair__box_Opair__box__size(_807856, _807852, _807848, _807844, _807840)), _807858 = _807856, _807854 = _807852, _807850 = _807848, _807846 = _807844, _807842 = _807840], (47441 ^ _779142) ^ [_1734479, _1734481, _1734483, _1734485, _1734487] : [class_Orderings_Olinorder(_1734479), 47447 ^ _779142 : [(47450 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1734479), hAPP(_1734485, _1734487)), hAPP(_1734485, 47446 ^ [_1734479, _1734481, _1734483, _1734485, _1734487])))], (47448 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734481), 47446 ^ [_1734479, _1734481, _1734483, _1734485, _1734487]), hAPP(c_List_Oset(_1734481), _1734483))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734481, _1734479, _1734485), _1734487), _1734483) = hAPP(hAPP(c_List_Olist_OCons(_1734481), _1734487), _1734483))], (8533 ^ _779142) ^ [_922249, _922251, _922253, _922255, _922257, _922259, _922261] : [c_Big__Operators_Ocomm__monoid__big(_922249, _922251, _922253, _922255, _922257), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_922251), _922259))), -(hAPP(hAPP(_922257, _922261), _922259) = _922255)], (38615 ^ _779142) ^ [_1526767, _1526769, _1526771, _1526773, _1526775] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526767, _1526769)), hAPP(hAPP(c_Product__Type_OPair(_1526767, _1526769), _1526771), _1526773)), _1526775)), -(hBOOL(hAPP(hAPP(c_member(_1526767), _1526771), hAPP(c_Relation_ODomain(_1526767, _1526769), _1526775))))], (45388 ^ _779142) ^ [_1690071, _1690073] : [c_List_Olist_ONil(_1690071) = c_List_Oremdups(_1690071, _1690073), -(_1690073 = c_List_Olist_ONil(_1690071))], (29223 ^ _779142) ^ [_1297496, _1297498, _1297500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1297496, tc_HOL_Obool)), _1297498), _1297500)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297496, tc_HOL_Obool)), _1297500), _1297498) = _1297498)], (29173 ^ _779142) ^ [_1296565, _1296567] : [class_Lattices_Olattice(_1296565), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296565), _1296567), _1296567) = _1296567)], (46588 ^ _779142) ^ [_1715693, _1715695, _1715697] : [hAPP(c_List_Orev(_1715693), _1715695) = hAPP(hAPP(c_List_Olist_OCons(_1715693), _1715697), c_List_Olist_ONil(_1715693)), -(_1715695 = hAPP(hAPP(c_List_Olist_OCons(_1715693), _1715697), c_List_Olist_ONil(_1715693)))], (41873 ^ _779142) ^ [_1609865, _1609867, _1609869, _1609871] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609865), tc_List_Olist(_1609865))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609865), tc_List_Olist(_1609865)), _1609867), _1609869)), c_List_Olexord(_1609865, _1609871)))), 41874 ^ _779142 : [(41881 ^ _779142) ^ [_1610172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610172), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609865)), _1609867)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609865)), _1609869)))), hAPP(hAPP(c_List_Otake(_1609865), _1610172), _1609867) = hAPP(hAPP(c_List_Otake(_1609865), _1610172), _1609869), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609865, _1609865)), hAPP(hAPP(c_Product__Type_OPair(_1609865, _1609865), hAPP(hAPP(c_List_Onth(_1609865), _1609867), _1610172)), hAPP(hAPP(c_List_Onth(_1609865), _1609869), _1610172))), _1609871))], (41875 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609865)), _1609867)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609865)), _1609869))), hAPP(hAPP(c_List_Otake(_1609865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609865)), _1609867)), _1609869) = _1609867]]], (50089 ^ _779142) ^ [_1792067, _1792069, _1792071, _1792073] : [c_Fun_Obij__betw(_1792067, _1792069, _1792071, c_Orderings_Obot__class_Obot(tc_fun(_1792067, tc_HOL_Obool)), _1792073), -(_1792073 = c_Orderings_Obot__class_Obot(tc_fun(_1792069, tc_HOL_Obool)))], (11408 ^ _779142) ^ [_975343, _975345, _975347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975345), _975347)), -(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, _975343)), _975345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _975343)), _975347))))], (24852 ^ _779142) ^ [_1216108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216108), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1216108)), c_Int_OPls)))], (31656 ^ _779142) ^ [_1347420, _1347422, _1347424] : [hBOOL(hAPP(hAPP(c_member(_1347420), _1347422), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1347420, tc_HOL_Obool), _1347424))), 31660 ^ _779142 : [(31663 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1347420, tc_HOL_Obool)), 31659 ^ [_1347420, _1347422, _1347424]), _1347424)))], (31661 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347420), _1347422), 31659 ^ [_1347420, _1347422, _1347424])))]]], (7392 ^ _779142) ^ [_901522, _901524, _901526] : [class_Orderings_Opreorder(_901522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901522), _901524), _901526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901522), _901526), _901524))], (14087 ^ _779142) ^ [_1024567, _1024569, _1024571] : [class_Fields_Olinordered__field(_1024567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024567), _1024569), c_Groups_Ozero__class_Ozero(_1024567))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024567), c_Groups_Ozero__class_Ozero(_1024567)), _1024571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024567), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024567), _1024569), _1024571)), c_Groups_Ozero__class_Ozero(_1024567))))], (45518 ^ _779142) ^ [_1692442, _1692444, _1692446] : [-(c_List_Oconcat(_1692442, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692442)), _1692444), _1692446)) = hAPP(hAPP(c_List_Oappend(_1692442), _1692444), c_List_Oconcat(_1692442, _1692446)))], (7932 ^ _779142) ^ [_909671, _909673, _909675, _909677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909671, tc_HOL_Obool)), _909673), _909675)), hBOOL(hAPP(hAPP(c_member(_909671), _909677), _909673)), -(hBOOL(hAPP(hAPP(c_member(_909671), _909677), _909675)))], (10837 ^ _779142) ^ [_966247, _966249] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966247), hAPP(c_Nat_OSuc, _966249)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966247), _966249)))], (15657 ^ _779142) ^ [_1053714, _1053716, _1053718, _1053720] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053714), _1053716), _1053718)), hAPP(c_Int_Onumber__class_Onumber__of(_1053714), _1053720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053714), _1053716), hAPP(c_Int_Onumber__class_Onumber__of(_1053714), _1053720))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053714), _1053718), hAPP(c_Int_Onumber__class_Onumber__of(_1053714), _1053720)))), class_Int_Onumber(_1053714), class_Rings_Osemiring(_1053714)], (21486 ^ _779142) ^ [_1156649, _1156651] : [c_Nat__Transfer_Onat__set(_1156649), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1156651), _1156649)), -(c_Nat__Transfer_Ois__nat(_1156651))], (48763 ^ _779142) ^ [_1763511, _1763513] : [c_Relation_Otrans(_1763511, _1763513), 48766 ^ _779142 : [(48767 ^ _779142) ^ [_1763647, _1763649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), _1763649), _1763647)), _1763513)), 48770 ^ _779142 : [(48771 ^ _779142) ^ [_1763790] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), _1763647), _1763790)), _1763513)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), _1763649), _1763790)), _1763513)))]]]]], (40544 ^ _779142) ^ [] : [-(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))))], (25606 ^ _779142) ^ [_1229188] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1229188)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1229188)))], (11145 ^ _779142) ^ [_971017] : [-(_971017 = 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)), _971017)))], (31306 ^ _779142) ^ [_1340459, _1340461, _1340463, _1340465] : [hBOOL(hAPP(hAPP(c_member(_1340459), _1340461), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1340459, tc_HOL_Obool), _1340463))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1340459, tc_HOL_Obool)), _1340465), _1340463)), -(hBOOL(hAPP(hAPP(c_member(_1340459), _1340461), _1340465)))], (27918 ^ _779142) ^ [_1272143, _1272145, _1272147, _1272149] : [class_Orderings_Olinorder(_1272143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272143), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272143), _1272145), _1272147)), _1272149)), 27925 ^ _779142 : [(27928 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272143), _1272147), _1272149)))], (27926 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272143), _1272145), _1272149)))]]], (33744 ^ _779142) ^ [_1396818] : [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), _1396818))), -(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), _1396818)) = 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), _1396818))))], (13004 ^ _779142) ^ [_1004339, _1004341, _1004343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004339), _1004341)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1004343), _1004341))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004339), _1004343)))], (17185 ^ _779142) ^ [_1081543, _1081545, _1081547] : [class_Orderings_Olinorder(_1081543), hAPP(_1081545, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081543), 17190 ^ [_1081543, _1081545, _1081547]), 17191 ^ [_1081543, _1081545, _1081547])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081543), hAPP(_1081545, 17190 ^ [_1081543, _1081545, _1081547])), hAPP(_1081545, 17191 ^ [_1081543, _1081545, _1081547])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081543), _1081547)), -(_1081547 = c_Orderings_Obot__class_Obot(tc_fun(_1081543, tc_HOL_Obool))), -(hAPP(_1081545, c_Big__Operators_Olattice_OInf__fin(_1081543, c_Orderings_Oord__class_Omin(_1081543), _1081547)) = c_Big__Operators_Olattice_OInf__fin(_1081543, c_Orderings_Oord__class_Omin(_1081543), hAPP(c_Set_Oimage(_1081543, _1081543, _1081545), _1081547)))], (12092 ^ _779142) ^ [_987880, _987882, _987884, _987886] : [class_Rings_Olinordered__ring__strict(_987880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987880), c_Groups_Ozero__class_Ozero(_987880)), _987882)), 12099 ^ _779142 : [(12106 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987880), _987884), _987886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987880), _987882), _987884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987880), _987882), _987886))))], (12100 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987880), _987882), _987884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987880), _987882), _987886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987880), _987884), _987886)))]]], (25366 ^ _779142) ^ [_1224906, _1224908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224906), 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)))), _1224908)), 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)))), _1224906)) = 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), _1224908), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224906))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9326 ^ _779142) ^ [_938139, _938141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938139), _938141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938141), _938139)), -(_938139 = _938141)], (31775 ^ _779142) ^ [_1350874, _1350876, _1350878, _1350880] : [hBOOL(hAPP(hAPP(c_member(_1350874), _1350880), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350874, tc_HOL_Obool)), _1350876), _1350878))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350874, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1350874, tc_fun(_1350874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350874)), _1350876)), hAPP(hAPP(c_COMBC(_1350874, tc_fun(_1350874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350874)), _1350878)), _1350880)))], (12590 ^ _779142) ^ [_996516, _996518, _996520, _996522] : [class_Groups_Oordered__comm__monoid__add(_996516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996516), c_Groups_Ozero__class_Ozero(_996516)), _996518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996516), _996520), _996522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996516), _996520), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996516), _996518), _996522))))], (3428 ^ _779142) ^ [_830296, _830298] : [_830298 = _830296, -(c_List_Otranspose__rel(_830298) = c_List_Otranspose__rel(_830296))], (51843 ^ _779142) ^ [_1825900, _1825902, _1825904] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825900), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1825902), _1825904))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825900), _1825902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1825904), _1825902)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825900), _1825904)))], (27352 ^ _779142) ^ [_1261654, _1261656, _1261658, _1261660] : [hBOOL(hAPP(_1261654, _1261656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261658, tc_HOL_Obool)), _1261654), _1261660)), -(hBOOL(hAPP(_1261660, _1261656)))], (22433 ^ _779142) ^ [_1173864, _1173866] : [22441 ^ _779142 : [(22444 ^ _779142) ^ [] : [-(hBOOL(hAPP(_1173866, 22440 ^ [_1173864, _1173866])))], (22442 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 22440 ^ [_1173864, _1173866]), _1173864)))]], 