TSTP Solution File: SWW318+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW318+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:56 EDT 2023

% Result   : Theorem 48.55s 47.22s
% Output   : Proof 48.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW318+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.14  % Command  : nanocop.sh %s %d
% 0.15/0.35  % Computer : n014.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 22:31:57 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 48.55/47.22  
% 48.55/47.22  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 48.55/47.22  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.55/47.22  %-----------------------------------------------------
% 48.55/47.22  ncf(matrix, plain, [(51952 ^ _2066607) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))], !, (51646 ^ _773908) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (15049 ^ _773908) ^ [_1028857, _1028859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028859)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1028857), hAPP(c_Int_Onat, _1028859)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028857, _1028859)))], (26637 ^ _773908) ^ [_1252046, _1252048, _1252050, _1252052, _1252054] : [c_Hoare__Mirabelle_Ohoare__derivs(_1252046, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1252046), tc_HOL_Obool)), _1252048), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1252046), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), hAPP(hAPP(c_COMBB(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1252046)), _1252050)), c_Com_Ocom_OBODY)), _1252052)), _1252054)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1252046), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), hAPP(hAPP(c_COMBB(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1252046)), _1252050)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1252052)), _1252054)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1252046, _1252048, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1252046), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), hAPP(hAPP(c_COMBB(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1252046, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1252046))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1252046)), _1252050)), c_Com_Ocom_OBODY)), _1252052)), _1252054)))], (42405 ^ _773908) ^ [_1614251, _1614253, _1614255, _1614257, _1614259] : [_1614251 = c_Orderings_Obot__class_Obot(tc_fun(_1614253, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614253, tc_fun(_1614255, tc_HOL_Obool)), _1614251), hAPP(hAPP(c_COMBC(_1614253, tc_fun(_1614255, tc_HOL_Obool), tc_fun(_1614255, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614255, tc_HOL_Obool), tc_fun(tc_fun(_1614255, tc_HOL_Obool), tc_fun(_1614255, tc_HOL_Obool)), _1614253), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614255, tc_HOL_Obool))), _1614257)), _1614259)) = c_Orderings_Otop__class_Otop(tc_fun(_1614255, tc_HOL_Obool)))], (38096 ^ _773908) ^ [_1498430, _1498432, _1498434] : [-(hBOOL(hAPP(_1498430, _1498432))), -(hAPP(c_Set_OCollect(_1498434), hAPP(hAPP(c_COMBS(_1498434, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498434), c_fconj), hAPP(hAPP(c_COMBC(_1498434, _1498434, tc_HOL_Obool), c_fequal), _1498432))), _1498430)) = c_Orderings_Obot__class_Obot(tc_fun(_1498434, tc_HOL_Obool)))], (25601 ^ _773908) ^ [_1227316, _1227318, _1227320, _1227322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227316), _1227318)), -(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), _1227316), _1227320)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1227318), _1227322))), c_FunDef_Opair__leq)))], (51496 ^ _773908) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (40595 ^ _773908) ^ [_1569617, _1569619, _1569621] : [-(hAPP(hAPP(c_List_Ozip(_1569617, _1569619), c_List_Olist_ONil(_1569617)), _1569621) = c_List_Olist_ONil(tc_prod(_1569617, _1569619)))], (10041 ^ _773908) ^ [_940878] : [class_Rings_Oring__1(_940878), -(hAPP(c_Int_Oring__1__class_Oof__int(_940878), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_940878))], (7853 ^ _773908) ^ [_902168, _902170, _902172, _902174, _902176, _902178, _902180] : [c_Hoare__Mirabelle_Ohoare__derivs(_902168, _902170, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_902168)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_902168), c_Hoare__Mirabelle_Opeek__and(_902168, _902172, _902174)), _902176), _902178)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_902168), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_902168, _902170, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_902168)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_902168), c_Hoare__Mirabelle_Opeek__and(_902168, _902172, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _902174))), _902180), _902178)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_902168), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_902168, _902170, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_902168)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_902168), _902172), c_Com_Ocom_OCond(_902174, _902176, _902180)), _902178)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_902168), tc_HOL_Obool)))))], (19493 ^ _773908) ^ [_1110369] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1110369)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110369))))], (33272 ^ _773908) ^ [_1391954, _1391956] : [-(c_Fun_Oinj__on(_1391954, _1391954, c_COMBI(_1391954), _1391956))], (17237 ^ _773908) ^ [_1071348, _1071350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071348)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071348), _1071350)))], (3514 ^ _773908) ^ [_826775, _826777, _826779, _826781, _826783, _826785, _826787, _826789, _826791, _826793] : [-(c_List_Ofoldr(_826793, _826789, _826785, _826781, _826777) = c_List_Ofoldr(_826791, _826787, _826783, _826779, _826775)), _826793 = _826791, _826789 = _826787, _826785 = _826783, _826781 = _826779, _826777 = _826775], (32930 ^ _773908) ^ [_1385423, _1385425, _1385427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385423)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1385425), _1385427)), 32937 ^ _773908 : [(32938 ^ _773908) ^ [_1385613] : [32940 ^ _773908 : [(32946 ^ _773908) ^ [] : [-(_1385613 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32942 ^ [_1385423, _1385425, _1385427, _1385613]), 32939 ^ [_1385423, _1385425, _1385427, _1385613]))], (32944 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32942 ^ [_1385423, _1385425, _1385427, _1385613]), _1385427)))], (32941 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32939 ^ [_1385423, _1385425, _1385427, _1385613]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1385423))))]], -(_1385613 = _1385425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385613), _1385423) = _1385425]]], (38697 ^ _773908) ^ [_1521557, _1521559, _1521561, _1521563] : [c_Wellfounded_Owf(_1521557, _1521559), c_Wellfounded_Owf(_1521561, _1521563), -(c_Wellfounded_Owf(tc_prod(_1521557, _1521561), c_Wellfounded_Olex__prod(_1521557, _1521561, _1521559, _1521563)))], (9718 ^ _773908) ^ [_935808, _935810] : [-(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), _935808))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935810))))], (20181 ^ _773908) ^ [_1122225, _1122227] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1122225)), c_Int_OBit1(_1122227)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1122225)), _1122227)))], (2830 ^ _773908) ^ [_816003, _816005, _816007, _816009, _816011, _816013, _816015, _816017] : [-(c_Nitpick_Oprod(_816017, _816013, _816009, _816005) = c_Nitpick_Oprod(_816015, _816011, _816007, _816003)), _816017 = _816015, _816013 = _816011, _816009 = _816007, _816005 = _816003], (6652 ^ _773908) ^ [_881964, _881966, _881968] : [class_Orderings_Oorder(_881964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881964), _881966), _881968)), _881968 = _881966], (51121 ^ _773908) ^ [_1808623, _1808625, _1808627, _1808629, _1808631, _1808633] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1808623, _1808625, _1808627, _1808629), _1808631), _1808633) = hAPP(_1808629, hAPP(hAPP(c_Product__Type_OPair(_1808623, _1808625), _1808631), _1808633)))], (31729 ^ _773908) ^ [_1359244, _1359246, _1359248, _1359250, _1359252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359244, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359246, tc_fun(_1359244, tc_HOL_Obool)), _1359248), _1359250)), _1359252)), 31732 ^ _773908 : [(31733 ^ _773908) ^ [_1359377] : [hBOOL(hAPP(hAPP(c_member(_1359246), _1359377), _1359248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359244, tc_HOL_Obool)), hAPP(_1359250, _1359377)), _1359252)))]]], (6266 ^ _773908) ^ [_875547, _875549] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_875547, _875549)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26723 ^ _773908) ^ [_1254623, _1254625] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1254623), _1254625)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254623)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254625))))], (42357 ^ _773908) ^ [_1613114, _1613116, _1613118, _1613120, _1613122, _1613124] : [-(hBOOL(hAPP(hAPP(c_member(_1613114), _1613116), hAPP(c_List_Oset(_1613114), _1613118)))), -(hAPP(hAPP(c_List_Omap(_1613114, _1613120), c_Fun_Ofun__upd(_1613114, _1613120, _1613122, _1613116, _1613124)), _1613118) = hAPP(hAPP(c_List_Omap(_1613114, _1613120), _1613122), _1613118))], (12580 ^ _773908) ^ [_984764, _984766, _984768, _984770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984764, tc_HOL_Obool)), _984766), _984768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984764, tc_HOL_Obool)), _984766), hAPP(hAPP(c_Set_Oinsert(_984764), _984770), _984768))))], (18305 ^ _773908) ^ [_1090001, _1090003, _1090005, _1090007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090001, tc_HOL_Obool)), _1090003), _1090005)), hBOOL(hAPP(hAPP(c_member(_1090001), _1090007), _1090003)), -(hBOOL(hAPP(hAPP(c_member(_1090001), _1090007), _1090005)))], (26870 ^ _773908) ^ [_1258015, _1258017] : [c_Nat__Transfer_Onat__set(_1258015), c_Nat__Transfer_Onat__set(_1258017), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258015), _1258017) = 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), _1258015)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258017))))], (22977 ^ _773908) ^ [_1172797, _1172799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172797), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172799)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172797)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172799))], (35104 ^ _773908) ^ [_1430477, _1430479, _1430481, _1430483, _1430485] : [class_Groups_Ocomm__monoid__add(_1430477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430479), _1430481)), hBOOL(hAPP(hAPP(c_member(_1430479), _1430483), _1430481)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430479, _1430477), _1430485), _1430481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430477), hAPP(_1430485, _1430483)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430479, _1430477), _1430485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430479, tc_HOL_Obool)), _1430481), hAPP(hAPP(c_Set_Oinsert(_1430479), _1430483), c_Orderings_Obot__class_Obot(tc_fun(_1430479, tc_HOL_Obool)))))))], (25551 ^ _773908) ^ [_1226313] : [class_Orderings_Olinorder(_1226313), -(c_Orderings_Oord_Omax(_1226313, hAPP(c_COMBC(_1226313, _1226313, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1226313))) = c_Orderings_Oord__class_Omin(_1226313))], (29071 ^ _773908) ^ [_1304608, _1304610, _1304612] : [class_Orderings_Olinorder(_1304608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304608), _1304610)), -(_1304610 = c_Orderings_Obot__class_Obot(tc_fun(_1304608, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1304608, hAPP(hAPP(c_Set_Oinsert(_1304608), _1304612), _1304610)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1304608), _1304612), c_Big__Operators_Olinorder__class_OMax(_1304608, _1304610)))], (37572 ^ _773908) ^ [_1485275, _1485277, _1485279, _1485281, _1485283, _1485285, _1485287, _1485289] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1485275, _1485277), tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485275, _1485277), _1485283), hAPP(c_COMBK(tc_fun(_1485277, tc_HOL_Obool), _1485275), _1485285))), hAPP(c_Product__Type_Oprod_Oprod__case(_1485275, _1485277, tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1485275, tc_fun(_1485277, tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool))), tc_fun(_1485277, tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool)), tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool)), tc_fun(tc_fun(_1485277, tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool))), tc_fun(_1485277, tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool))), _1485275), c_COMBB(tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool)), tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool), _1485277)), hAPP(hAPP(c_COMBB(tc_fun(_1485279, tc_HOL_Obool), tc_fun(tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool)), tc_fun(tc_prod(_1485279, _1485281), tc_HOL_Obool)), _1485275), c_Product__Type_OSigma(_1485279, _1485281)), _1485287))), hAPP(hAPP(c_COMBB(tc_fun(_1485281, tc_HOL_Obool), tc_fun(_1485279, tc_fun(_1485281, tc_HOL_Obool)), _1485277), c_COMBK(tc_fun(_1485281, tc_HOL_Obool), _1485279)), _1485289)))) = hAPP(hAPP(c_Product__Type_OSigma(_1485279, _1485281), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485275, tc_fun(_1485279, tc_HOL_Obool)), _1485283), _1485287)), hAPP(c_COMBK(tc_fun(_1485281, tc_HOL_Obool), _1485279), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485277, tc_fun(_1485281, tc_HOL_Obool)), _1485285), _1485289))))], (34 ^ _773908) ^ [_774361, _774363] : [-(class_Rings_Odivision__ring__inverse__zero(_774361)), _774363 = _774361, class_Rings_Odivision__ring__inverse__zero(_774363)], (23179 ^ _773908) ^ [_1177016, _1177018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1177016)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177018))), -(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(_1177018))), 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), _1177016)), c_Int_Onat))))))], (47667 ^ _773908) ^ [_1734078, _1734080, _1734082, _1734084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1734078, _1734078)), hAPP(hAPP(c_Product__Type_OPair(_1734078, _1734078), _1734080), _1734082)), c_Transitive__Closure_Otrancl(_1734078, _1734084))), 47671 ^ _773908 : [(47674 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734078, _1734078)), hAPP(hAPP(c_Product__Type_OPair(_1734078, _1734078), 47670 ^ [_1734078, _1734080, _1734082, _1734084]), _1734082)), _1734084)))], (47672 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734078, _1734078)), hAPP(hAPP(c_Product__Type_OPair(_1734078, _1734078), _1734080), 47670 ^ [_1734078, _1734080, _1734082, _1734084])), c_Transitive__Closure_Ortrancl(_1734078, _1734084))))]]], (6928 ^ _773908) ^ [_886089, _886091] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886089), _886091) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886091), _886089))], (2082 ^ _773908) ^ [_804133, _804135, _804137, _804139] : [-(c_Int_Onat__aux(_804139, _804135) = c_Int_Onat__aux(_804137, _804133)), _804139 = _804137, _804135 = _804133], (20413 ^ _773908) ^ [_1126166, _1126168] : [class_Rings_Oring__1__no__zero__divisors(_1126166), 20416 ^ _773908 : [(20417 ^ _773908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1126166), _1126168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1126166), -(_1126168 = c_Groups_Oone__class_Oone(_1126166)), -(_1126168 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126166), c_Groups_Oone__class_Oone(_1126166)))], (20427 ^ _773908) ^ [] : [20428 ^ _773908 : [(20431 ^ _773908) ^ [] : [_1126168 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126166), c_Groups_Oone__class_Oone(_1126166))], (20429 ^ _773908) ^ [] : [_1126168 = c_Groups_Oone__class_Oone(_1126166)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126166), _1126168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1126166))]]], (27013 ^ _773908) ^ [_1260135] : [c_Nat__Transfer_Onat__set(_1260135), -(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), _1260135)) = _1260135)], (49638 ^ _773908) ^ [_1775829, _1775831, _1775833] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1775829)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1775829, _1775831, _1775833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1775829)), _1775833)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51440 ^ _773908) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (8263 ^ _773908) ^ [_909963, _909965, _909967] : [class_Rings_Olinordered__semidom(_909963), 8266 ^ _773908 : [(8273 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909965), _909967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909963), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909963), _909965)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909963), _909967))))], (8267 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909963), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909963), _909965)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909963), _909967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909965), _909967)))]]], (41372 ^ _773908) ^ [_1589275, _1589277, _1589279] : [-(hAPP(c_List_Orotate(_1589275, _1589277), _1589279) = hAPP(hAPP(c_List_Oappend(_1589275), hAPP(hAPP(c_List_Odrop(_1589275), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1589277, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589275)), _1589279))), _1589279)), hAPP(hAPP(c_List_Otake(_1589275), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1589277, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589275)), _1589279))), _1589279)))], (42435 ^ _773908) ^ [_1615063, _1615065, _1615067, _1615069, _1615071] : [-(_1615063 = c_Orderings_Obot__class_Obot(tc_fun(_1615065, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615067, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615065, tc_fun(_1615067, tc_HOL_Obool)), _1615063), _1615069)), _1615071) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615065, tc_fun(_1615067, tc_HOL_Obool)), _1615063), hAPP(hAPP(c_COMBC(_1615065, tc_fun(_1615067, tc_HOL_Obool), tc_fun(_1615067, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615067, tc_HOL_Obool), tc_fun(tc_fun(_1615067, tc_HOL_Obool), tc_fun(_1615067, tc_HOL_Obool)), _1615065), c_Groups_Ominus__class_Ominus(tc_fun(_1615067, tc_HOL_Obool))), _1615069)), _1615071)))], (25671 ^ _773908) ^ [_1228678, _1228680, _1228682] : [-(c_Wellfounded_Omlex__prod(_1228678, _1228680, _1228682) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1228678), _1228678), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1228678, c_Wellfounded_Oless__than, _1228682)), hAPP(hAPP(c_COMBS(_1228678, _1228678, tc_prod(tc_Nat_Onat, _1228678)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1228678, tc_prod(tc_Nat_Onat, _1228678)), _1228678), c_Product__Type_OPair(tc_Nat_Onat, _1228678)), _1228680)), c_COMBI(_1228678))))], (18519 ^ _773908) ^ [_1093706, _1093708, _1093710, _1093712] : [-(hBOOL(hAPP(hAPP(c_member(_1093706), _1093708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093706, tc_HOL_Obool)), _1093710), _1093712)))), hBOOL(hAPP(hAPP(c_member(_1093706), _1093708), _1093710)), -(hBOOL(hAPP(hAPP(c_member(_1093706), _1093708), _1093712)))], (36412 ^ _773908) ^ [_1459457] : [-(c_Equiv__Relations_Oequivp(_1459457, c_fequal))], (24389 ^ _773908) ^ [_1201985, _1201987, _1201989] : [-(_1201985 = hAPP(hAPP(c_Product__Type_OPair(_1201987, _1201989), hAPP(c_Product__Type_Ofst(_1201987, _1201989), _1201985)), hAPP(c_Product__Type_Osnd(_1201987, _1201989), _1201985)))], (51402 ^ _773908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (10665 ^ _773908) ^ [_950751, _950753, _950755] : [class_Groups_Oordered__ab__group__add(_950751), 10668 ^ _773908 : [(10675 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950751), hAPP(c_Groups_Ouminus__class_Ouminus(_950751), _950755)), _950753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950751), hAPP(c_Groups_Ouminus__class_Ouminus(_950751), _950753)), _950755)))], (10669 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950751), hAPP(c_Groups_Ouminus__class_Ouminus(_950751), _950753)), _950755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950751), hAPP(c_Groups_Ouminus__class_Ouminus(_950751), _950755)), _950753)))]]], (27542 ^ _773908) ^ [_1271991, _1271993, _1271995, _1271997, _1271999, _1272001] : [c_Finite__Set_Ofolding(_1271991, _1271993, _1271995, _1271997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271991), _1271999)), -(hAPP(c_Fun_Ocomp(_1271993, _1271993, _1271993, hAPP(_1271995, _1272001)), hAPP(_1271997, _1271999)) = hAPP(c_Fun_Ocomp(_1271993, _1271993, _1271993, hAPP(_1271997, _1271999)), hAPP(_1271995, _1272001)))], (36271 ^ _773908) ^ [_1454803, _1454805, _1454807, _1454809, _1454811] : [c_Fun_Oinj__on(_1454803, _1454805, _1454807, c_Orderings_Otop__class_Otop(tc_fun(_1454803, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1454803, _1454805, _1454807), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454803, tc_HOL_Obool)), _1454809), _1454811)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454805, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1454803, _1454805, _1454807), _1454809)), hAPP(c_Set_Oimage(_1454803, _1454805, _1454807), _1454811)))], (12704 ^ _773908) ^ [_986733, _986735] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986733), _986735))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986733), _986735)), -(_986733 = _986735)], (6148 ^ _773908) ^ [_873562] : [hAPP(c_Nat_OSuc, _873562) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1684 ^ _773908) ^ [_797944, _797946] : [-(class_Rings_Oordered__semiring(_797944)), _797946 = _797944, class_Rings_Oordered__semiring(_797946)], (34854 ^ _773908) ^ [_1424891, _1424893, _1424895, _1424897, _1424899] : [class_Groups_Oab__group__add(_1424891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424893), _1424895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424893, tc_HOL_Obool)), _1424897), _1424895)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424893, _1424891), _1424899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1424893, tc_HOL_Obool)), _1424895), _1424897)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1424891), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424893, _1424891), _1424899), _1424895)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424893, _1424891), _1424899), _1424897)))], (44692 ^ _773908) ^ [_1667082, _1667084] : [44693 ^ _773908 : [(44696 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667084), _1667082))], (44694 ^ _773908) ^ [] : [_1667084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1667082, _1667084) = c_List_Olist_ONil(tc_Nat_Onat))], (26623 ^ _773908) ^ [_1251607, _1251609, _1251611] : [-(hAPP(c_Relation_OField(_1251607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1251607, _1251607), tc_HOL_Obool)), _1251609), _1251611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251607, tc_HOL_Obool)), hAPP(c_Relation_OField(_1251607), _1251609)), hAPP(c_Relation_OField(_1251607), _1251611)))], (21787 ^ _773908) ^ [_1150970, _1150972, _1150974, _1150976] : [class_Fields_Ofield(_1150970), -(_1150972 = c_Groups_Ozero__class_Ozero(_1150970)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150970), _1150974), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150970), _1150976), _1150972)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150970), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150970), _1150972), _1150974)), _1150976)), _1150972))], (13510 ^ _773908) ^ [_1000899, _1000901, _1000903] : [_1000901 = _1000903, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000899, tc_HOL_Obool)), _1000901) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000899, tc_HOL_Obool)), _1000903))], (24983 ^ _773908) ^ [_1214605, _1214607, _1214609] : [class_Orderings_Olinorder(_1214605), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214605), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214605), _1214607), _1214609)), _1214607)))], (10201 ^ _773908) ^ [_943394, _943396, _943398] : [class_Orderings_Opreorder(_943394), 10204 ^ _773908 : [(10213 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943394), _943396), _943398))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943394), _943396), _943398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943394), _943398), _943396)))], (10205 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943394), _943396), _943398)), 10208 ^ _773908 : [(10211 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943394), _943398), _943396))], (10209 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943394), _943396), _943398)))]]]]], (51830 ^ _773908) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (44979 ^ _773908) ^ [_1672891, _1672893, _1672895] : [class_Orderings_Olinorder(_1672891), c_List_Olinorder__class_Osorted(_1672891, _1672893), -(c_List_Olinorder__class_Osorted(_1672891, hAPP(hAPP(c_List_Odrop(_1672891), _1672895), _1672893)))], (38012 ^ _773908) ^ [_1496493, _1496495] : [-(hAPP(c_Set_OCollect(_1496493), _1496495) = _1496495)], (14649 ^ _773908) ^ [_1021609, _1021611, _1021613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021609), _1021611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021609), _1021613)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021611), _1021613))))], (41336 ^ _773908) ^ [_1588447, _1588449, _1588451] : [class_Lattices_Olattice(_1588447), -(c_Big__Operators_Olattice__class_OInf__fin(_1588447, hAPP(c_List_Oset(_1588447), hAPP(hAPP(c_List_Olist_OCons(_1588447), _1588449), _1588451))) = hAPP(c_List_Ofoldl(_1588447, _1588447, c_Lattices_Osemilattice__inf__class_Oinf(_1588447), _1588449), _1588451))], (5604 ^ _773908) ^ [_859610, _859612, _859614, _859616] : [-(c_COMBK(_859616, _859612) = c_COMBK(_859614, _859610)), _859616 = _859614, _859612 = _859610], (35034 ^ _773908) ^ [_1428889, _1428891, _1428893, _1428895] : [class_Groups_Ocomm__monoid__add(_1428889), 35037 ^ _773908 : [(35044 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1428891)), _1428893))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428889), _1428895), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1428893, hAPP(c_Nat_OSuc, _1428891))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428889), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428889), _1428895), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1428893, _1428891))), hAPP(_1428895, hAPP(c_Nat_OSuc, _1428891))))], (35038 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1428891)), _1428893)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428889), _1428895), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1428893, hAPP(c_Nat_OSuc, _1428891))) = c_Groups_Ozero__class_Ozero(_1428889))]]], (6364 ^ _773908) ^ [_877090, _877092, _877094, _877096] : [class_Groups_Ocancel__semigroup__add(_877090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877090), _877092), _877094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877090), _877092), _877096), -(_877094 = _877096)], (3184 ^ _773908) ^ [_821622, _821624, _821626, _821628] : [-(c_List_Olists(_821628, _821624) = c_List_Olists(_821626, _821622)), _821628 = _821626, _821624 = _821622], (38502 ^ _773908) ^ [_1514450, _1514452, _1514454, _1514456] : [c_Finite__Set_Ofolding(_1514450, _1514452, _1514454, _1514456), -(hAPP(_1514456, c_Orderings_Obot__class_Obot(tc_fun(_1514450, tc_HOL_Obool))) = c_Fun_Oid(_1514452))], (42557 ^ _773908) ^ [_1617931, _1617933, _1617935, _1617937, _1617939] : [42559 ^ _773908 : [(42562 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1617937, 42558 ^ [_1617931, _1617933, _1617935, _1617937, _1617939]), _1617939))], (42560 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617931), 42558 ^ [_1617931, _1617933, _1617935, _1617937, _1617939]), _1617935)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617931, tc_fun(_1617933, tc_HOL_Obool)), _1617935), _1617937), _1617939)))], (25955 ^ _773908) ^ [_1233780, _1233782, _1233784, _1233786] : [class_Lattices_Osemilattice__sup(_1233780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233780), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1233780), _1233782), _1233784)), _1233786)), 25962 ^ _773908 : [(25965 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233780), _1233784), _1233786)))], (25963 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233780), _1233782), _1233786)))]]], (46752 ^ _773908) ^ [_1710534, _1710536, _1710538, _1710540] : [46753 ^ _773908 : [(46756 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1710534, _1710534)), _1710536), c_Transitive__Closure_Ortrancl(_1710534, _1710540)))], (46754 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1710534, _1710534)), _1710536), c_Transitive__Closure_Ortrancl(_1710534, _1710538)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1710534, _1710534)), _1710536), c_Transitive__Closure_Ortrancl(_1710534, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1710534, _1710534), tc_HOL_Obool)), _1710538), _1710540)))))], (34812 ^ _773908) ^ [_1424030, _1424032, _1424034, _1424036, _1424038] : [class_Groups_Ocomm__monoid__add(_1424030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424032), _1424034)), -(hBOOL(hAPP(hAPP(c_member(_1424032), _1424036), _1424034))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424032, _1424030), _1424038), hAPP(hAPP(c_Set_Oinsert(_1424032), _1424036), _1424034)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424030), hAPP(_1424038, _1424036)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424032, _1424030), _1424038), _1424034)))], (12762 ^ _773908) ^ [_987782, _987784, _987786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987782), _987784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987784), _987786))))], (49336 ^ _773908) ^ [_1769357, _1769359] : [c_Wellfounded_Oacyclic(_1769357, hAPP(c_Set_OCollect(tc_prod(_1769357, _1769357)), hAPP(c_Product__Type_Oprod_Oprod__case(_1769357, _1769357, tc_HOL_Obool), _1769359))), -(c_Wellfounded_Oacyclic(_1769357, hAPP(c_Set_OCollect(tc_prod(_1769357, _1769357)), hAPP(c_Product__Type_Oprod_Oprod__case(_1769357, _1769357, tc_HOL_Obool), c_Predicate_Oconversep(_1769357, _1769357, _1769359)))))], (18351 ^ _773908) ^ [_1090791, _1090793, _1090795, _1090797] : [_1090791 = _1090793, 18354 ^ _773908 : [(18361 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1090795), _1090797), _1090793)), -(hBOOL(hAPP(hAPP(c_member(_1090795), _1090797), _1090791)))], (18355 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1090795), _1090797), _1090791)), -(hBOOL(hAPP(hAPP(c_member(_1090795), _1090797), _1090793)))]]], (28112 ^ _773908) ^ [_1283210, _1283212, _1283214, _1283216] : [class_Lattices_Olattice(_1283210), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283210), _1283212), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283210), _1283214), _1283216)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283210), _1283214), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283210), _1283212), _1283216)))], (46710 ^ _773908) ^ [_1709454, _1709456, _1709458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1709454, _1709454)), _1709456), _1709458)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1709454, _1709454)), _1709456), c_Transitive__Closure_Ortrancl(_1709454, _1709458))))], (49318 ^ _773908) ^ [_1768923, _1768925, _1768927] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768923)), c_List_Osplice(_1768923, _1768925, _1768927)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768923)), _1768925)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768923)), _1768927)))], (45551 ^ _773908) ^ [_1683783, _1683785] : [_1683785 = c_List_Olist_ONil(_1683783), -(c_List_Olist_ONil(_1683783) = hAPP(c_List_Orev(_1683783), _1683785))], (38482 ^ _773908) ^ [_1514112, _1514114, _1514116] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1514112)), _1514114) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1514112)), _1514116)), _1514114 = _1514116], (25655 ^ _773908) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (11175 ^ _773908) ^ [_959989, _959991, _959993, _959995] : [class_Rings_Oordered__semiring(_959989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959989), _959991), _959993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959989), c_Groups_Ozero__class_Ozero(_959989)), _959995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959989), _959991), _959995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959989), _959993), _959995))))], (37724 ^ _773908) ^ [_1490021, _1490023, _1490025, _1490027, _1490029, _1490031] : [-(c_Product__Type_Omap__pair(_1490021, _1490023, _1490025, _1490027, _1490029, _1490031) = hAPP(c_Product__Type_Oprod_Oprod__case(_1490021, _1490025, tc_prod(_1490023, _1490027)), hAPP(hAPP(c_COMBC(_1490021, tc_fun(_1490025, _1490027), tc_fun(_1490025, tc_prod(_1490023, _1490027))), hAPP(hAPP(c_COMBB(tc_fun(_1490027, tc_prod(_1490023, _1490027)), tc_fun(tc_fun(_1490025, _1490027), tc_fun(_1490025, tc_prod(_1490023, _1490027))), _1490021), c_COMBB(_1490027, tc_prod(_1490023, _1490027), _1490025)), hAPP(hAPP(c_COMBB(_1490023, tc_fun(_1490027, tc_prod(_1490023, _1490027)), _1490021), c_Product__Type_OPair(_1490023, _1490027)), _1490029))), _1490031)))], (6918 ^ _773908) ^ [_885882, _885884, _885886] : [_885884 = _885886, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885882), _885884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885882), _885886))], (49322 ^ _773908) ^ [_1769012, _1769014] : [-(c_List_Osplice(_1769012, _1769014, c_List_Olist_ONil(_1769012)) = _1769014)], (11614 ^ _773908) ^ [_967915] : [hBOOL(hAPP(_967915, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11615 ^ [_967915]))), 11618 ^ _773908 : [(11619 ^ _773908) ^ [_968015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _968015)), -(hBOOL(hAPP(_967915, _968015)))]]], (6548 ^ _773908) ^ [_880302, _880304, _880306, _880308] : [class_Orderings_Oorder(_880302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880302), _880304), _880306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880302), _880308), _880304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880302), _880308), _880306)))], (26245 ^ _773908) ^ [_1239989, _1239991, _1239993, _1239995] : [26246 ^ _773908 : [(26249 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1239989), _1239991), _1239995))], (26247 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1239989), _1239991), _1239993))]], -(hBOOL(hAPP(hAPP(c_member(_1239989), _1239991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239989, tc_HOL_Obool)), _1239993), _1239995))))], (26479 ^ _773908) ^ [_1248269, _1248271, _1248273, _1248275, _1248277, _1248279] : [-(hAPP(c_Set_Oimage(_1248269, _1248271, _1248273), hAPP(c_Set_Oimage(_1248275, _1248269, _1248277), _1248279)) = hAPP(c_Set_Oimage(_1248275, _1248271, hAPP(hAPP(c_COMBB(_1248269, _1248271, _1248275), _1248273), _1248277)), _1248279))], (38587 ^ _773908) ^ [_1517182, _1517184, _1517186, _1517188, _1517190, _1517192, _1517194] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517182, _1517184, _1517186), hAPP(hAPP(c_Relation_Orel__comp(_1517182, _1517188, _1517184), _1517190), _1517192)), _1517194) = hAPP(hAPP(c_Relation_Orel__comp(_1517182, _1517188, _1517186), _1517190), hAPP(hAPP(c_Relation_Orel__comp(_1517188, _1517184, _1517186), _1517192), _1517194)))], (47112 ^ _773908) ^ [_1719855, _1719857] : [-(hAPP(c_Relation_ORange(_1719855, _1719855), c_Transitive__Closure_Otrancl(_1719855, _1719857)) = hAPP(c_Relation_ORange(_1719855, _1719855), _1719857))], (20747 ^ _773908) ^ [_1132726, _1132728, _1132730, _1132732] : [class_Rings_Odivision__ring(_1132726), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132726), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132726), _1132728), _1132730)), _1132732) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132726), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132726), _1132728), _1132732)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132726), _1132730), _1132732)))], (19407 ^ _773908) ^ [_1108951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108951)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108951), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33206 ^ _773908) ^ [_1390822, _1390824, _1390826, _1390828, _1390830, _1390832] : [c_Fun_Oinj__on(_1390822, _1390824, hAPP(c_Fun_Ocomp(_1390826, _1390824, _1390822, _1390828), _1390830), _1390832), -(c_Fun_Oinj__on(_1390822, _1390826, _1390830, _1390832))], (40239 ^ _773908) ^ [_1560822, _1560824, _1560826, _1560828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1560822), _1560824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1560826, tc_HOL_Obool)), hAPP(c_List_Oset(_1560826), hAPP(hAPP(c_List_Odrop(_1560826), _1560824), _1560828))), hAPP(c_List_Oset(_1560826), hAPP(hAPP(c_List_Odrop(_1560826), _1560822), _1560828)))))], (40205 ^ _773908) ^ [_1560042, _1560044, _1560046] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1560042)), hAPP(hAPP(c_List_Odrop(_1560042), _1560044), _1560046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1560042)), _1560046)), _1560044))], (44682 ^ _773908) ^ [_1666980, _1666982] : [c_List_Oupt(_1666980, _1666982) = c_List_Olist_ONil(tc_Nat_Onat), -(_1666982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1666982), _1666980)))], (11535 ^ _773908) ^ [_966532, _966534] : [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), _966532), _966534))), 11538 ^ _773908 : [(11541 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966534)))], (11539 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966532)))]]], (28951 ^ _773908) ^ [_1302644, _1302646, _1302648] : [class_Lattices_Olattice(_1302644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302644), _1302646)), hBOOL(hAPP(hAPP(c_member(_1302644), _1302648), _1302646)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1302644), _1302648), c_Big__Operators_Olattice__class_OInf__fin(_1302644, _1302646)) = _1302648)], (34666 ^ _773908) ^ [_1420691, _1420693, _1420695, _1420697] : [class_Groups_Ocomm__monoid__add(_1420691), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420691), _1420693), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1420695), hAPP(c_Nat_OSuc, _1420697))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420691), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420691, tc_Nat_Onat), _1420693), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1420695, _1420697)))], (49660 ^ _773908) ^ [_1776229, _1776231, _1776233, _1776235, _1776237, _1776239] : [-(c_New__Random__Sequence_Opos__union(_1776229, _1776231, _1776233, _1776235, _1776237, _1776239) = c_New__DSequence_Opos__union(_1776229, hAPP(hAPP(hAPP(_1776231, _1776235), _1776237), _1776239), hAPP(hAPP(hAPP(_1776233, _1776235), _1776237), _1776239)))], (50997 ^ _773908) ^ [_1805691, _1805693, _1805695, _1805697, _1805699, _1805701, _1805703] : [c_Fun_Oinj__on(_1805691, _1805693, _1805695, hAPP(c_Set_Oimage(_1805697, _1805691, _1805699), _1805701)), c_Fun_Oinj__on(_1805697, _1805691, _1805699, _1805701), hBOOL(hAPP(hAPP(c_member(_1805693), _1805703), hAPP(c_Set_Oimage(_1805691, _1805693, _1805695), hAPP(c_Set_Oimage(_1805697, _1805691, _1805699), _1805701)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1805697, _1805693, _1805701, hAPP(c_Fun_Ocomp(_1805691, _1805693, _1805697, _1805695), _1805699)), _1805703) = hAPP(hAPP(c_Fun_Ocomp(_1805691, _1805697, _1805693, c_Hilbert__Choice_Oinv__into(_1805697, _1805691, _1805701, _1805699)), c_Hilbert__Choice_Oinv__into(_1805691, _1805693, hAPP(c_Set_Oimage(_1805697, _1805691, _1805699), _1805701), _1805695)), _1805703))], (23570 ^ _773908) ^ [_1185006, _1185008, _1185010, _1185012] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185006, _1185008), _1185010)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185006, _1185008), _1185012)), -(_1185010 = _1185012)], (29825 ^ _773908) ^ [_1318460, _1318462, _1318464, _1318466, _1318468] : [c_Finite__Set_Ofolding__idem(_1318460, _1318462, _1318464, _1318466), -(hAPP(c_Fun_Ocomp(_1318462, _1318462, _1318462, hAPP(_1318464, _1318468)), hAPP(_1318464, _1318468)) = hAPP(_1318464, _1318468))], (28136 ^ _773908) ^ [_1283746, _1283748, _1283750] : [class_Lattices_Osemilattice__inf(_1283746), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283746), _1283748), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283746), _1283748), _1283750)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283746), _1283748), _1283750))], (44317 ^ _773908) ^ [_1657470, _1657472, _1657474] : [-(hBOOL(hAPP(hAPP(c_member(_1657470), _1657472), hAPP(c_List_Oset(_1657470), _1657474)))), -(c_List_Oinsert(_1657470, _1657472, _1657474) = hAPP(hAPP(c_List_Olist_OCons(_1657470), _1657472), _1657474))], (42794 ^ _773908) ^ [_1622889, _1622891, _1622893, _1622895, _1622897] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1622889, _1622891, _1622889, _1622893), hAPP(c_Product__Type_OPair(_1622891, _1622889), _1622895)), _1622897) = hAPP(_1622897, _1622895))], (27324 ^ _773908) ^ [_1267267, _1267269, _1267271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267267, tc_HOL_Obool)), _1267269), _1267271)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267267), _1267271)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267267), _1267269)))], (25083 ^ _773908) ^ [_1216925, _1216927, _1216929, _1216931] : [class_Orderings_Olinorder(_1216925), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216925), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216925), _1216927), _1216929)), _1216931) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216925), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216925), _1216927), _1216931)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216925), _1216929), _1216931)))], (24191 ^ _773908) ^ [_1196942, _1196944, _1196946, _1196948] : [-(hAPP(c_Product__Type_Osnd(_1196942, _1196944), hAPP(hAPP(c_Product__Type_OPair(_1196942, _1196944), _1196946), _1196948)) = _1196948)], (12672 ^ _773908) ^ [_986236, _986238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986236), _986238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986236), _986238)))], (42187 ^ _773908) ^ [_1608789, _1608791, _1608793, _1608795] : [-(hAPP(c_Set_OPow(_1608789), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608791, tc_fun(_1608789, tc_HOL_Obool)), _1608793), _1608795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608791, tc_fun(tc_fun(_1608789, tc_HOL_Obool), tc_HOL_Obool)), _1608793), hAPP(hAPP(c_COMBB(tc_fun(_1608789, tc_HOL_Obool), tc_fun(tc_fun(_1608789, tc_HOL_Obool), tc_HOL_Obool), _1608791), c_Set_OPow(_1608789)), _1608795)))], (12678 ^ _773908) ^ [_986348, _986350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986348), _986350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986348), _986350))), -(_986348 = _986350)], (16495 ^ _773908) ^ [_1056844, _1056846, _1056848, _1056850] : [class_Rings_Ocomm__semiring__1(_1056844), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1056844), hAPP(hAPP(c_Power_Opower__class_Opower(_1056844), _1056846), _1056848)), _1056850) = hAPP(hAPP(c_Power_Opower__class_Opower(_1056844), _1056846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1056848), _1056850)))], (31598 ^ _773908) ^ [_1356355, _1356357, _1356359, _1356361, _1356363] : [class_Complete__Lattice_Ocomplete__lattice(_1356355), 31601 ^ _773908 : [(31602 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356355), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1356357, _1356355), _1356359), _1356361)), _1356363)), 31605 ^ _773908 : [(31606 ^ _773908) ^ [_1356536] : [hBOOL(hAPP(hAPP(c_member(_1356357), _1356536), _1356359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356355), hAPP(_1356361, _1356536)), _1356363)))]]], (31612 ^ _773908) ^ [] : [31614 ^ _773908 : [(31617 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356355), hAPP(_1356361, 31613 ^ [_1356355, _1356357, _1356359, _1356361, _1356363])), _1356363))], (31615 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356357), 31613 ^ [_1356355, _1356357, _1356359, _1356361, _1356363]), _1356359)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356355), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1356357, _1356355), _1356359), _1356361)), _1356363)))]]], (38659 ^ _773908) ^ [_1520273, _1520275, _1520277, _1520279, _1520281, _1520283, _1520285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520273, _1520277)), hAPP(hAPP(c_Product__Type_OPair(_1520273, _1520277), _1520283), _1520285)), hAPP(hAPP(c_Relation_Orel__comp(_1520273, _1520275, _1520277), _1520279), _1520281))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1520273, _1520275, _1520277, hAPP(hAPP(c_COMBC(_1520273, tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_fun(_1520275, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520275, tc_fun(tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_fun(_1520275, tc_HOL_Obool)), _1520273), c_COMBC(_1520275, tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520275, tc_prod(_1520273, _1520275)), tc_fun(_1520275, tc_fun(tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_HOL_Obool)), _1520273), hAPP(c_COMBB(tc_prod(_1520273, _1520275), tc_fun(tc_fun(tc_prod(_1520273, _1520275), tc_HOL_Obool), tc_HOL_Obool), _1520275), c_member(tc_prod(_1520273, _1520275)))), c_Product__Type_OPair(_1520273, _1520275)))), _1520279), hAPP(hAPP(c_COMBC(_1520275, tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_fun(_1520277, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520277, tc_fun(tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_fun(_1520277, tc_HOL_Obool)), _1520275), c_COMBC(_1520277, tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520277, tc_prod(_1520275, _1520277)), tc_fun(_1520277, tc_fun(tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_HOL_Obool)), _1520275), hAPP(c_COMBB(tc_prod(_1520275, _1520277), tc_fun(tc_fun(tc_prod(_1520275, _1520277), tc_HOL_Obool), tc_HOL_Obool), _1520277), c_member(tc_prod(_1520275, _1520277)))), c_Product__Type_OPair(_1520275, _1520277)))), _1520281)), _1520283), _1520285)))], (50500 ^ _773908) ^ [_1795944, _1795946] : [c_Relation_Osym(_1795944, _1795946), c_Relation_Otrans(_1795944, _1795946), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1795944, _1795944), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1795944, _1795944, _1795944), hAPP(c_Relation_Oconverse(_1795944, _1795944), _1795946)), _1795946)), _1795946)))], (10487 ^ _773908) ^ [_947621, _947623, _947625, _947627] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947621), 10490 ^ _773908 : [(10497 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947621), _947623), _947627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947621), _947623), _947625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947621), _947627), _947625))))], (10491 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947621), _947623), _947625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947621), _947627), _947625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947621), _947623), _947627)))]]], (47694 ^ _773908) ^ [_1734824, _1734826, _1734828] : [47696 ^ _773908 : [(47699 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1734824), 47695 ^ [_1734824, _1734826, _1734828]), c_Wellfounded_Oacc(_1734824, _1734828)))], (47697 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734824, _1734824)), hAPP(hAPP(c_Product__Type_OPair(_1734824, _1734824), 47695 ^ [_1734824, _1734826, _1734828]), _1734826)), _1734828)))]], -(hBOOL(hAPP(hAPP(c_member(_1734824), _1734826), c_Wellfounded_Oacc(_1734824, _1734828))))], (37410 ^ _773908) ^ [_1480839, _1480841, _1480843, _1480845, _1480847] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1480839, _1480841), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480839, tc_HOL_Obool)), _1480843), _1480845)), hAPP(c_COMBK(tc_fun(_1480841, tc_HOL_Obool), _1480839), _1480847)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480839, _1480841), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1480839, _1480841), _1480843), hAPP(c_COMBK(tc_fun(_1480841, tc_HOL_Obool), _1480839), _1480847))), hAPP(hAPP(c_Product__Type_OSigma(_1480839, _1480841), _1480845), hAPP(c_COMBK(tc_fun(_1480841, tc_HOL_Obool), _1480839), _1480847))))], (44740 ^ _773908) ^ [_1667986, _1667988] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667986)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667988)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667986), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667988)) = c_List_Olist_ONil(tc_Nat_Onat))], (22945 ^ _773908) ^ [_1172241, _1172243] : [-(_1172241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1172243, _1172241) = c_Nitpick_Onat__gcd(_1172241, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1172243, _1172241)))], (50900 ^ _773908) ^ [_1803519, _1803521, _1803523] : [hAPP(c_Set_Oimage(_1803519, _1803521, _1803523), c_Orderings_Otop__class_Otop(tc_fun(_1803519, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803521, tc_HOL_Obool)), 50903 ^ _773908 : [(50904 ^ _773908) ^ [_1803630] : [-(hAPP(_1803523, hAPP(c_Hilbert__Choice_Oinv__into(_1803519, _1803521, c_Orderings_Otop__class_Otop(tc_fun(_1803519, tc_HOL_Obool)), _1803523), _1803630)) = _1803630)]]], (8209 ^ _773908) ^ [_908939, _908941] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_908939, _908941)], (38074 ^ _773908) ^ [_1497900, _1497902] : [-(hAPP(c_Set_OCollect(_1497900), hAPP(c_fequal, _1497902)) = hAPP(hAPP(c_Set_Oinsert(_1497900), _1497902), c_Orderings_Obot__class_Obot(tc_fun(_1497900, tc_HOL_Obool))))], (44837 ^ _773908) ^ [_1670205, _1670207, _1670209] : [class_Groups_Oab__semigroup__add(_1670205), -(c_List_Ofoldr(_1670205, _1670205, c_Groups_Oplus__class_Oplus(_1670205), _1670207, _1670209) = hAPP(c_List_Ofoldl(_1670205, _1670205, c_Groups_Oplus__class_Oplus(_1670205), _1670209), _1670207))], (44309 ^ _773908) ^ [_1657244, _1657246, _1657248, _1657250, _1657252] : [c_Fun_Oinj__on(_1657244, _1657246, _1657248, c_Orderings_Otop__class_Otop(tc_fun(_1657244, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1657244, _1657246), _1657248), hAPP(c_List_OremoveAll(_1657244, _1657250), _1657252)) = hAPP(c_List_OremoveAll(_1657246, hAPP(_1657248, _1657250)), hAPP(hAPP(c_List_Omap(_1657244, _1657246), _1657248), _1657252)))], (23345 ^ _773908) ^ [_1180247, _1180249] : [23346 ^ _773908 : [(23349 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180249), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23347 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180247), _1180249))]], -(c_Divides_OposDivAlg(_1180247, _1180249) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180247))], (26483 ^ _773908) ^ [_1248367, _1248369, _1248371, _1248373, _1248375, _1248377] : [-(hAPP(c_Set_Oimage(_1248367, _1248369, hAPP(c_Fun_Ocomp(_1248371, _1248369, _1248367, _1248373), _1248375)), _1248377) = hAPP(c_Set_Oimage(_1248371, _1248369, _1248373), hAPP(c_Set_Oimage(_1248367, _1248371, _1248375), _1248377)))], (38565 ^ _773908) ^ [_1516062, _1516064, _1516066, _1516068, _1516070] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1516062, _1516064, _1516066), _1516068), _1516070) = hAPP(c_Set_OCollect(tc_prod(_1516062, _1516066)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516062, _1516066, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1516066, tc_fun(_1516064, tc_HOL_Obool)), tc_fun(_1516066, tc_HOL_Obool), _1516062), hAPP(c_COMBB(tc_fun(_1516064, tc_HOL_Obool), tc_HOL_Obool, _1516066), c_HOL_OEx(_1516064))), hAPP(hAPP(c_COMBC(_1516062, tc_fun(_1516066, tc_fun(_1516064, tc_HOL_Obool)), tc_fun(_1516066, tc_fun(_1516064, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1516064, tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), tc_fun(tc_fun(_1516066, tc_fun(_1516064, tc_HOL_Obool)), tc_fun(_1516066, tc_fun(_1516064, tc_HOL_Obool))), _1516062), c_COMBB(tc_fun(_1516064, tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool), _1516066)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1516064, tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), _1516062), c_COMBS(_1516064, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_HOL_Obool), tc_fun(_1516064, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1516062), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1516064), c_fconj)), hAPP(hAPP(c_COMBC(_1516062, tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_fun(tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), _1516062), c_COMBC(_1516064, tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_prod(_1516062, _1516064)), tc_fun(_1516064, tc_fun(tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_HOL_Obool)), _1516062), hAPP(c_COMBB(tc_prod(_1516062, _1516064), tc_fun(tc_fun(tc_prod(_1516062, _1516064), tc_HOL_Obool), tc_HOL_Obool), _1516064), c_member(tc_prod(_1516062, _1516064)))), c_Product__Type_OPair(_1516062, _1516064)))), _1516068))))), hAPP(hAPP(c_COMBC(_1516066, tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_fun(tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_fun(_1516064, tc_HOL_Obool)), _1516066), c_COMBC(_1516064, tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516064, tc_prod(_1516064, _1516066)), tc_fun(_1516064, tc_fun(tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_HOL_Obool)), _1516066), hAPP(c_COMBB(tc_prod(_1516064, _1516066), tc_fun(tc_fun(tc_prod(_1516064, _1516066), tc_HOL_Obool), tc_HOL_Obool), _1516064), c_member(tc_prod(_1516064, _1516066)))), hAPP(c_COMBC(_1516064, _1516066, tc_prod(_1516064, _1516066)), c_Product__Type_OPair(_1516064, _1516066))))), _1516070))))))], (8201 ^ _773908) ^ [_908721, _908723, _908725, _908727] : [c_Com_Ocom_OSemi(_908721, _908723) = c_Com_Ocom_OWhile(_908725, _908727)], (29453 ^ _773908) ^ [_1311531, _1311533] : [class_Lattices_Olattice(_1311531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311531), _1311533)), -(_1311533 = c_Orderings_Obot__class_Obot(tc_fun(_1311531, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1311531), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1311531), 29466 ^ [_1311531, _1311533]), 29467 ^ [_1311531, _1311533])), hAPP(hAPP(c_Set_Oinsert(_1311531), 29466 ^ [_1311531, _1311533]), hAPP(hAPP(c_Set_Oinsert(_1311531), 29467 ^ [_1311531, _1311533]), c_Orderings_Obot__class_Obot(tc_fun(_1311531, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1311531), c_Big__Operators_Olattice__class_OInf__fin(_1311531, _1311533)), _1311533)))], (38255 ^ _773908) ^ [_1504796, _1504798, _1504800, _1504802] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504796), hAPP(c_Set_OCollect(_1504796), _1504798))), 38258 ^ _773908 : [(38259 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504800), hAPP(c_Set_OCollect(_1504800), hAPP(hAPP(c_COMBB(tc_fun(_1504796, tc_HOL_Obool), tc_HOL_Obool, _1504800), c_HOL_OEx(_1504796)), hAPP(hAPP(c_COMBB(tc_fun(_1504796, tc_HOL_Obool), tc_fun(_1504796, tc_HOL_Obool), _1504800), hAPP(c_COMBS(_1504796, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504796), c_fconj), _1504798))), _1504802))))), 38262 ^ _773908 : [(38263 ^ _773908) ^ [_1505079] : [hBOOL(hAPP(_1504798, _1505079)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1504800), hAPP(c_Set_OCollect(_1504800), hAPP(hAPP(c_COMBC(_1504800, _1504796, tc_HOL_Obool), _1504802), _1505079)))))]]], (38269 ^ _773908) ^ [] : [38271 ^ _773908 : [(38274 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504800), hAPP(c_Set_OCollect(_1504800), hAPP(hAPP(c_COMBC(_1504800, _1504796, tc_HOL_Obool), _1504802), 38270 ^ [_1504796, _1504798, _1504800, _1504802]))))], (38272 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1504798, 38270 ^ [_1504796, _1504798, _1504800, _1504802])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1504800), hAPP(c_Set_OCollect(_1504800), hAPP(hAPP(c_COMBB(tc_fun(_1504796, tc_HOL_Obool), tc_HOL_Obool, _1504800), c_HOL_OEx(_1504796)), hAPP(hAPP(c_COMBB(tc_fun(_1504796, tc_HOL_Obool), tc_fun(_1504796, tc_HOL_Obool), _1504800), hAPP(c_COMBS(_1504796, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504796), c_fconj), _1504798))), _1504802))))))]]], (40025 ^ _773908) ^ [_1555554, _1555556, _1555558, _1555560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1555554), tc_List_Olist(_1555554))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1555554), tc_List_Olist(_1555554)), _1555556), _1555558)), c_List_Olexord(_1555554, _1555560))), 40030 ^ _773908 : [(40033 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1555554), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555554)), _1555556)), _1555558) = _1555556)], (40031 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555554)), _1555556)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555554)), _1555558))))]], 40035 ^ _773908 : [(40040 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555554, _1555554)), hAPP(hAPP(c_Product__Type_OPair(_1555554, _1555554), hAPP(hAPP(c_List_Onth(_1555554), _1555556), 40034 ^ [_1555554, _1555556, _1555558, _1555560])), hAPP(hAPP(c_List_Onth(_1555554), _1555558), 40034 ^ [_1555554, _1555556, _1555558, _1555560]))), _1555560)))], (40038 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1555554), 40034 ^ [_1555554, _1555556, _1555558, _1555560]), _1555556) = hAPP(hAPP(c_List_Otake(_1555554), 40034 ^ [_1555554, _1555556, _1555558, _1555560]), _1555558))], (40036 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40034 ^ [_1555554, _1555556, _1555558, _1555560]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555554)), _1555556)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555554)), _1555558)))))]]], (30750 ^ _773908) ^ [_1337247, _1337249, _1337251, _1337253] : [class_Rings_Ocomm__semiring__1(_1337247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337249), _1337251)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337249, _1337247), _1337253), _1337251) = c_Groups_Ozero__class_Ozero(_1337247)), 30759 ^ _773908 : [(30760 ^ _773908) ^ [_1337428] : [hBOOL(hAPP(hAPP(c_member(_1337249), _1337428), _1337251)), hAPP(_1337253, _1337428) = c_Groups_Ozero__class_Ozero(_1337247)]]], (35796 ^ _773908) ^ [_1445691, _1445693, _1445695] : [class_Lattices_Oboolean__algebra(_1445691), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445691), _1445693), _1445695) = c_Orderings_Obot__class_Obot(_1445691), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1445691), _1445693), _1445695) = c_Orderings_Otop__class_Otop(_1445691), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1445691), _1445693) = _1445695)], (40257 ^ _773908) ^ [_1561281, _1561283, _1561285, _1561287] : [hBOOL(hAPP(hAPP(c_member(_1561281), _1561283), hAPP(c_List_Oset(_1561281), c_List_Osublist(_1561281, _1561285, _1561287)))), -(hBOOL(hAPP(hAPP(c_member(_1561281), _1561283), hAPP(c_List_Oset(_1561281), _1561285))))], (42864 ^ _773908) ^ [_1624349] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624349)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (4518 ^ _773908) ^ [_842685, _842687] : [_842687 = _842685, -(c_List_Onth(_842687) = c_List_Onth(_842685))], (27428 ^ _773908) ^ [_1269374, _1269376, _1269378, _1269380, _1269382, _1269384] : [c_Finite__Set_Ofolding(_1269374, _1269376, _1269378, _1269380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269374), _1269382)), hBOOL(hAPP(hAPP(c_member(_1269374), _1269384), _1269382)), -(hAPP(_1269380, _1269382) = hAPP(c_Fun_Ocomp(_1269376, _1269376, _1269376, hAPP(_1269380, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269374, tc_HOL_Obool)), _1269382), hAPP(hAPP(c_Set_Oinsert(_1269374), _1269384), c_Orderings_Obot__class_Obot(tc_fun(_1269374, tc_HOL_Obool)))))), hAPP(_1269378, _1269384)))], (16501 ^ _773908) ^ [_1056983, _1056985, _1056987, _1056989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1056983, tc_HOL_Obool)), _1056985), _1056987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1056983, tc_HOL_Obool)), _1056987), _1056989)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056983, tc_HOL_Obool)), _1056987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056983, tc_HOL_Obool)), _1056989), _1056985)) = _1056985)], (43919 ^ _773908) ^ [_1647957, _1647959, _1647961] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1647957, tc_HOL_Obool)), _1647959), _1647961) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647957, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1647957, tc_HOL_Obool)), _1647959), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1647957, tc_HOL_Obool)), _1647961), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1647957, tc_HOL_Obool), tc_HOL_Obool))))))], (12364 ^ _773908) ^ [_980883, _980885, _980887] : [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), _980883), _980885)), _980887)), 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)), _980887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _980885), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27994 ^ _773908) ^ [_1280770, _1280772] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280770, tc_HOL_Obool)), _1280772), c_Orderings_Obot__class_Obot(tc_fun(_1280770, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1280770, tc_HOL_Obool)))], (49406 ^ _773908) ^ [_1771104, _1771106, _1771108, _1771110, _1771112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771106, _1771104)), hAPP(hAPP(c_Product__Type_OPair(_1771106, _1771104), _1771110), _1771112)), hAPP(c_Relation_Oconverse(_1771104, _1771106), _1771108))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1771104, _1771106, hAPP(hAPP(c_COMBC(_1771104, tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_fun(_1771106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771106, tc_fun(tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_fun(_1771106, tc_HOL_Obool)), _1771104), c_COMBC(_1771106, tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1771106, tc_prod(_1771104, _1771106)), tc_fun(_1771106, tc_fun(tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_HOL_Obool)), _1771104), hAPP(c_COMBB(tc_prod(_1771104, _1771106), tc_fun(tc_fun(tc_prod(_1771104, _1771106), tc_HOL_Obool), tc_HOL_Obool), _1771106), c_member(tc_prod(_1771104, _1771106)))), c_Product__Type_OPair(_1771104, _1771106)))), _1771108)), _1771110), _1771112)))], (25639 ^ _773908) ^ [_1228096, _1228098, _1228100, _1228102] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1228096), _1228098)), 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)), _1228100), _1228096)), 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)), _1228102), _1228098)), 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)), _1228100), _1228102)), _1228098)), c_FunDef_Omax__weak)))], (7978 ^ _773908) ^ [_904556] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _904556) = _904556)], (45331 ^ _773908) ^ [_1679096, _1679098, _1679100] : [class_Orderings_Olinorder(_1679096), hBOOL(hAPP(hAPP(c_member(_1679096), _1679098), hAPP(c_List_Oset(_1679096), _1679100))), c_List_Olinorder__class_Osorted(_1679096, _1679100), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679096, _1679096, c_COMBI(_1679096)), _1679098), c_List_Oremove1(_1679096, _1679098, _1679100)) = _1679100)], (4218 ^ _773908) ^ [_837775, _837777, _837779, _837781, _837783, _837785, _837787, _837789, _837791, _837793, _837795, _837797, _837799, _837801] : [-(c_New__Random__Sequence_Opos__decr__bind(_837801, _837797, _837793, _837789, _837785, _837781, _837777) = c_New__Random__Sequence_Opos__decr__bind(_837799, _837795, _837791, _837787, _837783, _837779, _837775)), _837801 = _837799, _837797 = _837795, _837793 = _837791, _837789 = _837787, _837785 = _837783, _837781 = _837779, _837777 = _837775], (30670 ^ _773908) ^ [_1335357, _1335359, _1335361, _1335363] : [30671 ^ _773908 : [(30674 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335361), _1335363)))], (30672 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1335357), _1335359)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1335357, _1335361)), c_Sum__Type_OPlus(_1335357, _1335361, _1335359, _1335363)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50832 ^ _773908) ^ [_1801953, _1801955, _1801957] : [hAPP(c_Fun_Ocomp(_1801955, _1801953, _1801953, c_Hilbert__Choice_Oinv__into(_1801953, _1801955, c_Orderings_Otop__class_Otop(tc_fun(_1801953, tc_HOL_Obool)), _1801957)), _1801957) = c_Fun_Oid(_1801953), -(c_Fun_Oinj__on(_1801953, _1801955, _1801957, c_Orderings_Otop__class_Otop(tc_fun(_1801953, tc_HOL_Obool))))], (24001 ^ _773908) ^ [_1193262, _1193264] : [-(_1193262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193264, _1193262), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1193264), _1193262)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1193264, _1193262)))))], (3264 ^ _773908) ^ [_822846, _822848] : [_822848 = _822846, -(c_HOL_OAll(_822848) = c_HOL_OAll(_822846))], (10739 ^ _773908) ^ [_952071] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _952071) = _952071)], (31824 ^ _773908) ^ [_1362369, _1362371, _1362373, _1362375, _1362377] : [-(_1362369 = c_Orderings_Obot__class_Obot(tc_fun(_1362371, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1362373), _1362375), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362371, tc_fun(_1362373, tc_HOL_Obool)), _1362369), _1362377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362371, tc_fun(_1362373, tc_HOL_Obool)), _1362369), hAPP(hAPP(c_COMBB(tc_fun(_1362373, tc_HOL_Obool), tc_fun(_1362373, tc_HOL_Obool), _1362371), hAPP(c_Set_Oinsert(_1362373), _1362375)), _1362377)))], (17341 ^ _773908) ^ [_1073089, _1073091] : [-(_1073089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1073091), _1073089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073091), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1073091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073089), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (5184 ^ _773908) ^ [_853190, _853192] : [_853192 = _853190, -(c_Groups_Ominus__class_Ominus(_853192) = c_Groups_Ominus__class_Ominus(_853190))], (17911 ^ _773908) ^ [_1083035, _1083037] : [class_Int_Onumber__ring(_1083035), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083035), hAPP(c_Int_Onumber__class_Onumber__of(_1083035), c_Int_OMin)), _1083037) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083035), _1083037))], (42257 ^ _773908) ^ [_1610675, _1610677, _1610679, _1610681, _1610683] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1610675, tc_fun(_1610677, tc_HOL_Obool)), _1610679), hAPP(hAPP(c_COMBB(tc_fun(_1610677, tc_HOL_Obool), tc_fun(_1610677, tc_HOL_Obool), _1610675), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610677, tc_HOL_Obool)), _1610681)), _1610683)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610677, tc_HOL_Obool)), _1610681), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610675, tc_fun(_1610677, tc_HOL_Obool)), _1610679), _1610683)))], (44670 ^ _773908) ^ [_1666802, _1666804] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666802), _1666804))), -(c_List_Oupt(_1666802, _1666804) = c_List_Olist_ONil(tc_Nat_Onat))], (4848 ^ _773908) ^ [_847834, _847836, _847838, _847840, _847842, _847844] : [-(c_FunDef_OTHE__default(_847844, _847840, _847836) = c_FunDef_OTHE__default(_847842, _847838, _847834)), _847844 = _847842, _847840 = _847838, _847836 = _847834], (7321 ^ _773908) ^ [_892407, _892409] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892407), _892409), 7326 ^ _773908 : [(7329 ^ _773908) ^ [] : [-(_892409 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7327 ^ _773908) ^ [] : [-(_892407 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7330 ^ _773908 : [(7333 ^ _773908) ^ [] : [-(_892409 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7331 ^ _773908) ^ [] : [-(_892407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31880 ^ _773908) ^ [_1363721, _1363723, _1363725, _1363727, _1363729] : [_1363721 = c_Orderings_Obot__class_Obot(tc_fun(_1363723, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363723, tc_fun(_1363725, tc_HOL_Obool)), _1363721), hAPP(hAPP(c_COMBB(tc_fun(_1363725, tc_HOL_Obool), tc_fun(_1363725, tc_HOL_Obool), _1363723), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363725, tc_HOL_Obool)), _1363727)), _1363729)) = c_Orderings_Obot__class_Obot(tc_fun(_1363725, tc_HOL_Obool)))], (7661 ^ _773908) ^ [_898176, _898178, _898180, _898182, _898184, _898186] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_898176, _898178, _898180), _898182, _898184, _898186)), 7662 ^ _773908 : [(7669 ^ _773908) ^ [] : [-(hBOOL(hAPP(_898176, _898182))), c_Natural_Oevaln(_898180, _898182, _898184, _898186)], (7663 ^ _773908) ^ [] : [hBOOL(hAPP(_898176, _898182)), c_Natural_Oevaln(_898178, _898182, _898184, _898186)]]], (37225 ^ _773908) ^ [_1475943, _1475945, _1475947, _1475949, _1475951] : [hAPP(c_Set_Oimage(_1475943, _1475945, _1475947), c_Orderings_Otop__class_Otop(tc_fun(_1475943, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1475945, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475943, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1475943, _1475945, _1475947), _1475949)), _1475951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475945, tc_HOL_Obool)), _1475949), hAPP(c_Set_Oimage(_1475943, _1475945, _1475947), _1475951))))], (28420 ^ _773908) ^ [_1290615, _1290617] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1290615), _1290617) = 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)), _1290615)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1290617))))], (49034 ^ _773908) ^ [_1762810, _1762812, _1762814] : [49036 ^ _773908 : [(49039 ^ _773908) ^ [] : [hBOOL(hAPP(_1762812, hAPP(hAPP(c_List_Onth(_1762810), _1762814), 49035 ^ [_1762810, _1762812, _1762814])))], (49037 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49035 ^ [_1762810, _1762812, _1762814]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762810)), _1762814))))]], -(c_List_Olist__all(_1762810, _1762812, _1762814))], (8621 ^ _773908) ^ [_916678, _916680, _916682] : [class_Groups_Ogroup__add(_916678), 8624 ^ _773908 : [(8631 ^ _773908) ^ [] : [_916680 = _916682, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916678), _916680) = hAPP(c_Groups_Ouminus__class_Ouminus(_916678), _916682))], (8625 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916678), _916680) = hAPP(c_Groups_Ouminus__class_Ouminus(_916678), _916682), -(_916680 = _916682)]]], (23596 ^ _773908) ^ [_1185420, _1185422, _1185424, _1185426] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185420, _1185422), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1185424), _1185426))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1185420), _1185422) = _1185424)], (39092 ^ _773908) ^ [_1530224, _1530226, _1530228, _1530230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530224, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530224, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530226, _1530224), _1530228)), hAPP(c_Relation_ORange(_1530226, _1530224), _1530230))), hAPP(c_Relation_ORange(_1530226, _1530224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530226, _1530224), tc_HOL_Obool)), _1530228), _1530230)))))], (51450 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (18491 ^ _773908) ^ [_1093140, _1093142, _1093144, _1093146] : [hBOOL(hAPP(hAPP(c_member(_1093140), _1093142), _1093144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1093140, tc_HOL_Obool)), _1093144), _1093146)), -(hBOOL(hAPP(hAPP(c_member(_1093140), _1093142), _1093146)))], (46947 ^ _773908) ^ [_1715569, _1715571, _1715573, _1715575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715569), tc_List_Olist(_1715569))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715569), tc_List_Olist(_1715569)), _1715571), _1715573)), c_List_Olistrel(_1715569, _1715575))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715569), tc_List_Olist(_1715569))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715569), tc_List_Olist(_1715569)), _1715571), _1715573)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1715569), c_List_Olistrel1(_1715569, _1715575)))))], (24553 ^ _773908) ^ [_1206289, _1206291, _1206293, _1206295, _1206297] : [-(c_Product__Type_Oprod_Oprod__size(_1206289, _1206291, _1206293, _1206295, _1206297) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1206293, hAPP(c_Product__Type_Ofst(_1206289, _1206291), _1206297))), hAPP(_1206295, hAPP(c_Product__Type_Osnd(_1206289, _1206291), _1206297)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51536 ^ _773908) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (43723 ^ _773908) ^ [_1643462, _1643464, _1643466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1643462, tc_HOL_Obool), tc_HOL_Obool)), _1643464), _1643466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643462, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643462, tc_HOL_Obool), _1643464)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643462, tc_HOL_Obool), _1643466))))], (3660 ^ _773908) ^ [_829072, _829074, _829076, _829078, _829080, _829082] : [-(c_Predicate_ODomainP(_829082, _829078, _829074) = c_Predicate_ODomainP(_829080, _829076, _829072)), _829082 = _829080, _829078 = _829076, _829074 = _829072], (23476 ^ _773908) ^ [_1183233, _1183235, _1183237, _1183239] : [-(hAPP(c_Nat_Onat_Onat__rec(_1183233, _1183235, _1183237), hAPP(c_Nat_OSuc, _1183239)) = hAPP(hAPP(_1183237, _1183239), hAPP(c_Nat_Onat_Onat__rec(_1183233, _1183235, _1183237), _1183239)))], (43657 ^ _773908) ^ [_1641978, _1641980] : [-(c_Enum_On__lists(_1641978, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1641980) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1641978)), c_List_Olist_ONil(_1641978)), c_List_Olist_ONil(tc_List_Olist(_1641978))))], (42125 ^ _773908) ^ [_1606787, _1606789, _1606791, _1606793, _1606795] : [-(hAPP(hAPP(c_Set_Oinsert(_1606787), _1606789), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606791, tc_fun(_1606787, tc_HOL_Obool)), _1606793), _1606795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606791, tc_fun(_1606787, tc_HOL_Obool)), _1606793), hAPP(hAPP(c_COMBB(tc_fun(_1606787, tc_HOL_Obool), tc_fun(_1606787, tc_HOL_Obool), _1606791), hAPP(c_Set_Oinsert(_1606787), _1606789)), _1606795)))], (10637 ^ _773908) ^ [_950240, _950242, _950244] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950240)), _950242) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950240)), _950244), -(_950242 = _950244)], (16657 ^ _773908) ^ [_1059662, _1059664, _1059666] : [class_Groups_Oordered__ab__group__add__abs(_1059662), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059662), hAPP(c_Groups_Oabs__class_Oabs(_1059662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059662), _1059664), _1059666))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059662), hAPP(c_Groups_Oabs__class_Oabs(_1059662), _1059664)), hAPP(c_Groups_Oabs__class_Oabs(_1059662), _1059666)))))], (22065 ^ _773908) ^ [_1155606, _1155608, _1155610, _1155612] : [class_Fields_Olinordered__field__inverse__zero(_1155606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155606), _1155608), _1155610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155606), _1155612), c_Groups_Ozero__class_Ozero(_1155606))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155606), c_Groups_Ozero__class_Ozero(_1155606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155606), _1155608), _1155610))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155606), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155606), _1155612), _1155608)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155606), _1155612), _1155610))))], (9855 ^ _773908) ^ [_938013, _938015, _938017, _938019] : [class_Orderings_Oorder(_938013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938013), _938015), _938017)), _938015 = _938019, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938013), _938019), _938017)))], (40625 ^ _773908) ^ [_1570262, _1570264, _1570266, _1570268, _1570270] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1570262, _1570264)), _1570266), hAPP(hAPP(c_List_Ozip(_1570262, _1570264), _1570268), _1570270)) = hAPP(hAPP(c_List_Ozip(_1570262, _1570264), hAPP(hAPP(c_List_Odrop(_1570262), _1570266), _1570268)), hAPP(hAPP(c_List_Odrop(_1570264), _1570266), _1570270)))], (25893 ^ _773908) ^ [_1232689, _1232691, _1232693] : [class_Lattices_Osemilattice__sup(_1232689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232689), _1232691), _1232693)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1232689), _1232691), _1232693) = _1232693)], (14464 ^ _773908) ^ [_1018551, _1018553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018551), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14467 ^ _773908 : [(14474 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018553), _1018551)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14468 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018553), _1018551)), 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)), _1018553)))]]], (23251 ^ _773908) ^ [_1178523, _1178525, _1178527] : [class_Int_Onumber__ring(_1178523), 23254 ^ _773908 : [(23261 ^ _773908) ^ [] : [-(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), _1178525)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178523), hAPP(c_Int_Onumber__class_Onumber__of(_1178523), _1178527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1178525))) = c_Groups_Oone__class_Oone(_1178523))], (23255 ^ _773908) ^ [] : [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), _1178525))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178523), hAPP(c_Int_Onumber__class_Onumber__of(_1178523), _1178527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1178525))) = hAPP(hAPP(c_HOL_OLet(_1178523, _1178523), hAPP(hAPP(c_Power_Opower__class_Opower(_1178523), hAPP(c_Int_Onumber__class_Onumber__of(_1178523), _1178527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1178525))), hAPP(hAPP(c_COMBS(_1178523, _1178523, _1178523), hAPP(hAPP(c_COMBB(_1178523, tc_fun(_1178523, _1178523), _1178523), c_Groups_Otimes__class_Otimes(_1178523)), hAPP(c_Groups_Otimes__class_Otimes(_1178523), hAPP(c_Int_Onumber__class_Onumber__of(_1178523), _1178527)))), c_COMBI(_1178523))))]]], (19413 ^ _773908) ^ [_1109046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109046), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1109046)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13113 ^ _773908) ^ [_993932, _993934, _993936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993934), _993936)), -(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, _993932)), _993934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993932)), _993936))))], (2674 ^ _773908) ^ [_813573, _813575, _813577, _813579, _813581, _813583, _813585, _813587] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_813587, _813583, _813579, _813575) = c_SetInterval_Oord_OgreaterThanLessThan(_813585, _813581, _813577, _813573)), _813587 = _813585, _813583 = _813581, _813579 = _813577, _813575 = _813573], (10615 ^ _773908) ^ [_949940, _949942] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949940), _949942) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_949940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_949942 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40319 ^ _773908) ^ [_1562815, _1562817, _1562819, _1562821] : [hAPP(hAPP(c_List_Oappend(_1562815), _1562817), _1562819) = _1562821, 40322 ^ _773908 : [(40325 ^ _773908) ^ [] : [-(_1562819 = hAPP(hAPP(c_List_Odrop(_1562815), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562815)), _1562817)), _1562821))], (40323 ^ _773908) ^ [] : [-(_1562817 = hAPP(hAPP(c_List_Otake(_1562815), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562815)), _1562817)), _1562821))]]], (26171 ^ _773908) ^ [_1238298, _1238300, _1238302] : [class_Lattices_Olattice(_1238298), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238298), _1238300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238298), _1238300), _1238302)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238298), _1238300), _1238302))], (33936 ^ _773908) ^ [_1404962, _1404964, _1404966, _1404968] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1404962), _1404964)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404966), _1404968)), 33943 ^ _773908 : [(33944 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1404962), _1404964)), hAPP(c_Finite__Set_Ocard(_1404966), _1404968)))), 33945 ^ _773908 : [(33946 ^ _773908) ^ [_1405173] : [c_Fun_Oinj__on(_1404962, _1404966, _1405173, _1404964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404966, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1404962, _1404966, _1405173), _1404964)), _1404968))]]], (33954 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1404962), _1404964)), hAPP(c_Finite__Set_Ocard(_1404966), _1404968))), 33958 ^ _773908 : [(33961 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404966, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1404962, _1404966, 33957 ^ [_1404962, _1404964, _1404966, _1404968]), _1404964)), _1404968)))], (33959 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1404962, _1404966, 33957 ^ [_1404962, _1404964, _1404966, _1404968], _1404964))]]]]], (28937 ^ _773908) ^ [_1302409, _1302411, _1302413] : [class_Lattices_Olattice(_1302409), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302409), _1302411)), hBOOL(hAPP(hAPP(c_member(_1302409), _1302413), _1302411)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1302409), _1302413), c_Big__Operators_Olattice__class_OSup__fin(_1302409, _1302411)) = c_Big__Operators_Olattice__class_OSup__fin(_1302409, _1302411))], (7833 ^ _773908) ^ [_901841] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _901841)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_901841)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19487 ^ _773908) ^ [_1110256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110256), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110256)), c_Int_OMin)))], (44595 ^ _773908) ^ [_1664853, _1664855] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1664853)), c_List_Otranspose__rel(_1664853)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664853)), c_List_Olist_ONil(_1664853)), _1664855))), -(c_List_Otranspose(_1664853, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664853)), c_List_Olist_ONil(_1664853)), _1664855)) = c_List_Otranspose(_1664853, _1664855))], (20517 ^ _773908) ^ [_1128072, _1128074, _1128076] : [class_Int_Onumber__ring(_1128072), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128072), _1128074), _1128076)), 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(_1128072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128072), hAPP(hAPP(c_Power_Opower__class_Opower(_1128072), _1128074), 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(_1128072), _1128076), 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(_1128072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128072), hAPP(c_Int_Onumber__class_Onumber__of(_1128072), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1128074)), _1128076)))], (46080 ^ _773908) ^ [_1694936, _1694938, _1694940, _1694942] : [46082 ^ _773908 : [(46085 ^ _773908) ^ [] : [hBOOL(hAPP(_1694938, hAPP(hAPP(c_List_Onth(_1694940), _1694942), 46081 ^ [_1694936, _1694938, _1694940, _1694942])))], (46083 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46081 ^ [_1694936, _1694938, _1694940, _1694942]), _1694936)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1694936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694940)), _1694942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1694936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694940)), c_List_OtakeWhile(_1694940, _1694938, _1694942)))))], (44428 ^ _773908) ^ [_1659662, _1659664, _1659666] : [hAPP(c_List_Ofilter(_1659662, _1659664), _1659666) = _1659666, 44431 ^ _773908 : [(44432 ^ _773908) ^ [_1659753] : [hBOOL(hAPP(hAPP(c_member(_1659662), _1659753), hAPP(c_List_Oset(_1659662), _1659666))), -(hBOOL(hAPP(_1659664, _1659753)))]]], (44451 ^ _773908) ^ [_1660146, _1660148, _1660150, _1660152] : [-(hBOOL(hAPP(_1660146, _1660148))), -(hAPP(c_List_OremoveAll(_1660150, _1660148), hAPP(c_List_Ofilter(_1660150, _1660146), _1660152)) = hAPP(c_List_Ofilter(_1660150, _1660146), _1660152))], (46359 ^ _773908) ^ [_1701502, _1701504, _1701506] : [class_Enum_Oenum(_1701502), class_Enum_Oenum(_1701504), 46366 ^ _773908 : [(46373 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1701504), hAPP(hAPP(c_COMBB(tc_fun(_1701502, tc_HOL_Obool), tc_HOL_Obool, _1701504), c_Enum_Oenum__class_Oenum__ex(_1701502)), hAPP(hAPP(c_COMBB(tc_fun(_1701502, tc_prod(_1701504, _1701502)), tc_fun(_1701502, tc_HOL_Obool), _1701504), hAPP(c_COMBB(tc_prod(_1701504, _1701502), tc_HOL_Obool, _1701502), _1701506)), c_Product__Type_OPair(_1701504, _1701502))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1701504, _1701502)), _1701506)))], (46367 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1701504, _1701502)), _1701506)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1701504), hAPP(hAPP(c_COMBB(tc_fun(_1701502, tc_HOL_Obool), tc_HOL_Obool, _1701504), c_Enum_Oenum__class_Oenum__ex(_1701502)), hAPP(hAPP(c_COMBB(tc_fun(_1701502, tc_prod(_1701504, _1701502)), tc_fun(_1701502, tc_HOL_Obool), _1701504), hAPP(c_COMBB(tc_prod(_1701504, _1701502), tc_HOL_Obool, _1701502), _1701506)), c_Product__Type_OPair(_1701504, _1701502))))))]]], (24413 ^ _773908) ^ [_1202621, _1202623, _1202625] : [_1202623 = _1202625, -(hBOOL(hAPP(hAPP(c_member(_1202621), _1202623), hAPP(c_fequal, _1202625))))], (50342 ^ _773908) ^ [_1793262, _1793264] : [c_Relation_Oantisym(_1793262, hAPP(c_Relation_Oconverse(_1793262, _1793262), _1793264)), -(c_Relation_Oantisym(_1793262, _1793264))], (37426 ^ _773908) ^ [_1481336, _1481338, _1481340] : [c_Equiv__Relations_Oequiv(_1481336, _1481338, _1481340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1481336, _1481336), tc_HOL_Obool)), _1481340), hAPP(hAPP(c_Product__Type_OSigma(_1481336, _1481336), _1481338), hAPP(c_COMBK(tc_fun(_1481336, tc_HOL_Obool), _1481336), _1481338)))))], (51492 ^ _773908) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (2848 ^ _773908) ^ [_816304, _816306, _816308, _816310, _816312, _816314, _816316, _816318] : [-(c_Product__Type_Oapfst(_816318, _816314, _816310, _816306) = c_Product__Type_Oapfst(_816316, _816312, _816308, _816304)), _816318 = _816316, _816314 = _816312, _816310 = _816308, _816306 = _816304], (18131 ^ _773908) ^ [_1086588, _1086590] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086588))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086588)), _1086590)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1086590))], (6334 ^ _773908) ^ [_876561, _876563, _876565, _876567] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_876561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876561), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876561), _876563), _876565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876561), _876567), _876565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876561), _876563), _876567)))], (7829 ^ _773908) ^ [_901763, _901765] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_901763, _901765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901765)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34582 ^ _773908) ^ [_1418685, _1418687, _1418689, _1418691, _1418693] : [class_Groups_Ocomm__monoid__add(_1418685), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418687, _1418685), hAPP(hAPP(c_COMBS(_1418687, _1418685, _1418685), hAPP(hAPP(c_COMBB(_1418685, tc_fun(_1418685, _1418685), _1418687), c_Groups_Oplus__class_Oplus(_1418685)), _1418689)), _1418691)), _1418693) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418685), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418687, _1418685), _1418689), _1418693)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418687, _1418685), _1418691), _1418693)))], (28216 ^ _773908) ^ [_1285360, _1285362, _1285364, _1285366] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285360, tc_HOL_Obool)), _1285362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285360, tc_HOL_Obool)), _1285364), _1285366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285360, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285360, tc_HOL_Obool)), _1285362), _1285364)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285360, tc_HOL_Obool)), _1285362), _1285366)))], (4248 ^ _773908) ^ [_838364, _838366, _838368, _838370, _838372, _838374, _838376, _838378] : [-(c_New__DSequence_Opos__decr__bind(_838378, _838374, _838370, _838366) = c_New__DSequence_Opos__decr__bind(_838376, _838372, _838368, _838364)), _838378 = _838376, _838374 = _838372, _838370 = _838368, _838366 = _838364], (25817 ^ _773908) ^ [_1231374, _1231376, _1231378] : [class_Lattices_Osemilattice__sup(_1231374), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231374), _1231376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231374), _1231376), _1231378))))], (49539 ^ _773908) ^ [_1773839, _1773841, _1773843, _1773845] : [49547 ^ _773908 : [(49550 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1773845, 49546 ^ [_1773839, _1773841, _1773843, _1773845])))], (49548 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773839), 49546 ^ [_1773839, _1773841, _1773843, _1773845]), hAPP(c_List_Oset(_1773839), c_List_Oreplicate(_1773839, _1773841, _1773843)))))]], hBOOL(hAPP(_1773845, _1773843)), -(_1773841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10625 ^ _773908) ^ [_950038, _950040] : [10626 ^ _773908 : [(10629 ^ _773908) ^ [] : [_950040 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10627 ^ _773908) ^ [] : [_950038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950038), _950040) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20277 ^ _773908) ^ [_1123888, _1123890, _1123892] : [class_Groups_Omonoid__mult(_1123888), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123888), _1123890), 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)))), _1123892)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1123888), hAPP(hAPP(c_Power_Opower__class_Opower(_1123888), _1123890), _1123892)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (7445 ^ _773908) ^ [_894407, _894409] : [class_Rings_Ocomm__semiring__1(_894407), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894407), c_Groups_Ozero__class_Ozero(_894407)), _894409) = _894409)], (5406 ^ _773908) ^ [_856569, _856571] : [_856571 = _856569, -(c_Set_OCollect(_856571) = c_Set_OCollect(_856569))], (16103 ^ _773908) ^ [_1049719, _1049721, _1049723, _1049725, _1049727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049719), _1049721)), 16106 ^ _773908 : [(16113 ^ _773908) ^ [] : [_1049725 = 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), _1049721), _1049719)), _1049723)), _1049727), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049719), _1049723)), _1049725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049721), _1049723)), _1049727))], (16107 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049719), _1049723)), _1049725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049721), _1049723)), _1049727), -(_1049725 = 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), _1049721), _1049719)), _1049723)), _1049727))]]], (51804 ^ _773908) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (8191 ^ _773908) ^ [_908441, _908443, _908445, _908447, _908449] : [c_Com_Ocom_OWhile(_908441, _908443) = c_Com_Ocom_OCond(_908445, _908447, _908449)], (26790 ^ _773908) ^ [_1256697, _1256699, _1256701, _1256703, _1256705] : [c_Fun_Ofun__upd(_1256697, _1256699, _1256701, _1256703, _1256705) = _1256701, -(hAPP(_1256701, _1256703) = _1256705)], (37542 ^ _773908) ^ [_1484466, _1484468, _1484470, _1484472] : [_1484466 = c_Orderings_Obot__class_Obot(tc_fun(_1484468, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1484468, _1484470), _1484470, c_Product__Type_Osnd(_1484468, _1484470)), hAPP(hAPP(c_Product__Type_OSigma(_1484468, _1484470), _1484466), hAPP(c_COMBK(tc_fun(_1484470, tc_HOL_Obool), _1484468), _1484472))) = c_Orderings_Obot__class_Obot(tc_fun(_1484470, tc_HOL_Obool)))], (46776 ^ _773908) ^ [_1711141, _1711143, _1711145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1711141, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1711141, _1711141, _1711143), _1711145)), _1711145)), -(hAPP(c_Relation_OImage(_1711141, _1711141, c_Transitive__Closure_Ortrancl(_1711141, _1711143)), _1711145) = _1711145)], (49989 ^ _773908) ^ [_1783900, _1783902, _1783904, _1783906] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1783900), _1783902), _1783904), _1783906) = 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(_1783900)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1783900), _1783902)))], (20347 ^ _773908) ^ [_1125154, _1125156] : [class_Rings_Olinordered__idom(_1125154), 20350 ^ _773908 : [(20357 ^ _773908) ^ [] : [-(_1125156 = c_Groups_Ozero__class_Ozero(_1125154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125154), c_Groups_Ozero__class_Ozero(_1125154)), hAPP(hAPP(c_Power_Opower__class_Opower(_1125154), _1125156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20351 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125154), c_Groups_Ozero__class_Ozero(_1125154)), hAPP(hAPP(c_Power_Opower__class_Opower(_1125154), _1125156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1125156 = c_Groups_Ozero__class_Ozero(_1125154)]]], (13382 ^ _773908) ^ [_998519, _998521, _998523, _998525] : [_998519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998521), _998523)), _998525), -(_998521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _998519, _998521) = _998525), 13389 ^ _773908 : [(13392 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998525), _998521))], (13390 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998521)))]], 13397 ^ _773908 : [(13400 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998521), _998525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998525), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13398 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998521))]]], (43741 ^ _773908) ^ [_1644056, _1644058, _1644060] : [-(hAPP(c_Relation_ORange(_1644056, _1644058), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1644056, _1644058), tc_HOL_Obool), _1644060)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1644056, _1644058), tc_HOL_Obool), tc_fun(_1644058, tc_HOL_Obool)), _1644060), c_Relation_ORange(_1644056, _1644058)))], (49636 ^ _773908) ^ [_1775783, _1775785, _1775787, _1775789] : [-(hAPP(c_New__DSequence_Opos__union(_1775783, _1775785, _1775787), _1775789) = c_Lazy__Sequence_Oappend(_1775783, hAPP(_1775785, _1775789), hAPP(_1775787, _1775789)))], (7137 ^ _773908) ^ [_889452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889452), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19745 ^ _773908) ^ [_1114397, _1114399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1114397)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114399)), _1114397) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114397), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (14436 ^ _773908) ^ [_1018107] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018107, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7763 ^ _773908) ^ [_900349, _900351, _900353, _900355, _900357] : [c_Com_Ocom_OCond(_900349, _900351, _900353) = c_Com_Ocom_OAss(_900355, _900357)], (23113 ^ _773908) ^ [_1175453, _1175455, _1175457] : [-(hAPP(c_Divides_Oadjust(_1175453), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1175455), _1175457)) = 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), _1175457), _1175453)), 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)))), _1175455)), 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)))), _1175455)), _1175457))))], (39406 ^ _773908) ^ [_1539233, _1539235] : [-(hAPP(hAPP(c_List_Oappend(_1539233), c_List_Olist_ONil(_1539233)), _1539235) = _1539235)], (40173 ^ _773908) ^ [_1559445, _1559447] : [c_Orderings_Obot__class_Obot(tc_fun(_1559445, tc_HOL_Obool)) = hAPP(c_List_Oset(_1559445), _1559447), -(_1559447 = c_List_Olist_ONil(_1559445))], (17399 ^ _773908) ^ [_1074157, _1074159] : [class_Groups_Omonoid__mult(_1074157), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1074157), c_Groups_Oone__class_Oone(_1074157)), _1074159) = c_Groups_Oone__class_Oone(_1074157))], (13472 ^ _773908) ^ [_1000193, _1000195, _1000197, _1000199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000193, tc_HOL_Obool)), _1000195), _1000197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000193, tc_HOL_Obool)), _1000197), _1000199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000193, tc_HOL_Obool)), _1000195), _1000199)))], (31687 ^ _773908) ^ [_1358232, _1358234, _1358236, _1358238] : [31689 ^ _773908 : [(31692 ^ _773908) ^ [] : [hAPP(_1358238, 31688 ^ [_1358232, _1358234, _1358236, _1358238]) = c_Orderings_Obot__class_Obot(tc_fun(_1358234, tc_HOL_Obool))], (31690 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358232), 31688 ^ [_1358232, _1358234, _1358236, _1358238]), _1358236)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358232, tc_fun(_1358234, tc_HOL_Obool)), _1358236), _1358238) = c_Orderings_Obot__class_Obot(tc_fun(_1358234, tc_HOL_Obool)))], (35474 ^ _773908) ^ [_1438877, _1438879, _1438881] : [class_Orderings_Oord(_1438877), 35477 ^ _773908 : [(35484 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438877), _1438881), _1438879)), -(hBOOL(hAPP(hAPP(c_member(_1438877), _1438879), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438877), _1438881))))], (35478 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1438877), _1438879), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438877), _1438881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438877), _1438881), _1438879)))]]], (26077 ^ _773908) ^ [_1236354, _1236356, _1236358, _1236360] : [26091 ^ _773908 : [(26094 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1236360, 26090 ^ [_1236354, _1236356, _1236358, _1236360])))], (26092 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1236354), 26090 ^ [_1236354, _1236356, _1236358, _1236360]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1236354, tc_HOL_Obool)), _1236356), _1236358))))]], 26078 ^ _773908 : [(26085 ^ _773908) ^ [_1236563] : [hBOOL(hAPP(hAPP(c_member(_1236354), _1236563), _1236358)), hBOOL(hAPP(_1236360, _1236563))], (26079 ^ _773908) ^ [_1236467] : [hBOOL(hAPP(hAPP(c_member(_1236354), _1236467), _1236356)), hBOOL(hAPP(_1236360, _1236467))]]], (32606 ^ _773908) ^ [_1378948, _1378950, _1378952] : [class_Groups_Oordered__ab__group__add(_1378948), -(hAPP(c_Set_Oimage(_1378948, _1378948, c_Groups_Ouminus__class_Ouminus(_1378948)), c_SetInterval_Oord__class_OatLeastAtMost(_1378948, _1378950, _1378952)) = c_SetInterval_Oord__class_OatLeastAtMost(_1378948, hAPP(c_Groups_Ouminus__class_Ouminus(_1378948), _1378952), hAPP(c_Groups_Ouminus__class_Ouminus(_1378948), _1378950)))], (7601 ^ _773908) ^ [_897114, _897116, _897118, _897120, _897122, _897124] : [-(c_Com_Ocom_OLocal(_897114, _897116, _897118) = c_Com_Ocom_OLocal(_897120, _897122, _897124)), _897114 = _897120, _897116 = _897122, _897118 = _897124], (2544 ^ _773908) ^ [_811464, _811466, _811468, _811470] : [-(c_Orderings_Oord_Omin(_811470, _811466) = c_Orderings_Oord_Omin(_811468, _811464)), _811470 = _811468, _811466 = _811464], (18991 ^ _773908) ^ [_1102018] : [class_Rings_Oring__1(_1102018), -(hBOOL(hAPP(hAPP(c_member(_1102018), c_Groups_Oone__class_Oone(_1102018)), c_Int_Oring__1__class_OInts(_1102018))))], (46716 ^ _773908) ^ [_1709579, _1709581, _1709583] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1709579, _1709579)), hAPP(hAPP(c_Product__Type_OPair(_1709579, _1709579), _1709581), _1709581)), c_Transitive__Closure_Ortrancl(_1709579, _1709583))))], (26418 ^ _773908) ^ [_1246811, _1246813, _1246815, _1246817, _1246819, _1246821] : [26419 ^ _773908 : [(26422 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1246817, _1246813), _1246815))], (26420 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1246811, _1246813), _1246815))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246819, tc_fun(_1246821, tc_HOL_Obool))), _1246817), _1246811), _1246813), _1246815)))], (33618 ^ _773908) ^ [_1398336, _1398338, _1398340] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398336), _1398338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398336, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398336, _1398336, _1398340), _1398338)), _1398338)), c_Fun_Oinj__on(_1398336, _1398336, _1398340, _1398338), -(hAPP(c_Set_Oimage(_1398336, _1398336, _1398340), _1398338) = _1398338)], (39954 ^ _773908) ^ [_1553989, _1553991, _1553993] : [_1553989 = _1553991, 39957 ^ _773908 : [(39960 ^ _773908) ^ [_1554137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1554137), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553993)), _1553989))), -(hAPP(hAPP(c_List_Onth(_1553993), _1553989), _1554137) = hAPP(hAPP(c_List_Onth(_1553993), _1553991), _1554137))], (39958 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553993)), _1553989) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553993)), _1553991))]]], (7439 ^ _773908) ^ [_894296, _894298, _894300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894296), _894298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _894300), _894298))))], (43049 ^ _773908) ^ [_1628193, _1628195, _1628197] : [-(hBOOL(hAPP(hAPP(c_member(_1628193), _1628195), hAPP(c_List_Oset(_1628193), _1628197)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628193)), c_List_Oremove1(_1628193, _1628195, _1628197)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628193)), _1628197))], (48065 ^ _773908) ^ [_1742332, _1742334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1742332, _1742332)), _1742334), c_Relation_OId(_1742332))), -(_1742334 = hAPP(hAPP(c_Product__Type_OPair(_1742332, _1742332), 48068 ^ [_1742332, _1742334]), 48068 ^ [_1742332, _1742334]))], (15695 ^ _773908) ^ [_1040922, _1040924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040922), _1040924)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040922), _1040924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5000 ^ _773908) ^ [_850254, _850256, _850258, _850260, _850262, _850264] : [-(c_Random__Sequence_Oempty(_850264, _850260, _850256) = c_Random__Sequence_Oempty(_850262, _850258, _850254)), _850264 = _850262, _850260 = _850258, _850256 = _850254], (9553 ^ _773908) ^ [_933053, _933055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _933053)), hAPP(c_Int_Onat, _933055))), 9556 ^ _773908 : [(9559 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933053), _933055)))], (9557 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _933055)))]]], (1724 ^ _773908) ^ [_798444, _798446] : [-(class_Groups_Osemigroup__add(_798444)), _798446 = _798444, class_Groups_Osemigroup__add(_798446)], (37342 ^ _773908) ^ [_1478908, _1478910, _1478912, _1478914, _1478916, _1478918] : [hBOOL(hAPP(hAPP(c_member(_1478908), _1478910), _1478912)), hBOOL(hAPP(hAPP(c_member(_1478914), _1478916), hAPP(_1478918, _1478910))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478908, _1478914)), hAPP(hAPP(c_Product__Type_OPair(_1478908, _1478914), _1478910), _1478916)), hAPP(hAPP(c_Product__Type_OSigma(_1478908, _1478914), _1478912), _1478918))))], (24481 ^ _773908) ^ [_1203895, _1203897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203897)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203895), _1203897) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1203895, _1203897)))], (41951 ^ _773908) ^ [_1601213, _1601215, _1601217, _1601219] : [-(hAPP(c_List_Oset(_1601213), hAPP(hAPP(c_List_Omap(_1601215, _1601213), _1601217), _1601219)) = hAPP(c_Set_Oimage(_1601215, _1601213, _1601217), hAPP(c_List_Oset(_1601215), _1601219)))], (20053 ^ _773908) ^ [_1119991, _1119993] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1119991))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1119993))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119991)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119993)))], (15651 ^ _773908) ^ [_1040118, _1040120, _1040122] : [class_Groups_Ogroup__add(_1040118), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040118), _1040120), hAPP(c_Groups_Ouminus__class_Ouminus(_1040118), _1040122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040118), _1040120), _1040122))], (40233 ^ _773908) ^ [_1560691, _1560693, _1560695, _1560697, _1560699] : [hAPP(hAPP(c_List_Odrop(_1560691), _1560693), _1560695) = hAPP(hAPP(c_List_Olist_OCons(_1560691), _1560697), _1560699), -(hAPP(hAPP(c_List_Onth(_1560691), _1560695), _1560693) = _1560697)], (39979 ^ _773908) ^ [_1554591, _1554593, _1554595] : [-(hAPP(hAPP(c_List_Onth(_1554591), hAPP(hAPP(c_List_Olist_OCons(_1554591), _1554593), _1554595)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1554593)], (20993 ^ _773908) ^ [_1137113, _1137115, _1137117] : [class_Fields_Olinordered__field(_1137113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137113), c_Groups_Ozero__class_Ozero(_1137113)), _1137115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137113), _1137117), c_Groups_Ozero__class_Ozero(_1137113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137113), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137113), _1137115), _1137117)), c_Groups_Ozero__class_Ozero(_1137113))))], (45621 ^ _773908) ^ [_1685281, _1685283, _1685285] : [-(hAPP(c_List_Orev(_1685281), hAPP(hAPP(c_List_Odrop(_1685281), _1685283), _1685285)) = hAPP(hAPP(c_List_Otake(_1685281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685281)), _1685285)), _1685283)), hAPP(c_List_Orev(_1685281), _1685285)))], (42963 ^ _773908) ^ [_1626499, _1626501, _1626503, _1626505, _1626507] : [class_Groups_Ocomm__monoid__add(_1626499), hBOOL(hAPP(hAPP(c_member(_1626501), _1626503), hAPP(c_List_Oset(_1626501), _1626505))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626499), hAPP(hAPP(c_List_Omap(_1626501, _1626499), _1626507), _1626505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1626499), hAPP(_1626507, _1626503)), hAPP(c_List_Omonoid__add__class_Olistsum(_1626499), hAPP(hAPP(c_List_Omap(_1626501, _1626499), _1626507), c_List_Oremove1(_1626501, _1626503, _1626505)))))], (8845 ^ _773908) ^ [_920419, _920421] : [class_Rings_Omult__zero(_920419), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920419), c_Groups_Ozero__class_Ozero(_920419)), _920421) = c_Groups_Ozero__class_Ozero(_920419))], (51570 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (6057 ^ _773908) ^ [_871367, _871369] : [_871367 = _871369, -(hAPP(c_Nat_OSuc, _871367) = hAPP(c_Nat_OSuc, _871369))], (12596 ^ _773908) ^ [_985040, _985042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985042)), _985040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985040), _985042))], (28174 ^ _773908) ^ [_1284453, _1284455, _1284457, _1284459] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284453, tc_HOL_Obool)), _1284455), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284453, tc_HOL_Obool)), _1284457), _1284459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284453, tc_HOL_Obool)), _1284457), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284453, tc_HOL_Obool)), _1284455), _1284459)))], (16533 ^ _773908) ^ [_1057690, _1057692] : [class_Int_Onumber__ring(_1057690), 16536 ^ _773908 : [(16543 ^ _773908) ^ [] : [-(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), _1057692)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1057690), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1057692)) = c_Groups_Ozero__class_Ozero(_1057690))], (16537 ^ _773908) ^ [] : [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), _1057692))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1057690), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1057692)) = hAPP(c_Int_Onumber__class_Onumber__of(_1057690), _1057692))]]], (10681 ^ _773908) ^ [_951034, _951036, _951038] : [class_Groups_Oordered__ab__group__add(_951034), 10684 ^ _773908 : [(10691 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951034), _951038), _951036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951034), hAPP(c_Groups_Ouminus__class_Ouminus(_951034), _951036)), hAPP(c_Groups_Ouminus__class_Ouminus(_951034), _951038))))], (10685 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951034), hAPP(c_Groups_Ouminus__class_Ouminus(_951034), _951036)), hAPP(c_Groups_Ouminus__class_Ouminus(_951034), _951038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951034), _951038), _951036)))]]], (19431 ^ _773908) ^ [_1109343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1109343)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109343), c_Int_OPls)))], (13097 ^ _773908) ^ [_993681, _993683] : [_993681 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993681), _993683), -(_993683 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_993681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3980 ^ _773908) ^ [_834036, _834038] : [_834038 = _834036, -(c_Orderings_Oord__class_Omax(_834038) = c_Orderings_Oord__class_Omax(_834036))], (50273 ^ _773908) ^ [_1791578, _1791580] : [c_Relation_Otrans(_1791578, _1791580), -(c_Relation_Otrans(_1791578, hAPP(c_Relation_Oconverse(_1791578, _1791578), _1791580)))], (45461 ^ _773908) ^ [_1682030, _1682032, _1682034, _1682036, _1682038] : [c_List_Olist__all2(_1682030, _1682032, _1682034, hAPP(c_List_Orev(_1682030), _1682036), hAPP(c_List_Orev(_1682032), _1682038)), -(c_List_Olist__all2(_1682030, _1682032, _1682034, _1682036, _1682038))], (37137 ^ _773908) ^ [_1473812, _1473814, _1473816, _1473818, _1473820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473812, tc_HOL_Obool)), _1473814), _1473816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473818, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473818, _1473812, _1473820), _1473814)), hAPP(c_Set_Ovimage(_1473818, _1473812, _1473820), _1473816))))], (16911 ^ _773908) ^ [_1064760, _1064762, _1064764, _1064766] : [class_Int_Onumber__ring(_1064760), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064760), hAPP(c_Int_Onumber__class_Onumber__of(_1064760), _1064762)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064760), hAPP(c_Int_Onumber__class_Onumber__of(_1064760), _1064764)), _1064766)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064760), hAPP(c_Int_Onumber__class_Onumber__of(_1064760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1064762), _1064764))), _1064766))], (23474 ^ _773908) ^ [_1183199, _1183201, _1183203] : [-(hAPP(c_Nat_Onat_Onat__rec(_1183199, _1183201, _1183203), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1183201)], (46379 ^ _773908) ^ [_1701941, _1701943] : [class_Enum_Oenum(_1701941), 46382 ^ _773908 : [(46390 ^ _773908) ^ [] : [46391 ^ _773908 : [(46392 ^ _773908) ^ [_1702121] : [hBOOL(hAPP(_1701943, _1702121))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1701941), _1701943)))], (46383 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1701941), _1701943)), -(hBOOL(hAPP(_1701943, 46386 ^ [_1701941, _1701943])))]]], (36369 ^ _773908) ^ [_1458104, _1458106] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1458104, tc_HOL_Obool)), _1458106)))], (18925 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (33850 ^ _773908) ^ [_1402916, _1402918, _1402920, _1402922, _1402924] : [class_Orderings_Olinorder(_1402916), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402916, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402916, _1402918), _1402920)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402916, _1402922), _1402924)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402916, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1402916), _1402918), _1402922)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402916), _1402920), _1402924)))], (38284 ^ _773908) ^ [_1505752, _1505754, _1505756, _1505758] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1505752, _1505754), _1505756), _1505758) = hAPP(c_Set_OCollect(tc_prod(_1505754, _1505754)), hAPP(c_Product__Type_Oprod_Oprod__case(_1505754, _1505754, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1505754, tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_fun(_1505754, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505754, tc_fun(tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_fun(_1505754, tc_HOL_Obool)), _1505754), c_COMBC(_1505754, tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505754, tc_prod(_1505752, _1505752)), tc_fun(_1505754, tc_fun(tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_HOL_Obool)), _1505754), hAPP(c_COMBB(tc_prod(_1505752, _1505752), tc_fun(tc_fun(tc_prod(_1505752, _1505752), tc_HOL_Obool), tc_HOL_Obool), _1505754), c_member(tc_prod(_1505752, _1505752)))), hAPP(hAPP(c_COMBC(_1505754, tc_fun(_1505754, _1505752), tc_fun(_1505754, tc_prod(_1505752, _1505752))), hAPP(hAPP(c_COMBB(tc_fun(_1505752, tc_prod(_1505752, _1505752)), tc_fun(tc_fun(_1505754, _1505752), tc_fun(_1505754, tc_prod(_1505752, _1505752))), _1505754), c_COMBB(_1505752, tc_prod(_1505752, _1505752), _1505754)), hAPP(hAPP(c_COMBB(_1505752, tc_fun(_1505752, tc_prod(_1505752, _1505752)), _1505754), c_Product__Type_OPair(_1505752, _1505752)), _1505758))), _1505758)))), _1505756))))], (44650 ^ _773908) ^ [_1666401, _1666403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666401), _1666403)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1666401, _1666403)) = _1666401)], (15497 ^ _773908) ^ [_1036925, _1036927, _1036929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036925), _1036927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036929), _1036927)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036929), _1036925))))], (928 ^ _773908) ^ [_788064, _788066, _788068, _788070] : [-(c_Relation_Oantisym(_788068, _788064)), c_Relation_Oantisym(_788070, _788066), _788070 = _788068, _788066 = _788064], (18875 ^ _773908) ^ [_1100255] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1100255), c_Int_OPls) = _1100255)], (5282 ^ _773908) ^ [_854645, _854647, _854649, _854651] : [-(c_Hilbert__Choice_OEps(_854651, _854647) = c_Hilbert__Choice_OEps(_854649, _854645)), _854651 = _854649, _854647 = _854645], (10783 ^ _773908) ^ [_952929, _952931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952931)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _952929)), hAPP(c_Int_Onat, _952931)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _952929), _952931)))], (40573 ^ _773908) ^ [_1569101, _1569103, _1569105, _1569107] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1569101, _1569103))), hAPP(hAPP(c_List_Ozip(_1569101, _1569103), _1569105), _1569107)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569101)), _1569105)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569103)), _1569107)))], (122 ^ _773908) ^ [_775667, _775669, _775671, _775673, _775675, _775677, _775679, _775681] : [-(c_Natural_Oevaln(_775679, _775675, _775671, _775667)), c_Natural_Oevaln(_775681, _775677, _775673, _775669), _775681 = _775679, _775677 = _775675, _775673 = _775671, _775669 = _775667], (51542 ^ _773908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (24555 ^ _773908) ^ [_1206356, _1206358, _1206360, _1206362, _1206364] : [hBOOL(hAPP(hAPP(_1206356, _1206358), _1206360)), -(hBOOL(hAPP(hAPP(_1206356, hAPP(c_Product__Type_Osnd(_1206362, _1206364), hAPP(hAPP(c_Product__Type_OPair(_1206362, _1206364), _1206360), _1206358))), hAPP(c_Product__Type_Ofst(_1206362, _1206364), hAPP(hAPP(c_Product__Type_OPair(_1206362, _1206364), _1206360), _1206358)))))], (6034 ^ _773908) ^ [_870948, _870950, _870952, _870954] : [-(c_Hoare__Mirabelle_Otriple__valid(_870948, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_870948), _870950), hAPP(c_Com_Ocom_OBODY, _870952)), _870954)))], (36315 ^ _773908) ^ [_1455891, _1455893, _1455895, _1455897] : [c_Fun_Oinj__on(_1455891, _1455893, _1455895, c_Orderings_Otop__class_Otop(tc_fun(_1455891, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455893, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1455891, _1455893, _1455895), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1455891, tc_HOL_Obool)), _1455897))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1455893, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1455891, _1455893, _1455895), _1455897)))))], (49089 ^ _773908) ^ [_1763844, _1763846, _1763848] : [49091 ^ _773908 : [(49094 ^ _773908) ^ [] : [hBOOL(hAPP(_1763846, 49090 ^ [_1763844, _1763846, _1763848]))], (49092 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763844), 49090 ^ [_1763844, _1763846, _1763848]), hAPP(c_List_Oset(_1763844), _1763848))))]], -(c_List_Olist__all(_1763844, _1763846, _1763848))], (19341 ^ _773908) ^ [_1107863, _1107865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107863)), c_Int_OBit1(_1107865))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107863), _1107865)))], (37746 ^ _773908) ^ [_1490796, _1490798, _1490800] : [c_Relation_Orefl__on(_1490796, _1490798, _1490800), 37749 ^ _773908 : [(37752 ^ _773908) ^ [_1490978] : [hBOOL(hAPP(hAPP(c_member(_1490796), _1490978), _1490798)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490796, _1490796)), hAPP(hAPP(c_Product__Type_OPair(_1490796, _1490796), _1490978), _1490978)), _1490800)))], (37750 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490796, _1490796), tc_HOL_Obool)), _1490800), hAPP(hAPP(c_Product__Type_OSigma(_1490796, _1490796), _1490798), hAPP(c_COMBK(tc_fun(_1490796, tc_HOL_Obool), _1490796), _1490798)))))]]], (13131 ^ _773908) ^ [_994315, _994317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994315)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994315), _994317)))], (8347 ^ _773908) ^ [_911490, _911492] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911490) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911492), -(_911490 = _911492)], (33186 ^ _773908) ^ [_1390478, _1390480, _1390482, _1390484, _1390486] : [c_Fun_Oinj__on(_1390478, _1390480, _1390482, _1390484), c_Fun_Oinj__on(_1390478, _1390480, _1390482, _1390486), -(c_Fun_Oinj__on(_1390478, _1390480, _1390482, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390478, tc_HOL_Obool)), _1390484), _1390486)))], (11583 ^ _773908) ^ [_967387] : [-(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), _967387))))], (8047 ^ _773908) ^ [_905680, _905682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905680), _905682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905680)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905682))))], (50348 ^ _773908) ^ [_1793347, _1793349] : [c_Relation_Oantisym(_1793347, _1793349), -(c_Relation_Oantisym(_1793347, hAPP(c_Relation_Oconverse(_1793347, _1793347), _1793349)))], (21767 ^ _773908) ^ [_1150614, _1150616, _1150618, _1150620] : [class_Fields_Ofield(_1150614), -(_1150616 = c_Groups_Ozero__class_Ozero(_1150614)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150614), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150614), _1150618), _1150616)), _1150620) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150614), _1150618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150614), _1150616), _1150620))), _1150616))], (35437 ^ _773908) ^ [_1438141, _1438143, _1438145, _1438147, _1438149] : [class_Groups_Ocomm__monoid__add(_1438141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438143), _1438145)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438143), _1438147)), 35451 ^ _773908 : [(35454 ^ _773908) ^ [] : [hAPP(_1438149, 35450 ^ [_1438141, _1438143, _1438145, _1438147, _1438149]) = c_Groups_Ozero__class_Ozero(_1438141)], (35452 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438143), 35450 ^ [_1438141, _1438143, _1438145, _1438147, _1438149]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438143, tc_HOL_Obool)), _1438145), _1438147))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438143, _1438141), _1438149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438143, tc_HOL_Obool)), _1438145), _1438147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438141), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438143, _1438141), _1438149), _1438145)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438143, _1438141), _1438149), _1438147)))], (12336 ^ _773908) ^ [_980421, _980423, _980425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980421)), _980421 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980421), _980425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _980423), _980421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _980425)))], (37110 ^ _773908) ^ [_1473210, _1473212, _1473214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473210), _1473212)), 37116 ^ _773908 : [(37119 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1473214, 37115 ^ [_1473210, _1473212, _1473214])))], (37117 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473210), 37115 ^ [_1473210, _1473212, _1473214]), _1473212)))]], -(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(_1473210, tc_Nat_Onat), _1473214), _1473212))))], (44949 ^ _773908) ^ [_1672424] : [class_Orderings_Olinorder(_1672424), -(c_List_Olinorder__class_Osorted(_1672424, c_List_Olist_ONil(_1672424)))], (51462 ^ _773908) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (19359 ^ _773908) ^ [_1108187, _1108189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108187), _1108189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108187)), c_Int_OBit1(_1108189))))], (51396 ^ _773908) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (14352 ^ _773908) ^ [_1016660, _1016662, _1016664] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016662), _1016664)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016660), _1016662)), _1016664))], (24709 ^ _773908) ^ [_1209553, _1209555] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1209553)), hAPP(c_Nat_OSuc, _1209555)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1209553), _1209555)))], (12164 ^ _773908) ^ [_977789] : [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)), _977789)), _977789)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _977789), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49745 ^ _773908) ^ [_1778221, _1778223, _1778225, _1778227] : [hBOOL(hAPP(hAPP(c_List_Omember(_1778221), hAPP(hAPP(c_List_Olist_OCons(_1778221), _1778223), _1778225)), _1778227)), -(_1778223 = _1778227), -(hBOOL(hAPP(hAPP(c_List_Omember(_1778221), _1778225), _1778227)))], (27910 ^ _773908) ^ [_1279070, _1279072, _1279074, _1279076, _1279078] : [class_Lattices_Osemilattice__inf(_1279070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279070), _1279072), _1279074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279070), _1279076), _1279078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279070), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1279070), _1279072), _1279076)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1279070), _1279074), _1279078))))], (7077 ^ _773908) ^ [_888554, _888556] : [class_Groups_Omonoid__add(_888554), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888554), _888556), c_Groups_Ozero__class_Ozero(_888554)) = _888556)], (28506 ^ _773908) ^ [_1292714, _1292716, _1292718, _1292720, _1292722] : [c_Finite__Set_Ofolding__one(_1292714, _1292716, _1292718), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292714), _1292720)), -(_1292720 = c_Orderings_Obot__class_Obot(tc_fun(_1292714, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292714), _1292722)), -(_1292722 = c_Orderings_Obot__class_Obot(tc_fun(_1292714, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292714, tc_HOL_Obool)), _1292720), _1292722) = c_Orderings_Obot__class_Obot(tc_fun(_1292714, tc_HOL_Obool)), -(hAPP(_1292718, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292714, tc_HOL_Obool)), _1292720), _1292722)) = hAPP(hAPP(_1292716, hAPP(_1292718, _1292720)), hAPP(_1292718, _1292722)))], (7948 ^ _773908) ^ [_903939, _903941, _903943, _903945, _903947] : [hBOOL(hAPP(_903939, _903941)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_903943), _903941), _903945)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_903939, _903943)), _903945), _903947)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_903939, _903943)), _903941), _903947)))], (36665 ^ _773908) ^ [_1464727, _1464729] : [-(c_Nitpick_Onumber__of__frac(_1464727, _1464729) = c_Nitpick_OAbs__Frac(_1464727, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1464729), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43093 ^ _773908) ^ [_1629114, _1629116] : [-(c_List_Opartition(_1629114, _1629116, c_List_Olist_ONil(_1629114)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629114), tc_List_Olist(_1629114)), c_List_Olist_ONil(_1629114)), c_List_Olist_ONil(_1629114)))], (45968 ^ _773908) ^ [_1692747, _1692749] : [class_Orderings_Olinorder(_1692747), 45975 ^ _773908 : [(45980 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1692747), hAPP(hAPP(c_List_Onth(_1692747), _1692749), 45973 ^ [_1692747, _1692749])), hAPP(hAPP(c_List_Onth(_1692747), _1692749), 45974 ^ [_1692747, _1692749])))], (45978 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45974 ^ [_1692747, _1692749]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692747)), _1692749))))], (45976 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45973 ^ [_1692747, _1692749]), 45974 ^ [_1692747, _1692749])))]], -(c_List_Olinorder__class_Osorted(_1692747, _1692749))], (42033 ^ _773908) ^ [_1604555, _1604557, _1604559, _1604561] : [hBOOL(hAPP(hAPP(c_member(_1604557), _1604561), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604555, tc_fun(_1604557, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604555, tc_HOL_Obool))), _1604559))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604555, tc_fun(_1604557, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604555, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1604557, tc_HOL_Obool), tc_fun(_1604557, tc_HOL_Obool), _1604555), hAPP(c_COMBC(_1604557, tc_fun(_1604557, tc_HOL_Obool), tc_HOL_Obool), c_member(_1604557))), _1604559)), _1604561)))], (46656 ^ _773908) ^ [_1707978, _1707980] : [46658 ^ _773908 : [(46661 ^ _773908) ^ [] : [46657 ^ [_1707978, _1707980] = c_Orderings_Obot__class_Obot(tc_fun(_1707978, tc_HOL_Obool))], (46659 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1707978, tc_HOL_Obool)), 46657 ^ [_1707978, _1707980]), hAPP(c_Relation_OImage(_1707978, _1707978, _1707980), 46657 ^ [_1707978, _1707980]))))]], -(c_Wellfounded_Owf(_1707978, _1707980))], (31993 ^ _773908) ^ [_1366834, _1366836] : [hAPP(c_Int_ORep__Integ, _1366834) = hAPP(c_Int_ORep__Integ, _1366836), -(_1366834 = _1366836)], (34882 ^ _773908) ^ [_1425483, _1425485, _1425487, _1425489] : [class_Groups_Ocomm__monoid__add(_1425483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425485), _1425487)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425485, _1425483), _1425489), _1425487) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425483, _1425485, c_Groups_Oplus__class_Oplus(_1425483)), _1425489), c_Groups_Ozero__class_Ozero(_1425483)), _1425487))], (51834 ^ _773908) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (30811 ^ _773908) ^ [_1338328, _1338330, _1338332, _1338334] : [class_Groups_Ocomm__monoid__mult(_1338328), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338330), _1338332))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338330, _1338328), _1338334), _1338332) = c_Groups_Oone__class_Oone(_1338328))], (11645 ^ _773908) ^ [_968403] : [11646 ^ _773908 : [(11647 ^ _773908) ^ [_968460] : [hBOOL(hAPP(_968403, _968460))]], 11649 ^ _773908 : [(11652 ^ _773908) ^ [] : [-(hBOOL(hAPP(_968403, hAPP(c_Int_Onat, 11648 ^ [_968403]))))], (11650 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11648 ^ [_968403])))]]], (51490 ^ _773908) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (26802 ^ _773908) ^ [_1256897, _1256899, _1256901, _1256903, _1256905, _1256907] : [-(c_Fun_Ofun__upd(_1256897, _1256899, c_Fun_Ofun__upd(_1256897, _1256899, _1256901, _1256903, _1256905), _1256903, _1256907) = c_Fun_Ofun__upd(_1256897, _1256899, _1256901, _1256903, _1256907))], (49205 ^ _773908) ^ [_1766225, _1766227, _1766229] : [-(c_List_Olist__ex1(_1766225, _1766227, _1766229)), 49206 ^ _773908 : [(49207 ^ _773908) ^ [_1766319] : [hBOOL(hAPP(hAPP(c_member(_1766225), _1766319), hAPP(c_List_Oset(_1766225), _1766229))), hBOOL(hAPP(_1766227, _1766319)), 49215 ^ _773908 : [(49220 ^ _773908) ^ [] : [49214 ^ [_1766225, _1766227, _1766229, _1766319] = _1766319], (49218 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1766227, 49214 ^ [_1766225, _1766227, _1766229, _1766319])))], (49216 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766225), 49214 ^ [_1766225, _1766227, _1766229, _1766319]), hAPP(c_List_Oset(_1766225), _1766229))))]]]]], (46971 ^ _773908) ^ [_1716246, _1716248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1716246), _1716248)), -(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), _1716246), _1716248)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (26631 ^ _773908) ^ [_1251869, _1251871, _1251873, _1251875, _1251877] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1251873, _1251869)), hAPP(hAPP(c_Product__Type_OPair(_1251873, _1251869), _1251877), _1251871)), _1251875)), -(hBOOL(hAPP(hAPP(c_member(_1251869), _1251871), hAPP(c_Relation_OImage(_1251873, _1251869, _1251875), hAPP(hAPP(c_Set_Oinsert(_1251873), _1251877), c_Orderings_Obot__class_Obot(tc_fun(_1251873, tc_HOL_Obool)))))))], (28458 ^ _773908) ^ [_1291580, _1291582, _1291584, _1291586, _1291588, _1291590, _1291592, _1291594] : [c_Finite__Set_Ofolding__image__simple(_1291580, _1291582, _1291584, _1291586, _1291588, _1291590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291582), _1291592)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291582), _1291594)), -(hAPP(hAPP(_1291584, hAPP(_1291590, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291582, tc_HOL_Obool)), _1291592), _1291594))), hAPP(_1291590, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291582, tc_HOL_Obool)), _1291592), _1291594))) = hAPP(hAPP(_1291584, hAPP(_1291590, _1291592)), hAPP(_1291590, _1291594)))], (51552 ^ _773908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (42876 ^ _773908) ^ [_1624550, _1624552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624550)), hAPP(c_Code__Numeral_Onat__of, _1624552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1624550), _1624552)))], (48792 ^ _773908) ^ [_1757136, _1757138, _1757140, _1757142] : [class_Lattices_Osemilattice__sup(_1757136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1757136), _1757138)), 48802 ^ _773908 : [(48805 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1757136), 48801 ^ [_1757136, _1757138, _1757140, _1757142]), _1757140))], (48803 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757136), 48801 ^ [_1757136, _1757138, _1757140, _1757142]), _1757138)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1757136), hAPP(hAPP(c_Finite__Set_Ofold(_1757136, _1757136, c_Lattices_Osemilattice__sup__class_Osup(_1757136)), _1757142), _1757138)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1757136), _1757140), _1757142))))], (46005 ^ _773908) ^ [_1693475, _1693477, _1693479] : [class_Orderings_Olinorder(_1693475), -(c_List_Olinorder__class_Osort__key(_1693477, _1693475, _1693479, c_List_Olist_ONil(_1693477)) = c_List_Olist_ONil(_1693477))], (11727 ^ _773908) ^ [_969758, _969760] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969760)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969758), _969760)))], (26741 ^ _773908) ^ [] : [-(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))))))], (2422 ^ _773908) ^ [_809537, _809539] : [_809539 = _809537, -(c_Divides_Oadjust(_809539) = c_Divides_Oadjust(_809537))], (51554 ^ _773908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (48421 ^ _773908) ^ [_1749900, _1749902, _1749904] : [class_Orderings_Olinorder(_1749900), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749900), _1749902)), -(c_Big__Operators_Olinorder__class_OMax(_1749900, hAPP(hAPP(c_Set_Oinsert(_1749900), _1749904), _1749902)) = hAPP(hAPP(c_Finite__Set_Ofold(_1749900, _1749900, c_Orderings_Oord__class_Omax(_1749900)), _1749904), _1749902))], (7209 ^ _773908) ^ [_890493, _890495] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890493), _890495))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890493), hAPP(c_Nat_OSuc, _890495))), -(_890495 = _890493)], (48983 ^ _773908) ^ [_1761738, _1761740, _1761742] : [c_Nitpick_Oless__frac(_1761738, _1761740, _1761742), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1761738), c_Nitpick_Oplus__frac(_1761738, _1761740, c_Nitpick_Ouminus__frac(_1761738, _1761742)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46274 ^ _773908) ^ [_1699601, _1699603, _1699605] : [c_Wellfounded_OwfP(_1699601, _1699603), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1699601, _1699603), _1699605)))], (46917 ^ _773908) ^ [_1714741, _1714743, _1714745, _1714747] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714741), tc_List_Olist(_1714741))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714741), tc_List_Olist(_1714741)), _1714743), _1714745)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1714741), c_List_Olistrel1(_1714741, _1714747)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714741)), _1714743) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714741)), _1714745))], (40765 ^ _773908) ^ [_1573930, _1573932, _1573934, _1573936] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1573930), tc_List_Olist(_1573930))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1573930), tc_List_Olist(_1573930)), _1573932), _1573934)), c_List_Olistrel1(_1573930, _1573936))), 40770 ^ _773908 : [(40775 ^ _773908) ^ [] : [-(_1573934 = hAPP(hAPP(c_List_Olist__update(_1573930, _1573932), 40769 ^ [_1573930, _1573932, _1573934, _1573936]), 40768 ^ [_1573930, _1573932, _1573934, _1573936]))], (40773 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40769 ^ [_1573930, _1573932, _1573934, _1573936]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573930)), _1573932))))], (40771 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573930, _1573930)), hAPP(hAPP(c_Product__Type_OPair(_1573930, _1573930), hAPP(hAPP(c_List_Onth(_1573930), _1573932), 40769 ^ [_1573930, _1573932, _1573934, _1573936])), 40768 ^ [_1573930, _1573932, _1573934, _1573936])), _1573936)))]]], (8207 ^ _773908) ^ [_908889, _908891, _908893, _908895, _908897] : [c_Com_Ocom_OWhile(_908889, _908891) = c_Com_Ocom_OLocal(_908893, _908895, _908897)], (4326 ^ _773908) ^ [_839653, _839655, _839657, _839659, _839661, _839663, _839665, _839667] : [-(c_New__Random__Sequence_Oneg__map(_839667, _839663, _839659, _839655) = c_New__Random__Sequence_Oneg__map(_839665, _839661, _839657, _839653)), _839667 = _839665, _839663 = _839661, _839659 = _839657, _839655 = _839653], (27675 ^ _773908) ^ [_1274621] : [27677 ^ _773908 : [(27680 ^ _773908) ^ [_1274731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27676 ^ [_1274621, _1274731]), _1274731))], (27678 ^ _773908) ^ [_1274697] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27676 ^ [_1274621, _1274697]), _1274621)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1274621)))], (49464 ^ _773908) ^ [_1772416, _1772418, _1772420] : [-(hAPP(c_List_Orev(_1772416), c_List_Oreplicate(_1772416, _1772418, _1772420)) = c_List_Oreplicate(_1772416, _1772418, _1772420))], (38735 ^ _773908) ^ [_1522179, _1522181, _1522183] : [c_Wellfounded_Owf(_1522179, _1522181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522179, _1522179), tc_HOL_Obool)), _1522183), _1522181)), -(c_Wellfounded_Owf(_1522179, _1522183))], (7267 ^ _773908) ^ [_891382, _891384, _891386] : [c_Com_Ocom_OAss(_891382, _891384) = hAPP(c_Com_Ocom_OBODY, _891386)], (39875 ^ _773908) ^ [_1551738, _1551740, _1551742, _1551744] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551738)), hAPP(hAPP(c_List_Olist_OCons(_1551738), _1551740), _1551742)), c_List_Olists(_1551738, _1551744))), 39878 ^ _773908 : [(39881 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551738)), _1551742), c_List_Olists(_1551738, _1551744))))], (39879 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551738), _1551740), _1551744)))]]], (20441 ^ _773908) ^ [_1126620, _1126622, _1126624] : [class_Rings_Oring__1(_1126620), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126620), hAPP(c_Groups_Ouminus__class_Ouminus(_1126620), _1126622)), 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)))), _1126624)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1126620), _1126622), 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)))), _1126624)))], (13668 ^ _773908) ^ [_1004127, _1004129] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004127, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1004129)) = 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), _1004127), _1004129)))], (20329 ^ _773908) ^ [_1124847, _1124849, _1124851] : [class_Rings_Olinordered__semidom(_1124847), hAPP(hAPP(c_Power_Opower__class_Opower(_1124847), _1124849), 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(_1124847), _1124851), 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(_1124847), c_Groups_Ozero__class_Ozero(_1124847)), _1124849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124847), c_Groups_Ozero__class_Ozero(_1124847)), _1124851)), -(_1124849 = _1124851)], (50856 ^ _773908) ^ [_1802501, _1802503, _1802505, _1802507, _1802509] : [c_Fun_Oinj__on(_1802501, _1802503, _1802505, _1802507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802501, tc_HOL_Obool)), _1802509), _1802507)), -(hAPP(c_Set_Oimage(_1802503, _1802501, c_Hilbert__Choice_Oinv__into(_1802501, _1802503, _1802507, _1802505)), hAPP(c_Set_Oimage(_1802501, _1802503, _1802505), _1802509)) = _1802509)], (38432 ^ _773908) ^ [_1512067, _1512069] : [c_Predicate_Oreflp(_1512067, _1512069), -(c_Relation_Orefl__on(_1512067, c_Orderings_Otop__class_Otop(tc_fun(_1512067, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1512067, _1512067)), hAPP(c_Product__Type_Oprod_Oprod__case(_1512067, _1512067, tc_HOL_Obool), _1512069))))], (36478 ^ _773908) ^ [] : [-(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))], (44603 ^ _773908) ^ [_1665046] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1665046)), c_List_Otranspose__rel(_1665046)), c_List_Olist_ONil(tc_List_Olist(_1665046)))), -(c_List_Otranspose(_1665046, c_List_Olist_ONil(tc_List_Olist(_1665046))) = c_List_Olist_ONil(tc_List_Olist(_1665046)))], (17219 ^ _773908) ^ [_1070986, _1070988, _1070990] : [class_Rings_Olinordered__semidom(_1070986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070986), c_Groups_Ozero__class_Ozero(_1070986)), _1070988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070986), _1070988), c_Groups_Oone__class_Oone(_1070986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070986), hAPP(hAPP(c_Power_Opower__class_Opower(_1070986), _1070988), hAPP(c_Nat_OSuc, _1070990))), c_Groups_Oone__class_Oone(_1070986))))], (37934 ^ _773908) ^ [_1494705, _1494707] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1494705))), -(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)), _1494705))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1494707)))) = 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)), _1494705))), 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, _1494707))))))], (48014 ^ _773908) ^ [_1741467, _1741469, _1741471, _1741473] : [c_List_Olist__ex(_1741467, _1741469, hAPP(hAPP(c_List_Oappend(_1741467), _1741471), _1741473)), -(c_List_Olist__ex(_1741467, _1741469, _1741471)), -(c_List_Olist__ex(_1741467, _1741469, _1741473))], (48187 ^ _773908) ^ [_1745131, _1745133, _1745135, _1745137, _1745139] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1745131, _1745133, _1745135), _1745137), _1745139) = c_HOL_OThe(_1745133, c_Finite__Set_Ofold__graph(_1745131, _1745133, _1745135, _1745137, _1745139)))], (41392 ^ _773908) ^ [_1589690, _1589692] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1589690, _1589692))))], (44845 ^ _773908) ^ [_1670385, _1670387] : [class_Groups_Omonoid__add(_1670385), -(hAPP(c_List_Ofoldl(_1670385, _1670385, c_Groups_Oplus__class_Oplus(_1670385), c_Groups_Ozero__class_Ozero(_1670385)), _1670387) = c_List_Ofoldr(_1670385, _1670385, c_Groups_Oplus__class_Oplus(_1670385), _1670387, c_Groups_Ozero__class_Ozero(_1670385)))], (48942 ^ _773908) ^ [_1760598, _1760600, _1760602, _1760604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760598, _1760600)), _1760602), hAPP(c_Relation_Oconverse(_1760600, _1760598), _1760604))), 48947 ^ _773908 : [(48950 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760600, _1760598)), hAPP(hAPP(c_Product__Type_OPair(_1760600, _1760598), 48945 ^ [_1760598, _1760600, _1760602, _1760604]), 48946 ^ [_1760598, _1760600, _1760602, _1760604])), _1760604)))], (48948 ^ _773908) ^ [] : [-(_1760602 = hAPP(hAPP(c_Product__Type_OPair(_1760598, _1760600), 48946 ^ [_1760598, _1760600, _1760602, _1760604]), 48945 ^ [_1760598, _1760600, _1760602, _1760604]))]]], (4368 ^ _773908) ^ [_840340, _840342, _840344, _840346, _840348, _840350, _840352, _840354] : [-(c_New__DSequence_Opos__bind(_840354, _840350, _840346, _840342) = c_New__DSequence_Opos__bind(_840352, _840348, _840344, _840340)), _840354 = _840352, _840350 = _840348, _840346 = _840344, _840342 = _840340], (12734 ^ _773908) ^ [_987246, _987248, _987250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987246), _987248)), _987250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987248), _987250)))], (14340 ^ _773908) ^ [_1016432, _1016434, _1016436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016432), _1016434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016432), _1016436)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016434), _1016436))))], (50995 ^ _773908) ^ [_1805623, _1805625, _1805627, _1805629] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1805623, _1805625, c_Orderings_Otop__class_Otop(tc_fun(_1805623, tc_HOL_Obool)), _1805627), _1805629) = c_Hilbert__Choice_OEps(_1805623, hAPP(hAPP(c_COMBC(_1805623, _1805625, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1805625, tc_fun(_1805625, tc_HOL_Obool), _1805623), c_fequal), _1805627)), _1805629)))], (19953 ^ _773908) ^ [_1118226, _1118228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118226), _1118228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1118226)), c_Int_OBit1(_1118228))))], (39735 ^ _773908) ^ [_1547565, _1547567, _1547569, _1547571, _1547573, _1547575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547565, _1547565)), hAPP(hAPP(c_Product__Type_OPair(_1547565, _1547565), _1547567), _1547569)), _1547571)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1547565), tc_List_Olist(_1547565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1547565), tc_List_Olist(_1547565)), _1547573), _1547575)), c_List_Olistrel(_1547565, _1547571))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1547565), tc_List_Olist(_1547565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1547565), tc_List_Olist(_1547565)), hAPP(hAPP(c_List_Olist_OCons(_1547565), _1547567), _1547573)), hAPP(hAPP(c_List_Olist_OCons(_1547565), _1547569), _1547575))), c_List_Olistrel(_1547565, _1547571))))], (40299 ^ _773908) ^ [_1562345, _1562347, _1562349] : [hAPP(hAPP(c_List_Odrop(_1562345), _1562347), _1562349) = c_List_Olist_ONil(_1562345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562345)), _1562349)), _1562347)))], (23620 ^ _773908) ^ [_1185985, _1185987] : [-(c_Divides_Opdivmod(_1185985, _1185987) = 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), _1185985)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1185987))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1185985), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1185987))))], (14549 ^ _773908) ^ [_1019960, _1019962, _1019964] : [class_Divides_Osemiring__div(_1019960), -(_1019962 = c_Groups_Ozero__class_Ozero(_1019960)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019960), _1019962), _1019964)), _1019962) = _1019964)], (12190 ^ _773908) ^ [_978234, _978236] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978234) = _978236), _978234 = hAPP(c_Int_Onat, _978236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978236))], (22155 ^ _773908) ^ [_1157355, _1157357, _1157359, _1157361] : [class_Fields_Olinordered__field(_1157355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157355), c_Groups_Ozero__class_Ozero(_1157355)), _1157357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157355), _1157359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157355), _1157361), _1157357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157355), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157355), _1157359), _1157357)), _1157361)))], (14348 ^ _773908) ^ [_1016591] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016591) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1614 ^ _773908) ^ [_797069, _797071] : [-(class_Rings_Oordered__comm__semiring(_797069)), _797071 = _797069, class_Rings_Oordered__comm__semiring(_797071)], (24221 ^ _773908) ^ [_1197655, _1197657] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197655, _1197657) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1197655, _1197657)))], (9969 ^ _773908) ^ [_939716, _939718, _939720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939716), _939718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939718), _939720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939716), _939720)))], (35249 ^ _773908) ^ [_1434132, _1434134, _1434136] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1434132), _1434134)), 35252 ^ _773908 : [(35253 ^ _773908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434132, tc_Nat_Onat), _1434136), _1434134) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 35256 ^ _773908 : [(35257 ^ _773908) ^ [_1434294] : [hBOOL(hAPP(hAPP(c_member(_1434132), _1434294), _1434134)), -(hAPP(_1434136, _1434294) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (35263 ^ _773908) ^ [] : [35265 ^ _773908 : [(35268 ^ _773908) ^ [] : [hAPP(_1434136, 35264 ^ [_1434132, _1434134, _1434136]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35266 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434132), 35264 ^ [_1434132, _1434134, _1434136]), _1434134)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434132, tc_Nat_Onat), _1434136), _1434134) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27896 ^ _773908) ^ [_1278821, _1278823, _1278825, _1278827] : [class_Lattices_Osemilattice__inf(_1278821), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278821), _1278823), _1278825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278821), _1278823), _1278827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278821), _1278823), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278821), _1278825), _1278827))))], (1914 ^ _773908) ^ [_800819, _800821] : [-(class_Groups_Oone(_800819)), _800821 = _800819, class_Groups_Oone(_800821)], (35810 ^ _773908) ^ [_1445926, _1445928, _1445930, _1445932, _1445934] : [class_Groups_Ocomm__monoid__add(_1445926), class_Groups_Ocomm__monoid__mult(_1445926), _1445928 = _1445930, c_Nat__Transfer_Onat__set(_1445930), 35828 ^ _773908 : [(35831 ^ _773908) ^ [] : [hAPP(_1445932, 35827 ^ [_1445926, _1445928, _1445930, _1445932, _1445934]) = hAPP(_1445934, 35827 ^ [_1445926, _1445928, _1445930, _1445932, _1445934])], (35829 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35827 ^ [_1445926, _1445928, _1445930, _1445932, _1445934])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1445926), _1445932), _1445928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1445926), _1445934), _1445930))], (19837 ^ _773908) ^ [_1116262, _1116264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116262), _1116264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116262)), c_Int_OBit0(_1116264))))], (12526 ^ _773908) ^ [_983751, _983753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983751), _983753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983753), _983751)), -(_983751 = _983753)], (47098 ^ _773908) ^ [_1719558, _1719560] : [-(hAPP(c_Relation_ODomain(_1719558, _1719558), c_Transitive__Closure_Otrancl(_1719558, _1719560)) = hAPP(c_Relation_ODomain(_1719558, _1719558), _1719560))], (42507 ^ _773908) ^ [_1616692, _1616694, _1616696, _1616698, _1616700] : [_1616692 = c_Orderings_Obot__class_Obot(tc_fun(_1616694, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616694, tc_fun(_1616696, tc_HOL_Obool)), _1616692), hAPP(hAPP(c_COMBB(tc_fun(_1616696, tc_HOL_Obool), tc_fun(_1616696, tc_HOL_Obool), _1616694), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616696, tc_HOL_Obool)), _1616698)), _1616700)) = c_Orderings_Otop__class_Otop(tc_fun(_1616696, tc_HOL_Obool)))], (38784 ^ _773908) ^ [_1523077, _1523079, _1523081, _1523083, _1523085, _1523087] : [hAPP(hAPP(c_List_Oappend(_1523077), _1523079), _1523081) = _1523083, _1523085 = hAPP(hAPP(c_List_Oappend(_1523077), _1523081), _1523087), -(hAPP(hAPP(c_List_Oappend(_1523077), _1523079), _1523085) = hAPP(hAPP(c_List_Oappend(_1523077), _1523083), _1523087))], (7495 ^ _773908) ^ [_895220, _895222, _895224, _895226, _895228, _895230] : [-(hBOOL(hAPP(_895220, _895222))), c_Natural_Oevaln(_895224, _895222, _895226, _895228), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_895220, _895230, _895224), _895222, _895226, _895228))], (13819 ^ _773908) ^ [_1006663, _1006665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006663), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006665), _1006663)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006663, _1006665) = _1006663)], (18565 ^ _773908) ^ [_1094621, _1094623, _1094625, _1094627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1094621, tc_HOL_Obool)), _1094623), _1094625)), hBOOL(hAPP(hAPP(c_member(_1094621), _1094627), _1094623)), -(hBOOL(hAPP(hAPP(c_member(_1094621), _1094627), _1094625)))], (26542 ^ _773908) ^ [_1249668, _1249670, _1249672, _1249674] : [_1249674 = c_Orderings_Obot__class_Obot(tc_fun(_1249668, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1249668, _1249670, _1249672), _1249674) = c_Orderings_Obot__class_Obot(tc_fun(_1249670, tc_HOL_Obool)))], (40723 ^ _773908) ^ [_1572744, _1572746, _1572748, _1572750] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572744, _1572744)), hAPP(hAPP(c_Product__Type_OPair(_1572744, _1572744), _1572746), _1572748)), hAPP(c_List_Oset(tc_prod(_1572744, _1572744)), hAPP(hAPP(c_List_Ozip(_1572744, _1572744), _1572750), _1572750))))), hBOOL(hAPP(hAPP(c_member(_1572744), _1572746), hAPP(c_List_Oset(_1572744), _1572750))), _1572746 = _1572748], (46513 ^ _773908) ^ [_1704534] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 46509 ^ [_1704534]), c_Int_OInteg)))], (13686 ^ _773908) ^ [_1004395] : [class_Groups_Osgn__if(_1004395), -(c_Groups_Osgn__class_Osgn(_1004395, c_Groups_Ozero__class_Ozero(_1004395)) = c_Groups_Ozero__class_Ozero(_1004395))], (32498 ^ _773908) ^ [_1377226, _1377228, _1377230] : [class_Orderings_Oorder(_1377226), 32501 ^ _773908 : [(32508 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377226), _1377228), _1377230))), -(c_Orderings_Obot__class_Obot(tc_fun(_1377226, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1377226, _1377228, _1377230))], (32502 ^ _773908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1377226, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1377226, _1377228, _1377230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377226), _1377228), _1377230))]]], (19971 ^ _773908) ^ [_1118568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1118568)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118568), c_Int_OPls)))], (39681 ^ _773908) ^ [_1546145, _1546147, _1546149, _1546151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1546145), tc_List_Olist(_1546145))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1546145), tc_List_Olist(_1546145)), _1546147), _1546149)), c_List_Olistrel1(_1546145, _1546151))), 39686 ^ _773908 : [(39693 ^ _773908) ^ [] : [-(_1546149 = hAPP(hAPP(c_List_Oappend(_1546145), 39688 ^ [_1546145, _1546147, _1546149, _1546151]), hAPP(hAPP(c_List_Olist_OCons(_1546145), 39685 ^ [_1546145, _1546147, _1546149, _1546151]), 39689 ^ [_1546145, _1546147, _1546149, _1546151])))], (39691 ^ _773908) ^ [] : [-(_1546147 = hAPP(hAPP(c_List_Oappend(_1546145), 39688 ^ [_1546145, _1546147, _1546149, _1546151]), hAPP(hAPP(c_List_Olist_OCons(_1546145), 39684 ^ [_1546145, _1546147, _1546149, _1546151]), 39689 ^ [_1546145, _1546147, _1546149, _1546151])))], (39687 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546145, _1546145)), hAPP(hAPP(c_Product__Type_OPair(_1546145, _1546145), 39684 ^ [_1546145, _1546147, _1546149, _1546151]), 39685 ^ [_1546145, _1546147, _1546149, _1546151])), _1546151)))]]], (15397 ^ _773908) ^ [_1035194, _1035196, _1035198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035194), _1035196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035194), _1035198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035198), _1035196)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035198), _1035194))))], (31275 ^ _773908) ^ [_1348507, _1348509, _1348511, _1348513] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1348507), _1348509)), 31278 ^ _773908 : [(31279 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1348511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1348507, tc_fun(_1348511, tc_HOL_Obool)), _1348509), _1348513))), 31282 ^ _773908 : [(31283 ^ _773908) ^ [_1348691] : [hBOOL(hAPP(hAPP(c_member(_1348507), _1348691), _1348509)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1348511), hAPP(_1348513, _1348691))))]]], (31289 ^ _773908) ^ [] : [31291 ^ _773908 : [(31294 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1348511), hAPP(_1348513, 31290 ^ [_1348507, _1348509, _1348511, _1348513])))], (31292 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348507), 31290 ^ [_1348507, _1348509, _1348511, _1348513]), _1348509)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1348511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1348507, tc_fun(_1348511, tc_HOL_Obool)), _1348509), _1348513))))]]], (44623 ^ _773908) ^ [_1665514, _1665516] : [44625 ^ _773908 : [(44628 ^ _773908) ^ [] : [44624 ^ [_1665514, _1665516] = c_List_Olist_ONil(_1665514)], (44626 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665514)), 44624 ^ [_1665514, _1665516]), hAPP(c_List_Oset(tc_List_Olist(_1665514)), _1665516))))]], -(c_List_Otranspose(_1665514, _1665516) = c_List_Olist_ONil(tc_List_Olist(_1665514)))], (21955 ^ _773908) ^ [_1153729, _1153731, _1153733, _1153735] : [class_Fields_Ofield__inverse__zero(_1153729), class_Int_Onumber(_1153729), 21962 ^ _773908 : [(21963 ^ _773908) ^ [] : [_1153731 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153729), _1153733), hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735)), 21966 ^ _773908 : [(21973 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735) = c_Groups_Ozero__class_Ozero(_1153729), -(_1153731 = c_Groups_Ozero__class_Ozero(_1153729))], (21967 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735) = c_Groups_Ozero__class_Ozero(_1153729)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153729), _1153731), hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735)) = _1153733)]]], (21979 ^ _773908) ^ [] : [-(_1153731 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153729), _1153733), hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735))), 21982 ^ _773908 : [(21985 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153729), _1153731), hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735)) = _1153733], (21983 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735) = c_Groups_Ozero__class_Ozero(_1153729)]], 21986 ^ _773908 : [(21989 ^ _773908) ^ [] : [_1153731 = c_Groups_Ozero__class_Ozero(_1153729)], (21987 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1153729), _1153735) = c_Groups_Ozero__class_Ozero(_1153729))]]]]], (13756 ^ _773908) ^ [_1005631, _1005633] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005631, _1005633) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1005631 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005633), 13759 ^ [_1005631, _1005633]))], (29053 ^ _773908) ^ [_1304294, _1304296, _1304298] : [class_Lattices_Olattice(_1304294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304294), _1304296)), -(_1304298 = c_Orderings_Obot__class_Obot(tc_fun(_1304294, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304294, tc_HOL_Obool)), _1304298), _1304296)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1304294), c_Big__Operators_Olattice__class_OSup__fin(_1304294, _1304298)), c_Big__Operators_Olattice__class_OSup__fin(_1304294, _1304296)) = c_Big__Operators_Olattice__class_OSup__fin(_1304294, _1304296))], (37712 ^ _773908) ^ [_1489540, _1489542, _1489544, _1489546, _1489548, _1489550, _1489552] : [-(hAPP(c_Product__Type_Osnd(_1489540, _1489542), hAPP(c_Product__Type_Omap__pair(_1489544, _1489540, _1489546, _1489542, _1489548, _1489550), _1489552)) = hAPP(_1489550, hAPP(c_Product__Type_Osnd(_1489544, _1489546), _1489552)))], (49908 ^ _773908) ^ [_1782007, _1782009] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1782007, _1782009), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1782007)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47186 ^ _773908) ^ [_1721685, _1721687] : [c_Wellfounded_Oacyclic(_1721685, _1721687), 47189 ^ _773908 : [(47190 ^ _773908) ^ [_1721770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1721685, _1721685)), hAPP(hAPP(c_Product__Type_OPair(_1721685, _1721685), _1721770), _1721770)), c_Transitive__Closure_Otrancl(_1721685, _1721687)))]]], (8741 ^ _773908) ^ [_918596, _918598] : [class_Groups_Ogroup__add(_918596), 8744 ^ _773908 : [(8751 ^ _773908) ^ [] : [_918598 = c_Groups_Ozero__class_Ozero(_918596), -(hAPP(c_Groups_Ouminus__class_Ouminus(_918596), _918598) = c_Groups_Ozero__class_Ozero(_918596))], (8745 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_918596), _918598) = c_Groups_Ozero__class_Ozero(_918596), -(_918598 = c_Groups_Ozero__class_Ozero(_918596))]]], (27148 ^ _773908) ^ [_1263598, _1263600, _1263602] : [27150 ^ _773908 : [(27151 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263598), 27149 ^ [_1263598, _1263600, _1263602]), _1263600)))], (27156 ^ _773908) ^ [] : [27149 ^ [_1263598, _1263600, _1263602] = 27152 ^ [_1263598, _1263600, _1263602]], (27160 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1263598, _1263598)), hAPP(hAPP(c_Product__Type_OPair(_1263598, _1263598), 27152 ^ [_1263598, _1263600, _1263602]), 27149 ^ [_1263598, _1263600, _1263602])), _1263602))], (27158 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1263598, _1263598)), hAPP(hAPP(c_Product__Type_OPair(_1263598, _1263598), 27149 ^ [_1263598, _1263600, _1263602]), 27152 ^ [_1263598, _1263600, _1263602])), _1263602))], (27154 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263598), 27152 ^ [_1263598, _1263600, _1263602]), _1263600)))]], -(c_Relation_Ototal__on(_1263598, _1263600, _1263602))], (14709 ^ _773908) ^ [_1022617, _1022619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022617), _1022619)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022617), _1022619) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15172 ^ _773908) ^ [_1031018, _1031020, _1031022] : [class_Fields_Olinordered__field__inverse__zero(_1031018), 15178 ^ _773908 : [(15183 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031018), 15177 ^ [_1031018, _1031020, _1031022]), _1031020)), _1031022))], (15181 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031018), 15177 ^ [_1031018, _1031020, _1031022]), c_Groups_Oone__class_Oone(_1031018))))], (15179 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031018), c_Groups_Ozero__class_Ozero(_1031018)), 15177 ^ [_1031018, _1031020, _1031022])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031018), _1031020), _1031022)))], (41926 ^ _773908) ^ [_1600517] : [-(hAPP(c_List_Omap(_1600517, _1600517), c_COMBI(_1600517)) = c_Fun_Oid(tc_List_Olist(_1600517)))], (8452 ^ _773908) ^ [_913222, _913224] : [-(hBOOL(hAPP(_913222, hAPP(c_Int_Onat, _913224)))), 8456 ^ _773908 : [(8459 ^ _773908) ^ [] : [hBOOL(hAPP(_913222, 8455 ^ [_913222, _913224]))], (8457 ^ _773908) ^ [] : [-(_913224 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8455 ^ [_913222, _913224]))]], 8460 ^ _773908 : [(8463 ^ _773908) ^ [] : [hBOOL(hAPP(_913222, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8461 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _913224), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11729 ^ _773908) ^ [_969804, _969806] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969804), _969806)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969804)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969806)))], (30734 ^ _773908) ^ [_1336855, _1336857, _1336859, _1336861, _1336863] : [class_Groups_Ocomm__monoid__mult(_1336855), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336857, _1336855), hAPP(hAPP(c_COMBS(_1336857, _1336855, _1336855), hAPP(hAPP(c_COMBB(_1336855, tc_fun(_1336855, _1336855), _1336857), c_Groups_Otimes__class_Otimes(_1336855)), _1336859)), _1336861)), _1336863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336855), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336857, _1336855), _1336859), _1336863)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336857, _1336855), _1336861), _1336863)))], (41500 ^ _773908) ^ [_1591307, _1591309] : [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), _1591307), _1591309))), 41503 ^ _773908 : [(41510 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1591307), _1591309))), -(c_List_Oupto(_1591307, _1591309) = c_List_Olist_ONil(tc_Int_Oint))], (41504 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1591307), _1591309)), -(c_List_Oupto(_1591307, _1591309) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1591307), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1591307), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1591309)))]]], (24871 ^ _773908) ^ [_1212684, _1212686, _1212688, _1212690] : [class_Orderings_Olinorder(_1212684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212684), _1212686), _1212688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212684), _1212686), _1212690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212684), _1212686), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212684), _1212688), _1212690))))], (42620 ^ _773908) ^ [_1619266, _1619268] : [42621 ^ _773908 : [(42622 ^ _773908) ^ [_1619312] : [hBOOL(hAPP(_1619266, _1619312))]], -(hBOOL(hAPP(_1619266, c_Hilbert__Choice_OEps(_1619268, _1619266))))], (17355 ^ _773908) ^ [_1073299, _1073301] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1073299) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073301)), _1073299 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073301)), 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), _1073301)))], (6067 ^ _773908) ^ [_871528, _871530, _871532, _871534] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _871528), _871530, _871532, _871534), 6071 ^ _773908 : [(6074 ^ _773908) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _871528)), _871530, 6070 ^ [_871528, _871530, _871532, _871534], _871534))], (6072 ^ _773908) ^ [] : [-(_871532 = hAPP(c_Nat_OSuc, 6070 ^ [_871528, _871530, _871532, _871534]))]]], (11289 ^ _773908) ^ [_962180, _962182, _962184] : [class_Rings_Oordered__ring(_962180), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962180), c_Groups_Ozero__class_Ozero(_962180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962180), _962182), _962184)))), 11294 ^ _773908 : [(11301 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962180), _962182), c_Groups_Ozero__class_Ozero(_962180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962180), _962184), c_Groups_Ozero__class_Ozero(_962180)))], (11295 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962180), c_Groups_Ozero__class_Ozero(_962180)), _962182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962180), c_Groups_Ozero__class_Ozero(_962180)), _962184))]]], (28757 ^ _773908) ^ [_1298975, _1298977, _1298979, _1298981, _1298983, _1298985] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298975, tc_fun(_1298977, tc_HOL_Obool))), _1298979), _1298981), _1298983), _1298985)), 28760 ^ _773908 : [(28763 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298981, _1298983), _1298985)))], (28761 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298979, _1298983), _1298985)))]]], (30884 ^ _773908) ^ [_1339563, _1339565, _1339567, _1339569] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1339563, _1339565)), c_Sum__Type_OPlus(_1339563, _1339565, _1339567, _1339569)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339563), _1339567)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339565), _1339569))], (18149 ^ _773908) ^ [_1086862] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086862)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086862)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1086862)))], (28284 ^ _773908) ^ [_1287212, _1287214, _1287216] : [_1287214 = c_Orderings_Obot__class_Obot(tc_fun(_1287212, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1287212), _1287214), _1287216) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1287212, tc_HOL_Obool), tc_HOL_Obool)))], (29039 ^ _773908) ^ [_1304086, _1304088, _1304090] : [class_Lattices_Olattice(_1304086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304086), _1304088)), -(_1304088 = c_Orderings_Obot__class_Obot(tc_fun(_1304086, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1304086, hAPP(hAPP(c_Set_Oinsert(_1304086), _1304090), _1304088)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304086), _1304090), c_Big__Operators_Olattice__class_OInf__fin(_1304086, _1304088)))], (12865 ^ _773908) ^ [_989646, _989648] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989646), _989648) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _989646 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _989648 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (25941 ^ _773908) ^ [_1233509, _1233511, _1233513, _1233515, _1233517] : [class_Lattices_Osemilattice__sup(_1233509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233509), _1233511), _1233513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233509), _1233515), _1233517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233509), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1233509), _1233511), _1233515)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1233509), _1233513), _1233517))))], (35570 ^ _773908) ^ [_1440724, _1440726, _1440728] : [class_Orderings_Olinorder(_1440724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440724), _1440726), _1440728)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440724, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1440724, _1440726, _1440728)), hAPP(c_SetInterval_Oord__class_OatLeast(_1440724), _1440728)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440724), _1440726))], (37438 ^ _773908) ^ [_1481787, _1481789] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1481787, _1481787), tc_HOL_Obool)), c_Relation_OId__on(_1481787, _1481789)), hAPP(hAPP(c_Product__Type_OSigma(_1481787, _1481787), _1481789), hAPP(c_COMBK(tc_fun(_1481787, tc_HOL_Obool), _1481787), _1481789)))))], (28296 ^ _773908) ^ [_1287555, _1287557, _1287559, _1287561] : [hBOOL(hAPP(hAPP(c_member(_1287555), _1287561), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287555, tc_HOL_Obool)), _1287557), _1287559))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287555, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1287555, tc_fun(_1287555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1287555)), _1287557)), hAPP(hAPP(c_COMBC(_1287555, tc_fun(_1287555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1287555)), _1287559)), _1287561)))], (43729 ^ _773908) ^ [_1643611, _1643613, _1643615, _1643617] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1643611, _1643613), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643611, tc_HOL_Obool), _1643615)), _1643617) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643611, tc_HOL_Obool), tc_fun(tc_prod(_1643611, _1643613), tc_HOL_Obool)), _1643615), hAPP(hAPP(c_COMBC(tc_fun(_1643611, tc_HOL_Obool), tc_fun(_1643611, tc_fun(_1643613, tc_HOL_Obool)), tc_fun(tc_prod(_1643611, _1643613), tc_HOL_Obool)), c_Product__Type_OSigma(_1643611, _1643613)), _1643617)))], (20553 ^ _773908) ^ [_1128987, _1128989] : [-(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), _1128987)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1128989))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128987))) = 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), _1128989)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128987)))], (46901 ^ _773908) ^ [_1714260, _1714262, _1714264, _1714266] : [-(c_Wellfounded_Owf(_1714260, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1714260, _1714260)), hAPP(hAPP(c_Product__Type_OPair(_1714260, _1714260), _1714262), _1714264)), _1714266))), c_Wellfounded_Owf(_1714260, _1714266), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714260, _1714260)), hAPP(hAPP(c_Product__Type_OPair(_1714260, _1714260), _1714264), _1714262)), c_Transitive__Closure_Ortrancl(_1714260, _1714266))))], (20233 ^ _773908) ^ [_1123175] : [class_Rings_Osemiring__1(_1123175), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123175), c_Groups_Ozero__class_Ozero(_1123175)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1123175))], (35012 ^ _773908) ^ [_1428416, _1428418, _1428420, _1428422] : [class_Orderings_Olinorder(_1428416), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428416, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1428416, _1428418, _1428420)), hAPP(c_SetInterval_Oord__class_OatLeast(_1428416), _1428422)) = c_SetInterval_Oord__class_OatLeastAtMost(_1428416, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1428416), _1428418), _1428422), _1428420))], (14849 ^ _773908) ^ [_1024794, _1024796, _1024798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024794)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024798), _1024794)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024796), _1024798)), _1024794))], (42371 ^ _773908) ^ [_1613366, _1613368, _1613370, _1613372] : [-(hBOOL(hAPP(c_List_Odistinct(_1613366), hAPP(hAPP(c_List_Omap(_1613368, _1613366), _1613370), _1613372)))), hBOOL(hAPP(c_List_Odistinct(_1613368), _1613372)), c_Fun_Oinj__on(_1613368, _1613366, _1613370, hAPP(c_List_Oset(_1613368), _1613372))], (17869 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34648 ^ _773908) ^ [_1420176, _1420178, _1420180] : [class_Groups_Ocomm__monoid__add(_1420176), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420176), _1420178), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1420180))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420176), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420176), _1420178), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1420180))), hAPP(_1420178, _1420180)))], (22101 ^ _773908) ^ [_1156324, _1156326, _1156328, _1156330] : [class_Fields_Olinordered__field(_1156324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156324), _1156326), c_Groups_Ozero__class_Ozero(_1156324))), 22108 ^ _773908 : [(22115 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156324), _1156330), _1156326)), _1156328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156324), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156324), _1156328), _1156326)), _1156330)))], (22109 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156324), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156324), _1156328), _1156326)), _1156330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156324), _1156330), _1156326)), _1156328)))]]], (9477 ^ _773908) ^ [_931814, _931816] : [class_Int_Oring__char__0(_931814), 9480 ^ _773908 : [(9487 ^ _773908) ^ [] : [_931816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_931814) = hAPP(c_Int_Oring__1__class_Oof__int(_931814), _931816))], (9481 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_931814) = hAPP(c_Int_Oring__1__class_Oof__int(_931814), _931816), -(_931816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (36355 ^ _773908) ^ [_1457494, _1457496, _1457498, _1457500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457494, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457494, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36356 ^ [_1457494, _1457496, _1457498, _1457500])), _1457496)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457494, 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), 36356 ^ [_1457494, _1457496, _1457498, _1457500]), _1457498))), _1457500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457494, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457494, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1457496)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457494, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1457500))))], (44718 ^ _773908) ^ [_1667525] : [-(c_List_Oupt(_1667525, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (33522 ^ _773908) ^ [_1396666] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1396666), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (5819 ^ _773908) ^ [_866339, _866341, _866343] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_866339, _866341, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866339)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866339), _866343), c_Com_Ocom_OSKIP), _866343)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866339), tc_HOL_Obool)))))], (47461 ^ _773908) ^ [_1728455, _1728457, _1728459, _1728461, _1728463] : [c_Relation_Osingle__valued(_1728455, _1728457, hAPP(c_Relation_Oconverse(_1728457, _1728455), _1728459)), -(hAPP(c_Relation_OImage(_1728457, _1728455, _1728459), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728457, tc_HOL_Obool)), _1728461), _1728463)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728455, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1728457, _1728455, _1728459), _1728461)), hAPP(c_Relation_OImage(_1728457, _1728455, _1728459), _1728463)))], (40447 ^ _773908) ^ [_1565780, _1565782, _1565784, _1565786, _1565788] : [-(hAPP(hAPP(c_List_Oappend(_1565780), _1565782), _1565784) = hAPP(hAPP(c_List_Oappend(_1565780), _1565786), _1565788)), 40450 ^ _773908 : [(40453 ^ _773908) ^ [] : [_1565782 = hAPP(hAPP(c_List_Otake(_1565780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565782)), _1565786), _1565784 = hAPP(hAPP(c_List_Oappend(_1565780), hAPP(hAPP(c_List_Odrop(_1565780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565782)), _1565786)), _1565788)], (40451 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565782)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565786))))]], 40458 ^ _773908 : [(40461 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Otake(_1565780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565786)), _1565782) = _1565786, hAPP(hAPP(c_List_Oappend(_1565780), hAPP(hAPP(c_List_Odrop(_1565780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565786)), _1565782)), _1565784) = _1565788], (40459 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565782)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565780)), _1565786)))]]], (6398 ^ _773908) ^ [_877723, _877725, _877727, _877729] : [class_Groups_Oordered__cancel__ab__semigroup__add(_877723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877723), _877725), _877727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877723), _877725), _877729)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877723), _877727), _877729))))], (1564 ^ _773908) ^ [_796444, _796446] : [-(class_Rings_Olinordered__semiring__strict(_796444)), _796446 = _796444, class_Rings_Olinordered__semiring__strict(_796446)], (18913 ^ _773908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (39488 ^ _773908) ^ [_1540933, _1540935, _1540937, _1540939, _1540941] : [-(hAPP(hAPP(c_List_Oappend(_1540933), _1540935), _1540937) = hAPP(hAPP(c_List_Olist_OCons(_1540933), _1540939), _1540941)), 39489 ^ _773908 : [(39496 ^ _773908) ^ [_1541116] : [_1540935 = hAPP(hAPP(c_List_Olist_OCons(_1540933), _1540939), _1541116), hAPP(hAPP(c_List_Oappend(_1540933), _1541116), _1540937) = _1540941], (39490 ^ _773908) ^ [] : [_1540935 = c_List_Olist_ONil(_1540933), _1540937 = hAPP(hAPP(c_List_Olist_OCons(_1540933), _1540939), _1540941)]]], (34372 ^ _773908) ^ [_1413839, _1413841, _1413843, _1413845, _1413847] : [c_Finite__Set_Ofolding__one__idem(_1413839, _1413841, _1413843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413839), _1413845)), hBOOL(hAPP(hAPP(c_member(_1413839), _1413847), _1413845)), -(hAPP(hAPP(_1413841, _1413847), hAPP(_1413843, _1413845)) = hAPP(_1413843, _1413845))], (490 ^ _773908) ^ [_781447, _781449, _781451, _781453] : [-(c_Nitpick_Owf_H(_781451, _781447)), c_Nitpick_Owf_H(_781453, _781449), _781453 = _781451, _781449 = _781447], (43202 ^ _773908) ^ [_1631964, _1631966, _1631968, _1631970] : [class_Orderings_Olinorder(_1631964), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1631964, _1631964, c_COMBI(_1631964)), _1631966), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1631964, _1631964, c_COMBI(_1631964)), _1631968), _1631970)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1631964, _1631964, c_COMBI(_1631964)), _1631968), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1631964, _1631964, c_COMBI(_1631964)), _1631966), _1631970)))], (41348 ^ _773908) ^ [_1588705, _1588707, _1588709] : [class_Orderings_Olinorder(_1588705), -(c_Big__Operators_Olinorder__class_OMax(_1588705, hAPP(c_List_Oset(_1588705), hAPP(hAPP(c_List_Olist_OCons(_1588705), _1588707), _1588709))) = hAPP(c_List_Ofoldl(_1588705, _1588705, c_Orderings_Oord__class_Omax(_1588705), _1588707), _1588709))], (7376 ^ _773908) ^ [_893246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893246), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_893246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17135 ^ _773908) ^ [_1069427, _1069429, _1069431] : [class_Rings_Olinordered__semidom(_1069427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069427), c_Groups_Oone__class_Oone(_1069427)), _1069429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069427), c_Groups_Oone__class_Oone(_1069427)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069427), _1069429), _1069431))))], (6136 ^ _773908) ^ [_873382, _873384, _873386] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _873382, _873384, _873386), -(_873386 = _873382)], (23955 ^ _773908) ^ [_1192691, _1192693] : [-(_1192691 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192693, _1192691), c_Divides_Odivmod__int(_1192693, _1192691))))], (42786 ^ _773908) ^ [_1622570, _1622572] : [-(c_Random_Oselect__weight(_1622570, _1622572) = 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(_1622570, 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, _1622570), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1622570)), _1622572)))), hAPP(hAPP(c_COMBB(_1622570, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1622570, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1622570, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1622570, _1622572))))], (29747 ^ _773908) ^ [_1316783, _1316785] : [class_Orderings_Olinorder(_1316783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316783), _1316785)), -(_1316785 = c_Orderings_Obot__class_Obot(tc_fun(_1316783, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1316783), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316783), 29760 ^ [_1316783, _1316785]), 29761 ^ [_1316783, _1316785])), hAPP(hAPP(c_Set_Oinsert(_1316783), 29760 ^ [_1316783, _1316785]), hAPP(hAPP(c_Set_Oinsert(_1316783), 29761 ^ [_1316783, _1316785]), c_Orderings_Obot__class_Obot(tc_fun(_1316783, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1316783), c_Big__Operators_Olinorder__class_OMin(_1316783, _1316785)), _1316785)))], (51478 ^ _773908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (38014 ^ _773908) ^ [_1496538, _1496540] : [hAPP(c_Set_OCollect(_1496538), _1496540) = c_Orderings_Obot__class_Obot(tc_fun(_1496538, tc_HOL_Obool)), 38017 ^ _773908 : [(38018 ^ _773908) ^ [_1496623] : [hBOOL(hAPP(_1496540, _1496623))]]], (5727 ^ _773908) ^ [_864365, _864367, _864369, _864371, _864373, _864375, _864377] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864365), _864367), _864369), _864371) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864365), _864373), _864375), _864377)), _864367 = _864373, _864369 = _864375, _864371 = _864377], (20489 ^ _773908) ^ [_1127553, _1127555, _1127557] : [class_Rings_Olinordered__idom(_1127553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127553), hAPP(hAPP(c_Power_Opower__class_Opower(_1127553), _1127555), 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(_1127553), _1127557), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1127553)))], (5959 ^ _773908) ^ [_869510, _869512] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _869510), _869512)), -(_869512 = _869510)], (51624 ^ _773908) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (24045 ^ _773908) ^ [_1194149, _1194151] : [-(c_Divides_Odivmod__nat(_1194151, _1194149) = 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), _1194151), _1194149), _1194149))), -(_1194149 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194151), _1194149)))], (3792 ^ _773908) ^ [_831108, _831110, _831112, _831114] : [-(c_Product__Type_OSigma(_831114, _831110) = c_Product__Type_OSigma(_831112, _831108)), _831114 = _831112, _831110 = _831108], (5967 ^ _773908) ^ [_869625, _869627, _869629, _869631] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869625), _869627), _869629)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869625), _869627), _869631)), -(_869631 = _869629)], (44732 ^ _773908) ^ [_1667787, _1667789] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1667787, _1667789)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1667789), _1667787))], (9343 ^ _773908) ^ [_929393, _929395, _929397, _929399] : [class_Rings_Olinordered__semiring__strict(_929393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929393), _929395), _929397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929393), c_Groups_Ozero__class_Ozero(_929393)), _929399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929393), _929399), _929395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929393), _929399), _929397))))], (5544 ^ _773908) ^ [_858738, _858740] : [_858740 = _858738, -(c_Finite__Set_Ocard(_858740) = c_Finite__Set_Ocard(_858738))], (44218 ^ _773908) ^ [_1655238, _1655240, _1655242] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1655238, tc_HOL_Obool)), _1655240)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1655238), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1655238, tc_HOL_Obool), _1655240))), 44228 ^ _773908 : [(44231 ^ _773908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1655238), 44227 ^ [_1655238, _1655240, _1655242]) = _1655242], (44229 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1655238, tc_HOL_Obool)), 44227 ^ [_1655238, _1655240, _1655242]), _1655240)))]], 44235 ^ _773908 : [(44239 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1655238, tc_HOL_Obool)), 44237 ^ [_1655238, _1655240, _1655242]), _1655240)))], (44241 ^ _773908) ^ [] : [44234 ^ [_1655238, _1655240, _1655242] = 44237 ^ [_1655238, _1655240, _1655242]], (44243 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655238, tc_HOL_Obool)), 44234 ^ [_1655238, _1655240, _1655242]), 44237 ^ [_1655238, _1655240, _1655242]) = c_Orderings_Obot__class_Obot(tc_fun(_1655238, tc_HOL_Obool))], (44236 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1655238, tc_HOL_Obool)), 44234 ^ [_1655238, _1655240, _1655242]), _1655240)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1655242), hAPP(c_Finite__Set_Ocard(tc_fun(_1655238, tc_HOL_Obool)), _1655240)) = hAPP(c_Finite__Set_Ocard(_1655238), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1655238, tc_HOL_Obool), _1655240)))], (19097 ^ _773908) ^ [_1103811, _1103813] : [class_Int_Onumber__ring(_1103811), class_Rings_Olinordered__idom(_1103811), 19104 ^ _773908 : [(19111 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103811), c_Groups_Ozero__class_Ozero(_1103811)), hAPP(c_Int_Onumber__class_Onumber__of(_1103811), _1103813))))], (19105 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103811), c_Groups_Ozero__class_Ozero(_1103811)), hAPP(c_Int_Onumber__class_Onumber__of(_1103811), _1103813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103813)))]]], (13107 ^ _773908) ^ [_993801, _993803, _993805] : [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, _993801)), _993803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993801)), _993805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993803), _993805)))], (26055 ^ _773908) ^ [_1235861, _1235863, _1235865, _1235867] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235861, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235861, tc_HOL_Obool)), _1235863), _1235865)), _1235867) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235861, tc_HOL_Obool)), _1235863), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235861, tc_HOL_Obool)), _1235865), _1235867)))], (42628 ^ _773908) ^ [_1619410, _1619412] : [-(c_Hilbert__Choice_OEps(_1619410, hAPP(c_fequal, _1619412)) = _1619412)], (28682 ^ _773908) ^ [_1296321, _1296323, _1296325, _1296327, _1296329, _1296331] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296321, tc_fun(_1296323, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1296321, tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_fun(_1296323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296323, tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_fun(_1296323, tc_HOL_Obool)), _1296321), c_COMBC(_1296323, tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296323, tc_prod(_1296321, _1296323)), tc_fun(_1296323, tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), _1296321), hAPP(c_COMBB(tc_prod(_1296321, _1296323), tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool), _1296323), c_member(tc_prod(_1296321, _1296323)))), c_Product__Type_OPair(_1296321, _1296323)))), _1296325)), hAPP(hAPP(c_COMBC(_1296321, tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_fun(_1296323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296323, tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_fun(_1296323, tc_HOL_Obool)), _1296321), c_COMBC(_1296323, tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296323, tc_prod(_1296321, _1296323)), tc_fun(_1296323, tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool)), _1296321), hAPP(c_COMBB(tc_prod(_1296321, _1296323), tc_fun(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool), tc_HOL_Obool), _1296323), c_member(tc_prod(_1296321, _1296323)))), c_Product__Type_OPair(_1296321, _1296323)))), _1296327)), _1296329), _1296331)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1296321, _1296323)), hAPP(hAPP(c_Product__Type_OPair(_1296321, _1296323), _1296329), _1296331)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1296321, _1296323), tc_HOL_Obool)), _1296325), _1296327))))], (20151 ^ _773908) ^ [_1121720, _1121722] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1121720)), _1121722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121720), _1121722))), _1121722))], (36371 ^ _773908) ^ [_1458151, _1458153, _1458155] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1458151, _1458153, c_Orderings_Obot__class_Obot(tc_fun(_1458151, tc_HOL_Obool))), _1458155))], (25505 ^ _773908) ^ [_1225399] : [class_Orderings_Oord(_1225399), -(c_Orderings_Oord__class_Omax(_1225399) = c_Orderings_Oord_Omax(_1225399, c_Orderings_Oord__class_Oless__eq(_1225399)))], (40397 ^ _773908) ^ [_1564542, _1564544, _1564546] : [-(hBOOL(hAPP(hAPP(c_member(_1564542), _1564544), hAPP(c_List_Oset(_1564542), _1564546)))), 40398 ^ _773908 : [(40399 ^ _773908) ^ [_1564616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1564616), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1564542)), _1564546))), hAPP(hAPP(c_List_Onth(_1564542), _1564546), _1564616) = _1564544]]], (48653 ^ _773908) ^ [_1754309, _1754311, _1754313, _1754315, _1754317, _1754319] : [c_Finite__Set_Ofun__left__comm(_1754309, _1754311, _1754313), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1754309, _1754311, _1754313, _1754315, _1754317), _1754319)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1754309, _1754311, _1754313), _1754315), _1754317) = _1754319)], (26685 ^ _773908) ^ [_1253941, _1253943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1253941), _1253943)), -(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)), _1253941)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253943))))], (47357 ^ _773908) ^ [_1725752, _1725754] : [-(c_List_Olistrel1(_1725752, hAPP(c_Relation_Oconverse(_1725752, _1725752), _1725754)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1725752), tc_List_Olist(_1725752)), c_List_Olistrel1(_1725752, _1725754)))], (40135 ^ _773908) ^ [_1558390, _1558392, _1558394, _1558396] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1558390) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1558392), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1558390)), hAPP(hAPP(c_List_Olist_OCons(_1558392), _1558394), _1558396)) = c_List_Olist_ONil(_1558392))], (8291 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51406 ^ _773908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (46280 ^ _773908) ^ [_1699705, _1699707] : [c_Wellfounded_OwfP(_1699705, _1699707), 46283 ^ _773908 : [(46284 ^ _773908) ^ [_1699769] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1699705, _1699707), _1699769)))]]], (10709 ^ _773908) ^ [_951553, _951555, _951557] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951553), _951555)), _951557) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951553), _951557)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951555), _951557)))], (23622 ^ _773908) ^ [_1186050, _1186052] : [_1186050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1186052, _1186050) = 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), _1186052)))], (15339 ^ _773908) ^ [_1034050, _1034052, _1034054, _1034056] : [class_Divides_Oring__div(_1034050), -(c_Divides_Odiv__class_Omod(_1034050, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034050), _1034052), _1034054), _1034056) = c_Divides_Odiv__class_Omod(_1034050, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034050), _1034052), c_Divides_Odiv__class_Omod(_1034050, _1034054, _1034056)), _1034056))], (14929 ^ _773908) ^ [_1026504, _1026506, _1026508] : [class_Divides_Osemiring__div(_1026504), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026504), c_Divides_Odiv__class_Omod(_1026504, _1026506, _1026508)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026504), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026504), _1026506), _1026508)), _1026508)) = _1026506)], (25725 ^ _773908) ^ [_1229701, _1229703, _1229705, _1229707] : [25726 ^ _773908 : [(25729 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1229701), _1229703), _1229707))], (25727 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1229701), _1229703), _1229705))]], -(hBOOL(hAPP(hAPP(c_member(_1229701), _1229703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229701, tc_HOL_Obool)), _1229707), _1229705))))], (7351 ^ _773908) ^ [_892832, _892834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _892832), hAPP(c_Nat_OSuc, _892834))), -(_892832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7359 ^ _773908 : [(7362 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 7358 ^ [_892832, _892834]), _892834)))], (7360 ^ _773908) ^ [] : [-(_892832 = hAPP(c_Nat_OSuc, 7358 ^ [_892832, _892834]))]]], (18287 ^ _773908) ^ [_1089696, _1089698, _1089700, _1089702] : [hBOOL(hAPP(hAPP(c_member(_1089696), _1089698), hAPP(hAPP(c_Set_Oinsert(_1089696), _1089700), _1089702))), -(_1089698 = _1089700), -(hBOOL(hAPP(hAPP(c_member(_1089696), _1089698), _1089702)))], (13081 ^ _773908) ^ [_993416, _993418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993416), _993418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993416)), _993418)))], (31455 ^ _773908) ^ [_1352624, _1352626, _1352628, _1352630] : [-(hAPP(c_Set_Oimage(_1352624, _1352626, _1352628), _1352630) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1352624, tc_fun(_1352626, tc_HOL_Obool)), _1352630), hAPP(hAPP(c_COMBC(_1352624, tc_fun(_1352626, tc_HOL_Obool), tc_fun(_1352626, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1352626, tc_fun(tc_fun(_1352626, tc_HOL_Obool), tc_fun(_1352626, tc_HOL_Obool)), _1352624), c_Set_Oinsert(_1352626)), _1352628)), c_Orderings_Obot__class_Obot(tc_fun(_1352626, tc_HOL_Obool)))))], (42453 ^ _773908) ^ [_1615560, _1615562, _1615564] : [c_Fun_Oinj__on(tc_List_Olist(_1615560), tc_List_Olist(_1615562), hAPP(c_List_Omap(_1615560, _1615562), _1615564), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1615560), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1615560, _1615562, _1615564, c_Orderings_Otop__class_Otop(tc_fun(_1615560, tc_HOL_Obool))))], (26285 ^ _773908) ^ [_1241102, _1241104, _1241106, _1241108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241102, tc_HOL_Obool)), _1241104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241102, tc_HOL_Obool)), _1241106), _1241108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241102, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241102, tc_HOL_Obool)), _1241104), _1241106)), _1241108)))], (51582 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (19079 ^ _773908) ^ [_1103520, _1103522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103520)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103520), _1103522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103520), c_Int_OPls)))], (49916 ^ _773908) ^ [_1782171, _1782173, _1782175] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1782171) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1782171, _1782173, _1782175)], (2914 ^ _773908) ^ [_817361, _817363] : [_817363 = _817361, -(c_Int_Oint__ge__less__than2(_817363) = c_Int_Oint__ge__less__than2(_817361))], (24741 ^ _773908) ^ [_1210296, _1210298, _1210300] : [class_Orderings_Olinorder(_1210296), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210296), _1210298), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210296), _1210298), _1210300)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210296), _1210298), _1210300))], (15669 ^ _773908) ^ [_1040468, _1040470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040470), _1040468)), _1040470)))], (18333 ^ _773908) ^ [_1090521, _1090523, _1090525] : [-(hBOOL(hAPP(hAPP(c_member(_1090521), _1090523), _1090525))), -(hBOOL(hAPP(hAPP(c_member(_1090521), _1090523), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1090521, tc_HOL_Obool)), _1090525))))], (43523 ^ _773908) ^ [_1638784, _1638786, _1638788, _1638790, _1638792, _1638794] : [c_List_Olist__all2(_1638784, _1638786, _1638788, _1638790, _1638792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638794), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638786)), _1638792))), -(hBOOL(hAPP(hAPP(_1638788, hAPP(hAPP(c_List_Onth(_1638784), _1638790), _1638794)), hAPP(hAPP(c_List_Onth(_1638786), _1638792), _1638794))))], (12142 ^ _773908) ^ [_977458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _977458) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11017 ^ _773908) ^ [_957170, _957172, _957174] : [class_Groups_Oordered__comm__monoid__add(_957170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957170), _957172), c_Groups_Ozero__class_Ozero(_957170))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957170), _957174), c_Groups_Ozero__class_Ozero(_957170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957170), _957172), _957174)), c_Groups_Ozero__class_Ozero(_957170))))], (45055 ^ _773908) ^ [_1674097, _1674099, _1674101, _1674103, _1674105] : [class_Orderings_Olinorder(_1674097), -(c_List_Olinorder__class_Osorted(_1674097, hAPP(hAPP(c_List_Omap(_1674099, _1674097), _1674101), hAPP(c_List_Ofilter(_1674099, hAPP(hAPP(c_COMBC(_1674099, _1674097, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1674097, tc_fun(_1674097, tc_HOL_Obool), _1674099), c_fequal), _1674101)), hAPP(_1674103, _1674105))), _1674105))))], (20735 ^ _773908) ^ [_1132406, _1132408, _1132410, _1132412, _1132414] : [class_Fields_Ofield__inverse__zero(_1132406), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132406), _1132408), _1132410)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132406), _1132412), _1132414)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132406), _1132408), _1132412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132406), _1132410), _1132414)))], (13482 ^ _773908) ^ [_1000390, _1000392, _1000394] : [_1000390 = _1000392, 13485 ^ _773908 : [(13488 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000394, tc_HOL_Obool)), _1000392), _1000390)))], (13486 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000394, tc_HOL_Obool)), _1000390), _1000392)))]]], (27924 ^ _773908) ^ [_1279341, _1279343, _1279345, _1279347] : [class_Lattices_Osemilattice__inf(_1279341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279341), _1279343), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1279341), _1279345), _1279347))), 27931 ^ _773908 : [(27934 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279341), _1279343), _1279347)))], (27932 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279341), _1279343), _1279345)))]]], (18909 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51808 ^ _773908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (35881 ^ _773908) ^ [_1447132, _1447134] : [-(hBOOL(hAPP(hAPP(c_member(_1447132), _1447134), c_Orderings_Otop__class_Otop(tc_fun(_1447132, tc_HOL_Obool)))))], (44531 ^ _773908) ^ [_1662128, _1662130, _1662132, _1662134] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1662128, tc_Nat_Onat), _1662128), c_Product__Type_Ofst(_1662128, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1662128, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1662128, tc_Nat_Onat)), _1662130), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1662128, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1662128, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1662128, tc_Nat_Onat), _1662132), _1662134))) = hAPP(hAPP(c_List_Omap(tc_prod(_1662128, tc_Nat_Onat), _1662128), c_Product__Type_Ofst(_1662128, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1662128, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1662128, tc_Nat_Onat)), _1662130), c_Product__Type_Osnd(_1662128, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1662128, tc_Nat_Onat), _1662132), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1662134)))))], (49584 ^ _773908) ^ [_1774655, _1774657, _1774659, _1774661] : [-(hBOOL(hAPP(hAPP(c_member(_1774655), _1774657), hAPP(c_List_Oset(_1774655), c_List_Oreplicate(_1774655, _1774659, _1774661))))), _1774657 = _1774661, -(_1774659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7769 ^ _773908) ^ [_900529, _900531, _900533, _900535, _900537, _900539] : [c_Com_Ocom_OCall(_900529, _900531, _900533) = c_Com_Ocom_OCond(_900535, _900537, _900539)], (39320 ^ _773908) ^ [_1537740, _1537742, _1537744] : [hAPP(hAPP(c_List_Oappend(_1537740), _1537742), _1537744) = _1537744, -(_1537742 = c_List_Olist_ONil(_1537740))], (31750 ^ _773908) ^ [_1359842, _1359844, _1359846, _1359848, _1359850, _1359852] : [-(hAPP(c_Set_Oimage(_1359842, _1359844, _1359846), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359848, tc_fun(_1359842, tc_HOL_Obool)), _1359850), _1359852)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359848, tc_fun(_1359844, tc_HOL_Obool)), _1359850), hAPP(hAPP(c_COMBB(tc_fun(_1359842, tc_HOL_Obool), tc_fun(_1359844, tc_HOL_Obool), _1359848), c_Set_Oimage(_1359842, _1359844, _1359846)), _1359852)))], (24017 ^ _773908) ^ [_1193472, _1193474, _1193476, _1193478, _1193480, _1193482, _1193484] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193472, _1193474), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1193476), _1193478))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193480, _1193474), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1193482), _1193484))), -(_1193474 = 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), _1193472), _1193480), _1193474), 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), _1193476), _1193482)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193478), _1193484)), _1193474))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193478), _1193484), _1193474)))))], (23233 ^ _773908) ^ [_1178292, _1178294] : [23234 ^ _773908 : [(23237 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178294), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23235 ^ _773908) ^ [] : [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), _1178292), _1178294)))]], -(c_Divides_OnegDivAlg(_1178292, _1178294) = 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), _1178292), _1178294)))], (17625 ^ _773908) ^ [_1078321, _1078323, _1078325] : [class_Rings_Olinordered__semidom(_1078321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078321), c_Groups_Oone__class_Oone(_1078321)), _1078323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078321), c_Groups_Oone__class_Oone(_1078321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078321), _1078323), hAPP(hAPP(c_Power_Opower__class_Opower(_1078321), _1078323), _1078325)))))], (43882 ^ _773908) ^ [_1647205] : [class_Complete__Lattice_Ocomplete__lattice(_1647205), -(c_Complete__Lattice_OSup__class_OSup(_1647205, c_Orderings_Obot__class_Obot(tc_fun(_1647205, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1647205))], (24405 ^ _773908) ^ [_1202449, _1202451, _1202453, _1202455, _1202457] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1202449, _1202451, _1202453), _1202455), _1202457) = hAPP(hAPP(_1202455, hAPP(c_Product__Type_Ofst(_1202449, _1202451), _1202457)), hAPP(c_Product__Type_Osnd(_1202449, _1202451), _1202457)))], (38237 ^ _773908) ^ [_1503810, _1503812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503810), _1503812)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1503810, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1503810, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1503810, tc_HOL_Obool), tc_fun(_1503810, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1503810, tc_HOL_Obool))), _1503812)))))], (18729 ^ _773908) ^ [_1097695, _1097697, _1097699, _1097701] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097695, tc_HOL_Obool)), _1097697), hAPP(hAPP(c_Set_Oinsert(_1097695), _1097699), _1097701)))), 18732 ^ _773908 : [(18735 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097695, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1097695, tc_HOL_Obool)), _1097697), hAPP(hAPP(c_Set_Oinsert(_1097695), _1097699), c_Orderings_Obot__class_Obot(tc_fun(_1097695, tc_HOL_Obool))))), _1097701))], (18733 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097695), _1097699), _1097697)))]], 18736 ^ _773908 : [(18739 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097695, tc_HOL_Obool)), _1097697), _1097701))], (18737 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1097695), _1097699), _1097697))]]], (50398 ^ _773908) ^ [_1794250, _1794252] : [50401 ^ _773908 : [(50406 ^ _773908) ^ [] : [50399 ^ [_1794250, _1794252] = 50400 ^ [_1794250, _1794252]], (50404 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1794250, _1794250)), hAPP(hAPP(c_Product__Type_OPair(_1794250, _1794250), 50400 ^ [_1794250, _1794252]), 50399 ^ [_1794250, _1794252])), _1794252)))], (50402 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1794250, _1794250)), hAPP(hAPP(c_Product__Type_OPair(_1794250, _1794250), 50399 ^ [_1794250, _1794252]), 50400 ^ [_1794250, _1794252])), _1794252)))]], -(c_Relation_Oantisym(_1794250, _1794252))], (38128 ^ _773908) ^ [_1499201, _1499203] : [-(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), _1499201)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1499203))))))], (31894 ^ _773908) ^ [_1364075] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1364075) = 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, _1364075)), 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))))))))], (15847 ^ _773908) ^ [_1043784, _1043786, _1043788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043784), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043788), _1043786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043784), _1043786)), _1043788)))], (15407 ^ _773908) ^ [_1035377, _1035379] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035377), _1035379))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035377, _1035379) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035377), _1035379), _1035379))], (5883 ^ _773908) ^ [_868027, _868029] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_868027, _868029)], (44192 ^ _773908) ^ [_1654810, _1654812, _1654814] : [class_Complete__Lattice_Ocomplete__lattice(_1654810), -(c_Complete__Lattice_OInf__class_OInf(_1654810, hAPP(hAPP(c_Set_Oinsert(_1654810), _1654812), hAPP(hAPP(c_Set_Oinsert(_1654810), _1654814), c_Orderings_Obot__class_Obot(tc_fun(_1654810, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1654810), _1654812), _1654814))], (18831 ^ _773908) ^ [_1099596, _1099598] : [class_Int_Onumber__ring(_1099596), 18834 ^ _773908 : [(18841 ^ _773908) ^ [] : [c_Int_Oiszero(_1099596, hAPP(c_Int_Onumber__class_Onumber__of(_1099596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1099598)))), -(c_Groups_Ozero__class_Ozero(_1099596) = hAPP(c_Int_Onumber__class_Onumber__of(_1099596), _1099598))], (18835 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_1099596) = hAPP(c_Int_Onumber__class_Onumber__of(_1099596), _1099598), -(c_Int_Oiszero(_1099596, hAPP(c_Int_Onumber__class_Onumber__of(_1099596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1099598)))))]]], (47349 ^ _773908) ^ [_1725534] : [-(hAPP(c_Relation_Oconverse(_1725534, _1725534), c_Relation_OId(_1725534)) = c_Relation_OId(_1725534))], (25239 ^ _773908) ^ [_1219748, _1219750, _1219752, _1219754] : [class_Orderings_Olinorder(_1219748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), _1219750), _1219752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), _1219754), _1219752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219748), _1219750), _1219754)), _1219752)))], (49294 ^ _773908) ^ [_1768122, _1768124, _1768126, _1768128, _1768130, _1768132, _1768134] : [-(c_New__Random__Sequence_Opos__decr__bind(_1768122, _1768124, _1768126, _1768128, _1768130, _1768132, _1768134) = c_New__DSequence_Opos__decr__bind(_1768122, _1768124, hAPP(hAPP(hAPP(_1768126, _1768130), _1768132), _1768134), hAPP(hAPP(c_COMBC(_1768122, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1768124))), hAPP(hAPP(c_COMBC(_1768122, 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(_1768124)))), hAPP(hAPP(c_COMBC(_1768122, 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(_1768124))))), _1768128), _1768130)), _1768132)), _1768134)))], (50624 ^ _773908) ^ [_1798213, _1798215] : [c_Equiv__Relations_Opart__equivp(_1798213, _1798215), 50628 ^ _773908 : [(50641 ^ _773908) ^ [_1798555, _1798557] : [-(hBOOL(hAPP(hAPP(_1798215, _1798557), _1798555))), hBOOL(hAPP(hAPP(_1798215, _1798557), _1798557)), hBOOL(hAPP(hAPP(_1798215, _1798555), _1798555)), hAPP(_1798215, _1798557) = hAPP(_1798215, _1798555)], (50631 ^ _773908) ^ [_1798386, _1798388] : [hBOOL(hAPP(hAPP(_1798215, _1798388), _1798386)), 50634 ^ _773908 : [(50639 ^ _773908) ^ [] : [-(hAPP(_1798215, _1798388) = hAPP(_1798215, _1798386))], (50637 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798215, _1798386), _1798386)))], (50635 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798215, _1798388), _1798388)))]]], (50629 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798215, 50627 ^ [_1798213, _1798215]), 50627 ^ [_1798213, _1798215])))]]], (302 ^ _773908) ^ [_778501, _778503, _778505, _778507, _778509, _778511] : [-(c_Big__Operators_Osemilattice__big(_778509, _778505, _778501)), c_Big__Operators_Osemilattice__big(_778511, _778507, _778503), _778511 = _778509, _778507 = _778505, _778503 = _778501], (39907 ^ _773908) ^ [_1552472, _1552474, _1552476, _1552478] : [39908 ^ _773908 : [(39909 ^ _773908) ^ [_1552569, _1552571] : [_1552472 = hAPP(hAPP(c_List_Olist_OCons(_1552474), _1552571), _1552569)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552474), tc_List_Olist(_1552474))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552474), tc_List_Olist(_1552474)), _1552476), hAPP(hAPP(c_List_Oappend(_1552474), _1552476), _1552472))), c_List_Olexord(_1552474, _1552478))))], (24961 ^ _773908) ^ [_1214242, _1214244, _1214246] : [class_Orderings_Olinorder(_1214242), 24964 ^ _773908 : [(24971 ^ _773908) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214242), _1214244), _1214246) = _1214244, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214242), _1214244), _1214246)))], (24965 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214242), _1214244), _1214246)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214242), _1214244), _1214246) = _1214244)]]], (45288 ^ _773908) ^ [_1678349, _1678351, _1678353] : [class_Orderings_Olinorder(_1678349), 45291 ^ _773908 : [(45304 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1678349, hAPP(hAPP(c_List_Olist_OCons(_1678349), _1678351), _1678353))), 45308 ^ _773908 : [(45311 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1678349), _1678351), 45307 ^ [_1678349, _1678351, _1678353]))], (45309 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678349), 45307 ^ [_1678349, _1678351, _1678353]), hAPP(c_List_Oset(_1678349), _1678353))))]], c_List_Olinorder__class_Osorted(_1678349, _1678353)], (45292 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1678349, hAPP(hAPP(c_List_Olist_OCons(_1678349), _1678351), _1678353)), 45295 ^ _773908 : [(45296 ^ _773908) ^ [_1678517] : [hBOOL(hAPP(hAPP(c_member(_1678349), _1678517), hAPP(c_List_Oset(_1678349), _1678353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1678349), _1678351), _1678517)))], (45302 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1678349, _1678353))]]]]], (45105 ^ _773908) ^ [_1675097, _1675099] : [-(hAPP(c_List_Oset(_1675097), c_List_Oremdups(_1675097, _1675099)) = hAPP(c_List_Oset(_1675097), _1675099))], (47676 ^ _773908) ^ [_1734338, _1734340, _1734342, _1734344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1734338, _1734338)), hAPP(hAPP(c_Product__Type_OPair(_1734338, _1734338), _1734340), _1734342)), c_Transitive__Closure_Otrancl(_1734338, _1734344))), 47680 ^ _773908 : [(47683 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734338, _1734338)), hAPP(hAPP(c_Product__Type_OPair(_1734338, _1734338), 47679 ^ [_1734338, _1734340, _1734342, _1734344]), _1734342)), c_Transitive__Closure_Ortrancl(_1734338, _1734344))))], (47681 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734338, _1734338)), hAPP(hAPP(c_Product__Type_OPair(_1734338, _1734338), _1734340), 47679 ^ [_1734338, _1734340, _1734342, _1734344])), _1734344)))]]], (51782 ^ _773908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (11489 ^ _773908) ^ [_965636, _965638, _965640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965636), _965638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965636), _965640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965638), _965640))))], (7091 ^ _773908) ^ [_888770] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _888770), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _888770)], (41690 ^ _773908) ^ [_1595294, _1595296, _1595298] : [-(c_List_Obutlast(_1595294, hAPP(hAPP(c_List_Odrop(_1595294), _1595296), _1595298)) = hAPP(hAPP(c_List_Odrop(_1595294), _1595296), c_List_Obutlast(_1595294, _1595298)))], (26402 ^ _773908) ^ [_1246516, _1246518] : [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)), _1246516), _1246518)), 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)), _1246516), 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)), _1246518), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (25409 ^ _773908) ^ [_1222985, _1222987, _1222989, _1222991] : [class_Orderings_Olinorder(_1222985), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222985), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222985), _1222987), _1222989)), _1222991) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222985), _1222987), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222985), _1222989), _1222991)))], (13490 ^ _773908) ^ [_1000539, _1000541, _1000543] : [class_Divides_Osemiring__div(_1000539), -(c_Divides_Odiv__class_Omod(_1000539, c_Divides_Odiv__class_Omod(_1000539, _1000541, _1000543), _1000543) = c_Divides_Odiv__class_Omod(_1000539, _1000541, _1000543))], (43356 ^ _773908) ^ [_1635040, _1635042, _1635044, _1635046, _1635048] : [class_Orderings_Olinorder(_1635040), hBOOL(hAPP(hAPP(c_member(_1635040), hAPP(_1635042, _1635044)), hAPP(c_Set_Oimage(_1635046, _1635040, _1635042), hAPP(c_List_Oset(_1635046), _1635048)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1635046, _1635040, _1635042, _1635044, _1635048) = _1635048)], (35679 ^ _773908) ^ [_1443218, _1443220, _1443222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1443218, 35680 ^ [_1443218, _1443220, _1443222])), hAPP(_1443220, 35680 ^ [_1443218, _1443220, _1443222]))), -(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), _1443220), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443222))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1443218), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443222))) = 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)), _1443220)), _1443218)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443222)))], (21215 ^ _773908) ^ [_1140794, _1140796, _1140798, _1140800] : [class_Rings_Odivision__ring(_1140794), -(_1140796 = c_Groups_Ozero__class_Ozero(_1140794)), _1140798 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140794), _1140800), _1140796), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140794), _1140798), _1140796) = _1140800)], (24507 ^ _773908) ^ [_1204356, _1204358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204356), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204358), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204356), _1204358) = 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), _1204356), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204358)))))], (5656 ^ _773908) ^ [_860422, _860424] : [_860424 = _860422, -(c_Set_Oinsert(_860424) = c_Set_Oinsert(_860422))], (10563 ^ _773908) ^ [_949091, _949093, _949095, _949097] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_949091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949091), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949091), _949093), _949095)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949091), _949093), _949097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949091), _949095), _949097)))], (13125 ^ _773908) ^ [_994189, _994191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994189), _994191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994189)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994191))))], (28142 ^ _773908) ^ [_1283871, _1283873, _1283875] : [class_Lattices_Osemilattice__inf(_1283871), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283871), _1283873), _1283875) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283871), _1283875), _1283873))], (11743 ^ _773908) ^ [_970029, _970031] : [11744 ^ _773908 : [(11747 ^ _773908) ^ [] : [_970029 = _970031], (11745 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _970029), _970031))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _970029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _970031), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42485 ^ _773908) ^ [_1616266, _1616268, _1616270, _1616272, _1616274] : [class_Complete__Lattice_Ocomplete__lattice(_1616266), hBOOL(hAPP(hAPP(c_member(_1616268), _1616270), _1616272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1616266), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616268, _1616266), _1616272), _1616274)), hAPP(_1616274, _1616270))))], (37267 ^ _773908) ^ [_1476854, _1476856, _1476858, _1476860, _1476862] : [c_Fun_Oinj__on(_1476854, _1476856, _1476858, c_Orderings_Otop__class_Otop(tc_fun(_1476854, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476856, tc_HOL_Obool)), _1476860), hAPP(c_Set_Oimage(_1476854, _1476856, _1476858), _1476862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476854, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1476854, _1476856, _1476858), _1476860)), _1476862)))], (39238 ^ _773908) ^ [_1534965, _1534967, _1534969, _1534971, _1534973, _1534975] : [hAPP(hAPP(c_List_Olist_OCons(_1534965), _1534967), _1534969) = _1534971, _1534973 = hAPP(hAPP(c_List_Oappend(_1534965), _1534969), _1534975), -(hAPP(hAPP(c_List_Olist_OCons(_1534965), _1534967), _1534973) = hAPP(hAPP(c_List_Oappend(_1534965), _1534971), _1534975))], (31677 ^ _773908) ^ [_1358003, _1358005, _1358007, _1358009] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358003, tc_fun(_1358005, tc_HOL_Obool)), _1358007), _1358009) = c_Orderings_Obot__class_Obot(tc_fun(_1358005, tc_HOL_Obool)), 31680 ^ _773908 : [(31681 ^ _773908) ^ [_1358119] : [hBOOL(hAPP(hAPP(c_member(_1358003), _1358119), _1358007)), -(hAPP(_1358009, _1358119) = c_Orderings_Obot__class_Obot(tc_fun(_1358005, tc_HOL_Obool)))]]], (26279 ^ _773908) ^ [_1240941, _1240943, _1240945, _1240947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240941, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240941, tc_HOL_Obool)), _1240943), _1240945)), _1240947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240941, tc_HOL_Obool)), _1240943), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240941, tc_HOL_Obool)), _1240945), _1240947))))], (41131 ^ _773908) ^ [_1584220, _1584222] : [41133 ^ _773908 : [(41137 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41135 ^ [_1584220, _1584222]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584220)), _1584222))))], (41139 ^ _773908) ^ [] : [41132 ^ [_1584220, _1584222] = 41135 ^ [_1584220, _1584222]], (41141 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1584220), _1584222), 41132 ^ [_1584220, _1584222]) = hAPP(hAPP(c_List_Onth(_1584220), _1584222), 41135 ^ [_1584220, _1584222]))], (41134 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41132 ^ [_1584220, _1584222]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584220)), _1584222))))]], -(hBOOL(hAPP(c_List_Odistinct(_1584220), _1584222)))], (24701 ^ _773908) ^ [_1209371, _1209373, _1209375, _1209377] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_1209371, _1209373)), _1209375), _1209377)), -(_1209377 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _1209375), _1209371), hAPP(_1209373, _1209375)))], (44587 ^ _773908) ^ [_1664094, _1664096, _1664098, _1664100] : [-(c_List_Otranspose(_1664094, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664094)), hAPP(hAPP(c_List_Olist_OCons(_1664094), _1664096), _1664098)), _1664100)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664094)), hAPP(hAPP(c_List_Olist_OCons(_1664094), _1664096), c_List_Oconcat(_1664094, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1664094), tc_List_Olist(_1664094)), c_List_Olist_Olist__case(tc_List_Olist(_1664094), _1664094, c_List_Olist_ONil(_1664094), hAPP(hAPP(c_COMBB(tc_List_Olist(_1664094), tc_fun(tc_List_Olist(_1664094), tc_List_Olist(_1664094)), _1664094), c_COMBK(tc_List_Olist(_1664094), tc_List_Olist(_1664094))), hAPP(hAPP(c_COMBC(_1664094, tc_List_Olist(_1664094), tc_List_Olist(_1664094)), c_List_Olist_OCons(_1664094)), c_List_Olist_ONil(_1664094))))), _1664100)))), c_List_Otranspose(_1664094, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664094)), _1664098), c_List_Oconcat(tc_List_Olist(_1664094), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1664094), tc_List_Olist(tc_List_Olist(_1664094))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1664094)), _1664094, c_List_Olist_ONil(tc_List_Olist(_1664094)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1664094), tc_List_Olist(tc_List_Olist(_1664094))), _1664094), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664094), tc_List_Olist(tc_List_Olist(_1664094)), tc_List_Olist(tc_List_Olist(_1664094))), c_List_Olist_OCons(tc_List_Olist(_1664094))), c_List_Olist_ONil(tc_List_Olist(_1664094)))))), _1664100))))))], (45473 ^ _773908) ^ [_1682258, _1682260] : [class_Groups_Ocomm__monoid__add(_1682258), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1682258), hAPP(c_List_Orev(_1682258), _1682260)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1682258), _1682260))], (17781 ^ _773908) ^ [_1081196] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081196)))), -(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), _1081196)) = 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), _1081196))))], (49714 ^ _773908) ^ [_1777249, _1777251] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1777249)), _1777251) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1777249, tc_Lazy__Sequence_Olazy__sequence(_1777249)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1777249, tc_Lazy__Sequence_Olazy__sequence(_1777249), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777249), tc_Nat_Onat), _1777249), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1777249), 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(_1777249)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1777249)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1777249), _1777251)))], (44863 ^ _773908) ^ [_1670933, _1670935, _1670937, _1670939, _1670941] : [class_Orderings_Olinorder(_1670933), hBOOL(hAPP(hAPP(c_member(_1670935), _1670937), hAPP(c_List_Oset(_1670935), _1670939))), c_List_Olinorder__class_Osorted(_1670933, hAPP(hAPP(c_List_Omap(_1670935, _1670933), _1670941), _1670939)), hAPP(c_List_Ohd(_1670935), hAPP(c_List_Ofilter(_1670935, hAPP(hAPP(c_COMBB(_1670933, tc_HOL_Obool, _1670935), hAPP(c_fequal, hAPP(_1670941, _1670937))), _1670941)), _1670939)) = _1670937, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670935, _1670933, _1670941), _1670937), c_List_Oremove1(_1670935, _1670937, _1670939)) = _1670939)], (19813 ^ _773908) ^ [_1115836, _1115838] : [_1115836 = _1115838, -(c_Int_OBit0(_1115836) = c_Int_OBit0(_1115838))], (31085 ^ _773908) ^ [_1344090, _1344092, _1344094, _1344096, _1344098] : [class_Groups_Ocomm__monoid__mult(_1344090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344092), _1344094)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344092), _1344096)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344092, tc_HOL_Obool)), _1344094), _1344096) = c_Orderings_Obot__class_Obot(tc_fun(_1344092, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344092, _1344090), _1344098), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1344092, tc_HOL_Obool)), _1344094), _1344096)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344090), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344092, _1344090), _1344098), _1344094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344092, _1344090), _1344098), _1344096)))], (34564 ^ _773908) ^ [_1418000, _1418002, _1418004, _1418006, _1418008] : [class_Rings_Osemiring__0(_1418000), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418000), _1418002), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418004, _1418000), _1418006), _1418008)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418004, _1418000), hAPP(hAPP(c_COMBB(_1418000, _1418000, _1418004), hAPP(c_Groups_Otimes__class_Otimes(_1418000), _1418002)), _1418006)), _1418008))], (17307 ^ _773908) ^ [_1072492, _1072494] : [17308 ^ _773908 : [(17311 ^ _773908) ^ [] : [_1072494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17309 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072492))]], -(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), _1072492), _1072494))))], (23779 ^ _773908) ^ [_1189587, _1189589, _1189591, _1189593, _1189595, _1189597] : [-(c_Nitpick_Opair__box_Opair__box__case(_1189587, _1189589, _1189591, _1189593, c_Nitpick_Opair__box_OPairBox(_1189587, _1189589, _1189595, _1189597)) = hAPP(hAPP(_1189593, _1189595), _1189597))], (37878 ^ _773908) ^ [_1493748, _1493750, _1493752, _1493754, _1493756] : [c_Finite__Set_Ofun__left__comm__idem(_1493748, _1493750, _1493752), -(c_Finite__Set_Ofun__left__comm__idem(_1493754, _1493750, hAPP(hAPP(c_COMBB(_1493748, tc_fun(_1493750, _1493750), _1493754), _1493752), _1493756)))], (48129 ^ _773908) ^ [_1743932, _1743934, _1743936] : [-(hBOOL(hAPP(hAPP(c_member(_1743932), _1743934), hAPP(c_List_Oset(_1743932), _1743936)))), 48130 ^ _773908 : [(48131 ^ _773908) ^ [_1744021, _1744023] : [_1743936 = hAPP(hAPP(c_List_Oappend(_1743932), _1744023), hAPP(hAPP(c_List_Olist_OCons(_1743932), _1743934), _1744021)), -(hBOOL(hAPP(hAPP(c_member(_1743932), _1743934), hAPP(c_List_Oset(_1743932), _1744021))))]]], (15865 ^ _773908) ^ [_1044158, _1044160] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044158), hAPP(c_Nat_OSuc, _1044160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044158), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1044160))], (44005 ^ _773908) ^ [_1650370, _1650372, _1650374] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1650370, tc_HOL_Obool)), _1650372), _1650374))), 44011 ^ _773908 : [(44015 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1650370, tc_HOL_Obool)), 44013 ^ [_1650370, _1650372, _1650374]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1650370, tc_HOL_Obool)), _1650372), _1650374))))], (44017 ^ _773908) ^ [] : [44010 ^ [_1650370, _1650372, _1650374] = 44013 ^ [_1650370, _1650372, _1650374]], (44019 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1650370, tc_HOL_Obool)), 44010 ^ [_1650370, _1650372, _1650374]), 44013 ^ [_1650370, _1650372, _1650374]) = c_Orderings_Obot__class_Obot(tc_fun(_1650370, tc_HOL_Obool))], (44012 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1650370, tc_HOL_Obool)), 44010 ^ [_1650370, _1650372, _1650374]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1650370, tc_HOL_Obool)), _1650372), _1650374))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1650370, tc_HOL_Obool)), _1650372), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650370, tc_HOL_Obool), _1650374)) = c_Orderings_Obot__class_Obot(tc_fun(_1650370, tc_HOL_Obool)))], (34294 ^ _773908) ^ [_1412534, _1412536, _1412538, _1412540] : [c_Finite__Set_Ofolding__one__idem(_1412534, _1412536, _1412538), -(hAPP(hAPP(_1412536, _1412540), _1412540) = _1412540)], (1784 ^ _773908) ^ [_799194, _799196] : [-(class_Orderings_Olinorder(_799194)), _799196 = _799194, class_Orderings_Olinorder(_799196)], (46893 ^ _773908) ^ [_1714065, _1714067, _1714069, _1714071] : [c_Wellfounded_Owf(_1714065, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1714065, _1714065)), hAPP(hAPP(c_Product__Type_OPair(_1714065, _1714065), _1714067), _1714069)), _1714071)), 46896 ^ _773908 : [(46899 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714065, _1714065)), hAPP(hAPP(c_Product__Type_OPair(_1714065, _1714065), _1714069), _1714067)), c_Transitive__Closure_Ortrancl(_1714065, _1714071)))], (46897 ^ _773908) ^ [] : [-(c_Wellfounded_Owf(_1714065, _1714071))]]], (16683 ^ _773908) ^ [_1060289, _1060291, _1060293] : [class_Groups_Oordered__ab__group__add__abs(_1060289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060289), hAPP(c_Groups_Oabs__class_Oabs(_1060289), _1060291)), hAPP(c_Groups_Oabs__class_Oabs(_1060289), _1060293))), hAPP(c_Groups_Oabs__class_Oabs(_1060289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060289), _1060291), _1060293)))))], (19195 ^ _773908) ^ [_1105358, _1105360] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105358), c_Int_OPls))), 19198 ^ _773908 : [(19205 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105360), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105358)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105358), _1105360)))], (19199 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105360), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105358)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105358))]]], (14430 ^ _773908) ^ [_1018048, _1018050] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018048, _1018050)) = _1018050), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1018048), _1018050) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018048, _1018050)))], (44212 ^ _773908) ^ [_1655123, _1655125] : [class_Complete__Lattice_Ocomplete__lattice(_1655123), -(c_Complete__Lattice_OInf__class_OInf(_1655123, hAPP(c_List_Oset(_1655123), _1655125)) = hAPP(c_List_Ofoldl(_1655123, _1655123, c_Lattices_Osemilattice__inf__class_Oinf(_1655123), c_Orderings_Otop__class_Otop(_1655123)), _1655125))], (44613 ^ _773908) ^ [_1665304, _1665306] : [c_List_Otranspose(_1665304, _1665306) = c_List_Olist_ONil(tc_List_Olist(_1665304)), 44616 ^ _773908 : [(44617 ^ _773908) ^ [_1665399] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665304)), _1665399), hAPP(c_List_Oset(tc_List_Olist(_1665304)), _1665306))), -(_1665399 = c_List_Olist_ONil(_1665304))]]], (40567 ^ _773908) ^ [_1568903, _1568905, _1568907, _1568909] : [-(hAPP(hAPP(c_List_Olist__update(_1568903, hAPP(hAPP(c_List_Olist_OCons(_1568903), _1568905), _1568907)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1568909) = hAPP(hAPP(c_List_Olist_OCons(_1568903), _1568909), _1568907))], (2900 ^ _773908) ^ [_817140, _817142, _817144, _817146, _817148, _817150] : [-(c_Wellfounded_Omlex__prod(_817150, _817146, _817142) = c_Wellfounded_Omlex__prod(_817148, _817144, _817140)), _817150 = _817148, _817146 = _817144, _817142 = _817140], (37456 ^ _773908) ^ [_1482439, _1482441, _1482443, _1482445, _1482447, _1482449] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482439, _1482441)), hAPP(hAPP(c_Product__Type_OPair(_1482439, _1482441), _1482443), _1482445)), hAPP(hAPP(c_Product__Type_OSigma(_1482439, _1482441), _1482447), _1482449)))), hBOOL(hAPP(hAPP(c_member(_1482439), _1482443), _1482447)), hBOOL(hAPP(hAPP(c_member(_1482441), _1482445), hAPP(_1482449, _1482443)))], (36715 ^ _773908) ^ [_1465708, _1465710, _1465712] : [-(hAPP(c_Finite__Set_Ofold1(_1465708, _1465710), _1465712) = c_HOL_OThe(_1465708, c_Finite__Set_Ofold1Set(_1465708, _1465710, _1465712)))], (12396 ^ _773908) ^ [_981471, _981473, _981475, _981477, _981479, _981481] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _981471), _981473)), _981475) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _981477), _981479)), _981481), 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), _981477), _981479)), _981481))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981481), _981477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981477), _981471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981473), _981479)))], (51131 ^ _773908) ^ [_1808834, _1808836, _1808838, _1808840, _1808842] : [c_Fun_Obij__betw(_1808834, _1808836, _1808838, c_Orderings_Otop__class_Otop(tc_fun(_1808834, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808836, tc_HOL_Obool))), c_Fun_Obij__betw(_1808840, _1808834, _1808842, c_Orderings_Otop__class_Otop(tc_fun(_1808840, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808834, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1808840, _1808836, c_Orderings_Otop__class_Otop(tc_fun(_1808840, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1808834, _1808836, _1808840, _1808838), _1808842)) = hAPP(c_Fun_Ocomp(_1808834, _1808840, _1808836, c_Hilbert__Choice_Oinv__into(_1808840, _1808834, c_Orderings_Otop__class_Otop(tc_fun(_1808840, tc_HOL_Obool)), _1808842)), c_Hilbert__Choice_Oinv__into(_1808834, _1808836, c_Orderings_Otop__class_Otop(tc_fun(_1808834, tc_HOL_Obool)), _1808838)))], (50356 ^ _773908) ^ [_1793466] : [-(c_Relation_Oantisym(_1793466, c_Relation_OId(_1793466)))], (23991 ^ _773908) ^ [_1193107, _1193109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193107), 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)), _1193109)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193107, _1193109), c_Divides_OnegDivAlg(_1193107, _1193109))))], (22937 ^ _773908) ^ [_1172109, _1172111] : [-(c_Nitpick_Oint__lcm(_1172109, _1172111) = 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), _1172109)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1172111)))))], (20577 ^ _773908) ^ [_1129359, _1129361, _1129363] : [class_Int_Onumber__ring(_1129359), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1129359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1129359), _1129361), _1129363)), 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(_1129359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129359), hAPP(hAPP(c_Power_Opower__class_Opower(_1129359), _1129361), 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(_1129359), _1129363), 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(_1129359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129359), hAPP(c_Int_Onumber__class_Onumber__of(_1129359), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1129361)), _1129363)))], (30541 ^ _773908) ^ [_1332503, _1332505, _1332507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332503), _1332505)), -(hBOOL(hAPP(hAPP(c_member(_1332503), _1332507), _1332505))), -(hAPP(c_Finite__Set_Ocard(_1332503), hAPP(hAPP(c_Set_Oinsert(_1332503), _1332507), _1332505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1332503), _1332505)))], (46537 ^ _773908) ^ [_1705031, _1705033, _1705035] : [c_Wellfounded_OwfP(_1705031, hAPP(_1705033, 46538 ^ [_1705031, _1705033, _1705035])), 46545 ^ _773908 : [(46548 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1705031, tc_HOL_Obool)), c_Predicate_ODomainP(_1705031, _1705031, hAPP(_1705033, 46543 ^ [_1705031, _1705033, _1705035]))), c_Predicate_ORangeP(_1705031, _1705031, hAPP(_1705033, 46544 ^ [_1705031, _1705033, _1705035]))) = c_Orderings_Obot__class_Obot(tc_fun(_1705031, tc_HOL_Obool))], (46546 ^ _773908) ^ [] : [hAPP(_1705033, 46543 ^ [_1705031, _1705033, _1705035]) = hAPP(_1705033, 46544 ^ [_1705031, _1705033, _1705035])]], -(c_Wellfounded_OwfP(_1705031, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1705035, tc_fun(_1705031, tc_fun(_1705031, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1705035, tc_HOL_Obool))), _1705033)))], (12548 ^ _773908) ^ [_984162, _984164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984162, tc_HOL_Obool)), _984164), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_984162, tc_HOL_Obool)), _984164))), -(_984164 = c_Orderings_Obot__class_Obot(tc_fun(_984162, tc_HOL_Obool)))], (16917 ^ _773908) ^ [_1064929, _1064931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064929)), -(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), _1064929), _1064931))))], (48381 ^ _773908) ^ [_1749150, _1749152, _1749154] : [class_Lattices_Oab__semigroup__idem__mult(_1749150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749150), _1749152)), -(hAPP(c_Finite__Set_Ofold1(_1749150, c_Groups_Otimes__class_Otimes(_1749150)), hAPP(hAPP(c_Set_Oinsert(_1749150), _1749154), _1749152)) = hAPP(hAPP(c_Finite__Set_Ofold(_1749150, _1749150, c_Groups_Otimes__class_Otimes(_1749150)), _1749154), _1749152))], (48967 ^ _773908) ^ [_1761360, _1761362, _1761364] : [-(c_Nitpick_Otimes__frac(_1761360, _1761362, _1761364) = hAPP(hAPP(c_Nitpick_Ofrac(_1761360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1761360), _1761362)), hAPP(c_Nitpick_Onum(_1761360), _1761364))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1761360), _1761362)), hAPP(c_Nitpick_Odenom(_1761360), _1761364))))], (42818 ^ _773908) ^ [_1623543, _1623545] : [-(c_Random_Oselect(_1623543, _1623545) = 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(_1623543, 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(_1623543)), _1623545)))), hAPP(hAPP(c_COMBB(_1623543, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1623543, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1623543, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1623543, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1623543), _1623545)), c_Code__Numeral_Onat__of))))], (48451 ^ _773908) ^ [_1750467, _1750469, _1750471] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1750467), _1750469)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1750467, tc_HOL_Obool)), _1750471), _1750469) = hAPP(hAPP(c_Finite__Set_Ofold(_1750467, tc_fun(_1750467, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1750467, tc_HOL_Obool), tc_fun(tc_fun(_1750467, tc_HOL_Obool), tc_fun(_1750467, tc_HOL_Obool)), _1750467), hAPP(c_COMBC(tc_fun(_1750467, tc_HOL_Obool), tc_fun(_1750467, tc_HOL_Obool), tc_fun(_1750467, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1750467, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1750467, tc_fun(_1750467, tc_HOL_Obool), tc_fun(_1750467, tc_HOL_Obool)), c_Set_Oinsert(_1750467)), c_Orderings_Obot__class_Obot(tc_fun(_1750467, tc_HOL_Obool))))), _1750471), _1750469))], (36029 ^ _773908) ^ [_1449812, _1449814, _1449816, _1449818] : [-(hBOOL(hAPP(hAPP(c_member(_1449812), hAPP(_1449814, _1449816)), hAPP(c_Set_Oimage(_1449818, _1449812, _1449814), c_Orderings_Otop__class_Otop(tc_fun(_1449818, tc_HOL_Obool))))))], (51798 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (49104 ^ _773908) ^ [_1764133, _1764135, _1764137] : [c_List_Olist__all(_1764133, _1764135, _1764137), -(c_List_Olist__all(_1764133, _1764135, hAPP(c_List_Orev(_1764133), _1764137)))], (25367 ^ _773908) ^ [_1222088, _1222090, _1222092] : [class_Orderings_Olinorder(_1222088), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222088), _1222090), _1222092) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222088), _1222092), _1222090))], (14509 ^ _773908) ^ [_1019222, _1019224] : [14510 ^ _773908 : [(14511 ^ _773908) ^ [_1019271] : [_1019222 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019224), _1019271)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019222, _1019224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6440 ^ _773908) ^ [_878532, _878534, _878536, _878538] : [class_Groups_Ocancel__semigroup__add(_878532), 6443 ^ _773908 : [(6450 ^ _773908) ^ [] : [_878534 = _878538, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878532), _878534), _878536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878532), _878538), _878536))], (6444 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878532), _878534), _878536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878532), _878538), _878536), -(_878534 = _878538)]]], (51400 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (38691 ^ _773908) ^ [_1521458, _1521460, _1521462, _1521464] : [c_Wellfounded_Owf(_1521458, _1521460), -(c_Wellfounded_Owf(_1521462, hAPP(hAPP(c_Relation_Oinv__image(_1521458, _1521462), _1521460), _1521464)))], (24561 ^ _773908) ^ [_1206519, _1206521, _1206523, _1206525, _1206527, _1206529] : [hBOOL(hAPP(_1206519, _1206521)), hBOOL(hAPP(_1206523, _1206525)), 24568 ^ _773908 : [(24571 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1206523, hAPP(c_Product__Type_Osnd(_1206527, _1206529), hAPP(hAPP(c_Product__Type_OPair(_1206527, _1206529), _1206521), _1206525)))))], (24569 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1206519, hAPP(c_Product__Type_Ofst(_1206527, _1206529), hAPP(hAPP(c_Product__Type_OPair(_1206527, _1206529), _1206521), _1206525)))))]]], (37922 ^ _773908) ^ [_1494402, _1494404] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1494402)), -(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)), _1494402))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1494404))))) = 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)), _1494402))), 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, _1494404))))))], (17805 ^ _773908) ^ [_1081540, _1081542] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081540))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081540), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081542)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6522 ^ _773908) ^ [_879969, _879971, _879973, _879975, _879977] : [c_Com_Ocom_OAss(_879969, _879971) = c_Com_Ocom_OCall(_879973, _879975, _879977)], (14362 ^ _773908) ^ [_1016840, _1016842, _1016844] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016840, _1016842)), _1016844) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016840), _1016844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016842), _1016844)))], (51444 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (40822 ^ _773908) ^ [_1576324, _1576326, _1576328] : [hBOOL(hAPP(c_Predicate_OPowp(_1576324, _1576326), _1576328)), 40825 ^ _773908 : [(40826 ^ _773908) ^ [_1576408] : [hBOOL(hAPP(hAPP(c_member(_1576324), _1576408), _1576328)), -(hBOOL(hAPP(_1576326, _1576408)))]]], (27624 ^ _773908) ^ [_1273526, _1273528, _1273530, _1273532, _1273534, _1273536, _1273538, _1273540] : [c_Finite__Set_Ofolding__image__simple(_1273526, _1273528, _1273530, _1273532, _1273534, _1273536), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273528), _1273538)), -(hAPP(_1273536, hAPP(hAPP(c_Set_Oinsert(_1273528), _1273540), _1273538)) = hAPP(hAPP(_1273530, hAPP(_1273534, _1273540)), hAPP(_1273536, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273528, tc_HOL_Obool)), _1273538), hAPP(hAPP(c_Set_Oinsert(_1273528), _1273540), c_Orderings_Obot__class_Obot(tc_fun(_1273528, tc_HOL_Obool)))))))], (22891 ^ _773908) ^ [_1170992] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1170992)], (24399 ^ _773908) ^ [_1202254, _1202256] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202254, _1202256) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1202254, _1202256)))], (18901 ^ _773908) ^ [_1100625, _1100627] : [class_Int_Onumber__ring(_1100625), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100625), hAPP(c_Int_Onumber__class_Onumber__of(_1100625), c_Int_OPls)), _1100627) = _1100627)], (51524 ^ _773908) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (2734 ^ _773908) ^ [_814561, _814563] : [_814563 = _814561, -(c_Int_OBit0(_814563) = c_Int_OBit0(_814561))], (41091 ^ _773908) ^ [_1583313, _1583315, _1583317] : [-(hBOOL(hAPP(c_List_Odistinct(_1583313), hAPP(hAPP(c_List_Olist_OCons(_1583313), _1583315), _1583317)))), -(hBOOL(hAPP(hAPP(c_member(_1583313), _1583315), hAPP(c_List_Oset(_1583313), _1583317)))), hBOOL(hAPP(c_List_Odistinct(_1583313), _1583317))], (25967 ^ _773908) ^ [_1234003, _1234005, _1234007, _1234009] : [hBOOL(hAPP(_1234003, _1234005)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234007, tc_HOL_Obool)), _1234003), _1234009), _1234005)))], (10323 ^ _773908) ^ [_945184, _945186, _945188] : [class_Orderings_Opreorder(_945184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945184), _945186), _945188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945184), _945186), _945188)))], (4730 ^ _773908) ^ [_846033, _846035, _846037, _846039] : [-(c_Lazy__Sequence_Osmall__lazy_H(_846039, _846035) = c_Lazy__Sequence_Osmall__lazy_H(_846037, _846033)), _846039 = _846037, _846035 = _846033], (31349 ^ _773908) ^ [_1350117, _1350119, _1350121, _1350123] : [-(hAPP(c_Relation_OImage(_1350117, _1350119, _1350121), _1350123) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1350117, tc_fun(_1350119, tc_HOL_Obool)), _1350123), hAPP(hAPP(c_COMBB(tc_fun(_1350117, tc_HOL_Obool), tc_fun(_1350119, tc_HOL_Obool), _1350117), c_Relation_OImage(_1350117, _1350119, _1350121)), hAPP(hAPP(c_COMBC(_1350117, tc_fun(_1350117, tc_HOL_Obool), tc_fun(_1350117, tc_HOL_Obool)), c_Set_Oinsert(_1350117)), c_Orderings_Obot__class_Obot(tc_fun(_1350117, tc_HOL_Obool))))))], (25107 ^ _773908) ^ [_1217511, _1217513, _1217515] : [class_Orderings_Olinorder(_1217511), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217511), _1217513), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217511), _1217513), _1217515)) = _1217513)], (40068 ^ _773908) ^ [_1556947, _1556949, _1556951] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556947, _1556947)), hAPP(hAPP(c_Product__Type_OPair(_1556947, _1556947), 40069 ^ [_1556947, _1556949, _1556951]), 40069 ^ [_1556947, _1556949, _1556951])), _1556949))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1556947), tc_List_Olist(_1556947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1556947), tc_List_Olist(_1556947)), _1556951), _1556951)), c_List_Olexord(_1556947, _1556949)))], (34976 ^ _773908) ^ [_1427582, _1427584, _1427586, _1427588, _1427590] : [class_Groups_Oab__group__add(_1427582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427584), _1427586)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427584), _1427588)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427584, _1427582), _1427590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427584, tc_HOL_Obool)), _1427586), _1427588)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1427582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427582), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427584, _1427582), _1427590), _1427586)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427584, _1427582), _1427590), _1427588))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427584, _1427582), _1427590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427584, tc_HOL_Obool)), _1427586), _1427588))))], (24909 ^ _773908) ^ [_1213343, _1213345, _1213347] : [class_Orderings_Olinorder(_1213343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213343), _1213345), _1213347)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213343), _1213345), _1213347) = _1213345)], (20243 ^ _773908) ^ [_1123308, _1123310] : [class_Rings_Ocomm__semiring__1(_1123308), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123308), _1123310), _1123310) = hAPP(hAPP(c_Power_Opower__class_Opower(_1123308), _1123310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (42281 ^ _773908) ^ [_1611629, _1611631, _1611633, _1611635] : [c_List_Olist_ONil(_1611629) = hAPP(hAPP(c_List_Omap(_1611631, _1611629), _1611633), _1611635), -(_1611635 = c_List_Olist_ONil(_1611631))], (14529 ^ _773908) ^ [_1019636, _1019638, _1019640, _1019642] : [class_Divides_Osemiring__div(_1019636), -(_1019638 = c_Groups_Ozero__class_Ozero(_1019636)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019636), _1019638), _1019640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019636), _1019638), _1019642)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019636), _1019640), _1019642))], (13811 ^ _773908) ^ [_1006514, _1006516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006514), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13814 ^ _773908 : [(13817 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006514), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006516, _1006514))))], (13815 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006516, _1006514)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (39082 ^ _773908) ^ [_1529911, _1529913, _1529915, _1529917] : [39083 ^ _773908 : [(39084 ^ _773908) ^ [_1529986] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529915, _1529911)), hAPP(hAPP(c_Product__Type_OPair(_1529915, _1529911), _1529986), _1529913)), _1529917))]], -(hBOOL(hAPP(hAPP(c_member(_1529911), _1529913), hAPP(c_Relation_ORange(_1529915, _1529911), _1529917))))], (34540 ^ _773908) ^ [_1417314, _1417316, _1417318, _1417320, _1417322, _1417324] : [class_Groups_Ocomm__monoid__add(_1417314), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417316, _1417314), hAPP(hAPP(c_COMBC(_1417316, tc_fun(_1417318, tc_HOL_Obool), _1417314), hAPP(hAPP(c_COMBB(tc_fun(_1417318, _1417314), tc_fun(tc_fun(_1417318, tc_HOL_Obool), _1417314), _1417316), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417318, _1417314)), _1417320)), _1417322)), _1417324) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417318, _1417314), hAPP(hAPP(c_COMBC(_1417318, tc_fun(_1417316, tc_HOL_Obool), _1417314), hAPP(hAPP(c_COMBB(tc_fun(_1417316, _1417314), tc_fun(tc_fun(_1417316, tc_HOL_Obool), _1417314), _1417318), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417316, _1417314)), hAPP(c_COMBC(_1417316, _1417318, _1417314), _1417320))), _1417324)), _1417322))], (51410 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (28923 ^ _773908) ^ [_1302229, _1302231] : [class_Orderings_Olinorder(_1302229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302229), _1302231)), -(_1302231 = c_Orderings_Obot__class_Obot(tc_fun(_1302229, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1302229), c_Big__Operators_Olinorder__class_OMax(_1302229, _1302231)), _1302231)))], (30854 ^ _773908) ^ [_1338996, _1338998, _1339000, _1339002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1338996, _1338998)), c_Sum__Type_OPlus(_1338996, _1338998, _1339000, _1339002))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338998), _1339002)))], (20495 ^ _773908) ^ [_1127697, _1127699, _1127701] : [class_Rings_Olinordered__idom(_1127697), 20498 ^ _773908 : [(20499 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127697), c_Groups_Ozero__class_Ozero(_1127697)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127697), hAPP(hAPP(c_Power_Opower__class_Opower(_1127697), _1127699), 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(_1127697), _1127701), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1127699 = c_Groups_Ozero__class_Ozero(_1127697), _1127701 = c_Groups_Ozero__class_Ozero(_1127697)], (20509 ^ _773908) ^ [] : [20510 ^ _773908 : [(20513 ^ _773908) ^ [] : [-(_1127701 = c_Groups_Ozero__class_Ozero(_1127697))], (20511 ^ _773908) ^ [] : [-(_1127699 = c_Groups_Ozero__class_Ozero(_1127697))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127697), c_Groups_Ozero__class_Ozero(_1127697)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127697), hAPP(hAPP(c_Power_Opower__class_Opower(_1127697), _1127699), 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(_1127697), _1127701), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (51592 ^ _773908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (43421 ^ _773908) ^ [_1636560, _1636562, _1636564] : [_1636560 = _1636562, -(c_List_Olist__all2(_1636564, _1636564, c_fequal, _1636560, _1636562))], (51584 ^ _773908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (35090 ^ _773908) ^ [_1430152, _1430154, _1430156, _1430158, _1430160] : [class_Groups_Ocomm__monoid__add(_1430152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430154), _1430156)), hBOOL(hAPP(hAPP(c_member(_1430154), _1430158), _1430156)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430154, _1430152), _1430160), _1430156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430152), hAPP(_1430160, _1430158)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430154, _1430152), _1430160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430154, tc_HOL_Obool)), _1430156), hAPP(hAPP(c_Set_Oinsert(_1430154), _1430158), c_Orderings_Obot__class_Obot(tc_fun(_1430154, tc_HOL_Obool)))))))], (21617 ^ _773908) ^ [_1147916, _1147918, _1147920, _1147922] : [class_Fields_Olinordered__field(_1147916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147916), c_Groups_Ozero__class_Ozero(_1147916)), _1147918)), 21624 ^ _773908 : [(21631 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147916), _1147920), _1147918)), _1147922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147916), _1147920), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147916), _1147922), _1147918))))], (21625 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147916), _1147920), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147916), _1147922), _1147918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147916), _1147920), _1147918)), _1147922)))]]], (32145 ^ _773908) ^ [_1369871, _1369873] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1369871, _1369873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1369873), _1369871))], (45515 ^ _773908) ^ [_1683091, _1683093, _1683095] : [-(hAPP(c_List_Orev(_1683091), hAPP(c_List_Ofilter(_1683091, _1683093), _1683095)) = hAPP(c_List_Ofilter(_1683091, _1683093), hAPP(c_List_Orev(_1683091), _1683095)))], (48701 ^ _773908) ^ [_1755183, _1755185, _1755187, _1755189, _1755191] : [c_Finite__Set_Ofun__left__comm(_1755183, _1755185, _1755187), -(hAPP(hAPP(c_Finite__Set_Ofold(_1755183, _1755185, _1755187), _1755189), hAPP(c_List_Oset(_1755183), _1755191)) = hAPP(c_List_Ofoldl(_1755185, _1755183, hAPP(c_COMBC(_1755183, _1755185, _1755185), _1755187), _1755189), c_List_Oremdups(_1755183, _1755191)))], (9577 ^ _773908) ^ [_933475, _933477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933475)), _933477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933475), hAPP(c_Int_Onat, _933477))))], (29433 ^ _773908) ^ [_1311087, _1311089] : [class_Orderings_Olinorder(_1311087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311087), _1311089)), -(_1311089 = c_Orderings_Obot__class_Obot(tc_fun(_1311087, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1311087), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311087), 29446 ^ [_1311087, _1311089]), 29447 ^ [_1311087, _1311089])), hAPP(hAPP(c_Set_Oinsert(_1311087), 29446 ^ [_1311087, _1311089]), hAPP(hAPP(c_Set_Oinsert(_1311087), 29447 ^ [_1311087, _1311089]), c_Orderings_Obot__class_Obot(tc_fun(_1311087, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1311087), c_Big__Operators_Olinorder__class_OMax(_1311087, _1311089)), _1311089)))], (39835 ^ _773908) ^ [_1550876] : [-(c_List_Olists(_1550876, c_Orderings_Otop__class_Otop(tc_fun(_1550876, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1550876), tc_HOL_Obool)))], (49182 ^ _773908) ^ [_1765688, _1765690] : [c_List_Olist__ex1(_1765688, _1765690, c_List_Olist_ONil(_1765688))], (38282 ^ _773908) ^ [_1505592] : [-(c_Wellfounded_Ofinite__psubset(_1505592) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1505592, tc_HOL_Obool), tc_fun(_1505592, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1505592, tc_HOL_Obool), tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1505592, tc_HOL_Obool), tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1505592, tc_HOL_Obool)), c_COMBS(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1505592, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1505592, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1505592, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1505592, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1505592)))))], (25035 ^ _773908) ^ [_1215548, _1215550] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1215548)), _1215550) = 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), _1215548)), _1215550))], (7615 ^ _773908) ^ [_897349, _897351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_897349, tc_HOL_Obool)), _897351), c_Orderings_Obot__class_Obot(tc_fun(_897349, tc_HOL_Obool))))], (43043 ^ _773908) ^ [_1628048, _1628050, _1628052] : [hBOOL(hAPP(hAPP(c_member(_1628048), _1628050), hAPP(c_List_Oset(_1628048), _1628052))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628048)), c_List_Oremove1(_1628048, _1628050, _1628052)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628048)), _1628052)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23167 ^ _773908) ^ [_1176741, _1176743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176741)), hAPP(c_Nat_OSuc, _1176743))), -(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(_1176741))), 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)), _1176743)))))], (6016 ^ _773908) ^ [_870590, _870592, _870594, _870596] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870590)), _870592, _870594, _870596), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _870590), _870592, hAPP(c_Nat_OSuc, _870594), _870596))], (10649 ^ _773908) ^ [_950468, _950470, _950472] : [class_Groups_Oordered__ab__group__add(_950468), 10652 ^ _773908 : [(10659 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950468), _950472), hAPP(c_Groups_Ouminus__class_Ouminus(_950468), _950470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950468), _950470), hAPP(c_Groups_Ouminus__class_Ouminus(_950468), _950472))))], (10653 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950468), _950470), hAPP(c_Groups_Ouminus__class_Ouminus(_950468), _950472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950468), _950472), hAPP(c_Groups_Ouminus__class_Ouminus(_950468), _950470))))]]], (23773 ^ _773908) ^ [_1189373, _1189375, _1189377, _1189379, _1189381, _1189383, _1189385, _1189387] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189373, _1189375, _1189377), _1189379), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189381, _1189383, tc_prod(_1189373, _1189375)), _1189385), _1189387)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189381, _1189383, _1189377), hAPP(hAPP(c_COMBB(tc_fun(_1189383, tc_prod(_1189373, _1189375)), tc_fun(_1189383, _1189377), _1189381), hAPP(c_COMBB(tc_prod(_1189373, _1189375), _1189377, _1189383), hAPP(c_Product__Type_Oprod_Oprod__case(_1189373, _1189375, _1189377), _1189379))), _1189385)), _1189387))], (15033 ^ _773908) ^ [_1028579, _1028581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1028579)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028579), _1028581)), _1028579) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11105 ^ _773908) ^ [_958714, _958716, _958718] : [class_Rings_Oordered__cancel__semiring(_958714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958714), c_Groups_Ozero__class_Ozero(_958714)), _958716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958714), c_Groups_Ozero__class_Ozero(_958714)), _958718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958714), c_Groups_Ozero__class_Ozero(_958714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958714), _958716), _958718))))], (20273 ^ _773908) ^ [_1123821] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1123821), 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), _1123821), _1123821))], (32476 ^ _773908) ^ [_1376827, _1376829] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1376827, _1376829)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1376827), hAPP(c_Nat_OSuc, _1376829)))], (32246 ^ _773908) ^ [_1371904, _1371906, _1371908] : [class_Orderings_Olinorder(_1371904), hAPP(_1371906, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371904), 32251 ^ [_1371904, _1371906, _1371908]), 32252 ^ [_1371904, _1371906, _1371908])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371904), hAPP(_1371906, 32251 ^ [_1371904, _1371906, _1371908])), hAPP(_1371906, 32252 ^ [_1371904, _1371906, _1371908])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371904), _1371908)), -(_1371908 = c_Orderings_Obot__class_Obot(tc_fun(_1371904, tc_HOL_Obool))), -(hAPP(_1371906, c_Big__Operators_Olattice_OInf__fin(_1371904, c_Orderings_Oord__class_Omin(_1371904), _1371908)) = c_Big__Operators_Olattice_OInf__fin(_1371904, c_Orderings_Oord__class_Omin(_1371904), hAPP(c_Set_Oimage(_1371904, _1371904, _1371906), _1371908)))], (14382 ^ _773908) ^ [_1017230, _1017232] : [class_Divides_Osemiring__div(_1017230), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1017230), _1017232), c_Groups_Oone__class_Oone(_1017230)) = _1017232)], (5240 ^ _773908) ^ [_854028, _854030, _854032, _854034] : [-(c_Relation_OId__on(_854034, _854030) = c_Relation_OId__on(_854032, _854028)), _854034 = _854032, _854030 = _854028], (39108 ^ _773908) ^ [_1531053, _1531055] : [-(c_List_Olenlex(_1531053, _1531055) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1531053)), tc_List_Olist(_1531053)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1531053), c_Wellfounded_Oless__than, c_List_Olex(_1531053, _1531055))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1531053), tc_List_Olist(_1531053), tc_prod(tc_Nat_Onat, tc_List_Olist(_1531053))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1531053), tc_prod(tc_Nat_Onat, tc_List_Olist(_1531053))), tc_List_Olist(_1531053)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1531053))), c_Nat_Osize__class_Osize(tc_List_Olist(_1531053)))), c_COMBI(tc_List_Olist(_1531053)))))], (12136 ^ _773908) ^ [_977365] : [_977365 = 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), _977365)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42800 ^ _773908) ^ [_1623080, _1623082, _1623084, _1623086] : [-(c_Hilbert__Choice_OEps(tc_prod(_1623080, _1623082), hAPP(c_Product__Type_Oprod_Oprod__case(_1623080, _1623082, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1623080, tc_fun(_1623082, tc_HOL_Obool), tc_fun(_1623082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1623082, tc_HOL_Obool), tc_fun(_1623082, tc_HOL_Obool)), _1623080), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1623082)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1623080), c_fconj), hAPP(c_fequal, _1623084)))), hAPP(c_fequal, _1623086)))) = hAPP(hAPP(c_Product__Type_OPair(_1623080, _1623082), _1623084), _1623086))], (22881 ^ _773908) ^ [_1170820, _1170822] : [_1170820 = _1170822, -(c_Code__Numeral_OSuc__code__numeral(_1170820) = c_Code__Numeral_OSuc__code__numeral(_1170822))], (17827 ^ _773908) ^ [_1081924, _1081926] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081924))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081924)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081926)) = 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), _1081926)))], (17441 ^ _773908) ^ [_1074961, _1074963, _1074965, _1074967] : [class_Rings_Olinordered__semidom(_1074961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074961), _1074963), _1074965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074961), c_Groups_Ozero__class_Ozero(_1074961)), _1074963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074961), hAPP(hAPP(c_Power_Opower__class_Opower(_1074961), _1074963), _1074967)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074961), _1074965), _1074967))))], (27404 ^ _773908) ^ [_1268773, _1268775, _1268777, _1268779] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268773, tc_HOL_Obool)), _1268775), _1268779))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268773, tc_HOL_Obool)), _1268775), hAPP(hAPP(c_Set_Oinsert(_1268773), _1268777), _1268779)))))], (34414 ^ _773908) ^ [_1414702] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414702)) = 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), _1414702))))], (24517 ^ _773908) ^ [_1204562, _1204564] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1204562, tc_HOL_Obool)), _1204564)), -(hBOOL(hAPP(hAPP(c_member(_1204562), _1204564), c_Orderings_Obot__class_Obot(tc_fun(_1204562, tc_HOL_Obool)))))], (42742 ^ _773908) ^ [_1621620, _1621622, _1621624] : [-(c_List_Olist_Olist__size(_1621620, _1621622, _1621624) = 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(_1621620, tc_Nat_Onat), _1621622), _1621624))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621620)), _1621624)))], (8055 ^ _773908) ^ [_905851, _905853] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905851)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905853)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _905851), _905853)))], (44529 ^ _773908) ^ [_1662064, _1662066, _1662068] : [-(c_List_Opartition(_1662064, _1662066, _1662068) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662064), tc_List_Olist(_1662064)), hAPP(c_List_Ofilter(_1662064, _1662066), _1662068)), hAPP(c_List_Ofilter(_1662064, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1662064, c_fNot), _1662066)), _1662068)))], (51562 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (47327 ^ _773908) ^ [_1725131, _1725133, _1725135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1725133, _1725131)), _1725135)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1725131, _1725133)), hAPP(c_Relation_Oconverse(_1725133, _1725131), _1725135))))], (8569 ^ _773908) ^ [_915570, _915572, _915574, _915576] : [class_Rings_Ocomm__semiring__1(_915570), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915570), _915572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915570), _915574), _915576)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915570), _915572), _915574)), _915576))], (24535 ^ _773908) ^ [_1204983, _1204985, _1204987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204983, tc_HOL_Obool)), _1204985), _1204987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204983, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1204983, tc_fun(_1204983, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204983)), _1204985)), hAPP(hAPP(c_COMBC(_1204983, tc_fun(_1204983, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204983)), _1204987))))], (4344 ^ _773908) ^ [_839954, _839956, _839958, _839960, _839962, _839964, _839966, _839968] : [-(c_New__Random__Sequence_Oneg__bind(_839968, _839964, _839960, _839956) = c_New__Random__Sequence_Oneg__bind(_839966, _839962, _839958, _839954)), _839968 = _839966, _839964 = _839962, _839960 = _839958, _839956 = _839954], (364 ^ _773908) ^ [_779508, _779510, _779512, _779514, _779516, _779518, _779520, _779522] : [-(c_List_Olistrelp(_779520, _779516, _779512, _779508)), c_List_Olistrelp(_779522, _779518, _779514, _779510), _779522 = _779520, _779518 = _779516, _779514 = _779512, _779510 = _779508], (19885 ^ _773908) ^ [_1117070] : [c_Int_OPls = _1117070, -(c_Int_OPls = c_Int_OBit0(_1117070))], (17371 ^ _773908) ^ [_1073581, _1073583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1073581)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1073581)), _1073583) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1073581), _1073583)))], (7745 ^ _773908) ^ [_899832, _899834, _899836, _899838, _899840] : [c_Com_Ocom_OAss(_899832, _899834) = c_Com_Ocom_OLocal(_899836, _899838, _899840)], (21753 ^ _773908) ^ [_1150367, _1150369, _1150371, _1150373, _1150375] : [class_Fields_Ofield(_1150367), -(_1150369 = c_Groups_Ozero__class_Ozero(_1150367)), -(_1150371 = c_Groups_Ozero__class_Ozero(_1150367)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150367), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150367), _1150373), _1150369)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150367), _1150375), _1150371)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150367), _1150373), _1150371)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150367), _1150375), _1150369))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150367), _1150369), _1150371)))], (15713 ^ _773908) ^ [_1041250, _1041252, _1041254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041250), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041252), _1041254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041250), _1041254)), _1041252)))], (42387 ^ _773908) ^ [_1613694, _1613696, _1613698, _1613700] : [class_Groups_Oab__group__add(_1613694), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1613694), hAPP(c_List_Omonoid__add__class_Olistsum(_1613694), hAPP(hAPP(c_List_Omap(_1613696, _1613694), _1613698), _1613700))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1613694), hAPP(hAPP(c_List_Omap(_1613696, _1613694), hAPP(c_Fun_Ocomp(_1613694, _1613694, _1613696, c_Groups_Ouminus__class_Ouminus(_1613694)), _1613698)), _1613700)))], (49350 ^ _773908) ^ [_1769724, _1769726, _1769728] : [-(c_Predicate_Oconversep(_1769724, _1769726, c_Predicate_Oconversep(_1769726, _1769724, _1769728)) = _1769728)], (46057 ^ _773908) ^ [_1694421, _1694423] : [class_Orderings_Olinorder(_1694421), -(c_List_Olinorder__class_Osorted__list__of__set(_1694421, hAPP(c_List_Oset(_1694421), _1694423)) = c_List_Olinorder__class_Osort__key(_1694421, _1694421, c_COMBI(_1694421), c_List_Oremdups(_1694421, _1694423)))], (25805 ^ _773908) ^ [_1231063, _1231065, _1231067, _1231069] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1231063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231063, tc_HOL_Obool)), _1231065), _1231067)), _1231069) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231063, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1231063, tc_HOL_Obool)), _1231065), _1231069)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1231063, tc_HOL_Obool)), _1231067), _1231069)))], (15491 ^ _773908) ^ [_1036802, _1036804, _1036806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036802), _1036804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036802), _1036806)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036804), _1036806))))], (51718 ^ _773908) ^ [_1816356, _1816358] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1816356, _1816358))), class_Lazy__Sequence_Osmall__lazy(_1816356), class_Lazy__Sequence_Osmall__lazy(_1816358)], (31886 ^ _773908) ^ [_1363890, _1363892, _1363894, _1363896, _1363898] : [-(_1363890 = c_Orderings_Obot__class_Obot(tc_fun(_1363892, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363892, tc_fun(_1363894, tc_HOL_Obool)), _1363890), hAPP(hAPP(c_COMBB(tc_fun(_1363894, tc_HOL_Obool), tc_fun(_1363894, tc_HOL_Obool), _1363892), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363894, tc_HOL_Obool)), _1363896)), _1363898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363894, tc_HOL_Obool)), _1363896), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363892, tc_fun(_1363894, tc_HOL_Obool)), _1363890), _1363898)))], (24285 ^ _773908) ^ [_1198734, _1198736, _1198738, _1198740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198734, tc_fun(_1198736, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1198734, tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_fun(_1198736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1198736, tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_fun(_1198736, tc_HOL_Obool)), _1198734), c_COMBC(_1198736, tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1198736, tc_prod(_1198734, _1198736)), tc_fun(_1198736, tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), _1198734), hAPP(c_COMBB(tc_prod(_1198734, _1198736), tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool), _1198736), c_member(tc_prod(_1198734, _1198736)))), c_Product__Type_OPair(_1198734, _1198736)))), _1198738)), hAPP(hAPP(c_COMBC(_1198734, tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_fun(_1198736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1198736, tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_fun(_1198736, tc_HOL_Obool)), _1198734), c_COMBC(_1198736, tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1198736, tc_prod(_1198734, _1198736)), tc_fun(_1198736, tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool)), _1198734), hAPP(c_COMBB(tc_prod(_1198734, _1198736), tc_fun(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool), tc_HOL_Obool), _1198736), c_member(tc_prod(_1198734, _1198736)))), c_Product__Type_OPair(_1198734, _1198736)))), _1198740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1198734, _1198736), tc_HOL_Obool)), _1198738), _1198740)))], (48843 ^ _773908) ^ [_1758510, _1758512, _1758514, _1758516, _1758518, _1758520, _1758522, _1758524] : [c_Finite__Set_Ofolding__image__simple__idem(_1758510, _1758512, _1758514, _1758516, _1758518, _1758520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1758512), _1758522)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1758512), _1758524)), -(hAPP(_1758520, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1758512, tc_HOL_Obool)), _1758522), _1758524)) = hAPP(hAPP(_1758514, hAPP(_1758520, _1758522)), hAPP(_1758520, _1758524)))], (26796 ^ _773908) ^ [_1256794, _1256796, _1256798, _1256800, _1256802] : [hAPP(_1256798, _1256800) = _1256802, -(c_Fun_Ofun__upd(_1256794, _1256796, _1256798, _1256800, _1256802) = _1256798)], (25913 ^ _773908) ^ [_1233011, _1233013, _1233015, _1233017] : [class_Lattices_Osemilattice__sup(_1233011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233011), _1233013), _1233015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233011), _1233017), _1233015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233011), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1233011), _1233013), _1233017)), _1233015)))], (49914 ^ _773908) ^ [_1782123, _1782125, _1782127] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1782123, _1782125, _1782127) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1782123)], (33902 ^ _773908) ^ [_1404080, _1404082, _1404084, _1404086, _1404088] : [-(c_Fun_Oinj__on(_1404080, _1404082, _1404084, hAPP(hAPP(c_Set_Oinsert(_1404080), _1404086), _1404088))), c_Fun_Oinj__on(_1404080, _1404082, _1404084, _1404088), -(hBOOL(hAPP(hAPP(c_member(_1404082), hAPP(_1404084, _1404086)), hAPP(c_Set_Oimage(_1404080, _1404082, _1404084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404080, tc_HOL_Obool)), _1404088), hAPP(hAPP(c_Set_Oinsert(_1404080), _1404086), c_Orderings_Obot__class_Obot(tc_fun(_1404080, tc_HOL_Obool))))))))], (10589 ^ _773908) ^ [_949509, _949511, _949513] : [10590 ^ _773908 : [(10593 ^ _773908) ^ [] : [_949511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10591 ^ _773908) ^ [] : [_949509 = _949513]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949509), _949511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949513), _949511))], (49051 ^ _773908) ^ [_1763166, _1763168, _1763170, _1763172] : [-(c_List_Olist__all(_1763166, _1763168, hAPP(hAPP(c_List_Olist_OCons(_1763166), _1763170), _1763172))), hBOOL(hAPP(_1763168, _1763170)), c_List_Olist__all(_1763166, _1763168, _1763172)], (37780 ^ _773908) ^ [_1491596] : [-(c_Relation_Orefl__on(_1491596, c_Orderings_Obot__class_Obot(tc_fun(_1491596, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1491596, _1491596), tc_HOL_Obool))))], (48809 ^ _773908) ^ [_1757515, _1757517] : [c_Wellfounded_Owf(_1757515, _1757517), 48812 ^ _773908 : [(48813 ^ _773908) ^ [_1757647] : [48814 ^ _773908 : [(48815 ^ _773908) ^ [_1757752] : [hBOOL(hAPP(hAPP(c_member(_1757515), _1757752), _1757647))]], 48817 ^ _773908 : [(48820 ^ _773908) ^ [_1757874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757515, _1757515)), hAPP(hAPP(c_Product__Type_OPair(_1757515, _1757515), _1757874), 48816 ^ [_1757515, _1757517, _1757647])), _1757517)), hBOOL(hAPP(hAPP(c_member(_1757515), _1757874), _1757647))], (48818 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757515), 48816 ^ [_1757515, _1757517, _1757647]), _1757647)))]]]]], (43226 ^ _773908) ^ [_1632499, _1632501, _1632503, _1632505] : [-(hBOOL(hAPP(c_List_Olistsp(_1632499, _1632501), hAPP(hAPP(c_List_Oappend(_1632499), _1632503), _1632505)))), hBOOL(hAPP(c_List_Olistsp(_1632499, _1632501), _1632503)), hBOOL(hAPP(c_List_Olistsp(_1632499, _1632501), _1632505))], (10125 ^ _773908) ^ [_942358] : [class_Rings_Ozero__neq__one(_942358), c_Groups_Ozero__class_Ozero(_942358) = c_Groups_Oone__class_Oone(_942358)], (5104 ^ _773908) ^ [_851872, _851874, _851876, _851878] : [-(c_Complete__Lattice_OSup__class_OSup(_851878, _851874) = c_Complete__Lattice_OSup__class_OSup(_851876, _851872)), _851878 = _851876, _851874 = _851872], (49722 ^ _773908) ^ [_1777633, _1777635, _1777637, _1777639, _1777641, _1777643] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1777633, _1777635, _1777637, _1777639, c_Lazy__Sequence_Olazy__sequence_OInsert(_1777635, _1777641, _1777643)) = hAPP(hAPP(_1777639, _1777641), _1777643))], (49316 ^ _773908) ^ [_1768875, _1768877, _1768879, _1768881, _1768883] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1768875), _1768877), _1768879), _1768881), _1768883) = c_New__DSequence_Opos__single(_1768875, _1768877))], (36103 ^ _773908) ^ [_1451262, _1451264] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451262, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451262, tc_HOL_Obool)), _1451264)), _1451264) = c_Orderings_Otop__class_Otop(tc_fun(_1451262, tc_HOL_Obool)))], (19773 ^ _773908) ^ [_1115066, _1115068] : [-(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), _1115066)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1115068)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115066))) = 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), _1115068)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115066)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47949 ^ _773908) ^ [_1740065, _1740067, _1740069] : [c_Wellfounded_Owf(_1740065, _1740067), hBOOL(hAPP(hAPP(c_member(tc_prod(_1740065, _1740065)), hAPP(hAPP(c_Product__Type_OPair(_1740065, _1740065), hAPP(_1740069, hAPP(c_Nat_OSuc, 47952 ^ [_1740065, _1740067, _1740069]))), hAPP(_1740069, 47952 ^ [_1740065, _1740067, _1740069]))), _1740067))], (454 ^ _773908) ^ [_780877, _780879, _780881, _780883, _780885, _780887, _780889, _780891, _780893, _780895] : [-(c_Typedef_Otype__definition(_780893, _780889, _780885, _780881, _780877)), c_Typedef_Otype__definition(_780895, _780891, _780887, _780883, _780879), _780895 = _780893, _780891 = _780889, _780887 = _780885, _780883 = _780881, _780879 = _780877], (17793 ^ _773908) ^ [_1081356, _1081358] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081356))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081356)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081358)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46142 ^ _773908) ^ [_1696257, _1696259, _1696261, _1696263] : [-(c_List_Oconcat(_1696257, hAPP(hAPP(c_List_Omap(_1696259, tc_List_Olist(_1696257)), _1696261), _1696263)) = c_List_Omaps(_1696259, _1696257, _1696261, _1696263))], (43184 ^ _773908) ^ [_1631582, _1631584, _1631586, _1631588] : [hBOOL(hAPP(c_List_Olistsp(_1631582, hAPP(hAPP(c_COMBS(_1631582, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631582), c_fconj), _1631584)), _1631586)), _1631588)), 43187 ^ _773908 : [(43190 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1631582, _1631586), _1631588)))], (43188 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1631582, _1631584), _1631588)))]]], (32600 ^ _773908) ^ [_1378839, _1378841] : [class_Orderings_Oorder(_1378839), -(c_SetInterval_Oord__class_OatLeastAtMost(_1378839, _1378841, _1378841) = hAPP(hAPP(c_Set_Oinsert(_1378839), _1378841), c_Orderings_Obot__class_Obot(tc_fun(_1378839, tc_HOL_Obool))))], (46256 ^ _773908) ^ [_1699295, _1699297] : [c_Wellfounded_Owf(_1699295, hAPP(c_Set_OCollect(tc_prod(_1699295, _1699295)), hAPP(c_Product__Type_Oprod_Oprod__case(_1699295, _1699295, tc_HOL_Obool), _1699297))), -(c_Wellfounded_OwfP(_1699295, _1699297))], (45517 ^ _773908) ^ [_1683140, _1683142] : [-(hAPP(c_List_Orev(_1683140), c_List_Oconcat(_1683140, _1683142)) = c_List_Oconcat(_1683140, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1683140), tc_List_Olist(_1683140)), c_List_Orev(_1683140)), hAPP(c_List_Orev(tc_List_Olist(_1683140)), _1683142))))], (4868 ^ _773908) ^ [_848140, _848142, _848144, _848146] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_848146, _848142) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_848144, _848140)), _848146 = _848144, _848142 = _848140], (47090 ^ _773908) ^ [_1719424, _1719426] : [-(c_Transitive__Closure_Otrancl(_1719424, c_Transitive__Closure_Ortrancl(_1719424, _1719426)) = c_Transitive__Closure_Ortrancl(_1719424, _1719426))], (2350 ^ _773908) ^ [_808309, _808311, _808313, _808315] : [-(c_Divides_Opdivmod(_808315, _808311) = c_Divides_Opdivmod(_808313, _808309)), _808315 = _808313, _808311 = _808309], (5068 ^ _773908) ^ [_851332, _851334, _851336, _851338, _851340, _851342] : [-(c_Relation_OImage(_851342, _851338, _851334) = c_Relation_OImage(_851340, _851336, _851332)), _851342 = _851340, _851338 = _851336, _851334 = _851332], (5334 ^ _773908) ^ [_855419, _855421] : [_855421 = _855419, -(c_Orderings_Oord__class_Oless(_855421) = c_Orderings_Oord__class_Oless(_855419))], (44140 ^ _773908) ^ [_1653604, _1653606] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653604, tc_HOL_Obool), _1653606) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1653604, tc_HOL_Obool), tc_fun(_1653604, tc_HOL_Obool)), _1653606), c_COMBI(tc_fun(_1653604, tc_HOL_Obool))))], (47068 ^ _773908) ^ [_1718844, _1718846, _1718848, _1718850, _1718852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1718844, _1718844)), hAPP(hAPP(c_Product__Type_OPair(_1718844, _1718844), _1718846), _1718848)), c_Transitive__Closure_Otrancl(_1718844, _1718850))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1718844, _1718844)), hAPP(hAPP(c_Product__Type_OPair(_1718844, _1718844), _1718848), _1718852)), c_Transitive__Closure_Ortrancl(_1718844, _1718850))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718844, _1718844)), hAPP(hAPP(c_Product__Type_OPair(_1718844, _1718844), _1718846), _1718852)), c_Transitive__Closure_Otrancl(_1718844, _1718850))))], (44796 ^ _773908) ^ [_1668994, _1668996, _1668998, _1669000] : [class_Groups_Ocomm__monoid__add(_1668994), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668994), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1668994), _1668996), c_List_Oupt(_1668998, _1669000))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1668994), _1668996), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1668998, _1669000))))], (15387 ^ _773908) ^ [_1034983, _1034985, _1034987] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034983)), _1034985)), hAPP(c_Nat_OSuc, _1034987)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034983), _1034985)), _1034987))], (20103 ^ _773908) ^ [_1120843, _1120845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120843)), c_Int_OBit1(_1120845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120843), _1120845)))], (26651 ^ _773908) ^ [_1252744, _1252746, _1252748, _1252750] : [-(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), _1252744), _1252746)), 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), _1252748), _1252750)), 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), _1252744), _1252748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252746), _1252750))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252744), _1252750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252746), _1252748)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37804 ^ _773908) ^ [_1492058, _1492060, _1492062, _1492064] : [c_Relation_Orefl__on(_1492058, _1492060, _1492062), hBOOL(hAPP(hAPP(c_member(_1492058), _1492064), _1492060)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492058, _1492058)), hAPP(hAPP(c_Product__Type_OPair(_1492058, _1492058), _1492064), _1492064)), _1492062)))], (30191 ^ _773908) ^ [_1325343, _1325345, _1325347] : [class_Orderings_Olinorder(_1325343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325343), _1325345)), -(hBOOL(hAPP(hAPP(c_member(_1325343), _1325347), _1325345))), -(_1325345 = c_Orderings_Obot__class_Obot(tc_fun(_1325343, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1325343, c_Orderings_Oord__class_Omin(_1325343), hAPP(hAPP(c_Set_Oinsert(_1325343), _1325347), _1325345)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325343), _1325347), c_Big__Operators_Olattice_OInf__fin(_1325343, c_Orderings_Oord__class_Omin(_1325343), _1325345)))], (42232 ^ _773908) ^ [_1610011, _1610013, _1610015, _1610017, _1610019] : [hBOOL(hAPP(hAPP(c_member(_1610011), _1610013), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610015, tc_fun(_1610011, tc_HOL_Obool)), _1610017), _1610019))), 42235 ^ _773908 : [(42236 ^ _773908) ^ [_1610135] : [hBOOL(hAPP(hAPP(c_member(_1610015), _1610135), _1610017)), -(hBOOL(hAPP(hAPP(c_member(_1610011), _1610013), hAPP(_1610019, _1610135))))]]], (6354 ^ _773908) ^ [_876923, _876925, _876927, _876929] : [class_Groups_Ocancel__ab__semigroup__add(_876923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876923), _876925), _876927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876923), _876925), _876929), -(_876927 = _876929)], (43254 ^ _773908) ^ [_1633027, _1633029, _1633031, _1633033, _1633035] : [class_Orderings_Olinorder(_1633027), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1633029, _1633027, _1633031), _1633033), _1633035) = c_List_Olist_ONil(_1633029)], (25435 ^ _773908) ^ [_1223693, _1223695, _1223697] : [class_Int_Onumber(_1223693), class_Orderings_Oord(_1223693), 25442 ^ _773908 : [(25449 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223693), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223695)), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223697)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1223693), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223695)), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223697)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223695))], (25443 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223693), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223695)), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223697))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1223693), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223695)), hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223697)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223693), _1223697))]]], (41169 ^ _773908) ^ [_1585087, _1585089, _1585091] : [-(hAPP(c_List_Otl(_1585087), hAPP(hAPP(c_List_Oappend(_1585087), _1585089), _1585091)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1585087), _1585087, hAPP(c_List_Otl(_1585087), _1585091), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1585087), tc_List_Olist(_1585087)), _1585087), hAPP(hAPP(c_COMBC(tc_List_Olist(_1585087), tc_List_Olist(_1585087), tc_List_Olist(_1585087)), c_List_Oappend(_1585087)), _1585091))), _1585089))], (43813 ^ _773908) ^ [_1645416, _1645418, _1645420, _1645422] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645416, tc_fun(_1645418, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645416, tc_HOL_Obool), _1645420)), _1645422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1645416, tc_HOL_Obool), tc_fun(_1645418, tc_HOL_Obool)), _1645420), hAPP(hAPP(c_COMBC(tc_fun(_1645416, tc_HOL_Obool), tc_fun(_1645416, tc_fun(_1645418, tc_HOL_Obool)), tc_fun(_1645418, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645416, tc_fun(_1645418, tc_HOL_Obool))), _1645422)))], (38027 ^ _773908) ^ [_1496718, _1496720] : [c_Orderings_Obot__class_Obot(tc_fun(_1496718, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1496718), _1496720), 38030 ^ _773908 : [(38031 ^ _773908) ^ [_1496803] : [hBOOL(hAPP(_1496720, _1496803))]]], (20073 ^ _773908) ^ [_1120330, _1120332] : [class_Int_Onumber__ring(_1120330), class_Int_Oring__char__0(_1120330), 20080 ^ _773908 : [(20087 ^ _773908) ^ [] : [c_Int_Oiszero(_1120330, hAPP(c_Int_Onumber__class_Onumber__of(_1120330), _1120332)), -(c_Int_Oiszero(_1120330, hAPP(c_Int_Onumber__class_Onumber__of(_1120330), c_Int_OBit0(_1120332))))], (20081 ^ _773908) ^ [] : [c_Int_Oiszero(_1120330, hAPP(c_Int_Onumber__class_Onumber__of(_1120330), c_Int_OBit0(_1120332))), -(c_Int_Oiszero(_1120330, hAPP(c_Int_Onumber__class_Onumber__of(_1120330), _1120332)))]]], (41015 ^ _773908) ^ [_1581878, _1581880] : [hBOOL(hAPP(c_List_Odistinct(_1581878), hAPP(c_List_Orotate1(_1581878), _1581880))), -(hBOOL(hAPP(c_List_Odistinct(_1581878), _1581880)))], (37442 ^ _773908) ^ [_1481961, _1481963, _1481965, _1481967, _1481969] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1481961, _1481963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1481961, tc_HOL_Obool)), _1481965), _1481967)), hAPP(c_COMBK(tc_fun(_1481963, tc_HOL_Obool), _1481961), _1481969)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1481961, _1481963), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1481961, _1481963), _1481965), hAPP(c_COMBK(tc_fun(_1481963, tc_HOL_Obool), _1481961), _1481969))), hAPP(hAPP(c_Product__Type_OSigma(_1481961, _1481963), _1481967), hAPP(c_COMBK(tc_fun(_1481963, tc_HOL_Obool), _1481961), _1481969))))], (45915 ^ _773908) ^ [_1691461, _1691463, _1691465, _1691467, _1691469] : [-(c_List_OdropWhile(_1691461, _1691463, hAPP(hAPP(c_List_Omap(_1691465, _1691461), _1691467), _1691469)) = hAPP(hAPP(c_List_Omap(_1691465, _1691461), _1691467), c_List_OdropWhile(_1691465, hAPP(c_Fun_Ocomp(_1691461, tc_HOL_Obool, _1691465, _1691463), _1691467), _1691469)))], (7119 ^ _773908) ^ [_889200, _889202] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889200)), _889202) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _889200), _889202)))], (9471 ^ _773908) ^ [_931727] : [class_Rings_Oring__1(_931727), -(hAPP(c_Int_Oring__1__class_Oof__int(_931727), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_931727))], (5925 ^ _773908) ^ [_868739, _868741, _868743] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _868739))), _868741), _868743)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _868739)), _868741), _868743)))], (20139 ^ _773908) ^ [_1121512, _1121514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121512)), c_Int_OBit0(_1121514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121512), _1121514)))], (46228 ^ _773908) ^ [_1698546, _1698548, _1698550] : [46230 ^ _773908 : [(46233 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1698546, tc_HOL_Obool)), 46229 ^ [_1698546, _1698548, _1698550]), _1698550))], (46231 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1698546, tc_HOL_Obool)), 46229 ^ [_1698546, _1698548, _1698550]), _1698548)))]], -(_1698548 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1698546, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1698546, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698546, tc_HOL_Obool), _1698548)), _1698550)))], (18609 ^ _773908) ^ [_1095305, _1095307, _1095309] : [_1095307 = _1095309, -(hBOOL(hAPP(hAPP(c_member(_1095305), _1095307), hAPP(hAPP(c_Set_Oinsert(_1095305), _1095309), c_Orderings_Obot__class_Obot(tc_fun(_1095305, tc_HOL_Obool))))))], (32157 ^ _773908) ^ [_1370155, _1370157, _1370159, _1370161] : [class_Orderings_Oorder(_1370155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370155, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1370155, _1370157, _1370159)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1370155, _1370159, _1370161)) = c_Orderings_Obot__class_Obot(tc_fun(_1370155, tc_HOL_Obool)))], (2144 ^ _773908) ^ [_805056, _805058] : [_805058 = _805056, -(c_Int_Osucc(_805058) = c_Int_Osucc(_805056))], (17875 ^ _773908) ^ [_1082604] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082604)))], (14346 ^ _773908) ^ [_1016555, _1016557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016555), _1016557)), _1016555)))], (26147 ^ _773908) ^ [_1237846, _1237848, _1237850] : [class_Lattices_Osemilattice__sup(_1237846), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237846), _1237848), _1237850) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237846), _1237850), _1237848))], (30918 ^ _773908) ^ [_1340254, _1340256, _1340258, _1340260, _1340262] : [class_Fields_Ofield__inverse__zero(_1340254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340256), _1340258)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340256, _1340254), hAPP(hAPP(c_COMBS(_1340256, _1340254, _1340254), hAPP(hAPP(c_COMBB(_1340254, tc_fun(_1340254, _1340254), _1340256), c_Rings_Oinverse__class_Odivide(_1340254)), _1340260)), _1340262)), _1340258) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340254), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340256, _1340254), _1340260), _1340258)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340256, _1340254), _1340262), _1340258)))], (42792 ^ _773908) ^ [_1622843, _1622845, _1622847, _1622849] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1622843, _1622845, _1622847, tc_prod(_1622845, _1622847)), _1622849), c_Product__Type_OPair(_1622845, _1622847)) = _1622849)], (46955 ^ _773908) ^ [_1715851, _1715853, _1715855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1715851, _1715851), tc_HOL_Obool)), c_Relation_OId(_1715851)), _1715853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1715851, _1715851), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1715851, _1715851, _1715851), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1715851, _1715851), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1715851, _1715855)), _1715853)), _1715855)), _1715853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1715851, _1715851), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1715851, _1715855)), _1715853)))], (45832 ^ _773908) ^ [_1689729, _1689731] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1689729), _1689731) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1689729)), c_List_Oembed__list(_1689731))))], (27087 ^ _773908) ^ [_1262104, _1262106, _1262108, _1262110] : [hBOOL(hAPP(hAPP(c_member(_1262104), _1262106), c_Wellfounded_Oacc(_1262104, _1262108))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1262104, _1262104)), hAPP(hAPP(c_Product__Type_OPair(_1262104, _1262104), _1262110), _1262106)), _1262108)), -(hBOOL(hAPP(hAPP(c_member(_1262104), _1262110), c_Wellfounded_Oacc(_1262104, _1262108))))], (28422 ^ _773908) ^ [_1290661, _1290663] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290661, tc_HOL_Obool)), _1290663), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290661, tc_HOL_Obool)), _1290663)) = c_Orderings_Obot__class_Obot(tc_fun(_1290661, tc_HOL_Obool)))], (31241 ^ _773908) ^ [_1347633, _1347635] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1347633, _1347635)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1347635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1347633), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (26842 ^ _773908) ^ [_1257501, _1257503, _1257505, _1257507, _1257509, _1257511] : [-(_1257501 = _1257503), -(hAPP(c_Fun_Ofun__upd(_1257505, _1257507, _1257509, _1257503, _1257511), _1257501) = hAPP(_1257509, _1257501))], (24939 ^ _773908) ^ [_1213862, _1213864, _1213866, _1213868] : [class_Orderings_Olinorder(_1213862), 24942 ^ _773908 : [(24951 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213862), _1213866), _1213868)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), _1213866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), _1213868))], (24943 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213862), _1213866), _1213868))), 24946 ^ _773908 : [(24949 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), _1213868)))], (24947 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213862), _1213864), _1213866)))]]]]], (38603 ^ _773908) ^ [_1517634, _1517636, _1517638, _1517640, _1517642, _1517644] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517634, _1517636, _1517638), _1517640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517636, _1517638), tc_HOL_Obool)), _1517642), _1517644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517634, _1517638), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517634, _1517636, _1517638), _1517640), _1517642)), hAPP(hAPP(c_Relation_Orel__comp(_1517634, _1517636, _1517638), _1517640), _1517644)))], (38593 ^ _773908) ^ [_1517367, _1517369, _1517371, _1517373, _1517375, _1517377, _1517379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517367, _1517369), tc_HOL_Obool)), _1517371), _1517373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517369, _1517375), tc_HOL_Obool)), _1517377), _1517379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517367, _1517375), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517367, _1517369, _1517375), _1517371), _1517377)), hAPP(hAPP(c_Relation_Orel__comp(_1517367, _1517369, _1517375), _1517373), _1517379))))], (10457 ^ _773908) ^ [_947146, _947148] : [class_Groups_Ocomm__monoid__mult(_947146), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947146), c_Groups_Oone__class_Oone(_947146)), _947148) = _947148)], (41145 ^ _773908) ^ [_1584652, _1584654, _1584656, _1584658] : [hBOOL(hAPP(c_List_Odistinct(_1584652), _1584654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1584656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584652)), _1584654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1584658), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584652)), _1584654))), 41156 ^ _773908 : [(41163 ^ _773908) ^ [] : [_1584656 = _1584658, -(hAPP(hAPP(c_List_Onth(_1584652), _1584654), _1584656) = hAPP(hAPP(c_List_Onth(_1584652), _1584654), _1584658))], (41157 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Onth(_1584652), _1584654), _1584656) = hAPP(hAPP(c_List_Onth(_1584652), _1584654), _1584658), -(_1584656 = _1584658)]]], (35526 ^ _773908) ^ [_1439818, _1439820, _1439822] : [class_Orderings_Olinorder(_1439818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439818), _1439820), _1439822)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439818, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1439818, _1439820, _1439822)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439818), _1439822)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439818), _1439820))], (11363 ^ _773908) ^ [_963589, _963591] : [class_Rings_Oring__1__no__zero__divisors(_963589), 11366 ^ _773908 : [(11367 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963589), _963591), _963591) = c_Groups_Oone__class_Oone(_963589), -(_963591 = c_Groups_Oone__class_Oone(_963589)), -(_963591 = hAPP(c_Groups_Ouminus__class_Ouminus(_963589), c_Groups_Oone__class_Oone(_963589)))], (11377 ^ _773908) ^ [] : [11378 ^ _773908 : [(11381 ^ _773908) ^ [] : [_963591 = hAPP(c_Groups_Ouminus__class_Ouminus(_963589), c_Groups_Oone__class_Oone(_963589))], (11379 ^ _773908) ^ [] : [_963591 = c_Groups_Oone__class_Oone(_963589)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963589), _963591), _963591) = c_Groups_Oone__class_Oone(_963589))]]], (10711 ^ _773908) ^ [] : [-(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))))], (7335 ^ _773908) ^ [_892591, _892593] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892591), _892593)), 7336 ^ _773908 : [(7343 ^ _773908) ^ [] : [_892591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _892593 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7337 ^ _773908) ^ [] : [_892591 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _892593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23755 ^ _773908) ^ [_1188894, _1188896] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1188894, _1188894), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1188896) = _1188896)], (2588 ^ _773908) ^ [_812132, _812134, _812136, _812138, _812140, _812142] : [-(c_SetInterval_Oord_OatLeast(_812142, _812138, _812134) = c_SetInterval_Oord_OatLeast(_812140, _812136, _812132)), _812142 = _812140, _812138 = _812136, _812134 = _812132], (31421 ^ _773908) ^ [_1351852, _1351854, _1351856, _1351858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351852), _1351854)), -(hAPP(c_Set_Oimage(_1351852, _1351856, _1351858), _1351854) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1351856, tc_HOL_Obool), _1351852, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351856, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1351852, tc_fun(_1351856, tc_HOL_Obool), tc_fun(_1351856, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1351856, tc_fun(tc_fun(_1351856, tc_HOL_Obool), tc_fun(_1351856, tc_HOL_Obool)), _1351852), c_Set_Oinsert(_1351856)), _1351858)), c_Orderings_Obot__class_Obot(tc_fun(_1351856, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1351856, tc_HOL_Obool))), _1351854))], (39518 ^ _773908) ^ [_1541484, _1541486, _1541488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1541484), tc_List_Olist(_1541484))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1541484), tc_List_Olist(_1541484)), _1541486), c_List_Olist_ONil(_1541484))), c_List_Olexord(_1541484, _1541488)))], (28010 ^ _773908) ^ [_1281148, _1281150, _1281152] : [28012 ^ _773908 : [(28018 ^ _773908) ^ [] : [-(28011 ^ [_1281148, _1281150, _1281152] = 28014 ^ [_1281148, _1281150, _1281152])], (28016 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281148), 28014 ^ [_1281148, _1281150, _1281152]), _1281152)))], (28013 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281148), 28011 ^ [_1281148, _1281150, _1281152]), _1281150)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281148, tc_HOL_Obool)), _1281150), _1281152) = c_Orderings_Obot__class_Obot(tc_fun(_1281148, tc_HOL_Obool)))], (34512 ^ _773908) ^ [_1416785, _1416787, _1416789, _1416791] : [class_Groups_Oordered__ab__group__add__abs(_1416785), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416785), c_Groups_Ozero__class_Ozero(_1416785)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1416787, _1416785), hAPP(hAPP(c_COMBB(_1416785, _1416785, _1416787), c_Groups_Oabs__class_Oabs(_1416785)), _1416789)), _1416791))))], (8381 ^ _773908) ^ [] : [-(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)))], (20067 ^ _773908) ^ [_1120252] : [-(c_Int_Opred(c_Int_OBit1(_1120252)) = c_Int_OBit0(_1120252))], (46501 ^ _773908) ^ [_1704339, _1704341] : [46503 ^ _773908 : [(46506 ^ _773908) ^ [] : [hBOOL(hAPP(_1704339, hAPP(c_Int_OAbs__Integ, 46502 ^ [_1704339, _1704341])))], (46504 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 46502 ^ [_1704339, _1704341]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1704339, _1704341)))], (49498 ^ _773908) ^ [_1772986, _1772988, _1772990] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772986)), c_List_Oreplicate(_1772986, _1772988, _1772990)) = _1772988)], (10451 ^ _773908) ^ [_947051, _947053] : [class_Groups_Omonoid__mult(_947051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947051), c_Groups_Oone__class_Oone(_947051)), _947053) = _947053)], (38958 ^ _773908) ^ [_1526851, _1526853, _1526855] : [c_Wellfounded_Owf(_1526851, _1526853), c_Wellfounded_Owf(_1526851, _1526855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526851, _1526851), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1526851, _1526851, _1526851), _1526853), _1526855)), _1526853)), -(c_Wellfounded_Owf(_1526851, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526851, _1526851), tc_HOL_Obool)), _1526853), _1526855)))], (32756 ^ _773908) ^ [_1381949, _1381951] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1381949, _1381951)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381951), _1381949)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35554 ^ _773908) ^ [_1440386, _1440388] : [class_Orderings_Olinorder(_1440386), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440386, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1440386), _1440388), c_Orderings_Obot__class_Obot(tc_fun(_1440386, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440386), _1440388)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1440386), _1440388))], (41866 ^ _773908) ^ [_1598755, _1598757, _1598759, _1598761] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1598759), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598755, tc_fun(_1598759, tc_HOL_Obool)), _1598757), _1598761)))), 41867 ^ _773908 : [(41868 ^ _773908) ^ [_1598829] : [hBOOL(hAPP(hAPP(c_member(_1598755), _1598829), _1598757)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598759), hAPP(_1598761, _1598829)))]]], (20179 ^ _773908) ^ [_1122192] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1122192)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1122192)))], (5440 ^ _773908) ^ [_857104, _857106] : [_857106 = _857104, -(c_member(_857106) = c_member(_857104))], (6982 ^ _773908) ^ [_886965, _886967] : [class_Groups_Olinordered__ab__group__add(_886965), 6985 ^ _773908 : [(6992 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886965), _886967), c_Groups_Ozero__class_Ozero(_886965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886965), _886967), _886967)), c_Groups_Ozero__class_Ozero(_886965))))], (6986 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886965), _886967), _886967)), c_Groups_Ozero__class_Ozero(_886965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886965), _886967), c_Groups_Ozero__class_Ozero(_886965))))]]], (2740 ^ _773908) ^ [_814646, _814648] : [_814648 = _814646, -(c_Nitpick_Ozero__frac(_814648) = c_Nitpick_Ozero__frac(_814646))], (21741 ^ _773908) ^ [_1150215] : [c_Nat__Transfer_Ois__nat(_1150215), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150215)))], (27504 ^ _773908) ^ [_1271132, _1271134, _1271136, _1271138, _1271140, _1271142, _1271144, _1271146] : [c_Finite__Set_Ofolding(_1271132, _1271134, _1271136, _1271138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271132), _1271140)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271132), _1271142)), -(hAPP(c_Fun_Ocomp(_1271134, _1271134, _1271144, hAPP(_1271138, _1271142)), hAPP(c_Fun_Ocomp(_1271134, _1271134, _1271144, hAPP(_1271138, _1271140)), _1271146)) = hAPP(c_Fun_Ocomp(_1271134, _1271134, _1271144, hAPP(_1271138, _1271140)), hAPP(c_Fun_Ocomp(_1271134, _1271134, _1271144, hAPP(_1271138, _1271142)), _1271146)))], (51672 ^ _773908) ^ [_1815771] : [class_Lazy__Sequence_Osmall__lazy(_1815771), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1815771)))], (9441 ^ _773908) ^ [_931229, _931231] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931229)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931231), 9444 ^ _773908 : [(9447 ^ _773908) ^ [] : [-(_931231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9445 ^ _773908) ^ [] : [-(_931229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5717 ^ _773908) ^ [_864188, _864190, _864192, _864194, _864196, _864198, _864200] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864188), _864190), _864192), _864194) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864188), _864196), _864198), _864200), 5720 ^ _773908 : [(5725 ^ _773908) ^ [] : [-(_864194 = _864200)], (5723 ^ _773908) ^ [] : [-(_864192 = _864198)], (5721 ^ _773908) ^ [] : [-(_864190 = _864196)]]], (43117 ^ _773908) ^ [_1630097, _1630099] : [-(hBOOL(hAPP(c_List_Olistsp(_1630097, _1630099), c_List_Olist_ONil(_1630097))))], (17013 ^ _773908) ^ [_1067023, _1067025, _1067027] : [class_Groups_Oordered__ab__group__add__abs(_1067023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067023), hAPP(c_Groups_Oabs__class_Oabs(_1067023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067023), _1067025), _1067027))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067023), hAPP(c_Groups_Oabs__class_Oabs(_1067023), _1067025)), hAPP(c_Groups_Oabs__class_Oabs(_1067023), _1067027)))))], (51540 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (45061 ^ _773908) ^ [_1674260, _1674262, _1674264, _1674266, _1674268] : [class_Orderings_Olinorder(_1674260), c_List_Olinorder__class_Osorted(_1674260, hAPP(hAPP(c_List_Omap(_1674262, _1674260), _1674264), _1674266)), -(c_List_Olinorder__class_Osorted(_1674260, hAPP(hAPP(c_List_Omap(_1674262, _1674260), _1674264), c_List_Oremove1(_1674262, _1674268, _1674266))))], (23604 ^ _773908) ^ [_1185578, _1185580] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185578, _1185580), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1185578), _1185580)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185578, _1185580)))))], (12482 ^ _773908) ^ [_983113, _983115, _983117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983113)), 12485 ^ _773908 : [(12492 ^ _773908) ^ [] : [_983115 = _983117, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983113), _983115) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983113), _983117))], (12486 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983113), _983115) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983113), _983117), -(_983115 = _983117)]]], (41195 ^ _773908) ^ [_1585689, _1585691] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585689)), hAPP(c_List_Otl(_1585689), _1585691)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585689)), _1585691)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (38794 ^ _773908) ^ [_1523307, _1523309, _1523311, _1523313] : [hAPP(hAPP(c_List_Oappend(_1523307), _1523309), _1523311) = hAPP(hAPP(c_List_Oappend(_1523307), _1523313), _1523311), -(_1523309 = _1523313)], (38768 ^ _773908) ^ [_1522768, _1522770, _1522772, _1522774, _1522776, _1522778, _1522780] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1522768, _1522770, _1522772, _1522774, _1522776), _1522778), _1522780))), 38769 ^ _773908 : [(38770 ^ _773908) ^ [_1522839] : [hBOOL(hAPP(hAPP(_1522774, _1522778), _1522839)), hBOOL(hAPP(hAPP(_1522776, _1522839), _1522780))]]], (18765 ^ _773908) ^ [_1098562, _1098564] : [class_Rings_Olinordered__idom(_1098562), hBOOL(hAPP(hAPP(c_member(_1098562), _1098564), c_Int_Oring__1__class_OInts(_1098562))), 18772 ^ _773908 : [(18779 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098562), _1098564), c_Groups_Ozero__class_Ozero(_1098562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098562), c_Groups_Oone__class_Oone(_1098562)), _1098564)), _1098564)), c_Groups_Ozero__class_Ozero(_1098562))))], (18773 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098562), c_Groups_Oone__class_Oone(_1098562)), _1098564)), _1098564)), c_Groups_Ozero__class_Ozero(_1098562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098562), _1098564), c_Groups_Ozero__class_Ozero(_1098562))))]]], (20029 ^ _773908) ^ [_1119611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1119611)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119611), c_Int_OMin)))], (48724 ^ _773908) ^ [_1755718, _1755720, _1755722, _1755724, _1755726, _1755728, _1755730] : [c_Finite__Set_Ofun__left__comm(_1755718, _1755720, _1755722), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1755718, _1755720, _1755722, _1755724, hAPP(hAPP(c_Set_Oinsert(_1755718), _1755726), _1755728)), _1755730)), -(hBOOL(hAPP(hAPP(c_member(_1755718), _1755726), _1755728))), 48736 ^ _773908 : [(48739 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1755718, _1755720, _1755722, _1755724, _1755728), 48735 ^ [_1755718, _1755720, _1755722, _1755724, _1755726, _1755728, _1755730])))], (48737 ^ _773908) ^ [] : [-(_1755730 = hAPP(hAPP(_1755722, _1755726), 48735 ^ [_1755718, _1755720, _1755722, _1755724, _1755726, _1755728, _1755730]))]]], (4784 ^ _773908) ^ [_846890, _846892] : [_846892 = _846890, -(c_Lazy__Sequence_Oyieldn(_846892) = c_Lazy__Sequence_Oyieldn(_846890))], (51934 ^ _773908) ^ [_1818825, _1818827] : [hBOOL(_1818825), -(hBOOL(hAPP(hAPP(c_fimplies, _1818827), _1818825)))], (4668 ^ _773908) ^ [_845008, _845010, _845012, _845014, _845016, _845018, _845020, _845022, _845024, _845026, _845028, _845030] : [-(c_New__Random__Sequence_Opos__union(_845030, _845026, _845022, _845018, _845014, _845010) = c_New__Random__Sequence_Opos__union(_845028, _845024, _845020, _845016, _845012, _845008)), _845030 = _845028, _845026 = _845024, _845022 = _845020, _845018 = _845016, _845014 = _845012, _845010 = _845008], (44568 ^ _773908) ^ [_1663366, _1663368, _1663370] : [c_List_Oconcat(_1663366, _1663368) = c_List_Oconcat(_1663366, _1663370), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1663366))), _1663368) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1663366))), _1663370), 44578 ^ _773908 : [(44581 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1663366), tc_List_Olist(_1663366), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1663366), tc_fun(tc_List_Olist(_1663366), tc_Nat_Onat), tc_fun(tc_List_Olist(_1663366), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1663366), tc_Nat_Onat), tc_fun(tc_List_Olist(_1663366), tc_HOL_Obool)), tc_List_Olist(_1663366)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1663366))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1663366)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1663366))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1663366)))), 44577 ^ [_1663366, _1663368, _1663370]))], (44579 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663366), tc_List_Olist(_1663366))), 44577 ^ [_1663366, _1663368, _1663370]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1663366), tc_List_Olist(_1663366))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1663366), tc_List_Olist(_1663366)), _1663368), _1663370)))))]], -(_1663368 = _1663370)], (31764 ^ _773908) ^ [_1360502, _1360504, _1360506, _1360508, _1360510] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360502, tc_HOL_Obool)), _1360504), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360506, tc_fun(_1360502, tc_HOL_Obool)), _1360508), _1360510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360506, tc_fun(_1360502, tc_HOL_Obool)), _1360508), hAPP(hAPP(c_COMBB(tc_fun(_1360502, tc_HOL_Obool), tc_fun(_1360502, tc_HOL_Obool), _1360506), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360502, tc_HOL_Obool)), _1360504)), _1360510)))], (39374 ^ _773908) ^ [_1538692, _1538694, _1538696] : [_1538692 = hAPP(hAPP(c_List_Oappend(_1538694), _1538692), _1538696), -(_1538696 = c_List_Olist_ONil(_1538694))], (44256 ^ _773908) ^ [_1656205, _1656207, _1656209, _1656211] : [44258 ^ _773908 : [(44261 ^ _773908) ^ [] : [hBOOL(hAPP(_1656209, hAPP(hAPP(c_List_Onth(_1656205), _1656207), 44257 ^ [_1656205, _1656207, _1656209, _1656211])))], (44259 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44257 ^ [_1656205, _1656207, _1656209, _1656211]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656205)), _1656207))))]], hBOOL(hAPP(hAPP(c_member(_1656205), _1656211), hAPP(c_List_Oset(_1656205), _1656207))), -(hBOOL(hAPP(_1656209, _1656211)))], (50466 ^ _773908) ^ [_1795466, _1795468, _1795470, _1795472] : [c_Predicate_Osymp(_1795466, _1795468), hBOOL(hAPP(hAPP(_1795468, _1795470), _1795472)), -(hBOOL(hAPP(hAPP(_1795468, _1795472), _1795470)))], (25415 ^ _773908) ^ [_1223128, _1223130, _1223132, _1223134, _1223136, _1223138] : [-(hAPP(c_Product__Type_Oapfst(_1223128, _1223130, _1223132, _1223134), hAPP(hAPP(c_Product__Type_OPair(_1223128, _1223132), _1223136), _1223138)) = hAPP(hAPP(c_Product__Type_OPair(_1223130, _1223132), hAPP(_1223134, _1223136)), _1223138))], (39851 ^ _773908) ^ [_1551261, _1551263, _1551265, _1551267] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551261)), hAPP(hAPP(c_List_Oappend(_1551261), _1551263), _1551265)), c_List_Olists(_1551261, _1551267)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551261)), _1551263), c_List_Olists(_1551261, _1551267))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551261)), _1551265), c_List_Olists(_1551261, _1551267)))], (39292 ^ _773908) ^ [_1536576, _1536578, _1536580] : [-(c_List_Oset__Cons(_1536576, _1536578, _1536580) = hAPP(c_Set_OCollect(tc_List_Olist(_1536576)), hAPP(hAPP(c_COMBB(tc_fun(_1536576, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1536576)), c_HOL_OEx(_1536576)), hAPP(hAPP(c_COMBB(tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_fun(_1536576, tc_HOL_Obool), tc_List_Olist(_1536576)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_HOL_Obool, _1536576), c_HOL_OEx(tc_List_Olist(_1536576)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1536576), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536576, tc_fun(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), tc_fun(tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), tc_List_Olist(_1536576)), c_COMBS(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1536576, tc_fun(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), tc_List_Olist(_1536576)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1536576), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), _1536576), c_COMBS(tc_List_Olist(_1536576), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1536576)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536576), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1536576)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1536576), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_List_Olist(_1536576))), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1536576), tc_List_Olist(_1536576)), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_fun(tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_List_Olist(_1536576))), tc_fun(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool))), tc_List_Olist(_1536576)), c_COMBB(tc_fun(tc_List_Olist(_1536576), tc_List_Olist(_1536576)), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), _1536576)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1536576), tc_List_Olist(_1536576)), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), tc_List_Olist(_1536576)), c_COMBB(tc_List_Olist(_1536576), tc_HOL_Obool, tc_List_Olist(_1536576))), c_fequal))), c_List_Olist_OCons(_1536576)))))), hAPP(hAPP(c_COMBC(_1536576, tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool)), _1536576), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1536576))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536576), c_fconj), hAPP(hAPP(c_COMBC(_1536576, tc_fun(_1536576, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536576)), _1536578)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1536576), tc_fun(tc_List_Olist(_1536576), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1536576))), _1536580)))))))], (23771 ^ _773908) ^ [_1189305, _1189307, _1189309, _1189311] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1189305, _1189307, _1189309), hAPP(hAPP(c_COMBB(tc_fun(_1189307, tc_prod(_1189305, _1189307)), tc_fun(_1189307, _1189309), _1189305), hAPP(c_COMBB(tc_prod(_1189305, _1189307), _1189309, _1189307), _1189311)), c_Product__Type_OPair(_1189305, _1189307))) = _1189311)], (34446 ^ _773908) ^ [_1415294, _1415296, _1415298, _1415300, _1415302] : [c_Finite__Set_Ofolding__one__idem(_1415294, _1415296, _1415298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415294), _1415300)), -(_1415302 = c_Orderings_Obot__class_Obot(tc_fun(_1415294, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415294, tc_HOL_Obool)), _1415302), _1415300)), -(hAPP(hAPP(_1415296, hAPP(_1415298, _1415302)), hAPP(_1415298, _1415300)) = hAPP(_1415298, _1415300))], (28240 ^ _773908) ^ [_1286137, _1286139, _1286141, _1286143] : [class_Lattices_Odistrib__lattice(_1286137), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286137), _1286139), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286137), _1286141), _1286143)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286137), _1286139), _1286141)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286137), _1286139), _1286143)))], (38444 ^ _773908) ^ [_1512303, _1512305, _1512307, _1512309, _1512311, _1512313, _1512315] : [class_Rings_Osemiring__0(_1512303), c_Fun_Oinj__on(tc_prod(_1512305, _1512307), _1512303, hAPP(c_Product__Type_Oprod_Oprod__case(_1512305, _1512307, _1512303), hAPP(hAPP(c_COMBC(_1512305, tc_fun(_1512307, _1512303), tc_fun(_1512307, _1512303)), hAPP(hAPP(c_COMBB(tc_fun(_1512303, _1512303), tc_fun(tc_fun(_1512307, _1512303), tc_fun(_1512307, _1512303)), _1512305), c_COMBB(_1512303, _1512303, _1512307)), hAPP(hAPP(c_COMBB(_1512303, tc_fun(_1512303, _1512303), _1512305), c_Groups_Otimes__class_Otimes(_1512303)), _1512309))), _1512311)), hAPP(hAPP(c_Product__Type_OSigma(_1512305, _1512307), _1512313), hAPP(c_COMBK(tc_fun(_1512307, tc_HOL_Obool), _1512305), _1512315))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512303), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512305, _1512303), _1512309), _1512313)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512307, _1512303), _1512311), _1512315)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512303, _1512303), c_Fun_Oid(_1512303)), hAPP(c_Set_OCollect(_1512303), hAPP(hAPP(c_COMBB(tc_fun(_1512305, tc_HOL_Obool), tc_HOL_Obool, _1512303), c_HOL_OEx(_1512305)), hAPP(hAPP(c_COMBB(tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool)), tc_fun(_1512305, tc_HOL_Obool), _1512303), hAPP(c_COMBB(tc_fun(_1512307, tc_HOL_Obool), tc_HOL_Obool, _1512305), c_HOL_OEx(_1512307))), hAPP(hAPP(c_COMBC(_1512303, tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool)), tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512305, tc_fun(tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool))), tc_fun(tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool)), tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool))), _1512303), c_COMBS(_1512305, tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512305, tc_fun(_1512307, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1512305, tc_fun(tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool))), _1512303), hAPP(c_COMBB(tc_fun(_1512307, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool)), _1512305), c_COMBS(_1512307, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool)), tc_fun(_1512305, tc_fun(_1512307, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1512303), hAPP(c_COMBB(tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512305), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512307), c_fconj))), hAPP(hAPP(c_COMBC(_1512303, tc_fun(_1512305, tc_fun(_1512307, _1512303)), tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1512307, _1512303), tc_fun(_1512307, tc_HOL_Obool)), tc_fun(tc_fun(_1512305, tc_fun(_1512307, _1512303)), tc_fun(_1512305, tc_fun(_1512307, tc_HOL_Obool))), _1512303), c_COMBB(tc_fun(_1512307, _1512303), tc_fun(_1512307, tc_HOL_Obool), _1512305)), hAPP(hAPP(c_COMBB(tc_fun(_1512303, tc_HOL_Obool), tc_fun(tc_fun(_1512307, _1512303), tc_fun(_1512307, tc_HOL_Obool)), _1512303), c_COMBB(_1512303, tc_HOL_Obool, _1512307)), c_fequal))), hAPP(hAPP(c_COMBC(_1512305, tc_fun(_1512307, _1512303), tc_fun(_1512307, _1512303)), hAPP(hAPP(c_COMBB(tc_fun(_1512303, _1512303), tc_fun(tc_fun(_1512307, _1512303), tc_fun(_1512307, _1512303)), _1512305), c_COMBB(_1512303, _1512303, _1512307)), hAPP(hAPP(c_COMBB(_1512303, tc_fun(_1512303, _1512303), _1512305), c_Groups_Otimes__class_Otimes(_1512303)), _1512309))), _1512311)))))), hAPP(hAPP(c_COMBC(_1512305, tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1512307, tc_HOL_Obool), tc_fun(_1512307, tc_HOL_Obool)), _1512305), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512307)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512305), c_fconj), hAPP(hAPP(c_COMBC(_1512305, tc_fun(_1512305, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512305)), _1512313)))), hAPP(hAPP(c_COMBC(_1512307, tc_fun(_1512307, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512307)), _1512315))))))))], (8014 ^ _773908) ^ [_905122] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905122) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_905122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10153 ^ _773908) ^ [_942731, _942733, _942735] : [class_Orderings_Olinorder(_942731), 10156 ^ _773908 : [(10163 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942731), _942735), _942733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942731), _942733), _942735))], (10157 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942731), _942733), _942735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942731), _942735), _942733)))]]], (4066 ^ _773908) ^ [_835337, _835339, _835341, _835343] : [-(c_Nitpick_Oinverse__frac(_835343, _835339) = c_Nitpick_Oinverse__frac(_835341, _835337)), _835343 = _835341, _835339 = _835337], (36009 ^ _773908) ^ [_1449469, _1449471] : [class_Lattices_Obounded__lattice__top(_1449469), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1449469), _1449471), c_Orderings_Otop__class_Otop(_1449469)) = c_Orderings_Otop__class_Otop(_1449469))], (19753 ^ _773908) ^ [_1114565, _1114567] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1114565))), _1114567) = 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)))), _1114565), _1114567))], (44426 ^ _773908) ^ [_1659591, _1659593, _1659595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1659591, tc_HOL_Obool)), hAPP(c_List_Oset(_1659591), hAPP(c_List_Ofilter(_1659591, _1659593), _1659595))), hAPP(c_List_Oset(_1659591), _1659595))))], (37576 ^ _773908) ^ [_1485829, _1485831, _1485833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485829), _1485831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485829, _1485829), tc_HOL_Obool)), _1485833), hAPP(hAPP(c_Product__Type_OSigma(_1485829, _1485829), _1485831), hAPP(c_COMBK(tc_fun(_1485829, tc_HOL_Obool), _1485829), _1485831)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1485829, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1485829), _1485831), _1485833))))], (28308 ^ _773908) ^ [_1287933, _1287935, _1287937, _1287939] : [class_Lattices_Olattice(_1287933), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1287933), _1287935), _1287937)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1287933), _1287935), _1287939))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1287933), _1287935), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287933), _1287937), _1287939)))))], (13259 ^ _773908) ^ [_996481, _996483, _996485, _996487] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996481), _996483)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996485), _996483)), _996487)) = 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), _996481), _996485)), _996483)), _996487))], (18807 ^ _773908) ^ [_1099295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099295), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099295)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9945 ^ _773908) ^ [_939429, _939431] : [class_Groups_Oone(_939429), 9948 ^ _773908 : [(9955 ^ _773908) ^ [] : [_939431 = c_Groups_Oone__class_Oone(_939429), -(c_Groups_Oone__class_Oone(_939429) = _939431)], (9949 ^ _773908) ^ [] : [c_Groups_Oone__class_Oone(_939429) = _939431, -(_939431 = c_Groups_Oone__class_Oone(_939429))]]], (16593 ^ _773908) ^ [_1058677, _1058679] : [class_Groups_Oordered__ab__group__add__abs(_1058677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058677), c_Groups_Ozero__class_Ozero(_1058677)), _1058679)), -(hAPP(c_Groups_Oabs__class_Oabs(_1058677), _1058679) = _1058679)], (51846 ^ _773908) ^ [_1817646, _1817648] : [-(hAPP(c_COMBI(_1817646), _1817648) = _1817648)], (19451 ^ _773908) ^ [_1109680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109680), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1109680)), c_Int_OMin)))], (20687 ^ _773908) ^ [_1131405, _1131407, _1131409, _1131411] : [20689 ^ _773908 : [(20694 ^ _773908) ^ [] : [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(_1131409, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 20688 ^ [_1131405, _1131407, _1131409, _1131411]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1131409, 20688 ^ [_1131405, _1131407, _1131409, _1131411])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20692 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20688 ^ [_1131405, _1131407, _1131409, _1131411]), _1131407)))], (20690 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1131405), 20688 ^ [_1131405, _1131407, _1131409, _1131411])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1131405), _1131407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1131409, _1131405)), _1131411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131411), hAPP(_1131409, _1131407))), 20708 ^ _773908 : [(20713 ^ _773908) ^ [] : [-(hAPP(_1131409, 20707 ^ [_1131405, _1131407, _1131409, _1131411]) = _1131411)], (20711 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20707 ^ [_1131405, _1131407, _1131409, _1131411]), _1131407)))], (20709 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1131405), 20707 ^ [_1131405, _1131407, _1131409, _1131411])))]]], (24349 ^ _773908) ^ [_1201183, _1201185, _1201187, _1201189] : [-(hAPP(c_Product__Type_Ofst(_1201183, _1201185), hAPP(hAPP(c_Product__Type_OPair(_1201183, _1201185), _1201187), _1201189)) = _1201187)], (15881 ^ _773908) ^ [_1044493, _1044495, _1044497, _1044499, _1044501, _1044503] : [class_Rings_Oordered__ring(_1044493), 15884 ^ _773908 : [(15891 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044493), _1044499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044493), _1044501), _1044495)), _1044497)), _1044503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), _1044495), _1044497)), _1044499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), _1044501), _1044497)), _1044503))))], (15885 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), _1044495), _1044497)), _1044499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), _1044501), _1044497)), _1044503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044493), _1044499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044493), _1044501), _1044495)), _1044497)), _1044503))))]]], (5114 ^ _773908) ^ [_852021, _852023, _852025, _852027] : [-(c_Complete__Lattice_OInf__class_OInf(_852027, _852023) = c_Complete__Lattice_OInf__class_OInf(_852025, _852021)), _852027 = _852025, _852023 = _852021], (11585 ^ _773908) ^ [_967427] : [-(hBOOL(hAPP(_967427, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11592 ^ [_967427])))), 11586 ^ _773908 : [(11587 ^ _773908) ^ [_967479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _967479)), hBOOL(hAPP(_967427, _967479))]]], (51412 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (3346 ^ _773908) ^ [_824121, _824123, _824125, _824127, _824129, _824131, _824133, _824135] : [-(c_List_Olist_Olist__case(_824135, _824131, _824127, _824123) = c_List_Olist_Olist__case(_824133, _824129, _824125, _824121)), _824135 = _824133, _824131 = _824129, _824127 = _824125, _824123 = _824121], (48707 ^ _773908) ^ [_1755334, _1755336, _1755338, _1755340, _1755342, _1755344, _1755346] : [c_Finite__Set_Ofun__left__comm(_1755334, _1755336, _1755338), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1755334, _1755336, _1755338, _1755340, _1755342), _1755344)), hBOOL(hAPP(hAPP(c_member(_1755334), _1755346), _1755342)), 48719 ^ _773908 : [(48722 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1755334, _1755336, _1755338, _1755340, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1755334, tc_HOL_Obool)), _1755342), hAPP(hAPP(c_Set_Oinsert(_1755334), _1755346), c_Orderings_Obot__class_Obot(tc_fun(_1755334, tc_HOL_Obool))))), 48718 ^ [_1755334, _1755336, _1755338, _1755340, _1755342, _1755344, _1755346])))], (48720 ^ _773908) ^ [] : [-(_1755344 = hAPP(hAPP(_1755338, _1755346), 48718 ^ [_1755334, _1755336, _1755338, _1755340, _1755342, _1755344, _1755346]))]]], (40207 ^ _773908) ^ [_1560097, _1560099, _1560101] : [-(hAPP(c_List_Oset(_1560097), hAPP(hAPP(c_List_Oappend(_1560097), _1560099), _1560101)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1560097, tc_HOL_Obool)), hAPP(c_List_Oset(_1560097), _1560099)), hAPP(c_List_Oset(_1560097), _1560101)))], (37370 ^ _773908) ^ [_1479545, _1479547, _1479549, _1479551] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1479545, _1479547)), hAPP(hAPP(c_Product__Type_OSigma(_1479545, _1479547), _1479549), hAPP(c_COMBK(tc_fun(_1479547, tc_HOL_Obool), _1479545), _1479551))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1479545), _1479549)), hAPP(c_Finite__Set_Ocard(_1479547), _1479551)))], (30521 ^ _773908) ^ [_1332039, _1332041, _1332043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332039), _1332041)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332039), _1332043)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332039, tc_HOL_Obool)), _1332041), _1332043) = c_Orderings_Obot__class_Obot(tc_fun(_1332039, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1332039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332039, tc_HOL_Obool)), _1332041), _1332043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332039), _1332041)), hAPP(c_Finite__Set_Ocard(_1332039), _1332043)))], (15973 ^ _773908) ^ [_1046757, _1046759, _1046761] : [-(hBOOL(hAPP(_1046757, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046759), _1046761)))), 15976 ^ _773908 : [(15979 ^ _773908) ^ [] : [hBOOL(hAPP(_1046757, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15977 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046759), _1046761)))]], 15981 ^ _773908 : [(15984 ^ _773908) ^ [] : [hBOOL(hAPP(_1046757, 15980 ^ [_1046757, _1046759, _1046761]))], (15982 ^ _773908) ^ [] : [-(_1046759 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046761), 15980 ^ [_1046757, _1046759, _1046761]))]]], (36171 ^ _773908) ^ [_1452829] : [class_Lattices_Oboolean__algebra(_1452829), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1452829), c_Orderings_Obot__class_Obot(_1452829)) = c_Orderings_Otop__class_Otop(_1452829))], (19879 ^ _773908) ^ [_1116995] : [c_Int_OPls = c_Int_OBit0(_1116995), -(c_Int_OPls = _1116995)], (42155 ^ _773908) ^ [_1607520, _1607522, _1607524, _1607526, _1607528] : [_1607520 = c_Orderings_Obot__class_Obot(tc_fun(_1607522, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607524, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607522, tc_fun(_1607524, tc_HOL_Obool)), _1607520), _1607526)), _1607528) = _1607528)], (9741 ^ _773908) ^ [_936281, _936283, _936285] : [class_Orderings_Olinorder(_936281), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936281), _936283), _936285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936281), _936285), _936283)))], (27996 ^ _773908) ^ [_1280834, _1280836, _1280838] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280834, tc_HOL_Obool)), _1280836), _1280838) = c_Orderings_Obot__class_Obot(tc_fun(_1280834, tc_HOL_Obool)), 27999 ^ _773908 : [(28000 ^ _773908) ^ [_1280958] : [hBOOL(hAPP(hAPP(c_member(_1280834), _1280958), _1280836)), 28003 ^ _773908 : [(28004 ^ _773908) ^ [_1281048] : [hBOOL(hAPP(hAPP(c_member(_1280834), _1281048), _1280838)), _1280958 = _1281048]]]]], (18155 ^ _773908) ^ [_1086914, _1086916, _1086918] : [18157 ^ _773908 : [(18160 ^ _773908) ^ [] : [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(_1086916, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18156 ^ [_1086914, _1086916, _1086918]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1086916, 18156 ^ [_1086914, _1086916, _1086918])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18158 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18156 ^ [_1086914, _1086916, _1086918]), _1086914)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1086916, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1086918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086918), hAPP(_1086916, _1086914))), 18170 ^ _773908 : [(18173 ^ _773908) ^ [] : [-(hAPP(_1086916, 18169 ^ [_1086914, _1086916, _1086918]) = _1086918)], (18171 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18169 ^ [_1086914, _1086916, _1086918]), _1086914)))]]], (8026 ^ _773908) ^ [] : [-(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))], (48741 ^ _773908) ^ [_1756044, _1756046, _1756048, _1756050] : [class_Orderings_Olinorder(_1756044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1756044), _1756046)), 48751 ^ _773908 : [(48754 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756044), 48750 ^ [_1756044, _1756046, _1756048, _1756050]), _1756048))], (48752 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756044), 48750 ^ [_1756044, _1756046, _1756048, _1756050]), _1756046)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756044), hAPP(hAPP(c_Finite__Set_Ofold(_1756044, _1756044, c_Orderings_Oord__class_Omax(_1756044)), _1756050), _1756046)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1756044), _1756048), _1756050))))], (44664 ^ _773908) ^ [_1666691, _1666693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666691), _1666693)), -(c_List_Oupt(_1666691, _1666693) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1666691), c_List_Oupt(hAPP(c_Nat_OSuc, _1666691), _1666693)))], (43705 ^ _773908) ^ [_1643038, _1643040, _1643042, _1643044] : [-(hAPP(c_Set_Oimage(_1643038, _1643040, _1643042), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643038, tc_HOL_Obool), _1643044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643038, tc_HOL_Obool), tc_fun(_1643040, tc_HOL_Obool)), _1643044), c_Set_Oimage(_1643038, _1643040, _1643042)))], (11665 ^ _773908) ^ [_968737] : [hBOOL(hAPP(_968737, 11666 ^ [_968737])), 11669 ^ _773908 : [(11670 ^ _773908) ^ [_968831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _968831)), -(hBOOL(hAPP(_968737, hAPP(c_Int_Onat, _968831))))]]], (27532 ^ _773908) ^ [_1271738, _1271740, _1271742, _1271744, _1271746, _1271748, _1271750, _1271752] : [c_Finite__Set_Ofolding(_1271738, _1271740, _1271742, _1271744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271738), _1271746)), -(hAPP(c_Fun_Ocomp(_1271740, _1271740, _1271748, hAPP(_1271742, _1271750)), hAPP(c_Fun_Ocomp(_1271740, _1271740, _1271748, hAPP(_1271744, _1271746)), _1271752)) = hAPP(c_Fun_Ocomp(_1271740, _1271740, _1271748, hAPP(_1271744, _1271746)), hAPP(c_Fun_Ocomp(_1271740, _1271740, _1271748, hAPP(_1271742, _1271750)), _1271752)))], (42447 ^ _773908) ^ [_1615415, _1615417, _1615419, _1615421, _1615423] : [-(_1615415 = c_Orderings_Obot__class_Obot(tc_fun(_1615417, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615417, tc_fun(_1615419, tc_HOL_Obool)), _1615415), hAPP(hAPP(c_COMBC(_1615417, tc_fun(_1615419, tc_HOL_Obool), tc_fun(_1615419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615419, tc_HOL_Obool), tc_fun(tc_fun(_1615419, tc_HOL_Obool), tc_fun(_1615419, tc_HOL_Obool)), _1615417), c_Groups_Ominus__class_Ominus(tc_fun(_1615419, tc_HOL_Obool))), _1615421)), _1615423)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615419, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615417, tc_fun(_1615419, tc_HOL_Obool)), _1615415), _1615421)), _1615423))], (22013 ^ _773908) ^ [_1154769, _1154771] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154769), _1154771), hAPP(c_Int_Onumber__class_Onumber__of(_1154769), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1154769)), class_Fields_Ofield__inverse__zero(_1154769), class_Int_Onumber__ring(_1154769)], (16701 ^ _773908) ^ [_1060704, _1060706, _1060708] : [class_Groups_Oordered__ab__group__add__abs(_1060704), 16704 ^ _773908 : [(16713 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), hAPP(c_Groups_Oabs__class_Oabs(_1060704), _1060706)), _1060708))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), _1060706), _1060708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), hAPP(c_Groups_Ouminus__class_Ouminus(_1060704), _1060706)), _1060708))], (16705 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), hAPP(c_Groups_Oabs__class_Oabs(_1060704), _1060706)), _1060708)), 16708 ^ _773908 : [(16711 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), hAPP(c_Groups_Ouminus__class_Ouminus(_1060704), _1060706)), _1060708)))], (16709 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060704), _1060706), _1060708)))]]]]], (43208 ^ _773908) ^ [_1632139, _1632141, _1632143, _1632145, _1632147, _1632149] : [class_Orderings_Olinorder(_1632139), -(hAPP(_1632141, _1632143) = hAPP(_1632141, _1632145)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1632147, _1632139, _1632141), _1632145), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1632147, _1632139, _1632141), _1632143), _1632149)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1632147, _1632139, _1632141), _1632143), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1632147, _1632139, _1632141), _1632145), _1632149)))], (39524 ^ _773908) ^ [_1541703, _1541705, _1541707] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1541703)), -(c_List_Osublist(_1541705, hAPP(hAPP(c_List_Olist_OCons(_1541705), _1541707), c_List_Olist_ONil(_1541705)), _1541703) = hAPP(hAPP(c_List_Olist_OCons(_1541705), _1541707), c_List_Olist_ONil(_1541705)))], (16663 ^ _773908) ^ [_1059815, _1059817, _1059819, _1059821, _1059823] : [class_Rings_Olinordered__idom(_1059815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059815), hAPP(c_Groups_Oabs__class_Oabs(_1059815), _1059817)), _1059819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059815), hAPP(c_Groups_Oabs__class_Oabs(_1059815), _1059821)), _1059823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059815), hAPP(c_Groups_Oabs__class_Oabs(_1059815), _1059817)), hAPP(c_Groups_Oabs__class_Oabs(_1059815), _1059821))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059815), _1059819), _1059823))))], (40709 ^ _773908) ^ [_1572343, _1572345, _1572347, _1572349, _1572351, _1572353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572343, _1572345)), hAPP(hAPP(c_Product__Type_OPair(_1572343, _1572345), _1572347), _1572349)), hAPP(c_List_Oset(tc_prod(_1572343, _1572345)), hAPP(hAPP(c_List_Ozip(_1572343, _1572345), _1572351), _1572353)))), -(hBOOL(hAPP(hAPP(c_member(_1572343), _1572347), hAPP(c_List_Oset(_1572343), _1572351))))], (41049 ^ _773908) ^ [_1582511, _1582513] : [hBOOL(hAPP(c_List_Odistinct(_1582511), _1582513)), -(hBOOL(hAPP(c_List_Odistinct(_1582511), hAPP(c_List_Otl(_1582511), _1582513))))], (46011 ^ _773908) ^ [_1693570, _1693572, _1693574, _1693576] : [class_Orderings_Olinorder(_1693570), 46014 ^ _773908 : [(46021 ^ _773908) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1693572), _1693576)), -(hBOOL(hAPP(c_List_Odistinct(_1693572), c_List_Olinorder__class_Osort__key(_1693572, _1693570, _1693574, _1693576))))], (46015 ^ _773908) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1693572), c_List_Olinorder__class_Osort__key(_1693572, _1693570, _1693574, _1693576))), -(hBOOL(hAPP(c_List_Odistinct(_1693572), _1693576)))]]], (34392 ^ _773908) ^ [_1414245, _1414247, _1414249] : [class_Orderings_Olinorder(_1414245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414245), _1414247), _1414249)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414245, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1414245), _1414247)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1414245, _1414247), _1414249)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1414245), _1414249))], (38715 ^ _773908) ^ [_1521848, _1521850] : [c_Wellfounded_Owf(_1521848, hAPP(hAPP(c_Relation_Orel__comp(_1521848, _1521848, _1521848), _1521850), _1521850)), -(c_Wellfounded_Owf(_1521848, _1521850))], (43939 ^ _773908) ^ [_1648669, _1648671] : [class_Complete__Lattice_Ocomplete__lattice(_1648669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648669), _1648671)), -(_1648671 = c_Orderings_Obot__class_Obot(tc_fun(_1648669, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1648669, _1648671) = c_Complete__Lattice_OSup__class_OSup(_1648669, _1648671))], (23043 ^ _773908) ^ [_1174069, _1174071, _1174073, _1174075, _1174077, _1174079] : [c_Nitpick_Opair__box_OPairBox(_1174069, _1174071, _1174073, _1174075) = c_Nitpick_Opair__box_OPairBox(_1174069, _1174071, _1174077, _1174079), 23046 ^ _773908 : [(23049 ^ _773908) ^ [] : [-(_1174075 = _1174079)], (23047 ^ _773908) ^ [] : [-(_1174073 = _1174077)]]], (21315 ^ _773908) ^ [_1142318, _1142320, _1142322] : [class_Rings_Odivision__ring(_1142318), -(_1142320 = c_Groups_Ozero__class_Ozero(_1142318)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142318), hAPP(c_Groups_Ouminus__class_Ouminus(_1142318), _1142322)), hAPP(c_Groups_Ouminus__class_Ouminus(_1142318), _1142320)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142318), _1142322), _1142320))], (8134 ^ _773908) ^ [_907282, _907284, _907286] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907282, _907284)), _907286), _907286))), 8135 ^ _773908 : [(8138 ^ _773908) ^ [_907382] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907284), _907286), _907382)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907282, _907284)), _907382), _907286))], (8136 ^ _773908) ^ [] : [-(hBOOL(hAPP(_907282, _907286)))]]], (6502 ^ _773908) ^ [_879623, _879625, _879627, _879629] : [c_Com_Ocom_OAss(_879623, _879625) = c_Com_Ocom_OAss(_879627, _879629), 6505 ^ _773908 : [(6508 ^ _773908) ^ [] : [-(_879625 = _879629)], (6506 ^ _773908) ^ [] : [-(_879623 = _879627)]]], (6858 ^ _773908) ^ [_884908, _884910, _884912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884908), _884910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884910), _884912))))], (17035 ^ _773908) ^ [_1067562, _1067564] : [class_Groups_Oordered__ab__group__add__abs(_1067562), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067562), hAPP(c_Groups_Ouminus__class_Ouminus(_1067562), hAPP(c_Groups_Oabs__class_Oabs(_1067562), _1067564))), c_Groups_Ozero__class_Ozero(_1067562))))], (12632 ^ _773908) ^ [_985659, _985661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985659), _985661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985659), hAPP(c_Nat_OSuc, _985661))))], (7679 ^ _773908) ^ [_898517, _898519, _898521, _898523] : [c_Com_Ocom_OLocal(_898517, _898519, _898521) = hAPP(c_Com_Ocom_OBODY, _898523)], (12855 ^ _773908) ^ [_989491] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989491), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _989491)], (18997 ^ _773908) ^ [_1102113, _1102115] : [class_Rings_Oring__1(_1102113), hBOOL(hAPP(hAPP(c_member(_1102113), _1102115), c_Int_Oring__1__class_OInts(_1102113))), -(hBOOL(hAPP(hAPP(c_member(_1102113), hAPP(c_Groups_Ouminus__class_Ouminus(_1102113), _1102115)), c_Int_Oring__1__class_OInts(_1102113))))], (13873 ^ _773908) ^ [_1007572, _1007574] : [class_Lattices_Oab__semigroup__idem__mult(_1007572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007572), _1007574), _1007574) = _1007574)], (970 ^ _773908) ^ [_788643, _788645, _788647, _788649, _788651, _788653] : [-(c_Equiv__Relations_Oequiv(_788651, _788647, _788643)), c_Equiv__Relations_Oequiv(_788653, _788649, _788645), _788653 = _788651, _788649 = _788647, _788645 = _788643], (10119 ^ _773908) ^ [_942249, _942251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942249), _942251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _942249), c_Groups_Oone__class_Oone(tc_Int_Oint))), _942251)))], (29845 ^ _773908) ^ [_1318828, _1318830] : [class_Orderings_Olinorder(_1318828), -(c_Big__Operators_Olattice_OSup__fin(_1318828, c_Orderings_Oord__class_Omax(_1318828), hAPP(hAPP(c_Set_Oinsert(_1318828), _1318830), c_Orderings_Obot__class_Obot(tc_fun(_1318828, tc_HOL_Obool)))) = _1318830)], (25135 ^ _773908) ^ [_1217969, _1217971, _1217973] : [class_Orderings_Olinorder(_1217969), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217969), _1217971), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217969), _1217971), _1217973))))], (50005 ^ _773908) ^ [_1784366, _1784368, _1784370] : [c_List_Olist__ex(_1784366, _1784370, _1784368), 50009 ^ _773908 : [(50012 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1784370, 50008 ^ [_1784366, _1784368, _1784370])))], (50010 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784366), 50008 ^ [_1784366, _1784368, _1784370]), hAPP(c_List_Oset(_1784366), _1784368))))]]], (26377 ^ _773908) ^ [_1245677, _1245679] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1245677, _1245677)), hAPP(hAPP(c_Product__Type_OPair(_1245677, _1245677), 26378 ^ [_1245677, _1245679]), 26378 ^ [_1245677, _1245679])), _1245679))), -(c_Relation_Oirrefl(_1245677, _1245679))], (51878 ^ _773908) ^ [_1818169] : [-(hBOOL(_1818169)), -(hBOOL(hAPP(c_fNot, _1818169)))], (5582 ^ _773908) ^ [_859291, _859293, _859295, _859297] : [-(tc_prod(_859297, _859293) = tc_prod(_859295, _859291)), _859297 = _859295, _859293 = _859291], (45780 ^ _773908) ^ [_1688648, _1688650, _1688652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688648)), c_List_OtakeWhile(_1688648, _1688650, _1688652))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688648)), _1688652))))], (41400 ^ _773908) ^ [_1589813, _1589815] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1589813, _1589815) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1589813, _1589815)))], (39154 ^ _773908) ^ [_1532491, _1532493] : [-(hAPP(c_List_Olexn(_1532491, _1532493), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1532491), tc_List_Olist(_1532491)), tc_HOL_Obool)))], (19903 ^ _773908) ^ [_1117366, _1117368] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1117366)), c_Int_OBit0(_1117368)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117366), _1117368)))], (28066 ^ _773908) ^ [_1282235] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1282235) = c_Orderings_Oord__class_Omin(_1282235)), class_Lattices_Osemilattice__inf(_1282235), class_Orderings_Olinorder(_1282235)], (38354 ^ _773908) ^ [_1508632, _1508634, _1508636] : [class_Lattices_Odistrib__lattice(_1508632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508632), _1508634)), -(_1508634 = c_Orderings_Obot__class_Obot(tc_fun(_1508632, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508632), _1508636)), -(_1508636 = c_Orderings_Obot__class_Obot(tc_fun(_1508632, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1508632), c_Big__Operators_Olattice__class_OSup__fin(_1508632, _1508634)), c_Big__Operators_Olattice__class_OSup__fin(_1508632, _1508636)) = c_Big__Operators_Olattice__class_OSup__fin(_1508632, hAPP(c_Set_OCollect(_1508632), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_HOL_Obool), tc_HOL_Obool, _1508632), c_HOL_OEx(_1508632)), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool)), tc_fun(_1508632, tc_HOL_Obool), _1508632), hAPP(c_COMBB(tc_fun(_1508632, tc_HOL_Obool), tc_HOL_Obool, _1508632), c_HOL_OEx(_1508632))), hAPP(hAPP(c_COMBC(_1508632, tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool)), tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_fun(tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool))), tc_fun(tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool)), tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool))), _1508632), c_COMBS(_1508632, tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_fun(_1508632, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1508632, tc_fun(tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool))), _1508632), hAPP(c_COMBB(tc_fun(_1508632, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool)), _1508632), c_COMBS(_1508632, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool)), tc_fun(_1508632, tc_fun(_1508632, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1508632), hAPP(c_COMBB(tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1508632), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508632), c_fconj))), hAPP(hAPP(c_COMBC(_1508632, tc_fun(_1508632, tc_fun(_1508632, _1508632)), tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1508632, _1508632), tc_fun(_1508632, tc_HOL_Obool)), tc_fun(tc_fun(_1508632, tc_fun(_1508632, _1508632)), tc_fun(_1508632, tc_fun(_1508632, tc_HOL_Obool))), _1508632), c_COMBB(tc_fun(_1508632, _1508632), tc_fun(_1508632, tc_HOL_Obool), _1508632)), hAPP(hAPP(c_COMBB(tc_fun(_1508632, tc_HOL_Obool), tc_fun(tc_fun(_1508632, _1508632), tc_fun(_1508632, tc_HOL_Obool)), _1508632), c_COMBB(_1508632, tc_HOL_Obool, _1508632)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1508632)))))), hAPP(hAPP(c_COMBC(_1508632, tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1508632, tc_HOL_Obool), tc_fun(_1508632, tc_HOL_Obool)), _1508632), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508632)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508632), c_fconj), hAPP(hAPP(c_COMBC(_1508632, tc_fun(_1508632, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508632)), _1508634)))), hAPP(hAPP(c_COMBC(_1508632, tc_fun(_1508632, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508632)), _1508636))))))))], (51638 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (39024 ^ _773908) ^ [_1528436, _1528438] : [c_Wellfounded_Owf(_1528436, _1528438), -(c_Wellfounded_Owf(tc_List_Olist(_1528436), c_List_Olenlex(_1528436, _1528438)))], (19383 ^ _773908) ^ [_1108615] : [c_Int_OMin = c_Int_OBit1(_1108615), -(c_Int_OMin = _1108615)], (25927 ^ _773908) ^ [_1233260, _1233262, _1233264, _1233266] : [class_Lattices_Osemilattice__sup(_1233260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233260), _1233262), _1233264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233260), _1233266), _1233264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233260), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1233260), _1233262), _1233266)), _1233264)))], (1244 ^ _773908) ^ [_792444, _792446] : [-(class_Groups_Oab__group__add(_792444)), _792446 = _792444, class_Groups_Oab__group__add(_792446)], (5885 ^ _773908) ^ [_868067, _868069] : [c_Com_Ocom_OSemi(_868067, _868069) = c_Com_Ocom_OSKIP], (38611 ^ _773908) ^ [_1517961, _1517963, _1517965, _1517967] : [hAPP(hAPP(c_Relation_Orel__comp(_1517961, _1517961, _1517961), _1517963), _1517965) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517961, _1517961), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517961, _1517961, _1517961), _1517963), _1517967) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517961, _1517961), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1517961, _1517961, _1517961), _1517963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517961, _1517961), tc_HOL_Obool)), _1517965), _1517967)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517961, _1517961), tc_HOL_Obool)))], (12350 ^ _773908) ^ [_980650, _980652, _980654] : [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), _980650), _980652)), _980654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _980654), _980650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980652)))], (41286 ^ _773908) ^ [_1587421, _1587423, _1587425] : [hAPP(c_List_Orotate(_1587421, _1587423), _1587425) = c_List_Olist_ONil(_1587421), -(_1587425 = c_List_Olist_ONil(_1587421))], (13590 ^ _773908) ^ [_1002461, _1002463, _1002465, _1002467] : [class_Divides_Osemiring__div(_1002461), -(c_Divides_Odiv__class_Omod(_1002461, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002461), _1002463), _1002465), _1002467) = c_Divides_Odiv__class_Omod(_1002461, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002461), _1002463), c_Divides_Odiv__class_Omod(_1002461, _1002465, _1002467)), _1002467))], (51237 ^ _773908) ^ [_1811054, _1811056, _1811058, _1811060] : [c_Fun_Obij__betw(_1811054, _1811056, _1811058, _1811060, c_Orderings_Obot__class_Obot(tc_fun(_1811056, tc_HOL_Obool))), -(_1811060 = c_Orderings_Obot__class_Obot(tc_fun(_1811054, tc_HOL_Obool)))], (8957 ^ _773908) ^ [_922288, _922290, _922292, _922294] : [class_Rings_Ocomm__semiring__1(_922288), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922288), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922288), _922290), _922292)), _922294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922288), _922290), _922294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922288), _922292), _922294)))], (914 ^ _773908) ^ [_787871, _787873, _787875, _787877] : [-(c_Wellfounded_Oacyclic(_787875, _787871)), c_Wellfounded_Oacyclic(_787877, _787873), _787877 = _787875, _787873 = _787871], (19785 ^ _773908) ^ [_1115289, _1115291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115289)), -(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)))), _1115291))), 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)))), _1115289)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1115291), _1115289))], (27634 ^ _773908) ^ [_1273789, _1273791, _1273793, _1273795, _1273797, _1273799] : [c_Finite__Set_Ofolding(_1273789, _1273791, _1273793, _1273795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273789), _1273797)), -(hAPP(_1273795, hAPP(hAPP(c_Set_Oinsert(_1273789), _1273799), _1273797)) = hAPP(c_Fun_Ocomp(_1273791, _1273791, _1273791, hAPP(_1273795, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273789, tc_HOL_Obool)), _1273797), hAPP(hAPP(c_Set_Oinsert(_1273789), _1273799), c_Orderings_Obot__class_Obot(tc_fun(_1273789, tc_HOL_Obool)))))), hAPP(_1273793, _1273799)))], (50251 ^ _773908) ^ [_1791239] : [-(c_Relation_Otrans(_1791239, c_Relation_OId(_1791239)))], (41041 ^ _773908) ^ [_1582371] : [-(hBOOL(hAPP(c_List_Odistinct(_1582371), c_List_Olist_ONil(_1582371))))], (35605 ^ _773908) ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473] : [class_Groups_Ocomm__monoid__add(_1441463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441465), _1441467)), 35615 ^ _773908 : [(35616 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441465), 35614 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473]), _1441467)))], (35621 ^ _773908) ^ [] : [35614 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473] = 35617 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473]], (35625 ^ _773908) ^ [] : [hAPP(_1441471, hAPP(_1441469, 35614 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473])) = c_Groups_Ozero__class_Ozero(_1441463)], (35623 ^ _773908) ^ [] : [-(hAPP(_1441469, 35614 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473]) = hAPP(_1441469, 35617 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473]))], (35619 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441465), 35617 ^ [_1441463, _1441465, _1441467, _1441469, _1441471, _1441473]), _1441467)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441473, _1441463), _1441471), hAPP(c_Set_Oimage(_1441465, _1441473, _1441469), _1441467)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441465, _1441463), hAPP(c_Fun_Ocomp(_1441473, _1441463, _1441465, _1441471), _1441469)), _1441467))], (2752 ^ _773908) ^ [_814816, _814818, _814820, _814822] : [-(c_Nitpick_Onumber__of__frac(_814822, _814818) = c_Nitpick_Onumber__of__frac(_814820, _814816)), _814822 = _814820, _814818 = _814816], (17327 ^ _773908) ^ [_1072819, _1072821] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1072819)), _1072821) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072819), _1072821)))], (49676 ^ _773908) ^ [_1776509, _1776511] : [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), _1776509), _1776511))), 49679 ^ _773908 : [(49686 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1776509), _1776511))), -(c_Lazy__Sequence_Osmall__lazy_H(_1776509, _1776511) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1776511), c_Lazy__Sequence_Osmall__lazy_H(_1776509, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1776511), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49680 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1776509), _1776511)), -(c_Lazy__Sequence_Osmall__lazy_H(_1776509, _1776511) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (38893 ^ _773908) ^ [_1525421] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1525421)))], (5174 ^ _773908) ^ [_853041, _853043, _853045, _853047] : [-(c_List_Olexord(_853047, _853043) = c_List_Olexord(_853045, _853041)), _853047 = _853045, _853043 = _853041], (12813 ^ _773908) ^ [_988759, _988761, _988763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988759), _988761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988759), _988763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988761), _988763))))], (29675 ^ _773908) ^ [_1315558, _1315560, _1315562] : [class_Orderings_Olinorder(_1315558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315558), _1315560)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315558), _1315562)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315558, tc_HOL_Obool)), _1315560), _1315562) = c_Orderings_Obot__class_Obot(tc_fun(_1315558, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315558), c_Big__Operators_Olinorder__class_OMin(_1315558, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315558, tc_HOL_Obool)), _1315560), _1315562))), c_Big__Operators_Olinorder__class_OMin(_1315558, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315558, tc_HOL_Obool)), _1315560), _1315562))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315558), c_Big__Operators_Olinorder__class_OMin(_1315558, _1315560)), c_Big__Operators_Olinorder__class_OMin(_1315558, _1315562)))], (23580 ^ _773908) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (9712 ^ _773908) ^ [_935719, _935721] : [class_Orderings_Opreorder(_935719), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935719), _935721), _935721)))], (44367 ^ _773908) ^ [_1658499, _1658501, _1658503, _1658505] : [-(hAPP(c_List_Ofilter(_1658499, _1658501), hAPP(c_List_Ofilter(_1658499, _1658503), _1658505)) = hAPP(c_List_Ofilter(_1658499, hAPP(hAPP(c_COMBS(_1658499, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1658499), c_fconj), _1658503)), _1658501)), _1658505))], (9225 ^ _773908) ^ [_927213, _927215, _927217] : [class_Rings_Olinordered__semiring__strict(_927213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927213), c_Groups_Ozero__class_Ozero(_927213)), _927215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927213), _927217), c_Groups_Ozero__class_Ozero(_927213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927213), _927215), _927217)), c_Groups_Ozero__class_Ozero(_927213))))], (28160 ^ _773908) ^ [_1284198, _1284200] : [class_Lattices_Osemilattice__inf(_1284198), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1284198), _1284200), _1284200) = _1284200)], (35654 ^ _773908) ^ [_1442698, _1442700, _1442702, _1442704, _1442706, _1442708] : [class_Groups_Oordered__ab__group__add(_1442698), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442700), _1442702)), 35664 ^ _773908 : [(35667 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442698), c_Groups_Ozero__class_Ozero(_1442698)), hAPP(_1442704, 35663 ^ [_1442698, _1442700, _1442702, _1442704, _1442706, _1442708])))], (35665 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442700), 35663 ^ [_1442698, _1442700, _1442702, _1442704, _1442706, _1442708]), _1442702)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442700, _1442698), _1442704), _1442702) = _1442706, hBOOL(hAPP(hAPP(c_member(_1442700), _1442708), _1442702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442698), hAPP(_1442704, _1442708)), _1442706)))], (19713 ^ _773908) ^ [_1113844, _1113846] : [class_Int_Onumber__ring(_1113844), class_Rings_Olinordered__idom(_1113844), 19720 ^ _773908 : [(19727 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1113846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113844), c_Groups_Oone__class_Oone(_1113844)), hAPP(c_Int_Onumber__class_Onumber__of(_1113844), _1113846))))], (19721 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113844), c_Groups_Oone__class_Oone(_1113844)), hAPP(c_Int_Onumber__class_Onumber__of(_1113844), _1113846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1113846)))]]], (35887 ^ _773908) ^ [_1447253, _1447255, _1447257, _1447259, _1447261] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1447253, _1447255, _1447257, _1447259, c_Orderings_Obot__class_Obot(tc_fun(_1447253, tc_HOL_Obool))), _1447261)), -(_1447261 = _1447259)], (8951 ^ _773908) ^ [_922129, _922131, _922133, _922135] : [class_Rings_Ocomm__semiring(_922129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922129), _922131), _922133)), _922135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922129), _922131), _922135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922129), _922133), _922135)))], (47475 ^ _773908) ^ [_1728774, _1728776, _1728778, _1728780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1728774, _1728776), tc_HOL_Obool)), _1728778), _1728780)), c_Relation_Osingle__valued(_1728774, _1728776, _1728780), -(c_Relation_Osingle__valued(_1728774, _1728776, _1728778))], (14376 ^ _773908) ^ [_1017131, _1017133] : [class_Divides_Osemiring__div(_1017131), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1017131), _1017133), c_Groups_Ozero__class_Ozero(_1017131)) = c_Groups_Ozero__class_Ozero(_1017131))], (18195 ^ _773908) ^ [_1087835, _1087837, _1087839, _1087841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1087835, tc_HOL_Obool)), _1087837), hAPP(hAPP(c_Set_Oinsert(_1087835), _1087839), _1087841))), 18198 ^ _773908 : [(18205 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087835), _1087839), _1087841))), 18208 ^ _773908 : [(18215 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087835), _1087839), _1087837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1087835, tc_HOL_Obool)), _1087837), _1087841)))], (18209 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1087835), _1087839), _1087837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1087835, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087835, tc_HOL_Obool)), _1087837), hAPP(hAPP(c_Set_Oinsert(_1087835), _1087839), c_Orderings_Obot__class_Obot(tc_fun(_1087835, tc_HOL_Obool))))), _1087841)))]]], (18199 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1087835), _1087839), _1087841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1087835, tc_HOL_Obool)), _1087837), _1087841)))]]], (40469 ^ _773908) ^ [_1566368, _1566370] : [-(hAPP(c_List_Oset(_1566368), _1566370) = hAPP(c_Set_OCollect(_1566368), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1566368), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1566368, 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)), _1566368), 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)), _1566368), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1566368, tc_fun(tc_Nat_Onat, _1566368), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566368, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1566368), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1566368), c_COMBB(_1566368, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1566368), _1566370))))), 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(_1566368)), _1566370))))))], (40115 ^ _773908) ^ [_1557903, _1557905, _1557907, _1557909] : [-(hAPP(hAPP(c_List_Otake(_1557903), _1557905), hAPP(hAPP(c_List_Olist_OCons(_1557903), _1557907), _1557909)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1557903), c_List_Olist_ONil(_1557903), hAPP(hAPP(c_COMBB(tc_List_Olist(_1557903), tc_List_Olist(_1557903), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1557903), _1557907)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1557903), tc_List_Olist(_1557903)), c_List_Otake(_1557903)), _1557909)), _1557905))], (51792 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (26297 ^ _773908) ^ [_1241412, _1241414, _1241416] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1241412, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241412, tc_HOL_Obool)), _1241414), _1241416)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241412, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1241412, tc_HOL_Obool)), _1241414)), _1241416))], (6305 ^ _773908) ^ [_876107] : [-(_876107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_876107 = hAPP(c_Nat_OSuc, 6308 ^ [_876107]))], (51856 ^ _773908) ^ [_1817873, _1817875] : [hBOOL(hAPP(hAPP(c_fequal, _1817873), _1817875)), -(_1817873 = _1817875)], (24593 ^ _773908) ^ [_1207188, _1207190, _1207192, _1207194, _1207196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1207188, _1207190)), hAPP(_1207188, _1207192))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1207194, _1207194)), hAPP(hAPP(c_Product__Type_OPair(_1207194, _1207194), _1207190), _1207192)), _1207196)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1207194, _1207194)), hAPP(hAPP(c_Product__Type_OPair(_1207194, _1207194), _1207190), _1207192)), c_Wellfounded_Omlex__prod(_1207194, _1207188, _1207196))))], (46689 ^ _773908) ^ [_1708928, _1708930, _1708932, _1708934, _1708936] : [-(hAPP(c_List_Ofilter(_1708928, _1708930), _1708932) = hAPP(hAPP(c_List_Olist_OCons(_1708928), _1708934), _1708936)), 46690 ^ _773908 : [(46691 ^ _773908) ^ [_1709056, _1709058] : [_1708932 = hAPP(hAPP(c_List_Oappend(_1708928), _1709058), hAPP(hAPP(c_List_Olist_OCons(_1708928), _1708934), _1709056)), 46697 ^ _773908 : [(46700 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1708930, 46696 ^ [_1708928, _1708930, _1708932, _1708934, _1708936, _1709056, _1709058])))], (46698 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708928), 46696 ^ [_1708928, _1708930, _1708932, _1708934, _1708936, _1709056, _1709058]), hAPP(c_List_Oset(_1708928), _1709058))))]], hBOOL(hAPP(_1708930, _1708934)), _1708936 = hAPP(c_List_Ofilter(_1708928, _1708930), _1709056)]]], (27268 ^ _773908) ^ [_1266391] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266391), c_Orderings_Obot__class_Obot(tc_fun(_1266391, tc_HOL_Obool)))))], (38332 ^ _773908) ^ [_1507533, _1507535, _1507537] : [class_Lattices_Odistrib__lattice(_1507533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507533), _1507535)), -(_1507535 = c_Orderings_Obot__class_Obot(tc_fun(_1507533, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507533), _1507537)), -(_1507537 = c_Orderings_Obot__class_Obot(tc_fun(_1507533, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1507533), c_Big__Operators_Olattice__class_OInf__fin(_1507533, _1507535)), c_Big__Operators_Olattice__class_OInf__fin(_1507533, _1507537)) = c_Big__Operators_Olattice__class_OInf__fin(_1507533, hAPP(c_Set_OCollect(_1507533), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_HOL_Obool), tc_HOL_Obool, _1507533), c_HOL_OEx(_1507533)), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool)), tc_fun(_1507533, tc_HOL_Obool), _1507533), hAPP(c_COMBB(tc_fun(_1507533, tc_HOL_Obool), tc_HOL_Obool, _1507533), c_HOL_OEx(_1507533))), hAPP(hAPP(c_COMBC(_1507533, tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool)), tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_fun(tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool))), tc_fun(tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool)), tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool))), _1507533), c_COMBS(_1507533, tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_fun(_1507533, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1507533, tc_fun(tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool))), _1507533), hAPP(c_COMBB(tc_fun(_1507533, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool)), _1507533), c_COMBS(_1507533, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool)), tc_fun(_1507533, tc_fun(_1507533, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1507533), hAPP(c_COMBB(tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507533), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507533), c_fconj))), hAPP(hAPP(c_COMBC(_1507533, tc_fun(_1507533, tc_fun(_1507533, _1507533)), tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507533, _1507533), tc_fun(_1507533, tc_HOL_Obool)), tc_fun(tc_fun(_1507533, tc_fun(_1507533, _1507533)), tc_fun(_1507533, tc_fun(_1507533, tc_HOL_Obool))), _1507533), c_COMBB(tc_fun(_1507533, _1507533), tc_fun(_1507533, tc_HOL_Obool), _1507533)), hAPP(hAPP(c_COMBB(tc_fun(_1507533, tc_HOL_Obool), tc_fun(tc_fun(_1507533, _1507533), tc_fun(_1507533, tc_HOL_Obool)), _1507533), c_COMBB(_1507533, tc_HOL_Obool, _1507533)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1507533)))))), hAPP(hAPP(c_COMBC(_1507533, tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1507533, tc_HOL_Obool), tc_fun(_1507533, tc_HOL_Obool)), _1507533), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1507533)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507533), c_fconj), hAPP(hAPP(c_COMBC(_1507533, tc_fun(_1507533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507533)), _1507535)))), hAPP(hAPP(c_COMBC(_1507533, tc_fun(_1507533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507533)), _1507537))))))))], (37472 ^ _773908) ^ [_1482831, _1482833, _1482835, _1482837, _1482839, _1482841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482831, _1482833)), hAPP(hAPP(c_Product__Type_OPair(_1482831, _1482833), _1482835), _1482837)), hAPP(hAPP(c_Product__Type_OSigma(_1482831, _1482833), _1482839), _1482841))), -(hBOOL(hAPP(hAPP(c_member(_1482833), _1482837), hAPP(_1482841, _1482835))))], (41942 ^ _773908) ^ [_1600956, _1600958, _1600960, _1600962, _1600964] : [41944 ^ _773908 : [(41947 ^ _773908) ^ [] : [hAPP(_1600960, 41943 ^ [_1600956, _1600958, _1600960, _1600962, _1600964]) = hAPP(_1600964, 41943 ^ [_1600956, _1600958, _1600960, _1600962, _1600964])], (41945 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600956), 41943 ^ [_1600956, _1600958, _1600960, _1600962, _1600964]), hAPP(c_List_Oset(_1600956), _1600962))))]], -(hAPP(hAPP(c_List_Omap(_1600956, _1600958), _1600960), _1600962) = hAPP(hAPP(c_List_Omap(_1600956, _1600958), _1600964), _1600962))], (43931 ^ _773908) ^ [_1648475, _1648477] : [-(hAPP(c_Relation_OField(_1648475), _1648477) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1648475, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1648475, _1648475), _1648477)), hAPP(c_Relation_ORange(_1648475, _1648475), _1648477)))], (9720 ^ _773908) ^ [_935847, _935849, _935851] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935847), _935849)), _935851) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935849), _935851)))], (11031 ^ _773908) ^ [_957425, _957427] : [class_Rings_Olinordered__ring(_957425), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957425), c_Groups_Ozero__class_Ozero(_957425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957425), _957427), _957427))))], (26349 ^ _773908) ^ [_1244350, _1244352, _1244354, _1244356, _1244358, _1244360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool)), _1244352), _1244354)), c_Wellfounded_Omax__ext(_1244350, _1244356))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool)), _1244358), _1244360)), c_Wellfounded_Omax__ext(_1244350, _1244356))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1244350, tc_HOL_Obool), tc_fun(_1244350, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1244350, tc_HOL_Obool)), _1244352), _1244358)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1244350, tc_HOL_Obool)), _1244354), _1244360))), c_Wellfounded_Omax__ext(_1244350, _1244356))))], (10907 ^ _773908) ^ [_955241, _955243] : [class_Rings_Ocomm__semiring__1(_955241), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955241), _955243), _955243) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955241), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955241), c_Groups_Oone__class_Oone(_955241)), c_Groups_Oone__class_Oone(_955241))), _955243))], (32656 ^ _773908) ^ [_1380060, _1380062, _1380064, _1380066, _1380068] : [class_Orderings_Olinorder(_1380060), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380060, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1380060, _1380062, _1380064)), c_SetInterval_Oord__class_OatLeastAtMost(_1380060, _1380066, _1380068)) = c_SetInterval_Oord__class_OatLeastAtMost(_1380060, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1380060), _1380062), _1380066), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380060), _1380064), _1380068)))], (292 ^ _773908) ^ [_778376, _778378] : [-(c_Nat__Transfer_Ois__nat(_778376)), _778378 = _778376, c_Nat__Transfer_Ois__nat(_778378)], (27270 ^ _773908) ^ [_1266435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1266435)), -(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)), _1266435))))], (37834 ^ _773908) ^ [_1492639, _1492641] : [-(c_Relation_Orefl__on(_1492639, c_Orderings_Otop__class_Otop(tc_fun(_1492639, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1492639, _1492639), tc_HOL_Obool)), _1492641), c_Relation_OId(_1492639))))], (47451 ^ _773908) ^ [_1728229, _1728231, _1728233, _1728235, _1728237, _1728239] : [c_Relation_Osingle__valued(_1728229, _1728231, hAPP(c_Relation_Oconverse(_1728231, _1728229), _1728233)), -(_1728235 = c_Orderings_Obot__class_Obot(tc_fun(_1728237, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1728231, _1728229, _1728233), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1728237, tc_fun(_1728231, tc_HOL_Obool)), _1728235), _1728239)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1728237, tc_fun(_1728229, tc_HOL_Obool)), _1728235), hAPP(hAPP(c_COMBB(tc_fun(_1728231, tc_HOL_Obool), tc_fun(_1728229, tc_HOL_Obool), _1728237), c_Relation_OImage(_1728231, _1728229, _1728233)), _1728239)))], (51284 ^ _773908) ^ [_1811826, _1811828] : [class_Complete__Lattice_Ocomplete__lattice(_1811826), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1811828, _1811826)))], (22917 ^ _773908) ^ [_1171588, _1171590, _1171592, _1171594, _1171596, _1171598, _1171600] : [-(c_Nitpick_Ofold__graph_H(_1171588, _1171590, _1171592, _1171594, _1171596, hAPP(hAPP(_1171592, _1171598), _1171600))), 22918 ^ _773908 : [(22925 ^ _773908) ^ [_1171817, _1171819] : [hAPP(hAPP(_1171592, _1171598), _1171600) = hAPP(hAPP(_1171592, _1171819), _1171817), hBOOL(hAPP(hAPP(c_member(_1171588), _1171819), _1171596)), c_Nitpick_Ofold__graph_H(_1171588, _1171590, _1171592, _1171594, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171588, tc_HOL_Obool)), _1171596), hAPP(hAPP(c_Set_Oinsert(_1171588), _1171819), c_Orderings_Obot__class_Obot(tc_fun(_1171588, tc_HOL_Obool)))), _1171817)], (22919 ^ _773908) ^ [] : [_1171596 = c_Orderings_Obot__class_Obot(tc_fun(_1171588, tc_HOL_Obool)), hAPP(hAPP(_1171592, _1171598), _1171600) = _1171594]]], (20791 ^ _773908) ^ [_1133683, _1133685] : [c_Nat__Transfer_Ois__nat(_1133683), c_Nat__Transfer_Ois__nat(_1133685), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1133683), _1133685)))], (43815 ^ _773908) ^ [_1645506, _1645508, _1645510, _1645512] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1645506, tc_HOL_Obool), tc_fun(_1645508, tc_HOL_Obool)), _1645510), hAPP(hAPP(c_COMBC(tc_fun(_1645506, tc_HOL_Obool), tc_fun(_1645506, tc_fun(_1645508, tc_HOL_Obool)), tc_fun(_1645508, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645506, tc_fun(_1645508, tc_HOL_Obool))), _1645512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645506, tc_fun(_1645508, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645506, tc_HOL_Obool), _1645510)), _1645512))], (24403 ^ _773908) ^ [_1202390, _1202392, _1202394, _1202396, _1202398] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1202390, _1202392, _1202394), _1202396), _1202398) = hAPP(hAPP(_1202396, hAPP(c_Product__Type_Ofst(_1202390, _1202392), _1202398)), hAPP(c_Product__Type_Osnd(_1202390, _1202392), _1202398)))], (4308 ^ _773908) ^ [_839352, _839354, _839356, _839358, _839360, _839362, _839364, _839366] : [-(c_New__DSequence_Oneg__bind(_839366, _839362, _839358, _839354) = c_New__DSequence_Oneg__bind(_839364, _839360, _839356, _839352)), _839366 = _839364, _839362 = _839360, _839358 = _839356, _839354 = _839352], (29897 ^ _773908) ^ [_1319728, _1319730, _1319732] : [class_Orderings_Olinorder(_1319728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319728), _1319730)), -(_1319730 = c_Orderings_Obot__class_Obot(tc_fun(_1319728, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319728), _1319732)), -(_1319732 = c_Orderings_Obot__class_Obot(tc_fun(_1319728, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1319728, c_Orderings_Oord__class_Omax(_1319728), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319728, tc_HOL_Obool)), _1319730), _1319732)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1319728), c_Big__Operators_Olattice_OSup__fin(_1319728, c_Orderings_Oord__class_Omax(_1319728), _1319730)), c_Big__Operators_Olattice_OSup__fin(_1319728, c_Orderings_Oord__class_Omax(_1319728), _1319732)))], (35378 ^ _773908) ^ [_1436757, _1436759, _1436761] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1436757), _1436759), _1436761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1436757), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1436757, tc_Int_Oint), _1436759), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1436761))), class_Groups_Ocomm__monoid__add(_1436757), class_Groups_Ocomm__monoid__mult(_1436757)], (10913 ^ _773908) ^ [_955372, _955374] : [class_Groups_Olinordered__ab__group__add(_955372), 10916 ^ _773908 : [(10923 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955372), c_Groups_Ozero__class_Ozero(_955372)), _955374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955372), c_Groups_Ozero__class_Ozero(_955372)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955372), _955374), _955374))))], (10917 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955372), c_Groups_Ozero__class_Ozero(_955372)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955372), _955374), _955374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955372), c_Groups_Ozero__class_Ozero(_955372)), _955374)))]]], (20603 ^ _773908) ^ [_1129964, _1129966] : [class_Rings_Oring__1(_1129964), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1129964), hAPP(c_Groups_Ouminus__class_Ouminus(_1129964), c_Groups_Oone__class_Oone(_1129964))), 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)))), _1129966))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129964), c_Groups_Oone__class_Oone(_1129964)))], (51594 ^ _773908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (3444 ^ _773908) ^ [_825646, _825648, _825650, _825652, _825654, _825656, _825658, _825660, _825662, _825664] : [-(c_List_Olinorder__class_Oinsort__insert__key(_825664, _825660, _825656, _825652, _825648) = c_List_Olinorder__class_Oinsort__insert__key(_825662, _825658, _825654, _825650, _825646)), _825664 = _825662, _825660 = _825658, _825656 = _825654, _825652 = _825650, _825648 = _825646], (31351 ^ _773908) ^ [_1350208, _1350210, _1350212, _1350214, _1350216] : [class_Groups_Ocomm__monoid__mult(_1350208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350210), _1350212)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350208, _1350210, c_Groups_Otimes__class_Otimes(_1350208)), hAPP(hAPP(c_COMBS(_1350210, _1350208, _1350208), hAPP(hAPP(c_COMBB(_1350208, tc_fun(_1350208, _1350208), _1350210), c_Groups_Otimes__class_Otimes(_1350208)), _1350214)), _1350216)), c_Groups_Oone__class_Oone(_1350208)), _1350212) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350208), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350208, _1350210, c_Groups_Otimes__class_Otimes(_1350208)), _1350214), c_Groups_Oone__class_Oone(_1350208)), _1350212)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350208, _1350210, c_Groups_Otimes__class_Otimes(_1350208)), _1350216), c_Groups_Oone__class_Oone(_1350208)), _1350212)))], (6520 ^ _773908) ^ [_879910, _879912, _879914, _879916, _879918] : [c_Com_Ocom_OCall(_879910, _879912, _879914) = c_Com_Ocom_OAss(_879916, _879918)], (29223 ^ _773908) ^ [_1306965, _1306967, _1306969] : [class_Orderings_Olinorder(_1306965), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306965), _1306967)), -(hBOOL(hAPP(hAPP(c_member(_1306965), _1306969), _1306967))), -(_1306967 = c_Orderings_Obot__class_Obot(tc_fun(_1306965, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306965, hAPP(hAPP(c_Set_Oinsert(_1306965), _1306969), _1306967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306965), _1306969), c_Big__Operators_Olinorder__class_OMax(_1306965, _1306967)))], (44511 ^ _773908) ^ [_1661563, _1661565, _1661567, _1661569, _1661571] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661563)), hAPP(c_List_Ofilter(_1661563, _1661565), hAPP(hAPP(c_List_Omap(_1661567, _1661563), _1661569), _1661571))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661567)), hAPP(c_List_Ofilter(_1661567, hAPP(c_Fun_Ocomp(_1661563, tc_HOL_Obool, _1661567, _1661565), _1661569)), _1661571)))], (43320 ^ _773908) ^ [_1634417, _1634419, _1634421] : [class_Orderings_Olinorder(_1634417), -(hBOOL(hAPP(hAPP(c_member(_1634417), _1634419), hAPP(c_List_Oset(_1634417), _1634421)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1634417, _1634417, c_COMBI(_1634417), _1634419, _1634421) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1634417, _1634417, c_COMBI(_1634417)), _1634419), _1634421))], (42287 ^ _773908) ^ [_1611732, _1611734, _1611736, _1611738] : [_1611738 = c_List_Olist_ONil(_1611734), -(c_List_Olist_ONil(_1611732) = hAPP(hAPP(c_List_Omap(_1611734, _1611732), _1611736), _1611738))], (16493 ^ _773908) ^ [_1056812] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056812)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056812))], (820 ^ _773908) ^ [_786442, _786444, _786446, _786448, _786450, _786452] : [-(c_List_Olist__ex1(_786450, _786446, _786442)), c_List_Olist__ex1(_786452, _786448, _786444), _786452 = _786450, _786448 = _786446, _786444 = _786442], (41061 ^ _773908) ^ [_1582717, _1582719, _1582721, _1582723] : [hBOOL(hAPP(c_List_Odistinct(_1582717), _1582719)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1582717, _1582721)), hAPP(hAPP(c_List_Ozip(_1582717, _1582721), _1582719), _1582723))))], (25767 ^ _773908) ^ [_1230516, _1230518, _1230520] : [class_Lattices_Obounded__lattice__bot(_1230516), 25770 ^ _773908 : [(25779 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1230516), _1230518), _1230520) = c_Orderings_Obot__class_Obot(_1230516)), _1230518 = c_Orderings_Obot__class_Obot(_1230516), _1230520 = c_Orderings_Obot__class_Obot(_1230516)], (25771 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1230516), _1230518), _1230520) = c_Orderings_Obot__class_Obot(_1230516), 25774 ^ _773908 : [(25777 ^ _773908) ^ [] : [-(_1230520 = c_Orderings_Obot__class_Obot(_1230516))], (25775 ^ _773908) ^ [] : [-(_1230518 = c_Orderings_Obot__class_Obot(_1230516))]]]]], (14523 ^ _773908) ^ [_1019469, _1019471, _1019473] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019469), _1019471)), _1019473) = 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), _1019469), _1019473)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019471), _1019473))), 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, _1019469, _1019473)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019471, _1019473))), _1019473)))], (17249 ^ _773908) ^ [_1071579, _1071581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071579)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071579), _1071581)))], (6846 ^ _773908) ^ [_884674, _884676, _884678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884674), _884676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884674), _884678)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884676), _884678))))], (51836 ^ _773908) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (26259 ^ _773908) ^ [_1240305, _1240307, _1240309, _1240311] : [hBOOL(hAPP(hAPP(c_member(_1240305), _1240307), _1240309)), -(hBOOL(hAPP(hAPP(c_member(_1240305), _1240307), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240305, tc_HOL_Obool)), _1240311), _1240309))))], (7145 ^ _773908) ^ [_889564] : [-(_889564 = 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)), _889564)))], (44961 ^ _773908) ^ [_1672603, _1672605] : [_1672605 = c_List_Olist_ONil(_1672603), -(c_List_Olist_ONil(_1672603) = c_List_Oremdups(_1672603, _1672605))], (47100 ^ _773908) ^ [_1719598, _1719600, _1719602, _1719604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1719598, _1719598)), _1719600), c_Transitive__Closure_Otrancl(_1719598, _1719602))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1719598, _1719598), tc_HOL_Obool)), _1719602), _1719604)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1719598, _1719598)), _1719600), c_Transitive__Closure_Otrancl(_1719598, _1719604))))], (38046 ^ _773908) ^ [_1497080, _1497082, _1497084] : [-(hAPP(c_Set_OCollect(_1497080), hAPP(hAPP(c_COMBS(_1497080, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497080), c_fconj), _1497082)), _1497084)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497080, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1497080), _1497082)), hAPP(c_Set_OCollect(_1497080), _1497084)))], (31667 ^ _773908) ^ [_1357848, _1357850, _1357852, _1357854] : [class_Complete__Lattice_Ocomplete__lattice(_1357848), -(_1357850 = c_Orderings_Obot__class_Obot(tc_fun(_1357852, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1357852, _1357848), _1357850), hAPP(c_COMBK(_1357848, _1357852), _1357854)) = _1357854)], (41199 ^ _773908) ^ [_1585794, _1585796, _1585798] : [-(_1585794 = c_List_Olist_ONil(_1585796)), -(hAPP(hAPP(c_List_Otake(_1585796), hAPP(c_Nat_OSuc, _1585798)), _1585794) = hAPP(hAPP(c_List_Olist_OCons(_1585796), hAPP(c_List_Ohd(_1585796), _1585794)), hAPP(hAPP(c_List_Otake(_1585796), _1585798), hAPP(c_List_Otl(_1585796), _1585794))))], (30083 ^ _773908) ^ [_1323343, _1323345, _1323347, _1323349] : [c_Finite__Set_Ofolding__one(_1323343, _1323345, _1323347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323343), _1323349)), -(_1323349 = c_Orderings_Obot__class_Obot(tc_fun(_1323343, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1323343), hAPP(hAPP(_1323345, 30096 ^ [_1323343, _1323345, _1323347, _1323349]), 30097 ^ [_1323343, _1323345, _1323347, _1323349])), hAPP(hAPP(c_Set_Oinsert(_1323343), 30096 ^ [_1323343, _1323345, _1323347, _1323349]), hAPP(hAPP(c_Set_Oinsert(_1323343), 30097 ^ [_1323343, _1323345, _1323347, _1323349]), c_Orderings_Obot__class_Obot(tc_fun(_1323343, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1323343), hAPP(_1323347, _1323349)), _1323349)))], (39310 ^ _773908) ^ [_1537511, _1537513, _1537515] : [c_List_Olist_ONil(_1537511) = hAPP(hAPP(c_List_Olist_OCons(_1537511), _1537513), _1537515)], (22083 ^ _773908) ^ [_1155965, _1155967, _1155969, _1155971] : [class_Fields_Olinordered__field(_1155965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155965), _1155967), _1155969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155965), c_Groups_Ozero__class_Ozero(_1155965)), _1155971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155965), c_Groups_Ozero__class_Ozero(_1155965)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155965), _1155969), _1155967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155965), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155965), _1155971), _1155969)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155965), _1155971), _1155967))))], (27976 ^ _773908) ^ [_1280386, _1280388, _1280390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280386, tc_HOL_Obool)), _1280388), _1280390)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280386, tc_HOL_Obool)), _1280390), _1280388) = _1280388)], (1494 ^ _773908) ^ [_795569, _795571] : [-(class_Lazy__Sequence_Osmall__lazy(_795569)), _795571 = _795569, class_Lazy__Sequence_Osmall__lazy(_795571)], (41043 ^ _773908) ^ [_1582400, _1582402, _1582404] : [hBOOL(hAPP(c_List_Odistinct(_1582400), _1582402)), -(hBOOL(hAPP(c_List_Odistinct(_1582400), hAPP(hAPP(c_List_Otake(_1582400), _1582404), _1582402))))], (25467 ^ _773908) ^ [_1224431, _1224433, _1224435] : [class_Groups_Olinordered__ab__group__add(_1224431), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1224431), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224431), _1224433), _1224435)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224431), hAPP(c_Groups_Ouminus__class_Ouminus(_1224431), _1224433)), hAPP(c_Groups_Ouminus__class_Ouminus(_1224431), _1224435)))], (31778 ^ _773908) ^ [_1361164, _1361166, _1361168, _1361170, _1361172] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361164, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361166, tc_fun(_1361164, tc_HOL_Obool)), _1361168), _1361170)), _1361172) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361166, tc_fun(_1361164, tc_HOL_Obool)), _1361168), hAPP(hAPP(c_COMBC(_1361166, tc_fun(_1361164, tc_HOL_Obool), tc_fun(_1361164, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361164, tc_HOL_Obool), tc_fun(tc_fun(_1361164, tc_HOL_Obool), tc_fun(_1361164, tc_HOL_Obool)), _1361166), c_Groups_Ominus__class_Ominus(tc_fun(_1361164, tc_HOL_Obool))), _1361170)), _1361172)))], (35426 ^ _773908) ^ [_1437864, _1437866, _1437868] : [35428 ^ _773908 : [(35431 ^ _773908) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1437868, 35427 ^ [_1437864, _1437866, _1437868]))], (35429 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437864), 35427 ^ [_1437864, _1437866, _1437868]), _1437866)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437864, tc_Int_Oint), _1437868), _1437866) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437864, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1437864), c_Int_Onat), _1437868)), _1437866)))], (51452 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (2428 ^ _773908) ^ [_809622, _809624, _809626, _809628] : [-(c_Divides_Odivmod__int__rel(_809628, _809624) = c_Divides_Odivmod__int__rel(_809626, _809622)), _809628 = _809626, _809624 = _809622], (21007 ^ _773908) ^ [_1137368, _1137370, _1137372] : [class_Fields_Olinordered__field(_1137368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137368), c_Groups_Ozero__class_Ozero(_1137368)), _1137370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137368), c_Groups_Ozero__class_Ozero(_1137368)), _1137372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137368), c_Groups_Ozero__class_Ozero(_1137368)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137368), _1137370), _1137372))))], (40677 ^ _773908) ^ [_1571534, _1571536, _1571538, _1571540, _1571542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1571534), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571536)), _1571538))), 40680 ^ _773908 : [(40687 ^ _773908) ^ [] : [-(_1571534 = _1571540), -(hAPP(hAPP(c_List_Onth(_1571536), hAPP(hAPP(c_List_Olist__update(_1571536, _1571538), _1571534), _1571542)), _1571540) = hAPP(hAPP(c_List_Onth(_1571536), _1571538), _1571540))], (40681 ^ _773908) ^ [] : [_1571534 = _1571540, -(hAPP(hAPP(c_List_Onth(_1571536), hAPP(hAPP(c_List_Olist__update(_1571536, _1571538), _1571534), _1571542)), _1571540) = _1571542)]]], (24351 ^ _773908) ^ [_1201227, _1201229, _1201231, _1201233] : [hAPP(c_Product__Type_Ofst(_1201227, _1201229), _1201231) = hAPP(c_Product__Type_Ofst(_1201227, _1201229), _1201233), hAPP(c_Product__Type_Osnd(_1201227, _1201229), _1201231) = hAPP(c_Product__Type_Osnd(_1201227, _1201229), _1201233), -(_1201231 = _1201233)], (28765 ^ _773908) ^ [_1299148, _1299150, _1299152, _1299154, _1299156, _1299158] : [hBOOL(hAPP(hAPP(_1299148, _1299150), _1299152)), hBOOL(hAPP(hAPP(_1299154, _1299150), _1299152)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299156, tc_fun(_1299158, tc_HOL_Obool))), _1299148), _1299154), _1299150), _1299152)))], (25979 ^ _773908) ^ [_1234225, _1234227, _1234229, _1234231, _1234233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234225, tc_HOL_Obool)), _1234227), _1234229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234225, tc_HOL_Obool)), _1234231), _1234233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234225, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234225, tc_HOL_Obool)), _1234227), _1234231)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234225, tc_HOL_Obool)), _1234229), _1234233))))], (25215 ^ _773908) ^ [_1219338, _1219340, _1219342] : [class_Orderings_Olinorder(_1219338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219338), _1219340), _1219342)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219338), _1219342), _1219340) = _1219342)], (51774 ^ _773908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (48299 ^ _773908) ^ [_1747599, _1747601, _1747603, _1747605, _1747607] : [c_Finite__Set_Ofun__left__comm__idem(_1747599, _1747601, _1747603), -(hAPP(hAPP(c_Finite__Set_Ofold(_1747599, _1747601, _1747603), _1747605), hAPP(c_List_Oset(_1747599), _1747607)) = hAPP(c_List_Ofoldl(_1747601, _1747599, hAPP(c_COMBC(_1747599, _1747601, _1747601), _1747603), _1747605), _1747607))], (20153 ^ _773908) ^ [_1121779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1121779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1121779)))], (23767 ^ _773908) ^ [_1189176, _1189178, _1189180, _1189182, _1189184, _1189186] : [-(hAPP(c_Product__Type_Oapsnd(_1189176, _1189178, _1189180, _1189182), hAPP(hAPP(c_Product__Type_OPair(_1189180, _1189176), _1189184), _1189186)) = hAPP(hAPP(c_Product__Type_OPair(_1189180, _1189178), _1189184), hAPP(_1189182, _1189186)))], (46750 ^ _773908) ^ [_1710495, _1710497] : [-(c_List_Olistrel(_1710495, c_Transitive__Closure_Ortrancl(_1710495, _1710497)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1710495), c_List_Olistrel1(_1710495, _1710497)))], (50977 ^ _773908) ^ [_1805209, _1805211, _1805213, _1805215] : [c_Fun_Oinj__on(_1805209, _1805211, _1805213, c_Orderings_Otop__class_Otop(tc_fun(_1805209, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1805209, _1805211, c_Orderings_Otop__class_Otop(tc_fun(_1805209, tc_HOL_Obool)), _1805213), hAPP(_1805213, _1805215)) = _1805215)], (9001 ^ _773908) ^ [_923314, _923316, _923318] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923314), _923316)), _923318) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923314), _923318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923316), _923318)))], (46671 ^ _773908) ^ [_1708410, _1708412, _1708414, _1708416, _1708418] : [hAPP(c_List_Ofilter(_1708410, _1708412), _1708414) = hAPP(hAPP(c_List_Olist_OCons(_1708410), _1708416), _1708418), 46676 ^ _773908 : [(46685 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1708412, _1708416)))], (46687 ^ _773908) ^ [] : [-(_1708418 = hAPP(c_List_Ofilter(_1708410, _1708412), 46675 ^ [_1708410, _1708412, _1708414, _1708416, _1708418]))], (46679 ^ _773908) ^ [_1708724] : [hBOOL(hAPP(hAPP(c_member(_1708410), _1708724), hAPP(c_List_Oset(_1708410), 46674 ^ [_1708410, _1708412, _1708414, _1708416, _1708418]))), hBOOL(hAPP(_1708412, _1708724))], (46677 ^ _773908) ^ [] : [-(_1708414 = hAPP(hAPP(c_List_Oappend(_1708410), 46674 ^ [_1708410, _1708412, _1708414, _1708416, _1708418]), hAPP(hAPP(c_List_Olist_OCons(_1708410), _1708416), 46675 ^ [_1708410, _1708412, _1708414, _1708416, _1708418])))]]], (6142 ^ _773908) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42858 ^ _773908) ^ [_1624238, _1624240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624238)), hAPP(c_Code__Numeral_Onat__of, _1624240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1624238), _1624240)))], (21229 ^ _773908) ^ [_1141024, _1141026, _1141028, _1141030] : [class_Rings_Odivision__ring(_1141024), -(_1141026 = c_Groups_Ozero__class_Ozero(_1141024)), 21236 ^ _773908 : [(21243 ^ _773908) ^ [] : [_1141028 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141024), _1141030), _1141026), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141024), _1141028), _1141026) = _1141030)], (21237 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141024), _1141028), _1141026) = _1141030, -(_1141028 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141024), _1141030), _1141026))]]], (39254 ^ _773908) ^ [_1535337, _1535339, _1535341, _1535343, _1535345, _1535347] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1535337), tc_List_Olist(_1535337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1535337), tc_List_Olist(_1535337)), hAPP(hAPP(c_List_Olist_OCons(_1535337), _1535339), _1535341)), hAPP(hAPP(c_List_Olist_OCons(_1535337), _1535343), _1535345))), c_List_Olexord(_1535337, _1535347))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1535337, _1535337)), hAPP(hAPP(c_Product__Type_OPair(_1535337, _1535337), _1535339), _1535343)), _1535347))), 39261 ^ _773908 : [(39264 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1535337), tc_List_Olist(_1535337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1535337), tc_List_Olist(_1535337)), _1535341), _1535345)), c_List_Olexord(_1535337, _1535347))))], (39262 ^ _773908) ^ [] : [-(_1535339 = _1535343)]]], (51378 ^ _773908) ^ [_1813061, _1813063] : [class_Groups_Ominus(_1813061), -(class_Groups_Ominus(tc_fun(_1813063, _1813061)))], (33376 ^ _773908) ^ [_1393923, _1393925, _1393927, _1393929, _1393931] : [class_Orderings_Olinorder(_1393923), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393923, _1393925), _1393927) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393923, _1393929), _1393931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393923), _1393925), _1393927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393923), _1393929), _1393931)), -(_1393927 = _1393931)], (42852 ^ _773908) ^ [_1624133, _1624135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1624133), _1624135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624133)), hAPP(c_Code__Numeral_Onat__of, _1624135))))], (12206 ^ _773908) ^ [_978472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978472))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _978472)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28414 ^ _773908) ^ [_1290387, _1290389, _1290391] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290387, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290387, tc_HOL_Obool)), _1290389), _1290391)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290387, tc_HOL_Obool)), _1290389), _1290391)) = _1290389)], (37311 ^ _773908) ^ [_1478291, _1478293, _1478295, _1478297, _1478299] : [c_Finite__Set_Ofolding__one__idem(_1478291, _1478293, _1478295), hAPP(_1478297, hAPP(hAPP(_1478293, 37316 ^ [_1478291, _1478293, _1478295, _1478297, _1478299]), 37317 ^ [_1478291, _1478293, _1478295, _1478297, _1478299])) = hAPP(hAPP(_1478293, hAPP(_1478297, 37316 ^ [_1478291, _1478293, _1478295, _1478297, _1478299])), hAPP(_1478297, 37317 ^ [_1478291, _1478293, _1478295, _1478297, _1478299])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478291), _1478299)), -(_1478299 = c_Orderings_Obot__class_Obot(tc_fun(_1478291, tc_HOL_Obool))), -(hAPP(_1478297, hAPP(_1478295, _1478299)) = hAPP(_1478295, hAPP(c_Set_Oimage(_1478291, _1478291, _1478297), _1478299)))], (41181 ^ _773908) ^ [_1585408, _1585410, _1585412] : [-(hBOOL(hAPP(c_List_Odistinct(_1585408), hAPP(hAPP(c_List_Oappend(_1585408), _1585410), _1585412)))), hBOOL(hAPP(c_List_Odistinct(_1585408), _1585410)), hBOOL(hAPP(c_List_Odistinct(_1585408), _1585412)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1585408, tc_HOL_Obool)), hAPP(c_List_Oset(_1585408), _1585410)), hAPP(c_List_Oset(_1585408), _1585412)) = c_Orderings_Obot__class_Obot(tc_fun(_1585408, tc_HOL_Obool))], (10245 ^ _773908) ^ [_944049, _944051, _944053] : [class_Orderings_Olinorder(_944049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944049), _944051), _944053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944049), _944053), _944051)))], (29103 ^ _773908) ^ [_1305130, _1305132, _1305134] : [class_Lattices_Olattice(_1305130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305130), _1305132)), -(_1305132 = c_Orderings_Obot__class_Obot(tc_fun(_1305130, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305130), _1305134)), -(_1305134 = c_Orderings_Obot__class_Obot(tc_fun(_1305130, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1305130, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305130, tc_HOL_Obool)), _1305132), _1305134)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305130), c_Big__Operators_Olattice__class_OSup__fin(_1305130, _1305132)), c_Big__Operators_Olattice__class_OSup__fin(_1305130, _1305134)))], (42902 ^ _773908) ^ [_1625042, _1625044] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1625042, _1625044) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1625042), hAPP(c_Code__Numeral_Onat__of, _1625044))))], (41197 ^ _773908) ^ [_1585739, _1585741, _1585743] : [-(hAPP(c_List_Otl(_1585739), hAPP(hAPP(c_List_Otake(_1585739), _1585741), _1585743)) = hAPP(hAPP(c_List_Otake(_1585739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1585741), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1585739), _1585743)))], (31710 ^ _773908) ^ [_1358761, _1358763, _1358765, _1358767] : [c_Orderings_Obot__class_Obot(tc_fun(_1358761, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358763, tc_fun(_1358761, tc_HOL_Obool)), _1358765), _1358767), 31713 ^ _773908 : [(31714 ^ _773908) ^ [_1358877] : [hBOOL(hAPP(hAPP(c_member(_1358763), _1358877), _1358765)), -(hAPP(_1358767, _1358877) = c_Orderings_Obot__class_Obot(tc_fun(_1358761, tc_HOL_Obool)))]]], (33538 ^ _773908) ^ [_1396948, _1396950, _1396952] : [class_Orderings_Oorder(_1396948), 33541 ^ _773908 : [(33548 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396948), _1396950), _1396952))), -(c_Orderings_Obot__class_Obot(tc_fun(_1396948, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1396948, _1396950), _1396952))], (33542 ^ _773908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1396948, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1396948, _1396950), _1396952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396948), _1396950), _1396952))]]], (15383 ^ _773908) ^ [_1034928] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034928), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1034928)], (24091 ^ _773908) ^ [_1194898, _1194900] : [-(c_Divides_Odivmod__int__rel(_1194898, _1194900) = 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, _1194898))), 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), _1194900)))))), 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)), _1194900))), 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)), _1194900))))), 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)), _1194900)))), 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), _1194900))), 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))))))))], (26396 ^ _773908) ^ [_1246385, _1246387] : [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)), _1246385), 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)), _1246387), 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)), _1246385), _1246387)), c_Int_Ointrel)))], (43147 ^ _773908) ^ [_1630783, _1630785, _1630787, _1630789] : [class_Orderings_Olinorder(_1630783), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630785, _1630783, _1630787), _1630789), c_List_Olist_ONil(_1630785)) = hAPP(hAPP(c_List_Olist_OCons(_1630785), _1630789), c_List_Olist_ONil(_1630785)))], (16737 ^ _773908) ^ [_1061329, _1061331, _1061333] : [class_Groups_Oordered__ab__group__add__abs(_1061329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061329), hAPP(c_Groups_Oabs__class_Oabs(_1061329), _1061331)), _1061333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061329), hAPP(c_Groups_Ouminus__class_Ouminus(_1061329), _1061331)), _1061333)))], (44782 ^ _773908) ^ [_1668700, _1668702, _1668704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668700), _1668702)), _1668704)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1668700, _1668704)), _1668702) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668700), _1668702))], (44535 ^ _773908) ^ [_1662334, _1662336] : [-(c_Random_Oselect__weight(_1662334, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1662334), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1662334, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1662334, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1662334)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1662336)) = c_Random_Oselect__weight(_1662334, _1662336))], (24729 ^ _773908) ^ [_1210028, _1210030, _1210032, _1210034] : [class_Orderings_Olinorder(_1210028), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210028), _1210030), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210028), _1210032), _1210034)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210028), _1210032), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210028), _1210030), _1210034)))], (9357 ^ _773908) ^ [_929662, _929664, _929666, _929668] : [class_Rings_Olinordered__comm__semiring__strict(_929662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929662), _929664), _929666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929662), c_Groups_Ozero__class_Ozero(_929662)), _929668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929662), _929668), _929664)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929662), _929668), _929666))))], (48229 ^ _773908) ^ [_1746052, _1746054, _1746056, _1746058] : [class_Orderings_Olinorder(_1746052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1746052), _1746054)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1746052, _1746052, c_Orderings_Oord__class_Omax(_1746052)), _1746056), hAPP(hAPP(c_Set_Oinsert(_1746052), _1746058), _1746054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1746052), _1746058), hAPP(hAPP(c_Finite__Set_Ofold(_1746052, _1746052, c_Orderings_Oord__class_Omax(_1746052)), _1746056), _1746054)))], (13917 ^ _773908) ^ [_1008291, _1008293] : [class_Rings_Olinordered__idom(_1008291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008291), c_Groups_Ozero__class_Ozero(_1008291)), _1008293)), -(c_Groups_Osgn__class_Osgn(_1008291, _1008293) = c_Groups_Oone__class_Oone(_1008291))], (16603 ^ _773908) ^ [_1058832, _1058834] : [class_Groups_Oordered__ab__group__add__abs(_1058832), 16606 ^ _773908 : [(16613 ^ _773908) ^ [] : [_1058834 = c_Groups_Ozero__class_Ozero(_1058832), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058832), hAPP(c_Groups_Oabs__class_Oabs(_1058832), _1058834)), c_Groups_Ozero__class_Ozero(_1058832))))], (16607 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058832), hAPP(c_Groups_Oabs__class_Oabs(_1058832), _1058834)), c_Groups_Ozero__class_Ozero(_1058832))), -(_1058834 = c_Groups_Ozero__class_Ozero(_1058832))]]], (32151 ^ _773908) ^ [_1369996, _1369998, _1370000, _1370002, _1370004] : [class_Orderings_Olinorder(_1369996), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369996, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369996, _1369998, _1370000)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369996, _1370002, _1370004)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1369996, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1369996), _1369998), _1370002), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369996), _1370000), _1370004)))], (10713 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (45479 ^ _773908) ^ [_1682381, _1682383, _1682385] : [hAPP(c_List_Orev(_1682381), _1682383) = hAPP(c_List_Orev(_1682381), _1682385), -(_1682383 = _1682385)], (25973 ^ _773908) ^ [_1234114, _1234116, _1234118, _1234120] : [hBOOL(hAPP(_1234114, _1234116)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234118, tc_HOL_Obool)), _1234120), _1234114), _1234116)))], (15465 ^ _773908) ^ [_1036368, _1036370, _1036372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036368), _1036370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036368), _1036372)), 15472 ^ _773908 : [(15479 ^ _773908) ^ [] : [_1036370 = _1036372, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036370), _1036368) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036372), _1036368))], (15473 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036370), _1036368) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036372), _1036368), -(_1036370 = _1036372)]]], (36671 ^ _773908) ^ [_1464875, _1464877, _1464879] : [class_Groups_Oab__semigroup__mult(_1464875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464875), _1464877)), -(_1464877 = c_Orderings_Obot__class_Obot(tc_fun(_1464875, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464875), _1464879)), -(_1464879 = c_Orderings_Obot__class_Obot(tc_fun(_1464875, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464875, tc_HOL_Obool)), _1464877), _1464879) = c_Orderings_Obot__class_Obot(tc_fun(_1464875, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1464875, c_Groups_Otimes__class_Otimes(_1464875)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464875, tc_HOL_Obool)), _1464877), _1464879)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1464875), hAPP(c_Finite__Set_Ofold1(_1464875, c_Groups_Otimes__class_Otimes(_1464875)), _1464877)), hAPP(c_Finite__Set_Ofold1(_1464875, c_Groups_Otimes__class_Otimes(_1464875)), _1464879)))], (40421 ^ _773908) ^ [_1565066, _1565068, _1565070, _1565072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1565066), _1565068)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565070)), _1565072))), -(hAPP(hAPP(c_List_Onth(_1565070), hAPP(hAPP(c_List_Odrop(_1565070), _1565066), _1565072)), _1565068) = hAPP(hAPP(c_List_Onth(_1565070), _1565072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1565066), _1565068)))], (31407 ^ _773908) ^ [_1351427, _1351429, _1351431, _1351433, _1351435] : [class_Groups_Ocomm__monoid__mult(_1351427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351429), _1351431)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351429), _1351433)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351427), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351427, _1351429, c_Groups_Otimes__class_Otimes(_1351427)), _1351435), c_Groups_Oone__class_Oone(_1351427)), _1351431)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351427, _1351429, c_Groups_Otimes__class_Otimes(_1351427)), _1351435), c_Groups_Oone__class_Oone(_1351427)), _1351433)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351427), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351427, _1351429, c_Groups_Otimes__class_Otimes(_1351427)), _1351435), c_Groups_Oone__class_Oone(_1351427)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351429, tc_HOL_Obool)), _1351431), _1351433))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351427, _1351429, c_Groups_Otimes__class_Otimes(_1351427)), _1351435), c_Groups_Oone__class_Oone(_1351427)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351429, tc_HOL_Obool)), _1351431), _1351433))))], (28224 ^ _773908) ^ [_1285696, _1285698, _1285700, _1285702] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285696, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285696, tc_HOL_Obool)), _1285698), _1285700)), _1285702) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285696, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285696, tc_HOL_Obool)), _1285698), _1285702)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285696, tc_HOL_Obool)), _1285700), _1285702)))], (37966 ^ _773908) ^ [_1495523, _1495525] : [-(hAPP(c_Set_OCollect(_1495523), hAPP(hAPP(c_COMBC(_1495523, tc_fun(_1495523, tc_HOL_Obool), tc_HOL_Obool), c_member(_1495523)), _1495525)) = _1495525)], (7972 ^ _773908) ^ [_904393, _904395, _904397, _904399, _904401, _904403, _904405, _904407, _904409, _904411, _904413] : [hAPP(_904393, hAPP(_904395, _904397)) = hAPP(_904399, hAPP(_904401, _904403)), -(hAPP(hAPP(c_Fun_Ocomp(_904405, _904407, _904409, _904393), _904395), _904397) = hAPP(hAPP(c_Fun_Ocomp(_904411, _904407, _904413, _904399), _904401), _904403))], (47315 ^ _773908) ^ [_1724763, _1724765, _1724767, _1724769] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724763), tc_List_Olist(_1724763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724763), tc_List_Olist(_1724763)), _1724765), _1724767)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1724763), tc_List_Olist(_1724763)), c_List_Olistrel1(_1724763, _1724769)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724763), tc_List_Olist(_1724763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724763), tc_List_Olist(_1724763)), _1724765), _1724767)), c_List_Olistrel1(_1724763, hAPP(c_Relation_Oconverse(_1724763, _1724763), _1724769)))))], (15429 ^ _773908) ^ [_1035661, _1035663, _1035665] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035661), _1035663)), _1035665) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035663), _1035665)))], (27063 ^ _773908) ^ [_1261620, _1261622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1261620, _1261620)), _1261622)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1261620), hAPP(c_Relation_OField(_1261620), _1261622))))], (8185 ^ _773908) ^ [_908280, _908282, _908284] : [c_Com_Ocom_OWhile(_908280, _908282) = hAPP(c_Com_Ocom_OBODY, _908284)], (38126 ^ _773908) ^ [_1499120, _1499122, _1499124] : [-(hAPP(c_Set_OCollect(_1499120), hAPP(hAPP(c_COMBS(_1499120, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499120), c_fimplies), _1499122)), _1499124)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499120, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499120, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1499120), _1499122))), hAPP(c_Set_OCollect(_1499120), _1499124)))], (36583 ^ _773908) ^ [_1462809, _1462811, _1462813, _1462815, _1462817, _1462819] : [c_Typedef_Otype__definition(_1462809, _1462811, _1462813, _1462815, _1462817), -(hAPP(_1462815, hAPP(_1462813, _1462819)) = _1462819)], (12066 ^ _773908) ^ [_976135, _976137, _976139] : [class_Rings_Olinordered__ring__strict(_976135), 12069 ^ _773908 : [(12078 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976135), _976137), _976137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976135), _976139), _976139))), c_Groups_Ozero__class_Ozero(_976135)))), _976137 = c_Groups_Ozero__class_Ozero(_976135), _976139 = c_Groups_Ozero__class_Ozero(_976135)], (12070 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976135), _976137), _976137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976135), _976139), _976139))), c_Groups_Ozero__class_Ozero(_976135))), 12073 ^ _773908 : [(12076 ^ _773908) ^ [] : [-(_976139 = c_Groups_Ozero__class_Ozero(_976135))], (12074 ^ _773908) ^ [] : [-(_976137 = c_Groups_Ozero__class_Ozero(_976135))]]]]], (42077 ^ _773908) ^ [_1605740, _1605742, _1605744, _1605746, _1605748] : [hAPP(hAPP(c_List_Omap(_1605740, _1605742), _1605744), _1605746) = hAPP(hAPP(c_List_Omap(_1605740, _1605742), _1605744), _1605748), c_Fun_Oinj__on(_1605740, _1605742, _1605744, c_Orderings_Otop__class_Otop(tc_fun(_1605740, tc_HOL_Obool))), -(_1605746 = _1605748)], (24735 ^ _773908) ^ [_1210171, _1210173, _1210175] : [class_Orderings_Olinorder(_1210171), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210171), _1210173), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210171), _1210173), _1210175)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210171), _1210173), _1210175))], (18743 ^ _773908) ^ [_1098059, _1098061, _1098063, _1098065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1098059, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1098059, tc_HOL_Obool)), _1098061), hAPP(hAPP(c_Set_Oinsert(_1098059), _1098063), c_Orderings_Obot__class_Obot(tc_fun(_1098059, tc_HOL_Obool))))), _1098065)), hBOOL(hAPP(hAPP(c_member(_1098059), _1098063), _1098061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1098059, tc_HOL_Obool)), _1098061), hAPP(hAPP(c_Set_Oinsert(_1098059), _1098063), _1098065))))], (180 ^ _773908) ^ [_776566, _776568] : [-(class_Fields_Olinordered__field(_776566)), _776568 = _776566, class_Fields_Olinordered__field(_776568)], (49364 ^ _773908) ^ [_1770027, _1770029, _1770031, _1770033, _1770035] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770027, _1770029, _1770031), _1770033), _1770035)), -(hBOOL(hAPP(hAPP(_1770031, _1770035), _1770033)))], (34201 ^ _773908) ^ [_1410685, _1410687] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1410685), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1410687) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1410685, _1410687))], (25185 ^ _773908) ^ [_1218819, _1218821, _1218823, _1218825] : [class_Orderings_Olinorder(_1218819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218819), _1218821), _1218823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218819), _1218821), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218819), _1218823), _1218825))))], (31323 ^ _773908) ^ [_1349626, _1349628, _1349630, _1349632, _1349634, _1349636, _1349638] : [c_Finite__Set_Ofolding__image__simple(_1349626, _1349628, _1349630, _1349632, _1349634, _1349636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349628), _1349638)), -(hAPP(_1349636, _1349638) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1349626, _1349628, _1349630), _1349634), _1349632), _1349638))], (36021 ^ _773908) ^ [] : [-(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)))], (37504 ^ _773908) ^ [_1483692, _1483694, _1483696, _1483698, _1483700, _1483702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1483692, _1483694), tc_HOL_Obool)), _1483696), hAPP(hAPP(c_Product__Type_OSigma(_1483692, _1483694), _1483698), hAPP(c_COMBK(tc_fun(_1483694, tc_HOL_Obool), _1483692), _1483700)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483694, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1483692, _1483694, _1483696), _1483702)), _1483700)))], (17073 ^ _773908) ^ [_1068179] : [_1068179 = 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), _1068179)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (25141 ^ _773908) ^ [_1218076, _1218078, _1218080] : [class_Orderings_Olinorder(_1218076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218076), _1218078), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218076), _1218080), _1218078))))], (1894 ^ _773908) ^ [_800569, _800571] : [-(class_Groups_Ozero(_800569)), _800571 = _800569, class_Groups_Ozero(_800571)], (12560 ^ _773908) ^ [_984406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984406)))], (42417 ^ _773908) ^ [_1614603, _1614605, _1614607, _1614609, _1614611] : [_1614603 = c_Orderings_Obot__class_Obot(tc_fun(_1614605, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614605, tc_fun(_1614607, tc_HOL_Obool)), _1614603), hAPP(hAPP(c_COMBB(tc_fun(_1614607, tc_HOL_Obool), tc_fun(_1614607, tc_HOL_Obool), _1614605), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614607, tc_HOL_Obool)), _1614609)), _1614611)) = c_Orderings_Otop__class_Otop(tc_fun(_1614607, tc_HOL_Obool)))], (37434 ^ _773908) ^ [_1481594, _1481596, _1481598, _1481600, _1481602] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1481594, _1481596), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481594, tc_HOL_Obool)), _1481598), _1481600)), hAPP(c_COMBK(tc_fun(_1481596, tc_HOL_Obool), _1481594), _1481602)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1481594, _1481596), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1481594, _1481596), _1481598), hAPP(c_COMBK(tc_fun(_1481596, tc_HOL_Obool), _1481594), _1481602))), hAPP(hAPP(c_Product__Type_OSigma(_1481594, _1481596), _1481600), hAPP(c_COMBK(tc_fun(_1481596, tc_HOL_Obool), _1481594), _1481602))))], (49024 ^ _773908) ^ [_1762596, _1762598, _1762600] : [c_List_Olist__all(_1762596, _1762598, _1762600), 49027 ^ _773908 : [(49028 ^ _773908) ^ [_1762685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762685), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762596)), _1762600))), -(hBOOL(hAPP(_1762598, hAPP(hAPP(c_List_Onth(_1762596), _1762600), _1762685))))]]], (25253 ^ _773908) ^ [_1219997, _1219999, _1220001, _1220003, _1220005] : [class_Orderings_Olinorder(_1219997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219997), _1219999), _1220001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219997), _1220003), _1220005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219997), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219997), _1219999), _1220003)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219997), _1220001), _1220005))))], (1624 ^ _773908) ^ [_797194, _797196] : [-(class_Groups_Ocancel__semigroup__add(_797194)), _797196 = _797194, class_Groups_Ocancel__semigroup__add(_797196)], (10089 ^ _773908) ^ [_941702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _941702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _941702)))], (22053 ^ _773908) ^ [_1155427, _1155429] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155427), _1155429), hAPP(c_Int_Onumber__class_Onumber__of(_1155427), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1155427), _1155429)), class_Fields_Ofield__inverse__zero(_1155427), class_Int_Onumber__ring(_1155427)], (21335 ^ _773908) ^ [_1142614, _1142616, _1142618, _1142620] : [class_Fields_Ofield(_1142614), -(_1142616 = c_Groups_Ozero__class_Ozero(_1142614)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142614), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142614), _1142618), _1142616)), _1142620) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142614), hAPP(hAPP(c_Power_Opower__class_Opower(_1142614), _1142618), _1142620)), hAPP(hAPP(c_Power_Opower__class_Opower(_1142614), _1142616), _1142620)))], (16097 ^ _773908) ^ [_1049518, _1049520, _1049522, _1049524, _1049526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049518), _1049520)), -(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), _1049518), _1049522)), _1049524)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049520), _1049522)), _1049526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049524), 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), _1049520), _1049518)), _1049522)), _1049526)))], (19649 ^ _773908) ^ [] : [-(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)))))], (24259 ^ _773908) ^ [_1198308, _1198310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198308), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198310), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198308, _1198310) = 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), _1198308), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198310)))))], (49618 ^ _773908) ^ [_1775222, _1775224] : [class_Lazy__Sequence_Osmall__lazy(_1775222), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1775222), _1775224) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1775222), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1775222)), c_List_Olist_ONil(_1775222)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1775222))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1775224)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1775222, tc_List_Olist(_1775222)), tc_List_Olist(_1775222), c_Lazy__Sequence_Oproduct(_1775222, tc_List_Olist(_1775222), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1775222, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1775224), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1775222), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1775224), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1775222, tc_List_Olist(_1775222), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1775222))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1775222), tc_List_Olist(_1775222)), tc_fun(tc_List_Olist(_1775222), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1775222))), _1775222), hAPP(c_COMBB(tc_List_Olist(_1775222), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1775222)), tc_List_Olist(_1775222)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1775222)))), c_List_Olist_OCons(_1775222))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1775222)))))], (38723 ^ _773908) ^ [_1521965, _1521967, _1521969] : [c_Wellfounded_Owf(_1521965, _1521967), -(c_Wellfounded_Owf(_1521965, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1521965, _1521965), tc_HOL_Obool)), _1521969), _1521967)))], (17563 ^ _773908) ^ [_1077094, _1077096, _1077098] : [class_Rings_Olinordered__idom(_1077094), -(hAPP(c_Groups_Oabs__class_Oabs(_1077094), hAPP(hAPP(c_Power_Opower__class_Opower(_1077094), hAPP(c_Groups_Ouminus__class_Ouminus(_1077094), _1077096)), _1077098)) = hAPP(c_Groups_Oabs__class_Oabs(_1077094), hAPP(hAPP(c_Power_Opower__class_Opower(_1077094), _1077096), _1077098)))], (8677 ^ _773908) ^ [_917555, _917557, _917559] : [class_Rings_Osemiring__1(_917555), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _917557), _917559)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917555), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917555), _917557)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917555), _917559)))], (45623 ^ _773908) ^ [_1685347, _1685349, _1685351] : [-(hAPP(c_List_Orotate(_1685347, _1685349), hAPP(c_List_Orev(_1685347), _1685351)) = hAPP(c_List_Orev(_1685347), hAPP(c_List_Orotate(_1685347, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685347)), _1685351)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1685349, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685347)), _1685351)))), _1685351)))], (16371 ^ _773908) ^ [_1054596, _1054598, _1054600] : [class_Int_Onumber(_1054596), 16374 ^ _773908 : [(16381 ^ _773908) ^ [] : [_1054600 = hAPP(c_Int_Onumber__class_Onumber__of(_1054596), _1054598), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054596), _1054598) = _1054600)], (16375 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054596), _1054598) = _1054600, -(_1054600 = hAPP(c_Int_Onumber__class_Onumber__of(_1054596), _1054598))]]], (16651 ^ _773908) ^ [_1059558, _1059560] : [class_Groups_Oordered__ab__group__add__abs(_1059558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059558), hAPP(c_Groups_Oabs__class_Oabs(_1059558), _1059560)), c_Groups_Ozero__class_Ozero(_1059558)))], (29851 ^ _773908) ^ [_1318941, _1318943, _1318945] : [class_Orderings_Olinorder(_1318941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318941), _1318943)), -(_1318943 = c_Orderings_Obot__class_Obot(tc_fun(_1318941, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1318941, c_Orderings_Oord__class_Omax(_1318941), hAPP(hAPP(c_Set_Oinsert(_1318941), _1318945), _1318943)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318941), _1318945), c_Big__Operators_Olattice_OSup__fin(_1318941, c_Orderings_Oord__class_Omax(_1318941), _1318943)))], (44507 ^ _773908) ^ [_1661328, _1661330] : [-(c_List_Oconcat(tc_List_Olist(_1661328), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661328), tc_List_Olist(tc_List_Olist(_1661328))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1661328)), _1661328, c_List_Olist_ONil(tc_List_Olist(_1661328)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1661328), tc_List_Olist(tc_List_Olist(_1661328))), _1661328), hAPP(hAPP(c_COMBC(tc_List_Olist(_1661328), tc_List_Olist(tc_List_Olist(_1661328)), tc_List_Olist(tc_List_Olist(_1661328))), c_List_Olist_OCons(tc_List_Olist(_1661328))), c_List_Olist_ONil(tc_List_Olist(_1661328)))))), _1661330)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661328), tc_List_Olist(_1661328)), c_List_Otl(_1661328)), hAPP(c_List_Ofilter(tc_List_Olist(_1661328), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1661328)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1661328), tc_List_Olist(_1661328), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1661328)))), _1661330)))], (30805 ^ _773908) ^ [_1338219, _1338221, _1338223] : [class_Groups_Ocomm__monoid__mult(_1338219), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338221, _1338219), _1338223), c_Orderings_Obot__class_Obot(tc_fun(_1338221, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1338219))], (7083 ^ _773908) ^ [_888649, _888651] : [class_Groups_Ocomm__monoid__add(_888649), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888649), _888651), c_Groups_Ozero__class_Ozero(_888649)) = _888651)], (28829 ^ _773908) ^ [_1300483, _1300485, _1300487] : [class_Lattices_Olattice(_1300483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300483), _1300485)), hBOOL(hAPP(hAPP(c_member(_1300483), _1300487), _1300485)), 28840 ^ _773908 : [(28847 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300483, tc_HOL_Obool)), _1300485), hAPP(hAPP(c_Set_Oinsert(_1300483), _1300487), c_Orderings_Obot__class_Obot(tc_fun(_1300483, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1300483, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1300483, _1300485) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1300483), _1300487), c_Big__Operators_Olattice__class_OSup__fin(_1300483, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300483, tc_HOL_Obool)), _1300485), hAPP(hAPP(c_Set_Oinsert(_1300483), _1300487), c_Orderings_Obot__class_Obot(tc_fun(_1300483, tc_HOL_Obool)))))))], (28841 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300483, tc_HOL_Obool)), _1300485), hAPP(hAPP(c_Set_Oinsert(_1300483), _1300487), c_Orderings_Obot__class_Obot(tc_fun(_1300483, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1300483, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1300483, _1300485) = _1300487)]]], (7725 ^ _773908) ^ [_899410, _899412, _899414, _899416, _899418] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_899410, _899412, _899414)), _899416), _899418))), 7726 ^ _773908 : [(7733 ^ _773908) ^ [] : [-(hBOOL(hAPP(_899410, _899416))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899414), _899416), _899418))], (7727 ^ _773908) ^ [] : [hBOOL(hAPP(_899410, _899416)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899412), _899416), _899418))]]], (43780 ^ _773908) ^ [_1644780, _1644782, _1644784] : [class_Complete__Lattice_Ocomplete__lattice(_1644780), 43783 ^ _773908 : [(43784 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644780), c_Complete__Lattice_OSup__class_OSup(_1644780, _1644782)), _1644784)), 43787 ^ _773908 : [(43788 ^ _773908) ^ [_1644938] : [hBOOL(hAPP(hAPP(c_member(_1644780), _1644938), _1644782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644780), _1644938), _1644784)))]]], (43794 ^ _773908) ^ [] : [43796 ^ _773908 : [(43799 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644780), 43795 ^ [_1644780, _1644782, _1644784]), _1644784))], (43797 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644780), 43795 ^ [_1644780, _1644782, _1644784]), _1644782)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644780), c_Complete__Lattice_OSup__class_OSup(_1644780, _1644782)), _1644784)))]]], (41037 ^ _773908) ^ [_1582299, _1582301, _1582303] : [-(hAPP(c_List_Otl(_1582299), hAPP(hAPP(c_List_Olist_OCons(_1582299), _1582301), _1582303)) = _1582303)], (40987 ^ _773908) ^ [_1581328, _1581330] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581328)), hAPP(c_List_Orotate1(_1581328), _1581330)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581328)), _1581330))], (39380 ^ _773908) ^ [_1538787, _1538789, _1538791] : [_1538791 = c_List_Olist_ONil(_1538789), -(_1538787 = hAPP(hAPP(c_List_Oappend(_1538789), _1538787), _1538791))], (44989 ^ _773908) ^ [_1673038, _1673040, _1673042] : [class_Orderings_Olinorder(_1673038), c_List_Olinorder__class_Osorted(_1673038, _1673040), -(c_List_Olinorder__class_Osorted(_1673038, hAPP(hAPP(c_List_Otake(_1673038), _1673042), _1673040)))], (46451 ^ _773908) ^ [_1702926, _1702928] : [-(c_Nitpick_Owf_H(_1702926, _1702928)), c_Wellfounded_Oacyclic(_1702926, _1702928), 46456 ^ _773908 : [(46459 ^ _773908) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (46457 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1702926, _1702926)), _1702928))]]], (17833 ^ _773908) ^ [_1082041, _1082043] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082041)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082041)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082043)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082041)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082043))))], (51662 ^ _773908) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (41215 ^ _773908) ^ [_1586027, _1586029, _1586031] : [-(_1586027 = c_List_Olist_ONil(_1586029)), -(hAPP(c_List_Ohd(_1586029), hAPP(c_List_Orotate(_1586029, _1586031), _1586027)) = hAPP(hAPP(c_List_Onth(_1586029), _1586027), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1586031, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586029)), _1586027))))], (1864 ^ _773908) ^ [_800194, _800196] : [-(class_Orderings_Oord(_800194)), _800196 = _800194, class_Orderings_Oord(_800196)], (18501 ^ _773908) ^ [_1093325, _1093327, _1093329, _1093331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1093325, tc_HOL_Obool)), _1093327), _1093329)), hBOOL(hAPP(hAPP(c_member(_1093325), _1093331), _1093327)), -(hBOOL(hAPP(hAPP(c_member(_1093325), _1093331), _1093329)))], (39837 ^ _773908) ^ [_1550914, _1550916, _1550918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1550914, tc_HOL_Obool)), _1550916), _1550918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1550914), tc_HOL_Obool)), c_List_Olists(_1550914, _1550916)), c_List_Olists(_1550914, _1550918))))], (19573 ^ _773908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (41704 ^ _773908) ^ [_1595591, _1595593, _1595595] : [-(_1595591 = c_List_Olist_ONil(_1595593)), -(c_List_Obutlast(_1595593, hAPP(hAPP(c_List_Olist_OCons(_1595593), _1595595), _1595591)) = hAPP(hAPP(c_List_Olist_OCons(_1595593), _1595595), c_List_Obutlast(_1595593, _1595591)))], (45637 ^ _773908) ^ [_1685796, _1685798, _1685800, _1685802] : [class_Orderings_Olinorder(_1685796), c_List_Olinorder__class_Osorted(_1685796, hAPP(c_List_Orev(_1685796), _1685798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1685800), _1685802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685802), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685796)), _1685798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1685796), hAPP(hAPP(c_List_Onth(_1685796), _1685798), _1685802)), hAPP(hAPP(c_List_Onth(_1685796), _1685798), _1685800))))], (9037 ^ _773908) ^ [_923945, _923947] : [class_Groups_Oordered__ab__group__add(_923945), 9040 ^ _773908 : [(9047 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923945), _923947), c_Groups_Ozero__class_Ozero(_923945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923945), c_Groups_Ozero__class_Ozero(_923945)), hAPP(c_Groups_Ouminus__class_Ouminus(_923945), _923947))))], (9041 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923945), c_Groups_Ozero__class_Ozero(_923945)), hAPP(c_Groups_Ouminus__class_Ouminus(_923945), _923947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923945), _923947), c_Groups_Ozero__class_Ozero(_923945))))]]], (28380 ^ _773908) ^ [_1289475, _1289477, _1289479, _1289481] : [hBOOL(hAPP(hAPP(c_member(_1289475), _1289477), _1289479)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289475, tc_HOL_Obool)), _1289479), hAPP(hAPP(c_Set_Oinsert(_1289475), _1289477), _1289481)) = hAPP(hAPP(c_Set_Oinsert(_1289475), _1289477), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289475, tc_HOL_Obool)), _1289479), _1289481)))], (24541 ^ _773908) ^ [_1205185, _1205187, _1205189, _1205191] : [hAPP(hAPP(c_COMBC(_1205185, tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_fun(_1205187, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205187, tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_fun(_1205187, tc_HOL_Obool)), _1205185), c_COMBC(_1205187, tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205187, tc_prod(_1205185, _1205187)), tc_fun(_1205187, tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), _1205185), hAPP(c_COMBB(tc_prod(_1205185, _1205187), tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool), _1205187), c_member(tc_prod(_1205185, _1205187)))), c_Product__Type_OPair(_1205185, _1205187)))), _1205189) = hAPP(hAPP(c_COMBC(_1205185, tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_fun(_1205187, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205187, tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_fun(_1205187, tc_HOL_Obool)), _1205185), c_COMBC(_1205187, tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205187, tc_prod(_1205185, _1205187)), tc_fun(_1205187, tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool)), _1205185), hAPP(c_COMBB(tc_prod(_1205185, _1205187), tc_fun(tc_fun(tc_prod(_1205185, _1205187), tc_HOL_Obool), tc_HOL_Obool), _1205187), c_member(tc_prod(_1205185, _1205187)))), c_Product__Type_OPair(_1205185, _1205187)))), _1205191), -(_1205189 = _1205191)], (46185 ^ _773908) ^ [_1697513, _1697515, _1697517, _1697519, _1697521] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1697513, _1697513)), hAPP(hAPP(c_Product__Type_OPair(_1697513, _1697513), _1697515), _1697517)), c_List_Omeasures(_1697513, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1697513, tc_Nat_Onat)), _1697519), _1697521)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1697519, _1697515)), hAPP(_1697519, _1697517)))), 46192 ^ _773908 : [(46195 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697513, _1697513)), hAPP(hAPP(c_Product__Type_OPair(_1697513, _1697513), _1697515), _1697517)), c_List_Omeasures(_1697513, _1697521))))], (46193 ^ _773908) ^ [] : [-(hAPP(_1697519, _1697515) = hAPP(_1697519, _1697517))]]], (22537 ^ _773908) ^ [_1164658, _1164660, _1164662, _1164664] : [class_Fields_Ofield(_1164658), -(_1164660 = c_Groups_Ozero__class_Ozero(_1164658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164662), _1164664)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164658), _1164660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164664), _1164662)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164658), hAPP(hAPP(c_Power_Opower__class_Opower(_1164658), _1164660), _1164664)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164658), _1164660), _1164662)))], (4816 ^ _773908) ^ [_847366, _847368] : [_847368 = _847366, -(c_List_Olist_ONil(_847368) = c_List_Olist_ONil(_847366))], (25073 ^ _773908) ^ [_1216616, _1216618] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1216616)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1216618)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1216618))), 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, _1216616))), 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), _1216616)), c_Int_Onat)))))], (28588 ^ _773908) ^ [_1294386, _1294388, _1294390, _1294392, _1294394, _1294396, _1294398] : [c_Equiv__Relations_Oequiv(_1294386, _1294388, _1294390), hBOOL(hAPP(hAPP(c_member(tc_fun(_1294386, tc_HOL_Obool)), _1294392), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1294386), _1294388), _1294390))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1294386, tc_HOL_Obool)), _1294394), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1294386), _1294388), _1294390))), hBOOL(hAPP(hAPP(c_member(_1294386), _1294396), _1294392)), hBOOL(hAPP(hAPP(c_member(_1294386), _1294398), _1294394)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1294386, _1294386)), hAPP(hAPP(c_Product__Type_OPair(_1294386, _1294386), _1294396), _1294398)), _1294390)), -(_1294392 = _1294394)], (46039 ^ _773908) ^ [_1694060, _1694062, _1694064, _1694066] : [class_Orderings_Olinorder(_1694060), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694062)), c_List_Olinorder__class_Osort__key(_1694062, _1694060, _1694064, _1694066)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694062)), _1694066))], (16549 ^ _773908) ^ [_1057930, _1057932] : [class_Int_Onumber__ring(_1057930), -(hAPP(c_Int_Onumber__class_Onumber__of(_1057930), _1057932) = hAPP(c_Int_Oring__1__class_Oof__int(_1057930), _1057932))], (22023 ^ _773908) ^ [_1154924, _1154926, _1154928] : [class_Fields_Olinordered__field__inverse__zero(_1154924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154924), c_Groups_Ozero__class_Ozero(_1154924)), _1154926)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154924), hAPP(c_Groups_Oabs__class_Oabs(_1154924), _1154928)), _1154926) = hAPP(c_Groups_Oabs__class_Oabs(_1154924), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154924), _1154928), _1154926)))], (42644 ^ _773908) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (26852 ^ _773908) ^ [_1257677, _1257679, _1257681] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1257677, _1257677)), hAPP(hAPP(c_Product__Type_OPair(_1257677, _1257677), _1257679), _1257681)), c_Relation_OId(_1257677))), -(_1257679 = _1257681)], (39641 ^ _773908) ^ [_1544952, _1544954, _1544956, _1544958, _1544960, _1544962] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544952), tc_List_Olist(_1544952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544952), tc_List_Olist(_1544952)), hAPP(hAPP(c_List_Olist_OCons(_1544952), _1544954), _1544956)), hAPP(hAPP(c_List_Olist_OCons(_1544952), _1544958), _1544960))), c_List_Olistrel1(_1544952, _1544962)))), 39642 ^ _773908 : [(39649 ^ _773908) ^ [] : [_1544954 = _1544958, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544952), tc_List_Olist(_1544952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544952), tc_List_Olist(_1544952)), _1544956), _1544960)), c_List_Olistrel1(_1544952, _1544962)))], (39643 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544952, _1544952)), hAPP(hAPP(c_Product__Type_OPair(_1544952, _1544952), _1544954), _1544958)), _1544962)), _1544956 = _1544960]]], (44609 ^ _773908) ^ [_1665173, _1665175] : [-(c_List_Otranspose(_1665173, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1665173)), c_List_Olist_ONil(_1665173)), _1665175)) = c_List_Otranspose(_1665173, _1665175))], (27312 ^ _773908) ^ [_1267047, _1267049, _1267051] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267047), hAPP(hAPP(c_Set_Oinsert(_1267047), _1267049), _1267051))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267047), _1267051)))], (39088 ^ _773908) ^ [_1530071, _1530073, _1530075, _1530077, _1530079] : [-(hAPP(c_Relation_ORange(_1530071, _1530073), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1530071, _1530073)), hAPP(hAPP(c_Product__Type_OPair(_1530071, _1530073), _1530075), _1530077)), _1530079)) = hAPP(hAPP(c_Set_Oinsert(_1530073), _1530077), hAPP(c_Relation_ORange(_1530071, _1530073), _1530079)))], (51728 ^ _773908) ^ [_1816485, _1816487] : [-(class_Finite__Set_Ofinite(tc_prod(_1816485, _1816487))), class_Finite__Set_Ofinite(_1816485), class_Finite__Set_Ofinite(_1816487)], (8035 ^ _773908) ^ [_905434, _905436] : [8036 ^ _773908 : [(8037 ^ _773908) ^ [_905490] : [_905436 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _905434), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _905490)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _905434), _905436)))], (23536 ^ _773908) ^ [_1184266, _1184268] : [_1184266 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1184266, _1184268) = 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)))], (7061 ^ _773908) ^ [_888313, _888315] : [class_Groups_Olinordered__ab__group__add(_888313), 7064 ^ _773908 : [(7071 ^ _773908) ^ [] : [_888315 = c_Groups_Ozero__class_Ozero(_888313), -(c_Groups_Ozero__class_Ozero(_888313) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888313), _888315), _888315))], (7065 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_888313) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888313), _888315), _888315), -(_888315 = c_Groups_Ozero__class_Ozero(_888313))]]], (34195 ^ _773908) ^ [_1410560, _1410562] : [-(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)), _1410560)), 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), _1410562), _1410560))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1410560), _1410562))], (26159 ^ _773908) ^ [_1238064, _1238066, _1238068] : [class_Lattices_Osemilattice__sup(_1238064), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238064), _1238066), _1238068) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238064), _1238068), _1238066))], (4462 ^ _773908) ^ [_841847, _841849, _841851, _841853] : [-(c_New__DSequence_Opos__single(_841853, _841849) = c_New__DSequence_Opos__single(_841851, _841847)), _841853 = _841851, _841849 = _841847], (20951 ^ _773908) ^ [_1136334, _1136336, _1136338, _1136340] : [class_Fields_Olinordered__field(_1136334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136334), _1136336), _1136338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136334), c_Groups_Ozero__class_Ozero(_1136334)), _1136340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136334), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136334), _1136336), _1136340)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136334), _1136338), _1136340))))], (26520 ^ _773908) ^ [_1249179, _1249181, _1249183, _1249185, _1249187] : [-(hAPP(c_Set_Oimage(_1249179, _1249181, _1249183), hAPP(hAPP(c_Set_Oinsert(_1249179), _1249185), _1249187)) = hAPP(hAPP(c_Set_Oinsert(_1249181), hAPP(_1249183, _1249185)), hAPP(c_Set_Oimage(_1249179, _1249181, _1249183), _1249187)))], (38978 ^ _773908) ^ [_1527234, _1527236] : [c_FunDef_Oreduction__pair(_1527234, _1527236), 38981 ^ _773908 : [(38984 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527234, _1527234, _1527234), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool), tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool)), _1527236)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool), tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool)), _1527236))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool), tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool)), _1527236))))], (38982 ^ _773908) ^ [] : [-(c_Wellfounded_Owf(_1527234, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool), tc_fun(tc_prod(_1527234, _1527234), tc_HOL_Obool)), _1527236)))]]], (26460 ^ _773908) ^ [_1247820, _1247822, _1247824, _1247826, _1247828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247820, tc_HOL_Obool)), _1247822), hAPP(c_Set_Oimage(_1247824, _1247820, _1247826), _1247828))), 26464 ^ _773908 : [(26467 ^ _773908) ^ [] : [-(_1247822 = hAPP(c_Set_Oimage(_1247824, _1247820, _1247826), 26463 ^ [_1247820, _1247822, _1247824, _1247826, _1247828]))], (26465 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247824, tc_HOL_Obool)), 26463 ^ [_1247820, _1247822, _1247824, _1247826, _1247828]), _1247828)))]]], (27230 ^ _773908) ^ [_1265661, _1265663, _1265665, _1265667, _1265669] : [c_Equiv__Relations_Oequiv(_1265661, _1265663, _1265665), hBOOL(hAPP(hAPP(c_member(tc_prod(_1265661, _1265661)), hAPP(hAPP(c_Product__Type_OPair(_1265661, _1265661), _1265667), _1265669)), _1265665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265661, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1265661, _1265661, _1265665), hAPP(hAPP(c_Set_Oinsert(_1265661), _1265667), c_Orderings_Obot__class_Obot(tc_fun(_1265661, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1265661, _1265661, _1265665), hAPP(hAPP(c_Set_Oinsert(_1265661), _1265669), c_Orderings_Obot__class_Obot(tc_fun(_1265661, tc_HOL_Obool)))))))], (36524 ^ _773908) ^ [_1461580, _1461582, _1461584, _1461586] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461580), _1461582)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461580), _1461584)), -(_1461584 = c_Orderings_Obot__class_Obot(tc_fun(_1461580, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1461580, tc_HOL_Obool), tc_fun(_1461580, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1461580, tc_HOL_Obool), tc_fun(_1461580, tc_HOL_Obool)), _1461582), _1461584)), c_Wellfounded_Omax__ext(_1461580, _1461586)))), 36538 ^ _773908 : [(36541 ^ _773908) ^ [_1461985] : [hBOOL(hAPP(hAPP(c_member(_1461580), _1461985), _1461584)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1461580, _1461580)), hAPP(hAPP(c_Product__Type_OPair(_1461580, _1461580), 36537 ^ [_1461580, _1461582, _1461584, _1461586]), _1461985)), _1461586))], (36539 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461580), 36537 ^ [_1461580, _1461582, _1461584, _1461586]), _1461582)))]]], (51430 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (45121 ^ _773908) ^ [_1675423, _1675425, _1675427] : [class_Orderings_Olinorder(_1675423), c_List_Olinorder__class_Osorted(_1675423, _1675425), -(c_List_Olinorder__class_Osorted(_1675423, c_List_Olinorder__class_Oinsort__insert__key(_1675423, _1675423, c_COMBI(_1675423), _1675427, _1675425)))], (4822 ^ _773908) ^ [_847451, _847453] : [_847453 = _847451, -(c_List_Omember(_847453) = c_List_Omember(_847451))], (32828 ^ _773908) ^ [_1383487, _1383489, _1383491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1383487)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1383489), _1383491)), 32835 ^ _773908 : [(32836 ^ _773908) ^ [_1383677] : [32838 ^ _773908 : [(32844 ^ _773908) ^ [] : [-(_1383677 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32840 ^ [_1383487, _1383489, _1383491, _1383677]), 32837 ^ [_1383487, _1383489, _1383491, _1383677]))], (32842 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32840 ^ [_1383487, _1383489, _1383491, _1383677]), _1383491)))], (32839 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32837 ^ [_1383487, _1383489, _1383491, _1383677]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1383487))))]], -(_1383677 = _1383489), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1383677), _1383487) = _1383489]]], (15093 ^ _773908) ^ [_1029568, _1029570] : [-(_1029568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15096 ^ _773908 : [(15103 ^ _773908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029570, _1029568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029570), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029568)) = 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), _1029570), _1029568))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15097 ^ _773908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029570, _1029568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029570), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029568)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029570), _1029568)))]]], (15861 ^ _773908) ^ [_1044086, _1044088] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044086), _1044088) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044086), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044088)))], (35580 ^ _773908) ^ [_1440919, _1440921, _1440923, _1440925, _1440927] : [class_Groups_Ocomm__monoid__add(_1440919), class_Groups_Oordered__ab__semigroup__add(_1440919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440921), _1440923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440921, tc_HOL_Obool)), _1440925), _1440923)), 35598 ^ _773908 : [(35601 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440919), c_Groups_Ozero__class_Ozero(_1440919)), hAPP(_1440927, 35597 ^ [_1440919, _1440921, _1440923, _1440925, _1440927])))], (35599 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440921), 35597 ^ [_1440919, _1440921, _1440923, _1440925, _1440927]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1440921, tc_HOL_Obool)), _1440923), _1440925))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440919), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440921, _1440919), _1440927), _1440925)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440921, _1440919), _1440927), _1440923))))], (44447 ^ _773908) ^ [_1660054, _1660056, _1660058] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1660054), tc_List_Olist(_1660054), c_List_Oappend(_1660054), _1660056), _1660058) = hAPP(hAPP(c_List_Oappend(_1660054), _1660056), c_List_Oconcat(_1660054, _1660058)))], (46197 ^ _773908) ^ [_1697792, _1697794, _1697796, _1697798, _1697800] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697792, _1697792)), hAPP(hAPP(c_Product__Type_OPair(_1697792, _1697792), _1697794), _1697796)), c_List_Omeasures(_1697792, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1697792, tc_Nat_Onat)), _1697798), _1697800))))), 46198 ^ _773908 : [(46201 ^ _773908) ^ [] : [hAPP(_1697798, _1697794) = hAPP(_1697798, _1697796), hBOOL(hAPP(hAPP(c_member(tc_prod(_1697792, _1697792)), hAPP(hAPP(c_Product__Type_OPair(_1697792, _1697792), _1697794), _1697796)), c_List_Omeasures(_1697792, _1697800)))], (46199 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1697798, _1697794)), hAPP(_1697798, _1697796)))]]], (44808 ^ _773908) ^ [_1669280, _1669282, _1669284, _1669286, _1669288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1669282), _1669284))), -(hAPP(hAPP(c_List_Onth(_1669286), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1669286), _1669288), c_List_Oupt(_1669284, _1669282))), _1669280) = hAPP(_1669288, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1669284), _1669280)))], (28877 ^ _773908) ^ [_1301495, _1301497] : [class_Lattices_Olattice(_1301495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301495), _1301497)), -(_1301497 = c_Orderings_Obot__class_Obot(tc_fun(_1301495, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301495), c_Big__Operators_Olattice__class_OInf__fin(_1301495, _1301497)), c_Big__Operators_Olattice__class_OSup__fin(_1301495, _1301497))))], (39214 ^ _773908) ^ [_1534492, _1534494, _1534496, _1534498, _1534500] : [hAPP(hAPP(c_List_Olist_OCons(_1534492), _1534494), _1534496) = hAPP(hAPP(c_List_Olist_OCons(_1534492), _1534498), _1534500), 39217 ^ _773908 : [(39220 ^ _773908) ^ [] : [-(_1534496 = _1534500)], (39218 ^ _773908) ^ [] : [-(_1534494 = _1534498)]]], (16131 ^ _773908) ^ [_1050250, _1050252] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050250, _1050252) = 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), _1050250), _1050252) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30329 ^ _773908) ^ [_1328225] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1328225) = 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)), _1328225)))], (37940 ^ _773908) ^ [_1494788, _1494790, _1494792] : [hBOOL(hAPP(_1494788, _1494790)), -(hBOOL(hAPP(hAPP(c_member(_1494792), _1494790), hAPP(c_Set_OCollect(_1494792), _1494788))))], (47261 ^ _773908) ^ [_1723315, _1723317] : [-(c_Transitive__Closure_Otrancl(_1723315, hAPP(c_Relation_Oconverse(_1723315, _1723315), _1723317)) = hAPP(c_Relation_Oconverse(_1723315, _1723315), c_Transitive__Closure_Otrancl(_1723315, _1723317)))], (30123 ^ _773908) ^ [_1324189, _1324191, _1324193] : [class_Orderings_Olinorder(_1324189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324189), _1324191)), -(_1324191 = c_Orderings_Obot__class_Obot(tc_fun(_1324189, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1324189, c_Orderings_Oord__class_Omin(_1324189), hAPP(hAPP(c_Set_Oinsert(_1324189), _1324193), _1324191)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324189), _1324193), c_Big__Operators_Olattice_OInf__fin(_1324189, c_Orderings_Oord__class_Omin(_1324189), _1324191)))], (28226 ^ _773908) ^ [_1285780, _1285782, _1285784, _1285786] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285780, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285780, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285780, tc_HOL_Obool)), _1285782), _1285784)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285780, tc_HOL_Obool)), _1285784), _1285786))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285780, tc_HOL_Obool)), _1285786), _1285782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285780, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285780, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285780, tc_HOL_Obool)), _1285782), _1285784)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285780, tc_HOL_Obool)), _1285784), _1285786))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285780, tc_HOL_Obool)), _1285786), _1285782)))], (45539 ^ _773908) ^ [_1683580, _1683582] : [_1683582 = c_List_Olist_ONil(_1683580), -(hAPP(c_List_Orev(_1683580), _1683582) = c_List_Olist_ONil(_1683580))], (28408 ^ _773908) ^ [_1290196, _1290198, _1290200, _1290202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290196, tc_HOL_Obool)), _1290202), _1290198)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290196, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290196, tc_HOL_Obool)), _1290198), _1290200)), _1290202) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290196, tc_HOL_Obool)), _1290198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290196, tc_HOL_Obool)), _1290200), _1290202)))], (39090 ^ _773908) ^ [_1530142, _1530144, _1530146, _1530148] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530142, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530144, _1530142), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1530144, _1530142), tc_HOL_Obool)), _1530146), _1530148))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530142, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530144, _1530142), _1530146)), hAPP(c_Relation_ORange(_1530144, _1530142), _1530148)))))], (50102 ^ _773908) ^ [_1787498, _1787500, _1787502, _1787504] : [class_Complete__Lattice_Ocomplete__lattice(_1787498), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1787500, _1787498), _1787502), _1787504) = c_Complete__Lattice_OInf__class_OInf(_1787498, hAPP(c_Set_OCollect(_1787498), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool), tc_HOL_Obool, _1787498), c_HOL_OEx(tc_fun(_1787500, _1787498))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool), tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool), _1787498), hAPP(c_COMBS(tc_fun(_1787500, _1787498), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1787500, _1787498)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1787500, _1787498), tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1787500, _1787498))), _1787502)))), hAPP(hAPP(c_COMBC(_1787498, tc_fun(tc_fun(_1787500, _1787498), _1787498), tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1787498, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1787500, _1787498), _1787498), tc_fun(tc_fun(_1787500, _1787498), tc_HOL_Obool)), _1787498), c_COMBB(_1787498, tc_HOL_Obool, tc_fun(_1787500, _1787498))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1787500, _1787498), _1787500, _1787498), c_COMBI(tc_fun(_1787500, _1787498))), _1787504)))))))], (8323 ^ _773908) ^ [_911152, _911154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911152), _911154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911152)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911154))))], (31495 ^ _773908) ^ [_1353629, _1353631, _1353633, _1353635, _1353637, _1353639, _1353641, _1353643] : [c_Equiv__Relations_Oequiv(_1353629, _1353631, _1353633), c_Equiv__Relations_Ocongruent2(_1353629, _1353635, _1353637, _1353633, _1353639, _1353641), hBOOL(hAPP(hAPP(c_member(_1353629), _1353643), _1353631)), -(c_Equiv__Relations_Ocongruent(_1353635, _1353637, _1353639, hAPP(_1353641, _1353643)))], (40938 ^ _773908) ^ [_1580200, _1580202, _1580204] : [c_Hoare__Mirabelle_Ohoare__valids(_1580200, _1580202, _1580204), 40941 ^ _773908 : [(40942 ^ _773908) ^ [_1580309] : [40944 ^ _773908 : [(40947 ^ _773908) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1580200, _1580309, 40943 ^ [_1580200, _1580202, _1580204, _1580309])], (40945 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1580200)), 40943 ^ [_1580200, _1580202, _1580204, _1580309]), _1580202)))]], 40948 ^ _773908 : [(40949 ^ _773908) ^ [_1580481] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1580200)), _1580481), _1580204)), -(c_Hoare__Mirabelle_Otriple__valid(_1580200, _1580309, _1580481))]]]]], (5715 ^ _773908) ^ [_864125, _864127] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_864125, _864127, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_864125), tc_HOL_Obool))))], (15523 ^ _773908) ^ [_1037529, _1037531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037529), _1037531)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037531), _1037529)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1037531)), hAPP(c_Int_Onat, _1037529)))], (8923 ^ _773908) ^ [_921552, _921554, _921556, _921558] : [class_Rings_Ocomm__semiring__1(_921552), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921552), _921554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921552), _921556), _921558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921552), _921554), _921556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921552), _921554), _921558)))], (39232 ^ _773908) ^ [_1534819, _1534821, _1534823] : [hAPP(hAPP(c_List_Olist_OCons(_1534819), _1534821), _1534823) = _1534823], (20293 ^ _773908) ^ [_1124172, _1124174] : [class_Rings_Olinordered__idom(_1124172), -(hAPP(c_Groups_Oabs__class_Oabs(_1124172), hAPP(hAPP(c_Power_Opower__class_Opower(_1124172), _1124174), 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(_1124172), _1124174), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (36235 ^ _773908) ^ [_1454072, _1454074] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1454072), c_Orderings_Otop__class_Otop(tc_fun(_1454072, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1454072, _1454072, _1454074), c_Orderings_Otop__class_Otop(tc_fun(_1454072, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1454072, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1454072, _1454072, _1454074, c_Orderings_Otop__class_Otop(tc_fun(_1454072, tc_HOL_Obool))))], (49286 ^ _773908) ^ [_1767925, _1767927, _1767929, _1767931, _1767933] : [-(_1767925 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1767927, _1767929, _1767931, _1767933), _1767925) = hAPP(c_Lazy__Sequence_Obind(_1767927, _1767929, hAPP(_1767931, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1767925), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1767927, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1767929)), _1767933), _1767925)))], (48981 ^ _773908) ^ [_1761670, _1761672] : [-(c_Nitpick_Ouminus__frac(_1761670, _1761672) = c_Nitpick_OAbs__Frac(_1761670, 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(_1761670), _1761672))), hAPP(c_Nitpick_Odenom(_1761670), _1761672))))], (24637 ^ _773908) ^ [_1208026, _1208028, _1208030] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1208026, _1208028), _1208030))), _1208026 = 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), _1208030)), _1208028)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1208030)), 24644 ^ _773908 : [(24647 ^ _773908) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1208030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24645 ^ _773908) ^ [] : [-(_1208028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24648 ^ _773908 : [(24651 ^ _773908) ^ [] : [24652 ^ _773908 : [(24655 ^ _773908) ^ [] : [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), _1208030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1208030)), _1208028))], (24653 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208028)))]], 24660 ^ _773908 : [(24663 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1208028), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1208030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1208030)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24661 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208028))]]], (24649 ^ _773908) ^ [] : [_1208028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (26053 ^ _773908) ^ [_1235788, _1235790, _1235792, _1235794] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235788, tc_HOL_Obool)), _1235790), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235788, tc_HOL_Obool)), _1235792), _1235794)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235788, tc_HOL_Obool)), _1235792), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235788, tc_HOL_Obool)), _1235790), _1235794)))], (47826 ^ _773908) ^ [_1737465, _1737467, _1737469, _1737471] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1737465, tc_HOL_Obool), tc_fun(_1737465, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1737465, tc_HOL_Obool), tc_fun(_1737465, tc_HOL_Obool)), _1737467), _1737469)), c_Wellfounded_Omax__ext(_1737465, _1737471)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1737465), _1737467)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1737465), _1737469)), -(_1737469 = c_Orderings_Obot__class_Obot(tc_fun(_1737465, tc_HOL_Obool))), 47840 ^ _773908 : [(47843 ^ _773908) ^ [_1737870] : [hBOOL(hAPP(hAPP(c_member(_1737465), _1737870), _1737469)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1737465, _1737465)), hAPP(hAPP(c_Product__Type_OPair(_1737465, _1737465), 47839 ^ [_1737465, _1737467, _1737469, _1737471]), _1737870)), _1737471))], (47841 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737465), 47839 ^ [_1737465, _1737467, _1737469, _1737471]), _1737467)))]]], (19401 ^ _773908) ^ [_1108858] : [_1108858 = c_Int_OMin, -(c_Int_OBit1(_1108858) = c_Int_OMin)], (23893 ^ _773908) ^ [_1191731, _1191733, _1191735, _1191737, _1191739, _1191741, _1191743] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1191731, _1191733, tc_fun(_1191735, tc_HOL_Obool)), _1191737), hAPP(hAPP(c_Product__Type_OPair(_1191731, _1191733), _1191739), _1191741)), _1191743)), -(hBOOL(hAPP(hAPP(hAPP(_1191737, _1191739), _1191741), _1191743)))], (11161 ^ _773908) ^ [_959734, _959736, _959738] : [class_Rings_Oordered__ring(_959734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959734), _959736), c_Groups_Ozero__class_Ozero(_959734))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959734), _959738), c_Groups_Ozero__class_Ozero(_959734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959734), c_Groups_Ozero__class_Ozero(_959734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959734), _959736), _959738))))], (25741 ^ _773908) ^ [_1230057, _1230059, _1230061] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230057, tc_HOL_Obool)), _1230059), _1230061) = c_Orderings_Obot__class_Obot(tc_fun(_1230057, tc_HOL_Obool))), _1230059 = c_Orderings_Obot__class_Obot(tc_fun(_1230057, tc_HOL_Obool)), _1230061 = c_Orderings_Obot__class_Obot(tc_fun(_1230057, tc_HOL_Obool))], (28124 ^ _773908) ^ [_1283496, _1283498, _1283500] : [class_Lattices_Osemilattice__inf(_1283496), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283496), _1283498), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283496), _1283498), _1283500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283496), _1283498), _1283500))], (3466 ^ _773908) ^ [_826035, _826037, _826039, _826041, _826043, _826045] : [-(c_List_Oremove1(_826045, _826041, _826037) = c_List_Oremove1(_826043, _826039, _826035)), _826045 = _826043, _826041 = _826039, _826037 = _826035], (31151 ^ _773908) ^ [_1345562, _1345564, _1345566, _1345568, _1345570] : [class_Fields_Ofield(_1345562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345564), _1345566)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345564), _1345568)), 31165 ^ _773908 : [(31168 ^ _773908) ^ [] : [-(hAPP(_1345570, 31164 ^ [_1345562, _1345564, _1345566, _1345568, _1345570]) = c_Groups_Ozero__class_Ozero(_1345562))], (31166 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345564), 31164 ^ [_1345562, _1345564, _1345566, _1345568, _1345570]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1345564, tc_HOL_Obool)), _1345566), _1345568))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345564, _1345562), _1345570), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1345564, tc_HOL_Obool)), _1345566), _1345568)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345562), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345564, _1345562), _1345570), _1345566)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345564, _1345562), _1345570), _1345568))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345564, _1345562), _1345570), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1345564, tc_HOL_Obool)), _1345566), _1345568))))], (12897 ^ _773908) ^ [_990181, _990183, _990185, _990187, _990189] : [c_Natural_Oevaln(_990181, _990183, _990185, _990187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990185), _990189)), -(c_Natural_Oevaln(_990181, _990183, _990189, _990187))], (23971 ^ _773908) ^ [_1192851, _1192853, _1192855, _1192857] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192851, _1192853), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192855), _1192857))), -(_1192853 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1192851, _1192853) = _1192857)], (20013 ^ _773908) ^ [_1119287, _1119289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119287), _1119289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1119287)), c_Int_OBit0(_1119289))))], (27780 ^ _773908) ^ [_1276828, _1276830, _1276832] : [class_Lattices_Olattice(_1276828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276828), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1276828), _1276830), _1276832)), _1276830)))], (25391 ^ _773908) ^ [_1222556, _1222558, _1222560, _1222562] : [class_Orderings_Olinorder(_1222556), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222556), _1222558), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222556), _1222560), _1222562)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222556), _1222560), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222556), _1222558), _1222562)))], (50088 ^ _773908) ^ [_1786428, _1786430, _1786432, _1786434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1786428, tc_fun(_1786430, tc_HOL_Obool)), _1786432), _1786434) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1786430, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1786430, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1786428, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1786430, tc_HOL_Obool)), c_HOL_OEx(_1786428)), hAPP(hAPP(c_COMBB(tc_fun(_1786428, tc_HOL_Obool), tc_fun(_1786428, tc_HOL_Obool), tc_fun(_1786430, tc_HOL_Obool)), hAPP(c_COMBS(_1786428, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1786428), c_fconj), hAPP(hAPP(c_COMBC(_1786428, tc_fun(_1786428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1786428)), _1786432)))), hAPP(hAPP(c_COMBC(tc_fun(_1786430, tc_HOL_Obool), tc_fun(_1786428, tc_fun(_1786430, tc_HOL_Obool)), tc_fun(_1786428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786430, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1786428, tc_fun(_1786430, tc_HOL_Obool)), tc_fun(_1786428, tc_HOL_Obool)), tc_fun(_1786430, tc_HOL_Obool)), c_COMBB(tc_fun(_1786430, tc_HOL_Obool), tc_HOL_Obool, _1786428)), c_fequal)), _1786434))))))], (42185 ^ _773908) ^ [_1608753, _1608755] : [-(hAPP(hAPP(c_List_Omap(_1608753, _1608753), c_COMBI(_1608753)), _1608755) = _1608755)], (19861 ^ _773908) ^ [_1116708, _1116710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116708), _1116710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116708)), c_Int_OBit0(_1116710))))], (27762 ^ _773908) ^ [_1276510, _1276512, _1276514, _1276516, _1276518] : [c_Equiv__Relations_Oequiv(_1276510, _1276512, _1276514), hBOOL(hAPP(hAPP(c_member(tc_fun(_1276510, tc_HOL_Obool)), _1276516), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1276510), _1276512), _1276514))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1276510, tc_HOL_Obool)), _1276518), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1276510), _1276512), _1276514))), -(_1276516 = _1276518), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1276510, tc_HOL_Obool)), _1276516), _1276518) = c_Orderings_Obot__class_Obot(tc_fun(_1276510, tc_HOL_Obool)))], (47890 ^ _773908) ^ [_1738916, _1738918, _1738920, _1738922, _1738924, _1738926] : [class_Groups_Oab__semigroup__mult(_1738916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1738918), _1738920)), 47900 ^ _773908 : [(47903 ^ _773908) ^ [] : [hAPP(_1738922, 47899 ^ [_1738916, _1738918, _1738920, _1738922, _1738924, _1738926]) = hAPP(_1738924, 47899 ^ [_1738916, _1738918, _1738920, _1738922, _1738924, _1738926])], (47901 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738918), 47899 ^ [_1738916, _1738918, _1738920, _1738922, _1738924, _1738926]), _1738920)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1738916, _1738918, c_Groups_Otimes__class_Otimes(_1738916)), _1738922), _1738926), _1738920) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1738916, _1738918, c_Groups_Otimes__class_Otimes(_1738916)), _1738924), _1738926), _1738920))], (4650 ^ _773908) ^ [_844707, _844709, _844711, _844713, _844715, _844717, _844719, _844721] : [-(c_Lazy__Sequence_Oproduct(_844721, _844717, _844713, _844709) = c_Lazy__Sequence_Oproduct(_844719, _844715, _844711, _844707)), _844721 = _844719, _844717 = _844715, _844713 = _844711, _844709 = _844707], (51650 ^ _773908) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (35997 ^ _773908) ^ [_1449279, _1449281] : [class_Lattices_Obounded__lattice__top(_1449279), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449279), _1449281), c_Orderings_Otop__class_Otop(_1449279)) = _1449281)], (27486 ^ _773908) ^ [_1270697, _1270699, _1270701, _1270703, _1270705, _1270707] : [c_Finite__Set_Ofolding(_1270697, _1270699, _1270701, _1270703), -(hAPP(c_Fun_Ocomp(_1270699, _1270699, _1270699, hAPP(_1270701, _1270705)), hAPP(_1270701, _1270707)) = hAPP(c_Fun_Ocomp(_1270699, _1270699, _1270699, hAPP(_1270701, _1270707)), hAPP(_1270701, _1270705)))], (44889 ^ _773908) ^ [_1671421, _1671423] : [class_Orderings_Olinorder(_1671421), -(c_List_Olinorder__class_Osorted(_1671421, hAPP(hAPP(c_List_Olist_OCons(_1671421), _1671423), c_List_Olist_ONil(_1671421))))], (24491 ^ _773908) ^ [_1204056] : [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), _1204056))), -(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), _1204056)) = 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), _1204056))))], (49924 ^ _773908) ^ [_1782307, _1782309, _1782311] : [c_List_Oall__interval__int(_1782307, _1782309, _1782311), -(c_List_Olist__all(tc_Int_Oint, _1782307, c_List_Oupto(_1782309, _1782311)))], (13087 ^ _773908) ^ [_993515, _993517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993515)), _993517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993515), _993517)))], (19577 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28386 ^ _773908) ^ [_1289640, _1289642, _1289644, _1289646] : [-(hBOOL(hAPP(hAPP(c_member(_1289640), _1289642), _1289644))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289640, tc_HOL_Obool)), _1289644), hAPP(hAPP(c_Set_Oinsert(_1289640), _1289642), _1289646)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289640, tc_HOL_Obool)), _1289644), _1289646))], (54 ^ _773908) ^ [_774611, _774613] : [-(class_Fields_Olinordered__field__inverse__zero(_774611)), _774613 = _774611, class_Fields_Olinordered__field__inverse__zero(_774613)], (51568 ^ _773908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (40495 ^ _773908) ^ [_1567107, _1567109, _1567111] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567107), _1567109)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1567107)), hAPP(c_Set_OCollect(tc_List_Olist(_1567107)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1567107), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1567107)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1567107), tc_fun(_1567107, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1567107, tc_HOL_Obool), tc_fun(tc_fun(_1567107, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1567107)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1567107, tc_HOL_Obool))), c_List_Oset(_1567107))), _1567109))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1567107), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1567107)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1567107)))), _1567111))))))], (51778 ^ _773908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (4562 ^ _773908) ^ [_843323, _843325] : [_843325 = _843323, -(c_Orderings_Oord__class_Omin(_843325) = c_Orderings_Oord__class_Omin(_843323))], (30345 ^ _773908) ^ [_1328437, _1328439] : [hAPP(c_Finite__Set_Ocard(_1328437), _1328439) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1328439 = c_Orderings_Obot__class_Obot(tc_fun(_1328437, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328437), _1328439))], (49718 ^ _773908) ^ [_1777538, _1777540, _1777542, _1777544, _1777546] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1777538, _1777540, _1777542, _1777544, _1777546) = c_Option_Ooption_Ooption__case(_1777538, tc_prod(_1777540, tc_Lazy__Sequence_Olazy__sequence(_1777540)), _1777542, hAPP(c_Product__Type_Oprod_Oprod__case(_1777540, tc_Lazy__Sequence_Olazy__sequence(_1777540), _1777538), _1777544), hAPP(c_Lazy__Sequence_Oyield(_1777540), _1777546)))], (14418 ^ _773908) ^ [_1017876, _1017878, _1017880] : [-(_1017876 = 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), _1017876), _1017878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017876), _1017880)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017878), _1017880))], (38621 ^ _773908) ^ [_1518234, _1518236, _1518238, _1518240] : [hAPP(hAPP(c_Relation_Orel__comp(_1518234, _1518234, _1518234), _1518236), _1518238) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518234, _1518234), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518234, _1518234, _1518234), _1518240), _1518238) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518234, _1518234), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1518234, _1518234, _1518234), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518234, _1518234), tc_HOL_Obool)), _1518236), _1518240)), _1518238) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518234, _1518234), tc_HOL_Obool)))], (51083 ^ _773908) ^ [_1807949, _1807951] : [51085 ^ _773908 : [(51088 ^ _773908) ^ [] : [hBOOL(hAPP(_1807949, hAPP(c_Code__Numeral_Oof__nat, 51084 ^ [_1807949, _1807951])))], (51086 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51084 ^ [_1807949, _1807951]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1807949, _1807951)))], (41928 ^ _773908) ^ [_1600552, _1600554, _1600556, _1600558, _1600560, _1600562] : [-(hAPP(hAPP(c_List_Omap(_1600552, _1600554), _1600556), hAPP(hAPP(c_List_Omap(_1600558, _1600552), _1600560), _1600562)) = hAPP(hAPP(c_List_Omap(_1600558, _1600554), hAPP(c_Fun_Ocomp(_1600552, _1600554, _1600558, _1600556), _1600560)), _1600562))], (12654 ^ _773908) ^ [_985989, _985991] : [12655 ^ _773908 : [(12658 ^ _773908) ^ [] : [_985989 = _985991], (12656 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985989), _985991))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985989), _985991)))], (12498 ^ _773908) ^ [_983366, _983368] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983366, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_983366, tc_HOL_Obool))), _983368)))], (51912 ^ _773908) ^ [_1818604, _1818606] : [hBOOL(_1818604), -(hBOOL(hAPP(hAPP(c_fdisj, _1818606), _1818604)))], (38084 ^ _773908) ^ [_1498170, _1498172, _1498174] : [-(hBOOL(hAPP(_1498170, _1498172))), -(hAPP(c_Set_OCollect(_1498174), hAPP(hAPP(c_COMBS(_1498174, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498174), c_fconj), hAPP(c_fequal, _1498172))), _1498170)) = c_Orderings_Obot__class_Obot(tc_fun(_1498174, tc_HOL_Obool)))], (50199 ^ _773908) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (46843 ^ _773908) ^ [_1712858, _1712860, _1712862, _1712864, _1712866] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712858), tc_List_Olist(_1712858))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712858), tc_List_Olist(_1712858)), _1712860), _1712862)), c_List_Olistrel(_1712858, c_Transitive__Closure_Ortrancl(_1712858, _1712864)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712858), tc_List_Olist(_1712858))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712858), tc_List_Olist(_1712858)), _1712862), _1712866)), c_List_Olistrel(_1712858, c_Transitive__Closure_Ortrancl(_1712858, _1712864)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712858), tc_List_Olist(_1712858))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712858), tc_List_Olist(_1712858)), _1712860), _1712866)), c_List_Olistrel(_1712858, c_Transitive__Closure_Ortrancl(_1712858, _1712864)))))], (426 ^ _773908) ^ [_780483, _780485, _780487, _780489, _780491, _780493] : [-(c_Hoare__Mirabelle_Otriple__valid(_780491, _780487, _780483)), c_Hoare__Mirabelle_Otriple__valid(_780493, _780489, _780485), _780493 = _780491, _780489 = _780487, _780485 = _780483], (23353 ^ _773908) ^ [_1180388, _1180390] : [-(c_Divides_OposDivAlg(_1180388, _1180390) = hAPP(c_Divides_Oadjust(_1180390), c_Divides_OposDivAlg(_1180388, 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)))), _1180390)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180388), _1180390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180390), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18813 ^ _773908) ^ [_1099392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099392), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099392)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1099392)))], (26235 ^ _773908) ^ [_1239835, _1239837, _1239839, _1239841] : [hBOOL(hAPP(hAPP(c_member(_1239835), _1239837), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239835, tc_HOL_Obool)), _1239839), _1239841))), -(hBOOL(hAPP(hAPP(c_member(_1239835), _1239837), _1239839))), -(hBOOL(hAPP(hAPP(c_member(_1239835), _1239837), _1239841)))], (9509 ^ _773908) ^ [_932266, _932268, _932270] : [class_Rings_Olinordered__idom(_932266), 9512 ^ _773908 : [(9519 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _932268), _932270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932266), hAPP(c_Int_Oring__1__class_Oof__int(_932266), _932268)), hAPP(c_Int_Oring__1__class_Oof__int(_932266), _932270))))], (9513 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932266), hAPP(c_Int_Oring__1__class_Oof__int(_932266), _932268)), hAPP(c_Int_Oring__1__class_Oof__int(_932266), _932270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _932268), _932270)))]]], (27480 ^ _773908) ^ [_1270534, _1270536, _1270538, _1270540, _1270542, _1270544, _1270546, _1270548, _1270550, _1270552, _1270554] : [c_Finite__Set_Ofolding(_1270534, _1270536, _1270538, _1270540), -(hAPP(c_Fun_Ocomp(_1270542, _1270544, _1270546, _1270548), hAPP(c_Fun_Ocomp(_1270550, _1270542, _1270546, _1270552), _1270554)) = hAPP(c_Fun_Ocomp(_1270550, _1270544, _1270546, hAPP(c_Fun_Ocomp(_1270542, _1270544, _1270550, _1270548), _1270552)), _1270554))], (25989 ^ _773908) ^ [_1234470, _1234472, _1234474, _1234476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234470, tc_HOL_Obool)), _1234472), _1234474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234470, tc_HOL_Obool)), _1234476), _1234474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234470, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234470, tc_HOL_Obool)), _1234472), _1234476)), _1234474)))], (36749 ^ _773908) ^ [_1466419, _1466421] : [class_Lattices_Olattice(_1466419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466419), _1466421)), -(c_Big__Operators_Olattice__class_OInf__fin(_1466419, _1466421) = hAPP(c_Finite__Set_Ofold1(_1466419, c_Lattices_Osemilattice__inf__class_Oinf(_1466419)), _1466421))], (51802 ^ _773908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (46665 ^ _773908) ^ [_1708175, _1708177, _1708179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1708175, _1708175)), _1708177), c_Transitive__Closure_Ortrancl(_1708175, _1708179))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708175, _1708175)), _1708177), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1708175, _1708175), 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(_1708175, _1708175), tc_HOL_Obool), tc_fun(tc_prod(_1708175, _1708175), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1708175, _1708175), tc_HOL_Obool)), _1708179)))))], (19237 ^ _773908) ^ [_1106056, _1106058] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106056), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106056)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106058)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1106056), _1106058)))], (8146 ^ _773908) ^ [_907559, _907561, _907563, _907565] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907559, _907561)), _907563), _907565)), 8151 ^ _773908 : [(8154 ^ _773908) ^ [] : [hBOOL(hAPP(_907559, _907563))], (8152 ^ _773908) ^ [] : [-(_907565 = _907563)]], 8155 ^ _773908 : [(8161 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907559, _907561)), 8157 ^ [_907559, _907561, _907563, _907565]), _907565)))], (8159 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907561), _907563), 8157 ^ [_907559, _907561, _907563, _907565])))], (8156 ^ _773908) ^ [] : [-(hBOOL(hAPP(_907559, _907563)))]]], (4584 ^ _773908) ^ [_843642, _843644, _843646, _843648] : [-(c_List_Oupt(_843648, _843644) = c_List_Oupt(_843646, _843642)), _843648 = _843646, _843644 = _843642], (31874 ^ _773908) ^ [_1363576, _1363578, _1363580, _1363582, _1363584] : [-(_1363576 = c_Orderings_Obot__class_Obot(tc_fun(_1363578, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363578, tc_fun(_1363580, tc_HOL_Obool)), _1363576), hAPP(hAPP(c_COMBC(_1363578, tc_fun(_1363580, tc_HOL_Obool), tc_fun(_1363580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363580, tc_HOL_Obool), tc_fun(tc_fun(_1363580, tc_HOL_Obool), tc_fun(_1363580, tc_HOL_Obool)), _1363578), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363580, tc_HOL_Obool))), _1363582)), _1363584)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363580, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363578, tc_fun(_1363580, tc_HOL_Obool)), _1363576), _1363582)), _1363584))], (5751 ^ _773908) ^ [_864765, _864767, _864769, _864771] : [c_Hoare__Mirabelle_Ohoare__derivs(_864765, _864767, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_864765)), _864769), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_864765), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_864765, _864767, _864771), -(c_Hoare__Mirabelle_Ohoare__derivs(_864765, _864767, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_864765)), _864769), _864771)))], (15873 ^ _773908) ^ [_1044345, _1044347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044345), _1044347)), -(c_Nat__Transfer_Otsub(_1044347, _1044345) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044347), _1044345))], (29551 ^ _773908) ^ [_1313439, _1313441, _1313443] : [class_Orderings_Olinorder(_1313439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313439), _1313441)), hBOOL(hAPP(hAPP(c_member(_1313439), _1313443), _1313441)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313439), _1313443), c_Big__Operators_Olinorder__class_OMin(_1313439, _1313441)) = c_Big__Operators_Olinorder__class_OMin(_1313439, _1313441))], (24233 ^ _773908) ^ [_1197853, _1197855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197855)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197853, _1197855) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1197853, _1197855)))], (45907 ^ _773908) ^ [_1691313, _1691315, _1691317] : [-(hAPP(hAPP(c_List_Oappend(_1691313), c_List_OtakeWhile(_1691313, _1691315, _1691317)), c_List_OdropWhile(_1691313, _1691315, _1691317)) = _1691317)], (8539 ^ _773908) ^ [_915028, _915030, _915032] : [class_Rings_Oring(_915028), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915028), hAPP(c_Groups_Ouminus__class_Ouminus(_915028), _915030)), hAPP(c_Groups_Ouminus__class_Ouminus(_915028), _915032)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915028), _915030), _915032))], (48167 ^ _773908) ^ [_1744761, _1744763, _1744765] : [class_Complete__Lattice_Ocomplete__lattice(_1744761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1744761), _1744763)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1744761), _1744765), c_Complete__Lattice_OSup__class_OSup(_1744761, _1744763)) = hAPP(hAPP(c_Finite__Set_Ofold(_1744761, _1744761, c_Lattices_Osemilattice__sup__class_Osup(_1744761)), _1744765), _1744763))], (12244 ^ _773908) ^ [_978994, _978996] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978994)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978996))))), _978994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _978996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41722 ^ _773908) ^ [_1595835, _1595837] : [-(_1595835 = c_List_Olist_ONil(_1595837)), hBOOL(hAPP(c_List_Odistinct(_1595837), _1595835)), -(hBOOL(hAPP(c_List_Odistinct(_1595837), c_List_Obutlast(_1595837, _1595835))))], (3828 ^ _773908) ^ [_831640, _831642, _831644, _831646] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_831646, _831642) = c_SetInterval_Oord__class_OatLeastLessThan(_831644, _831640)), _831646 = _831644, _831642 = _831640], (48663 ^ _773908) ^ [_1754492, _1754494, _1754496, _1754498, _1754500] : [c_Finite__Set_Ofun__left__comm(_1754492, _1754494, _1754496), hBOOL(hAPP(c_Finite__Set_Ofinite(_1754492), _1754498)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1754492, _1754494, _1754496, _1754500, _1754498), hAPP(hAPP(c_Finite__Set_Ofold(_1754492, _1754494, _1754496), _1754500), _1754498))))], (44329 ^ _773908) ^ [_1657649, _1657651, _1657653] : [-(hBOOL(hAPP(hAPP(c_member(_1657649), _1657651), hAPP(c_List_Oset(_1657649), _1657653)))), -(c_List_Oinsert(_1657649, _1657651, _1657653) = hAPP(hAPP(c_List_Olist_OCons(_1657649), _1657651), _1657653))], (16929 ^ _773908) ^ [_1065259, _1065261, _1065263, _1065265] : [class_Int_Onumber__ring(_1065259), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065259), hAPP(c_Int_Onumber__class_Onumber__of(_1065259), _1065261)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065259), hAPP(c_Int_Onumber__class_Onumber__of(_1065259), _1065263)), _1065265)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065259), hAPP(c_Int_Onumber__class_Onumber__of(_1065259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065261), _1065263))), _1065265))], (19693 ^ _773908) ^ [_1113530, _1113532] : [class_Int_Onumber__ring(_1113530), class_Rings_Olinordered__idom(_1113530), 19700 ^ _773908 : [(19707 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113532), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113530), hAPP(c_Int_Onumber__class_Onumber__of(_1113530), _1113532)), c_Groups_Oone__class_Oone(_1113530))))], (19701 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113530), hAPP(c_Int_Onumber__class_Onumber__of(_1113530), _1113532)), c_Groups_Oone__class_Oone(_1113530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113532), c_Int_OBit1(c_Int_OPls))))]]], (38800 ^ _773908) ^ [_1523416, _1523418, _1523420, _1523422] : [_1523418 = _1523422, -(hAPP(hAPP(c_List_Oappend(_1523416), _1523418), _1523420) = hAPP(hAPP(c_List_Oappend(_1523416), _1523422), _1523420))], (15125 ^ _773908) ^ [_1030115, _1030117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030115), _1030117)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1030117), _1030115) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030117), _1030115)), _1030115)))], (26683 ^ _773908) ^ [_1253880, _1253882] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1253880), _1253882) = 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)), _1253880)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253882))))], (19977 ^ _773908) ^ [_1118663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118663), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1118663)), c_Int_OPls)))], (34500 ^ _773908) ^ [_1416479, _1416481] : [class_Orderings_Oorder(_1416479), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416479, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1416479), _1416481)), hAPP(c_SetInterval_Oord__class_OatLeast(_1416479), _1416481)) = hAPP(hAPP(c_Set_Oinsert(_1416479), _1416481), c_Orderings_Obot__class_Obot(tc_fun(_1416479, tc_HOL_Obool))))], (20535 ^ _773908) ^ [_1128573, _1128575, _1128577] : [class_Groups_Omonoid__mult(_1128573), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128573), _1128575), 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)))), _1128577))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128573), _1128575), hAPP(hAPP(c_Power_Opower__class_Opower(_1128573), hAPP(hAPP(c_Power_Opower__class_Opower(_1128573), _1128575), _1128577)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (4396 ^ _773908) ^ [_840790, _840792, _840794, _840796] : [-(c_Lazy__Sequence_Ohb__single(_840796, _840792) = c_Lazy__Sequence_Ohb__single(_840794, _840790)), _840796 = _840794, _840792 = _840790], (41067 ^ _773908) ^ [_1582838, _1582840, _1582842, _1582844] : [hBOOL(hAPP(c_List_Odistinct(_1582838), _1582840)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1582842, _1582838)), hAPP(hAPP(c_List_Ozip(_1582842, _1582838), _1582844), _1582840))))], (33744 ^ _773908) ^ [_1400830] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1400830)) = hAPP(c_Nat_OSuc, _1400830))], (9449 ^ _773908) ^ [_931346, _931348] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931346)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931348)), _931346 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _931348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36071 ^ _773908) ^ [_1450654, _1450656, _1450658, _1450660, _1450662] : [c_Fun_Oinj__on(_1450654, _1450656, _1450658, c_Orderings_Otop__class_Otop(tc_fun(_1450654, tc_HOL_Obool))), c_Fun_Oinj__on(_1450660, _1450654, _1450662, c_Orderings_Otop__class_Otop(tc_fun(_1450660, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1450660, _1450656, hAPP(c_Fun_Ocomp(_1450654, _1450656, _1450660, _1450658), _1450662), c_Orderings_Otop__class_Otop(tc_fun(_1450660, tc_HOL_Obool))))], (43735 ^ _773908) ^ [_1643842, _1643844, _1643846, _1643848] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1643842, tc_fun(_1643844, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643842, tc_HOL_Obool), _1643846)), _1643848) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643842, tc_HOL_Obool), tc_fun(_1643844, tc_HOL_Obool)), _1643846), hAPP(hAPP(c_COMBC(tc_fun(_1643842, tc_HOL_Obool), tc_fun(_1643842, tc_fun(_1643844, tc_HOL_Obool)), tc_fun(_1643844, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1643842, tc_fun(_1643844, tc_HOL_Obool))), _1643848)))], (26900 ^ _773908) ^ [_1258485, _1258487] : [c_Nat__Transfer_Onat__set(_1258485), c_Nat__Transfer_Onat__set(_1258487), 26907 ^ _773908 : [(26914 ^ _773908) ^ [] : [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), _1258485)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258485), _1258487)))], (26908 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258485), _1258487)), -(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), _1258485)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258487))))]]], (51173 ^ _773908) ^ [_1809799, _1809801, _1809803, _1809805, _1809807, _1809809, _1809811] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1809799, tc_HOL_Obool)), _1809801), _1809803) = c_Orderings_Obot__class_Obot(tc_fun(_1809799, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1809805, tc_HOL_Obool)), _1809807), _1809809) = c_Orderings_Obot__class_Obot(tc_fun(_1809805, tc_HOL_Obool)), c_Fun_Obij__betw(_1809799, _1809805, _1809811, _1809801, _1809807), c_Fun_Obij__betw(_1809799, _1809805, _1809811, _1809803, _1809809), -(c_Fun_Obij__betw(_1809799, _1809805, _1809811, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1809799, tc_HOL_Obool)), _1809801), _1809803), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1809805, tc_HOL_Obool)), _1809807), _1809809)))], (2500 ^ _773908) ^ [_810756, _810758, _810760, _810762, _810764, _810766, _810768, _810770, _810772, _810774] : [-(c_Product__Type_Oprod_Oprod__rec(_810774, _810770, _810766, _810762, _810758) = c_Product__Type_Oprod_Oprod__rec(_810772, _810768, _810764, _810760, _810756)), _810774 = _810772, _810770 = _810768, _810766 = _810764, _810762 = _810760, _810758 = _810756], (5550 ^ _773908) ^ [_858823, _858825] : [_858825 = _858823, -(tc_List_Olist(_858825) = tc_List_Olist(_858823))], (46063 ^ _773908) ^ [_1694532, _1694534, _1694536, _1694538] : [46065 ^ _773908 : [(46070 ^ _773908) ^ [] : [hBOOL(hAPP(_1694538, hAPP(hAPP(c_List_Onth(_1694534), _1694536), 46064 ^ [_1694532, _1694534, _1694536, _1694538])))], (46068 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46064 ^ [_1694532, _1694534, _1694536, _1694538]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694534)), _1694536))))], (46066 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46064 ^ [_1694532, _1694534, _1694536, _1694538]), _1694532)))]], 46073 ^ _773908 : [(46076 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1694538, hAPP(hAPP(c_List_Onth(_1694534), _1694536), _1694532))))], (46074 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694532), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694534)), _1694536))))]], -(c_List_OtakeWhile(_1694534, _1694538, _1694536) = hAPP(hAPP(c_List_Otake(_1694534), _1694532), _1694536))], (13147 ^ _773908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (39952 ^ _773908) ^ [_1553935] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1553935)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1553935), tc_HOL_Obool))))], (28220 ^ _773908) ^ [_1285528, _1285530, _1285532, _1285534] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285528, tc_HOL_Obool)), _1285530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285528, tc_HOL_Obool)), _1285532), _1285534)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285528, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285528, tc_HOL_Obool)), _1285530), _1285532)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285528, tc_HOL_Obool)), _1285530), _1285534)))], (37187 ^ _773908) ^ [_1475021, _1475023, _1475025, _1475027, _1475029] : [hBOOL(hAPP(hAPP(c_member(_1475025), hAPP(_1475027, _1475023)), _1475029)), -(hBOOL(hAPP(hAPP(c_member(_1475021), _1475023), hAPP(c_Set_Ovimage(_1475021, _1475025, _1475027), _1475029))))], (13602 ^ _773908) ^ [_1002731, _1002733, _1002735, _1002737] : [class_Divides_Osemiring__div(_1002731), -(c_Divides_Odiv__class_Omod(_1002731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002731), _1002733), _1002735), _1002737) = c_Divides_Odiv__class_Omod(_1002731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002731), c_Divides_Odiv__class_Omod(_1002731, _1002733, _1002737)), c_Divides_Odiv__class_Omod(_1002731, _1002735, _1002737)), _1002737))], (43894 ^ _773908) ^ [_1647405, _1647407, _1647409] : [class_Complete__Lattice_Ocomplete__lattice(_1647405), -(c_Complete__Lattice_OSup__class_OSup(_1647405, hAPP(hAPP(c_Set_Oinsert(_1647405), _1647407), _1647409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1647405), _1647407), c_Complete__Lattice_OSup__class_OSup(_1647405, _1647409)))], (39412 ^ _773908) ^ [_1539348, _1539350] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1539348)), _1539350) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1539350 = c_List_Olist_ONil(_1539348))], (51530 ^ _773908) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (5328 ^ _773908) ^ [_855334, _855336] : [_855336 = _855334, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_855336) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_855334))], (38456 ^ _773908) ^ [_1513646, _1513648] : [-(c_Fun_Oinj__on(_1513646, _1513646, c_Fun_Oid(_1513646), _1513648))], (43687 ^ _773908) ^ [_1642631, _1642633, _1642635, _1642637] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1642631, tc_HOL_Obool)), _1642633), _1642635)), hBOOL(hAPP(hAPP(c_member(_1642631), _1642637), _1642633)), -(hBOOL(hAPP(hAPP(c_member(_1642631), _1642637), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642631, tc_HOL_Obool), _1642635))))], (26365 ^ _773908) ^ [_1245149, _1245151, _1245153, _1245155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1245149, tc_HOL_Obool), tc_fun(_1245149, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1245149, tc_HOL_Obool), tc_fun(_1245149, tc_HOL_Obool)), _1245153), _1245155)), c_Wellfounded_Omax__ext(_1245149, _1245151))), -(c_Wellfounded_Omax__extp(_1245149, hAPP(hAPP(c_COMBC(_1245149, tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_fun(_1245149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1245149, tc_fun(tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_fun(_1245149, tc_HOL_Obool)), _1245149), c_COMBC(_1245149, tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1245149, tc_prod(_1245149, _1245149)), tc_fun(_1245149, tc_fun(tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_HOL_Obool)), _1245149), hAPP(c_COMBB(tc_prod(_1245149, _1245149), tc_fun(tc_fun(tc_prod(_1245149, _1245149), tc_HOL_Obool), tc_HOL_Obool), _1245149), c_member(tc_prod(_1245149, _1245149)))), c_Product__Type_OPair(_1245149, _1245149)))), _1245151), _1245153, _1245155))], (41732 ^ _773908) ^ [_1595986, _1595988, _1595990, _1595992] : [41733 ^ _773908 : [(41736 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1595986), _1595988), hAPP(c_List_Oset(_1595986), c_List_Obutlast(_1595986, _1595992))))], (41734 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1595986), _1595988), hAPP(c_List_Oset(_1595986), c_List_Obutlast(_1595986, _1595990))))]], -(hBOOL(hAPP(hAPP(c_member(_1595986), _1595988), hAPP(c_List_Oset(_1595986), c_List_Obutlast(_1595986, hAPP(hAPP(c_List_Oappend(_1595986), _1595990), _1595992))))))], (49474 ^ _773908) ^ [_1772651, _1772653, _1772655, _1772657, _1772659] : [c_List_Oreplicate(_1772651, _1772653, _1772655) = c_List_Oreplicate(_1772651, _1772657, _1772659), 49477 ^ _773908 : [(49480 ^ _773908) ^ [] : [-(_1772653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1772655 = _1772659)], (49478 ^ _773908) ^ [] : [-(_1772653 = _1772657)]]], (26962 ^ _773908) ^ [_1259413] : [26964 ^ _773908 : [(26967 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26963 ^ [_1259413]))], (26965 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26963 ^ [_1259413]), _1259413)))]], -(c_Nat__Transfer_Onat__set(_1259413))], (5887 ^ _773908) ^ [_868104] : [hAPP(c_Com_Ocom_OBODY, _868104) = c_Com_Ocom_OSKIP], (28694 ^ _773908) ^ [_1297641, _1297643, _1297645, _1297647] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1297641, tc_HOL_Obool)), _1297643), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1297641), _1297645), _1297647))), 28698 ^ _773908 : [(28701 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1297641), 28697 ^ [_1297641, _1297643, _1297645, _1297647]), _1297645)))], (28699 ^ _773908) ^ [] : [-(_1297643 = hAPP(c_Relation_OImage(_1297641, _1297641, _1297647), hAPP(hAPP(c_Set_Oinsert(_1297641), 28697 ^ [_1297641, _1297643, _1297645, _1297647]), c_Orderings_Obot__class_Obot(tc_fun(_1297641, tc_HOL_Obool)))))]]], (672 ^ _773908) ^ [_784150, _784152, _784154, _784156, _784158, _784160] : [-(c_Finite__Set_Ofolding__one(_784158, _784154, _784150)), c_Finite__Set_Ofolding__one(_784160, _784156, _784152), _784160 = _784158, _784156 = _784154, _784152 = _784150], (40503 ^ _773908) ^ [_1567550, _1567552, _1567554] : [-(_1567550 = c_List_Olist_ONil(_1567552)), -(hBOOL(hAPP(hAPP(c_member(_1567552), hAPP(c_Product__Type_Ofst(_1567552, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1567552, _1567550), _1567554))), hAPP(c_List_Oset(_1567552), _1567550))))], (28214 ^ _773908) ^ [_1285287, _1285289, _1285291, _1285293] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285287, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285287, tc_HOL_Obool)), _1285289), _1285291)), _1285293) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285287, tc_HOL_Obool)), _1285289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285287, tc_HOL_Obool)), _1285291), _1285293)))], (34826 ^ _773908) ^ [_1424280, _1424282, _1424284, _1424286, _1424288] : [class_Groups_Ocomm__monoid__add(_1424280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424282), _1424284)), -(hBOOL(hAPP(hAPP(c_member(_1424282), _1424286), _1424284))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424282, _1424280), _1424288), hAPP(hAPP(c_Set_Oinsert(_1424282), _1424286), _1424284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424280), hAPP(_1424288, _1424286)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424282, _1424280), _1424288), _1424284)))], (25679 ^ _773908) ^ [_1228814, _1228816, _1228818, _1228820, _1228822] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1228814, _1228814)), hAPP(hAPP(c_Product__Type_OPair(_1228814, _1228814), _1228816), _1228818)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1228814, _1228814), tc_HOL_Obool), _1228820), _1228822))), 25684 ^ _773908 : [(25687 ^ _773908) ^ [] : [-(_1228816 = _1228818)], (25685 ^ _773908) ^ [] : [-(_1228820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25690 ^ _773908 : [(25695 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1228814, _1228814)), hAPP(hAPP(c_Product__Type_OPair(_1228814, _1228814), 25688 ^ [_1228814, _1228816, _1228818, _1228820, _1228822]), _1228818)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1228814, _1228814), tc_HOL_Obool), 25689 ^ [_1228814, _1228816, _1228818, _1228820, _1228822]), _1228822))))], (25693 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1228814, _1228814)), hAPP(hAPP(c_Product__Type_OPair(_1228814, _1228814), _1228816), 25688 ^ [_1228814, _1228816, _1228818, _1228820, _1228822])), _1228822)))], (25691 ^ _773908) ^ [] : [-(_1228820 = hAPP(c_Nat_OSuc, 25689 ^ [_1228814, _1228816, _1228818, _1228820, _1228822]))]]], (18429 ^ _773908) ^ [_1092015, _1092017, _1092019] : [-(hBOOL(hAPP(hAPP(c_member(_1092015), _1092017), hAPP(hAPP(c_Set_Oinsert(_1092015), _1092017), _1092019))))], (39300 ^ _773908) ^ [_1537269, _1537271, _1537273, _1537275] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1537269), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1537271), _1537273)))), -(hAPP(c_Random_Opick(_1537271, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1537271)), _1537273), _1537275)), _1537269) = hAPP(c_Random_Opick(_1537271, _1537275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1537269), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1537271), _1537273))))], (36385 ^ _773908) ^ [_1458429, _1458431, _1458433, _1458435] : [_1458433 = _1458435, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1458429, _1458431, hAPP(hAPP(c_Set_Oinsert(_1458429), _1458433), c_Orderings_Obot__class_Obot(tc_fun(_1458429, tc_HOL_Obool)))), _1458435)))], (42189 ^ _773908) ^ [_1608871, _1608873, _1608875, _1608877, _1608879, _1608881] : [class_Complete__Lattice_Ocomplete__lattice(_1608871), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608873, _1608871), _1608875), hAPP(hAPP(c_COMBB(tc_fun(_1608877, _1608871), _1608871, _1608873), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608877, _1608871), _1608879)), _1608881)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608877, _1608871), _1608879), hAPP(hAPP(c_COMBB(tc_fun(_1608873, _1608871), _1608871, _1608877), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608873, _1608871), _1608875)), hAPP(c_COMBC(_1608873, _1608877, _1608871), _1608881))))], (7187 ^ _773908) ^ [_890150, _890152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890150), _890152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890150)), hAPP(c_Nat_OSuc, _890152))))], (11231 ^ _773908) ^ [_961065, _961067, _961069, _961071] : [class_Rings_Oordered__ring(_961065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961065), _961067), _961069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961065), _961071), c_Groups_Ozero__class_Ozero(_961065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961065), _961071), _961069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961065), _961071), _961067))))], (39278 ^ _773908) ^ [_1536037, _1536039, _1536041, _1536043, _1536045, _1536047, _1536049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536037, _1536037)), hAPP(hAPP(c_Product__Type_OPair(_1536037, _1536037), _1536039), _1536041)), _1536043)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1536037), tc_List_Olist(_1536037))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1536037), tc_List_Olist(_1536037)), hAPP(hAPP(c_List_Oappend(_1536037), _1536045), hAPP(hAPP(c_List_Olist_OCons(_1536037), _1536039), _1536047))), hAPP(hAPP(c_List_Oappend(_1536037), _1536045), hAPP(hAPP(c_List_Olist_OCons(_1536037), _1536041), _1536049)))), c_List_Olexord(_1536037, _1536043))))], (51690 ^ _773908) ^ [_1815999, _1816001] : [-(class_Enum_Oenum(tc_sum(_1815999, _1816001))), class_Enum_Oenum(_1815999), class_Enum_Oenum(_1816001)], (40733 ^ _773908) ^ [_1572979, _1572981, _1572983, _1572985, _1572987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1572979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572981)), _1572983))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1572979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572985)), _1572987))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1572981, _1572985)), hAPP(hAPP(c_List_Ozip(_1572981, _1572985), _1572983), _1572987)), _1572979) = hAPP(hAPP(c_Product__Type_OPair(_1572981, _1572985), hAPP(hAPP(c_List_Onth(_1572981), _1572983), _1572979)), hAPP(hAPP(c_List_Onth(_1572985), _1572987), _1572979)))], (3630 ^ _773908) ^ [_828617, _828619, _828621, _828623] : [-(c_List_Omeasures(_828623, _828619) = c_List_Omeasures(_828621, _828617)), _828623 = _828621, _828619 = _828617], (41882 ^ _773908) ^ [_1599114, _1599116, _1599118, _1599120, _1599122] : [class_Groups_Oab__group__add(_1599114), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1599114), hAPP(hAPP(c_List_Omap(_1599116, _1599114), hAPP(hAPP(c_COMBS(_1599116, _1599114, _1599114), hAPP(hAPP(c_COMBB(_1599114, tc_fun(_1599114, _1599114), _1599116), c_Groups_Ominus__class_Ominus(_1599114)), _1599118)), _1599120)), _1599122)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1599114), hAPP(c_List_Omonoid__add__class_Olistsum(_1599114), hAPP(hAPP(c_List_Omap(_1599116, _1599114), _1599118), _1599122))), hAPP(c_List_Omonoid__add__class_Olistsum(_1599114), hAPP(hAPP(c_List_Omap(_1599116, _1599114), _1599120), _1599122))))], (3640 ^ _773908) ^ [_828766, _828768, _828770, _828772, _828774, _828776] : [-(c_FunDef_Oin__rel(_828776, _828772, _828768) = c_FunDef_Oin__rel(_828774, _828770, _828766)), _828776 = _828774, _828772 = _828770, _828768 = _828766], (26818 ^ _773908) ^ [_1257160, _1257162, _1257164, _1257166, _1257168, _1257170, _1257172] : [-(_1257160 = _1257162), -(c_Fun_Ofun__upd(_1257164, _1257166, c_Fun_Ofun__upd(_1257164, _1257166, _1257168, _1257160, _1257170), _1257162, _1257172) = c_Fun_Ofun__upd(_1257164, _1257166, c_Fun_Ofun__upd(_1257164, _1257166, _1257168, _1257162, _1257172), _1257160, _1257170))], (20741 ^ _773908) ^ [_1132583, _1132585, _1132587, _1132589] : [class_Rings_Odivision__ring(_1132583), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132583), _1132585), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132583), _1132587), _1132589)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132583), _1132585), _1132587)), _1132589))], (16215 ^ _773908) ^ [_1051777, _1051779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051777)), 16218 ^ _773908 : [(16225 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051779), _1051777))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051779), _1051777) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051779), _1051777)), _1051777)))], (16219 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051779), _1051777)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051779), _1051777) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17857 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (8637 ^ _773908) ^ [_916919, _916921, _916923] : [class_Groups_Ogroup__add(_916919), 8640 ^ _773908 : [(8647 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916919), _916923) = _916921, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916919), _916921) = _916923)], (8641 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916919), _916921) = _916923, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916919), _916923) = _916921)]]], (23692 ^ _773908) ^ [_1187466, _1187468, _1187470, _1187472, _1187474, _1187476] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1187466, _1187466)), hAPP(hAPP(c_Product__Type_OPair(_1187466, _1187466), _1187468), _1187470)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1187466, _1187466), tc_HOL_Obool), _1187472), _1187474))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1187466, _1187466)), hAPP(hAPP(c_Product__Type_OPair(_1187466, _1187466), _1187470), _1187476)), _1187474)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1187466, _1187466)), hAPP(hAPP(c_Product__Type_OPair(_1187466, _1187466), _1187468), _1187476)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1187466, _1187466), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1187472)), _1187474))))], (36400 ^ _773908) ^ [_1458809, _1458811] : [c_Equiv__Relations_Oequiv(_1458809, c_Orderings_Otop__class_Otop(tc_fun(_1458809, tc_HOL_Obool)), _1458811), -(c_Equiv__Relations_Oequivp(_1458809, hAPP(hAPP(c_COMBC(_1458809, tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_fun(_1458809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458809, tc_fun(tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_fun(_1458809, tc_HOL_Obool)), _1458809), c_COMBC(_1458809, tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458809, tc_prod(_1458809, _1458809)), tc_fun(_1458809, tc_fun(tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_HOL_Obool)), _1458809), hAPP(c_COMBB(tc_prod(_1458809, _1458809), tc_fun(tc_fun(tc_prod(_1458809, _1458809), tc_HOL_Obool), tc_HOL_Obool), _1458809), c_member(tc_prod(_1458809, _1458809)))), c_Product__Type_OPair(_1458809, _1458809)))), _1458811)))], (49001 ^ _773908) ^ [_1762095, _1762097, _1762099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1762095), c_Nitpick_Oplus__frac(_1762095, _1762097, c_Nitpick_Ouminus__frac(_1762095, _1762099)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1762095, _1762097, _1762099))], (41794 ^ _773908) ^ [_1597236, _1597238] : [-(_1597236 = c_List_Olist_ONil(_1597238)), -(c_Random_Oselect__weight(_1597238, hAPP(hAPP(c_List_Omap(_1597238, tc_prod(tc_Code__Numeral_Ocode__numeral, _1597238)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1597238), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1597236)) = c_Random_Oselect(_1597238, _1597236))], (46810 ^ _773908) ^ [_1711937, _1711939, _1711941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1711937, _1711937)), _1711939), c_Transitive__Closure_Ortrancl(_1711937, _1711941))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1711937, _1711937)), _1711939), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1711937, _1711937), tc_HOL_Obool), 46813 ^ [_1711937, _1711939, _1711941]), _1711941))))], (43645 ^ _773908) ^ [_1641815, _1641817] : [_1641815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1641817, _1641815, c_List_Olist_ONil(_1641817)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1641817)), c_List_Olist_ONil(_1641817)), c_List_Olist_ONil(tc_List_Olist(_1641817))))], (3130 ^ _773908) ^ [_820835, _820837, _820839, _820841] : [-(c_Random_Oselect(_820841, _820837) = c_Random_Oselect(_820839, _820835)), _820841 = _820839, _820837 = _820835], (45589 ^ _773908) ^ [_1684653, _1684655, _1684657, _1684659] : [hAPP(c_List_Orev(_1684653), _1684655) = hAPP(hAPP(c_List_Olist_OCons(_1684653), _1684657), _1684659), -(_1684655 = hAPP(hAPP(c_List_Oappend(_1684653), hAPP(c_List_Orev(_1684653), _1684659)), hAPP(hAPP(c_List_Olist_OCons(_1684653), _1684657), c_List_Olist_ONil(_1684653))))], (28290 ^ _773908) ^ [_1287356, _1287358, _1287360, _1287362] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287356, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1287356, tc_fun(_1287356, tc_HOL_Obool), tc_HOL_Obool), c_member(_1287356)), _1287358)), hAPP(hAPP(c_COMBC(_1287356, tc_fun(_1287356, tc_HOL_Obool), tc_HOL_Obool), c_member(_1287356)), _1287360)), _1287362)), -(hBOOL(hAPP(hAPP(c_member(_1287356), _1287362), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287356, tc_HOL_Obool)), _1287358), _1287360))))], (17859 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (29007 ^ _773908) ^ [_1303572, _1303574, _1303576] : [class_Orderings_Olinorder(_1303572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303572, tc_HOL_Obool)), _1303574), _1303576)), -(_1303574 = c_Orderings_Obot__class_Obot(tc_fun(_1303572, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303572), _1303576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303572), c_Big__Operators_Olinorder__class_OMax(_1303572, _1303574)), c_Big__Operators_Olinorder__class_OMax(_1303572, _1303576))))], (41312 ^ _773908) ^ [_1587981, _1587983, _1587985] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1587981, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587983)), _1587985)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1587983, _1587981), _1587985) = _1587985)], (17091 ^ _773908) ^ [_1068538] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068538), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068538) = _1068538)], (19831 ^ _773908) ^ [_1116161, _1116163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116161)), c_Int_OBit0(_1116163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116161), _1116163)))], (8545 ^ _773908) ^ [_915157, _915159, _915161] : [class_Int_Oring__char__0(_915157), 8548 ^ _773908 : [(8555 ^ _773908) ^ [] : [_915159 = _915161, -(hAPP(c_Int_Oring__1__class_Oof__int(_915157), _915159) = hAPP(c_Int_Oring__1__class_Oof__int(_915157), _915161))], (8549 ^ _773908) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_915157), _915159) = hAPP(c_Int_Oring__1__class_Oof__int(_915157), _915161), -(_915159 = _915161)]]], (14781 ^ _773908) ^ [_1023754, _1023756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023754)), 14784 ^ _773908 : [(14791 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023756)), -(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), _1023756), _1023754))))], (14785 ^ _773908) ^ [] : [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), _1023756), _1023754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023756)))]]], (12927 ^ _773908) ^ [_990670, _990672, _990674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_990670), tc_HOL_Obool)), _990672), _990674)), -(c_Hoare__Mirabelle_Ohoare__derivs(_990670, _990674, _990672))], (19047 ^ _773908) ^ [_1102966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102966), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102966))], (35686 ^ _773908) ^ [_1443451, _1443453, _1443455, _1443457, _1443459] : [class_Groups_Ocomm__monoid__add(_1443451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443453), _1443455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443453, tc_HOL_Obool)), _1443457), _1443455)), 35700 ^ _773908 : [(35703 ^ _773908) ^ [] : [hAPP(_1443459, 35699 ^ [_1443451, _1443453, _1443455, _1443457, _1443459]) = c_Groups_Ozero__class_Ozero(_1443451)], (35701 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443453), 35699 ^ [_1443451, _1443453, _1443455, _1443457, _1443459]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443453, tc_HOL_Obool)), _1443455), _1443457))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443453, _1443451), _1443459), _1443457) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443453, _1443451), _1443459), _1443455))], (8383 ^ _773908) ^ [_912069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912069)), 8387 ^ _773908 : [(8390 ^ _773908) ^ [] : [-(_912069 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8386 ^ [_912069]))], (8388 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8386 ^ [_912069])))]]], (14093 ^ _773908) ^ [_1011490, _1011492, _1011494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011490)), 14096 ^ _773908 : [(14097 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1011492, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011494), _1011490)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011494, _1011490))), 14100 ^ _773908 : [(14101 ^ _773908) ^ [_1011691, _1011693] : [-(hBOOL(hAPP(hAPP(_1011492, _1011693), _1011691))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011691), _1011490)), _1011494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011490), _1011693)), _1011691)]]], (14115 ^ _773908) ^ [] : [14118 ^ _773908 : [(14121 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14117 ^ [_1011490, _1011492, _1011494]), _1011490)))], (14123 ^ _773908) ^ [] : [-(_1011494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011490), 14116 ^ [_1011490, _1011492, _1011494])), 14117 ^ [_1011490, _1011492, _1011494]))], (14125 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1011492, 14116 ^ [_1011490, _1011492, _1011494]), 14117 ^ [_1011490, _1011492, _1011494]))], (14119 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14117 ^ [_1011490, _1011492, _1011494])))]], -(hBOOL(hAPP(hAPP(_1011492, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011494), _1011490)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011494, _1011490))))]]], (25657 ^ _773908) ^ [_1228444, _1228446] : [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), _1228444), _1228446)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228444), _1228446)))], (35542 ^ _773908) ^ [_1440136, _1440138] : [class_Groups_Oordered__ab__group__add(_1440136), -(hAPP(c_Set_Oimage(_1440136, _1440136, c_Groups_Ouminus__class_Ouminus(_1440136)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440136), _1440138)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1440136), hAPP(c_Groups_Ouminus__class_Ouminus(_1440136), _1440138)))], (19255 ^ _773908) ^ [_1106329, _1106331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1106329)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106329)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1106331), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1106329))))], (43236 ^ _773908) ^ [_1632705, _1632707, _1632709, _1632711] : [hBOOL(hAPP(c_List_Olistsp(_1632705, _1632707), hAPP(hAPP(c_List_Olist_OCons(_1632705), _1632709), _1632711))), 43239 ^ _773908 : [(43242 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1632705, _1632707), _1632711)))], (43240 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1632707, _1632709)))]]], (16973 ^ _773908) ^ [_1066213, _1066215] : [class_Rings_Olinordered__idom(_1066213), -(hAPP(c_Groups_Oabs__class_Oabs(_1066213), _1066215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066213), _1066215), c_Groups_Osgn__class_Osgn(_1066213, _1066215)))], (50890 ^ _773908) ^ [_1803284, _1803286, _1803288, _1803290, _1803292, _1803294] : [hAPP(c_Set_Oimage(_1803284, _1803286, _1803288), _1803290) = _1803292, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803286, tc_HOL_Obool)), _1803294), _1803292)), -(hAPP(c_Set_Oimage(_1803284, _1803286, _1803288), hAPP(c_Set_Oimage(_1803286, _1803284, c_Hilbert__Choice_Oinv__into(_1803284, _1803286, _1803290, _1803288)), _1803294)) = _1803294)], (23105 ^ _773908) ^ [_1175284, _1175286] : [class_Rings_Osemiring__1(_1175284), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1175284), _1175286) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1175284, hAPP(hAPP(c_COMBC(_1175284, _1175284, _1175284), c_Groups_Oplus__class_Oplus(_1175284)), c_Groups_Oone__class_Oone(_1175284)), _1175286, c_Groups_Ozero__class_Ozero(_1175284)))], (41752 ^ _773908) ^ [_1596512, _1596514, _1596516, _1596518] : [_1596512 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596514)), _1596516)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1596514, hAPP(hAPP(c_List_Olist__update(_1596514, _1596516), _1596512), _1596518)) = c_List_Obutlast(_1596514, _1596516))], (24269 ^ _773908) ^ [_1198495, _1198497] : [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), _1198495), _1198497))), 24272 ^ _773908 : [(24279 ^ _773908) ^ [] : [-(_1198497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1198495, _1198497) = c_Nitpick_Onat__gcd(_1198497, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1198495, _1198497)))], (24273 ^ _773908) ^ [] : [_1198497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1198495, _1198497) = _1198495)]]], (48561 ^ _773908) ^ [_1752466, _1752468, _1752470] : [class_Orderings_Olinorder(_1752466), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752466), _1752468)), -(hBOOL(hAPP(hAPP(c_member(_1752466), _1752470), _1752468))), -(c_Big__Operators_Olattice_OInf__fin(_1752466, c_Orderings_Oord__class_Omin(_1752466), hAPP(hAPP(c_Set_Oinsert(_1752466), _1752470), _1752468)) = hAPP(hAPP(c_Finite__Set_Ofold(_1752466, _1752466, c_Orderings_Oord__class_Omin(_1752466)), _1752470), _1752468))], (51656 ^ _773908) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (19117 ^ _773908) ^ [_1104116, _1104118] : [class_Int_Onumber__ring(_1104116), class_Rings_Olinordered__idom(_1104116), 19124 ^ _773908 : [(19131 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104118), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104116), hAPP(c_Int_Onumber__class_Onumber__of(_1104116), _1104118)), c_Groups_Ozero__class_Ozero(_1104116))))], (19125 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104116), hAPP(c_Int_Onumber__class_Onumber__of(_1104116), _1104118)), c_Groups_Ozero__class_Ozero(_1104116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104118), c_Int_OPls)))]]], (19329 ^ _773908) ^ [_1107640, _1107642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107640)), c_Int_OBit1(_1107642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107640), _1107642)))], (37169 ^ _773908) ^ [_1474608, _1474610, _1474612, _1474614, _1474616] : [hBOOL(hAPP(hAPP(c_member(_1474608), hAPP(_1474610, _1474612)), _1474614)), -(hBOOL(hAPP(hAPP(c_member(_1474616), _1474612), hAPP(c_Set_Ovimage(_1474616, _1474608, _1474610), _1474614))))], (18869 ^ _773908) ^ [_1100174] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1100174) = _1100174)], (2448 ^ _773908) ^ [_809920, _809922, _809924, _809926] : [-(c_Divides_Odivmod__int(_809926, _809922) = c_Divides_Odivmod__int(_809924, _809920)), _809926 = _809924, _809922 = _809920], (48863 ^ _773908) ^ [_1758910, _1758912, _1758914, _1758916, _1758918, _1758920, _1758922, _1758924] : [c_Finite__Set_Ofolding__image__simple__idem(_1758910, _1758912, _1758914, _1758916, _1758918, _1758920), hBOOL(hAPP(c_Finite__Set_Ofinite(_1758912), _1758922)), hBOOL(hAPP(hAPP(c_member(_1758912), _1758924), _1758922)), -(hAPP(hAPP(_1758914, hAPP(_1758918, _1758924)), hAPP(_1758920, _1758922)) = hAPP(_1758920, _1758922))], (51446 ^ _773908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (22481 ^ _773908) ^ [_1163544, _1163546, _1163548, _1163550] : [class_Fields_Olinordered__field__inverse__zero(_1163544), class_Int_Onumber(_1163544), 22488 ^ _773908 : [(22489 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163544), _1163546), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))), _1163550)), 22492 ^ _773908 : [(22499 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)))), 22502 ^ _773908 : [(22509 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)), c_Groups_Ozero__class_Ozero(_1163544)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), _1163550)))], (22503 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)), c_Groups_Ozero__class_Ozero(_1163544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163544), _1163550), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))), _1163546)))]]], (22493 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), _1163546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163544), _1163550), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)))))]]], (22515 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163544), _1163546), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))), _1163550))), 22518 ^ _773908 : [(22521 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), _1163546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163544), _1163550), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))))], (22519 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))))]], 22522 ^ _773908 : [(22525 ^ _773908) ^ [] : [22526 ^ _773908 : [(22529 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163544), _1163550), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548))), _1163546))], (22527 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)), c_Groups_Ozero__class_Ozero(_1163544))))]], 22530 ^ _773908 : [(22533 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), _1163550))], (22531 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)), c_Groups_Ozero__class_Ozero(_1163544)))]]], (22523 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163544), c_Groups_Ozero__class_Ozero(_1163544)), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)))]]]]], (42888 ^ _773908) ^ [_1624761, _1624763] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1624761), _1624763) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624761)), hAPP(c_Code__Numeral_Onat__of, _1624763))))], (19437 ^ _773908) ^ [_1109438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109438), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1109438)), c_Int_OPls)))], (38895 ^ _773908) ^ [_1525446] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1525446)))], (6906 ^ _773908) ^ [_885660, _885662, _885664] : [_885660 = _885664, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885660), _885662) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885664), _885662))], (9611 ^ _773908) ^ [_934105, _934107] : [-(c_Int_Onat__aux(_934105, _934107) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _934105)), _934107))], (26023 ^ _773908) ^ [_1235189, _1235191, _1235193] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1235189, tc_HOL_Obool)), _1235191), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235189, tc_HOL_Obool)), _1235193), _1235191))))], (29919 ^ _773908) ^ [_1320095, _1320097, _1320099] : [class_Orderings_Olinorder(_1320095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320095), _1320097)), -(hBOOL(hAPP(hAPP(c_member(_1320095), _1320099), _1320097))), -(_1320097 = c_Orderings_Obot__class_Obot(tc_fun(_1320095, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1320095, c_Orderings_Oord__class_Omax(_1320095), hAPP(hAPP(c_Set_Oinsert(_1320095), _1320099), _1320097)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320095), _1320099), c_Big__Operators_Olattice_OSup__fin(_1320095, c_Orderings_Oord__class_Omax(_1320095), _1320097)))], (5496 ^ _773908) ^ [_858012, _858014] : [_858014 = _858012, -(c_Lattices_Osemilattice__inf__class_Oinf(_858014) = c_Lattices_Osemilattice__inf__class_Oinf(_858012))], (26806 ^ _773908) ^ [_1257009, _1257011, _1257013, _1257015, _1257017, _1257019] : [_1257009 = _1257011, -(hAPP(c_Fun_Ofun__upd(_1257013, _1257015, _1257017, _1257011, _1257019), _1257009) = _1257019)], (34546 ^ _773908) ^ [_1417587, _1417589, _1417591, _1417593] : [class_Rings_Osemiring__1(_1417587), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1417587), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417589, tc_Nat_Onat), _1417591), _1417593)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417589, _1417587), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417587, _1417589), c_Nat_Osemiring__1__class_Oof__nat(_1417587)), _1417591)), _1417593))], (49642 ^ _773908) ^ [_1775949, _1775951, _1775953, _1775955, _1775957] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1775949, _1775951, _1775953) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1775949, _1775955, _1775957), 49645 ^ _773908 : [(49648 ^ _773908) ^ [] : [-(_1775953 = _1775957)], (49646 ^ _773908) ^ [] : [-(_1775951 = _1775955)]]], (9773 ^ _773908) ^ [_936726, _936728, _936730] : [class_Orderings_Opreorder(_936726), _936728 = _936730, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936726), _936728), _936730)))], (43707 ^ _773908) ^ [_1643099] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643099, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1643099, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1643099, tc_HOL_Obool)))], (35873 ^ _773908) ^ [_1447017, _1447019, _1447021] : [class_Orderings_Otop(_1447017), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1447019, _1447017)), _1447021) = c_Orderings_Otop__class_Otop(_1447017))], (43163 ^ _773908) ^ [_1631122, _1631124, _1631126] : [43165 ^ _773908 : [(43168 ^ _773908) ^ [] : [hBOOL(hAPP(_1631124, 43164 ^ [_1631122, _1631124, _1631126]))], (43166 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631122), 43164 ^ [_1631122, _1631124, _1631126]), hAPP(c_List_Oset(_1631122), _1631126))))]], -(hBOOL(hAPP(c_List_Olistsp(_1631122, _1631124), _1631126)))], (38934 ^ _773908) ^ [_1526370, _1526372] : [c_Wellfounded_Owf(_1526370, _1526372), 38938 ^ _773908 : [(38939 ^ _773908) ^ [_1526506] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526370, _1526370)), hAPP(hAPP(c_Product__Type_OPair(_1526370, _1526370), hAPP(_1526506, hAPP(c_Nat_OSuc, 38937 ^ [_1526370, _1526372, _1526506]))), hAPP(_1526506, 38937 ^ [_1526370, _1526372, _1526506]))), _1526372))]]], (2160 ^ _773908) ^ [_805290, _805292, _805294, _805296] : [-(c_Random_Olog(_805296, _805292) = c_Random_Olog(_805294, _805290)), _805296 = _805294, _805292 = _805290], (8905 ^ _773908) ^ [_921333, _921335, _921337] : [class_Rings_Ono__zero__divisors(_921333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921333), _921335), _921337) = c_Groups_Ozero__class_Ozero(_921333), -(_921335 = c_Groups_Ozero__class_Ozero(_921333)), -(_921337 = c_Groups_Ozero__class_Ozero(_921333))], (44190 ^ _773908) ^ [_1654730, _1654732, _1654734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654730, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654730, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654730, tc_HOL_Obool), _1654732)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654730, tc_HOL_Obool), _1654734))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654730, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1654730, tc_HOL_Obool), tc_HOL_Obool)), _1654732), _1654734)))))], (27684 ^ _773908) ^ [_1274800, _1274802, _1274804, _1274806, _1274808] : [c_Equiv__Relations_Oequiv(_1274800, _1274802, _1274804), hBOOL(hAPP(hAPP(c_member(_1274800), _1274806), _1274802)), hBOOL(hAPP(hAPP(c_member(_1274800), _1274808), _1274802)), 27695 ^ _773908 : [(27702 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1274800, _1274800)), hAPP(hAPP(c_Product__Type_OPair(_1274800, _1274800), _1274806), _1274808)), _1274804)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1274800), hAPP(hAPP(c_Set_Oinsert(_1274800), _1274806), c_Orderings_Obot__class_Obot(tc_fun(_1274800, tc_HOL_Obool)))), _1274804) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1274800), hAPP(hAPP(c_Set_Oinsert(_1274800), _1274808), c_Orderings_Obot__class_Obot(tc_fun(_1274800, tc_HOL_Obool)))), _1274804))], (27696 ^ _773908) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1274800), hAPP(hAPP(c_Set_Oinsert(_1274800), _1274806), c_Orderings_Obot__class_Obot(tc_fun(_1274800, tc_HOL_Obool)))), _1274804) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1274800), hAPP(hAPP(c_Set_Oinsert(_1274800), _1274808), c_Orderings_Obot__class_Obot(tc_fun(_1274800, tc_HOL_Obool)))), _1274804), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1274800, _1274800)), hAPP(hAPP(c_Product__Type_OPair(_1274800, _1274800), _1274806), _1274808)), _1274804)))]]], (11457 ^ _773908) ^ [_965106, _965108] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965106), _965108) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965106 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965108 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41422 ^ _773908) ^ [_1590100, _1590102, _1590104] : [_1590100 = c_List_Olist_ONil(_1590102), -(c_List_Olast(_1590102, hAPP(hAPP(c_List_Olist_OCons(_1590102), _1590104), _1590100)) = _1590104)], (23919 ^ _773908) ^ [_1192223, _1192225, _1192227, _1192229, _1192231, _1192233] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192223, _1192225), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192227), _1192229))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192223, _1192225), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192231), _1192233))), -(_1192225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1192227 = _1192231)], (26568 ^ _773908) ^ [_1250225, _1250227, _1250229, _1250231, _1250233, _1250235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1250225, _1250227), tc_HOL_Obool)), _1250229), _1250231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250225, tc_HOL_Obool)), _1250233), _1250235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250227, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1250225, _1250227, _1250229), _1250233)), hAPP(c_Relation_OImage(_1250225, _1250227, _1250231), _1250235))))], (40745 ^ _773908) ^ [_1573365, _1573367, _1573369, _1573371, _1573373] : [-(hAPP(hAPP(c_List_Ozip(_1573365, _1573367), hAPP(hAPP(c_List_Oappend(_1573365), _1573369), _1573371)), _1573373) = hAPP(hAPP(c_List_Oappend(tc_prod(_1573365, _1573367)), hAPP(hAPP(c_List_Ozip(_1573365, _1573367), _1573369), hAPP(hAPP(c_List_Otake(_1573367), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573365)), _1573369)), _1573373))), hAPP(hAPP(c_List_Ozip(_1573365, _1573367), _1573371), hAPP(hAPP(c_List_Odrop(_1573367), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573365)), _1573369)), _1573373))))], (43715 ^ _773908) ^ [_1643292, _1643294, _1643296] : [c_Equiv__Relations_Oequiv(_1643292, _1643294, _1643296), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643292, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1643292), _1643294), _1643296)) = _1643294)], (49342 ^ _773908) ^ [_1769504, _1769506, _1769508, _1769510] : [-(c_Predicate_Oconversep(_1769504, _1769506, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1769504, tc_fun(_1769506, tc_HOL_Obool))), _1769508), _1769510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1769506, tc_fun(_1769504, tc_HOL_Obool))), c_Predicate_Oconversep(_1769504, _1769506, _1769508)), c_Predicate_Oconversep(_1769504, _1769506, _1769510)))], (27077 ^ _773908) ^ [_1261897, _1261899, _1261901, _1261903] : [c_Equiv__Relations_Oequiv(_1261897, _1261899, _1261901), hBOOL(hAPP(hAPP(c_member(_1261897), _1261903), _1261899)), -(hBOOL(hAPP(hAPP(c_member(_1261897), _1261903), hAPP(c_Relation_OImage(_1261897, _1261897, _1261901), hAPP(hAPP(c_Set_Oinsert(_1261897), _1261903), c_Orderings_Obot__class_Obot(tc_fun(_1261897, tc_HOL_Obool)))))))], (36393 ^ _773908) ^ [_1458568, _1458570, _1458572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458568, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1458568, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36394 ^ [_1458568, _1458570, _1458572])), _1458570)), _1458572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458568, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1458568, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1458570)), _1458572)))], (19243 ^ _773908) ^ [_1106132, _1106134, _1106136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106132), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106134)), _1106136)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38778 ^ _773908) ^ [_1522988, _1522990] : [c_Wellfounded_Owf(_1522988, _1522990), -(c_Wellfounded_Owf(tc_fun(_1522988, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1522988, _1522990)))], (30971 ^ _773908) ^ [_1341467, _1341469, _1341471, _1341473, _1341475] : [class_Groups_Ocomm__monoid__mult(_1341467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341469), _1341471)), 30978 ^ _773908 : [(30985 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341469), _1341473), _1341471))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341469, _1341467), hAPP(hAPP(c_COMBC(_1341469, _1341467, _1341467), hAPP(hAPP(c_COMBS(_1341469, _1341467, tc_fun(_1341467, _1341467)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1341467, tc_fun(_1341467, _1341467)), _1341469), c_If(_1341467)), hAPP(hAPP(c_COMBC(_1341469, _1341469, tc_HOL_Obool), c_fequal), _1341473))), _1341475)), c_Groups_Oone__class_Oone(_1341467))), _1341471) = c_Groups_Oone__class_Oone(_1341467))], (30979 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1341469), _1341473), _1341471)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341469, _1341467), hAPP(hAPP(c_COMBC(_1341469, _1341467, _1341467), hAPP(hAPP(c_COMBS(_1341469, _1341467, tc_fun(_1341467, _1341467)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1341467, tc_fun(_1341467, _1341467)), _1341469), c_If(_1341467)), hAPP(hAPP(c_COMBC(_1341469, _1341469, tc_HOL_Obool), c_fequal), _1341473))), _1341475)), c_Groups_Oone__class_Oone(_1341467))), _1341471) = hAPP(_1341475, _1341473))]]], (26037 ^ _773908) ^ [_1235464, _1235466, _1235468, _1235470] : [class_Lattices_Osemilattice__sup(_1235464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235464), _1235466), _1235468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235464), _1235466), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1235464), _1235468), _1235470))))], (50953 ^ _773908) ^ [_1804783, _1804785, _1804787, _1804789, _1804791, _1804793] : [c_Fun_Oinj__on(_1804783, _1804785, _1804787, _1804789), hBOOL(hAPP(hAPP(c_member(_1804783), _1804791), _1804789)), hAPP(_1804787, _1804791) = _1804793, -(hAPP(c_Hilbert__Choice_Oinv__into(_1804783, _1804785, _1804789, _1804787), _1804793) = _1804791)], (34702 ^ _773908) ^ [_1421573, _1421575, _1421577, _1421579, _1421581] : [class_Groups_Oab__group__add(_1421573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421575), _1421577)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421577), _1421579)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1421573), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421573), _1421581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421575), _1421579))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421573), _1421581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421575), _1421577))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421573), _1421581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421577), _1421579)))], (16147 ^ _773908) ^ [_1050505, _1050507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050505), _1050507)), -(c_Nat__Transfer_Otsub(_1050507, _1050505) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050507), _1050505))], (42173 ^ _773908) ^ [_1608181, _1608183, _1608185, _1608187, _1608189] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608181, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608183, tc_fun(_1608181, tc_HOL_Obool)), _1608185), _1608187)), _1608189) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608183, tc_fun(_1608181, tc_HOL_Obool)), _1608185), hAPP(hAPP(c_COMBC(_1608183, tc_fun(_1608181, tc_HOL_Obool), tc_fun(_1608181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608181, tc_HOL_Obool), tc_fun(tc_fun(_1608181, tc_HOL_Obool), tc_fun(_1608181, tc_HOL_Obool)), _1608183), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608181, tc_HOL_Obool))), _1608187)), _1608189)))], (25225 ^ _773908) ^ [_1219499, _1219501, _1219503, _1219505] : [class_Orderings_Olinorder(_1219499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219499), _1219501), _1219503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219499), _1219505), _1219503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219499), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219499), _1219501), _1219505)), _1219503)))], (39522 ^ _773908) ^ [_1541632, _1541634, _1541636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1541632), tc_List_Olist(_1541632))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1541632), tc_List_Olist(_1541632)), _1541634), c_List_Olist_ONil(_1541632))), c_List_Olex(_1541632, _1541636)))], (49918 ^ _773908) ^ [_1782222, _1782224, _1782226] : [c_List_Olist__all(tc_Int_Oint, _1782222, c_List_Oupto(_1782224, _1782226)), -(c_List_Oall__interval__int(_1782222, _1782224, _1782226))], (41932 ^ _773908) ^ [_1600712, _1600714, _1600716, _1600718, _1600720] : [hAPP(hAPP(c_List_Omap(_1600712, _1600714), _1600716), _1600718) = hAPP(hAPP(c_List_Omap(_1600712, _1600714), _1600720), _1600718), 41935 ^ _773908 : [(41936 ^ _773908) ^ [_1600835] : [hBOOL(hAPP(hAPP(c_member(_1600712), _1600835), hAPP(c_List_Oset(_1600712), _1600718))), -(hAPP(_1600716, _1600835) = hAPP(_1600720, _1600835))]]], (51342 ^ _773908) ^ [_1812587, _1812589] : [class_Lattices_Olattice(_1812587), -(class_Lattices_Olattice(tc_fun(_1812589, _1812587)))], (47321 ^ _773908) ^ [_1725016, _1725018, _1725020] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1725016, _1725018)), hAPP(c_Relation_Oconverse(_1725018, _1725016), _1725020))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1725018, _1725016)), _1725020)))], (44857 ^ _773908) ^ [_1670637, _1670639] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1670637))), c_List_Otranspose(_1670637, _1670639)) = c_List_Ofoldr(tc_List_Olist(_1670637), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670637)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670637))), _1670639, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34145 ^ _773908) ^ [_1409568] : [-(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)), _1409568))))], (42301 ^ _773908) ^ [_1612005, _1612007, _1612009, _1612011] : [_1612011 = c_List_Olist_ONil(_1612005), -(hAPP(hAPP(c_List_Omap(_1612005, _1612007), _1612009), _1612011) = c_List_Olist_ONil(_1612007))], (3726 ^ _773908) ^ [_830121, _830123] : [_830123 = _830121, -(c_List_Odistinct(_830123) = c_List_Odistinct(_830121))], (18431 ^ _773908) ^ [_1092078, _1092080, _1092082, _1092084] : [hBOOL(hAPP(hAPP(c_member(_1092078), _1092080), hAPP(hAPP(c_Set_Oinsert(_1092078), _1092082), _1092084))), -(_1092080 = _1092082), -(hBOOL(hAPP(hAPP(c_member(_1092078), _1092080), _1092084)))], (30015 ^ _773908) ^ [_1321964, _1321966, _1321968, _1321970, _1321972, _1321974] : [c_Finite__Set_Ofolding__idem(_1321964, _1321966, _1321968, _1321970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321964), _1321972)), -(hAPP(_1321970, hAPP(hAPP(c_Set_Oinsert(_1321964), _1321974), _1321972)) = hAPP(c_Fun_Ocomp(_1321966, _1321966, _1321966, hAPP(_1321970, _1321972)), hAPP(_1321968, _1321974)))], (42169 ^ _773908) ^ [_1607857, _1607859, _1607861, _1607863, _1607865] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607857, tc_fun(_1607859, tc_HOL_Obool)), _1607861), hAPP(hAPP(c_COMBS(_1607857, tc_fun(_1607859, tc_HOL_Obool), tc_fun(_1607859, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1607859, tc_HOL_Obool), tc_fun(tc_fun(_1607859, tc_HOL_Obool), tc_fun(_1607859, tc_HOL_Obool)), _1607857), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607859, tc_HOL_Obool))), _1607863)), _1607865)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607859, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607857, tc_fun(_1607859, tc_HOL_Obool)), _1607861), _1607863)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607857, tc_fun(_1607859, tc_HOL_Obool)), _1607861), _1607865)))], (42768 ^ _773908) ^ [_1622082, _1622084, _1622086] : [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, _1622082), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1622082)), _1622084)))), -(hBOOL(hAPP(hAPP(c_member(_1622082), hAPP(c_Product__Type_Ofst(_1622082, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1622082, _1622084), _1622086))), hAPP(c_List_Oset(_1622082), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1622082), _1622082), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1622082)), _1622084)))))], (21689 ^ _773908) ^ [_1149250, _1149252, _1149254, _1149256] : [class_Fields_Olinordered__field__inverse__zero(_1149250), 21692 ^ _773908 : [(21693 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149250), _1149254), _1149256))), 21696 ^ _773908 : [(21703 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), c_Groups_Ozero__class_Ozero(_1149250)), _1149256))), 21706 ^ _773908 : [(21713 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149256), c_Groups_Ozero__class_Ozero(_1149250)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149252), c_Groups_Ozero__class_Ozero(_1149250))))], (21707 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149256), c_Groups_Ozero__class_Ozero(_1149250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149250), _1149252), _1149256))))]]], (21697 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), c_Groups_Ozero__class_Ozero(_1149250)), _1149256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149250), _1149252), _1149256)), _1149254)))]]], (21719 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149250), _1149254), _1149256)))), 21722 ^ _773908 : [(21725 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149250), _1149252), _1149256)), _1149254))], (21723 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), c_Groups_Ozero__class_Ozero(_1149250)), _1149256)))]], 21726 ^ _773908 : [(21729 ^ _773908) ^ [] : [21730 ^ _773908 : [(21733 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149250), _1149252), _1149256)))], (21731 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149256), c_Groups_Ozero__class_Ozero(_1149250))))]], 21734 ^ _773908 : [(21737 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149252), c_Groups_Ozero__class_Ozero(_1149250)))], (21735 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), _1149256), c_Groups_Ozero__class_Ozero(_1149250)))]]], (21727 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149250), c_Groups_Ozero__class_Ozero(_1149250)), _1149256))]]]]], (29025 ^ _773908) ^ [_1303878, _1303880, _1303882] : [class_Lattices_Olattice(_1303878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303878), _1303880)), -(_1303880 = c_Orderings_Obot__class_Obot(tc_fun(_1303878, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1303878, hAPP(hAPP(c_Set_Oinsert(_1303878), _1303882), _1303880)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1303878), _1303882), c_Big__Operators_Olattice__class_OSup__fin(_1303878, _1303880)))], (47234 ^ _773908) ^ [_1722802, _1722804] : [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), _1722802), _1722804)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722802), _1722804)))], (50293 ^ _773908) ^ [_1791997, _1791999] : [c_Relation_Otrans(_1791997, _1791999), 50296 ^ _773908 : [(50297 ^ _773908) ^ [_1792133, _1792135] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791997, _1791997)), hAPP(hAPP(c_Product__Type_OPair(_1791997, _1791997), _1792135), _1792133)), _1791999)), 50300 ^ _773908 : [(50301 ^ _773908) ^ [_1792276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791997, _1791997)), hAPP(hAPP(c_Product__Type_OPair(_1791997, _1791997), _1792133), _1792276)), _1791999)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791997, _1791997)), hAPP(hAPP(c_Product__Type_OPair(_1791997, _1791997), _1792135), _1792276)), _1791999)))]]]]], (10131 ^ _773908) ^ [_942440] : [class_Rings_Ozero__neq__one(_942440), c_Groups_Oone__class_Oone(_942440) = c_Groups_Ozero__class_Ozero(_942440)], (50572 ^ _773908) ^ [_1797382, _1797384] : [hAPP(c_Relation_Oconverse(_1797382, _1797382), _1797384) = _1797384, -(c_Relation_Osym(_1797382, _1797384))], (7261 ^ _773908) ^ [_891258, _891260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _891258)), hAPP(c_Nat_OSuc, _891260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891258), _891260)))], (626 ^ _773908) ^ [_783487, _783489, _783491, _783493, _783495, _783497] : [-(c_Finite__Set_Ofolding__one__idem(_783495, _783491, _783487)), c_Finite__Set_Ofolding__one__idem(_783497, _783493, _783489), _783497 = _783495, _783493 = _783491, _783489 = _783487], (38044 ^ _773908) ^ [_1497007, _1497009, _1497011] : [-(hAPP(c_Set_OCollect(_1497007), hAPP(hAPP(c_COMBS(_1497007, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497007), c_fdisj), _1497009)), _1497011)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1497007, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1497007), _1497009)), hAPP(c_Set_OCollect(_1497007), _1497011)))], (19053 ^ _773908) ^ [] : [-(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))))], (51528 ^ _773908) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (6258 ^ _773908) ^ [_875385, _875387] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_875385, _875387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _875385)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _875387))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2616 ^ _773908) ^ [_812574, _812576, _812578, _812580, _812582, _812584] : [-(c_SetInterval_Oord_OgreaterThan(_812584, _812580, _812576) = c_SetInterval_Oord_OgreaterThan(_812582, _812578, _812574)), _812584 = _812582, _812580 = _812578, _812576 = _812574], (34268 ^ _773908) ^ [_1412112, _1412114, _1412116, _1412118, _1412120] : [c_Finite__Set_Ofolding__one__idem(_1412112, _1412114, _1412116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412112), _1412118)), -(_1412118 = c_Orderings_Obot__class_Obot(tc_fun(_1412112, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412112), _1412120)), -(_1412120 = c_Orderings_Obot__class_Obot(tc_fun(_1412112, tc_HOL_Obool))), -(hAPP(_1412116, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412112, tc_HOL_Obool)), _1412118), _1412120)) = hAPP(hAPP(_1412114, hAPP(_1412116, _1412118)), hAPP(_1412116, _1412120)))], (3258 ^ _773908) ^ [_822761, _822763] : [_822763 = _822761, -(c_Set_OPow(_822763) = c_Set_OPow(_822761))], (4574 ^ _773908) ^ [_843493, _843495, _843497, _843499] : [-(c_List_Omap(_843499, _843495) = c_List_Omap(_843497, _843493)), _843499 = _843497, _843495 = _843493], (26450 ^ _773908) ^ [_1247497, _1247499, _1247501, _1247503, _1247505] : [-(hAPP(c_Set_Oimage(_1247497, _1247499, _1247501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247497, tc_HOL_Obool)), _1247503), _1247505)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247499, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1247497, _1247499, _1247501), _1247503)), hAPP(c_Set_Oimage(_1247497, _1247499, _1247501), _1247505)))], (26495 ^ _773908) ^ [_1248622, _1248624, _1248626, _1248628, _1248630] : [hBOOL(hAPP(hAPP(c_member(_1248622), _1248624), _1248626)), -(hBOOL(hAPP(hAPP(c_member(_1248628), hAPP(_1248630, _1248624)), hAPP(c_Set_Oimage(_1248622, _1248628, _1248630), _1248626))))], (20283 ^ _773908) ^ [] : [-(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)))))], (31962 ^ _773908) ^ [_1366085, _1366087, _1366089, _1366091, _1366093, _1366095, _1366097] : [c_Equiv__Relations_Oequiv(_1366085, _1366087, _1366089), c_Equiv__Relations_Ocongruent(_1366085, tc_fun(_1366091, tc_HOL_Obool), _1366089, _1366093), hBOOL(hAPP(hAPP(c_member(tc_fun(_1366085, tc_HOL_Obool)), _1366095), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1366085), _1366087), _1366089))), 31976 ^ _773908 : [(31979 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1366091, tc_HOL_Obool)), hAPP(_1366093, 31975 ^ [_1366085, _1366087, _1366089, _1366091, _1366093, _1366095, _1366097])), _1366097))], (31977 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366085), 31975 ^ [_1366085, _1366087, _1366089, _1366091, _1366093, _1366095, _1366097]), _1366087)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1366091, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1366085, tc_fun(_1366091, tc_HOL_Obool)), _1366095), _1366093)), _1366097)))], (8709 ^ _773908) ^ [_918138, _918140] : [class_Groups_Ogroup__add(_918138), 8712 ^ _773908 : [(8719 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_918138) = _918140, -(c_Groups_Ozero__class_Ozero(_918138) = hAPP(c_Groups_Ouminus__class_Ouminus(_918138), _918140))], (8713 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_918138) = hAPP(c_Groups_Ouminus__class_Ouminus(_918138), _918140), -(c_Groups_Ozero__class_Ozero(_918138) = _918140)]]], (12809 ^ _773908) ^ [_988685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988685), _988685))))], (23267 ^ _773908) ^ [_1178921, _1178923, _1178925] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1178921, _1178923, _1178925, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1178923)], (26265 ^ _773908) ^ [_1240457, _1240459, _1240461, _1240463] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240457, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1240457, tc_fun(_1240457, tc_HOL_Obool), tc_HOL_Obool), c_member(_1240457)), _1240459)), hAPP(hAPP(c_COMBC(_1240457, tc_fun(_1240457, tc_HOL_Obool), tc_HOL_Obool), c_member(_1240457)), _1240461)), _1240463)), -(hBOOL(hAPP(hAPP(c_member(_1240457), _1240463), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240457, tc_HOL_Obool)), _1240459), _1240461))))], (41640 ^ _773908) ^ [_1594223] : [41642 ^ _773908 : [(41645 ^ _773908) ^ [] : [41641 ^ [_1594223] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41643 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 41641 ^ [_1594223]), hAPP(c_List_Oset(tc_Nat_Onat), _1594223))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1594223) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16387 ^ _773908) ^ [_1054837, _1054839] : [class_Groups_Oordered__ab__group__add__abs(_1054837), -(hAPP(c_Groups_Oabs__class_Oabs(_1054837), hAPP(c_Groups_Oabs__class_Oabs(_1054837), _1054839)) = hAPP(c_Groups_Oabs__class_Oabs(_1054837), _1054839))], (51502 ^ _773908) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (35885 ^ _773908) ^ [_1447211, _1447213, _1447215, _1447217] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1447211, _1447213, _1447215, _1447217, c_Orderings_Obot__class_Obot(tc_fun(_1447211, tc_HOL_Obool))), _1447217)))], (15957 ^ _773908) ^ [_1046473, _1046475, _1046477] : [hBOOL(hAPP(_1046473, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046475), _1046477))), 15960 ^ _773908 : [(15967 ^ _773908) ^ [_1046658] : [_1046475 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046477), _1046658), -(hBOOL(hAPP(_1046473, _1046658)))], (15961 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046475), _1046477)), -(hBOOL(hAPP(_1046473, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (20211 ^ _773908) ^ [_1122827] : [class_Int_Onumber__ring(_1122827), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122827), c_Groups_Oone__class_Oone(_1122827)), c_Groups_Oone__class_Oone(_1122827)) = hAPP(c_Int_Onumber__class_Onumber__of(_1122827), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (20095 ^ _773908) ^ [_1120652] : [-(c_Int_Osucc(c_Int_OBit1(_1120652)) = c_Int_OBit0(c_Int_Osucc(_1120652)))], (25011 ^ _773908) ^ [_1215061, _1215063, _1215065] : [class_Int_Onumber(_1215061), class_Orderings_Oord(_1215061), 25018 ^ _773908 : [(25025 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215061), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215063)), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215065)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215061), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215063)), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215065)) = hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215065))], (25019 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215061), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215063)), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215065))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215061), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215063)), hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215065)) = hAPP(c_Int_Onumber__class_Onumber__of(_1215061), _1215063))]]], (3146 ^ _773908) ^ [_821069, _821071, _821073, _821075] : [-(c_Code__Numeral_Onat__of__aux(_821075, _821071) = c_Code__Numeral_Onat__of__aux(_821073, _821069)), _821075 = _821073, _821071 = _821069], (34013 ^ _773908) ^ [_1406556, _1406558, _1406560] : [class_Orderings_Oorder(_1406556), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406556, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1406556), _1406558)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1406556, _1406558, _1406560)) = c_Orderings_Obot__class_Obot(tc_fun(_1406556, tc_HOL_Obool)))], (36717 ^ _773908) ^ [_1465748, _1465750, _1465752, _1465754] : [_1465748 = c_Finite__Set_Ofold1(_1465750, _1465752), -(hAPP(_1465748, hAPP(hAPP(c_Set_Oinsert(_1465750), _1465754), c_Orderings_Obot__class_Obot(tc_fun(_1465750, tc_HOL_Obool)))) = _1465754)], (18093 ^ _773908) ^ [_1086031] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086031))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086031)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51586 ^ _773908) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (12793 ^ _773908) ^ [_988391, _988393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988391), _988393))))], (49500 ^ _773908) ^ [_1773024, _1773026, _1773028, _1773030, _1773032, _1773034] : [-(hAPP(hAPP(c_List_Ozip(_1773024, _1773026), c_List_Oreplicate(_1773024, _1773028, _1773030)), c_List_Oreplicate(_1773026, _1773032, _1773034)) = c_List_Oreplicate(tc_prod(_1773024, _1773026), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1773028), _1773032), hAPP(hAPP(c_Product__Type_OPair(_1773024, _1773026), _1773030), _1773034)))], (8479 ^ _773908) ^ [_913673, _913675] : [-(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, _913673)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913675))))], (11685 ^ _773908) ^ [_969088, _969090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _969088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _969090)), 11692 ^ _773908 : [(11699 ^ _773908) ^ [] : [_969088 = _969090, -(hAPP(c_Int_Onat, _969088) = hAPP(c_Int_Onat, _969090))], (11693 ^ _773908) ^ [] : [hAPP(c_Int_Onat, _969088) = hAPP(c_Int_Onat, _969090), -(_969088 = _969090)]]], (14394 ^ _773908) ^ [_1017448, _1017450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017450)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1017448)), hAPP(c_Int_Onat, _1017450)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017448), _1017450)))], (25903 ^ _773908) ^ [_1232850, _1232852, _1232854] : [class_Lattices_Osemilattice__sup(_1232850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232850), _1232852), _1232854)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1232850), _1232854), _1232852) = _1232854)], (39129 ^ _773908) ^ [_1531489, _1531491, _1531493, _1531495] : [39130 ^ _773908 : [(39131 ^ _773908) ^ [_1531543] : [hBOOL(hAPP(hAPP(_1531493, _1531543), _1531495))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1531489, _1531491, _1531493), _1531495)))], (42313 ^ _773908) ^ [_1612170, _1612172, _1612174, _1612176] : [-(_1612170 = c_List_Olist_ONil(_1612172)), -(c_List_Olast(_1612174, hAPP(hAPP(c_List_Omap(_1612172, _1612174), _1612176), _1612170)) = hAPP(_1612176, c_List_Olast(_1612172, _1612170)))], (20723 ^ _773908) ^ [_1132148, _1132150] : [class_Rings_Odivision__ring(_1132148), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132148), c_Groups_Ozero__class_Ozero(_1132148)), _1132150) = c_Groups_Ozero__class_Ozero(_1132148))], (20777 ^ _773908) ^ [_1133367, _1133369, _1133371, _1133373] : [class_Fields_Ofield__inverse__zero(_1133367), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1133367), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133367), _1133369), _1133371)), _1133373) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133367), hAPP(hAPP(c_Power_Opower__class_Opower(_1133367), _1133369), _1133373)), hAPP(hAPP(c_Power_Opower__class_Opower(_1133367), _1133371), _1133373)))], (1814 ^ _773908) ^ [_799569, _799571] : [-(class_Rings_Osemiring__1(_799569)), _799571 = _799569, class_Rings_Osemiring__1(_799571)], (23582 ^ _773908) ^ [_1185181, _1185183, _1185185] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185181, _1185183), _1185185)), -(c_Divides_Odivmod__nat(_1185181, _1185183) = _1185185)], (10285 ^ _773908) ^ [_944592, _944594, _944596] : [class_Orderings_Oorder(_944592), -(_944594 = _944596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944592), _944594), _944596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944592), _944594), _944596)))], (24523 ^ _773908) ^ [_1204673, _1204675] : [hBOOL(hAPP(hAPP(c_member(_1204673), _1204675), c_Orderings_Obot__class_Obot(tc_fun(_1204673, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1204673, tc_HOL_Obool)), _1204675)))], (6750 ^ _773908) ^ [_883247, _883249, _883251] : [class_Orderings_Olinorder(_883247), 6753 ^ _773908 : [(6754 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883247), _883249), _883251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883247), _883251), _883249))), -(_883249 = _883251)], (6764 ^ _773908) ^ [] : [6765 ^ _773908 : [(6768 ^ _773908) ^ [] : [_883249 = _883251], (6766 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883247), _883251), _883249))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883247), _883249), _883251))]]], (51438 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (39995 ^ _773908) ^ [_1555033, _1555035, _1555037, _1555039] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1555033), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555035)), _1555037)))), -(hAPP(hAPP(c_List_Onth(_1555035), hAPP(hAPP(c_List_Oappend(_1555035), _1555037), _1555039)), _1555033) = hAPP(hAPP(c_List_Onth(_1555035), _1555039), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1555033), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555035)), _1555037))))], (2382 ^ _773908) ^ [_808847, _808849, _808851, _808853, _808855, _808857, _808859, _808861, _808863, _808865] : [-(c_Nitpick_Opair__box_Opair__box__case(_808865, _808861, _808857, _808853, _808849) = c_Nitpick_Opair__box_Opair__box__case(_808863, _808859, _808855, _808851, _808847)), _808865 = _808863, _808861 = _808859, _808857 = _808855, _808853 = _808851, _808849 = _808847], (37145 ^ _773908) ^ [_1474025, _1474027, _1474029] : [-(hAPP(c_Set_Ovimage(_1474025, _1474027, _1474029), c_Orderings_Obot__class_Obot(tc_fun(_1474027, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1474025, tc_HOL_Obool)))], (36015 ^ _773908) ^ [_1449568, _1449570] : [class_Lattices_Obounded__lattice__top(_1449568), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1449568), c_Orderings_Otop__class_Otop(_1449568)), _1449570) = c_Orderings_Otop__class_Otop(_1449568))], (49662 ^ _773908) ^ [_1776291, _1776293, _1776295, _1776297] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1776291, _1776293), c_Lazy__Sequence_Olazy__sequence_OInsert(_1776291, _1776295, _1776297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1776293, _1776295)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1776291, _1776293), _1776297))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37181 ^ _773908) ^ [_1474894, _1474896, _1474898, _1474900, _1474902] : [hBOOL(hAPP(hAPP(c_member(_1474894), _1474896), hAPP(c_Set_Ovimage(_1474894, _1474898, _1474900), _1474902))), -(hBOOL(hAPP(hAPP(c_member(_1474898), hAPP(_1474900, _1474896)), _1474902)))], (14595 ^ _773908) ^ [_1020636, _1020638, _1020640] : [class_Divides_Osemiring__div(_1020636), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020636), c_Divides_Odiv__class_Omod(_1020636, _1020638, _1020640)), _1020640) = c_Groups_Ozero__class_Ozero(_1020636))], (41548 ^ _773908) ^ [_1592216, _1592218, _1592220, _1592222] : [41551 ^ _773908 : [(41556 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592216, _1592216)), hAPP(hAPP(c_Product__Type_OPair(_1592216, _1592216), 41550 ^ [_1592216, _1592218, _1592220, _1592222]), 41549 ^ [_1592216, _1592218, _1592220, _1592222])), _1592218))], (41554 ^ _773908) ^ [] : [41549 ^ [_1592216, _1592218, _1592220, _1592222] = 41550 ^ [_1592216, _1592218, _1592220, _1592222]], (41552 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592216, _1592216)), hAPP(hAPP(c_Product__Type_OPair(_1592216, _1592216), 41549 ^ [_1592216, _1592218, _1592220, _1592222]), 41550 ^ [_1592216, _1592218, _1592220, _1592222])), _1592218))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592216), tc_List_Olist(_1592216))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592216), tc_List_Olist(_1592216)), _1592220), _1592222)), c_List_Olexord(_1592216, _1592218)))), -(_1592220 = _1592222), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592216), tc_List_Olist(_1592216))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592216), tc_List_Olist(_1592216)), _1592222), _1592220)), c_List_Olexord(_1592216, _1592218))))], (38040 ^ _773908) ^ [_1496883] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1496883, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1496883), hAPP(c_COMBK(tc_HOL_Obool, _1496883), c_fFalse)))], (37872 ^ _773908) ^ [_1493627, _1493629, _1493631, _1493633, _1493635] : [c_Finite__Set_Ofun__left__comm__idem(_1493627, _1493629, _1493631), -(hAPP(hAPP(_1493631, _1493633), hAPP(hAPP(_1493631, _1493633), _1493635)) = hAPP(hAPP(_1493631, _1493633), _1493635))], (44438 ^ _773908) ^ [_1659862, _1659864, _1659866] : [44440 ^ _773908 : [(44443 ^ _773908) ^ [] : [hBOOL(hAPP(_1659864, 44439 ^ [_1659862, _1659864, _1659866]))], (44441 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659862), 44439 ^ [_1659862, _1659864, _1659866]), hAPP(c_List_Oset(_1659862), _1659866))))]], -(hAPP(c_List_Ofilter(_1659862, _1659864), _1659866) = _1659866)], (36862 ^ _773908) ^ [_1468402, _1468404, _1468406] : [class_Lattices_Oab__semigroup__idem__mult(_1468402), -(_1468404 = c_Orderings_Obot__class_Obot(tc_fun(_1468402, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468402), _1468404)), -(hAPP(c_Finite__Set_Ofold1(_1468402, c_Groups_Otimes__class_Otimes(_1468402)), hAPP(hAPP(c_Set_Oinsert(_1468402), _1468406), _1468404)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1468402), _1468406), hAPP(c_Finite__Set_Ofold1(_1468402, c_Groups_Otimes__class_Otimes(_1468402)), _1468404)))], (7755 ^ _773908) ^ [_900136, _900138, _900140, _900142, _900144, _900146] : [c_Com_Ocom_OLocal(_900136, _900138, _900140) = c_Com_Ocom_OCall(_900142, _900144, _900146)], (14053 ^ _773908) ^ [_1010812, _1010814, _1010816, _1010818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010814), _1010816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1010816), 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), _1010814), _1010812)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010814), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010818, _1010812))), _1010816))))], (22033 ^ _773908) ^ [_1155125, _1155127] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155125), _1155127), hAPP(c_Int_Onumber__class_Onumber__of(_1155125), c_Int_OBit1(c_Int_OPls))) = _1155127), class_Fields_Ofield(_1155125), class_Int_Onumber__ring(_1155125)], (19629 ^ _773908) ^ [_1112560, _1112562] : [class_Rings_Osemiring__1(_1112560), -(hBOOL(hAPP(hAPP(c_member(_1112560), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1112560), _1112562)), c_Nat_Osemiring__1__class_ONats(_1112560))))], (20717 ^ _773908) ^ [_1132049, _1132051] : [class_Rings_Odivision__ring__inverse__zero(_1132049), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132049), _1132051), c_Groups_Ozero__class_Ozero(_1132049)) = c_Groups_Ozero__class_Ozero(_1132049))], (33726 ^ _773908) ^ [_1400481, _1400483, _1400485, _1400487, _1400489, _1400491, _1400493, _1400495] : [class_Groups_Ocomm__monoid__mult(_1400481), c_Fun_Oinj__on(_1400483, _1400485, _1400487, _1400489), _1400491 = hAPP(c_Set_Oimage(_1400483, _1400485, _1400487), _1400489), _1400493 = hAPP(c_Fun_Ocomp(_1400485, _1400481, _1400483, _1400495), _1400487), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400485, _1400481), _1400495), _1400491) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400483, _1400481), _1400493), _1400489))], (40305 ^ _773908) ^ [_1562464, _1562466, _1562468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562464)), _1562468)), _1562466)), -(hAPP(hAPP(c_List_Odrop(_1562464), _1562466), _1562468) = c_List_Olist_ONil(_1562464))], (19905 ^ _773908) ^ [_1117409] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1117409)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117409)))], (49568 ^ _773908) ^ [_1774260, _1774262, _1774264, _1774266] : [-(hAPP(hAPP(c_List_Oappend(_1774260), c_List_Oreplicate(_1774260, _1774262, _1774264)), c_List_Oreplicate(_1774260, _1774266, _1774264)) = hAPP(hAPP(c_List_Oappend(_1774260), c_List_Oreplicate(_1774260, _1774266, _1774264)), c_List_Oreplicate(_1774260, _1774262, _1774264)))], (45519 ^ _773908) ^ [_1683198, _1683200, _1683202, _1683204] : [-(hAPP(c_List_Orev(_1683198), hAPP(hAPP(c_List_Omap(_1683200, _1683198), _1683202), _1683204)) = hAPP(hAPP(c_List_Omap(_1683200, _1683198), _1683202), hAPP(c_List_Orev(_1683200), _1683204)))], (18687 ^ _773908) ^ [_1096907] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1096907) = c_Int_Opred(_1096907))], (40579 ^ _773908) ^ [_1569301, _1569303, _1569305] : [-(hAPP(hAPP(c_List_Olist__update(_1569301, c_List_Olist_ONil(_1569301)), _1569303), _1569305) = c_List_Olist_ONil(_1569301))], (13829 ^ _773908) ^ [_1006820, _1006822] : [class_Rings_Olinordered__idom(_1006820), 13832 ^ _773908 : [(13839 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006820), _1006822), c_Groups_Ozero__class_Ozero(_1006820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006820), c_Groups_Osgn__class_Osgn(_1006820, _1006822)), c_Groups_Ozero__class_Ozero(_1006820))))], (13833 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006820), c_Groups_Osgn__class_Osgn(_1006820, _1006822)), c_Groups_Ozero__class_Ozero(_1006820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006820), _1006822), c_Groups_Ozero__class_Ozero(_1006820))))]]], (16619 ^ _773908) ^ [_1059085, _1059087] : [class_Groups_Oordered__ab__group__add__abs(_1059085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059085), c_Groups_Ozero__class_Ozero(_1059085)), hAPP(c_Groups_Oabs__class_Oabs(_1059085), _1059087))))], (8857 ^ _773908) ^ [_920617, _920619] : [class_Rings_Omult__zero(_920617), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920617), _920619), c_Groups_Ozero__class_Ozero(_920617)) = c_Groups_Ozero__class_Ozero(_920617))], (49324 ^ _773908) ^ [_1769043, _1769045, _1769047, _1769049, _1769051] : [-(c_List_Osplice(_1769043, hAPP(hAPP(c_List_Olist_OCons(_1769043), _1769045), _1769047), hAPP(hAPP(c_List_Olist_OCons(_1769043), _1769049), _1769051)) = hAPP(hAPP(c_List_Olist_OCons(_1769043), _1769045), hAPP(hAPP(c_List_Olist_OCons(_1769043), _1769049), c_List_Osplice(_1769043, _1769047, _1769051))))], (7093 ^ _773908) ^ [_888814, _888816] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _888814), _888816) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 7096 ^ _773908 : [(7099 ^ _773908) ^ [] : [-(_888816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7097 ^ _773908) ^ [] : [-(_888814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36373 ^ _773908) ^ [_1458189, _1458191, _1458193, _1458195] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1458189, _1458191, _1458193), _1458195)), _1458193 = c_Orderings_Obot__class_Obot(tc_fun(_1458189, tc_HOL_Obool))], (19055 ^ _773908) ^ [_1103092, _1103094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103092)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103094))), 19058 ^ _773908 : [(19059 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103092), _1103094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1103094)))], (19065 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103092), _1103094)))]]], (9537 ^ _773908) ^ [_932779, _932781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _932779)), 9540 ^ _773908 : [(9547 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _932781), _932779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _932781)), hAPP(c_Int_Onat, _932779))))], (9541 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _932781)), hAPP(c_Int_Onat, _932779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _932781), _932779)))]]], (17417 ^ _773908) ^ [_1074520] : [-(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), _1074520)) = 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), _1074520))))], (49310 ^ _773908) ^ [_1768659, _1768661, _1768663, _1768665, _1768667, _1768669, _1768671] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1768659, _1768661, _1768663, _1768665), _1768667), _1768669), _1768671) = c_New__DSequence_Opos__bind(_1768659, _1768661, hAPP(hAPP(hAPP(_1768663, _1768667), _1768669), _1768671), hAPP(hAPP(c_COMBC(_1768659, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1768661))), hAPP(hAPP(c_COMBC(_1768659, 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(_1768661)))), hAPP(hAPP(c_COMBC(_1768659, 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(_1768661))))), _1768665), _1768667)), _1768669)), _1768671)))], (26659 ^ _773908) ^ [_1253083, _1253085, _1253087, _1253089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253083), _1253089)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253087), _1253085))), -(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), _1253083), _1253085)), 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), _1253087), _1253089)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (39236 ^ _773908) ^ [_1534904, _1534906, _1534908, _1534910] : [-(hAPP(hAPP(c_List_Oappend(_1534904), hAPP(hAPP(c_List_Olist_OCons(_1534904), _1534906), _1534908)), _1534910) = hAPP(hAPP(c_List_Olist_OCons(_1534904), _1534906), hAPP(hAPP(c_List_Oappend(_1534904), _1534908), _1534910)))], (7767 ^ _773908) ^ [_900467, _900469, _900471, _900473, _900475] : [c_Com_Ocom_OSemi(_900467, _900469) = c_Com_Ocom_OCond(_900471, _900473, _900475)], (40409 ^ _773908) ^ [_1564871, _1564873, _1564875, _1564877] : [_1564871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1564873), _1564871), hAPP(hAPP(c_List_Olist_OCons(_1564873), _1564875), _1564877)) = hAPP(hAPP(c_List_Olist_OCons(_1564873), _1564875), _1564877))], (25809 ^ _773908) ^ [_1231207, _1231209, _1231211] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231207, tc_HOL_Obool)), _1231209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1231207, tc_HOL_Obool)), _1231211), _1231209)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231207, tc_HOL_Obool)), _1231209), _1231211))], (11467 ^ _773908) ^ [_965249, _965251] : [class_Rings_Olinordered__semidom(_965249), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965249), c_Groups_Ozero__class_Ozero(_965249)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_965249), _965251))))], (33912 ^ _773908) ^ [_1404356, _1404358, _1404360, _1404362, _1404364] : [c_Fun_Oinj__on(_1404356, _1404358, _1404360, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404356, tc_HOL_Obool)), _1404362), _1404364)), 33915 ^ _773908 : [(33920 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404358, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1404356, _1404358, _1404360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404356, tc_HOL_Obool)), _1404362), _1404364))), hAPP(c_Set_Oimage(_1404356, _1404358, _1404360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404356, tc_HOL_Obool)), _1404364), _1404362))) = c_Orderings_Obot__class_Obot(tc_fun(_1404358, tc_HOL_Obool)))], (33918 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1404356, _1404358, _1404360, _1404364))], (33916 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1404356, _1404358, _1404360, _1404362))]]], (38916 ^ _773908) ^ [_1525820, _1525822] : [hAPP(hAPP(c_Relation_Orel__comp(_1525820, _1525820, _1525820), _1525822), _1525822) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1525820, _1525820), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1525820, _1525822))], (51129 ^ _773908) ^ [_1808804, _1808806] : [-(c_Fun_Obij__betw(_1808804, _1808804, c_Fun_Oid(_1808804), _1808806, _1808806))], (11579 ^ _773908) ^ [] : [-(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))))], (40919 ^ _773908) ^ [_1579581, _1579583, _1579585, _1579587, _1579589] : [-(hAPP(hAPP(c_List_Ozip(_1579581, _1579583), _1579585), hAPP(hAPP(c_List_Olist_OCons(_1579583), _1579587), _1579589)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1579581, _1579583)), _1579581, c_List_Olist_ONil(tc_prod(_1579581, _1579583)), hAPP(hAPP(c_COMBC(_1579581, tc_fun(tc_List_Olist(_1579581), tc_List_Olist(tc_prod(_1579581, _1579583))), tc_fun(tc_List_Olist(_1579581), tc_List_Olist(tc_prod(_1579581, _1579583)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1579581, _1579583)), tc_List_Olist(tc_prod(_1579581, _1579583))), tc_fun(tc_fun(tc_List_Olist(_1579581), tc_List_Olist(tc_prod(_1579581, _1579583))), tc_fun(tc_List_Olist(_1579581), tc_List_Olist(tc_prod(_1579581, _1579583)))), _1579581), c_COMBB(tc_List_Olist(tc_prod(_1579581, _1579583)), tc_List_Olist(tc_prod(_1579581, _1579583)), tc_List_Olist(_1579581))), hAPP(hAPP(c_COMBB(tc_prod(_1579581, _1579583), tc_fun(tc_List_Olist(tc_prod(_1579581, _1579583)), tc_List_Olist(tc_prod(_1579581, _1579583))), _1579581), c_List_Olist_OCons(tc_prod(_1579581, _1579583))), hAPP(hAPP(c_COMBC(_1579581, _1579583, tc_prod(_1579581, _1579583)), c_Product__Type_OPair(_1579581, _1579583)), _1579587)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1579581), tc_List_Olist(_1579583), tc_List_Olist(tc_prod(_1579581, _1579583))), c_List_Ozip(_1579581, _1579583)), _1579589))), _1579585))], (18259 ^ _773908) ^ [_1089196] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1089196)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36305 ^ _773908) ^ [_1455700] : [-(c_Fun_Oinj__on(_1455700, tc_fun(_1455700, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1455700, tc_fun(_1455700, tc_HOL_Obool), tc_fun(_1455700, tc_HOL_Obool)), c_Set_Oinsert(_1455700)), c_Orderings_Obot__class_Obot(tc_fun(_1455700, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1455700, tc_HOL_Obool))))], (19505 ^ _773908) ^ [_1110565] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1110565)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1110565))))], (23143 ^ _773908) ^ [_1176271] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176271))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1176271)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43967 ^ _773908) ^ [_1649396, _1649398, _1649400, _1649402] : [hBOOL(hAPP(hAPP(c_member(_1649396), _1649402), hAPP(c_Relation_ODomain(_1649396, _1649398), _1649400))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1649396, _1649398, hAPP(hAPP(c_COMBC(_1649396, tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_fun(_1649398, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649398, tc_fun(tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_fun(_1649398, tc_HOL_Obool)), _1649396), c_COMBC(_1649398, tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649398, tc_prod(_1649396, _1649398)), tc_fun(_1649398, tc_fun(tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_HOL_Obool)), _1649396), hAPP(c_COMBB(tc_prod(_1649396, _1649398), tc_fun(tc_fun(tc_prod(_1649396, _1649398), tc_HOL_Obool), tc_HOL_Obool), _1649398), c_member(tc_prod(_1649396, _1649398)))), c_Product__Type_OPair(_1649396, _1649398)))), _1649400)), _1649402)))], (27862 ^ _773908) ^ [_1278250, _1278252, _1278254] : [class_Lattices_Osemilattice__inf(_1278250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278250), _1278252), _1278254)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278250), _1278252), _1278254) = _1278252)], (33856 ^ _773908) ^ [_1403087, _1403089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1403087), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1403089), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1403087))))), -(_1403087 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1403089), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1403087))))], (51458 ^ _773908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (42868 ^ _773908) ^ [] : [-(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))], (8309 ^ _773908) ^ [_910832, _910834, _910836, _910838, _910840, _910842, _910844, _910846] : [hAPP(c_Fun_Ocomp(_910832, _910834, _910836, _910838), _910840) = hAPP(c_Fun_Ocomp(_910842, _910834, _910836, _910844), _910846), 8312 ^ _773908 : [(8313 ^ _773908) ^ [_910947] : [-(hAPP(_910838, hAPP(_910840, _910947)) = hAPP(_910844, hAPP(_910846, _910947)))]]], (17713 ^ _773908) ^ [_1079888, _1079890, _1079892] : [class_Rings_Olinordered__idom(_1079888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079888), c_Groups_Ozero__class_Ozero(_1079888)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079888), hAPP(c_Groups_Oabs__class_Oabs(_1079888), _1079890)), _1079892))))], (11960 ^ _773908) ^ [_974104, _974106, _974108, _974110, _974112] : [class_Rings_Olinordered__semiring__strict(_974104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974104), _974106), _974108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974104), _974110), _974112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974104), c_Groups_Ozero__class_Ozero(_974104)), _974106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974104), c_Groups_Ozero__class_Ozero(_974104)), _974110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974104), _974106), _974110)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974104), _974108), _974112))))], (18383 ^ _773908) ^ [_1091313, _1091315, _1091317, _1091319] : [_1091313 = _1091315, hBOOL(hAPP(hAPP(c_member(_1091317), _1091315), _1091319)), -(hBOOL(hAPP(hAPP(c_member(_1091317), _1091313), _1091319)))], (18679 ^ _773908) ^ [_1096773, _1096775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1096773)), _1096775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096773), _1096775)))], (20007 ^ _773908) ^ [_1119186, _1119188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1119186)), c_Int_OBit0(_1119188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119186), _1119188)))], (23061 ^ _773908) ^ [_1174363] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174363) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1174363)))], (40489 ^ _773908) ^ [_1566898, _1566900, _1566902, _1566904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1566898), _1566900)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1566902)), _1566904))), -(hAPP(hAPP(c_List_Otake(_1566902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1566898), _1566900)), _1566904) = hAPP(hAPP(c_List_Oappend(_1566902), hAPP(hAPP(c_List_Otake(_1566902), _1566898), _1566904)), hAPP(hAPP(c_List_Otake(_1566902), _1566900), hAPP(hAPP(c_List_Odrop(_1566902), _1566898), _1566904))))], (42279 ^ _773908) ^ [_1611540, _1611542, _1611544, _1611546, _1611548] : [-(hAPP(hAPP(c_List_Omap(_1611540, _1611542), _1611544), hAPP(hAPP(c_List_Olist_OCons(_1611540), _1611546), _1611548)) = hAPP(hAPP(c_List_Olist_OCons(_1611542), hAPP(_1611544, _1611546)), hAPP(hAPP(c_List_Omap(_1611540, _1611542), _1611544), _1611548)))], (20259 ^ _773908) ^ [_1123572] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123572), 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, _1123572)))], (6826 ^ _773908) ^ [_884302, _884304, _884306, _884308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884302), _884304)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884306), _884304) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884302), _884308), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884306), _884308)))], (8041 ^ _773908) ^ [_905575, _905577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905575)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905575), _905577)))], (7395 ^ _773908) ^ [_893517] : [7396 ^ _773908 : [(7397 ^ _773908) ^ [_893559] : [_893517 = hAPP(c_Nat_OSuc, _893559)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893517)))], (10367 ^ _773908) ^ [_945771, _945773, _945775] : [class_Orderings_Oorder(_945771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945771), _945773), _945775)), -(_945773 = _945775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945771), _945773), _945775)))], (47132 ^ _773908) ^ [_1720225, _1720227] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1720225, _1720225)), _1720227)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1720225, _1720225)), c_Transitive__Closure_Otrancl(_1720225, _1720227))))], (5482 ^ _773908) ^ [_857791, _857793, _857795, _857797, _857799, _857801] : [-(c_Product__Type_Oprod_Oprod__case(_857801, _857797, _857793) = c_Product__Type_Oprod_Oprod__case(_857799, _857795, _857791)), _857801 = _857799, _857797 = _857795, _857793 = _857791], (26589 ^ _773908) ^ [_1250781, _1250783, _1250785, _1250787, _1250789] : [-(hBOOL(hAPP(hAPP(c_member(_1250781), _1250783), hAPP(c_Relation_OImage(_1250785, _1250781, _1250787), _1250789)))), 26590 ^ _773908 : [(26591 ^ _773908) ^ [_1250867] : [hBOOL(hAPP(hAPP(c_member(_1250785), _1250867), _1250789)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1250785, _1250781)), hAPP(hAPP(c_Product__Type_OPair(_1250785, _1250781), _1250867), _1250783)), _1250787))]]], (13763 ^ _773908) ^ [_1005736, _1005738] : [13764 ^ _773908 : [(13765 ^ _773908) ^ [_1005785] : [_1005736 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005738), _1005785)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005736, _1005738) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50884 ^ _773908) ^ [_1803137, _1803139, _1803141] : [hAPP(c_Set_Oimage(_1803137, _1803139, _1803141), c_Orderings_Otop__class_Otop(tc_fun(_1803137, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803139, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1803139, _1803137, c_Hilbert__Choice_Oinv__into(_1803137, _1803139, c_Orderings_Otop__class_Otop(tc_fun(_1803137, tc_HOL_Obool)), _1803141), c_Orderings_Otop__class_Otop(tc_fun(_1803139, tc_HOL_Obool))))], (37277 ^ _773908) ^ [_1477098, _1477100, _1477102, _1477104, _1477106, _1477108] : [hBOOL(hAPP(hAPP(c_member(_1477098), _1477100), _1477102)), 37280 ^ _773908 : [(37287 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477098), _1477104), _1477102))), -(hAPP(c_Set_Ovimage(_1477106, _1477098, hAPP(hAPP(c_COMBC(_1477106, _1477098, _1477098), hAPP(hAPP(c_COMBC(_1477106, _1477098, tc_fun(_1477098, _1477098)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477098, tc_fun(_1477098, _1477098)), _1477106), c_If(_1477098)), hAPP(hAPP(c_COMBC(_1477106, tc_fun(_1477106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1477106)), _1477108))), _1477100)), _1477104)), _1477102) = _1477108)], (37281 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1477098), _1477104), _1477102)), -(hAPP(c_Set_Ovimage(_1477106, _1477098, hAPP(hAPP(c_COMBC(_1477106, _1477098, _1477098), hAPP(hAPP(c_COMBC(_1477106, _1477098, tc_fun(_1477098, _1477098)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477098, tc_fun(_1477098, _1477098)), _1477106), c_If(_1477098)), hAPP(hAPP(c_COMBC(_1477106, tc_fun(_1477106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1477106)), _1477108))), _1477100)), _1477104)), _1477102) = c_Orderings_Otop__class_Otop(tc_fun(_1477106, tc_HOL_Obool)))]]], (51750 ^ _773908) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (51456 ^ _773908) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (39506 ^ _773908) ^ [_1541326, _1541328] : [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(_1541326)), _1541328))), _1541328 = c_List_Olist_ONil(_1541326)], (36081 ^ _773908) ^ [_1450853] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450853, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1450853, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1450853, tc_HOL_Obool)))], (41961 ^ _773908) ^ [_1601664, _1601666, _1601668, _1601670, _1601672, _1601674, _1601676, _1601678] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1601664, _1601666), _1601668), _1601670), hAPP(hAPP(c_List_Ozip(_1601664, _1601666), hAPP(hAPP(c_List_Omap(_1601672, _1601664), _1601674), _1601676)), _1601678)) = hAPP(hAPP(c_List_Omap(tc_prod(_1601672, _1601666), _1601668), hAPP(c_Product__Type_Oprod_Oprod__case(_1601672, _1601666, _1601668), hAPP(hAPP(c_COMBB(tc_fun(_1601666, tc_prod(_1601664, _1601666)), tc_fun(_1601666, _1601668), _1601672), hAPP(c_COMBB(tc_prod(_1601664, _1601666), _1601668, _1601666), _1601670)), hAPP(hAPP(c_COMBB(_1601664, tc_fun(_1601666, tc_prod(_1601664, _1601666)), _1601672), c_Product__Type_OPair(_1601664, _1601666)), _1601674)))), hAPP(hAPP(c_List_Ozip(_1601672, _1601666), _1601676), _1601678)))], (50598 ^ _773908) ^ [_1797787] : [-(c_Relation_Osym(_1797787, c_Relation_OId(_1797787)))], (6223 ^ _773908) ^ [_874859, _874861] : [class_Groups_Ozero(_874859), 6226 ^ _773908 : [(6233 ^ _773908) ^ [] : [_874861 = c_Groups_Ozero__class_Ozero(_874859), -(c_Groups_Ozero__class_Ozero(_874859) = _874861)], (6227 ^ _773908) ^ [] : [c_Groups_Ozero__class_Ozero(_874859) = _874861, -(_874861 = c_Groups_Ozero__class_Ozero(_874859))]]], (49566 ^ _773908) ^ [_1774209, _1774211, _1774213, _1774215] : [-(hAPP(hAPP(c_List_Otake(_1774209), _1774211), c_List_Oreplicate(_1774209, _1774213, _1774215)) = c_List_Oreplicate(_1774209, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1774211), _1774213), _1774215))], (44142 ^ _773908) ^ [_1653655] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653655, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1653655, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1653655, tc_HOL_Obool)))], (42513 ^ _773908) ^ [_1616861, _1616863, _1616865, _1616867, _1616869] : [-(_1616861 = c_Orderings_Obot__class_Obot(tc_fun(_1616863, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616863, tc_fun(_1616865, tc_HOL_Obool)), _1616861), hAPP(hAPP(c_COMBB(tc_fun(_1616865, tc_HOL_Obool), tc_fun(_1616865, tc_HOL_Obool), _1616863), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616865, tc_HOL_Obool)), _1616867)), _1616869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616865, tc_HOL_Obool)), _1616867), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1616863, tc_fun(_1616865, tc_HOL_Obool)), _1616861), _1616869)))], (19635 ^ _773908) ^ [] : [-(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)))))], (17865 ^ _773908) ^ [_1082481] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1082481)))], (41876 ^ _773908) ^ [_1598983, _1598985, _1598987] : [c_Fun_Oinj__on(_1598983, _1598985, _1598987, c_Orderings_Otop__class_Otop(tc_fun(_1598983, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1598983), tc_List_Olist(_1598985), hAPP(c_List_Omap(_1598983, _1598985), _1598987), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1598983), tc_HOL_Obool))))], (18911 ^ _773908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (10895 ^ _773908) ^ [_954951, _954953, _954955] : [class_Rings_Ocomm__semiring__1(_954951), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954951), _954953), _954955)), _954955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954951), _954953), c_Groups_Oone__class_Oone(_954951))), _954955))], (43497 ^ _773908) ^ [_1638031, _1638033, _1638035, _1638037, _1638039, _1638041, _1638043] : [c_List_Olist__all2(_1638031, _1638033, _1638035, hAPP(hAPP(c_List_Omap(_1638037, _1638031), _1638039), _1638041), _1638043), -(c_List_Olist__all2(_1638037, _1638033, hAPP(hAPP(c_COMBB(_1638031, tc_fun(_1638033, tc_HOL_Obool), _1638037), _1638035), _1638039), _1638041, _1638043))], (14729 ^ _773908) ^ [_1022937, _1022939, _1022941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022939), _1022941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022937), _1022941)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022937), _1022939))))], (12322 ^ _773908) ^ [_980192, _980194, _980196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980192)), _980192 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _980192), _980196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _980196), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (31381 ^ _773908) ^ [_1350960, _1350962, _1350964, _1350966] : [class_Groups_Ocomm__monoid__mult(_1350960), 31384 ^ _773908 : [(31391 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1350962), _1350964))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1350962, _1350960), _1350966), _1350964) = c_Groups_Oone__class_Oone(_1350960))], (31385 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350962), _1350964)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1350962, _1350960), _1350966), _1350964) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350960, _1350962, c_Groups_Otimes__class_Otimes(_1350960)), _1350966), c_Groups_Oone__class_Oone(_1350960)), _1350964))]]], (47036 ^ _773908) ^ [_1718048, _1718050, _1718052, _1718054, _1718056] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1718048, _1718048)), hAPP(hAPP(c_Product__Type_OPair(_1718048, _1718048), _1718050), _1718052)), _1718054)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1718048, _1718048)), hAPP(hAPP(c_Product__Type_OPair(_1718048, _1718048), _1718052), _1718056)), c_Transitive__Closure_Ortrancl(_1718048, _1718054))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718048, _1718048)), hAPP(hAPP(c_Product__Type_OPair(_1718048, _1718048), _1718050), _1718056)), c_Transitive__Closure_Otrancl(_1718048, _1718054))))], (16523 ^ _773908) ^ [_1057497, _1057499, _1057501] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1057497), _1057499)), _1057501) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1057497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057499), _1057501)))], (21831 ^ _773908) ^ [_1151751, _1151753, _1151755, _1151757] : [class_Fields_Ofield(_1151751), -(_1151753 = c_Groups_Ozero__class_Ozero(_1151751)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151751), _1151755), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151751), _1151757), _1151753)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151751), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151751), _1151753), _1151755)), _1151757)), _1151753))], (46554 ^ _773908) ^ [_1705516, _1705518, _1705520, _1705522] : [46556 ^ _773908 : [(46559 ^ _773908) ^ [] : [hBOOL(hAPP(_1705520, 46555 ^ [_1705516, _1705518, _1705520, _1705522]))], (46557 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1705516), 46555 ^ [_1705516, _1705518, _1705520, _1705522]), hAPP(c_List_Oset(_1705516), _1705518))))]], -(c_List_OdropWhile(_1705516, _1705520, hAPP(hAPP(c_List_Oappend(_1705516), _1705518), _1705522)) = c_List_OdropWhile(_1705516, _1705520, _1705522))], (51348 ^ _773908) ^ [_1812666, _1812668] : [class_Orderings_Oorder(_1812666), -(class_Orderings_Oorder(tc_fun(_1812668, _1812666)))], (44475 ^ _773908) ^ [_1660609, _1660611] : [44477 ^ _773908 : [(44480 ^ _773908) ^ [] : [44476 ^ [_1660609, _1660611] = c_List_Olist_ONil(_1660609)], (44478 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1660609)), 44476 ^ [_1660609, _1660611]), hAPP(c_List_Oset(tc_List_Olist(_1660609)), _1660611))))]], -(c_List_Oconcat(_1660609, _1660611) = c_List_Olist_ONil(_1660609))], (29307 ^ _773908) ^ [_1308619, _1308621, _1308623] : [class_Lattices_Olattice(_1308619), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308619), _1308621)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308619), _1308623)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308619, tc_HOL_Obool)), _1308621), _1308623) = c_Orderings_Obot__class_Obot(tc_fun(_1308619, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1308619), c_Big__Operators_Olattice__class_OSup__fin(_1308619, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308619, tc_HOL_Obool)), _1308621), _1308623))), c_Big__Operators_Olattice__class_OSup__fin(_1308619, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308619, tc_HOL_Obool)), _1308621), _1308623))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1308619), c_Big__Operators_Olattice__class_OSup__fin(_1308619, _1308621)), c_Big__Operators_Olattice__class_OSup__fin(_1308619, _1308623)))], (32416 ^ _773908) ^ [_1375485, _1375487, _1375489, _1375491] : [class_Orderings_Olinorder(_1375485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375485), _1375487), _1375489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375485), _1375489), _1375491)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1375485, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1375485, _1375487, _1375489)), c_SetInterval_Oord__class_OatLeastAtMost(_1375485, _1375489, _1375491)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1375485, _1375487, _1375491))], (17679 ^ _773908) ^ [_1079248, _1079250, _1079252, _1079254] : [class_Rings_Olinordered__semidom(_1079248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079248), c_Groups_Oone__class_Oone(_1079248)), _1079250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079248), hAPP(hAPP(c_Power_Opower__class_Opower(_1079248), _1079250), _1079252)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079248), _1079250), _1079254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1079252), _1079254)))], (49434 ^ _773908) ^ [_1771914, _1771916, _1771918] : [c_List_Oreplicate(_1771914, _1771916, _1771918) = c_List_Olist_ONil(_1771914), -(_1771916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13787 ^ _773908) ^ [_1006121, _1006123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006121)), 13790 ^ _773908 : [(13793 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006123, _1006121)), _1006121)))], (13791 ^ _773908) ^ [] : [-(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, _1006123, _1006121))))]]], (2438 ^ _773908) ^ [_809771, _809773, _809775, _809777] : [-(c_Nitpick_Onat__gcd(_809777, _809773) = c_Nitpick_Onat__gcd(_809775, _809771)), _809777 = _809775, _809773 = _809771], (33176 ^ _773908) ^ [_1390334, _1390336] : [class_Groups_Oordered__ab__group__add(_1390334), -(c_Fun_Oinj__on(_1390334, _1390334, c_Groups_Ouminus__class_Ouminus(_1390334), _1390336))], (49502 ^ _773908) ^ [_1773117, _1773119, _1773121, _1773123] : [49504 ^ _773908 : [(49507 ^ _773908) ^ [] : [hBOOL(hAPP(_1773123, 49503 ^ [_1773117, _1773119, _1773121, _1773123]))], (49505 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773117), 49503 ^ [_1773117, _1773119, _1773121, _1773123]), hAPP(c_List_Oset(_1773117), c_List_Oreplicate(_1773117, _1773119, _1773121)))))]], -(hBOOL(hAPP(_1773123, _1773121))), -(_1773119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6146 ^ _773908) ^ [_873527] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _873527)], (23115 ^ _773908) ^ [_1175533, _1175535, _1175537, _1175539, _1175541] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1175533, _1175535, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1175533)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1175533), hAPP(hAPP(c_COMBC(_1175533, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1175533), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1175533), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1175537))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1175539))), c_Com_Ocom_OWhile(_1175539, _1175541)), _1175537)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1175533), tc_HOL_Obool)))))], (47126 ^ _773908) ^ [_1720118, _1720120] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1720118, _1720118)), c_Transitive__Closure_Otrancl(_1720118, _1720120))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1720118, _1720118)), _1720120)))], (38812 ^ _773908) ^ [_1523661, _1523663, _1523665, _1523667] : [_1523665 = _1523667, -(hAPP(hAPP(c_List_Oappend(_1523661), _1523663), _1523665) = hAPP(hAPP(c_List_Oappend(_1523661), _1523663), _1523667))], (1544 ^ _773908) ^ [_796194, _796196] : [-(class_Rings_Olinordered__comm__semiring__strict(_796194)), _796196 = _796194, class_Rings_Olinordered__comm__semiring__strict(_796196)], (39607 ^ _773908) ^ [_1543974, _1543976, _1543978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1543974), tc_List_Olist(_1543974))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1543974), tc_List_Olist(_1543974)), c_List_Olist_ONil(_1543974)), _1543976)), c_List_Olistrel1(_1543974, _1543978)))], (15431 ^ _773908) ^ [_1035712, _1035714, _1035716] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035712), _1035714)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035712), _1035716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035714), _1035716))], (1034 ^ _773908) ^ [_789567, _789569, _789571, _789573] : [-(c_Predicate_Osymp(_789571, _789567)), c_Predicate_Osymp(_789573, _789569), _789573 = _789571, _789569 = _789567], (43433 ^ _773908) ^ [_1636728, _1636730, _1636732, _1636734, _1636736, _1636738] : [c_List_Olist__all2(_1636728, _1636730, _1636732, _1636734, _1636736), -(c_List_Olist__all2(_1636728, _1636730, _1636732, hAPP(hAPP(c_List_Otake(_1636728), _1636738), _1636734), hAPP(hAPP(c_List_Otake(_1636730), _1636738), _1636736)))], (37994 ^ _773908) ^ [_1496069, _1496071, _1496073] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496069), hAPP(c_Set_OCollect(_1496069), hAPP(hAPP(c_COMBS(_1496069, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496069), c_fdisj), _1496071)), _1496073)))), 37997 ^ _773908 : [(38000 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496069), hAPP(c_Set_OCollect(_1496069), _1496073))))], (37998 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496069), hAPP(c_Set_OCollect(_1496069), _1496071))))]]], (13620 ^ _773908) ^ [_1003160, _1003162, _1003164, _1003166] : [class_Divides_Osemiring__div(_1003160), -(c_Divides_Odiv__class_Omod(_1003160, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003160), c_Divides_Odiv__class_Omod(_1003160, _1003162, _1003164)), _1003166), _1003164) = c_Divides_Odiv__class_Omod(_1003160, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003160), _1003162), _1003166), _1003164))], (41742 ^ _773908) ^ [_1596259, _1596261, _1596263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596259), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596261)), _1596263))), -(hAPP(hAPP(c_List_Otake(_1596261), _1596259), c_List_Obutlast(_1596261, _1596263)) = hAPP(hAPP(c_List_Otake(_1596261), _1596259), _1596263))], (32640 ^ _773908) ^ [_1379760, _1379762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1379760)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1379760, _1379762)))], (5020 ^ _773908) ^ [_850560, _850562] : [_850562 = _850560, -(c_DSequence_Osingle(_850562) = c_DSequence_Osingle(_850560))], (30309 ^ _773908) ^ [_1327761, _1327763, _1327765] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327761), _1327763)), hBOOL(hAPP(hAPP(c_member(_1327761), _1327765), _1327763)), -(hAPP(c_Finite__Set_Ocard(_1327761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327761, tc_HOL_Obool)), _1327763), hAPP(hAPP(c_Set_Oinsert(_1327761), _1327765), c_Orderings_Obot__class_Obot(tc_fun(_1327761, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327761), _1327763)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47120 ^ _773908) ^ [_1719978, _1719980, _1719982] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1719978, _1719978)), _1719980), _1719982)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1719978, _1719978)), _1719980), c_Transitive__Closure_Otrancl(_1719978, _1719982))))], (35903 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (32871 ^ _773908) ^ [_1384319, _1384321] : [32879 ^ _773908 : [(32882 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1384321, 32878 ^ [_1384319, _1384321])))], (32880 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32878 ^ [_1384319, _1384321]), _1384319)))]], 32872 ^ _773908 : [(32873 ^ _773908) ^ [_1384388] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1384388), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1384319))), hBOOL(hAPP(_1384321, _1384388))]]], (13540 ^ _773908) ^ [_1001386, _1001388, _1001390] : [class_Divides_Osemiring__div(_1001386), -(c_Divides_Odiv__class_Omod(_1001386, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001386), _1001388), _1001390), _1001388) = c_Divides_Odiv__class_Omod(_1001386, _1001390, _1001388))], (50114 ^ _773908) ^ [_1788384, _1788386, _1788388, _1788390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1788384), _1788386)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788384), _1788388)), -(_1788388 = c_Orderings_Obot__class_Obot(tc_fun(_1788384, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1788384, _1788390, _1788386, _1788388)), 50128 ^ _773908 : [(50131 ^ _773908) ^ [_1788729] : [hBOOL(hAPP(hAPP(c_member(_1788384), _1788729), _1788388)), hBOOL(hAPP(hAPP(_1788390, 50127 ^ [_1788384, _1788386, _1788388, _1788390]), _1788729))], (50129 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788384), 50127 ^ [_1788384, _1788386, _1788388, _1788390]), _1788386)))]]], (51500 ^ _773908) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (31113 ^ _773908) ^ [_1344696, _1344698, _1344700, _1344702, _1344704] : [class_Groups_Ocomm__monoid__mult(_1344696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344698), _1344700)), hBOOL(hAPP(hAPP(c_member(_1344698), _1344702), _1344700)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344698, _1344696), _1344704), _1344700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344696), hAPP(_1344704, _1344702)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344698, _1344696), _1344704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1344698, tc_HOL_Obool)), _1344700), hAPP(hAPP(c_Set_Oinsert(_1344698), _1344702), c_Orderings_Obot__class_Obot(tc_fun(_1344698, tc_HOL_Obool)))))))], (43439 ^ _773908) ^ [_1636857, _1636859, _1636861, _1636863, _1636865, _1636867, _1636869] : [c_List_Olist__all2(_1636857, _1636859, _1636861, _1636863, _1636865), c_List_Olist__all2(_1636857, _1636859, _1636861, _1636867, _1636869), -(c_List_Olist__all2(_1636857, _1636859, _1636861, hAPP(hAPP(c_List_Oappend(_1636857), _1636863), _1636867), hAPP(hAPP(c_List_Oappend(_1636859), _1636865), _1636869)))], (1874 ^ _773908) ^ [_800319, _800321] : [-(class_Groups_Ominus(_800319)), _800321 = _800319, class_Groups_Ominus(_800321)], (40627 ^ _773908) ^ [_1570338, _1570340, _1570342, _1570344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570338)), _1570340)), _1570342)), -(hAPP(hAPP(c_List_Olist__update(_1570338, _1570340), _1570342), _1570344) = _1570340)], (13263 ^ _773908) ^ [_996570, _996572, _996574] : [class_Lattices_Oboolean__algebra(_996570), 13266 ^ _773908 : [(13273 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996570), _996574), _996572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996570), hAPP(c_Groups_Ouminus__class_Ouminus(_996570), _996572)), hAPP(c_Groups_Ouminus__class_Ouminus(_996570), _996574))))], (13267 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996570), hAPP(c_Groups_Ouminus__class_Ouminus(_996570), _996572)), hAPP(c_Groups_Ouminus__class_Ouminus(_996570), _996574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996570), _996574), _996572)))]]], (5412 ^ _773908) ^ [_856654, _856656, _856658, _856660] : [-(c_Product__Type_OPair(_856660, _856656) = c_Product__Type_OPair(_856658, _856654)), _856660 = _856658, _856656 = _856654], (39014 ^ _773908) ^ [_1528245, _1528247, _1528249, _1528251] : [c_Wellfounded_Owf(_1528245, _1528247), c_Fun_Oinj__on(_1528245, _1528249, _1528251, c_Orderings_Otop__class_Otop(tc_fun(_1528245, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1528249, hAPP(c_Set_Oimage(tc_prod(_1528245, _1528245), tc_prod(_1528249, _1528249), c_Product__Type_Omap__pair(_1528245, _1528249, _1528245, _1528249, _1528251, _1528251)), _1528247)))], (20621 ^ _773908) ^ [_1130329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1130329)), -(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), _1130329), 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)))))))], (5849 ^ _773908) ^ [_867253, _867255, _867257, _867259, _867261, _867263, _867265] : [c_Hoare__Mirabelle_Ohoare__derivs(_867253, _867255, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867253)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_867253), _867257), _867259), _867261)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867253), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_867253, _867255, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867253)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_867253), _867261), _867263), _867265)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867253), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_867253, _867255, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867253)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_867253), _867257), c_Com_Ocom_OSemi(_867259, _867263)), _867265)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867253), tc_HOL_Obool)))))], (8703 ^ _773908) ^ [_918047] : [class_Groups_Ogroup__add(_918047), -(hAPP(c_Groups_Ouminus__class_Ouminus(_918047), c_Groups_Ozero__class_Ozero(_918047)) = c_Groups_Ozero__class_Ozero(_918047))], (23389 ^ _773908) ^ [_1181019, _1181021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181019)), 23392 ^ _773908 : [(23399 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181021), _1181019))), -(c_Divides_OposDivAlg(_1181021, _1181019) = hAPP(c_Divides_Oadjust(_1181019), c_Divides_OposDivAlg(_1181021, 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)))), _1181019))))], (23393 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181021), _1181019)), -(c_Divides_OposDivAlg(_1181021, _1181019) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181021))]]], (51076 ^ _773908) ^ [_1807844] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807844), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1807844 = hAPP(c_Code__Numeral_Onat__of, 51079 ^ [_1807844]))], (24529 ^ _773908) ^ [_1204808, _1204810, _1204812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204808, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1204808, tc_fun(_1204808, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204808)), _1204810)), hAPP(hAPP(c_COMBC(_1204808, tc_fun(_1204808, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204808)), _1204812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204808, tc_HOL_Obool)), _1204810), _1204812)))], (43612 ^ _773908) ^ [_1640841] : [-(c_Enum_Osublists(_1640841, c_List_Olist_ONil(_1640841)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1640841)), c_List_Olist_ONil(_1640841)), c_List_Olist_ONil(tc_List_Olist(_1640841))))], (18703 ^ _773908) ^ [_1097196] : [-(c_Int_Osucc(_1097196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097196), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38462 ^ _773908) ^ [_1513749, _1513751, _1513753, _1513755, _1513757, _1513759, _1513761] : [hAPP(c_Fun_Ocomp(_1513749, _1513751, _1513753, _1513755), _1513757) = hAPP(c_Fun_Ocomp(_1513751, _1513751, _1513753, c_Fun_Oid(_1513751)), _1513759), -(hAPP(_1513755, hAPP(_1513757, _1513761)) = hAPP(_1513759, _1513761))], (4938 ^ _773908) ^ [_849269, _849271, _849273, _849275, _849277, _849279, _849281, _849283] : [-(c_Product__Type_Oscomp(_849283, _849279, _849275, _849271) = c_Product__Type_Oscomp(_849281, _849277, _849273, _849269)), _849283 = _849281, _849279 = _849277, _849275 = _849273, _849271 = _849269], (16445 ^ _773908) ^ [_1055829, _1055831] : [class_Rings_Olinordered__idom(_1055829), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055829), hAPP(c_Groups_Oabs__class_Oabs(_1055829), _1055831)), hAPP(c_Groups_Oabs__class_Oabs(_1055829), _1055831)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055829), _1055831), _1055831))], (6878 ^ _773908) ^ [_885228, _885230] : [-(_885228 = _885230), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885228), _885230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885230), _885228)))], (11003 ^ _773908) ^ [_956917, _956919, _956921, _956923] : [class_Groups_Oordered__comm__monoid__add(_956917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956917), c_Groups_Ozero__class_Ozero(_956917)), _956919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956917), _956921), _956923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956917), _956921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956917), _956923), _956919))))], (10107 ^ _773908) ^ [_942033, _942035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _942033), c_Groups_Oone__class_Oone(tc_Int_Oint))), _942035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942033), _942035)))], (37726 ^ _773908) ^ [_1490144, _1490146, _1490148, _1490150, _1490152, _1490154, _1490156, _1490158, _1490160, _1490162] : [hAPP(c_Set_Oimage(_1490144, _1490146, _1490148), _1490150) = _1490152, hAPP(c_Set_Oimage(_1490154, _1490156, _1490158), _1490160) = _1490162, -(hAPP(c_Set_Oimage(tc_prod(_1490144, _1490154), tc_prod(_1490146, _1490156), c_Product__Type_Omap__pair(_1490144, _1490146, _1490154, _1490156, _1490148, _1490158)), hAPP(hAPP(c_Product__Type_OSigma(_1490144, _1490154), _1490150), hAPP(c_COMBK(tc_fun(_1490154, tc_HOL_Obool), _1490144), _1490160))) = hAPP(hAPP(c_Product__Type_OSigma(_1490146, _1490156), _1490152), hAPP(c_COMBK(tc_fun(_1490156, tc_HOL_Obool), _1490146), _1490162)))], (41079 ^ _773908) ^ [_1583021, _1583023, _1583025] : [-(hAPP(hAPP(c_List_Otake(_1583021), _1583023), hAPP(c_List_Otl(_1583021), _1583025)) = hAPP(c_List_Otl(_1583021), hAPP(hAPP(c_List_Otake(_1583021), hAPP(c_Nat_OSuc, _1583023)), _1583025)))], (26759 ^ _773908) ^ [_1255423, _1255425, _1255427, _1255429, _1255431, _1255433] : [-(hBOOL(hAPP(hAPP(c_member(_1255423), _1255425), _1255427))), -(hAPP(c_Set_Oimage(_1255423, _1255429, c_Fun_Ofun__upd(_1255423, _1255429, _1255431, _1255425, _1255433)), _1255427) = hAPP(c_Set_Oimage(_1255423, _1255429, _1255431), _1255427))], (35973 ^ _773908) ^ [_1448911, _1448913] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448911, tc_HOL_Obool)), _1448913), c_Orderings_Otop__class_Otop(tc_fun(_1448911, tc_HOL_Obool))) = _1448913)], (27069 ^ _773908) ^ [_1261729, _1261731] : [-(c_Relation_Ototal__on(_1261729, c_Orderings_Obot__class_Obot(tc_fun(_1261729, tc_HOL_Obool)), _1261731))], (17431 ^ _773908) ^ [_1074778, _1074780, _1074782] : [class_Rings_Olinordered__semidom(_1074778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074778), c_Groups_Ozero__class_Ozero(_1074778)), _1074780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074778), c_Groups_Ozero__class_Ozero(_1074778)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074778), _1074780), _1074782))))], (2920 ^ _773908) ^ [_817446, _817448] : [_817448 = _817446, -(c_Int_Oint__ge__less__than(_817448) = c_Int_Oint__ge__less__than(_817446))], (10741 ^ _773908) ^ [_952097] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _952097), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _952097)], (44648 ^ _773908) ^ [_1666364, _1666366] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1666364), _1666366)) = c_List_Oupt(_1666364, _1666366))], (11567 ^ _773908) ^ [_967142, _967144] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967142)), _967144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967142), _967144)))], (8057 ^ _773908) ^ [] : [-(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))], (13570 ^ _773908) ^ [_1002043, _1002045, _1002047, _1002049] : [class_Divides_Osemiring__div(_1002043), -(c_Divides_Odiv__class_Omod(_1002043, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002043), c_Divides_Odiv__class_Omod(_1002043, _1002045, _1002047)), _1002049), _1002047) = c_Divides_Odiv__class_Omod(_1002043, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002043), _1002045), _1002049), _1002047))], (51596 ^ _773908) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (42519 ^ _773908) ^ [_1616969, _1616971, _1616973, _1616975] : [class_Rings_Osemiring__1(_1616969), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616969), hAPP(hAPP(c_List_Omap(_1616971, _1616969), hAPP(c_COMBK(_1616969, _1616971), _1616973)), _1616975)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1616969), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1616969), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616971)), _1616975))), _1616973))], (8183 ^ _773908) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28278 ^ _773908) ^ [_1287095, _1287097, _1287099] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1287095), _1287097), _1287099) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1287095, tc_HOL_Obool), tc_HOL_Obool)), -(_1287097 = c_Orderings_Obot__class_Obot(tc_fun(_1287095, tc_HOL_Obool)))], (30247 ^ _773908) ^ [_1326452, _1326454, _1326456] : [class_Orderings_Olinorder(_1326452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326452), _1326454)), -(_1326454 = c_Orderings_Obot__class_Obot(tc_fun(_1326452, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326452), _1326456)), -(_1326456 = c_Orderings_Obot__class_Obot(tc_fun(_1326452, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326452, tc_HOL_Obool)), _1326454), _1326456) = c_Orderings_Obot__class_Obot(tc_fun(_1326452, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1326452, c_Orderings_Oord__class_Omin(_1326452), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326452, tc_HOL_Obool)), _1326454), _1326456)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326452), c_Big__Operators_Olattice_OInf__fin(_1326452, c_Orderings_Oord__class_Omin(_1326452), _1326454)), c_Big__Operators_Olattice_OInf__fin(_1326452, c_Orderings_Oord__class_Omin(_1326452), _1326456)))], (9315 ^ _773908) ^ [_928869, _928871, _928873] : [class_Rings_Olinordered__ring__strict(_928869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928869), _928871), c_Groups_Ozero__class_Ozero(_928869))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928869), _928873), c_Groups_Ozero__class_Ozero(_928869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928869), c_Groups_Ozero__class_Ozero(_928869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928869), _928871), _928873))))], (14332 ^ _773908) ^ [_1016204, _1016206] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016204)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016206)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016204), _1016206)))], (27003 ^ _773908) ^ [_1259994, _1259996] : [c_Nat__Transfer_Onat__set(_1259994), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259996), _1259994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259996)))], (12542 ^ _773908) ^ [_984028, _984030] : [_984030 = c_Orderings_Obot__class_Obot(tc_fun(_984028, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984028, tc_HOL_Obool)), _984030), c_Orderings_Obot__class_Obot(tc_fun(_984028, tc_HOL_Obool)))))], (24707 ^ _773908) ^ [_1209496, _1209498, _1209500] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209496), _1209498)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209500), _1209498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1209496), _1209500)), _1209498))], (45866 ^ _773908) ^ [_1690542, _1690544, _1690546, _1690548] : [hBOOL(hAPP(_1690542, _1690544)), -(c_List_OdropWhile(_1690546, _1690542, hAPP(hAPP(c_List_Olist_OCons(_1690546), _1690544), _1690548)) = c_List_OdropWhile(_1690546, _1690542, _1690548))], (37954 ^ _773908) ^ [_1495106] : [-(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)), _1495106)))))], (50510 ^ _773908) ^ [_1796131, _1796133] : [50511 ^ _773908 : [(50512 ^ _773908) ^ [_1796187] : [hBOOL(hAPP(hAPP(_1796131, _1796187), _1796187))]], c_Predicate_Osymp(_1796133, _1796131), c_Predicate_Otransp(_1796133, _1796131), -(c_Equiv__Relations_Opart__equivp(_1796133, _1796131))], (32367 ^ _773908) ^ [_1374382, _1374384, _1374386, _1374388, _1374390] : [class_Groups_Ocomm__monoid__mult(_1374382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374384), _1374386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374384, tc_HOL_Obool)), _1374388), _1374386)), 32381 ^ _773908 : [(32384 ^ _773908) ^ [] : [hAPP(_1374390, 32380 ^ [_1374382, _1374384, _1374386, _1374388, _1374390]) = c_Groups_Oone__class_Oone(_1374382)], (32382 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374384), 32380 ^ [_1374382, _1374384, _1374386, _1374388, _1374390]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374384, tc_HOL_Obool)), _1374386), _1374388))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374384, _1374382), _1374390), _1374388) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374384, _1374382), _1374390), _1374386))], (15693 ^ _773908) ^ [_1040885, _1040887] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040885), _1040887)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45513 ^ _773908) ^ [_1683051, _1683053] : [-(hAPP(c_List_Oset(_1683051), hAPP(c_List_Orev(_1683051), _1683053)) = hAPP(c_List_Oset(_1683051), _1683053))], (40483 ^ _773908) ^ [_1566817, _1566819, _1566821, _1566823] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1566817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1566819), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1566817)), hAPP(hAPP(c_List_Olist_OCons(_1566819), _1566821), _1566823)) = hAPP(hAPP(c_List_Odrop(_1566819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1566817)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1566823))], (19733 ^ _773908) ^ [_1114149, _1114151] : [class_Int_Onumber__ring(_1114149), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114149), c_Groups_Oone__class_Oone(_1114149)), hAPP(c_Int_Onumber__class_Onumber__of(_1114149), _1114151)) = hAPP(c_Int_Onumber__class_Onumber__of(_1114149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1114151)))], (856 ^ _773908) ^ [_786980, _786982, _786984, _786986, _786988, _786990] : [-(c_List_Oall__interval__int(_786988, _786984, _786980)), c_List_Oall__interval__int(_786990, _786986, _786982), _786990 = _786988, _786986 = _786984, _786982 = _786980], (37849 ^ _773908) ^ [_1493033] : [-(c_Finite__Set_Ofun__left__comm__idem(_1493033, tc_fun(_1493033, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1493033, tc_HOL_Obool), tc_fun(tc_fun(_1493033, tc_HOL_Obool), tc_fun(_1493033, tc_HOL_Obool)), _1493033), hAPP(c_COMBC(tc_fun(_1493033, tc_HOL_Obool), tc_fun(_1493033, tc_HOL_Obool), tc_fun(_1493033, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1493033, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1493033, tc_fun(_1493033, tc_HOL_Obool), tc_fun(_1493033, tc_HOL_Obool)), c_Set_Oinsert(_1493033)), c_Orderings_Obot__class_Obot(tc_fun(_1493033, tc_HOL_Obool))))))], (8483 ^ _773908) ^ [_913785, _913787, _913789] : [-(hAPP(hAPP(c_Nat_Ocompow(_913785, _913785), hAPP(c_Nat_OSuc, _913787)), _913789) = hAPP(c_Fun_Ocomp(_913785, _913785, _913785, _913789), hAPP(hAPP(c_Nat_Ocompow(_913785, _913785), _913787), _913789)))], (32897 ^ _773908) ^ [_1384828, _1384830] : [32899 ^ _773908 : [(32902 ^ _773908) ^ [] : [hBOOL(hAPP(_1384830, 32898 ^ [_1384828, _1384830]))], (32900 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 32898 ^ [_1384828, _1384830]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1384828))))]], 32903 ^ _773908 : [(32904 ^ _773908) ^ [_1384983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1384983), _1384828)), -(hBOOL(hAPP(_1384830, _1384983)))]]], (20069 ^ _773908) ^ [_1120281] : [-(c_Int_Opred(c_Int_OBit0(_1120281)) = c_Int_OBit1(c_Int_Opred(_1120281)))], (11401 ^ _773908) ^ [_964170, _964172] : [class_Groups_Olinordered__ab__group__add(_964170), 11404 ^ _773908 : [(11411 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964170), _964172), c_Groups_Ozero__class_Ozero(_964170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964170), _964172), hAPP(c_Groups_Ouminus__class_Ouminus(_964170), _964172))))], (11405 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964170), _964172), hAPP(c_Groups_Ouminus__class_Ouminus(_964170), _964172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964170), _964172), c_Groups_Ozero__class_Ozero(_964170))))]]], (26804 ^ _773908) ^ [_1256948, _1256950, _1256952, _1256954, _1256956] : [-(hAPP(c_Fun_Ofun__upd(_1256948, _1256950, _1256952, _1256954, _1256956), _1256954) = _1256956)], (43614 ^ _773908) ^ [_1640885, _1640887, _1640889] : [-(c_Enum_Osublists(_1640885, hAPP(hAPP(c_List_Olist_OCons(_1640885), _1640887), _1640889)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1640885)), tc_List_Olist(tc_List_Olist(_1640885))), c_Enum_Osublists(_1640885, _1640889)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1640885)), tc_List_Olist(tc_List_Olist(_1640885)), tc_List_Olist(tc_List_Olist(_1640885))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1640885)), tc_fun(tc_List_Olist(tc_List_Olist(_1640885)), tc_List_Olist(tc_List_Olist(_1640885))), tc_List_Olist(tc_List_Olist(_1640885))), c_List_Oappend(tc_List_Olist(_1640885))), hAPP(c_List_Omap(tc_List_Olist(_1640885), tc_List_Olist(_1640885)), hAPP(c_List_Olist_OCons(_1640885), _1640887)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1640885))))))], (18449 ^ _773908) ^ [_1092376, _1092378, _1092380, _1092382] : [-(hBOOL(hAPP(hAPP(c_member(_1092376), _1092378), _1092380))), -(hBOOL(hAPP(hAPP(c_member(_1092376), _1092378), _1092382))), 18456 ^ _773908 : [(18463 ^ _773908) ^ [] : [_1092380 = _1092382, -(hAPP(hAPP(c_Set_Oinsert(_1092376), _1092378), _1092380) = hAPP(hAPP(c_Set_Oinsert(_1092376), _1092378), _1092382))], (18457 ^ _773908) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1092376), _1092378), _1092380) = hAPP(hAPP(c_Set_Oinsert(_1092376), _1092378), _1092382), -(_1092380 = _1092382)]]], (11329 ^ _773908) ^ [_962932, _962934, _962936, _962938, _962940] : [class_Groups_Oordered__cancel__ab__semigroup__add(_962932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962932), _962934), _962936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962932), _962938), _962940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962932), _962934), _962938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962932), _962936), _962940))))], (51171 ^ _773908) ^ [_1809758, _1809760, _1809762, _1809764] : [-(c_Product__Type_Ocurry(_1809758, _1809760, _1809762, hAPP(c_Product__Type_Oprod_Oprod__case(_1809758, _1809760, _1809762), _1809764)) = _1809764)], (21177 ^ _773908) ^ [_1140115, _1140117, _1140119, _1140121, _1140123] : [class_Fields_Ofield(_1140115), -(_1140117 = c_Groups_Ozero__class_Ozero(_1140115)), -(_1140119 = c_Groups_Ozero__class_Ozero(_1140115)), 21188 ^ _773908 : [(21195 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140115), _1140121), _1140119) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140115), _1140123), _1140117), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140115), _1140121), _1140117) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140115), _1140123), _1140119))], (21189 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140115), _1140121), _1140117) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140115), _1140123), _1140119), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140115), _1140121), _1140119) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140115), _1140123), _1140117))]]], (12154 ^ _773908) ^ [_977648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977648), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _977648) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42251 ^ _773908) ^ [_1610502, _1610504, _1610506, _1610508, _1610510] : [hBOOL(hAPP(hAPP(c_member(_1610502), _1610504), _1610506)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610508, tc_HOL_Obool)), hAPP(_1610510, _1610504)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610502, tc_fun(_1610508, tc_HOL_Obool)), _1610506), _1610510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610502, tc_fun(_1610508, tc_HOL_Obool)), _1610506), _1610510))], (51113 ^ _773908) ^ [_1808384, _1808386, _1808388, _1808390, _1808392, _1808394] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1808384, _1808386, _1808388, _1808390, c_Lazy__Sequence_Olazy__sequence_OInsert(_1808386, _1808392, _1808394)) = hAPP(hAPP(hAPP(_1808390, _1808392), _1808394), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1808384, _1808386, _1808388, _1808390, _1808394)))], (45053 ^ _773908) ^ [_1674041, _1674043, _1674045, _1674047] : [-(c_List_Oremdups(_1674041, hAPP(hAPP(c_List_Omap(_1674043, _1674041), _1674045), c_List_Oremdups(_1674043, _1674047))) = c_List_Oremdups(_1674041, hAPP(hAPP(c_List_Omap(_1674043, _1674041), _1674045), _1674047)))], (42656 ^ _773908) ^ [_1619852, _1619854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619852), _1619854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1619852)), hAPP(c_Code__Numeral_Oof__nat, _1619854))))], (28194 ^ _773908) ^ [_1284893, _1284895] : [class_Lattices_Olattice(_1284893), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1284893), _1284895), _1284895) = _1284895)], (20447 ^ _773908) ^ [_1126751, _1126753, _1126755] : [class_Rings_Olinordered__semidom(_1126751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126751), hAPP(hAPP(c_Power_Opower__class_Opower(_1126751), _1126753), 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(_1126751), _1126755), 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(_1126751), c_Groups_Ozero__class_Ozero(_1126751)), _1126755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126751), _1126753), _1126755)))], (37414 ^ _773908) ^ [_1481032, _1481034, _1481036, _1481038] : [-(hAPP(c_Set_Oimage(tc_prod(_1481032, _1481034), tc_prod(_1481034, _1481032), hAPP(c_Product__Type_Oprod_Oprod__case(_1481032, _1481034, tc_prod(_1481034, _1481032)), hAPP(c_COMBC(_1481034, _1481032, tc_prod(_1481034, _1481032)), c_Product__Type_OPair(_1481034, _1481032)))), hAPP(hAPP(c_Product__Type_OSigma(_1481032, _1481034), _1481036), hAPP(c_COMBK(tc_fun(_1481034, tc_HOL_Obool), _1481032), _1481038))) = hAPP(hAPP(c_Product__Type_OSigma(_1481034, _1481032), _1481038), hAPP(c_COMBK(tc_fun(_1481032, tc_HOL_Obool), _1481034), _1481036)))], (47538 ^ _773908) ^ [_1730179, _1730181, _1730183, _1730185, _1730187] : [c_Relation_Osingle__valued(_1730179, _1730179, _1730181), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730179, _1730179)), hAPP(hAPP(c_Product__Type_OPair(_1730179, _1730179), _1730183), _1730185)), c_Transitive__Closure_Ortrancl(_1730179, _1730181))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730179, _1730179)), hAPP(hAPP(c_Product__Type_OPair(_1730179, _1730179), _1730183), _1730187)), c_Transitive__Closure_Ortrancl(_1730179, _1730181))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730179, _1730179)), hAPP(hAPP(c_Product__Type_OPair(_1730179, _1730179), _1730185), _1730187)), c_Transitive__Closure_Ortrancl(_1730179, _1730181)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730179, _1730179)), hAPP(hAPP(c_Product__Type_OPair(_1730179, _1730179), _1730187), _1730185)), c_Transitive__Closure_Ortrancl(_1730179, _1730181))))], (39388 ^ _773908) ^ [_1538941, _1538943, _1538945] : [c_List_Olist_ONil(_1538941) = hAPP(hAPP(c_List_Oappend(_1538941), _1538943), _1538945), 39391 ^ _773908 : [(39394 ^ _773908) ^ [] : [-(_1538945 = c_List_Olist_ONil(_1538941))], (39392 ^ _773908) ^ [] : [-(_1538943 = c_List_Olist_ONil(_1538941))]]], (40087 ^ _773908) ^ [_1557380, _1557382, _1557384, _1557386] : [-(hAPP(hAPP(c_List_Otake(_1557380), hAPP(c_Nat_OSuc, _1557382)), hAPP(hAPP(c_List_Olist_OCons(_1557380), _1557384), _1557386)) = hAPP(hAPP(c_List_Olist_OCons(_1557380), _1557384), hAPP(hAPP(c_List_Otake(_1557380), _1557382), _1557386)))], (48177 ^ _773908) ^ [_1744946, _1744948, _1744950] : [class_Complete__Lattice_Ocomplete__lattice(_1744946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1744946), _1744948)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1744946), _1744950), c_Complete__Lattice_OInf__class_OInf(_1744946, _1744948)) = hAPP(hAPP(c_Finite__Set_Ofold(_1744946, _1744946, c_Lattices_Osemilattice__inf__class_Oinf(_1744946)), _1744950), _1744948))], (6926 ^ _773908) ^ [_886038, _886040, _886042] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886040), _886042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886038), _886042)))], (40703 ^ _773908) ^ [_1572162, _1572164, _1572166, _1572168, _1572170, _1572172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572162, _1572164)), hAPP(hAPP(c_Product__Type_OPair(_1572162, _1572164), _1572166), _1572168)), hAPP(c_List_Oset(tc_prod(_1572162, _1572164)), hAPP(hAPP(c_List_Ozip(_1572162, _1572164), _1572170), _1572172)))), -(hBOOL(hAPP(hAPP(c_member(_1572164), _1572168), hAPP(c_List_Oset(_1572164), _1572172))))], (25539 ^ _773908) ^ [_1226131, _1226133] : [class_Orderings_Olinorder(_1226131), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1226131), _1226133), _1226133) = _1226133)], (7101 ^ _773908) ^ [_888925, _888927] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _888925), _888927) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _888925 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _888927 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40816 ^ _773908) ^ [_1576199, _1576201, _1576203] : [hBOOL(hAPP(hAPP(c_member(_1576201), _1576199), c_Orderings_Obot__class_Obot(tc_fun(_1576201, tc_HOL_Obool)))), -(hBOOL(hAPP(_1576203, _1576199)))], (42483 ^ _773908) ^ [_1616210, _1616212, _1616214, _1616216, _1616218] : [-(c_List_Olist_Olist__size(_1616210, _1616212, hAPP(hAPP(c_List_Omap(_1616214, _1616210), _1616216), _1616218)) = c_List_Olist_Olist__size(_1616214, hAPP(c_Fun_Ocomp(_1616210, tc_Nat_Onat, _1616214, _1616212), _1616216), _1616218))], (50430 ^ _773908) ^ [_1794960, _1794962] : [c_Relation_Oantisym(_1794960, _1794962), -(c_Relation_Oantisym(_1794960, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1794960, _1794960), tc_HOL_Obool)), _1794962), c_Relation_OId(_1794960))))], (24687 ^ _773908) ^ [_1209013, _1209015, _1209017, _1209019, _1209021, _1209023] : [-(c_Product__Type_Oprod_Oprod__rec(_1209013, _1209015, _1209017, _1209019, hAPP(hAPP(c_Product__Type_OPair(_1209013, _1209015), _1209021), _1209023)) = hAPP(hAPP(_1209019, _1209021), _1209023))], (24223 ^ _773908) ^ [_1197690, _1197692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197690), 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)), _1197692)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197690, _1197692) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1197690, _1197692)))], (14129 ^ _773908) ^ [_1012205, _1012207, _1012209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012205), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14132 ^ _773908 : [(14133 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1012207, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012209), _1012205)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012209, _1012205))), 14136 ^ _773908 : [(14137 ^ _773908) ^ [_1012415, _1012417] : [-(hBOOL(hAPP(hAPP(_1012207, _1012417), _1012415))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012205), _1012415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012415), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1012209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012205), _1012417)), _1012415)]]], (14151 ^ _773908) ^ [] : [14154 ^ _773908 : [(14157 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14153 ^ [_1012205, _1012207, _1012209]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14159 ^ _773908) ^ [] : [-(_1012209 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012205), 14152 ^ [_1012205, _1012207, _1012209])), 14153 ^ [_1012205, _1012207, _1012209]))], (14161 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1012207, 14152 ^ [_1012205, _1012207, _1012209]), 14153 ^ [_1012205, _1012207, _1012209]))], (14155 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012205), 14153 ^ [_1012205, _1012207, _1012209])))]], -(hBOOL(hAPP(hAPP(_1012207, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012209), _1012205)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012209, _1012205))))]]], (11725 ^ _773908) ^ [_969726] : [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)), _969726)), _969726) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (45701 ^ _773908) ^ [_1687066, _1687068] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687066), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1687066))), _1687068))), -(c_List_Otranspose(_1687066, c_List_Otranspose(_1687066, _1687068)) = c_List_OtakeWhile(tc_List_Olist(_1687066), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1687066)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687066), tc_List_Olist(_1687066), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1687066))), _1687068))], (41268 ^ _773908) ^ [_1587012, _1587014, _1587016, _1587018] : [class_Groups_Osemigroup__add(_1587012), -(hAPP(c_List_Ofoldl(_1587012, _1587012, c_Groups_Oplus__class_Oplus(_1587012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1587012), _1587014), _1587016)), _1587018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1587012), _1587014), hAPP(c_List_Ofoldl(_1587012, _1587012, c_Groups_Oplus__class_Oplus(_1587012), _1587016), _1587018)))], (23855 ^ _773908) ^ [_1190969, _1190971, _1190973] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1190969, _1190971), _1190973)), 23858 ^ _773908 : [(23859 ^ _773908) ^ [_1191054] : [hBOOL(hAPP(hAPP(_1190971, _1191054), _1190973)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1190969, _1190971), _1191054)))]]], (17405 ^ _773908) ^ [_1074256, _1074258, _1074260] : [class_Rings_Osemiring__1(_1074256), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1074256), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1074258), _1074260)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074256), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1074256), _1074258)), _1074260))], (23759 ^ _773908) ^ [_1188989, _1188991, _1188993, _1188995, _1188997, _1188999] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188989, _1188991, _1188993), _1188995), hAPP(hAPP(c_Product__Type_OPair(_1188989, _1188991), _1188997), _1188999)) = hAPP(hAPP(_1188995, _1188997), _1188999))], (31780 ^ _773908) ^ [_1361273, _1361275, _1361277, _1361279, _1361281] : [class_Complete__Lattice_Ocomplete__lattice(_1361273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1361275, tc_HOL_Obool)), _1361277), _1361279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361273), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361275, _1361273), _1361277), _1361281)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361275, _1361273), _1361279), _1361281))))], (6318 ^ _773908) ^ [_876257, _876259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876257), _876259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _876257)), hAPP(c_Nat_OSuc, _876259))))], (27362 ^ _773908) ^ [_1267949, _1267951, _1267953] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267949), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267949, tc_HOL_Obool)), _1267951), _1267953)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267949), _1267951)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267949), _1267953))], (2184 ^ _773908) ^ [_805660, _805662, _805664, _805666] : [-(c_Random_Oinc__shift(_805666, _805662) = c_Random_Oinc__shift(_805664, _805660)), _805666 = _805664, _805662 = _805660], (9281 ^ _773908) ^ [_928233, _928235, _928237, _928239] : [class_Rings_Olinordered__ring__strict(_928233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928233), _928235), c_Groups_Ozero__class_Ozero(_928233))), 9288 ^ _773908 : [(9295 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928233), _928239), _928237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928233), _928235), _928237)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928233), _928235), _928239))))], (9289 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928233), _928235), _928237)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928233), _928235), _928239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928233), _928239), _928237)))]]], (5356 ^ _773908) ^ [_855738, _855740, _855742, _855744, _855746, _855748] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_855748, _855744, _855740) = c_Lazy__Sequence_Olazy__sequence_OInsert(_855746, _855742, _855738)), _855748 = _855746, _855744 = _855742, _855740 = _855738], (45727 ^ _773908) ^ [_1687623, _1687625, _1687627, _1687629] : [-(hBOOL(hAPP(_1687623, _1687625))), -(c_List_OtakeWhile(_1687627, _1687623, hAPP(hAPP(c_List_Olist_OCons(_1687627), _1687625), _1687629)) = c_List_Olist_ONil(_1687627))], (45806 ^ _773908) ^ [_1689204, _1689206] : [-(_1689204 = c_List_Olist_ONil(_1689206)), hBOOL(hAPP(c_List_Odistinct(_1689206), _1689204)), -(c_List_OtakeWhile(_1689206, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1689206), c_fNot), hAPP(hAPP(c_COMBC(_1689206, _1689206, tc_HOL_Obool), c_fequal), c_List_Olast(_1689206, _1689204))), _1689204) = c_List_Obutlast(_1689206, _1689204))], (26534 ^ _773908) ^ [_1249492, _1249494, _1249496] : [-(hAPP(c_Set_Oimage(_1249492, _1249494, _1249496), c_Orderings_Obot__class_Obot(tc_fun(_1249492, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1249494, tc_HOL_Obool)))], (45834 ^ _773908) ^ [_1689772] : [-(c_List_Oembed__list(_1689772) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1689772))], (26850 ^ _773908) ^ [_1257625, _1257627] : [-(hAPP(c_Relation_OImage(_1257625, _1257625, c_Relation_OId(_1257625)), _1257627) = _1257627)], (26277 ^ _773908) ^ [_1240861, _1240863, _1240865] : [-(hAPP(hAPP(c_Set_Oinsert(_1240861), _1240863), _1240865) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240861, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1240861), _1240863), c_Orderings_Obot__class_Obot(tc_fun(_1240861, tc_HOL_Obool)))), _1240865))], (22983 ^ _773908) ^ [_1172908, _1172910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172908), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172908)) = 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), _1172910), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1172908)))), 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)))], (50090 ^ _773908) ^ [_1786612, _1786614, _1786616, _1786618] : [class_Complete__Lattice_Ocomplete__lattice(_1786612), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1786614, _1786612), _1786616), _1786618) = c_Complete__Lattice_OSup__class_OSup(_1786612, hAPP(c_Set_OCollect(_1786612), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool), tc_HOL_Obool, _1786612), c_HOL_OEx(tc_fun(_1786614, _1786612))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool), tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool), _1786612), hAPP(c_COMBS(tc_fun(_1786614, _1786612), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1786614, _1786612)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1786614, _1786612), tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1786614, _1786612))), _1786616)))), hAPP(hAPP(c_COMBC(_1786612, tc_fun(tc_fun(_1786614, _1786612), _1786612), tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1786612, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1786614, _1786612), _1786612), tc_fun(tc_fun(_1786614, _1786612), tc_HOL_Obool)), _1786612), c_COMBB(_1786612, tc_HOL_Obool, tc_fun(_1786614, _1786612))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1786614, _1786612), _1786614, _1786612), c_COMBI(tc_fun(_1786614, _1786612))), _1786618)))))))], (30501 ^ _773908) ^ [_1331597, _1331599, _1331601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331597), _1331599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331597, tc_HOL_Obool)), _1331601), _1331599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331597), _1331601)), hAPP(c_Finite__Set_Ocard(_1331597), _1331599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1331597, tc_HOL_Obool)), _1331601), _1331599)))], (42607 ^ _773908) ^ [_1619048, _1619050] : [42608 ^ _773908 : [(42609 ^ _773908) ^ [_1619094] : [hBOOL(hAPP(_1619048, _1619094))]], -(hBOOL(hAPP(_1619048, c_Hilbert__Choice_OEps(_1619050, _1619048))))], (39983 ^ _773908) ^ [_1554690, _1554692, _1554694, _1554696] : [-(hAPP(hAPP(c_List_Onth(_1554690), hAPP(hAPP(c_List_Olist_OCons(_1554690), _1554692), _1554694)), _1554696) = c_Nat_Onat_Onat__case(_1554690, _1554692, hAPP(c_List_Onth(_1554690), _1554694), _1554696))], (28965 ^ _773908) ^ [_1302873, _1302875, _1302877] : [class_Lattices_Olattice(_1302873), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302873), _1302875)), hBOOL(hAPP(hAPP(c_member(_1302873), _1302877), _1302875)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302873), _1302877), c_Big__Operators_Olattice__class_OInf__fin(_1302873, _1302875)) = c_Big__Operators_Olattice__class_OInf__fin(_1302873, _1302875))], (47429 ^ _773908) ^ [_1727719, _1727721, _1727723] : [hAPP(hAPP(c_Relation_Orel__comp(_1727719, _1727719, _1727719), hAPP(c_Relation_Oconverse(_1727719, _1727719), _1727721)), _1727721) = _1727721, hAPP(c_Relation_ODomain(_1727719, _1727719), _1727721) = _1727723, -(c_Equiv__Relations_Oequiv(_1727719, _1727723, _1727721))], (18667 ^ _773908) ^ [_1096574, _1096576, _1096578, _1096580] : [-(hBOOL(hAPP(hAPP(c_member(_1096574), _1096576), _1096578))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096574, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1096574), _1096576), _1096580)), _1096578) = hAPP(hAPP(c_Set_Oinsert(_1096574), _1096576), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096574, tc_HOL_Obool)), _1096580), _1096578)))], (4266 ^ _773908) ^ [_838665, _838667, _838669, _838671, _838673, _838675, _838677, _838679] : [-(c_Lazy__Sequence_Ohb__bind(_838679, _838675, _838671, _838667) = c_Lazy__Sequence_Ohb__bind(_838677, _838673, _838669, _838665)), _838679 = _838677, _838675 = _838673, _838671 = _838669, _838667 = _838665], (10989 ^ _773908) ^ [_956664, _956666, _956668, _956670] : [class_Groups_Oordered__comm__monoid__add(_956664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956664), c_Groups_Ozero__class_Ozero(_956664)), _956666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956664), _956668), _956670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956664), _956668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956664), _956666), _956670))))], (4694 ^ _773908) ^ [_845493, _845495, _845497, _845499, _845501, _845503] : [-(c_New__DSequence_Opos__union(_845503, _845499, _845495) = c_New__DSequence_Opos__union(_845501, _845497, _845493)), _845503 = _845501, _845499 = _845497, _845495 = _845493], (40388 ^ _773908) ^ [_1564354, _1564356, _1564358] : [hBOOL(hAPP(hAPP(c_member(_1564354), _1564356), hAPP(c_List_Oset(_1564354), _1564358))), 40392 ^ _773908 : [(40395 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1564354), _1564358), 40391 ^ [_1564354, _1564356, _1564358]) = _1564356)], (40393 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40391 ^ [_1564354, _1564356, _1564358]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1564354)), _1564358))))]]], (41404 ^ _773908) ^ [_1589895, _1589897, _1589899] : [_1589895 = c_List_Olist_ONil(_1589897), -(c_List_Olast(_1589897, hAPP(hAPP(c_List_Olist_OCons(_1589897), _1589899), _1589895)) = _1589899)], (42341 ^ _773908) ^ [_1612732, _1612734, _1612736, _1612738, _1612740] : [hAPP(hAPP(c_List_Omap(_1612732, _1612734), _1612736), _1612738) = hAPP(hAPP(c_List_Omap(_1612732, _1612734), _1612736), _1612740), c_Fun_Oinj__on(_1612732, _1612734, _1612736, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1612732, tc_HOL_Obool)), hAPP(c_List_Oset(_1612732), _1612738)), hAPP(c_List_Oset(_1612732), _1612740))), -(_1612738 = _1612740)], (1734 ^ _773908) ^ [_798569, _798571] : [-(class_Divides_Osemiring__div(_798569)), _798571 = _798569, class_Divides_Osemiring__div(_798571)], (4076 ^ _773908) ^ [_835486, _835488] : [_835488 = _835486, -(c_Nitpick_Ofrac(_835488) = c_Nitpick_Ofrac(_835486))], (51384 ^ _773908) ^ [_1813140, _1813142] : [-(class_Enum_Oenum(tc_fun(_1813140, _1813142))), class_Enum_Oenum(_1813140), class_Enum_Oenum(_1813142)], (3838 ^ _773908) ^ [_831789, _831791, _831793, _831795, _831797, _831799] : [-(c_Big__Operators_Olattice_OSup__fin(_831799, _831795, _831791) = c_Big__Operators_Olattice_OSup__fin(_831797, _831793, _831789)), _831799 = _831797, _831795 = _831793, _831791 = _831789], (16025 ^ _773908) ^ [_1047765, _1047767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047765), _1047767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047767), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (16575 ^ _773908) ^ [_1058392, _1058394] : [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), _1058392)), _1058394))), _1058392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1058394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40981 ^ _773908) ^ [_1581231, _1581233] : [_1581233 = c_List_Olist_ONil(_1581231), -(hAPP(c_List_Orotate1(_1581231), _1581233) = c_List_Olist_ONil(_1581231))], (24455 ^ _773908) ^ [_1203372, _1203374, _1203376] : [_1203374 = _1203376, -(hAPP(hAPP(c_COMBC(_1203372, tc_fun(_1203372, tc_HOL_Obool), tc_HOL_Obool), c_member(_1203372)), _1203374) = hAPP(hAPP(c_COMBC(_1203372, tc_fun(_1203372, tc_HOL_Obool), tc_HOL_Obool), c_member(_1203372)), _1203376))], (33686 ^ _773908) ^ [_1399655, _1399657, _1399659, _1399661, _1399663, _1399665] : [c_Fun_Oinj__on(_1399655, _1399657, _1399659, _1399661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1399655, tc_HOL_Obool)), _1399663), _1399661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1399655, tc_HOL_Obool)), _1399665), _1399661)), -(hAPP(c_Set_Oimage(_1399655, _1399657, _1399659), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399655, tc_HOL_Obool)), _1399663), _1399665)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399657, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1399655, _1399657, _1399659), _1399663)), hAPP(c_Set_Oimage(_1399655, _1399657, _1399659), _1399665)))], (35132 ^ _773908) ^ [_1431127, _1431129, _1431131, _1431133, _1431135] : [class_Groups_Oab__group__add(_1431127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431129), _1431131)), 35139 ^ _773908 : [(35146 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1431129), _1431133), _1431131))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431129, _1431127), _1431135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431129, tc_HOL_Obool)), _1431131), hAPP(hAPP(c_Set_Oinsert(_1431129), _1431133), c_Orderings_Obot__class_Obot(tc_fun(_1431129, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431129, _1431127), _1431135), _1431131))], (35140 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1431129), _1431133), _1431131)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431129, _1431127), _1431135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431129, tc_HOL_Obool)), _1431131), hAPP(hAPP(c_Set_Oinsert(_1431129), _1431133), c_Orderings_Obot__class_Obot(tc_fun(_1431129, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431127), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431129, _1431127), _1431135), _1431131)), hAPP(_1431135, _1431133)))]]], (12648 ^ _773908) ^ [_985886, _985888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985886)), _985888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985886), _985888)))], (49394 ^ _773908) ^ [_1770625, _1770627, _1770629] : [-(_1770627 = _1770629), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770625, _1770625, hAPP(hAPP(c_COMBB(tc_fun(_1770625, tc_HOL_Obool), tc_fun(_1770625, tc_HOL_Obool), _1770625), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1770625), c_fNot)), c_fequal)), _1770627), _1770629)))], (13744 ^ _773908) ^ [_1005412, _1005414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005414, _1005412)), _1005412)))], (51320 ^ _773908) ^ [_1812300, _1812302] : [class_Lattices_Oboolean__algebra(_1812300), -(class_Lattices_Oboolean__algebra(tc_fun(_1812302, _1812300)))], (11896 ^ _773908) ^ [_972874, _972876, _972878, _972880] : [class_Rings_Olinordered__semiring(_972874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972874), _972876), _972878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972874), _972876), _972880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972874), c_Groups_Ozero__class_Ozero(_972874)), _972876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972874), _972878), _972880)))], (27552 ^ _773908) ^ [_1272204, _1272206, _1272208, _1272210] : [c_Finite__Set_Ofolding__one(_1272204, _1272206, _1272208), -(hAPP(_1272208, hAPP(hAPP(c_Set_Oinsert(_1272204), _1272210), c_Orderings_Obot__class_Obot(tc_fun(_1272204, tc_HOL_Obool)))) = _1272210)], (13223 ^ _773908) ^ [_995907, _995909] : [13224 ^ _773908 : [(13227 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995909))], (13225 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995907))]], 13228 ^ _773908 : [(13235 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _995907), _995909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _995907)), hAPP(c_Int_Onat, _995909))))], (13229 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _995907)), hAPP(c_Int_Onat, _995909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _995907), _995909)))]]], (18937 ^ _773908) ^ [_1101055] : [class_Rings_Oring__1(_1101055), -(hBOOL(hAPP(hAPP(c_member(_1101055), c_Groups_Ozero__class_Ozero(_1101055)), c_Int_Oring__1__class_OInts(_1101055))))], (2 ^ _773908) ^ [_773935] : [-(_773935 = _773935)], (1006 ^ _773908) ^ [_789181, _789183, _789185, _789187] : [-(c_Relation_Otrans(_789185, _789181)), c_Relation_Otrans(_789187, _789183), _789187 = _789185, _789183 = _789181], (25607 ^ _773908) ^ [_1227474, _1227476, _1227478, _1227480] : [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), _1227474), _1227476)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1227478), _1227480))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227474), _1227480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227478), _1227476))], (43921 ^ _773908) ^ [_1648031, _1648033, _1648035, _1648037, _1648039] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648031, tc_fun(_1648033, tc_HOL_Obool)), _1648035), hAPP(hAPP(c_COMBS(_1648031, tc_fun(_1648033, tc_HOL_Obool), tc_fun(_1648033, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648033, tc_HOL_Obool), tc_fun(tc_fun(_1648033, tc_HOL_Obool), tc_fun(_1648033, tc_HOL_Obool)), _1648031), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1648033, tc_HOL_Obool))), _1648037)), _1648039)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1648033, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648033, tc_HOL_Obool), hAPP(c_Set_Oimage(_1648031, tc_fun(_1648033, tc_HOL_Obool), _1648037), _1648035))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648033, tc_HOL_Obool), hAPP(c_Set_Oimage(_1648031, tc_fun(_1648033, tc_HOL_Obool), _1648039), _1648035))))], (38986 ^ _773908) ^ [_1527523, _1527525] : [-(c_FunDef_Oreduction__pair(_1527523, _1527525)), c_Wellfounded_Owf(_1527523, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool), tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool)), _1527525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527523, _1527523, _1527523), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool), tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool)), _1527525)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool), tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool)), _1527525))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool), tc_fun(tc_prod(_1527523, _1527523), tc_HOL_Obool)), _1527525)))], (14412 ^ _773908) ^ [_1017767, _1017769, _1017771] : [_1017767 = 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), _1017767), _1017769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017767), _1017771)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34386 ^ _773908) ^ [_1414086, _1414088] : [class_Orderings_Oorder(_1414086), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414086, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1414086), _1414088), c_Orderings_Obot__class_Obot(tc_fun(_1414086, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1414086), _1414088)) = hAPP(hAPP(c_Set_Oinsert(_1414086), _1414088), c_Orderings_Obot__class_Obot(tc_fun(_1414086, tc_HOL_Obool))))], (15187 ^ _773908) ^ [_1031367, _1031369, _1031371] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031367), _1031369)), _1031371) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031367), _1031371)), _1031369))], (49594 ^ _773908) ^ [_1774829, _1774831, _1774833] : [-(hAPP(hAPP(c_List_Oappend(_1774829), c_List_Oreplicate(_1774829, _1774831, _1774833)), hAPP(hAPP(c_List_Olist_OCons(_1774829), _1774833), c_List_Olist_ONil(_1774829))) = hAPP(hAPP(c_List_Olist_OCons(_1774829), _1774833), c_List_Oreplicate(_1774829, _1774831, _1774833)))], (13023 ^ _773908) ^ [_992413, _992415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992413)), _992415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992413), _992415)))], (5879 ^ _773908) ^ [_867923, _867925, _867927] : [-(hAPP(hAPP(c_Set_Oinsert(_867923), _867925), hAPP(hAPP(c_Set_Oinsert(_867923), _867925), _867927)) = hAPP(hAPP(c_Set_Oinsert(_867923), _867925), _867927))], (13440 ^ _773908) ^ [_999626, _999628] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999626, tc_HOL_Obool)), _999628), _999628)))], (3732 ^ _773908) ^ [_830206, _830208, _830210, _830212, _830214, _830216] : [-(c_List_OtakeWhile(_830216, _830212, _830208) = c_List_OtakeWhile(_830214, _830210, _830206)), _830216 = _830214, _830212 = _830210, _830208 = _830206], (21299 ^ _773908) ^ [_1142096, _1142098] : [class_Rings_Odivision__ring__inverse__zero(_1142096), 21302 ^ _773908 : [(21309 ^ _773908) ^ [] : [-(_1142098 = c_Groups_Ozero__class_Ozero(_1142096)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142096), _1142098), _1142098) = c_Groups_Oone__class_Oone(_1142096))], (21303 ^ _773908) ^ [] : [_1142098 = c_Groups_Ozero__class_Ozero(_1142096), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142096), _1142098), _1142098) = c_Groups_Ozero__class_Ozero(_1142096))]]], (34340 ^ _773908) ^ [_1413255, _1413257, _1413259] : [class_Orderings_Olinorder(_1413255), 34343 ^ _773908 : [(34350 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413255), _1413257), _1413259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413255, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413255), _1413257)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413255), _1413259))))], (34344 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413255, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413255), _1413257)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413255), _1413259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413255), _1413257), _1413259)))]]], (10793 ^ _773908) ^ [_953108, _953110] : [class_Rings_Olinordered__idom(_953108), 10796 ^ _773908 : [(10803 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _953110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953108), c_Groups_Ozero__class_Ozero(_953108)), hAPP(c_Int_Oring__1__class_Oof__int(_953108), _953110))))], (10797 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953108), c_Groups_Ozero__class_Ozero(_953108)), hAPP(c_Int_Oring__1__class_Oof__int(_953108), _953110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _953110)))]]], (1464 ^ _773908) ^ [_795194, _795196] : [-(class_Orderings_Otop(_795194)), _795196 = _795194, class_Orderings_Otop(_795196)], (38122 ^ _773908) ^ [_1498985, _1498987] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498985, tc_HOL_Obool)), _1498987) = hAPP(c_Set_OCollect(_1498985), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498985), c_fNot), hAPP(hAPP(c_COMBC(_1498985, tc_fun(_1498985, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498985)), _1498987))))], (37446 ^ _773908) ^ [_1482154, _1482156] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1482154, _1482156), c_Orderings_Otop__class_Otop(tc_fun(_1482154, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1482156, tc_HOL_Obool), _1482154), c_Orderings_Otop__class_Otop(tc_fun(_1482156, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1482154, _1482156), tc_HOL_Obool)))], (27418 ^ _773908) ^ [_1269145, _1269147, _1269149] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1269145, tc_HOL_Obool), tc_fun(_1269145, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1269145, tc_HOL_Obool), tc_fun(_1269145, tc_HOL_Obool)), _1269147), _1269149)), c_Wellfounded_Ofinite__psubset(_1269145)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1269145, tc_HOL_Obool)), _1269147), _1269149)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269145), _1269149))], (42141 ^ _773908) ^ [_1607166, _1607168, _1607170, _1607172, _1607174, _1607176] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607166, tc_fun(_1607168, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1607170, _1607166, _1607172), _1607174)), _1607176) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607170, tc_fun(_1607168, tc_HOL_Obool)), _1607174), hAPP(hAPP(c_COMBB(_1607166, tc_fun(_1607168, tc_HOL_Obool), _1607170), _1607176), _1607172)))], (33782 ^ _773908) ^ [_1401545] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1401545), hAPP(c_Nat_OSuc, _1401545)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1401545), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (25619 ^ _773908) ^ [_1227770] : [-(_1227770 = 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)), _1227770), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (5992 ^ _773908) ^ [_870078, _870080, _870082, _870084] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_870078, _870080)), _870082), _870084))), 5993 ^ _773908 : [(5994 ^ _773908) ^ [_870146] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870078), _870082), _870146)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870080), _870146), _870084))]]], (39063 ^ _773908) ^ [_1529466, _1529468, _1529470, _1529472] : [-(hAPP(c_Relation_ORange(_1529466, _1529468), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529466, _1529468), tc_HOL_Obool)), _1529470), _1529472)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529468, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1529466, _1529468), _1529470)), hAPP(c_Relation_ORange(_1529466, _1529468), _1529472)))], (15039 ^ _773908) ^ [_1028686, _1028688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028688)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028686, _1028688)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1028686), hAPP(c_Int_Onat, _1028688)))], (42321 ^ _773908) ^ [_1612301, _1612303, _1612305, _1612307, _1612309] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1612301), tc_List_Olist(_1612303), tc_List_Olist(_1612305), hAPP(c_List_Omap(_1612301, _1612303), _1612307)), hAPP(c_List_Omap(_1612305, _1612301), _1612309)) = hAPP(c_List_Omap(_1612305, _1612303), hAPP(c_Fun_Ocomp(_1612301, _1612303, _1612305, _1612307), _1612309)))], (7382 ^ _773908) ^ [_893327] : [_893327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893327), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (43852 ^ _773908) ^ [_1646506, _1646508, _1646510] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646506, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646506, tc_HOL_Obool), _1646508)), _1646510) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646506, tc_HOL_Obool), tc_fun(_1646506, tc_HOL_Obool)), _1646508), hAPP(hAPP(c_COMBC(tc_fun(_1646506, tc_HOL_Obool), tc_fun(_1646506, tc_HOL_Obool), tc_fun(_1646506, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646506, tc_HOL_Obool))), _1646510)))], (12959 ^ _773908) ^ [_991306, _991308, _991310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991306, tc_HOL_Obool)), _991308), _991310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991306, tc_HOL_Obool)), _991308), _991310))), -(_991308 = _991310)], (30489 ^ _773908) ^ [_1331241, _1331243, _1331245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331241), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331241, tc_HOL_Obool)), _1331243), _1331245))), -(hAPP(c_Finite__Set_Ocard(_1331241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331241, tc_HOL_Obool)), _1331243), _1331245)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331241), _1331243)), hAPP(c_Finite__Set_Ocard(_1331241), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331241, tc_HOL_Obool)), _1331243), _1331245))))], (21399 ^ _773908) ^ [_1143738, _1143740, _1143742, _1143744, _1143746] : [class_Fields_Olinordered__field(_1143738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143738), c_Groups_Ozero__class_Ozero(_1143738)), _1143740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143738), _1143740), _1143742)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143738), c_Groups_Ozero__class_Ozero(_1143738)), _1143744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143738), _1143744), _1143746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143738), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143738), _1143740), _1143746)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143738), _1143742), _1143744))))], (12662 ^ _773908) ^ [_986124, _986126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986124), _986126)), -(_986124 = _986126), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986124), _986126)))], (32125 ^ _773908) ^ [_1369479, _1369481, _1369483, _1369485] : [class_Orderings_Olinorder(_1369479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369479), _1369481), _1369483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369479), _1369483), _1369485)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1369479, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369479, _1369481, _1369483)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369479, _1369483, _1369485)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1369479, _1369481, _1369485))], (26812 ^ _773908) ^ [_1257106, _1257108, _1257110, _1257112, _1257114, _1257116] : [-(_1257106 = _1257108), -(hAPP(c_Fun_Ofun__upd(_1257110, _1257112, _1257114, _1257108, _1257116), _1257106) = hAPP(_1257114, _1257106))], (1454 ^ _773908) ^ [_795069, _795071] : [-(class_Lattices_Olattice(_795069)), _795071 = _795069, class_Lattices_Olattice(_795071)], (25033 ^ _773908) ^ [_1215499, _1215501, _1215503] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_1215499, _1215501)), _1215503), hAPP(hAPP(hAPP(c_Natural_Oupdate, _1215503), _1215499), hAPP(_1215501, _1215503)))))], (47203 ^ _773908) ^ [_1721981, _1721983, _1721985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721981, _1721981), tc_HOL_Obool)), _1721983), _1721985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721981, _1721981), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1721981, _1721981, _1721981), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1721981, _1721981), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1721981, _1721983)), _1721985)), _1721983)), _1721985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721981, _1721981), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1721981, _1721983)), _1721985)))], (22561 ^ _773908) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (37710 ^ _773908) ^ [_1489499, _1489501, _1489503] : [-(hAPP(c_Product__Type_Omap__pair(_1489499, _1489499, _1489501, _1489501, c_COMBI(_1489499), c_COMBI(_1489501)), _1489503) = _1489503)], (27956 ^ _773908) ^ [_1279922, _1279924, _1279926, _1279928, _1279930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279922, tc_HOL_Obool)), _1279924), _1279926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279922, tc_HOL_Obool)), _1279928), _1279930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279922, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1279922, tc_HOL_Obool)), _1279924), _1279928)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1279922, tc_HOL_Obool)), _1279926), _1279930))))], (12574 ^ _773908) ^ [_984611, _984613, _984615, _984617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984611, tc_HOL_Obool)), _984613), _984615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984611, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984611), _984617), _984613)), hAPP(hAPP(c_Set_Oinsert(_984611), _984617), _984615))))], (5891 ^ _773908) ^ [_868180, _868182, _868184] : [c_Com_Ocom_OSemi(_868180, _868182) = hAPP(c_Com_Ocom_OBODY, _868184)], (45816 ^ _773908) ^ [_1689401, _1689403, _1689405, _1689407, _1689409] : [class_Orderings_Olinorder(_1689401), c_List_Olinorder__class_Osorted(_1689401, hAPP(c_List_Orev(_1689401), hAPP(hAPP(c_List_Omap(_1689403, _1689401), _1689405), _1689407))), -(hAPP(c_List_Ofilter(_1689403, hAPP(hAPP(c_COMBB(_1689401, tc_HOL_Obool, _1689403), hAPP(c_Orderings_Oord__class_Oless(_1689401), _1689409)), _1689405)), _1689407) = c_List_OtakeWhile(_1689403, hAPP(hAPP(c_COMBB(_1689401, tc_HOL_Obool, _1689403), hAPP(c_Orderings_Oord__class_Oless(_1689401), _1689409)), _1689405), _1689407))], (47467 ^ _773908) ^ [_1728638, _1728640, _1728642] : [c_Relation_Osingle__valued(_1728638, _1728638, _1728640), -(c_Relation_Osingle__valued(_1728638, _1728638, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1728638, _1728638), tc_HOL_Obool), _1728642), _1728640)))], (40901 ^ _773908) ^ [_1578739, _1578741, _1578743] : [-(c_Relation_Orefl__on(_1578739, _1578741, _1578743)), 40905 ^ _773908 : [(40908 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1578739, _1578739, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1578739, tc_fun(_1578739, tc_HOL_Obool), tc_fun(_1578739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578739, tc_HOL_Obool), tc_fun(_1578739, tc_HOL_Obool)), _1578739), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578739), c_fconj), hAPP(hAPP(c_COMBC(_1578739, tc_fun(_1578739, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578739)), _1578741)))), hAPP(hAPP(c_COMBC(_1578739, tc_fun(_1578739, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578739)), _1578741))), 40904 ^ [_1578739, _1578741, _1578743]))], (40906 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578739, _1578739)), 40904 ^ [_1578739, _1578741, _1578743]), _1578743)))]], 40910 ^ _773908 : [(40913 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578739, _1578739)), hAPP(hAPP(c_Product__Type_OPair(_1578739, _1578739), 40909 ^ [_1578739, _1578741, _1578743]), 40909 ^ [_1578739, _1578741, _1578743])), _1578743))], (40911 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578739), 40909 ^ [_1578739, _1578741, _1578743]), _1578741)))]]], (5270 ^ _773908) ^ [_854475, _854477] : [_854477 = _854475, -(c_HOL_OEx(_854477) = c_HOL_OEx(_854475))], (7473 ^ _773908) ^ [_894838, _894840] : [class_Groups_Olinordered__ab__group__add(_894838), 7476 ^ _773908 : [(7483 ^ _773908) ^ [] : [_894840 = c_Groups_Ozero__class_Ozero(_894838), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894838), _894840), _894840) = c_Groups_Ozero__class_Ozero(_894838))], (7477 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894838), _894840), _894840) = c_Groups_Ozero__class_Ozero(_894838), -(_894840 = c_Groups_Ozero__class_Ozero(_894838))]]], (17923 ^ _773908) ^ [_1083257] : [class_Int_Onumber__ring(_1083257), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1083257), c_Groups_Oone__class_Oone(_1083257)) = hAPP(c_Int_Onumber__class_Onumber__of(_1083257), c_Int_OMin))], (26864 ^ _773908) ^ [_1257917, _1257919] : [-(c_Relation_Oirrefl(_1257917, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1257917, _1257917), tc_HOL_Obool)), _1257919), c_Relation_OId(_1257917))))], (43055 ^ _773908) ^ [_1628263, _1628265, _1628267] : [class_Orderings_Olinorder(_1628263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628263), _1628265)), -(c_List_Olinorder__class_Osorted__list__of__set(_1628263, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1628263, tc_HOL_Obool)), _1628265), hAPP(hAPP(c_Set_Oinsert(_1628263), _1628267), c_Orderings_Obot__class_Obot(tc_fun(_1628263, tc_HOL_Obool))))) = c_List_Oremove1(_1628263, _1628267, c_List_Olinorder__class_Osorted__list__of__set(_1628263, _1628265)))], (5014 ^ _773908) ^ [_850475, _850477] : [_850477 = _850475, -(c_DSequence_Oempty(_850477) = c_DSequence_Oempty(_850475))], (37416 ^ _773908) ^ [_1481133, _1481135, _1481137, _1481139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1481133), _1481135)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481137), _1481139)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1481133, _1481137)), hAPP(hAPP(c_Product__Type_OSigma(_1481133, _1481137), _1481135), hAPP(c_COMBK(tc_fun(_1481137, tc_HOL_Obool), _1481133), _1481139)))))], (4486 ^ _773908) ^ [_842217, _842219] : [_842219 = _842217, -(c_List_Otl(_842219) = c_List_Otl(_842217))], (230 ^ _773908) ^ [_777361, _777363, _777365, _777367, _777369, _777371, _777373, _777375, _777377, _777379] : [-(c_Big__Operators_Ocomm__monoid__big(_777377, _777373, _777369, _777365, _777361)), c_Big__Operators_Ocomm__monoid__big(_777379, _777375, _777371, _777367, _777363), _777379 = _777377, _777375 = _777373, _777371 = _777369, _777367 = _777365, _777363 = _777361], (37147 ^ _773908) ^ [_1474069, _1474071, _1474073, _1474075] : [-(hAPP(c_Set_Ovimage(_1474069, _1474071, _1474073), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1474071, tc_HOL_Obool)), _1474075)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1474069, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1474069, _1474071, _1474073), _1474075)))], (41957 ^ _773908) ^ [_1601389, _1601391, _1601393, _1601395, _1601397, _1601399, _1601401, _1601403] : [-(hAPP(hAPP(c_List_Ozip(_1601389, _1601391), hAPP(hAPP(c_List_Omap(_1601393, _1601389), _1601395), _1601397)), hAPP(hAPP(c_List_Omap(_1601399, _1601391), _1601401), _1601403)) = hAPP(hAPP(c_List_Omap(tc_prod(_1601393, _1601399), tc_prod(_1601389, _1601391)), hAPP(c_Product__Type_Oprod_Oprod__case(_1601393, _1601399, tc_prod(_1601389, _1601391)), hAPP(hAPP(c_COMBC(_1601393, tc_fun(_1601399, _1601391), tc_fun(_1601399, tc_prod(_1601389, _1601391))), hAPP(hAPP(c_COMBB(tc_fun(_1601391, tc_prod(_1601389, _1601391)), tc_fun(tc_fun(_1601399, _1601391), tc_fun(_1601399, tc_prod(_1601389, _1601391))), _1601393), c_COMBB(_1601391, tc_prod(_1601389, _1601391), _1601399)), hAPP(hAPP(c_COMBB(_1601389, tc_fun(_1601391, tc_prod(_1601389, _1601391)), _1601393), c_Product__Type_OPair(_1601389, _1601391)), _1601395))), _1601401))), hAPP(hAPP(c_List_Ozip(_1601393, _1601399), _1601397), _1601403)))], (44036 ^ _773908) ^ [_1651370, _1651372] : [class_Complete__Lattice_Ocomplete__lattice(_1651370), -(c_Complete__Lattice_OInf__class_OInf(_1651370, _1651372) = c_Complete__Lattice_OSup__class_OSup(_1651370, hAPP(c_Set_OCollect(_1651370), hAPP(hAPP(c_COMBB(tc_fun(_1651370, tc_HOL_Obool), tc_HOL_Obool, _1651370), c_HOL_OAll(_1651370)), hAPP(hAPP(c_COMBB(tc_fun(_1651370, tc_HOL_Obool), tc_fun(_1651370, tc_HOL_Obool), _1651370), hAPP(c_COMBS(_1651370, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1651370), c_fimplies), hAPP(hAPP(c_COMBC(_1651370, tc_fun(_1651370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1651370)), _1651372)))), c_Orderings_Oord__class_Oless__eq(_1651370))))))], (7032 ^ _773908) ^ [_887812, _887814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887812), _887814)), -(_887814 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887812), 7035 ^ [_887812, _887814])))], (15835 ^ _773908) ^ [_1043524, _1043526, _1043528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043524), _1043526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043526), _1043528)), _1043524))))], (40113 ^ _773908) ^ [_1557848, _1557850, _1557852] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557848)), hAPP(hAPP(c_List_Otake(_1557848), _1557850), _1557852)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557848)), _1557852)), _1557850))], (48965 ^ _773908) ^ [_1761229, _1761231, _1761233] : [-(c_Nitpick_Oplus__frac(_1761229, _1761231, _1761233) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1761229), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1761229), _1761231), hAPP(c_Nitpick_Odenom(_1761229), _1761233))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1761229), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1761229), tc_Int_Oint), c_Nitpick_Ofrac(_1761229)), 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(_1761229), _1761231))), 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(_1761229), _1761231))))), 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(_1761229), _1761233))), 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(_1761229), _1761233)))))), c_COMBI(tc_Int_Oint))))], (20559 ^ _773908) ^ [_1129076] : [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, _1129076, 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, _1129076, 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))], (28452 ^ _773908) ^ [_1291431, _1291433, _1291435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291431, tc_HOL_Obool)), _1291433), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1291431, tc_HOL_Obool)), _1291435))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291431, tc_HOL_Obool)), _1291433), _1291435) = c_Orderings_Obot__class_Obot(tc_fun(_1291431, tc_HOL_Obool)))], (13710 ^ _773908) ^ [_1004819, _1004821, _1004823, _1004825] : [class_Divides_Osemiring__div(_1004819), -(c_Divides_Odiv__class_Omod(_1004819, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004819), _1004821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004819), _1004823), _1004825)), _1004823) = c_Divides_Odiv__class_Omod(_1004819, _1004821, _1004823))], (24691 ^ _773908) ^ [_1209159, _1209161, _1209163, _1209165, _1209167] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_1209159, _1209161), _1209163, _1209165, _1209167), -(_1209167 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _1209163), _1209159), hAPP(_1209161, _1209163)))], (38490 ^ _773908) ^ [_1514238, _1514240] : [-(c_Product__Type_Omap__pair(_1514238, _1514238, _1514240, _1514240, c_Fun_Oid(_1514238), c_Fun_Oid(_1514240)) = c_Fun_Oid(tc_prod(_1514238, _1514240)))], (30209 ^ _773908) ^ [_1325592, _1325594, _1325596] : [class_Orderings_Olinorder(_1325592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325592), _1325594)), 30216 ^ _773908 : [(30223 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325592, tc_HOL_Obool)), _1325594), hAPP(hAPP(c_Set_Oinsert(_1325592), _1325596), c_Orderings_Obot__class_Obot(tc_fun(_1325592, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1325592, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1325592, c_Orderings_Oord__class_Omin(_1325592), hAPP(hAPP(c_Set_Oinsert(_1325592), _1325596), _1325594)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325592), _1325596), c_Big__Operators_Olattice_OInf__fin(_1325592, c_Orderings_Oord__class_Omin(_1325592), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325592, tc_HOL_Obool)), _1325594), hAPP(hAPP(c_Set_Oinsert(_1325592), _1325596), c_Orderings_Obot__class_Obot(tc_fun(_1325592, tc_HOL_Obool)))))))], (30217 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325592, tc_HOL_Obool)), _1325594), hAPP(hAPP(c_Set_Oinsert(_1325592), _1325596), c_Orderings_Obot__class_Obot(tc_fun(_1325592, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1325592, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1325592, c_Orderings_Oord__class_Omin(_1325592), hAPP(hAPP(c_Set_Oinsert(_1325592), _1325596), _1325594)) = _1325596)]]], (37024 ^ _773908) ^ [_1471388, _1471390, _1471392] : [class_Groups_Oab__semigroup__mult(_1471388), -(_1471390 = c_Orderings_Obot__class_Obot(tc_fun(_1471388, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471388), _1471390)), -(hBOOL(hAPP(hAPP(c_member(_1471388), _1471392), _1471390))), -(hAPP(c_Finite__Set_Ofold1(_1471388, c_Groups_Otimes__class_Otimes(_1471388)), hAPP(hAPP(c_Set_Oinsert(_1471388), _1471392), _1471390)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471388), _1471392), hAPP(c_Finite__Set_Ofold1(_1471388, c_Groups_Otimes__class_Otimes(_1471388)), _1471390)))], (38184 ^ _773908) ^ [_1501505, _1501507, _1501509, _1501511, _1501513, _1501515] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501505), _1501507)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501509), _1501511)), 38194 ^ _773908 : [(38197 ^ _773908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1501505), hAPP(c_Set_OCollect(_1501505), hAPP(hAPP(c_COMBS(_1501505, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501505), c_fconj), hAPP(hAPP(c_COMBC(_1501505, tc_fun(_1501505, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501505)), _1501507))), hAPP(hAPP(c_COMBC(_1501505, _1501509, tc_HOL_Obool), _1501513), 38193 ^ [_1501505, _1501507, _1501509, _1501511, _1501513, _1501515])))) = _1501515], (38195 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501509), 38193 ^ [_1501505, _1501507, _1501509, _1501511, _1501513, _1501515]), _1501511)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501505, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1501509, tc_HOL_Obool), tc_Nat_Onat, _1501505), c_Finite__Set_Ocard(_1501509)), hAPP(hAPP(c_COMBB(tc_fun(_1501509, tc_HOL_Obool), tc_fun(_1501509, tc_HOL_Obool), _1501505), c_Set_OCollect(_1501509)), hAPP(hAPP(c_COMBB(tc_fun(_1501509, tc_HOL_Obool), tc_fun(_1501509, tc_HOL_Obool), _1501505), hAPP(c_COMBS(_1501509, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501509), c_fconj), hAPP(hAPP(c_COMBC(_1501509, tc_fun(_1501509, tc_HOL_Obool), tc_HOL_Obool), c_member(_1501509)), _1501511)))), _1501513)))), _1501507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1501515), hAPP(c_Finite__Set_Ocard(_1501509), _1501511)))], (51788 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (51598 ^ _773908) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (3546 ^ _773908) ^ [_827313, _827315, _827317, _827319] : [-(c_List_Obutlast(_827319, _827315) = c_List_Obutlast(_827317, _827313)), _827319 = _827317, _827315 = _827313], (2170 ^ _773908) ^ [_805439, _805441, _805443, _805445, _805447, _805449] : [-(c_Random_Ominus__shift(_805449, _805445, _805441) = c_Random_Ominus__shift(_805447, _805443, _805439)), _805449 = _805447, _805445 = _805443, _805441 = _805439], (34320 ^ _773908) ^ [_1412917] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412917)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1412917))], (17331 ^ _773908) ^ [_1072905, _1072907] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1072905)), _1072907) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072905), _1072907)))], (38591 ^ _773908) ^ [_1517312, _1517314, _1517316, _1517318] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517312, _1517314, _1517316), _1517318), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517314, _1517316), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517312, _1517316), tc_HOL_Obool)))], (15209 ^ _773908) ^ [_1031731, _1031733, _1031735] : [class_Rings_Oring__1(_1031731), -(hAPP(c_Int_Oring__1__class_Oof__int(_1031731), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031733), _1031735)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031731), hAPP(c_Int_Oring__1__class_Oof__int(_1031731), _1031733)), hAPP(c_Int_Oring__1__class_Oof__int(_1031731), _1031735)))], (13901 ^ _773908) ^ [_1008021, _1008023] : [class_Lattices_Oboolean__algebra(_1008021), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1008021), hAPP(c_Groups_Ouminus__class_Ouminus(_1008021), _1008023)) = _1008023)], (31720 ^ _773908) ^ [_1358990, _1358992, _1358994, _1358996] : [31722 ^ _773908 : [(31725 ^ _773908) ^ [] : [hAPP(_1358996, 31721 ^ [_1358990, _1358992, _1358994, _1358996]) = c_Orderings_Obot__class_Obot(tc_fun(_1358990, tc_HOL_Obool))], (31723 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358992), 31721 ^ [_1358990, _1358992, _1358994, _1358996]), _1358994)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1358990, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358992, tc_fun(_1358990, tc_HOL_Obool)), _1358994), _1358996))], (6562 ^ _773908) ^ [_880535, _880537, _880539, _880541] : [class_Orderings_Opreorder(_880535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880535), _880537), _880539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880535), _880539), _880541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880535), _880537), _880541)))], (16439 ^ _773908) ^ [_1055670, _1055672, _1055674] : [class_Groups_Oordered__ab__group__add__abs(_1055670), -(hAPP(c_Groups_Oabs__class_Oabs(_1055670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055670), hAPP(c_Groups_Oabs__class_Oabs(_1055670), _1055672)), hAPP(c_Groups_Oabs__class_Oabs(_1055670), _1055674))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055670), hAPP(c_Groups_Oabs__class_Oabs(_1055670), _1055672)), hAPP(c_Groups_Oabs__class_Oabs(_1055670), _1055674)))], (25113 ^ _773908) ^ [_1217620, _1217622, _1217624, _1217626] : [class_Orderings_Olinorder(_1217620), 25116 ^ _773908 : [(25117 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217620), _1217624), _1217626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), _1217624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), _1217626)))], (25127 ^ _773908) ^ [] : [25128 ^ _773908 : [(25131 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), _1217626))], (25129 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), _1217624))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217620), _1217622), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217620), _1217624), _1217626))))]]], (13662 ^ _773908) ^ [_1003991, _1003993, _1003995] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003991), _1003993), _1003995) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003991), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003993, _1003995)), _1003995))], (20909 ^ _773908) ^ [_1135527, _1135529, _1135531, _1135533] : [class_Fields_Olinordered__field__inverse__zero(_1135527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135527), _1135529), _1135531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135527), c_Groups_Ozero__class_Ozero(_1135527)), _1135533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135527), _1135529), _1135533)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135527), _1135531), _1135533))))], (44895 ^ _773908) ^ [_1671516, _1671518] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671516)), c_List_Oremdups(_1671516, _1671518))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671516)), _1671518))))], (19549 ^ _773908) ^ [_1111291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111291)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111291), c_Int_OPls)))], (41846 ^ _773908) ^ [_1598305, _1598307, _1598309, _1598311, _1598313, _1598315, _1598317, _1598319] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598305, tc_fun(_1598307, tc_fun(_1598309, tc_HOL_Obool))), _1598311), _1598313), _1598315), _1598317)), hBOOL(hAPP(hAPP(c_member(_1598305), _1598319), _1598311)), -(hBOOL(hAPP(hAPP(hAPP(_1598313, _1598319), _1598315), _1598317)))], (34678 ^ _773908) ^ [_1421037, _1421039, _1421041, _1421043, _1421045, _1421047] : [class_Groups_Ocomm__monoid__add(_1421037), c_Fun_Oinj__on(_1421039, _1421041, _1421043, _1421045), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421041, _1421037), _1421047), hAPP(c_Set_Oimage(_1421039, _1421041, _1421043), _1421045)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421039, _1421037), hAPP(c_Fun_Ocomp(_1421041, _1421037, _1421039, _1421047), _1421043)), _1421045))], (26717 ^ _773908) ^ [_1254497, _1254499] : [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)), _1254497)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254497), _1254499)))], (33748 ^ _773908) ^ [_1400903, _1400905, _1400907] : [class_Orderings_Oord(_1400903), 33751 ^ _773908 : [(33758 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400903), _1400905), _1400907)), -(hBOOL(hAPP(hAPP(c_member(_1400903), _1400905), hAPP(c_SetInterval_Oord__class_OatMost(_1400903), _1400907))))], (33752 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1400903), _1400905), hAPP(c_SetInterval_Oord__class_OatMost(_1400903), _1400907))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400903), _1400905), _1400907)))]]], (45109 ^ _773908) ^ [_1675191, _1675193] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675191)), c_List_Oremdups(_1675191, _1675193)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675191)), _1675193), -(c_List_Oremdups(_1675191, _1675193) = _1675193)], (11189 ^ _773908) ^ [_960258, _960260, _960262, _960264] : [class_Rings_Oordered__semiring(_960258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960258), _960260), _960262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960258), c_Groups_Ozero__class_Ozero(_960258)), _960264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960258), _960264), _960260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960258), _960264), _960262))))], (39927 ^ _773908) ^ [_1553074, _1553076, _1553078, _1553080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553074), tc_List_Olist(_1553074))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553074), tc_List_Olist(_1553074)), _1553076), _1553078)), c_List_Olistrel(_1553074, _1553080))), 39930 ^ _773908 : [(39933 ^ _773908) ^ [_1553303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1553303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553074)), _1553076))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553074, _1553074)), hAPP(hAPP(c_Product__Type_OPair(_1553074, _1553074), hAPP(hAPP(c_List_Onth(_1553074), _1553076), _1553303)), hAPP(hAPP(c_List_Onth(_1553074), _1553078), _1553303))), _1553080)))], (39931 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553074)), _1553076) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553074)), _1553078))]]], (14743 ^ _773908) ^ [_1023176, _1023178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023176)), 14746 ^ _773908 : [(14755 ^ _773908) ^ [] : [-(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), _1023176), _1023178)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023178), _1023176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023178))], (14747 ^ _773908) ^ [] : [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), _1023176), _1023178))), 14750 ^ _773908 : [(14753 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023178)))], (14751 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023178), _1023176)))]]]]], (8295 ^ _773908) ^ [_910514, _910516, _910518, _910520, _910522, _910524] : [-(hAPP(hAPP(c_Fun_Ocomp(_910514, _910516, _910518, _910520), _910522), _910524) = hAPP(_910520, hAPP(_910522, _910524)))], (44676 ^ _773908) ^ [_1666848, _1666850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666848), _1666850)), -(c_List_Oupt(_1666848, _1666850) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1666848), c_List_Oupt(hAPP(c_Nat_OSuc, _1666848), _1666850)))], (5082 ^ _773908) ^ [_851553, _851555] : [_851555 = _851553, -(c_List_Oset(_851555) = c_List_Oset(_851553))], (7269 ^ _773908) ^ [_891430, _891432, _891434] : [hAPP(c_Com_Ocom_OBODY, _891430) = c_Com_Ocom_OAss(_891432, _891434)], (1654 ^ _773908) ^ [_797569, _797571] : [-(class_Groups_Oab__semigroup__mult(_797569)), _797571 = _797569, class_Groups_Oab__semigroup__mult(_797571)], (17545 ^ _773908) ^ [_1076713, _1076715, _1076717] : [class_Groups_Omonoid__mult(_1076713), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076713), _1076715), hAPP(c_Nat_OSuc, _1076717)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076713), hAPP(hAPP(c_Power_Opower__class_Opower(_1076713), _1076715), _1076717)), _1076715))], (40147 ^ _773908) ^ [_1558602, _1558604, _1558606] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558602), _1558604)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1558602)), hAPP(c_Set_OCollect(tc_List_Olist(_1558602)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1558602), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1558602)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1558602), tc_fun(_1558602, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1558602, tc_HOL_Obool), tc_fun(tc_fun(_1558602, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1558602)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1558602, tc_HOL_Obool))), c_List_Oset(_1558602))), _1558604))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1558602), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1558602)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1558602)))), _1558606))))))], (23488 ^ _773908) ^ [_1183457, _1183459] : [-(c_Divides_Odivmod__int(_1183457, _1183459) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1183457), _1183459)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183457, _1183459)))], (26643 ^ _773908) ^ [_1252567, _1252569, _1252571] : [class_Rings_Oring__1(_1252567), -(hAPP(c_Int_Oring__1__class_Oof__int(_1252567), 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), _1252569), _1252571)), 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(_1252567), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1252567), _1252569)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1252567), _1252571)))], (40267 ^ _773908) ^ [_1561534, _1561536, _1561538] : [40269 ^ _773908 : [(40272 ^ _773908) ^ [] : [hBOOL(hAPP(_1561538, 40268 ^ [_1561534, _1561536, _1561538]))], (40270 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561534), 40268 ^ [_1561534, _1561536, _1561538]), hAPP(c_List_Oset(_1561534), _1561536))))]], 40273 ^ _773908 : [(40274 ^ _773908) ^ [_1561718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1561718), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561534)), _1561536))), -(hBOOL(hAPP(_1561538, hAPP(hAPP(c_List_Onth(_1561534), _1561536), _1561718))))]]], (8434 ^ _773908) ^ [_912907] : [-(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, _912907)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30399 ^ _773908) ^ [_1329404, _1329406, _1329408, _1329410] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329404), _1329406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329408), hAPP(c_Set_Oimage(_1329404, _1329408, _1329410), _1329406))), hAPP(c_Finite__Set_Ocard(_1329404), _1329406))))], (33510 ^ _773908) ^ [_1396415, _1396417, _1396419, _1396421, _1396423] : [c_Fun_Oinj__on(_1396415, _1396417, _1396419, _1396421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1396415, tc_HOL_Obool)), _1396423), _1396421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1396417, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1396415, _1396417, _1396419), _1396423)), hAPP(c_Set_Oimage(_1396415, _1396417, _1396419), _1396421))))], (25433 ^ _773908) ^ [_1223642, _1223644, _1223646, _1223648, _1223650] : [-(hAPP(c_Product__Type_Osnd(_1223642, _1223644), hAPP(c_Product__Type_Oapfst(_1223646, _1223642, _1223644, _1223648), _1223650)) = hAPP(c_Product__Type_Osnd(_1223646, _1223644), _1223650))], (50913 ^ _773908) ^ [_1803869, _1803871, _1803873, _1803875] : [hAPP(c_Set_Oimage(_1803869, _1803871, _1803873), c_Orderings_Otop__class_Otop(tc_fun(_1803869, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803871, tc_HOL_Obool)), -(hAPP(_1803873, hAPP(c_Hilbert__Choice_Oinv__into(_1803869, _1803871, c_Orderings_Otop__class_Otop(tc_fun(_1803869, tc_HOL_Obool)), _1803873), _1803875)) = _1803875)], (8315 ^ _773908) ^ [_910986, _910988] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910986)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910988)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _910986), _910988)))], (43296 ^ _773908) ^ [_1633829, _1633831, _1633833] : [hBOOL(hAPP(c_List_Olistsp(_1633829, hAPP(hAPP(c_COMBC(_1633829, tc_fun(_1633829, tc_HOL_Obool), tc_HOL_Obool), c_member(_1633829)), _1633831)), _1633833)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633829)), _1633833), c_List_Olists(_1633829, _1633831))))], (34570 ^ _773908) ^ [_1418163, _1418165, _1418167, _1418169, _1418171] : [class_Rings_Osemiring__0(_1418163), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418163), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418165, _1418163), _1418167), _1418169)), _1418171) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418165, _1418163), hAPP(hAPP(c_COMBC(_1418165, _1418163, _1418163), hAPP(hAPP(c_COMBB(_1418163, tc_fun(_1418163, _1418163), _1418165), c_Groups_Otimes__class_Otimes(_1418163)), _1418167)), _1418171)), _1418169))], (49112 ^ _773908) ^ [_1764274, _1764276, _1764278] : [49114 ^ _773908 : [(49117 ^ _773908) ^ [] : [hBOOL(hAPP(_1764278, 49113 ^ [_1764274, _1764276, _1764278]))], (49115 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764274), 49113 ^ [_1764274, _1764276, _1764278]), hAPP(c_List_Oset(_1764274), _1764276))))]], -(c_List_Olist__all(_1764274, _1764278, _1764276))], (51852 ^ _773908) ^ [_1817766, _1817768, _1817770, _1817772, _1817774, _1817776] : [-(hAPP(hAPP(hAPP(c_COMBC(_1817766, _1817768, _1817770), _1817772), _1817774), _1817776) = hAPP(hAPP(_1817772, _1817776), _1817774))], (45856 ^ _773908) ^ [_1690388, _1690390, _1690392] : [class_Orderings_Olinorder(_1690388), c_List_Olinorder__class_Osorted(_1690388, _1690390), -(c_List_Olinorder__class_Osorted(_1690388, c_List_OdropWhile(_1690388, _1690392, _1690390)))], (51604 ^ _773908) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (38853 ^ _773908) ^ [_1524608, _1524610, _1524612] : [c_Wellfounded_Owf(_1524608, _1524610), -(c_Wellfounded_Owf(_1524608, c_Wellfounded_Omlex__prod(_1524608, _1524612, _1524610)))], (36105 ^ _773908) ^ [_1451311, _1451313] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451311, tc_HOL_Obool)), _1451313) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1451311, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451311, tc_HOL_Obool))), _1451313))], (24829 ^ _773908) ^ [_1211817, _1211819, _1211821, _1211823] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1211817), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211817), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211817), _1211819), _1211821)), _1211823) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211817), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211817), _1211819), _1211823)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211817), _1211821), _1211823)))], (51652 ^ _773908) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (47556 ^ _773908) ^ [_1730569, _1730571, _1730573, _1730575, _1730577] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730569, _1730569)), hAPP(hAPP(c_Product__Type_OPair(_1730569, _1730569), _1730571), _1730573)), c_Transitive__Closure_Ortrancl(_1730569, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1730569, _1730569), tc_HOL_Obool)), _1730575), _1730577)))), 47562 ^ _773908 : [(47568 ^ _773908) ^ [] : [47564 ^ [_1730569, _1730571, _1730573, _1730575, _1730577] = 47561 ^ [_1730569, _1730571, _1730573, _1730575, _1730577]], (47566 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730569, _1730569)), hAPP(hAPP(c_Product__Type_OPair(_1730569, _1730569), 47564 ^ [_1730569, _1730571, _1730573, _1730575, _1730577]), 47561 ^ [_1730569, _1730571, _1730573, _1730575, _1730577])), _1730577)))], (47563 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730569, _1730569)), hAPP(hAPP(c_Product__Type_OPair(_1730569, _1730569), 47561 ^ [_1730569, _1730571, _1730573, _1730575, _1730577]), _1730573)), c_Transitive__Closure_Ortrancl(_1730569, _1730575))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730569, _1730569)), hAPP(hAPP(c_Product__Type_OPair(_1730569, _1730569), _1730571), _1730573)), c_Transitive__Closure_Ortrancl(_1730569, _1730575))))], (36183 ^ _773908) ^ [_1453025, _1453027] : [class_Lattices_Oboolean__algebra(_1453025), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1453025), _1453027), hAPP(c_Groups_Ouminus__class_Ouminus(_1453025), _1453027)) = c_Orderings_Otop__class_Otop(_1453025))], (13534 ^ _773908) ^ [_1001277, _1001279, _1001281] : [class_Divides_Osemiring__div(_1001277), -(c_Divides_Odiv__class_Omod(_1001277, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001277), _1001279), _1001281), _1001281) = c_Divides_Odiv__class_Omod(_1001277, _1001279, _1001281))], (44076 ^ _773908) ^ [_1652388, _1652390, _1652392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1652388, tc_HOL_Obool), tc_HOL_Obool)), _1652390), _1652392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652388, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652388, tc_HOL_Obool), _1652392)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652388, tc_HOL_Obool), _1652390))))], (35965 ^ _773908) ^ [_1448738, _1448740] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448738, tc_HOL_Obool)), _1448740), c_Orderings_Otop__class_Otop(tc_fun(_1448738, tc_HOL_Obool)))))], (15419 ^ _773908) ^ [_1035530, _1035532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035530), _1035532))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035530, _1035532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035530), _1035532), _1035532))], (34588 ^ _773908) ^ [_1418886, _1418888, _1418890, _1418892] : [class_Groups_Oordered__ab__group__add__abs(_1418886), -(hAPP(c_Groups_Oabs__class_Oabs(_1418886), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418888, _1418886), hAPP(hAPP(c_COMBB(_1418886, _1418886, _1418888), c_Groups_Oabs__class_Oabs(_1418886)), _1418890)), _1418892)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418888, _1418886), hAPP(hAPP(c_COMBB(_1418886, _1418886, _1418888), c_Groups_Oabs__class_Oabs(_1418886)), _1418890)), _1418892))], (15435 ^ _773908) ^ [_1035814, _1035816, _1035818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035814), _1035816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035814), _1035818)), 15442 ^ _773908 : [(15449 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035816), _1035818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035816), _1035814)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035818), _1035814))))], (15443 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035816), _1035814)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035818), _1035814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035816), _1035818)))]]], (42632 ^ _773908) ^ [_1619502, _1619504] : [hAPP(c_Code__Numeral_Oof__nat, _1619502) = hAPP(c_Code__Numeral_Oof__nat, _1619504), -(_1619502 = _1619504)], (15455 ^ _773908) ^ [_1036167, _1036169, _1036171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036167), _1036169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036167), _1036171)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036169), _1036167)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036171), _1036167)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036169), _1036171))], (36333 ^ _773908) ^ [_1456366, _1456368, _1456370, _1456372, _1456374, _1456376] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456366, tc_fun(_1456368, tc_fun(_1456370, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1456366, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_fun(_1456368, tc_fun(_1456370, tc_HOL_Obool)), _1456366), hAPP(c_COMBC(_1456368, tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_fun(_1456370, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456370, tc_fun(tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_fun(_1456370, tc_HOL_Obool)), _1456368), c_COMBC(_1456370, tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456370, tc_prod(_1456368, _1456370)), tc_fun(_1456370, tc_fun(tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_HOL_Obool)), _1456368), hAPP(c_COMBB(tc_prod(_1456368, _1456370), tc_fun(tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool), tc_HOL_Obool), _1456370), c_member(tc_prod(_1456368, _1456370)))), c_Product__Type_OPair(_1456368, _1456370))))), _1456372)), _1456374), _1456376)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456368, _1456370)), hAPP(hAPP(c_Product__Type_OPair(_1456368, _1456370), _1456374), _1456376)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456366, tc_fun(tc_prod(_1456368, _1456370), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1456366, tc_HOL_Obool))), _1456372))))], (28266 ^ _773908) ^ [_1286837, _1286839, _1286841] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286837, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1286837), _1286839), _1286841), -(_1286839 = c_Orderings_Obot__class_Obot(tc_fun(_1286837, tc_HOL_Obool)))], (37084 ^ _773908) ^ [_1472554, _1472556, _1472558, _1472560] : [c_Fun_Oinj__on(_1472554, _1472556, _1472558, c_Orderings_Otop__class_Otop(tc_fun(_1472554, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472554, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472554, _1472556, _1472558), hAPP(hAPP(c_Set_Oinsert(_1472556), _1472560), c_Orderings_Obot__class_Obot(tc_fun(_1472556, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1472554), c_HOL_OThe(_1472554, hAPP(hAPP(c_COMBC(_1472554, _1472556, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1472556, tc_fun(_1472556, tc_HOL_Obool), _1472554), c_fequal), _1472558)), _1472560))), c_Orderings_Obot__class_Obot(tc_fun(_1472554, tc_HOL_Obool))))))], (15988 ^ _773908) ^ [_1047060, _1047062, _1047064] : [hBOOL(hAPP(_1047060, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047062), _1047064))), 15991 ^ _773908 : [(15998 ^ _773908) ^ [_1047251] : [_1047062 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047064), _1047251), -(hBOOL(hAPP(_1047060, _1047251)))], (15992 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047062), _1047064)), -(hBOOL(hAPP(_1047060, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (3602 ^ _773908) ^ [_828167, _828169, _828171, _828173, _828175, _828177, _828179, _828181] : [-(c_List_Omaps(_828181, _828177, _828173, _828169) = c_List_Omaps(_828179, _828175, _828171, _828167)), _828181 = _828179, _828177 = _828175, _828173 = _828171, _828169 = _828167], (32181 ^ _773908) ^ [_1370659, _1370661, _1370663, _1370665] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1370659, _1370659)), hAPP(hAPP(c_Product__Type_OPair(_1370659, _1370659), _1370661), _1370663)), c_Relation_OId__on(_1370659, _1370665)))), _1370661 = _1370663, hBOOL(hAPP(hAPP(c_member(_1370659), _1370661), _1370665))], (33254 ^ _773908) ^ [_1391641, _1391643, _1391645, _1391647, _1391649, _1391651] : [c_Fun_Oinj__on(_1391641, _1391643, _1391645, _1391647), -(_1391649 = _1391651), hBOOL(hAPP(hAPP(c_member(_1391641), _1391649), _1391647)), hBOOL(hAPP(hAPP(c_member(_1391641), _1391651), _1391647)), hAPP(_1391645, _1391649) = hAPP(_1391645, _1391651)], (42058 ^ _773908) ^ [_1605281, _1605283, _1605285, _1605287] : [c_Orderings_Otop__class_Otop(tc_fun(_1605281, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605283, tc_fun(_1605281, tc_HOL_Obool)), _1605285), _1605287), 42061 ^ _773908 : [(42062 ^ _773908) ^ [_1605397] : [hBOOL(hAPP(hAPP(c_member(_1605283), _1605397), _1605285)), -(hAPP(_1605287, _1605397) = c_Orderings_Otop__class_Otop(tc_fun(_1605281, tc_HOL_Obool)))]]], (51416 ^ _773908) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (5949 ^ _773908) ^ [_869321, _869323, _869325, _869327, _869329] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869321), _869323), _869325)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869327), _869325), _869329)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_869321, _869327)), _869323), _869329)))], (39825 ^ _773908) ^ [_1550532, _1550534, _1550536, _1550538] : [-(c_List_Olist_Olist__size(_1550532, _1550534, hAPP(hAPP(c_List_Olist_OCons(_1550532), _1550536), _1550538)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1550534, _1550536)), c_List_Olist_Olist__size(_1550532, _1550534, _1550538))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7803 ^ _773908) ^ [_901182, _901184, _901186, _901188] : [class_Rings_Ocomm__semiring__1(_901182), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901182), _901184), _901186)), _901188) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901182), _901184), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901182), _901186), _901188)))], (23449 ^ _773908) ^ [_1182549, _1182551] : [c_Nitpick_Orefl_H(_1182549, _1182551), 23452 ^ _773908 : [(23453 ^ _773908) ^ [_1182627] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1182549, _1182549)), hAPP(hAPP(c_Product__Type_OPair(_1182549, _1182549), _1182627), _1182627)), _1182551)))]]], (51884 ^ _773908) ^ [_1818204, _1818206] : [hBOOL(_1818204), hBOOL(_1818206), -(hBOOL(hAPP(hAPP(c_fconj, _1818204), _1818206)))], (2972 ^ _773908) ^ [_818314, _818316, _818318, _818320, _818322, _818324] : [-(c_List_Oset__Cons(_818324, _818320, _818316) = c_List_Oset__Cons(_818322, _818318, _818314)), _818324 = _818322, _818320 = _818318, _818316 = _818314], (38492 ^ _773908) ^ [_1514279, _1514281] : [-(c_Product__Type_Omap__pair(_1514279, _1514279, _1514281, _1514281, c_COMBI(_1514279), c_COMBI(_1514281)) = c_Fun_Oid(tc_prod(_1514279, _1514281)))], (28154 ^ _773908) ^ [_1284089, _1284091, _1284093] : [class_Lattices_Osemilattice__inf(_1284089), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1284089), _1284091), _1284093) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1284089), _1284093), _1284091))], (40197 ^ _773908) ^ [_1559860, _1559862] : [-(hAPP(hAPP(c_List_Odrop(_1559860), _1559862), c_List_Olist_ONil(_1559860)) = c_List_Olist_ONil(_1559860))], (34948 ^ _773908) ^ [_1426918, _1426920, _1426922, _1426924, _1426926] : [class_Groups_Ocomm__monoid__add(_1426918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426920), _1426922)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426920, _1426918), _1426924), hAPP(hAPP(c_Set_Oinsert(_1426920), _1426926), _1426922)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426918), hAPP(_1426924, _1426926)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426920, _1426918), _1426924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426920, tc_HOL_Obool)), _1426922), hAPP(hAPP(c_Set_Oinsert(_1426920), _1426926), c_Orderings_Obot__class_Obot(tc_fun(_1426920, tc_HOL_Obool)))))))], (49664 ^ _773908) ^ [_1776360, _1776362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1776360), _1776362)), -(c_Lazy__Sequence_Osmall__lazy_H(_1776360, _1776362) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (7277 ^ _773908) ^ [_891642, _891644, _891646, _891648] : [c_Com_Ocom_OSemi(_891642, _891644) = c_Com_Ocom_OAss(_891646, _891648)], (19457 ^ _773908) ^ [_1109793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1109793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1109793)))], (34654 ^ _773908) ^ [_1420329, _1420331, _1420333, _1420335] : [class_Groups_Ocomm__monoid__add(_1420329), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420329), _1420331), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1420333)), hAPP(c_Nat_OSuc, _1420335))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420329), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420329, tc_Nat_Onat), _1420331), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1420333), _1420335)))], (18753 ^ _773908) ^ [_1098314, _1098316] : [class_Int_Onumber__ring(_1098314), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098314), c_Int_Osucc(_1098316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098314), c_Groups_Oone__class_Oone(_1098314)), hAPP(c_Int_Onumber__class_Onumber__of(_1098314), _1098316)))], (24397 ^ _773908) ^ [_1202217, _1202219] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202217), _1202219) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1202217, _1202219)))], (5204 ^ _773908) ^ [_853496, _853498, _853500, _853502] : [-(c_Transitive__Closure_Ortrancl(_853502, _853498) = c_Transitive__Closure_Ortrancl(_853500, _853496)), _853502 = _853500, _853498 = _853496], (31509 ^ _773908) ^ [_1353904, _1353906, _1353908, _1353910, _1353912] : [31511 ^ _773908 : [(31514 ^ _773908) ^ [] : [hBOOL(hAPP(_1353912, 31510 ^ [_1353904, _1353906, _1353908, _1353910, _1353912]))], (31512 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1353904), 31510 ^ [_1353904, _1353906, _1353908, _1353910, _1353912]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353906, tc_fun(_1353904, tc_HOL_Obool)), _1353908), _1353910))))]], 31515 ^ _773908 : [(31516 ^ _773908) ^ [_1354126] : [hBOOL(hAPP(hAPP(c_member(_1353906), _1354126), _1353908)), 31519 ^ _773908 : [(31520 ^ _773908) ^ [_1354223] : [hBOOL(hAPP(hAPP(c_member(_1353904), _1354223), hAPP(_1353910, _1354126))), -(hBOOL(hAPP(_1353912, _1354223)))]]]]], (37309 ^ _773908) ^ [_1478094, _1478096, _1478098, _1478100, _1478102, _1478104] : [-(hAPP(c_Set_Oimage(_1478094, tc_prod(_1478096, _1478098), hAPP(hAPP(c_COMBS(_1478094, _1478098, tc_prod(_1478096, _1478098)), hAPP(hAPP(c_COMBB(_1478096, tc_fun(_1478098, tc_prod(_1478096, _1478098)), _1478094), c_Product__Type_OPair(_1478096, _1478098)), _1478100)), _1478102)), _1478104) = hAPP(hAPP(c_Product__Type_OSigma(_1478096, _1478098), hAPP(c_Set_Oimage(_1478094, _1478096, _1478100), _1478104)), hAPP(hAPP(c_COMBB(tc_fun(_1478094, tc_HOL_Obool), tc_fun(_1478098, tc_HOL_Obool), _1478096), c_Set_Oimage(_1478094, _1478098, _1478102)), hAPP(hAPP(c_COMBC(_1478096, tc_fun(_1478094, tc_HOL_Obool), tc_fun(_1478094, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478094, tc_HOL_Obool), tc_fun(tc_fun(_1478094, tc_HOL_Obool), tc_fun(_1478094, tc_HOL_Obool)), _1478096), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478094, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1478096, tc_HOL_Obool), tc_fun(_1478094, tc_HOL_Obool), _1478096), c_Set_Ovimage(_1478094, _1478096, _1478100)), hAPP(hAPP(c_COMBC(_1478096, tc_fun(_1478096, tc_HOL_Obool), tc_fun(_1478096, tc_HOL_Obool)), c_Set_Oinsert(_1478096)), c_Orderings_Obot__class_Obot(tc_fun(_1478096, tc_HOL_Obool)))))), _1478104))))], (40955 ^ _773908) ^ [_1580590, _1580592, _1580594] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1580590, _1580592, _1580594)), 40957 ^ _773908 : [(40958 ^ _773908) ^ [_1580736] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1580590)), _1580736), _1580592)), -(c_Hoare__Mirabelle_Otriple__valid(_1580590, 40956 ^ [_1580590, _1580592, _1580594], _1580736))], (40967 ^ _773908) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1580590, 40956 ^ [_1580590, _1580592, _1580594], 40963 ^ [_1580590, _1580592, _1580594])], (40965 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1580590)), 40963 ^ [_1580590, _1580592, _1580594]), _1580594)))]]], (39442 ^ _773908) ^ [_1539976, _1539978, _1539980, _1539982, _1539984] : [hAPP(hAPP(c_List_Olist_OCons(_1539976), _1539978), _1539980) = hAPP(hAPP(c_List_Oappend(_1539976), _1539982), _1539984), 39447 ^ _773908 : [(39450 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1539976), _1539978), _1539980) = _1539984)], (39448 ^ _773908) ^ [] : [-(_1539982 = c_List_Olist_ONil(_1539976))]], 39452 ^ _773908 : [(39455 ^ _773908) ^ [] : [-(_1539980 = hAPP(hAPP(c_List_Oappend(_1539976), 39451 ^ [_1539976, _1539978, _1539980, _1539982, _1539984]), _1539984))], (39453 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1539976), _1539978), 39451 ^ [_1539976, _1539978, _1539980, _1539982, _1539984]) = _1539982)]]], (33862 ^ _773908) ^ [_1403234, _1403236, _1403238, _1403240] : [class_Orderings_Oorder(_1403234), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403234, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1403234, _1403236, _1403238)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1403234, _1403238), _1403240)) = c_Orderings_Obot__class_Obot(tc_fun(_1403234, tc_HOL_Obool)))], (51666 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (7543 ^ _773908) ^ [_896056, _896058, _896060, _896062, _896064] : [hBOOL(hAPP(_896056, _896058)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_896060), _896058), _896062)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_896056, _896060, _896064)), _896058), _896062)))], (23494 ^ _773908) ^ [_1183659, _1183661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183659)), 23497 ^ _773908 : [(23504 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183661))), 23507 ^ _773908 : [(23514 ^ _773908) ^ [] : [-(_1183659 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1183659, _1183661) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183659), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183661))))], (23508 ^ _773908) ^ [] : [_1183659 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1183659, _1183661) = 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)))]]], (23498 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183661)), -(c_Divides_Odivmod__int(_1183659, _1183661) = c_Divides_OposDivAlg(_1183659, _1183661))]]], (2602 ^ _773908) ^ [_812353, _812355, _812357, _812359, _812361, _812363] : [-(c_SetInterval_Oord_OlessThan(_812363, _812359, _812355) = c_SetInterval_Oord_OlessThan(_812361, _812357, _812353)), _812363 = _812361, _812359 = _812357, _812355 = _812353], (3364 ^ _773908) ^ [_824422, _824424] : [_824424 = _824422, -(c_List_Otranspose__rel(_824424) = c_List_Otranspose__rel(_824422))], (19481 ^ _773908) ^ [_1110161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1110161)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110161), c_Int_OMin)))], (26920 ^ _773908) ^ [_1258788, _1258790] : [c_Nat__Transfer_Ois__nat(_1258788), c_Nat__Transfer_Onat__set(_1258790), 26927 ^ _773908 : [(26934 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1258788)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258790))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1258788), _1258790)))], (26928 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1258788), _1258790)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1258788)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258790))))]]], (16635 ^ _773908) ^ [_1059343, _1059345] : [class_Groups_Oordered__ab__group__add__abs(_1059343), 16638 ^ _773908 : [(16645 ^ _773908) ^ [] : [-(_1059345 = c_Groups_Ozero__class_Ozero(_1059343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059343), c_Groups_Ozero__class_Ozero(_1059343)), hAPP(c_Groups_Oabs__class_Oabs(_1059343), _1059345))))], (16639 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059343), c_Groups_Ozero__class_Ozero(_1059343)), hAPP(c_Groups_Oabs__class_Oabs(_1059343), _1059345))), _1059345 = c_Groups_Ozero__class_Ozero(_1059343)]]], (47201 ^ _773908) ^ [_1721934, _1721936] : [-(c_Transitive__Closure_Otrancl(_1721934, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721934, _1721934), tc_HOL_Obool)), _1721936), c_Relation_OId(_1721934))) = c_Transitive__Closure_Ortrancl(_1721934, _1721936))], (22993 ^ _773908) ^ [_1173078, _1173080, _1173082, _1173084, _1173086, _1173088] : [-(hAPP(hAPP(c_Fun_Ocomp(_1173078, _1173080, _1173082, hAPP(c_COMBK(_1173080, _1173078), _1173084)), _1173086), _1173088) = _1173084)], (29085 ^ _773908) ^ [_1304816, _1304818, _1304820] : [class_Lattices_Olattice(_1304816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304816), _1304818)), -(_1304820 = c_Orderings_Obot__class_Obot(tc_fun(_1304816, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304816, tc_HOL_Obool)), _1304820), _1304818)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304816), c_Big__Operators_Olattice__class_OInf__fin(_1304816, _1304820)), c_Big__Operators_Olattice__class_OInf__fin(_1304816, _1304818)) = c_Big__Operators_Olattice__class_OInf__fin(_1304816, _1304818))], (18921 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (42273 ^ _773908) ^ [_1611317, _1611319, _1611321, _1611323] : [-(hAPP(c_Set_OCollect(_1611317), hAPP(hAPP(c_COMBB(tc_fun(_1611319, tc_HOL_Obool), tc_HOL_Obool, _1611317), c_HOL_OAll(_1611319)), hAPP(hAPP(c_COMBB(tc_fun(_1611319, tc_HOL_Obool), tc_fun(_1611319, tc_HOL_Obool), _1611317), hAPP(c_COMBS(_1611319, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1611319), c_fimplies), hAPP(hAPP(c_COMBC(_1611319, tc_fun(_1611319, tc_HOL_Obool), tc_HOL_Obool), c_member(_1611319)), _1611321)))), _1611323))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611319, tc_fun(_1611317, tc_HOL_Obool)), _1611321), hAPP(hAPP(c_COMBB(tc_fun(_1611317, tc_HOL_Obool), tc_fun(_1611317, tc_HOL_Obool), _1611319), c_Set_OCollect(_1611317)), hAPP(c_COMBC(_1611317, _1611319, tc_HOL_Obool), _1611323))))], (33420 ^ _773908) ^ [_1394694, _1394696, _1394698, _1394700, _1394702, _1394704] : [c_Fun_Oinj__on(_1394694, _1394696, _1394698, _1394700), 33423 ^ _773908 : [(33430 ^ _773908) ^ [] : [c_Fun_Oinj__on(_1394694, _1394702, hAPP(c_Fun_Ocomp(_1394696, _1394702, _1394694, _1394704), _1394698), _1394700), -(c_Fun_Oinj__on(_1394696, _1394702, _1394704, hAPP(c_Set_Oimage(_1394694, _1394696, _1394698), _1394700)))], (33424 ^ _773908) ^ [] : [c_Fun_Oinj__on(_1394696, _1394702, _1394704, hAPP(c_Set_Oimage(_1394694, _1394696, _1394698), _1394700)), -(c_Fun_Oinj__on(_1394694, _1394702, hAPP(c_Fun_Ocomp(_1394696, _1394702, _1394694, _1394704), _1394698), _1394700))]]], (38581 ^ _773908) ^ [_1517033, _1517035, _1517037] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517033, _1517033, _1517033), _1517035), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517033, _1517033), tc_HOL_Obool), _1517037), _1517035)) = hAPP(hAPP(c_Relation_Orel__comp(_1517033, _1517033, _1517033), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517033, _1517033), tc_HOL_Obool), _1517037), _1517035)), _1517035))], (7797 ^ _773908) ^ [_901039, _901041, _901043, _901045] : [class_Rings_Ocomm__semiring__1(_901039), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901039), _901041), _901043)), _901045) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901039), _901041), _901045)), _901043))], (12588 ^ _773908) ^ [_984955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984955)), _984955))], (21371 ^ _773908) ^ [_1143228, _1143230, _1143232] : [class_Fields_Olinordered__field(_1143228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143228), _1143230), c_Groups_Ozero__class_Ozero(_1143228))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143228), _1143232), c_Groups_Ozero__class_Ozero(_1143228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143228), c_Groups_Ozero__class_Ozero(_1143228)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143228), _1143230), _1143232))))], (46855 ^ _773908) ^ [_1713254, _1713256] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1713254), tc_List_Olist(_1713254)), tc_HOL_Obool)), c_List_Olistrel(_1713254, _1713256)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1713254), c_List_Olistrel1(_1713254, _1713256)))))], (5937 ^ _773908) ^ [_869013, _869015, _869017, _869019, _869021] : [c_Hoare__Mirabelle_Otriple__valid(_869013, _869015, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869013), _869017), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _869019))), _869021)), -(c_Hoare__Mirabelle_Otriple__valid(_869013, hAPP(c_Nat_OSuc, _869015), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869013), _869017), hAPP(c_Com_Ocom_OBODY, _869019)), _869021)))], (51211 ^ _773908) ^ [_1810596, _1810598, _1810600] : [c_Fun_Obij__betw(_1810596, _1810598, _1810600, c_Orderings_Otop__class_Otop(tc_fun(_1810596, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810598, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1810596, _1810598, _1810600, c_Orderings_Otop__class_Otop(tc_fun(_1810596, tc_HOL_Obool))))], (13564 ^ _773908) ^ [_1001908, _1001910, _1001912, _1001914] : [class_Divides_Osemiring__div(_1001908), -(c_Divides_Odiv__class_Omod(_1001908, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001908), _1001910), c_Divides_Odiv__class_Omod(_1001908, _1001912, _1001914)), _1001914) = c_Divides_Odiv__class_Omod(_1001908, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001908), _1001910), _1001912), _1001914))], (11758 ^ _773908) ^ [_970306, _970308] : [11759 ^ _773908 : [(11760 ^ _773908) ^ [_970359] : [_970308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _970306), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _970359))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _970306), _970308)))], (27572 ^ _773908) ^ [_1272563, _1272565, _1272567, _1272569, _1272571, _1272573] : [c_Finite__Set_Ofolding(_1272563, _1272565, _1272567, _1272569), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272563), _1272571)), -(hBOOL(hAPP(hAPP(c_member(_1272563), _1272573), _1272571))), -(hAPP(_1272569, hAPP(hAPP(c_Set_Oinsert(_1272563), _1272573), _1272571)) = hAPP(c_Fun_Ocomp(_1272565, _1272565, _1272565, hAPP(_1272569, _1272571)), hAPP(_1272567, _1272573)))], (23542 ^ _773908) ^ [_1184344, _1184346] : [-(_1184344 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23545 ^ _773908 : [(23552 ^ _773908) ^ [] : [-(_1184346 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1184344, _1184346) = 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, _1184346))), 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)), _1184346)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184344))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184346), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184344), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1184344, _1184346)), 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), _1184346))))), c_Divides_Opdivmod(_1184344, _1184346)))))], (23546 ^ _773908) ^ [] : [_1184346 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1184344, _1184346) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184344))]]], (23761 ^ _773908) ^ [_1189047, _1189049, _1189051, _1189053, _1189055] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189047, _1189049, tc_HOL_Obool), _1189051), hAPP(hAPP(c_Product__Type_OPair(_1189047, _1189049), _1189053), _1189055))), -(hBOOL(hAPP(hAPP(_1189051, _1189053), _1189055)))], (838 ^ _773908) ^ [_786711, _786713, _786715, _786717, _786719, _786721] : [-(c_List_Olist__all(_786719, _786715, _786711)), c_List_Olist__all(_786721, _786717, _786713), _786721 = _786719, _786717 = _786715, _786713 = _786711], (18547 ^ _773908) ^ [_1094311, _1094313, _1094315] : [-(hBOOL(hAPP(hAPP(c_member(_1094311), _1094313), _1094315))), -(hBOOL(hAPP(hAPP(c_member(_1094311), _1094313), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1094311, tc_HOL_Obool)), _1094315))))], (5662 ^ _773908) ^ [_860507, _860509] : [_860509 = _860507, -(c_Hoare__Mirabelle_Otriple_Otriple(_860509) = c_Hoare__Mirabelle_Otriple_Otriple(_860507))], (6820 ^ _773908) ^ [_884191, _884193, _884195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884191), _884193)), _884195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884191), _884195)))], (46993 ^ _773908) ^ [_1716878, _1716880, _1716882, _1716884, _1716886] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1716878, _1716878)), hAPP(hAPP(c_Product__Type_OPair(_1716878, _1716878), hAPP(_1716880, hAPP(c_Nat_OSuc, 46994 ^ [_1716878, _1716880, _1716882, _1716884, _1716886]))), hAPP(_1716880, 46994 ^ [_1716878, _1716880, _1716882, _1716884, _1716886]))), c_Transitive__Closure_Ortrancl(_1716878, _1716882))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1716878, _1716878)), hAPP(hAPP(c_Product__Type_OPair(_1716878, _1716878), hAPP(_1716880, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716884), _1716886))), hAPP(_1716880, _1716884))), c_Transitive__Closure_Ortrancl(_1716878, _1716882))))], (350 ^ _773908) ^ [_779315, _779317, _779319, _779321] : [-(c_FunDef_Oreduction__pair(_779319, _779315)), c_FunDef_Oreduction__pair(_779321, _779317), _779321 = _779319, _779317 = _779315], (34290 ^ _773908) ^ [_1412477] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412477))))], (14025 ^ _773908) ^ [_1010300, _1010302, _1010304, _1010306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010302), _1010304)), -(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), _1010304), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010306, _1010300))), _1010302))))], (14350 ^ _773908) ^ [_1016617, _1016619] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1016617), _1016619) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016617, _1016619)), _1016619))], (36637 ^ _773908) ^ [_1463945, _1463947, _1463949, _1463951, _1463953] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1463945, _1463947, hAPP(hAPP(c_Set_Oinsert(_1463945), _1463949), _1463951)), _1463953))), 36638 ^ _773908 : [(36639 ^ _773908) ^ [_1464049, _1464051] : [hAPP(hAPP(c_Set_Oinsert(_1463945), _1463949), _1463951) = hAPP(hAPP(c_Set_Oinsert(_1463945), _1464051), _1464049), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1463945, _1463945, _1463947, _1464051, _1464049), _1463953)), -(hBOOL(hAPP(hAPP(c_member(_1463945), _1464051), _1464049)))]]], (22959 ^ _773908) ^ [_1172436, _1172438, _1172440, _1172442, _1172444, _1172446] : [-(c_Nitpick_Opair__box_Opair__box__size(_1172436, _1172438, _1172440, _1172442, c_Nitpick_Opair__box_OPairBox(_1172436, _1172438, _1172444, _1172446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1172440, _1172444)), hAPP(_1172442, _1172446))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23019 ^ _773908) ^ [_1173609, _1173611, _1173613] : [class_Orderings_Obot(_1173609), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1173611, _1173609)), _1173613) = c_Orderings_Obot__class_Obot(_1173609))], (11715 ^ _773908) ^ [_969564, _969566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _969564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _969566)), -(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), _969564), _969566))))], (18759 ^ _773908) ^ [_1098433, _1098435] : [class_Int_Onumber__ring(_1098433), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098433), c_Int_Opred(_1098435)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098433), hAPP(c_Groups_Ouminus__class_Ouminus(_1098433), c_Groups_Oone__class_Oone(_1098433))), hAPP(c_Int_Onumber__class_Onumber__of(_1098433), _1098435)))], (31544 ^ _773908) ^ [_1354826, _1354828, _1354830, _1354832, _1354834, _1354836] : [class_Complete__Lattice_Ocomplete__lattice(_1354826), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354828, _1354826), _1354830), hAPP(hAPP(c_COMBB(tc_fun(_1354832, _1354826), _1354826, _1354828), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354832, _1354826), _1354834)), _1354836)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354832, _1354826), _1354834), hAPP(hAPP(c_COMBB(tc_fun(_1354828, _1354826), _1354826, _1354832), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354828, _1354826), _1354830)), hAPP(c_COMBC(_1354828, _1354832, _1354826), _1354836))))], (15345 ^ _773908) ^ [_1034185, _1034187, _1034189, _1034191] : [class_Divides_Oring__div(_1034185), -(c_Divides_Odiv__class_Omod(_1034185, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034185), _1034187), _1034189), _1034191) = c_Divides_Odiv__class_Omod(_1034185, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034185), c_Divides_Odiv__class_Omod(_1034185, _1034187, _1034191)), _1034189), _1034191))], (19499 ^ _773908) ^ [_1110464] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110464))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1110464)))))], (51764 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (35512 ^ _773908) ^ [_1439548, _1439550] : [class_Orderings_Olinorder(_1439548), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1439548, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439548), _1439550)) = hAPP(c_SetInterval_Oord__class_OatMost(_1439548), _1439550))], (34061 ^ _773908) ^ [_1407831, _1407833, _1407835] : [class_Orderings_Olinorder(_1407831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407831), _1407833), _1407835)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407831, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1407831), _1407833), c_Orderings_Obot__class_Obot(tc_fun(_1407831, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1407831, _1407833, _1407835)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1407831, _1407833), _1407835))], (43455 ^ _773908) ^ [_1637215, _1637217, _1637219, _1637221, _1637223, _1637225, _1637227] : [c_List_Olist__all2(_1637215, _1637217, _1637219, hAPP(hAPP(c_List_Olist_OCons(_1637215), _1637221), _1637223), hAPP(hAPP(c_List_Olist_OCons(_1637217), _1637225), _1637227)), 43458 ^ _773908 : [(43461 ^ _773908) ^ [] : [-(c_List_Olist__all2(_1637215, _1637217, _1637219, _1637223, _1637227))], (43459 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1637219, _1637221), _1637225)))]]], (45503 ^ _773908) ^ [_1682791, _1682793] : [-(hAPP(c_List_Orev(_1682791), hAPP(c_List_Orev(_1682791), _1682793)) = _1682793)], (17323 ^ _773908) ^ [_1072755] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072755)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072755))], (12819 ^ _773908) ^ [_988882, _988884, _988886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988882), _988884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988886), _988882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988886), _988884))))], (25147 ^ _773908) ^ [_1218183, _1218185, _1218187] : [class_Orderings_Olinorder(_1218183), 25150 ^ _773908 : [(25157 ^ _773908) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218183), _1218185), _1218187) = _1218187, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218183), _1218185), _1218187)))], (25151 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218183), _1218185), _1218187)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218183), _1218185), _1218187) = _1218187)]]], (25669 ^ _773908) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (25755 ^ _773908) ^ [_1230326, _1230328] : [class_Lattices_Obounded__lattice__bot(_1230326), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1230326), c_Orderings_Obot__class_Obot(_1230326)), _1230328) = _1230328)], (42774 ^ _773908) ^ [_1622288, _1622290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1622288), _1622290)), -(c_Nitpick_Ocard_H(_1622288, _1622290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622288)), c_Hilbert__Choice_OEps(tc_List_Olist(_1622288), hAPP(hAPP(c_COMBS(tc_List_Olist(_1622288), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1622288)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1622288), tc_fun(_1622288, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1622288, tc_HOL_Obool), tc_fun(tc_fun(_1622288, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1622288)), c_fequal), c_List_Oset(_1622288))), _1622290))), c_List_Odistinct(_1622288)))))], (25999 ^ _773908) ^ [_1234689, _1234691, _1234693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234689, tc_HOL_Obool)), _1234691), _1234693)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234689, tc_HOL_Obool)), _1234693), _1234691) = _1234693)], (22731 ^ _773908) ^ [_1168393, _1168395, _1168397, _1168399] : [class_Fields_Olinordered__field__inverse__zero(_1168393), class_Int_Onumber(_1168393), 22738 ^ _773908 : [(22739 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168395), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168393), _1168397), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)))), 22742 ^ _773908 : [(22749 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), c_Groups_Ozero__class_Ozero(_1168393)), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)))), 22752 ^ _773908 : [(22759 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)), c_Groups_Ozero__class_Ozero(_1168393)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168395), c_Groups_Ozero__class_Ozero(_1168393))))], (22753 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)), c_Groups_Ozero__class_Ozero(_1168393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168393), _1168395), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)))))]]], (22743 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), c_Groups_Ozero__class_Ozero(_1168393)), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168393), _1168395), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))), _1168397)))]]], (22765 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168395), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168393), _1168397), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))))), 22768 ^ _773908 : [(22771 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168393), _1168395), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))), _1168397))], (22769 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), c_Groups_Ozero__class_Ozero(_1168393)), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))))]], 22772 ^ _773908 : [(22775 ^ _773908) ^ [] : [22776 ^ _773908 : [(22779 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168393), _1168395), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399))))], (22777 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)), c_Groups_Ozero__class_Ozero(_1168393))))]], 22780 ^ _773908 : [(22783 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168393), _1168395), c_Groups_Ozero__class_Ozero(_1168393)))], (22781 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)), c_Groups_Ozero__class_Ozero(_1168393)))]]], (22773 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168393), c_Groups_Ozero__class_Ozero(_1168393)), hAPP(c_Int_Onumber__class_Onumber__of(_1168393), _1168399)))]]]]], (26609 ^ _773908) ^ [_1251272, _1251274, _1251276, _1251278, _1251280] : [hBOOL(hAPP(hAPP(c_member(_1251272), _1251274), _1251276)), -(hAPP(c_Set_Oimage(_1251272, _1251278, hAPP(c_COMBK(_1251278, _1251272), _1251280)), _1251276) = hAPP(hAPP(c_Set_Oinsert(_1251278), _1251280), c_Orderings_Obot__class_Obot(tc_fun(_1251278, tc_HOL_Obool))))], (41924 ^ _773908) ^ [_1600415, _1600417, _1600419, _1600421, _1600423, _1600425, _1600427] : [-(hAPP(c_List_Ofoldl(_1600415, _1600417, _1600419, _1600421), hAPP(hAPP(c_List_Omap(_1600423, _1600417), _1600425), _1600427)) = hAPP(c_List_Ofoldl(_1600415, _1600423, hAPP(hAPP(c_COMBC(_1600415, tc_fun(_1600423, _1600417), tc_fun(_1600423, _1600415)), hAPP(hAPP(c_COMBB(tc_fun(_1600417, _1600415), tc_fun(tc_fun(_1600423, _1600417), tc_fun(_1600423, _1600415)), _1600415), c_COMBB(_1600417, _1600415, _1600423)), _1600419)), _1600425), _1600421), _1600427))], (40581 ^ _773908) ^ [_1569362, _1569364, _1569366, _1569368] : [hAPP(hAPP(c_List_Olist__update(_1569362, _1569364), _1569366), _1569368) = c_List_Olist_ONil(_1569362), -(_1569364 = c_List_Olist_ONil(_1569362))], (9107 ^ _773908) ^ [_925114, _925116] : [class_Groups_Ogroup__add(_925114), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925114), _925116), hAPP(c_Groups_Ouminus__class_Ouminus(_925114), _925116)) = c_Groups_Ozero__class_Ozero(_925114))], (17961 ^ _773908) ^ [_1083822, _1083824] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083822), _1083824) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 17962 ^ _773908 : [(17969 ^ _773908) ^ [] : [_1083822 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1083824 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (17963 ^ _773908) ^ [] : [_1083822 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1083824 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (26780 ^ _773908) ^ [_1256162, _1256164, _1256166, _1256168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1256162, _1256162)), hAPP(hAPP(c_Product__Type_OPair(_1256162, _1256162), _1256166), _1256168)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool)), _1256164), c_Relation_OId(_1256162)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256162, tc_fun(_1256162, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1256162, tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_fun(_1256162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256162, tc_fun(tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_fun(_1256162, tc_HOL_Obool)), _1256162), c_COMBC(_1256162, tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256162, tc_prod(_1256162, _1256162)), tc_fun(_1256162, tc_fun(tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_HOL_Obool)), _1256162), hAPP(c_COMBB(tc_prod(_1256162, _1256162), tc_fun(tc_fun(tc_prod(_1256162, _1256162), tc_HOL_Obool), tc_HOL_Obool), _1256162), c_member(tc_prod(_1256162, _1256162)))), c_Product__Type_OPair(_1256162, _1256162)))), _1256164)), c_fequal), _1256166), _1256168)))], (14885 ^ _773908) ^ [_1025576, _1025578, _1025580] : [class_Divides_Osemiring__div(_1025576), -(_1025578 = c_Groups_Ozero__class_Ozero(_1025576)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025576), _1025580), _1025578)), _1025578) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025576), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025576), _1025580), _1025578)), c_Groups_Oone__class_Oone(_1025576)))], (7591 ^ _773908) ^ [_896967, _896969, _896971, _896973, _896975, _896977] : [c_Com_Ocom_OLocal(_896967, _896969, _896971) = c_Com_Ocom_OLocal(_896973, _896975, _896977), 7594 ^ _773908 : [(7599 ^ _773908) ^ [] : [-(_896971 = _896977)], (7597 ^ _773908) ^ [] : [-(_896969 = _896975)], (7595 ^ _773908) ^ [] : [-(_896967 = _896973)]]], (49110 ^ _773908) ^ [_1764228, _1764230] : [-(c_List_Olist__all(_1764228, _1764230, c_List_Olist_ONil(_1764228)))], (8076 ^ _773908) ^ [_906224, _906226, _906228, _906230, _906232] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_906224, _906226), _906228, _906230, _906232)), 8077 ^ _773908 : [(8084 ^ _773908) ^ [] : [hBOOL(hAPP(_906224, _906228)), 8087 ^ _773908 : [(8088 ^ _773908) ^ [_906434] : [c_Natural_Oevaln(_906226, _906228, _906230, _906434), c_Natural_Oevaln(c_Com_Ocom_OWhile(_906224, _906226), _906434, _906230, _906232)]]], (8078 ^ _773908) ^ [] : [_906232 = _906228, -(hBOOL(hAPP(_906224, _906228)))]]], (19891 ^ _773908) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (33120 ^ _773908) ^ [_1389074, _1389076, _1389078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1389074)), 33123 ^ _773908 : [(33124 ^ _773908) ^ [_1389208] : [33126 ^ _773908 : [(33132 ^ _773908) ^ [] : [-(_1389208 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33128 ^ [_1389074, _1389076, _1389078, _1389208]), 33125 ^ [_1389074, _1389076, _1389078, _1389208]))], (33130 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33128 ^ [_1389074, _1389076, _1389078, _1389208]), _1389076)))], (33127 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33125 ^ [_1389074, _1389076, _1389078, _1389208]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1389074))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1389078), _1389208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1389078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389208), _1389074))))]]], (28472 ^ _773908) ^ [_1291913, _1291915, _1291917] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1291913), hAPP(hAPP(c_Set_Oinsert(_1291913), _1291915), c_Orderings_Obot__class_Obot(tc_fun(_1291913, tc_HOL_Obool)))), _1291917) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1291913, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1291913, _1291913, _1291917), hAPP(hAPP(c_Set_Oinsert(_1291913), _1291915), c_Orderings_Obot__class_Obot(tc_fun(_1291913, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1291913, tc_HOL_Obool), tc_HOL_Obool))))], (43900 ^ _773908) ^ [_1647526] : [class_Complete__Lattice_Ocomplete__lattice(_1647526), -(c_Complete__Lattice_OSup__class_OSup(_1647526, c_Orderings_Otop__class_Otop(tc_fun(_1647526, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1647526))], (45794 ^ _773908) ^ [_1688884, _1688886, _1688888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688884)), c_List_OtakeWhile(_1688884, _1688886, _1688888))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688884)), _1688888))), hBOOL(hAPP(_1688886, hAPP(hAPP(c_List_Onth(_1688884), _1688888), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688884)), c_List_OtakeWhile(_1688884, _1688886, _1688888)))))], (15357 ^ _773908) ^ [_1034463, _1034465, _1034467, _1034469, _1034471, _1034473] : [class_Divides_Oring__div(_1034463), c_Divides_Odiv__class_Omod(_1034463, _1034465, _1034467) = c_Divides_Odiv__class_Omod(_1034463, _1034469, _1034467), c_Divides_Odiv__class_Omod(_1034463, _1034471, _1034467) = c_Divides_Odiv__class_Omod(_1034463, _1034473, _1034467), -(c_Divides_Odiv__class_Omod(_1034463, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034463), _1034465), _1034471), _1034467) = c_Divides_Odiv__class_Omod(_1034463, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034463), _1034469), _1034473), _1034467))], (34213 ^ _773908) ^ [_1410927, _1410929, _1410931, _1410933, _1410935] : [c_Fun_Oinj__on(_1410927, _1410929, _1410931, _1410933), hBOOL(hAPP(hAPP(c_member(_1410929), _1410935), hAPP(c_Set_Oimage(_1410927, _1410929, _1410931), _1410933))), -(hAPP(_1410931, hAPP(c_Fun_Othe__inv__into(_1410927, _1410929, _1410933, _1410931), _1410935)) = _1410935)], (32530 ^ _773908) ^ [_1377664, _1377666, _1377668] : [class_Orderings_Oorder(_1377664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377664), _1377666), _1377668)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1377664, _1377668, _1377666) = c_Orderings_Obot__class_Obot(tc_fun(_1377664, tc_HOL_Obool)))], (6324 ^ _773908) ^ [_876366, _876368, _876370, _876372] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_876366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876366), _876368), _876370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876366), _876368), _876372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876366), _876370), _876372)))], (7567 ^ _773908) ^ [_896570, _896572, _896574, _896576, _896578, _896580] : [c_Com_Ocom_OCond(_896570, _896572, _896574) = c_Com_Ocom_OCond(_896576, _896578, _896580), 7570 ^ _773908 : [(7575 ^ _773908) ^ [] : [-(_896574 = _896580)], (7573 ^ _773908) ^ [] : [-(_896572 = _896578)], (7571 ^ _773908) ^ [] : [-(_896570 = _896576)]]], (16119 ^ _773908) ^ [_1050089, _1050091] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050089, _1050091) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050089, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050091)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1294 ^ _773908) ^ [_793069, _793071] : [-(class_Int_Oring__char__0(_793069)), _793071 = _793069, class_Int_Oring__char__0(_793071)], (51714 ^ _773908) ^ [_1816305] : [-(class_Nat_Osize(tc_Option_Ooption(_1816305)))], (43065 ^ _773908) ^ [_1628470, _1628472, _1628474, _1628476, _1628478] : [c_List_Opartition(_1628470, _1628472, _1628474) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628470), tc_List_Olist(_1628470)), _1628476), _1628478), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1628470, tc_HOL_Obool)), hAPP(c_List_Oset(_1628470), _1628476)), hAPP(c_List_Oset(_1628470), _1628478)) = hAPP(c_List_Oset(_1628470), _1628474))], (9963 ^ _773908) ^ [_939670, _939672] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939670), _939672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939672), _939670)))], (33497 ^ _773908) ^ [_1396161, _1396163] : [33499 ^ _773908 : [(33502 ^ _773908) ^ [] : [hBOOL(hAPP(_1396163, 33498 ^ [_1396161, _1396163]))], (33500 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33498 ^ [_1396161, _1396163]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1396161))))]], 33503 ^ _773908 : [(33504 ^ _773908) ^ [_1396314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1396314), _1396161)), -(hBOOL(hAPP(_1396163, _1396314)))]]], (94 ^ _773908) ^ [_775281, _775283, _775285, _775287] : [-(c_Nitpick_Orefl_H(_775285, _775281)), c_Nitpick_Orefl_H(_775287, _775283), _775287 = _775285, _775283 = _775281], (23981 ^ _773908) ^ [_1192977, _1192979, _1192981, _1192983] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192977, _1192979), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192981), _1192983))), -(_1192979 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1192977), _1192979) = _1192981)], (7157 ^ _773908) ^ [_889654, _889656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889656), hAPP(c_Nat_OSuc, _889654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889654), _889656))], (3556 ^ _773908) ^ [_827462, _827464] : [_827464 = _827462, -(c_List_Oreturn__list(_827464) = c_List_Oreturn__list(_827462))], (41021 ^ _773908) ^ [_1581977, _1581979] : [hBOOL(hAPP(c_List_Odistinct(_1581977), _1581979)), -(hBOOL(hAPP(c_List_Odistinct(_1581977), hAPP(c_List_Orotate1(_1581977), _1581979))))], (51940 ^ _773908) ^ [_1818912, _1818914] : [hBOOL(hAPP(hAPP(c_fimplies, _1818912), _1818914)), hBOOL(_1818912), -(hBOOL(_1818914))], (10875 ^ _773908) ^ [_954587, _954589] : [class_Rings_Olinordered__semidom(_954587), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954587), _954589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954587), _954589), c_Groups_Oone__class_Oone(_954587)))))], (37986 ^ _773908) ^ [_1495905, _1495907, _1495909] : [hBOOL(hAPP(hAPP(c_member(_1495905), _1495907), hAPP(c_Set_OCollect(_1495905), _1495909))), -(hBOOL(hAPP(_1495909, _1495907)))], (16059 ^ _773908) ^ [_1048565, _1048567, _1048569, _1048571, _1048573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048565), _1048567)), -(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), _1048567), _1048569)), _1048571)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048565), _1048569)), _1048573)) = 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), _1048567), _1048565)), _1048569)), _1048571)), _1048573))], (19673 ^ _773908) ^ [_1113216, _1113218] : [class_Int_Onumber__ring(_1113216), class_Rings_Olinordered__idom(_1113216), 19680 ^ _773908 : [(19687 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113218), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113216), hAPP(c_Int_Onumber__class_Onumber__of(_1113216), _1113218)), c_Groups_Oone__class_Oone(_1113216))))], (19681 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113216), hAPP(c_Int_Onumber__class_Onumber__of(_1113216), _1113218)), c_Groups_Oone__class_Oone(_1113216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113218), c_Int_OBit1(c_Int_OPls))))]]], (39410 ^ _773908) ^ [_1539301] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1539301)), c_List_Olist_ONil(_1539301)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26183 ^ _773908) ^ [_1238548, _1238550, _1238552, _1238554] : [class_Lattices_Osemilattice__sup(_1238548), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238548), _1238550), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238548), _1238552), _1238554)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238548), _1238552), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238548), _1238550), _1238554)))], (14895 ^ _773908) ^ [_1025740, _1025742, _1025744] : [class_Divides_Osemiring__div(_1025740), -(_1025742 = c_Groups_Ozero__class_Ozero(_1025740)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025740), _1025742), _1025744)), _1025742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025740), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025740), _1025744), _1025742)), c_Groups_Oone__class_Oone(_1025740)))], (47096 ^ _773908) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (320 ^ _773908) ^ [_778770, _778772, _778774, _778776, _778778, _778780, _778782, _778784, _778786, _778788, _778790, _778792] : [-(c_Finite__Set_Ofolding__image__simple(_778790, _778786, _778782, _778778, _778774, _778770)), c_Finite__Set_Ofolding__image__simple(_778792, _778788, _778784, _778780, _778776, _778772), _778792 = _778790, _778788 = _778786, _778784 = _778782, _778780 = _778778, _778776 = _778774, _778772 = _778770], (6065 ^ _773908) ^ [_871502] : [_871502 = hAPP(c_Nat_OSuc, _871502)], (18597 ^ _773908) ^ [_1095094] : [class_Rings_Osemiring__1(_1095094), c_Int_Oiszero(_1095094, c_Groups_Oone__class_Oone(_1095094))], (43097 ^ _773908) ^ [_1629581, _1629583, _1629585] : [class_Orderings_Olinorder(_1629581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629581), _1629583)), -(c_List_Olinorder__class_Osorted__list__of__set(_1629581, hAPP(hAPP(c_Set_Oinsert(_1629581), _1629585), _1629583)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1629581, _1629581, c_COMBI(_1629581)), _1629585), c_List_Olinorder__class_Osorted__list__of__set(_1629581, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629581, tc_HOL_Obool)), _1629583), hAPP(hAPP(c_Set_Oinsert(_1629581), _1629585), c_Orderings_Obot__class_Obot(tc_fun(_1629581, tc_HOL_Obool)))))))], (16247 ^ _773908) ^ [_1052271, _1052273] : [-(_1052271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052271), _1052273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052271), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1052273)))], (34085 ^ _773908) ^ [_1408312, _1408314, _1408316, _1408318] : [-(_1408312 = c_Orderings_Obot__class_Obot(tc_fun(_1408314, tc_HOL_Obool))), 34088 ^ _773908 : [(34089 ^ _773908) ^ [] : [-(hAPP(c_Set_Oimage(_1408316, _1408314, 34096 ^ [_1408312, _1408314, _1408316, _1408318]), _1408318) = _1408312), 34090 ^ _773908 : [(34091 ^ _773908) ^ [_1408453] : [c_Fun_Oinj__on(_1408314, _1408316, _1408453, _1408312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408316, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1408314, _1408316, _1408453), _1408312)), _1408318))]]], (34100 ^ _773908) ^ [] : [34101 ^ _773908 : [(34102 ^ _773908) ^ [_1408645] : [hAPP(c_Set_Oimage(_1408316, _1408314, _1408645), _1408318) = _1408312]], 34104 ^ _773908 : [(34107 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408316, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1408314, _1408316, 34103 ^ [_1408312, _1408314, _1408316, _1408318]), _1408312)), _1408318)))], (34105 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1408314, _1408316, 34103 ^ [_1408312, _1408314, _1408316, _1408318], _1408312))]]]]], (49370 ^ _773908) ^ [_1770134, _1770136, _1770138, _1770140, _1770142] : [hBOOL(hAPP(hAPP(_1770138, _1770142), _1770140)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770134, _1770136, _1770138), _1770140), _1770142)))], (41304 ^ _773908) ^ [_1587792, _1587794, _1587796] : [-(hAPP(c_List_Orotate1(_1587792), hAPP(c_List_Orotate(_1587792, _1587794), _1587796)) = hAPP(c_List_Orotate(_1587792, _1587794), hAPP(c_List_Orotate1(_1587792), _1587796)))], (41460 ^ _773908) ^ [_1590636, _1590638, _1590640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1590636), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1590638)), _1590640))), -(c_List_Olast(_1590638, hAPP(hAPP(c_List_Odrop(_1590638), _1590636), _1590640)) = c_List_Olast(_1590638, _1590640))], (47240 ^ _773908) ^ [_1722907, _1722909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722907), _1722909)), -(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), _1722907), _1722909)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30479 ^ _773908) ^ [_1331016, _1331018, _1331020] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331016), _1331018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331016, tc_HOL_Obool)), _1331018), _1331020)), -(hAPP(c_Finite__Set_Ocard(_1331016), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331016, tc_HOL_Obool)), _1331020), _1331018)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331016), _1331020)), hAPP(c_Finite__Set_Ocard(_1331016), _1331018)))], (47252 ^ _773908) ^ [_1723200, _1723202] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723200, _1723200)), hAPP(hAPP(c_Product__Type_OPair(_1723200, _1723200), 47253 ^ [_1723200, _1723202]), 47253 ^ [_1723200, _1723202])), c_Transitive__Closure_Otrancl(_1723200, _1723202)))), -(c_Wellfounded_Oacyclic(_1723200, _1723202))], (26057 ^ _773908) ^ [_1235955, _1235957, _1235959, _1235961] : [26058 ^ _773908 : [(26059 ^ _773908) ^ [_1236065] : [hBOOL(hAPP(hAPP(c_member(_1235955), _1236065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235955, tc_HOL_Obool)), _1235957), _1235959))), hBOOL(hAPP(_1235961, _1236065))]], 26067 ^ _773908 : [(26070 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1235961, 26066 ^ [_1235955, _1235957, _1235959, _1235961])))], (26068 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1235955), 26066 ^ [_1235955, _1235957, _1235959, _1235961]), _1235957)))]], 26072 ^ _773908 : [(26075 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1235961, 26071 ^ [_1235955, _1235957, _1235959, _1235961])))], (26073 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1235955), 26071 ^ [_1235955, _1235957, _1235959, _1235961]), _1235959)))]]], (18791 ^ _773908) ^ [_1099048] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099048), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099048)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1099048)))], (4900 ^ _773908) ^ [_848678, _848680, _848682, _848684, _848686, _848688] : [-(c_Lazy__Sequence_Oappend(_848688, _848684, _848680) = c_Lazy__Sequence_Oappend(_848686, _848682, _848678)), _848688 = _848686, _848684 = _848682, _848680 = _848678], (36667 ^ _773908) ^ [_1464764, _1464766, _1464768] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1464764), _1464766), _1464768) = c_Nitpick_OAbs__Frac(_1464764, c_Nitpick_Onorm__frac(_1464766, _1464768)))], (25427 ^ _773908) ^ [_1223487, _1223489, _1223491, _1223493, _1223495, _1223497] : [hAPP(_1223493, hAPP(c_Product__Type_Ofst(_1223487, _1223491), _1223495)) = hAPP(_1223497, hAPP(c_Product__Type_Ofst(_1223487, _1223491), _1223495)), -(hAPP(c_Product__Type_Oapfst(_1223487, _1223489, _1223491, _1223493), _1223495) = hAPP(c_Product__Type_Oapfst(_1223487, _1223489, _1223491, _1223497), _1223495))], (36123 ^ _773908) ^ [_1451813, _1451815, _1451817, _1451819] : [hBOOL(hAPP(hAPP(c_member(_1451815), _1451819), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451813, tc_fun(_1451815, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451813, tc_HOL_Obool))), _1451817))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451813, tc_fun(_1451815, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451813, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451815, tc_HOL_Obool), tc_fun(_1451815, tc_HOL_Obool), _1451813), hAPP(c_COMBC(_1451815, tc_fun(_1451815, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451815))), _1451817)), _1451819)))], (17799 ^ _773908) ^ [_1081461, _1081463] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081461)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081461)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081463)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081461)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081463))))], (28446 ^ _773908) ^ [_1291288, _1291290, _1291292] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291288, tc_HOL_Obool)), _1291290), _1291292) = c_Orderings_Obot__class_Obot(tc_fun(_1291288, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291288, tc_HOL_Obool)), _1291290), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1291288, tc_HOL_Obool)), _1291292))))], (6202 ^ _773908) ^ [_874511, _874513, _874515, _874517, _874519] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_874511, _874513, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874511), _874515), _874517), _874519)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4756 ^ _773908) ^ [_846416, _846418] : [_846418 = _846416, -(c_Groups_Oplus__class_Oplus(_846418) = c_Groups_Oplus__class_Oplus(_846416))], (50014 ^ _773908) ^ [_1784544, _1784546, _1784548] : [c_List_Olist__ex(_1784544, _1784546, _1784548), 50018 ^ _773908 : [(50021 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1784546, 50017 ^ [_1784544, _1784546, _1784548])))], (50019 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784544), 50017 ^ [_1784544, _1784546, _1784548]), hAPP(c_List_Oset(_1784544), _1784548))))]]], (16463 ^ _773908) ^ [_1056224] : [class_Rings_Olinordered__idom(_1056224), -(hAPP(c_Groups_Oabs__class_Oabs(_1056224), c_Groups_Oone__class_Oone(_1056224)) = c_Groups_Oone__class_Oone(_1056224))], (3674 ^ _773908) ^ [_829293, _829295, _829297, _829299, _829301, _829303] : [-(c_Predicate_ORangeP(_829303, _829299, _829295) = c_Predicate_ORangeP(_829301, _829297, _829293)), _829303 = _829301, _829299 = _829297, _829295 = _829293], (43503 ^ _773908) ^ [_1638170, _1638172, _1638174, _1638176, _1638178, _1638180, _1638182] : [c_List_Olist__all2(_1638176, _1638172, hAPP(hAPP(c_COMBB(_1638170, tc_fun(_1638172, tc_HOL_Obool), _1638176), _1638174), _1638178), _1638180, _1638182), -(c_List_Olist__all2(_1638170, _1638172, _1638174, hAPP(hAPP(c_List_Omap(_1638176, _1638170), _1638178), _1638180), _1638182))], (8975 ^ _773908) ^ [_922799, _922801, _922803, _922805, _922807] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_922799), 8978 ^ _773908 : [(8979 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922801), _922803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922805), _922807)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922801), _922807)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922805), _922803)), -(_922801 = _922805), -(_922803 = _922807)], (8989 ^ _773908) ^ [] : [8990 ^ _773908 : [(8993 ^ _773908) ^ [] : [_922803 = _922807], (8991 ^ _773908) ^ [] : [_922801 = _922805]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922801), _922803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922805), _922807)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922801), _922807)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922799), _922805), _922803)))]]], (17615 ^ _773908) ^ [_1078110, _1078112, _1078114] : [class_Rings_Olinordered__semidom(_1078110), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078110), c_Groups_Oone__class_Oone(_1078110)), _1078112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078110), hAPP(hAPP(c_Power_Opower__class_Opower(_1078110), _1078112), _1078114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078110), _1078112), hAPP(hAPP(c_Power_Opower__class_Opower(_1078110), _1078112), _1078114)))))], (10475 ^ _773908) ^ [_947431, _947433] : [class_Rings_Ocomm__semiring__1(_947431), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947431), c_Groups_Oone__class_Oone(_947431)), _947433) = _947433)], (32266 ^ _773908) ^ [_1372319, _1372321, _1372323] : [class_Orderings_Olinorder(_1372319), hAPP(_1372321, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372319), 32271 ^ [_1372319, _1372321, _1372323]), 32272 ^ [_1372319, _1372321, _1372323])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372319), hAPP(_1372321, 32271 ^ [_1372319, _1372321, _1372323])), hAPP(_1372321, 32272 ^ [_1372319, _1372321, _1372323])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372319), _1372323)), -(_1372323 = c_Orderings_Obot__class_Obot(tc_fun(_1372319, tc_HOL_Obool))), -(hAPP(_1372321, c_Big__Operators_Olinorder__class_OMax(_1372319, _1372323)) = c_Big__Operators_Olinorder__class_OMax(_1372319, hAPP(c_Set_Oimage(_1372319, _1372319, _1372321), _1372323)))], (31766 ^ _773908) ^ [_1360592, _1360594, _1360596, _1360598, _1360600] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360592, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360594, tc_fun(_1360592, tc_HOL_Obool)), _1360596), _1360598)), _1360600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360594, tc_fun(_1360592, tc_HOL_Obool)), _1360596), hAPP(hAPP(c_COMBC(_1360594, tc_fun(_1360592, tc_HOL_Obool), tc_fun(_1360592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360592, tc_HOL_Obool), tc_fun(tc_fun(_1360592, tc_HOL_Obool), tc_fun(_1360592, tc_HOL_Obool)), _1360594), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360592, tc_HOL_Obool))), _1360598)), _1360600)))], (19555 ^ _773908) ^ [_1111386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111386), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1111386)), c_Int_OPls)))], (32093 ^ _773908) ^ [_1369041, _1369043, _1369045] : [class_Orderings_Oorder(_1369041), 32096 ^ _773908 : [(32103 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369041), _1369043), _1369045))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1369041, _1369043, _1369045) = c_Orderings_Obot__class_Obot(tc_fun(_1369041, tc_HOL_Obool)))], (32097 ^ _773908) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1369041, _1369043, _1369045) = c_Orderings_Obot__class_Obot(tc_fun(_1369041, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369041), _1369043), _1369045))]]], (26225 ^ _773908) ^ [_1239543, _1239545, _1239547, _1239549, _1239551] : [class_Lattices_Olattice(_1239543), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239545, _1239543)), _1239547), _1239549), _1239551) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239543), hAPP(_1239547, _1239551)), hAPP(_1239549, _1239551)))], (11037 ^ _773908) ^ [_957534, _957536, _957538] : [class_Rings_Olinordered__ring__strict(_957534), 11040 ^ _773908 : [(11055 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957534), _957536), _957538)))), 11056 ^ _773908 : [(11063 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), _957536), c_Groups_Ozero__class_Ozero(_957534))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), _957538), c_Groups_Ozero__class_Ozero(_957534)))], (11057 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), _957536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), _957538))]]], (11041 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957534), _957536), _957538))), 11046 ^ _773908 : [(11049 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), _957538)))], (11047 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), c_Groups_Ozero__class_Ozero(_957534)), _957536)))]], 11050 ^ _773908 : [(11053 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), _957538), c_Groups_Ozero__class_Ozero(_957534))))], (11051 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957534), _957536), c_Groups_Ozero__class_Ozero(_957534))))]]]]], (50320 ^ _773908) ^ [_1792874, _1792876] : [c_Predicate_Otransp(_1792874, _1792876), -(c_Relation_Otrans(_1792874, hAPP(c_Set_OCollect(tc_prod(_1792874, _1792874)), hAPP(c_Product__Type_Oprod_Oprod__case(_1792874, _1792874, tc_HOL_Obool), _1792876))))], (6940 ^ _773908) ^ [_886184, _886186] : [6941 ^ _773908 : [(6944 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886186), _886184))], (6942 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886184), _886186))]], _886184 = _886186], (18414 ^ _773908) ^ [_1091805, _1091807] : [-(_1091807 = c_Orderings_Obot__class_Obot(tc_fun(_1091805, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1091805), 18417 ^ [_1091805, _1091807]), _1091807)))], (19989 ^ _773908) ^ [_1118859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1118859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1118859))))], (42630 ^ _773908) ^ [_1619441, _1619443] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1619441)), hAPP(c_Code__Numeral_Oof__nat, _1619443)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1619441), _1619443)))], (554 ^ _773908) ^ [_782403, _782405, _782407, _782409, _782411, _782413] : [-(c_Relation_Ototal__on(_782411, _782407, _782403)), c_Relation_Ototal__on(_782413, _782409, _782405), _782413 = _782411, _782409 = _782407, _782405 = _782403], (44198 ^ _773908) ^ [_1654951, _1654953] : [class_Complete__Lattice_Ocomplete__lattice(_1654951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1654951), _1654953)), -(_1654953 = c_Orderings_Obot__class_Obot(tc_fun(_1654951, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1654951, _1654953) = c_Complete__Lattice_OInf__class_OInf(_1654951, _1654953))], (33922 ^ _773908) ^ [_1404623, _1404625, _1404627, _1404629, _1404631] : [-(c_Fun_Oinj__on(_1404623, _1404625, _1404627, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404623, tc_HOL_Obool)), _1404629), _1404631))), c_Fun_Oinj__on(_1404623, _1404625, _1404627, _1404629), c_Fun_Oinj__on(_1404623, _1404625, _1404627, _1404631), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404625, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1404623, _1404625, _1404627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404623, tc_HOL_Obool)), _1404629), _1404631))), hAPP(c_Set_Oimage(_1404623, _1404625, _1404627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404623, tc_HOL_Obool)), _1404631), _1404629))) = c_Orderings_Obot__class_Obot(tc_fun(_1404625, tc_HOL_Obool))], (22991 ^ _773908) ^ [_1173028, _1173030, _1173032, _1173034, _1173036, _1173038] : [-(hAPP(hAPP(c_Fun_Ocomp(_1173028, _1173030, _1173032, _1173034), _1173036), _1173038) = hAPP(_1173034, hAPP(_1173036, _1173038)))], (38318 ^ _773908) ^ [_1507047, _1507049, _1507051] : [class_Lattices_Odistrib__lattice(_1507047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507047), _1507049)), -(_1507049 = c_Orderings_Obot__class_Obot(tc_fun(_1507047, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1507047), _1507051), c_Big__Operators_Olattice__class_OInf__fin(_1507047, _1507049)) = c_Big__Operators_Olattice__class_OInf__fin(_1507047, hAPP(c_Set_OCollect(_1507047), hAPP(hAPP(c_COMBB(tc_fun(_1507047, tc_HOL_Obool), tc_HOL_Obool, _1507047), c_HOL_OEx(_1507047)), hAPP(hAPP(c_COMBC(_1507047, tc_fun(_1507047, tc_HOL_Obool), tc_fun(_1507047, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507047, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507047, tc_HOL_Obool), tc_fun(_1507047, tc_HOL_Obool)), _1507047), c_COMBS(_1507047, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507047, tc_HOL_Obool), tc_fun(_1507047, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507047), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507047), c_fconj)), hAPP(hAPP(c_COMBC(_1507047, tc_fun(_1507047, _1507047), tc_fun(_1507047, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507047, tc_HOL_Obool), tc_fun(tc_fun(_1507047, _1507047), tc_fun(_1507047, tc_HOL_Obool)), _1507047), c_COMBB(_1507047, tc_HOL_Obool, _1507047)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1507047), _1507051))))), hAPP(hAPP(c_COMBC(_1507047, tc_fun(_1507047, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507047)), _1507049))))))], (18339 ^ _773908) ^ [_1090599, _1090601, _1090603] : [hBOOL(hAPP(hAPP(c_member(_1090599), _1090601), _1090603)), -(hBOOL(hAPP(_1090603, _1090601)))], (7553 ^ _773908) ^ [_896236, _896238, _896240, _896242, _896244] : [-(hBOOL(hAPP(_896236, _896238))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_896240), _896238), _896242)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_896236, _896244, _896240)), _896238), _896242)))], (33963 ^ _773908) ^ [_1405489, _1405491, _1405493, _1405495, _1405497] : [c_Fun_Oinj__on(_1405489, _1405491, _1405493, _1405495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405491, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1405489, _1405491, _1405493), _1405495)), _1405497)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405491), _1405497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1405489), _1405495)), hAPP(c_Finite__Set_Ocard(_1405491), _1405497))))], (5168 ^ _773908) ^ [_852956, _852958] : [_852958 = _852956, -(c_Wellfounded_Ofinite__psubset(_852958) = c_Wellfounded_Ofinite__psubset(_852956))], (32758 ^ _773908) ^ [_1381996, _1381998, _1382000] : [class_Orderings_Olinorder(_1381996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381996), _1381998), _1382000)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1381996, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1381996), _1381998), c_Orderings_Obot__class_Obot(tc_fun(_1381996, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1381996, _1381998, _1382000)) = c_SetInterval_Oord__class_OatLeastAtMost(_1381996, _1381998, _1382000))], (16689 ^ _773908) ^ [_1060442, _1060444, _1060446] : [class_Groups_Oordered__ab__group__add__abs(_1060442), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060442), hAPP(c_Groups_Oabs__class_Oabs(_1060442), _1060444)), hAPP(c_Groups_Oabs__class_Oabs(_1060442), _1060446))), hAPP(c_Groups_Oabs__class_Oabs(_1060442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060442), _1060446), _1060444)))))], (8353 ^ _773908) ^ [_911575, _911577] : [_911575 = _911577, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911575) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911577))], (41033 ^ _773908) ^ [_1582193, _1582195, _1582197] : [-(hAPP(hAPP(c_List_Odrop(_1582193), _1582195), hAPP(c_List_Otl(_1582193), _1582197)) = hAPP(c_List_Otl(_1582193), hAPP(hAPP(c_List_Odrop(_1582193), _1582195), _1582197)))], (16345 ^ _773908) ^ [_1054176, _1054178, _1054180] : [class_Rings_Oring__1(_1054176), -(hAPP(c_Int_Oring__1__class_Oof__int(_1054176), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1054178), _1054180)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1054176), hAPP(c_Int_Oring__1__class_Oof__int(_1054176), _1054178)), _1054180))], (45071 ^ _773908) ^ [_1674443, _1674445, _1674447, _1674449, _1674451] : [class_Orderings_Olinorder(_1674443), 45074 ^ _773908 : [(45081 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1674443, hAPP(hAPP(c_List_Omap(_1674445, _1674443), _1674447), _1674451)), -(c_List_Olinorder__class_Osorted(_1674443, hAPP(hAPP(c_List_Omap(_1674445, _1674443), _1674447), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1674445, _1674443, _1674447), _1674449), _1674451))))], (45075 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1674443, hAPP(hAPP(c_List_Omap(_1674445, _1674443), _1674447), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1674445, _1674443, _1674447), _1674449), _1674451))), -(c_List_Olinorder__class_Osorted(_1674443, hAPP(hAPP(c_List_Omap(_1674445, _1674443), _1674447), _1674451)))]]], (39308 ^ _773908) ^ [_1537459, _1537461, _1537463] : [hAPP(hAPP(c_List_Olist_OCons(_1537459), _1537461), _1537463) = c_List_Olist_ONil(_1537459)], (39067 ^ _773908) ^ [_1529574, _1529576, _1529578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1529574, _1529576)), _1529578)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529576), hAPP(c_Relation_ORange(_1529574, _1529576), _1529578))))], (15549 ^ _773908) ^ [_1038021, _1038023, _1038025] : [-(hBOOL(hAPP(_1038021, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038023), _1038025))))), 15552 ^ _773908 : [(15555 ^ _773908) ^ [] : [hBOOL(hAPP(_1038021, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1038023)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1038025))))], (15553 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1038025), _1038023)))]], 15556 ^ _773908 : [(15559 ^ _773908) ^ [] : [hBOOL(hAPP(_1038021, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15557 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038023), _1038025)))]]], (34594 ^ _773908) ^ [_1419059, _1419061, _1419063, _1419065, _1419067] : [class_Fields_Ofield(_1419059), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419059), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419061, _1419059), _1419063), _1419065)), _1419067) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419061, _1419059), hAPP(hAPP(c_COMBC(_1419061, _1419059, _1419059), hAPP(hAPP(c_COMBB(_1419059, tc_fun(_1419059, _1419059), _1419061), c_Rings_Oinverse__class_Odivide(_1419059)), _1419063)), _1419067)), _1419065))], (12728 ^ _773908) ^ [_987135, _987137, _987139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987135), _987137)), _987139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987135), _987139)))], (1844 ^ _773908) ^ [_799944, _799946] : [-(class_Orderings_Oorder(_799944)), _799946 = _799944, class_Orderings_Oorder(_799946)], (37792 ^ _773908) ^ [_1491830] : [-(c_Relation_Orefl__on(_1491830, c_Orderings_Otop__class_Otop(tc_fun(_1491830, tc_HOL_Obool)), c_Relation_OId(_1491830)))], (17103 ^ _773908) ^ [_1068727, _1068729] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068727), _1068729))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068727))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068729))))], (13861 ^ _773908) ^ [_1007356, _1007358, _1007360] : [class_Lattices_Oab__semigroup__idem__mult(_1007356), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007356), _1007358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007356), _1007358), _1007360)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007356), _1007358), _1007360))], (31526 ^ _773908) ^ [_1354340, _1354342, _1354344, _1354346, _1354348] : [31528 ^ _773908 : [(31534 ^ _773908) ^ [] : [hBOOL(hAPP(_1354348, 31530 ^ [_1354340, _1354342, _1354344, _1354346, _1354348]))], (31532 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1354340), 31530 ^ [_1354340, _1354342, _1354344, _1354346, _1354348]), hAPP(_1354346, 31527 ^ [_1354340, _1354342, _1354344, _1354346, _1354348]))))], (31529 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1354342), 31527 ^ [_1354340, _1354342, _1354344, _1354346, _1354348]), _1354344)))]], 31535 ^ _773908 : [(31536 ^ _773908) ^ [_1354650] : [hBOOL(hAPP(hAPP(c_member(_1354340), _1354650), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354342, tc_fun(_1354340, tc_HOL_Obool)), _1354344), _1354346))), -(hBOOL(hAPP(_1354348, _1354650)))]]], (17425 ^ _773908) ^ [_1074687, _1074689] : [class_Groups_Omonoid__mult(_1074687), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1074687), _1074689), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1074689)], (42576 ^ _773908) ^ [_1618431, _1618433, _1618435, _1618437, _1618439, _1618441, _1618443] : [42578 ^ _773908 : [(42581 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1618439, 42577 ^ [_1618431, _1618433, _1618435, _1618437, _1618439, _1618441, _1618443]), _1618441), _1618443))], (42579 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618431), 42577 ^ [_1618431, _1618433, _1618435, _1618437, _1618439, _1618441, _1618443]), _1618437)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618431, tc_fun(_1618433, tc_fun(_1618435, tc_HOL_Obool))), _1618437), _1618439), _1618441), _1618443)))], (42411 ^ _773908) ^ [_1614458, _1614460, _1614462, _1614464, _1614466] : [-(_1614458 = c_Orderings_Obot__class_Obot(tc_fun(_1614460, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614460, tc_fun(_1614462, tc_HOL_Obool)), _1614458), hAPP(hAPP(c_COMBC(_1614460, tc_fun(_1614462, tc_HOL_Obool), tc_fun(_1614462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614462, tc_HOL_Obool), tc_fun(tc_fun(_1614462, tc_HOL_Obool), tc_fun(_1614462, tc_HOL_Obool)), _1614460), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614462, tc_HOL_Obool))), _1614464)), _1614466)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614462, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614460, tc_fun(_1614462, tc_HOL_Obool)), _1614458), _1614464)), _1614466))], (44859 ^ _773908) ^ [_1670698, _1670700, _1670702, _1670704] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670698)), _1670700))), c_List_Ofoldr(tc_List_Olist(_1670702), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670702)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670702))), _1670704, 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(_1670698)), _1670700)), c_List_Ofoldr(tc_List_Olist(_1670702), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670702)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670702), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670702)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670702)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1670702), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1670702)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670702), tc_List_Olist(_1670702), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1670702)))), _1670704), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (29637 ^ _773908) ^ [_1314851, _1314853, _1314855] : [class_Orderings_Olinorder(_1314851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314851), _1314853)), -(hBOOL(hAPP(hAPP(c_member(_1314851), _1314855), _1314853))), -(_1314853 = c_Orderings_Obot__class_Obot(tc_fun(_1314851, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1314851, hAPP(hAPP(c_Set_Oinsert(_1314851), _1314855), _1314853)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314851), _1314855), c_Big__Operators_Olinorder__class_OMin(_1314851, _1314853)))], (48119 ^ _773908) ^ [_1743677, _1743679, _1743681] : [hBOOL(hAPP(hAPP(c_member(_1743677), _1743679), hAPP(c_List_Oset(_1743677), _1743681))), 48124 ^ _773908 : [(48127 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1743677), _1743679), hAPP(c_List_Oset(_1743677), 48123 ^ [_1743677, _1743679, _1743681])))], (48125 ^ _773908) ^ [] : [-(_1743681 = hAPP(hAPP(c_List_Oappend(_1743677), 48122 ^ [_1743677, _1743679, _1743681]), hAPP(hAPP(c_List_Olist_OCons(_1743677), _1743679), 48123 ^ [_1743677, _1743679, _1743681])))]]], (46740 ^ _773908) ^ [_1710228, _1710230, _1710232, _1710234, _1710236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1710228, _1710228)), hAPP(hAPP(c_Product__Type_OPair(_1710228, _1710228), _1710230), _1710232)), _1710234)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1710228, _1710228)), hAPP(hAPP(c_Product__Type_OPair(_1710228, _1710228), _1710232), _1710236)), c_Transitive__Closure_Ortrancl(_1710228, _1710234))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1710228, _1710228)), hAPP(hAPP(c_Product__Type_OPair(_1710228, _1710228), _1710230), _1710236)), c_Transitive__Closure_Ortrancl(_1710228, _1710234))))], (19309 ^ _773908) ^ [_1107260, _1107262] : [class_Int_Onumber__ring(_1107260), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1107260), hAPP(c_Int_Onumber__class_Onumber__of(_1107260), _1107262)), c_Groups_Oone__class_Oone(_1107260)) = hAPP(c_Int_Onumber__class_Onumber__of(_1107260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1107262), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (18591 ^ _773908) ^ [_1095017] : [class_Rings_Osemiring__1(_1095017), -(c_Int_Oiszero(_1095017, c_Groups_Ozero__class_Ozero(_1095017)))], (42129 ^ _773908) ^ [_1606955, _1606957, _1606959, _1606961] : [class_Complete__Lattice_Ocomplete__lattice(_1606955), -(_1606957 = c_Orderings_Obot__class_Obot(tc_fun(_1606959, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606959, _1606955), _1606957), hAPP(c_COMBK(_1606955, _1606959), _1606961)) = _1606961)], (10333 ^ _773908) ^ [_945343, _945345, _945347] : [class_Orderings_Olinorder(_945343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945343), _945345), _945347)), 10340 ^ _773908 : [(10347 ^ _773908) ^ [] : [_945345 = _945347, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945343), _945345), _945347))], (10341 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945343), _945345), _945347))), -(_945345 = _945347)]]], (43141 ^ _773908) ^ [_1630648, _1630650, _1630652, _1630654, _1630656] : [class_Orderings_Olinorder(_1630648), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630650)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630650, _1630648, _1630652), _1630654), _1630656)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630650)), _1630656)))], (25163 ^ _773908) ^ [_1218439, _1218441, _1218443, _1218445] : [class_Orderings_Olinorder(_1218439), 25166 ^ _773908 : [(25175 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218439), _1218441), _1218443)), _1218445))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), _1218441), _1218445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), _1218443), _1218445))], (25167 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218439), _1218441), _1218443)), _1218445)), 25170 ^ _773908 : [(25173 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), _1218443), _1218445)))], (25171 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218439), _1218441), _1218445)))]]]]], (24055 ^ _773908) ^ [_1194214, _1194216, _1194218, _1194220] : [_1194214 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194216), _1194218)), _1194220), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1194214, _1194216), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1194218), _1194220)))), 24062 ^ _773908 : [(24065 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194220), _1194216))], (24063 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194216)))]], 24070 ^ _773908 : [(24073 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194216), _1194220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194220), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24071 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194216))]]], (27726 ^ _773908) ^ [_1275800, _1275802, _1275804, _1275806] : [hBOOL(hAPP(_1275800, _1275802)), hBOOL(hAPP(_1275804, _1275802)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275806, tc_HOL_Obool)), _1275800), _1275804), _1275802)))], (28258 ^ _773908) ^ [_1286614, _1286616, _1286618, _1286620] : [class_Lattices_Odistrib__lattice(_1286614), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286614), _1286616), _1286618)), _1286620) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286614), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286614), _1286616), _1286620)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286614), _1286618), _1286620)))], (31001 ^ _773908) ^ [_1342204, _1342206, _1342208, _1342210, _1342212] : [class_Groups_Ocomm__monoid__mult(_1342204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342206), _1342208)), -(hBOOL(hAPP(hAPP(c_member(_1342206), _1342210), _1342208))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342206, _1342204), _1342212), hAPP(hAPP(c_Set_Oinsert(_1342206), _1342210), _1342208)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342204), hAPP(_1342212, _1342210)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342206, _1342204), _1342212), _1342208)))], (37706 ^ _773908) ^ [_1489368, _1489370, _1489372, _1489374, _1489376, _1489378, _1489380] : [-(hAPP(c_Product__Type_Ofst(_1489368, _1489370), hAPP(c_Product__Type_Omap__pair(_1489372, _1489368, _1489374, _1489370, _1489376, _1489378), _1489380)) = hAPP(_1489376, hAPP(c_Product__Type_Ofst(_1489372, _1489374), _1489380)))], (29241 ^ _773908) ^ [_1307202, _1307204, _1307206] : [class_Lattices_Olattice(_1307202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307202), _1307204)), 29248 ^ _773908 : [(29255 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307202, tc_HOL_Obool)), _1307204), hAPP(hAPP(c_Set_Oinsert(_1307202), _1307206), c_Orderings_Obot__class_Obot(tc_fun(_1307202, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307202, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1307202, hAPP(hAPP(c_Set_Oinsert(_1307202), _1307206), _1307204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1307202), _1307206), c_Big__Operators_Olattice__class_OSup__fin(_1307202, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307202, tc_HOL_Obool)), _1307204), hAPP(hAPP(c_Set_Oinsert(_1307202), _1307206), c_Orderings_Obot__class_Obot(tc_fun(_1307202, tc_HOL_Obool)))))))], (29249 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307202, tc_HOL_Obool)), _1307204), hAPP(hAPP(c_Set_Oinsert(_1307202), _1307206), c_Orderings_Obot__class_Obot(tc_fun(_1307202, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307202, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1307202, hAPP(hAPP(c_Set_Oinsert(_1307202), _1307206), _1307204)) = _1307206)]]], (7647 ^ _773908) ^ [_897944, _897946, _897948, _897950, _897952, _897954] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_897944, _897946, _897948), _897950, _897952, _897954), 7652 ^ _773908 : [(7655 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_897946, _897950, _897952, _897954))], (7653 ^ _773908) ^ [] : [-(hBOOL(hAPP(_897944, _897950)))]], 7656 ^ _773908 : [(7659 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_897948, _897950, _897952, _897954))], (7657 ^ _773908) ^ [] : [hBOOL(hAPP(_897944, _897950))]]], (6852 ^ _773908) ^ [_884797, _884799, _884801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884797), _884799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884801), _884799))))], (25351 ^ _773908) ^ [_1221818, _1221820, _1221822, _1221824] : [class_Orderings_Olinorder(_1221818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221818), _1221820), _1221822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221818), _1221820), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221818), _1221822), _1221824))))], (42505 ^ _773908) ^ [] : [-(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)))], (9813 ^ _773908) ^ [_937356, _937358, _937360, _937362] : [class_Orderings_Oord(_937356), _937358 = _937360, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937356), _937360), _937362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937356), _937358), _937362)))], (32394 ^ _773908) ^ [_1374960, _1374962, _1374964] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1374960), _1374962)), hBOOL(hAPP(_1374964, _1374962)), 32405 ^ _773908 : [(32408 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374960), 32403 ^ [_1374960, _1374962, _1374964]), 32404 ^ [_1374960, _1374962, _1374964])))], (32410 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1374964, 32404 ^ [_1374960, _1374962, _1374964])))], (32412 ^ _773908) ^ [] : [hBOOL(hAPP(_1374964, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374960, tc_HOL_Obool)), 32404 ^ [_1374960, _1374962, _1374964]), hAPP(hAPP(c_Set_Oinsert(_1374960), 32403 ^ [_1374960, _1374962, _1374964]), c_Orderings_Obot__class_Obot(tc_fun(_1374960, tc_HOL_Obool))))))], (32406 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1374960), 32404 ^ [_1374960, _1374962, _1374964])))]], -(hBOOL(hAPP(_1374964, c_Orderings_Obot__class_Obot(tc_fun(_1374960, tc_HOL_Obool)))))], (9115 ^ _773908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9531 ^ _773908) ^ [_932678, _932680] : [class_Rings_Oring__1(_932678), -(hAPP(c_Int_Oring__1__class_Oof__int(_932678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _932680)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_932678), _932680))], (37201 ^ _773908) ^ [_1475374, _1475376, _1475378, _1475380, _1475382] : [hBOOL(hAPP(hAPP(c_member(_1475374), _1475376), hAPP(c_Set_Ovimage(_1475374, _1475378, _1475380), hAPP(hAPP(c_Set_Oinsert(_1475378), _1475382), c_Orderings_Obot__class_Obot(tc_fun(_1475378, tc_HOL_Obool)))))), -(hAPP(_1475380, _1475376) = _1475382)], (25789 ^ _773908) ^ [_1230843] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1230843) = c_Orderings_Oord__class_Omax(_1230843)), class_Lattices_Osemilattice__sup(_1230843), class_Orderings_Olinorder(_1230843)], (8725 ^ _773908) ^ [_918370, _918372] : [class_Groups_Olinordered__ab__group__add(_918370), 8728 ^ _773908 : [(8735 ^ _773908) ^ [] : [_918372 = c_Groups_Ozero__class_Ozero(_918370), -(_918372 = hAPP(c_Groups_Ouminus__class_Ouminus(_918370), _918372))], (8729 ^ _773908) ^ [] : [_918372 = hAPP(c_Groups_Ouminus__class_Ouminus(_918370), _918372), -(_918372 = c_Groups_Ozero__class_Ozero(_918370))]]], (34506 ^ _773908) ^ [_1416622, _1416624, _1416626, _1416628] : [class_Groups_Oordered__ab__group__add__abs(_1416622), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416622), hAPP(c_Groups_Oabs__class_Oabs(_1416622), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1416624, _1416622), _1416626), _1416628))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1416624, _1416622), hAPP(hAPP(c_COMBB(_1416622, _1416622, _1416624), c_Groups_Oabs__class_Oabs(_1416622)), _1416626)), _1416628))))], (43805 ^ _773908) ^ [_1645256, _1645258] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1645256, tc_HOL_Obool), tc_HOL_Obool)), _1645258), hAPP(c_Set_OPow(_1645256), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645256, tc_HOL_Obool), _1645258)))))], (49268 ^ _773908) ^ [_1767633, _1767635, _1767637, _1767639, _1767641] : [_1767633 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1767635, _1767637, _1767639, _1767641), _1767633) = c_Lazy__Sequence_Ohit__bound(_1767637))], (24031 ^ _773908) ^ [_1193782, _1193784, _1193786, _1193788] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193782, _1193784), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1193786), _1193788))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193782), _1193784), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1193788), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193786)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193786)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1193788), 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), _1193784), _1193788))))))], (35837 ^ _773908) ^ [] : [-(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)))], (36165 ^ _773908) ^ [_1452738] : [class_Lattices_Oboolean__algebra(_1452738), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1452738), c_Orderings_Otop__class_Otop(_1452738)) = c_Orderings_Obot__class_Obot(_1452738))], (45741 ^ _773908) ^ [_1687778, _1687780, _1687782] : [-(c_List_OtakeWhile(_1687778, _1687780, _1687782) = hAPP(hAPP(c_List_Otake(_1687778), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687778)), c_List_OtakeWhile(_1687778, _1687780, _1687782))), _1687782))], (10083 ^ _773908) ^ [_941623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _941623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _941623)))], (2218 ^ _773908) ^ [_806195, _806197, _806199, _806201] : [-(c_Nitpick_Onat__lcm(_806201, _806197) = c_Nitpick_Onat__lcm(_806199, _806195)), _806201 = _806199, _806197 = _806195], (51768 ^ _773908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (11982 ^ _773908) ^ [_974527, _974529, _974531, _974533, _974535] : [class_Rings_Olinordered__semiring__strict(_974527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974527), _974529), _974531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974527), _974533), _974535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974527), c_Groups_Ozero__class_Ozero(_974527)), _974529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974527), c_Groups_Ozero__class_Ozero(_974527)), _974533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974527), _974529), _974533)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974527), _974531), _974535))))], (5566 ^ _773908) ^ [_859057, _859059] : [_859059 = _859057, -(tc_Option_Ooption(_859059) = tc_Option_Ooption(_859057))], (51472 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (36277 ^ _773908) ^ [_1454986, _1454988, _1454990, _1454992, _1454994] : [c_Fun_Oinj__on(_1454986, _1454988, _1454990, c_Orderings_Otop__class_Otop(tc_fun(_1454986, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1454986, _1454988, _1454990), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1454986, tc_HOL_Obool)), _1454992), _1454994)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1454988, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1454986, _1454988, _1454990), _1454992)), hAPP(c_Set_Oimage(_1454986, _1454988, _1454990), _1454994)))], (39723 ^ _773908) ^ [_1547300, _1547302, _1547304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547300, _1547300), tc_HOL_Obool)), _1547302), _1547304)), c_Relation_Orefl__on(_1547300, c_Orderings_Otop__class_Otop(tc_fun(_1547300, tc_HOL_Obool)), _1547304), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1547300), tc_List_Olist(_1547300)), tc_HOL_Obool)), c_List_Olistrel1(_1547300, _1547302)), c_List_Olistrel(_1547300, _1547304))))], (16821 ^ _773908) ^ [_1062961, _1062963, _1062965] : [class_Rings_Ocomm__semiring__1(_1062961), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062961), hAPP(hAPP(c_Power_Opower__class_Opower(_1062961), _1062963), _1062965)), _1062963) = hAPP(hAPP(c_Power_Opower__class_Opower(_1062961), _1062963), hAPP(c_Nat_OSuc, _1062965)))], (31313 ^ _773908) ^ [_1349402, _1349404, _1349406, _1349408, _1349410] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349402, tc_fun(_1349404, tc_HOL_Obool)), _1349406), _1349408), _1349410))), 31314 ^ _773908 : [(31315 ^ _773908) ^ [_1349474] : [hBOOL(hAPP(hAPP(c_member(_1349402), _1349474), _1349406)), hBOOL(hAPP(hAPP(_1349408, _1349474), _1349410))]]], (5446 ^ _773908) ^ [_857189, _857191, _857193, _857195, _857197, _857199, _857201, _857203] : [-(c_Hilbert__Choice_Oinv__into(_857203, _857199, _857195, _857191) = c_Hilbert__Choice_Oinv__into(_857201, _857197, _857193, _857189)), _857203 = _857201, _857199 = _857197, _857195 = _857193, _857191 = _857189], (39883 ^ _773908) ^ [_1551919, _1551921, _1551923, _1551925] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551919)), hAPP(hAPP(c_List_Olist_OCons(_1551919), _1551921), _1551923)), c_List_Olists(_1551919, _1551925)))), hBOOL(hAPP(hAPP(c_member(_1551919), _1551921), _1551925)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551919)), _1551923), c_List_Olists(_1551919, _1551925)))], (37207 ^ _773908) ^ [_1475513, _1475515, _1475517, _1475519, _1475521] : [hAPP(_1475519, _1475515) = _1475521, -(hBOOL(hAPP(hAPP(c_member(_1475513), _1475515), hAPP(c_Set_Ovimage(_1475513, _1475517, _1475519), hAPP(hAPP(c_Set_Oinsert(_1475517), _1475521), c_Orderings_Obot__class_Obot(tc_fun(_1475517, tc_HOL_Obool)))))))], (34576 ^ _773908) ^ [_1418346, _1418348, _1418350, _1418352, _1418354, _1418356, _1418358] : [class_Rings_Osemiring__0(_1418346), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418346), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418348, _1418346), _1418350), _1418352)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418354, _1418346), _1418356), _1418358)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418348, _1418346), hAPP(hAPP(c_COMBC(_1418348, tc_fun(_1418354, tc_HOL_Obool), _1418346), hAPP(hAPP(c_COMBB(tc_fun(_1418354, _1418346), tc_fun(tc_fun(_1418354, tc_HOL_Obool), _1418346), _1418348), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418354, _1418346)), hAPP(hAPP(c_COMBC(_1418348, tc_fun(_1418354, _1418346), tc_fun(_1418354, _1418346)), hAPP(hAPP(c_COMBB(tc_fun(_1418346, _1418346), tc_fun(tc_fun(_1418354, _1418346), tc_fun(_1418354, _1418346)), _1418348), c_COMBB(_1418346, _1418346, _1418354)), hAPP(hAPP(c_COMBB(_1418346, tc_fun(_1418346, _1418346), _1418348), c_Groups_Otimes__class_Otimes(_1418346)), _1418350))), _1418356))), _1418358)), _1418352))], (51255 ^ _773908) ^ [_1811375, _1811377, _1811379, _1811381] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1811375), _1811377)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1811379), _1811381)), 51262 ^ _773908 : [(51269 ^ _773908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1811375), _1811377) = hAPP(c_Finite__Set_Ocard(_1811379), _1811381), -(c_Fun_Obij__betw(_1811375, _1811379, 51272 ^ [_1811375, _1811377, _1811379, _1811381], _1811377, _1811381))], (51263 ^ _773908) ^ [] : [51264 ^ _773908 : [(51265 ^ _773908) ^ [_1811564] : [c_Fun_Obij__betw(_1811375, _1811379, _1811564, _1811377, _1811381)]], -(hAPP(c_Finite__Set_Ocard(_1811375), _1811377) = hAPP(c_Finite__Set_Ocard(_1811379), _1811381))]]], (14875 ^ _773908) ^ [_1025398, _1025400, _1025402, _1025404] : [class_Divides_Osemiring__div(_1025398), -(_1025400 = c_Groups_Ozero__class_Ozero(_1025398)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025398), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025398), _1025402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025398), _1025404), _1025400))), _1025400) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025398), _1025404), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025398), _1025402), _1025400)))], (23757 ^ _773908) ^ [_1188931, _1188933, _1188935, _1188937, _1188939, _1188941] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188931, _1188933, _1188935), _1188937), hAPP(hAPP(c_Product__Type_OPair(_1188931, _1188933), _1188939), _1188941)) = hAPP(hAPP(_1188937, _1188939), _1188941))], (15257 ^ _773908) ^ [_1032686, _1032688, _1032690] : [class_Groups_Ogroup__add(_1032686), 15260 ^ _773908 : [(15267 ^ _773908) ^ [] : [_1032688 = _1032690, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032686), _1032688), _1032690) = c_Groups_Ozero__class_Ozero(_1032686))], (15261 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032686), _1032688), _1032690) = c_Groups_Ozero__class_Ozero(_1032686), -(_1032688 = _1032690)]]], (38288 ^ _773908) ^ [_1506034] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1506034) = 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), _1506034), c_Int_Onat)))))], (34534 ^ _773908) ^ [_1417165, _1417167, _1417169, _1417171] : [class_Groups_Oab__group__add(_1417165), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417167, _1417165), hAPP(hAPP(c_COMBB(_1417165, _1417165, _1417167), c_Groups_Ouminus__class_Ouminus(_1417165)), _1417169)), _1417171) = hAPP(c_Groups_Ouminus__class_Ouminus(_1417165), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417167, _1417165), _1417169), _1417171)))], (35168 ^ _773908) ^ [_1432122, _1432124] : [class_Rings_Ocomm__semiring__1(_1432122), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432122), c_Groups_Oone__class_Oone(_1432122)), c_Groups_Oone__class_Oone(_1432122))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1432122), c_Nat_Osemiring__1__class_Oof__nat(_1432122)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1432124))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432122), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1432122), _1432124)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432122), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1432122), _1432124)), c_Groups_Oone__class_Oone(_1432122))))], (40111 ^ _773908) ^ [_1557811, _1557813] : [-(hAPP(hAPP(c_List_Otake(_1557811), _1557813), c_List_Olist_ONil(_1557811)) = c_List_Olist_ONil(_1557811))], (41912 ^ _773908) ^ [_1600087, _1600089, _1600091, _1600093, _1600095, _1600097] : [-(hAPP(hAPP(c_List_Omap(_1600087, _1600089), _1600091), hAPP(hAPP(c_List_Olist__update(_1600087, _1600093), _1600095), _1600097)) = hAPP(hAPP(c_List_Olist__update(_1600089, hAPP(hAPP(c_List_Omap(_1600087, _1600089), _1600091), _1600093)), _1600095), hAPP(_1600091, _1600097)))], (23307 ^ _773908) ^ [_1179680, _1179682] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179680), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23310 ^ _773908 : [(23319 ^ _773908) ^ [] : [-(c_Nitpick_Onorm__frac(_1179682, _1179680) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1179682), _1179680)), 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), _1179682))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179680)))), -(_1179682 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1179680 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23311 ^ _773908) ^ [] : [23312 ^ _773908 : [(23315 ^ _773908) ^ [] : [_1179680 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23313 ^ _773908) ^ [] : [_1179682 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1179682, _1179680) = 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)))]]], (12510 ^ _773908) ^ [_983501, _983503] : [_983501 = _983503, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983501), _983503)))], (44347 ^ _773908) ^ [_1657927, _1657929, _1657931] : [-(hAPP(c_List_Oset(_1657927), c_List_Oinsert(_1657927, _1657929, _1657931)) = hAPP(hAPP(c_Set_Oinsert(_1657927), _1657929), hAPP(c_List_Oset(_1657927), _1657931)))], (572 ^ _773908) ^ [_782672, _782674, _782676, _782678, _782680, _782682] : [-(c_Relation_Osingle__valued(_782680, _782676, _782672)), c_Relation_Osingle__valued(_782682, _782678, _782674), _782682 = _782680, _782678 = _782676, _782674 = _782672], (11499 ^ _773908) ^ [_965835, _965837, _965839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965835), _965837)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965839), _965837))), 11502 ^ _773908 : [(11505 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965835), _965839)))], (11503 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965837)))]]], (44601 ^ _773908) ^ [_1665012] : [-(c_List_Otranspose(_1665012, c_List_Olist_ONil(tc_List_Olist(_1665012))) = c_List_Olist_ONil(tc_List_Olist(_1665012)))], (50372 ^ _773908) ^ [_1793720] : [-(c_Relation_Oantisym(_1793720, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1793720, _1793720), tc_HOL_Obool))))], (34143 ^ _773908) ^ [_1409510, _1409512, _1409514] : [-(c_Fun_Oinj__on(tc_prod(_1409510, _1409512), tc_prod(_1409512, _1409510), hAPP(c_Product__Type_Oprod_Oprod__case(_1409510, _1409512, tc_prod(_1409512, _1409510)), hAPP(c_COMBC(_1409512, _1409510, tc_prod(_1409512, _1409510)), c_Product__Type_OPair(_1409512, _1409510))), _1409514))], (34892 ^ _773908) ^ [_1425678, _1425680, _1425682, _1425684] : [class_Groups_Ocomm__monoid__add(_1425678), 34895 ^ _773908 : [(34902 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1425680), _1425682))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425680, _1425678), _1425684), _1425682) = c_Groups_Ozero__class_Ozero(_1425678))], (34896 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1425680), _1425682)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425680, _1425678), _1425684), _1425682) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425678, _1425680, c_Groups_Oplus__class_Oplus(_1425678)), _1425684), c_Groups_Ozero__class_Ozero(_1425678)), _1425682))]]], (15725 ^ _773908) ^ [_1041490, _1041492] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041490), _1041492))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041490), _1041492)) = _1041490)], (32480 ^ _773908) ^ [_1376948, _1376950] : [hAPP(c_Set_OPow(_1376948), _1376950) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376948, tc_HOL_Obool), tc_HOL_Obool))], (7433 ^ _773908) ^ [_894185, _894187, _894189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894185), _894187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _894187), _894189))))], (45776 ^ _773908) ^ [_1688500, _1688502, _1688504, _1688506, _1688508] : [-(hAPP(hAPP(c_List_Ozip(_1688500, _1688502), _1688504), c_List_OtakeWhile(_1688502, _1688506, _1688508)) = c_List_OtakeWhile(tc_prod(_1688500, _1688502), hAPP(c_Fun_Ocomp(_1688502, tc_HOL_Obool, tc_prod(_1688500, _1688502), _1688506), c_Product__Type_Osnd(_1688500, _1688502)), hAPP(hAPP(c_List_Ozip(_1688500, _1688502), _1688504), _1688508)))], (43007 ^ _773908) ^ [_1627321, _1627323, _1627325, _1627327] : [-(hBOOL(hAPP(hAPP(c_member(_1627321), _1627323), hAPP(c_List_Oset(_1627321), _1627325)))), hBOOL(hAPP(hAPP(c_member(_1627321), _1627323), hAPP(c_List_Oset(_1627321), c_List_Oremove1(_1627321, _1627327, _1627325))))], (43340 ^ _773908) ^ [_1634740, _1634742, _1634744] : [class_Orderings_Olinorder(_1634740), hBOOL(hAPP(hAPP(c_member(_1634740), _1634742), hAPP(c_List_Oset(_1634740), _1634744))), -(c_List_Olinorder__class_Oinsort__insert__key(_1634740, _1634740, c_COMBI(_1634740), _1634742, _1634744) = _1634744)], (20239 ^ _773908) ^ [] : [-(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))))], (41171 ^ _773908) ^ [_1585191, _1585193, _1585195] : [hBOOL(hAPP(c_List_Odistinct(_1585191), hAPP(hAPP(c_List_Oappend(_1585191), _1585193), _1585195))), 41174 ^ _773908 : [(41179 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1585191, tc_HOL_Obool)), hAPP(c_List_Oset(_1585191), _1585193)), hAPP(c_List_Oset(_1585191), _1585195)) = c_Orderings_Obot__class_Obot(tc_fun(_1585191, tc_HOL_Obool)))], (41177 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1585191), _1585195)))], (41175 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1585191), _1585193)))]]], (40605 ^ _773908) ^ [_1569794, _1569796, _1569798, _1569800] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569794)), hAPP(hAPP(c_List_Olist__update(_1569794, _1569796), _1569798), _1569800)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569794)), _1569796))], (51488 ^ _773908) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (15731 ^ _773908) ^ [_1041543, _1041545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041543), _1041545)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1041545)), _1041543) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041545), _1041543)))], (35018 ^ _773908) ^ [_1428559, _1428561, _1428563, _1428565] : [class_Groups_Ocomm__monoid__add(_1428559), 35021 ^ _773908 : [(35028 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1428561), _1428563))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428559), _1428565), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1428563), hAPP(c_Nat_OSuc, _1428561))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428559), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428559), _1428565), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1428563), _1428561))), hAPP(_1428565, _1428561)))], (35022 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1428561), _1428563)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1428559), _1428565), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1428563), hAPP(c_Nat_OSuc, _1428561))) = c_Groups_Ozero__class_Ozero(_1428559))]]], (41655 ^ _773908) ^ [_1594540] : [class_Groups_Omonoid__add(_1594540), -(c_List_Omonoid__add__class_Olistsum(_1594540) = c_List_Ofoldl(_1594540, _1594540, c_Groups_Oplus__class_Oplus(_1594540), c_Groups_Ozero__class_Ozero(_1594540)))], (46883 ^ _773908) ^ [_1713823, _1713825, _1713827, _1713829] : [hBOOL(hAPP(hAPP(c_member(_1713823), _1713825), c_Wellfounded_Oacc(_1713823, _1713827))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1713823, _1713823)), hAPP(hAPP(c_Product__Type_OPair(_1713823, _1713823), _1713829), _1713825)), c_Transitive__Closure_Ortrancl(_1713823, _1713827))), -(hBOOL(hAPP(hAPP(c_member(_1713823), _1713829), c_Wellfounded_Oacc(_1713823, _1713827))))], (35366 ^ _773908) ^ [_1436446, _1436448, _1436450] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436446, tc_Nat_Onat), _1436448), _1436450) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436446, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1436446), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1436448)), _1436450)))], (2228 ^ _773908) ^ [_806344, _806346, _806348, _806350, _806352, _806354, _806356, _806358, _806360, _806362] : [-(c_Nitpick_Opair__box_Opair__box__size(_806362, _806358, _806354, _806350, _806346) = c_Nitpick_Opair__box_Opair__box__size(_806360, _806356, _806352, _806348, _806344)), _806362 = _806360, _806358 = _806356, _806354 = _806352, _806350 = _806348, _806346 = _806344], (16837 ^ _773908) ^ [_1063335, _1063337, _1063339, _1063341] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063335), hAPP(c_Int_Onumber__class_Onumber__of(_1063335), _1063337)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063335), _1063339), _1063341)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063335), hAPP(c_Int_Onumber__class_Onumber__of(_1063335), _1063337)), _1063339)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063335), hAPP(c_Int_Onumber__class_Onumber__of(_1063335), _1063337)), _1063341))), class_Int_Onumber(_1063335), class_Rings_Oring(_1063335)], (48239 ^ _773908) ^ [_1746275, _1746277, _1746279, _1746281] : [class_Orderings_Olinorder(_1746275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1746275), _1746277)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1746275, _1746275, c_Orderings_Oord__class_Omin(_1746275)), _1746279), hAPP(hAPP(c_Set_Oinsert(_1746275), _1746281), _1746277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1746275), _1746281), hAPP(hAPP(c_Finite__Set_Ofold(_1746275, _1746275, c_Orderings_Oord__class_Omin(_1746275)), _1746279), _1746277)))], (9638 ^ _773908) ^ [_934554] : [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, _934554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _934554)))], (9883 ^ _773908) ^ [_938445, _938447, _938449, _938451] : [class_Orderings_Opreorder(_938445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938445), _938447), _938449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938445), _938449), _938451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938445), _938447), _938451)))], (34552 ^ _773908) ^ [_1417736, _1417738, _1417740, _1417742] : [class_Rings_Oring__1(_1417736), -(hAPP(c_Int_Oring__1__class_Oof__int(_1417736), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417738, tc_Int_Oint), _1417740), _1417742)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417738, _1417736), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1417736, _1417738), c_Int_Oring__1__class_Oof__int(_1417736)), _1417740)), _1417742))], (41528 ^ _773908) ^ [_1591725, _1591727, _1591729] : [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), _1591725), _1591727))), -(hBOOL(hAPP(hAPP(_1591729, _1591725), _1591727))), 41535 ^ _773908 : [(41538 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 41533 ^ [_1591725, _1591727, _1591729]), 41534 ^ [_1591725, _1591727, _1591729])), -(hBOOL(hAPP(hAPP(_1591729, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 41533 ^ [_1591725, _1591727, _1591729]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 41534 ^ [_1591725, _1591727, _1591729])))], (41544 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1591729, 41533 ^ [_1591725, _1591727, _1591729]), 41534 ^ [_1591725, _1591727, _1591729]))], (41536 ^ _773908) ^ [] : [-(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), 41533 ^ [_1591725, _1591727, _1591729]), 41534 ^ [_1591725, _1591727, _1591729]))))]]], (51394 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (6772 ^ _773908) ^ [_883501, _883503, _883505] : [class_Orderings_Olinorder(_883501), 6775 ^ _773908 : [(6776 ^ _773908) ^ [] : [-(_883503 = _883505), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883501), _883503), _883505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883501), _883505), _883503)))], (6786 ^ _773908) ^ [] : [6787 ^ _773908 : [(6790 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883501), _883505), _883503))], (6788 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883501), _883503), _883505))]], _883503 = _883505]]], (42021 ^ _773908) ^ [_1604168, _1604170, _1604172, _1604174, _1604176] : [hBOOL(hAPP(hAPP(c_member(_1604168), _1604170), _1604172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604174, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604168, tc_fun(_1604174, tc_HOL_Obool)), _1604172), _1604176)), hAPP(_1604176, _1604170))))], (12500 ^ _773908) ^ [_983406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983406)))], (19443 ^ _773908) ^ [_1109539] : [-(c_Int_OBit1(_1109539) = 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)), _1109539)), _1109539))], (17977 ^ _773908) ^ [_1084048, _1084050] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1084048), _1084050) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1084048 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1084048 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (44162 ^ _773908) ^ [_1654039] : [class_Complete__Lattice_Ocomplete__lattice(_1654039), -(c_Complete__Lattice_OInf__class_OInf(_1654039, c_Orderings_Obot__class_Obot(tc_fun(_1654039, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1654039))], (40860 ^ _773908) ^ [_1577477, _1577479, _1577481] : [_1577477 = _1577479, 40863 ^ _773908 : [(40866 ^ _773908) ^ [_1577633] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577481, _1577481)), _1577633), hAPP(c_List_Oset(tc_prod(_1577481, _1577481)), hAPP(hAPP(c_List_Ozip(_1577481, _1577481), _1577477), _1577479)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1577481, _1577481, tc_HOL_Obool), c_fequal), _1577633)))], (40864 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577481)), _1577477) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577481)), _1577479))]]], (42838 ^ _773908) ^ [_1623922, _1623924] : [_1623922 = _1623924, -(hAPP(c_Code__Numeral_Onat__of, _1623922) = hAPP(c_Code__Numeral_Onat__of, _1623924))], (46823 ^ _773908) ^ [_1712260, _1712262, _1712264, _1712266] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712260, _1712260)), _1712262), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1712260, _1712260), tc_HOL_Obool), _1712264), _1712266))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1712260, _1712260)), _1712262), c_Transitive__Closure_Ortrancl(_1712260, _1712266))))], (43302 ^ _773908) ^ [_1633968, _1633970, _1633972] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633968)), _1633972), c_List_Olists(_1633968, _1633970))), -(hBOOL(hAPP(c_List_Olistsp(_1633968, hAPP(hAPP(c_COMBC(_1633968, tc_fun(_1633968, tc_HOL_Obool), tc_HOL_Obool), c_member(_1633968)), _1633970)), _1633972)))], (17635 ^ _773908) ^ [_1078520, _1078522] : [class_Power_Opower(_1078520), class_Rings_Osemiring__0(_1078520), 17642 ^ _773908 : [(17649 ^ _773908) ^ [] : [-(_1078522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078520), c_Groups_Ozero__class_Ozero(_1078520)), _1078522) = c_Groups_Ozero__class_Ozero(_1078520))], (17643 ^ _773908) ^ [] : [_1078522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078520), c_Groups_Ozero__class_Ozero(_1078520)), _1078522) = c_Groups_Oone__class_Oone(_1078520))]]], (1944 ^ _773908) ^ [_801190, _801192, _801194, _801196, _801198, _801200] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_801198, _801194, _801190)), c_Hoare__Mirabelle_Ohoare__derivs(_801200, _801196, _801192), _801200 = _801198, _801196 = _801194, _801192 = _801190], (35560 ^ _773908) ^ [_1440529, _1440531, _1440533] : [class_Orderings_Olinorder(_1440529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440529), _1440531), _1440533)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440529, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1440529, _1440531, _1440533)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440529), _1440533)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1440529), _1440531))], (1098 ^ _773908) ^ [_790499, _790501, _790503, _790505, _790507, _790509, _790511, _790513, _790515, _790517] : [-(c_Fun_Obij__betw(_790515, _790511, _790507, _790503, _790499)), c_Fun_Obij__betw(_790517, _790513, _790509, _790505, _790501), _790517 = _790515, _790513 = _790511, _790509 = _790507, _790505 = _790503, _790501 = _790499], (44418 ^ _773908) ^ [_1659464, _1659466, _1659468, _1659470] : [-(hBOOL(hAPP(_1659464, _1659466))), -(hAPP(c_List_Ofilter(_1659468, _1659464), hAPP(hAPP(c_List_Olist_OCons(_1659468), _1659466), _1659470)) = hAPP(c_List_Ofilter(_1659468, _1659464), _1659470))], (43772 ^ _773908) ^ [_1644613, _1644615] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1644613, tc_HOL_Obool), hAPP(c_Set_OPow(_1644613), _1644615)) = _1644615)], (50033 ^ _773908) ^ [_1784894, _1784896, _1784898, _1784900] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1784894, tc_fun(_1784896, tc_HOL_Obool)), _1784898), _1784900) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1784896, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1784896, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784894, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1784896, tc_HOL_Obool)), c_HOL_OEx(_1784894)), hAPP(hAPP(c_COMBB(tc_fun(_1784894, tc_HOL_Obool), tc_fun(_1784894, tc_HOL_Obool), tc_fun(_1784896, tc_HOL_Obool)), hAPP(c_COMBS(_1784894, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784894), c_fconj), hAPP(hAPP(c_COMBC(_1784894, tc_fun(_1784894, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784894)), _1784898)))), hAPP(hAPP(c_COMBC(tc_fun(_1784896, tc_HOL_Obool), tc_fun(_1784894, tc_fun(_1784896, tc_HOL_Obool)), tc_fun(_1784894, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784896, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1784894, tc_fun(_1784896, tc_HOL_Obool)), tc_fun(_1784894, tc_HOL_Obool)), tc_fun(_1784896, tc_HOL_Obool)), c_COMBB(tc_fun(_1784896, tc_HOL_Obool), tc_HOL_Obool, _1784894)), c_fequal)), _1784900))))))], (25455 ^ _773908) ^ [_1224085, _1224087, _1224089, _1224091] : [class_Orderings_Olinorder(_1224085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224085), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224085), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224085), _1224087), _1224089)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224085), _1224087), _1224091))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224085), _1224087), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224085), _1224089), _1224091)))))], (40973 ^ _773908) ^ [_1581085, _1581087] : [-(hAPP(c_List_Oset(_1581085), hAPP(c_List_Orotate1(_1581085), _1581087)) = hAPP(c_List_Oset(_1581085), _1581087))], (35629 ^ _773908) ^ [_1442200, _1442202, _1442204, _1442206, _1442208] : [class_Groups_Oordered__ab__group__add(_1442200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442202), _1442204)), 35639 ^ _773908 : [(35642 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442200), c_Groups_Ozero__class_Ozero(_1442200)), hAPP(_1442206, 35638 ^ [_1442200, _1442202, _1442204, _1442206, _1442208])))], (35640 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442202), 35638 ^ [_1442200, _1442202, _1442204, _1442206, _1442208]), _1442204)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442202, _1442200), _1442206), _1442204) = c_Groups_Ozero__class_Ozero(_1442200), hBOOL(hAPP(hAPP(c_member(_1442202), _1442208), _1442204)), -(hAPP(_1442206, _1442208) = c_Groups_Ozero__class_Ozero(_1442200))], (48617 ^ _773908) ^ [_1753675, _1753677, _1753679, _1753681, _1753683, _1753685, _1753687] : [c_Finite__Set_Ofun__left__comm(_1753675, _1753677, _1753679), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1753675, _1753677, _1753679, _1753681, _1753683), _1753685)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1753675, _1753677, _1753679, _1753681, _1753683), _1753687)), -(_1753687 = _1753685)], (38534 ^ _773908) ^ [_1515070, _1515072, _1515074, _1515076, _1515078, _1515080] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515070), _1515072)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515074), _1515076)), 38544 ^ _773908 : [(38547 ^ _773908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1515070), hAPP(c_Set_OCollect(_1515070), hAPP(hAPP(c_COMBS(_1515070, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515070), c_fconj), hAPP(hAPP(c_COMBC(_1515070, tc_fun(_1515070, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515070)), _1515072))), hAPP(hAPP(c_COMBC(_1515070, _1515074, tc_HOL_Obool), _1515078), 38543 ^ [_1515070, _1515072, _1515074, _1515076, _1515078, _1515080])))) = hAPP(_1515080, 38543 ^ [_1515070, _1515072, _1515074, _1515076, _1515078, _1515080])], (38545 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515074), 38543 ^ [_1515070, _1515072, _1515074, _1515076, _1515078, _1515080]), _1515076)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515070, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1515074, tc_HOL_Obool), tc_Nat_Onat, _1515070), c_Finite__Set_Ocard(_1515074)), hAPP(hAPP(c_COMBB(tc_fun(_1515074, tc_HOL_Obool), tc_fun(_1515074, tc_HOL_Obool), _1515070), c_Set_OCollect(_1515074)), hAPP(hAPP(c_COMBB(tc_fun(_1515074, tc_HOL_Obool), tc_fun(_1515074, tc_HOL_Obool), _1515070), hAPP(c_COMBS(_1515074, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515074), c_fconj), hAPP(hAPP(c_COMBC(_1515074, tc_fun(_1515074, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515074)), _1515076)))), _1515078)))), _1515072) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515074, tc_Nat_Onat), _1515080), _1515076))], (40577 ^ _773908) ^ [_1569261, _1569263, _1569265] : [-(hAPP(hAPP(c_List_Olist__update(_1569261, c_List_Olist_ONil(_1569261)), _1569263), _1569265) = c_List_Olist_ONil(_1569261))], (13095 ^ _773908) ^ [_993652] : [-(hAPP(c_Nat_OSuc, _993652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _993652))], (44700 ^ _773908) ^ [_1667215, _1667217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667215), _1667217)), -(c_List_Oupt(_1667215, hAPP(c_Nat_OSuc, _1667217)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1667215, _1667217)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1667217), c_List_Olist_ONil(tc_Nat_Onat))))], (19637 ^ _773908) ^ [] : [-(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)))], (21443 ^ _773908) ^ [_1144584, _1144586, _1144588, _1144590, _1144592] : [class_Fields_Olinordered__field(_1144584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144584), c_Groups_Ozero__class_Ozero(_1144584)), _1144586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144584), _1144586), _1144588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144584), c_Groups_Ozero__class_Ozero(_1144584)), _1144590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144584), _1144590), _1144592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144584), _1144586), _1144592)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144584), _1144588), _1144590))))], (27936 ^ _773908) ^ [_1279564, _1279566, _1279568, _1279570] : [class_Lattices_Osemilattice__inf(_1279564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279564), _1279566), _1279568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279564), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1279564), _1279570), _1279566)), _1279568)))], (42103 ^ _773908) ^ [_1606224, _1606226, _1606228] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606224, tc_fun(_1606226, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1606224, tc_HOL_Obool))), _1606228) = c_Orderings_Otop__class_Otop(tc_fun(_1606226, tc_HOL_Obool)))], (24775 ^ _773908) ^ [_1210909, _1210911, _1210913, _1210915] : [class_Orderings_Olinorder(_1210909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210909), _1210911), _1210913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210909), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210909), _1210915), _1210911)), _1210913)))], (32638 ^ _773908) ^ [_1379724, _1379726] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1379724), _1379726) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1379724, _1379726))], (26868 ^ _773908) ^ [] : [-(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))))], (36801 ^ _773908) ^ [_1467316, _1467318] : [-(c_Divides_Odivmod__nat(_1467316, _1467318) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1467316, _1467318)))], (42149 ^ _773908) ^ [_1607394, _1607396, _1607398, _1607400, _1607402] : [-(_1607394 = c_Orderings_Obot__class_Obot(tc_fun(_1607396, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607398, tc_HOL_Obool)), _1607400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607396, tc_fun(_1607398, tc_HOL_Obool)), _1607394), _1607402)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607396, tc_fun(_1607398, tc_HOL_Obool)), _1607394), hAPP(hAPP(c_COMBB(tc_fun(_1607398, tc_HOL_Obool), tc_fun(_1607398, tc_HOL_Obool), _1607396), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607398, tc_HOL_Obool)), _1607400)), _1607402)))], (27045 ^ _773908) ^ [_1260837, _1260839, _1260841] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1260837, hAPP(hAPP(c_COMBC(_1260837, tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_fun(_1260837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260837, tc_fun(tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_fun(_1260837, tc_HOL_Obool)), _1260837), c_COMBC(_1260837, tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260837, tc_prod(_1260837, _1260837)), tc_fun(_1260837, tc_fun(tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_HOL_Obool)), _1260837), hAPP(c_COMBB(tc_prod(_1260837, _1260837), tc_fun(tc_fun(tc_prod(_1260837, _1260837), tc_HOL_Obool), tc_HOL_Obool), _1260837), c_member(tc_prod(_1260837, _1260837)))), c_Product__Type_OPair(_1260837, _1260837)))), _1260839)), _1260841)), -(hBOOL(hAPP(hAPP(c_member(_1260837), _1260841), c_Wellfounded_Oacc(_1260837, _1260839))))], (17845 ^ _773908) ^ [_1082225, _1082227] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082225)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082225)), _1082227) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082225)), _1082227)))], (41748 ^ _773908) ^ [_1596400, _1596402] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596400)), c_List_Obutlast(_1596400, _1596402)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596400)), _1596402)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (35969 ^ _773908) ^ [_1448824, _1448826] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448824, tc_HOL_Obool)), _1448826), c_Orderings_Otop__class_Otop(tc_fun(_1448824, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448824, tc_HOL_Obool)))], (6312 ^ _773908) ^ [_876149, _876151, _876153, _876155] : [-(c_Nat_Onat_Onat__case(_876149, _876151, _876153, hAPP(c_Nat_OSuc, _876155)) = hAPP(_876153, _876155))], (37992 ^ _773908) ^ [_1496012] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1496012, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1496012), hAPP(c_COMBK(tc_HOL_Obool, _1496012), c_fTrue)))], (4524 ^ _773908) ^ [_842770, _842772, _842774, _842776] : [-(c_List_Ozip(_842776, _842772) = c_List_Ozip(_842774, _842770)), _842776 = _842774, _842772 = _842770], (38849 ^ _773908) ^ [_1524519, _1524521, _1524523, _1524525] : [-(hAPP(hAPP(c_List_Oappend(_1524519), hAPP(hAPP(c_List_Oappend(_1524519), _1524521), _1524523)), _1524525) = hAPP(hAPP(c_List_Oappend(_1524519), _1524521), hAPP(hAPP(c_List_Oappend(_1524519), _1524523), _1524525)))], (49650 ^ _773908) ^ [_1776070, _1776072, _1776074, _1776076, _1776078] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1776070, _1776072, _1776074) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1776070, _1776076, _1776078)), _1776072 = _1776076, _1776074 = _1776078], (50332 ^ _773908) ^ [_1793086, _1793088] : [c_Relation_Otrans(_1793086, _1793088), c_Relation_Oantisym(_1793086, _1793088), -(c_Relation_Otrans(_1793086, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1793086, _1793086), tc_HOL_Obool)), _1793088), c_Relation_OId(_1793086))))], (20369 ^ _773908) ^ [_1125488, _1125490, _1125492] : [class_Rings_Olinordered__idom(_1125488), 20372 ^ _773908 : [(20381 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125488), hAPP(hAPP(c_Power_Opower__class_Opower(_1125488), _1125490), 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(_1125488), _1125492), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1125488)), _1125490 = c_Groups_Ozero__class_Ozero(_1125488), _1125492 = c_Groups_Ozero__class_Ozero(_1125488)], (20373 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125488), hAPP(hAPP(c_Power_Opower__class_Opower(_1125488), _1125490), 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(_1125488), _1125492), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1125488), 20376 ^ _773908 : [(20379 ^ _773908) ^ [] : [-(_1125492 = c_Groups_Ozero__class_Ozero(_1125488))], (20377 ^ _773908) ^ [] : [-(_1125490 = c_Groups_Ozero__class_Ozero(_1125488))]]]]], (1062 ^ _773908) ^ [_789953, _789955, _789957, _789959] : [-(c_Equiv__Relations_Opart__equivp(_789957, _789953)), c_Equiv__Relations_Opart__equivp(_789959, _789955), _789959 = _789957, _789955 = _789953], (49280 ^ _773908) ^ [_1767828, _1767830, _1767832, _1767834, _1767836] : [_1767828 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1767830, _1767832, _1767834, _1767836), _1767828) = c_Lazy__Sequence_Oempty(_1767832))], (20875 ^ _773908) ^ [_1134937, _1134939, _1134941] : [class_Fields_Olinordered__field__inverse__zero(_1134937), 20878 ^ _773908 : [(20893 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134937), _1134939), _1134941)), c_Groups_Ozero__class_Ozero(_1134937)))), 20894 ^ _773908 : [(20901 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), _1134939), c_Groups_Ozero__class_Ozero(_1134937))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), c_Groups_Ozero__class_Ozero(_1134937)), _1134941))], (20895 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), c_Groups_Ozero__class_Ozero(_1134937)), _1134939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), _1134941), c_Groups_Ozero__class_Ozero(_1134937)))]]], (20879 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134937), _1134939), _1134941)), c_Groups_Ozero__class_Ozero(_1134937))), 20884 ^ _773908 : [(20887 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), _1134941), c_Groups_Ozero__class_Ozero(_1134937))))], (20885 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), c_Groups_Ozero__class_Ozero(_1134937)), _1134939)))]], 20888 ^ _773908 : [(20891 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), c_Groups_Ozero__class_Ozero(_1134937)), _1134941)))], (20889 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134937), _1134939), c_Groups_Ozero__class_Ozero(_1134937))))]]]]], (3312 ^ _773908) ^ [_823602, _823604, _823606, _823608, _823610, _823612] : [-(c_List_Opartition(_823612, _823608, _823604) = c_List_Opartition(_823610, _823606, _823602)), _823612 = _823610, _823608 = _823606, _823604 = _823602], (48401 ^ _773908) ^ [_1749530, _1749532, _1749534] : [class_Lattices_Olattice(_1749530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749530), _1749532)), -(c_Big__Operators_Olattice__class_OInf__fin(_1749530, hAPP(hAPP(c_Set_Oinsert(_1749530), _1749534), _1749532)) = hAPP(hAPP(c_Finite__Set_Ofold(_1749530, _1749530, c_Lattices_Osemilattice__inf__class_Oinf(_1749530)), _1749534), _1749532))], (44377 ^ _773908) ^ [_1658669, _1658671, _1658673, _1658675, _1658677, _1658679] : [class_Orderings_Olinorder(_1658669), -(hBOOL(hAPP(_1658671, _1658673))), -(hAPP(c_List_Ofilter(_1658675, _1658671), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658675, _1658669, _1658677), _1658673), _1658679)) = hAPP(c_List_Ofilter(_1658675, _1658671), _1658679))], (6010 ^ _773908) ^ [_870463, _870465, _870467] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870463))), _870465), _870467)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _870463)), _870465), _870467)))], (41494 ^ _773908) ^ [_1591245, _1591247] : [-(_1591245 = c_List_Olist_ONil(_1591247)), -(c_List_Olast(_1591247, _1591245) = hAPP(hAPP(c_List_Onth(_1591247), _1591245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591247)), _1591245)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50259 ^ _773908) ^ [_1791351, _1791353, _1791355, _1791357] : [c_Relation_Otrans(_1791351, _1791353), -(c_Relation_Otrans(_1791355, hAPP(hAPP(c_Relation_Oinv__image(_1791351, _1791355), _1791353), _1791357)))], (40557 ^ _773908) ^ [_1568392, _1568394, _1568396, _1568398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1568394)), _1568396))), -(hAPP(hAPP(c_List_Olist__update(_1568394, _1568396), _1568392), _1568398) = hAPP(hAPP(c_List_Oappend(_1568394), hAPP(hAPP(c_List_Otake(_1568394), _1568392), _1568396)), hAPP(hAPP(c_List_Olist_OCons(_1568394), _1568398), hAPP(hAPP(c_List_Odrop(_1568394), hAPP(c_Nat_OSuc, _1568392)), _1568396))))], (44515 ^ _773908) ^ [_1661693, _1661695] : [-(c_List_Oconcat(_1661693, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661693), tc_List_Olist(_1661693)), c_List_Olist_Olist__case(tc_List_Olist(_1661693), _1661693, c_List_Olist_ONil(_1661693), hAPP(hAPP(c_COMBB(tc_List_Olist(_1661693), tc_fun(tc_List_Olist(_1661693), tc_List_Olist(_1661693)), _1661693), c_COMBK(tc_List_Olist(_1661693), tc_List_Olist(_1661693))), hAPP(hAPP(c_COMBC(_1661693, tc_List_Olist(_1661693), tc_List_Olist(_1661693)), c_List_Olist_OCons(_1661693)), c_List_Olist_ONil(_1661693))))), _1661695)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661693), _1661693), c_List_Ohd(_1661693)), hAPP(c_List_Ofilter(tc_List_Olist(_1661693), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1661693)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1661693), tc_List_Olist(_1661693), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1661693)))), _1661695)))], (17753 ^ _773908) ^ [_1080722, _1080724, _1080726, _1080728] : [class_Rings_Olinordered__semidom(_1080722), hAPP(hAPP(c_Power_Opower__class_Opower(_1080722), _1080724), _1080726) = hAPP(hAPP(c_Power_Opower__class_Opower(_1080722), _1080728), _1080726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080722), c_Groups_Ozero__class_Ozero(_1080722)), _1080724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080722), c_Groups_Ozero__class_Ozero(_1080722)), _1080728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1080726)), -(_1080724 = _1080728)], (9493 ^ _773908) ^ [_932040, _932042] : [class_Int_Oring__char__0(_932040), 9496 ^ _773908 : [(9503 ^ _773908) ^ [] : [_932042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_932040), _932042) = c_Groups_Ozero__class_Ozero(_932040))], (9497 ^ _773908) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_932040), _932042) = c_Groups_Ozero__class_Ozero(_932040), -(_932042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (39122 ^ _773908) ^ [_1531374, _1531376, _1531378, _1531380] : [hBOOL(hAPP(c_Predicate_ORangeP(_1531374, _1531376, _1531378), _1531380)), -(hBOOL(hAPP(hAPP(_1531378, 39125 ^ [_1531374, _1531376, _1531378, _1531380]), _1531380)))], (26993 ^ _773908) ^ [_1259859, _1259861] : [c_Nat__Transfer_Onat__set(_1259859), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259861), _1259859)), -(c_Nat__Transfer_Ois__nat(_1259861))], (40191 ^ _773908) ^ [_1559757, _1559759] : [_1559759 = c_List_Olist_ONil(_1559757), -(hAPP(c_List_Oset(_1559757), _1559759) = c_Orderings_Obot__class_Obot(tc_fun(_1559757, tc_HOL_Obool)))], (8205 ^ _773908) ^ [_908830, _908832, _908834, _908836, _908838] : [c_Com_Ocom_OLocal(_908830, _908832, _908834) = c_Com_Ocom_OWhile(_908836, _908838)], (38249 ^ _773908) ^ [_1504435, _1504437, _1504439, _1504441] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504435), hAPP(c_Set_OCollect(_1504435), _1504437))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1504439), hAPP(c_Set_OCollect(_1504439), hAPP(hAPP(c_COMBB(tc_fun(_1504435, tc_HOL_Obool), tc_HOL_Obool, _1504439), c_HOL_OEx(_1504435)), hAPP(hAPP(c_COMBC(_1504439, tc_fun(_1504435, tc_HOL_Obool), tc_fun(_1504435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504435, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1504435, tc_HOL_Obool), tc_fun(_1504435, tc_HOL_Obool)), _1504439), c_COMBS(_1504435, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504435, tc_HOL_Obool), tc_fun(_1504435, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1504439), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504435), c_fconj)), hAPP(hAPP(c_COMBC(_1504439, tc_fun(_1504435, _1504439), tc_fun(_1504435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504439, tc_HOL_Obool), tc_fun(tc_fun(_1504435, _1504439), tc_fun(_1504435, tc_HOL_Obool)), _1504439), c_COMBB(_1504439, tc_HOL_Obool, _1504435)), c_fequal)), _1504441)))), _1504437))))))], (1664 ^ _773908) ^ [_797694, _797696] : [-(class_Groups_Ocomm__monoid__mult(_797694)), _797696 = _797694, class_Groups_Ocomm__monoid__mult(_797696)], (42798 ^ _773908) ^ [_1623002, _1623004, _1623006] : [-(c_Hilbert__Choice_OEps(tc_prod(_1623002, _1623004), _1623006) = c_Hilbert__Choice_OEps(tc_prod(_1623002, _1623004), hAPP(c_Product__Type_Oprod_Oprod__case(_1623002, _1623004, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623004, tc_prod(_1623002, _1623004)), tc_fun(_1623004, tc_HOL_Obool), _1623002), hAPP(c_COMBB(tc_prod(_1623002, _1623004), tc_HOL_Obool, _1623004), _1623006)), c_Product__Type_OPair(_1623002, _1623004)))))], (36723 ^ _773908) ^ [_1465867, _1465869, _1465871] : [-(hAPP(c_Finite__Set_Ofold1(_1465867, _1465869), hAPP(hAPP(c_Set_Oinsert(_1465867), _1465871), c_Orderings_Obot__class_Obot(tc_fun(_1465867, tc_HOL_Obool)))) = _1465871)], (49626 ^ _773908) ^ [_1775620, _1775622, _1775624] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1775620, _1775622), _1775624) = c_Lazy__Sequence_Oproduct(_1775620, _1775622, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1775620, _1775624), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1775622, _1775624))), class_Lazy__Sequence_Osmall__lazy(_1775620), class_Lazy__Sequence_Osmall__lazy(_1775622)], (20249 ^ _773908) ^ [_1123415, _1123417] : [class_Groups_Omonoid__mult(_1123415), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123415), _1123417), 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(_1123415), _1123417), _1123417))], (37680 ^ _773908) ^ [_1488637, _1488639, _1488641, _1488643, _1488645, _1488647] : [hAPP(c_Set_Oimage(_1488637, _1488639, _1488641), c_Orderings_Otop__class_Otop(tc_fun(_1488637, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1488639, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1488643, _1488645, _1488647), c_Orderings_Otop__class_Otop(tc_fun(_1488643, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1488645, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1488637, _1488643), tc_prod(_1488639, _1488645), c_Product__Type_Omap__pair(_1488637, _1488639, _1488643, _1488645, _1488641, _1488647)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1488637, _1488643), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1488639, _1488645), tc_HOL_Obool)))], (10851 ^ _773908) ^ [_954152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _954152)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _954152)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _954152)))], (40619 ^ _773908) ^ [_1570195, _1570197, _1570199, _1570201, _1570203] : [-(_1570195 = _1570197), -(hAPP(hAPP(c_List_Onth(_1570199), hAPP(hAPP(c_List_Olist__update(_1570199, _1570201), _1570195), _1570203)), _1570197) = hAPP(hAPP(c_List_Onth(_1570199), _1570201), _1570197))], (1924 ^ _773908) ^ [_800944, _800946] : [-(class_Nat_Osize(_800944)), _800946 = _800944, class_Nat_Osize(_800946)], (36589 ^ _773908) ^ [_1462912, _1462914, _1462916, _1462918, _1462920, _1462922, _1462924] : [c_Typedef_Otype__definition(_1462912, _1462914, _1462916, _1462918, _1462920), hBOOL(hAPP(hAPP(c_member(_1462914), _1462922), _1462920)), hBOOL(hAPP(hAPP(c_member(_1462914), _1462924), _1462920)), 36600 ^ _773908 : [(36607 ^ _773908) ^ [] : [_1462922 = _1462924, -(hAPP(_1462918, _1462922) = hAPP(_1462918, _1462924))], (36601 ^ _773908) ^ [] : [hAPP(_1462918, _1462922) = hAPP(_1462918, _1462924), -(_1462922 = _1462924)]]], (40655 ^ _773908) ^ [_1571101, _1571103, _1571105, _1571107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1571101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571103)), _1571105))), -(hAPP(hAPP(c_List_Onth(_1571103), hAPP(hAPP(c_List_Olist__update(_1571103, _1571105), _1571101), _1571107)), _1571101) = _1571107)], (47046 ^ _773908) ^ [_1718315, _1718317, _1718319, _1718321] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1718315, _1718315)), hAPP(hAPP(c_Product__Type_OPair(_1718315, _1718315), _1718317), _1718319)), c_Transitive__Closure_Ortrancl(_1718315, _1718321))), -(_1718317 = _1718319), 47053 ^ _773908 : [(47056 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718315, _1718315)), hAPP(hAPP(c_Product__Type_OPair(_1718315, _1718315), _1718317), _1718319)), c_Transitive__Closure_Otrancl(_1718315, _1718321))))], (47054 ^ _773908) ^ [] : [_1718317 = _1718319]]], (12160 ^ _773908) ^ [] : [-(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))], (32612 ^ _773908) ^ [_1379079, _1379081] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1379079, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1379079, tc_HOL_Obool))), hAPP(c_Set_OPow(_1379079), _1379081))))], (6968 ^ _773908) ^ [_886710, _886712, _886714] : [class_Groups_Oordered__comm__monoid__add(_886710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886710), c_Groups_Ozero__class_Ozero(_886710)), _886712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886710), c_Groups_Ozero__class_Ozero(_886710)), _886714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886710), c_Groups_Ozero__class_Ozero(_886710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886710), _886712), _886714))))], (15951 ^ _773908) ^ [_1046346, _1046348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046346), hAPP(c_Nat_OSuc, _1046348))), _1046346)))], (51918 ^ _773908) ^ [_1818691, _1818693] : [hBOOL(hAPP(hAPP(c_fdisj, _1818691), _1818693)), -(hBOOL(_1818691)), -(hBOOL(_1818693))], (9827 ^ _773908) ^ [_937575, _937577, _937579, _937581] : [class_Orderings_Oorder(_937575), _937577 = _937579, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937575), _937581), _937579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937575), _937581), _937577)))], (49306 ^ _773908) ^ [_1768546, _1768548, _1768550, _1768552] : [-(c_New__Random__Sequence_Oneg__map(_1768546, _1768548, _1768550, _1768552) = c_New__Random__Sequence_Oneg__bind(_1768546, _1768548, _1768552, hAPP(c_Fun_Ocomp(_1768548, 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(_1768548)))))), _1768546, c_New__Random__Sequence_Oneg__single(_1768548)), _1768550)))], (30229 ^ _773908) ^ [_1326080, _1326082, _1