22434 ^ _779142 : [(22435 ^ _779142) ^ [_1173933] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173933), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1173864))), hBOOL(hAPP(_1173866, _1173933))]]], (6203 ^ _779142) ^ [_878477, _878479, _878481] : [_878477 = _878479, 6206 ^ _779142 : [(6209 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878481, tc_HOL_Obool)), _878479), _878477)))], (6207 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878481, tc_HOL_Obool)), _878477), _878479)))]]], (46282 ^ _779142) ^ [_1709486, _1709488, _1709490, _1709492, _1709494] : [class_Orderings_Olinorder(_1709486), c_List_Olinorder__class_Osorted(_1709486, hAPP(hAPP(c_List_Omap(_1709488, _1709486), _1709490), _1709492)), -(c_List_Olinorder__class_Osorted(_1709486, hAPP(hAPP(c_List_Omap(_1709488, _1709486), _1709490), hAPP(c_List_Ofilter(_1709488, _1709494), _1709492))))], (8917 ^ _779142) ^ [_929613, _929615, _929617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929613), _929615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929613, tc_HOL_Obool)), _929615), _929617)), -(hAPP(c_Finite__Set_Ocard(_929613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929613, tc_HOL_Obool)), _929617), _929615)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_929613), _929617)), hAPP(c_Finite__Set_Ocard(_929613), _929615)))], (44327 ^ _779142) ^ [_1665985, _1665987, _1665989, _1665991, _1665993, _1665995, _1665997, _1665999] : [-(hAPP(hAPP(c_List_Ozip(_1665985, _1665987), hAPP(hAPP(c_List_Omap(_1665989, _1665985), _1665991), _1665993)), hAPP(hAPP(c_List_Omap(_1665995, _1665987), _1665997), _1665999)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665989, _1665995), tc_prod(_1665985, _1665987)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665989, _1665995, tc_prod(_1665985, _1665987)), hAPP(hAPP(c_COMBC(_1665989, tc_fun(_1665995, _1665987), tc_fun(_1665995, tc_prod(_1665985, _1665987))), hAPP(hAPP(c_COMBB(tc_fun(_1665987, tc_prod(_1665985, _1665987)), tc_fun(tc_fun(_1665995, _1665987), tc_fun(_1665995, tc_prod(_1665985, _1665987))), _1665989), c_COMBB(_1665987, tc_prod(_1665985, _1665987), _1665995)), hAPP(hAPP(c_COMBB(_1665985, tc_fun(_1665987, tc_prod(_1665985, _1665987)), _1665989), c_Product__Type_OPair(_1665985, _1665987)), _1665991))), _1665997))), hAPP(hAPP(c_List_Ozip(_1665989, _1665995), _1665993), _1665999)))], (44576 ^ _779142) ^ [_1672008, _1672010, _1672012, _1672014] : [class_Rings_Osemiring__1(_1672008), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672008), hAPP(hAPP(c_List_Omap(_1672010, _1672008), hAPP(c_COMBK(_1672008, _1672010), _1672012)), _1672014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672008), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1672008), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672010)), _1672014))), _1672012))], (35796 ^ _779142) ^ [_1450232, _1450234, _1450236, _1450238, _1450240, _1450242, _1450244] : [c_Equiv__Relations_Oequiv(_1450232, _1450234, _1450236), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450232, tc_HOL_Obool)), _1450238), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450232), _1450234), _1450236))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450232, tc_HOL_Obool)), _1450240), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450232), _1450234), _1450236))), hBOOL(hAPP(hAPP(c_member(_1450232), _1450242), _1450238)), hBOOL(hAPP(hAPP(c_member(_1450232), _1450244), _1450240)), 35815 ^ _779142 : [(35822 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450232, _1450232)), hAPP(hAPP(c_Product__Type_OPair(_1450232, _1450232), _1450242), _1450244)), _1450236)), -(_1450238 = _1450240)], (35816 ^ _779142) ^ [] : [_1450238 = _1450240, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450232, _1450232)), hAPP(hAPP(c_Product__Type_OPair(_1450232, _1450232), _1450242), _1450244)), _1450236)))]]], (23787 ^ _779142) ^ [_1198140, _1198142, _1198144] : [class_Orderings_Oorder(_1198140), 23790 ^ _779142 : [(23797 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198140), _1198142), _1198144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198140, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1198140), _1198142)), hAPP(c_SetInterval_Oord__class_OatMost(_1198140), _1198144))))], (23791 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198140, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1198140), _1198142)), hAPP(c_SetInterval_Oord__class_OatMost(_1198140), _1198144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198140), _1198142), _1198144)))]]], (23675 ^ _779142) ^ [_1196158, _1196160] : [class_Groups_Oordered__ab__group__add__abs(_1196158), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196158), hAPP(c_Groups_Ouminus__class_Ouminus(_1196158), hAPP(c_Groups_Oabs__class_Oabs(_1196158), _1196160))), c_Groups_Ozero__class_Ozero(_1196158))))], (44121 ^ _779142) ^ [_1661975, _1661977, _1661979] : [class_Orderings_Olinorder(_1661975), hBOOL(hAPP(hAPP(c_member(_1661975), _1661977), hAPP(c_List_Oset(_1661975), _1661979))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661975, _1661975, c_COMBI(_1661975), _1661977, _1661979) = _1661979)], (43917 ^ _779142) ^ [_1657654, _1657656] : [class_Complete__Lattice_Ocomplete__lattice(_1657654), -(c_Complete__Lattice_OInf__class_OInf(_1657654, hAPP(c_List_Oset(_1657654), _1657656)) = hAPP(c_List_Ofoldl(_1657654, _1657654, c_Lattices_Osemilattice__inf__class_Oinf(_1657654), c_Orderings_Otop__class_Otop(_1657654)), _1657656))], (47207 ^ _779142) ^ [_1728764, _1728766, _1728768] : [-(c_List_Omaps(_1728764, _1728766, _1728768, c_List_Olist_ONil(_1728764)) = c_List_Olist_ONil(_1728766))], (25886 ^ _779142) ^ [_1234033] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1234033)), 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, _1234033, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (49429 ^ _779142) ^ [_1777936, _1777938] : [-(c_Equiv__Relations_Opart__equivp(_1777936, _1777938)), 49432 ^ _779142 : [(49433 ^ _779142) ^ [_1778013] : [hBOOL(hAPP(hAPP(_1777938, _1778013), _1778013))]], c_Predicate_Osymp(_1777936, _1777938), c_Predicate_Otransp(_1777936, _1777938)], (52737 ^ _779142) ^ [_1837351, _1837353] : [hBOOL(hAPP(hAPP(c_fconj, _1837351), _1837353)), -(hBOOL(_1837353))], (19421 ^ _779142) ^ [_1120724, _1120726, _1120728] : [class_Groups_Oordered__ab__group__add__abs(_1120724), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120724), hAPP(c_Groups_Oabs__class_Oabs(_1120724), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120724), hAPP(c_Groups_Oabs__class_Oabs(_1120724), _1120726)), hAPP(c_Groups_Oabs__class_Oabs(_1120724), _1120728)))), hAPP(c_Groups_Oabs__class_Oabs(_1120724), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120724), _1120726), _1120728)))))], (52281 ^ _779142) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (47868 ^ _779142) ^ [_1743559, _1743561, _1743563] : [c_List_Olist__all(_1743559, _1743561, _1743563), -(c_List_Olist__all(_1743559, _1743561, hAPP(c_List_Orev(_1743559), _1743563)))], (35866 ^ _779142) ^ [_1451757, _1451759, _1451761, _1451763, _1451765] : [c_Equiv__Relations_Oequiv(_1451757, _1451759, _1451761), 35869 ^ _779142 : [(35880 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451757, _1451757)), hAPP(hAPP(c_Product__Type_OPair(_1451757, _1451757), _1451763), _1451765)), _1451761))), hAPP(c_Relation_OImage(_1451757, _1451757, _1451761), hAPP(hAPP(c_Set_Oinsert(_1451757), _1451763), c_Orderings_Obot__class_Obot(tc_fun(_1451757, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451757, _1451757, _1451761), hAPP(hAPP(c_Set_Oinsert(_1451757), _1451765), c_Orderings_Obot__class_Obot(tc_fun(_1451757, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1451757), _1451763), _1451759)), hBOOL(hAPP(hAPP(c_member(_1451757), _1451765), _1451759))], (35870 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451757, _1451757)), hAPP(hAPP(c_Product__Type_OPair(_1451757, _1451757), _1451763), _1451765)), _1451761)), 35873 ^ _779142 : [(35878 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451757), _1451765), _1451759)))], (35876 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451757), _1451763), _1451759)))], (35874 ^ _779142) ^ [] : [-(hAPP(c_Relation_OImage(_1451757, _1451757, _1451761), hAPP(hAPP(c_Set_Oinsert(_1451757), _1451763), c_Orderings_Obot__class_Obot(tc_fun(_1451757, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451757, _1451757, _1451761), hAPP(hAPP(c_Set_Oinsert(_1451757), _1451765), c_Orderings_Obot__class_Obot(tc_fun(_1451757, tc_HOL_Obool)))))]]]]], (10153 ^ _779142) ^ [_953899, _953901, _953903] : [class_Rings_Ocomm__semiring__1(_953899), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953899), _953901), _953903) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953899), _953903), _953901))], (42940 ^ _779142) ^ [_1635177] : [class_Orderings_Olinorder(_1635177), -(c_List_Olinorder__class_Osorted__list__of__set(_1635177, c_Orderings_Obot__class_Obot(tc_fun(_1635177, tc_HOL_Obool))) = c_List_Olist_ONil(_1635177))], (33481 ^ _779142) ^ [_1391470, _1391472, _1391474, _1391476, _1391478, _1391480, _1391482] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391470, _1391472), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391474), _1391476))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391478, _1391472), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391480), _1391482))), -(_1391472 = 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), _1391470), _1391478), _1391472), 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), _1391474), _1391480)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1391476), _1391482)), _1391472))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1391476), _1391482), _1391472)))))], (33640 ^ _779142) ^ [_1394707, _1394709, _1394711] : [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), _1394707), _1394709))), -(hBOOL(hAPP(hAPP(_1394711, _1394707), _1394709))), 33647 ^ _779142 : [(33650 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1394711, 33645 ^ [_1394707, _1394709, _1394711]), 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)))), 33646 ^ [_1394707, _1394709, _1394711])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 33645 ^ [_1394707, _1394709, _1394711]), 33646 ^ [_1394707, _1394709, _1394711]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 33646 ^ [_1394707, _1394709, _1394711]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33660 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1394711, 33645 ^ [_1394707, _1394709, _1394711]), 33646 ^ [_1394707, _1394709, _1394711]))], (33648 ^ _779142) ^ [] : [-(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), 33645 ^ [_1394707, _1394709, _1394711]), 33646 ^ [_1394707, _1394709, _1394711]))))]]], (25138 ^ _779142) ^ [] : [-(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)))], (9286 ^ _779142) ^ [_937602, _937604] : [class_Groups_Oone(_937602), 9289 ^ _779142 : [(9296 ^ _779142) ^ [] : [_937604 = c_Groups_Oone__class_Oone(_937602), -(c_Groups_Oone__class_Oone(_937602) = _937604)], (9290 ^ _779142) ^ [] : [c_Groups_Oone__class_Oone(_937602) = _937604, -(_937604 = c_Groups_Oone__class_Oone(_937602))]]], (4398 ^ _779142) ^ [_845893, _845895, _845897, _845899, _845901, _845903] : [-(c_Lazy__Sequence_Oanamorph(_845903, _845899, _845895) = c_Lazy__Sequence_Oanamorph(_845901, _845897, _845893)), _845903 = _845901, _845899 = _845897, _845895 = _845893], (19817 ^ _779142) ^ [_1127227, _1127229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127227)), 19820 ^ _779142 : [(19827 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127227), _1127229)), -(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), _1127229), _1127227))))], (19821 ^ _779142) ^ [] : [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), _1127229), _1127227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1127227), _1127229)))]]], (7090 ^ _779142) ^ [_896195, _896197, _896199, _896201, _896203, _896205] : [c_Finite__Set_Ofun__left__comm(_896195, _896197, _896199), hBOOL(hAPP(c_Finite__Set_Ofinite(_896195), _896201)), -(hAPP(hAPP(c_Finite__Set_Ofold(_896195, _896197, _896199), _896203), hAPP(hAPP(c_Set_Oinsert(_896195), _896205), _896201)) = hAPP(hAPP(_896199, _896205), hAPP(hAPP(c_Finite__Set_Ofold(_896195, _896197, _896199), _896203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896195, tc_HOL_Obool)), _896201), hAPP(hAPP(c_Set_Oinsert(_896195), _896205), c_Orderings_Obot__class_Obot(tc_fun(_896195, tc_HOL_Obool)))))))], (48713 ^ _779142) ^ [_1762210, _1762212, _1762214] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1762210, _1762212, _1762214, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1762212)], (45298 ^ _779142) ^ [_1688135, _1688137, _1688139, _1688141] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688135)), _1688137), hAPP(c_List_Oset(tc_List_Olist(_1688135)), c_Enum_On__lists(_1688135, _1688139, _1688141)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688135)), _1688137) = _1688139)], (26520 ^ _779142) ^ [_1245579, _1245581, _1245583] : [class_Lattices_Olattice(_1245579), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245579), _1245581), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245579), _1245581), _1245583))))], (49610 ^ _779142) ^ [_1781589, _1781591, _1781593, _1781595] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781589, _1781591, c_Orderings_Otop__class_Otop(tc_fun(_1781589, tc_HOL_Obool)), _1781593), _1781595) = c_Hilbert__Choice_OEps(_1781589, hAPP(hAPP(c_COMBC(_1781589, _1781591, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781591, tc_fun(_1781591, tc_HOL_Obool), _1781589), c_fequal), _1781593)), _1781595)))], (18907 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (38739 ^ _779142) ^ [_1528988, _1528990] : [hBOOL(hAPP(hAPP(c_member(_1528988), 38740 ^ [_1528988, _1528990]), c_Wellfounded_Oacc(_1528988, _1528990))), -(c_Wellfounded_Owf(_1528988, _1528990))], (32379 ^ _779142) ^ [_1368991, _1368993, _1368995] : [class_Groups_Ocomm__monoid__add(_1368991), class_Groups_Ocomm__monoid__mult(_1368991), c_Nat__Transfer_Onat__set(_1368993), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1368991), _1368995), _1368993) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368991), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1368991, tc_Nat_Onat), _1368995), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1368993)))], (16349 ^ _779142) ^ [_1066657, _1066659, _1066661, _1066663] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1066657, _1066659)), c_Nitpick_Opair__box_OPairBox(_1066657, _1066659, _1066661, _1066663)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48278 ^ _779142) ^ [_1752628, _1752630, _1752632, _1752634] : [-(hBOOL(hAPP(_1752628, _1752630))), -(hAPP(c_List_Ofilter(_1752632, _1752628), c_List_Oreplicate(_1752632, _1752634, _1752630)) = c_List_Olist_ONil(_1752632))], (47199 ^ _779142) ^ [_1728578, _1728580, _1728582] : [-(hAPP(c_List_Oset(_1728578), c_List_Oinsert(_1728578, _1728580, _1728582)) = hAPP(hAPP(c_Set_Oinsert(_1728578), _1728580), hAPP(c_List_Oset(_1728578), _1728582)))], (15289 ^ _779142) ^ [_1046956, _1046958, _1046960, _1046962] : [class_Orderings_Olinorder(_1046956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046956), _1046958), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046956), _1046960), _1046962))), 15296 ^ _779142 : [(15299 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046956), _1046958), _1046962)))], (15297 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1046956), _1046958), _1046960)))]]], (42047 ^ _779142) ^ [_1614150, _1614152, _1614154] : [-(hBOOL(hAPP(hAPP(c_member(_1614150), _1614152), hAPP(c_List_Oset(_1614150), _1614154)))), 42048 ^ _779142 : [(42049 ^ _779142) ^ [_1614224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1614224), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614150)), _1614154))), hAPP(hAPP(c_List_Onth(_1614150), _1614154), _1614224) = _1614152]]], (15279 ^ _779142) ^ [_1046789, _1046791, _1046793, _1046795, _1046797, _1046799] : [-(c_Nitpick_Opair__box_OPairBox(_1046789, _1046791, _1046793, _1046795) = c_Nitpick_Opair__box_OPairBox(_1046789, _1046791, _1046797, _1046799)), _1046793 = _1046797, _1046795 = _1046799], (18696 ^ _779142) ^ [_1108220, _1108222, _1108224] : [class_Rings_Osemiring__1(_1108220), hBOOL(hAPP(hAPP(c_member(_1108220), _1108222), c_Nat_Osemiring__1__class_ONats(_1108220))), hBOOL(hAPP(hAPP(c_member(_1108220), _1108224), c_Nat_Osemiring__1__class_ONats(_1108220))), -(hBOOL(hAPP(hAPP(c_member(_1108220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108220), _1108222), _1108224)), c_Nat_Osemiring__1__class_ONats(_1108220))))], (4164 ^ _779142) ^ [_842164, _842166] : [_842166 = _842164, -(c_List_Otake(_842166) = c_List_Otake(_842164))], (38306 ^ _779142) ^ [_1516470, _1516472, _1516474, _1516476, _1516478, _1516480, _1516482] : [-(hAPP(c_Product__Type_Ofst(_1516470, _1516472), hAPP(c_Product__Type_Omap__pair(_1516474, _1516470, _1516476, _1516472, _1516478, _1516480), _1516482)) = hAPP(_1516478, hAPP(c_Product__Type_Ofst(_1516474, _1516476), _1516482)))], (8741 ^ _779142) ^ [_926194, _926196, _926198, _926200, _926202] : [class_Groups_Oordered__cancel__ab__semigroup__add(_926194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926194), _926196), _926198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926194), _926200), _926202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926194), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926194), _926196), _926200)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926194), _926198), _926202))))], (42744 ^ _779142) ^ [_1630922, _1630924, _1630926] : [-(hAPP(hAPP(c_List_Olist__update(_1630922, c_List_Olist_ONil(_1630922)), _1630924), _1630926) = c_List_Olist_ONil(_1630922))], (18214 ^ _779142) ^ [_1099733, _1099735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099733), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099733)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099735)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099735))], (274 ^ _779142) ^ [_783357, _783359, _783361, _783363] : [-(c_Nitpick_Orefl_H(_783361, _783357)), c_Nitpick_Orefl_H(_783363, _783359), _783363 = _783361, _783359 = _783357], (48462 ^ _779142) ^ [_1756391, _1756393, _1756395, _1756397, _1756399] : [48464 ^ _779142 : [(48467 ^ _779142) ^ [] : [c_Relation_Orefl__on(_1756395, hAPP(_1756397, 48463 ^ [_1756391, _1756393, _1756395, _1756397, _1756399]), hAPP(_1756399, 48463 ^ [_1756391, _1756393, _1756395, _1756397, _1756399]))], (48465 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756391), 48463 ^ [_1756391, _1756393, _1756395, _1756397, _1756399]), _1756393)))]], -(c_Relation_Orefl__on(_1756395, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756391, tc_fun(_1756395, tc_HOL_Obool)), _1756393), _1756397), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756391, tc_fun(tc_prod(_1756395, _1756395), tc_HOL_Obool)), _1756393), _1756399)))], (30902 ^ _779142) ^ [_1332828, _1332830, _1332832] : [class_Lattices_Obounded__lattice__top(_1332828), 30905 ^ _779142 : [(30914 ^ _779142) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332828), _1332830), _1332832) = c_Orderings_Otop__class_Otop(_1332828)), _1332830 = c_Orderings_Otop__class_Otop(_1332828), _1332832 = c_Orderings_Otop__class_Otop(_1332828)], (30906 ^ _779142) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332828), _1332830), _1332832) = c_Orderings_Otop__class_Otop(_1332828), 30909 ^ _779142 : [(30912 ^ _779142) ^ [] : [-(_1332832 = c_Orderings_Otop__class_Otop(_1332828))], (30910 ^ _779142) ^ [] : [-(_1332830 = c_Orderings_Otop__class_Otop(_1332828))]]]]], (35994 ^ _779142) ^ [_1455075, _1455077] : [-(c_Equiv__Relations_Oequivp(_1455075, _1455077)), 35999 ^ _779142 : [(36002 ^ _779142) ^ [] : [hAPP(_1455077, 35995 ^ [_1455075, _1455077]) = hAPP(_1455077, 35996 ^ [_1455075, _1455077])], (36000 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(_1455077, 35995 ^ [_1455075, _1455077]), 35996 ^ [_1455075, _1455077])))]], 36003 ^ _779142 : [(36006 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(_1455077, 35995 ^ [_1455075, _1455077]), 35996 ^ [_1455075, _1455077]))], (36004 ^ _779142) ^ [] : [-(hAPP(_1455077, 35995 ^ [_1455075, _1455077]) = hAPP(_1455077, 35996 ^ [_1455075, _1455077]))]]], (44163 ^ _779142) ^ [_1662755, _1662757] : [-(_1662755 = c_List_Olist_ONil(_1662757)), -(c_List_Olast(_1662757, _1662755) = hAPP(hAPP(c_List_Onth(_1662757), _1662755), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662757)), _1662755)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33553 ^ _779142) ^ [_1393167, _1393169] : [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), _1393167), _1393169))), 33556 ^ _779142 : [(33565 ^ _779142) ^ [] : [-(c_Divides_OposDivAlg(_1393167, _1393169) = hAPP(c_Divides_Oadjust(_1393169), c_Divides_OposDivAlg(_1393167, 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)))), _1393169)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393167), _1393169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393169), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33557 ^ _779142) ^ [] : [33558 ^ _779142 : [(33561 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1393169), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33559 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393167), _1393169))]], -(c_Divides_OposDivAlg(_1393167, _1393169) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393167))]]], (47276 ^ _779142) ^ [_1730670, _1730672, _1730674, _1730676, _1730678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730670, _1730672)), hAPP(_1730670, _1730674))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730676, _1730676)), hAPP(hAPP(c_Product__Type_OPair(_1730676, _1730676), _1730672), _1730674)), c_List_Omeasures(_1730676, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730676, tc_Nat_Onat)), _1730670), _1730678)))))], (14891 ^ _779142) ^ [_1039463, _1039465] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039463), _1039465)), 14897 ^ _779142 : [(14900 ^ _779142) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14898 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039463), 14896 ^ [_1039463, _1039465]), _1039465)))]], -(hAPP(c_Finite__Set_Ocard(_1039463), _1039465) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14177 ^ _779142) ^ [_1026226, _1026228, _1026230, _1026232] : [class_Fields_Ofield__inverse__zero(_1026226), -(_1026228 = c_Groups_Ozero__class_Ozero(_1026226)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026226), _1026230), _1026228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026226), _1026232), _1026228)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026226), _1026230), _1026232))], (31252 ^ _779142) ^ [_1339377, _1339379] : [class_Complete__Lattice_Ocomplete__lattice(_1339377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339377), _1339379)), -(c_Complete__Lattice_OInf__class_OInf(_1339377, _1339379) = hAPP(hAPP(c_Finite__Set_Ofold(_1339377, _1339377, c_Lattices_Osemilattice__inf__class_Oinf(_1339377)), c_Orderings_Otop__class_Otop(_1339377)), _1339379))], (2182 ^ _779142) ^ [_810915, _810917, _810919, _810921, _810923, _810925, _810927, _810929] : [-(c_Sum__Type_OPlus(_810929, _810925, _810921, _810917) = c_Sum__Type_OPlus(_810927, _810923, _810919, _810915)), _810929 = _810927, _810925 = _810923, _810921 = _810919, _810917 = _810915], (35087 ^ _779142) ^ [_1431616, _1431618, _1431620] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431616, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1431618)), _1431620) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431616, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431616, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1431618)), _1431620)), hAPP(_1431620, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45516 ^ _779142) ^ [_1692410] : [-(c_List_Oconcat(_1692410, c_List_Olist_ONil(tc_List_Olist(_1692410))) = c_List_Olist_ONil(_1692410))], (15301 ^ _779142) ^ [_1047179, _1047181, _1047183, _1047185, _1047187] : [class_Orderings_Olinorder(_1047179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047179), _1047181), _1047183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047179), _1047185), _1047187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047179), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047179), _1047181), _1047185)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047179), _1047183), _1047187))))], (39558 ^ _779142) ^ [_1548917, _1548919, _1548921, _1548923, _1548925, _1548927, _1548929, _1548931, _1548933, _1548935] : [-(c_Product__Type_Omap__pair(_1548917, _1548919, _1548921, _1548923, hAPP(c_Fun_Ocomp(_1548925, _1548919, _1548917, _1548927), _1548929), hAPP(c_Fun_Ocomp(_1548931, _1548923, _1548921, _1548933), _1548935)) = hAPP(c_Fun_Ocomp(tc_prod(_1548925, _1548931), tc_prod(_1548919, _1548923), tc_prod(_1548917, _1548921), c_Product__Type_Omap__pair(_1548925, _1548919, _1548931, _1548923, _1548927, _1548933)), c_Product__Type_Omap__pair(_1548917, _1548925, _1548921, _1548931, _1548929, _1548935)))], (41266 ^ _779142) ^ [_1591784, _1591786, _1591788] : [-(c_Nitpick_Otimes__frac(_1591784, _1591786, _1591788) = hAPP(hAPP(c_Nitpick_Ofrac(_1591784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591784), _1591786)), hAPP(c_Nitpick_Onum(_1591784), _1591788))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1591784), _1591786)), hAPP(c_Nitpick_Odenom(_1591784), _1591788))))], (46389 ^ _779142) ^ [_1711613, _1711615, _1711617] : [class_Orderings_Olinorder(_1711613), 46392 ^ _779142 : [(46405 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711613, hAPP(hAPP(c_List_Olist_OCons(_1711613), _1711615), _1711617))), 46409 ^ _779142 : [(46412 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711613), _1711615), 46408 ^ [_1711613, _1711615, _1711617]))], (46410 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711613), 46408 ^ [_1711613, _1711615, _1711617]), hAPP(c_List_Oset(_1711613), _1711617))))]], c_List_Olinorder__class_Osorted(_1711613, _1711617)], (46393 ^ _779142) ^ [] : [c_List_Olinorder__class_Osorted(_1711613, hAPP(hAPP(c_List_Olist_OCons(_1711613), _1711615), _1711617)), 46396 ^ _779142 : [(46397 ^ _779142) ^ [_1711781] : [hBOOL(hAPP(hAPP(c_member(_1711613), _1711781), hAPP(c_List_Oset(_1711613), _1711617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711613), _1711615), _1711781)))], (46403 ^ _779142) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711613, _1711617))]]]]], (26864 ^ _779142) ^ [_1252633, _1252635, _1252637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252633, tc_HOL_Obool)), _1252635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252633, tc_HOL_Obool)), _1252637), _1252635))))], (8372 ^ _779142) ^ [_918723, _918725, _918727, _918729, _918731] : [class_Groups_Oab__semigroup__mult(_918723), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_918723, _918723, c_Groups_Otimes__class_Otimes(_918723), _918725, _918727), _918729)), -(hBOOL(hAPP(hAPP(c_member(_918723), _918725), _918727))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_918723, _918723, c_Groups_Otimes__class_Otimes(_918723), _918731, hAPP(hAPP(c_Set_Oinsert(_918723), _918725), _918727)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918723), _918731), _918729))))], (23265 ^ _779142) ^ [_1189079] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1189079)) = _1189079)], (11314 ^ _779142) ^ [_973561, _973563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973561)), _973563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973561), _973563)))], (45744 ^ _779142) ^ [_1698148, _1698150, _1698152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698148), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698150))), c_List_Otranspose(_1698150, _1698152)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1698150)), c_List_Otranspose(_1698150, _1698152)), _1698148) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698150), _1698150), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698150), tc_Nat_Onat, _1698150), c_List_Onth(_1698150)), _1698148)), hAPP(c_List_Ofilter(tc_List_Olist(_1698150), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1698150)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698148)), c_Nat_Osize__class_Osize(tc_List_Olist(_1698150)))), _1698152)))], (6490 ^ _779142) ^ [_883126, _883128, _883130, _883132, _883134, _883136, _883138, _883140] : [c_Finite__Set_Ofolding__image__simple__idem(_883126, _883128, _883130, _883132, _883134, _883136), hBOOL(hAPP(c_Finite__Set_Ofinite(_883128), _883138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883128, tc_HOL_Obool)), _883140), _883138)), -(hAPP(hAPP(_883130, hAPP(_883136, _883140)), hAPP(_883136, _883138)) = hAPP(_883136, _883138))], (41755 ^ _779142) ^ [_1606743, _1606745, _1606747] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606743)), _1606745), c_Wellfounded_Oacc(tc_List_Olist(_1606743), c_List_Olistrel1(_1606743, _1606747)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606743)), _1606745), c_List_Olists(_1606743, c_Wellfounded_Oacc(_1606743, _1606747)))))], (43742 ^ _779142) ^ [_1654034, _1654036, _1654038] : [-(hAPP(c_List_Otl(_1654034), hAPP(hAPP(c_List_Odrop(_1654034), _1654036), _1654038)) = hAPP(hAPP(c_List_Odrop(_1654034), _1654036), hAPP(c_List_Otl(_1654034), _1654038)))], (25478 ^ _779142) ^ [_1226930, _1226932] : [c_Int_OBit1(_1226930) = c_Int_OBit0(_1226932)], (19719 ^ _779142) ^ [_1125645, _1125647, _1125649] : [class_Groups_Oordered__ab__group__add__abs(_1125645), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125645), hAPP(c_Groups_Oabs__class_Oabs(_1125645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125645), _1125647), _1125649))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125645), hAPP(c_Groups_Oabs__class_Oabs(_1125645), _1125647)), hAPP(c_Groups_Oabs__class_Oabs(_1125645), _1125649)))))], (8032 ^ _779142) ^ [_911560] : [-(c_Finite__Set_Ofun__left__comm__idem(_911560, tc_fun(_911560, tc_HOL_Obool), c_Set_Oinsert(_911560)))], (20113 ^ _779142) ^ [_1132198, _1132200, _1132202, _1132204] : [class_Divides_Osemiring__div(_1132198), -(_1132200 = c_Groups_Ozero__class_Ozero(_1132198)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132198), _1132202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132198), _1132200), _1132204))), _1132200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132198), _1132204), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132198), _1132202), _1132200)))], (21836 ^ _779142) ^ [_1162872, _1162874] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162872)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162872)), _1162874) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162872)), _1162874)))], (52639 ^ _779142) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (10521 ^ _779142) ^ [_961238, _961240] : [_961238 = _961240, -(hAPP(c_Nat_OSuc, _961238) = hAPP(c_Nat_OSuc, _961240))], (40107 ^ _779142) ^ [_1561910, _1561912, _1561914, _1561916, _1561918, _1561920, _1561922] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561910, _1561912, _1561914, _1561916), _1561918), _1561920), _1561922) = hAPP(hAPP(_1561920, hAPP(c_Product__Type_Ofst(_1561912, _1561914), hAPP(_1561918, _1561922))), hAPP(c_Product__Type_Osnd(_1561912, _1561914), hAPP(_1561918, _1561922))))], (17677 ^ _779142) ^ [_1090540, _1090542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090540)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1090542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090540), _1090542)))], (48162 ^ _779142) ^ [_1750470, _1750472, _1750474, _1750476] : [-(hAPP(hAPP(c_List_Omap(_1750470, _1750472), hAPP(c_COMBK(_1750472, _1750470), _1750474)), _1750476) = c_List_Oreplicate(_1750472, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750470)), _1750476), _1750474))], (50571 ^ _779142) ^ [_1803619] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1803619)))], (27182 ^ _779142) ^ [_1258834, _1258836, _1258838] : [class_Orderings_Olinorder(_1258834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258834, tc_HOL_Obool)), _1258836), _1258838)), -(_1258836 = c_Orderings_Obot__class_Obot(tc_fun(_1258834, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258834), _1258838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258834), c_Big__Operators_Olinorder__class_OMax(_1258834, _1258836)), c_Big__Operators_Olinorder__class_OMax(_1258834, _1258838))))], (27726 ^ _779142) ^ [_1268615] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1268615) = _1268615)], (31711 ^ _779142) ^ [_1348359] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1348359)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1348359)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3148 ^ _779142) ^ [_825920, _825922, _825924, _825926, _825928, _825930] : [-(c_Big__Operators_Olattice_OSup__fin(_825930, _825926, _825922) = c_Big__Operators_Olattice_OSup__fin(_825928, _825924, _825920)), _825930 = _825928, _825926 = _825924, _825922 = _825920], (23205 ^ _779142) ^ [_1187756] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187756)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187756)))], (43794 ^ _779142) ^ [_1655076, _1655078, _1655080] : [-(_1655076 = c_List_Olist_ONil(_1655078)), -(hAPP(c_List_Otl(_1655078), hAPP(hAPP(c_List_Oappend(_1655078), _1655076), _1655080)) = hAPP(hAPP(c_List_Oappend(_1655078), hAPP(c_List_Otl(_1655078), _1655076)), _1655080))], (37094 ^ _779142) ^ [_1478898, _1478900] : [-(c_Nitpick_Onumber__of__frac(_1478898, _1478900) = c_Nitpick_OAbs__Frac(_1478898, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478900), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37241 ^ _779142) ^ [_1482495, _1482497, _1482499, _1482501] : [-(hAPP(c_Set_Ovimage(_1482495, _1482497, _1482499), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482497, tc_HOL_Obool), _1482501)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1482497, tc_HOL_Obool), tc_fun(_1482495, tc_HOL_Obool)), _1482501), c_Set_Ovimage(_1482495, _1482497, _1482499)))], (28286 ^ _779142) ^ [_1278947, _1278949, _1278951] : [class_Orderings_Olinorder(_1278947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278947), _1278949)), -(hBOOL(hAPP(hAPP(c_member(_1278947), _1278951), _1278949))), -(_1278949 = c_Orderings_Obot__class_Obot(tc_fun(_1278947, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1278947, hAPP(hAPP(c_Set_Oinsert(_1278947), _1278951), _1278949)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278947), _1278951), c_Big__Operators_Olinorder__class_OMax(_1278947, _1278949)))], (44734 ^ _779142) ^ [_1675250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1675250)), _1675250 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17738 ^ _779142) ^ [_1091681, _1091683, _1091685] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091681)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1091683)), _1091685)) = 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), _1091681), _1091683))), _1091685))], (50997 ^ _779142) ^ [_1811471, _1811473] : [50998 ^ _779142 : [(51001 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811473), _1811471))], (50999 ^ _779142) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811471), _1811473)))]], -(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)))), _1811471, _1811473))], (47264 ^ _779142) ^ [_1730347, _1730349, _1730351, _1730353, _1730355] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730347, _1730347)), hAPP(hAPP(c_Product__Type_OPair(_1730347, _1730347), _1730349), _1730351)), c_List_Omeasures(_1730347, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730347, tc_Nat_Onat)), _1730353), _1730355))))), 47265 ^ _779142 : [(47268 ^ _779142) ^ [] : [hAPP(_1730353, _1730349) = hAPP(_1730353, _1730351), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730347, _1730347)), hAPP(hAPP(c_Product__Type_OPair(_1730347, _1730347), _1730349), _1730351)), c_List_Omeasures(_1730347, _1730355)))], (47266 ^ _779142) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730353, _1730349)), hAPP(_1730353, _1730351)))]]], (26534 ^ _779142) ^ [_1245841, _1245843, _1245845, _1245847] : [class_Lattices_Osemilattice__sup(_1245841), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245841), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245841), _1245843), _1245845)), _1245847) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245841), _1245843), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1245841), _1245845), _1245847)))], (6914 ^ _779142) ^ [_892264, _892266, _892268, _892270] : [hBOOL(hAPP(hAPP(c_member(_892264), _892266), _892268)), -(hBOOL(hAPP(hAPP(c_member(_892264), _892266), _892270))), -(hBOOL(hAPP(hAPP(c_member(_892264), _892266), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892264, tc_HOL_Obool)), _892268), _892270))))], (49568 ^ _779142) ^ [_1780612, _1780614, _1780616] : [c_Fun_Oinj__on(_1780612, _1780614, _1780616, c_Orderings_Otop__class_Otop(tc_fun(_1780612, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780614, _1780612, _1780612, c_Hilbert__Choice_Oinv__into(_1780612, _1780614, c_Orderings_Otop__class_Otop(tc_fun(_1780612, tc_HOL_Obool)), _1780616)), _1780616) = c_Fun_Oid(_1780612))], (43844 ^ _779142) ^ [_1656081, _1656083, _1656085, _1656087] : [43845 ^ _779142 : [(43846 ^ _779142) ^ [_1656178, _1656180] : [_1656081 = hAPP(hAPP(c_List_Olist_OCons(_1656083), _1656180), _1656178)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656083), tc_List_Olist(_1656083))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656083), tc_List_Olist(_1656083)), _1656085), hAPP(hAPP(c_List_Oappend(_1656083), _1656085), _1656081))), c_List_Olexord(_1656083, _1656087))))], (6313 ^ _779142) ^ [_880321, _880323, _880325] : [class_Orderings_Oorder(_880321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880321), _880323), _880325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880321), _880325), _880323)), -(_880323 = _880325)], (39750 ^ _779142) ^ [_1553447, _1553449, _1553451, _1553453, _1553455, _1553457, _1553459] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1553447, _1553449, _1553451), hAPP(c_Fun_Ocomp(_1553453, tc_fun(_1553449, _1553451), _1553447, _1553455), _1553457)), _1553459) = hAPP(hAPP(_1553455, hAPP(_1553457, hAPP(c_Product__Type_Ofst(_1553447, _1553449), _1553459))), hAPP(c_Product__Type_Osnd(_1553447, _1553449), _1553459)))], (23889 ^ _779142) ^ [_1199764] : [-(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, _1199764))))))]], input).
% 95.01/91.71  ncf('1',plain,[v_P(hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))],start(52793 ^ 0)).
% 95.01/91.71  ncf('1.1',plain,[-(v_P(hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],extension(6073 ^ 1,bind([[_876067, _876069], [hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 95.01/91.71  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],extension(6637 ^ 2,bind([[_886141, _886143, _886145, _886147], [t_a, hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 95.01/91.71  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U))],extension(5934 ^ 3,bind([[_873273, _873275, _873277, _873279, _873281], [tc_Com_Opname, v_pn, v_U, t_a, v_mgt__call]]))).
% 95.01/91.71  ncf('1.1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))],extension(52791 ^ 4)).
% 95.01/91.71  ncf('1.1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))],extension(6199 ^ 3,bind([[_878384, _878386], [t_a, hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 95.01/91.71  %-----------------------------------------------------
% 95.01/91.71  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------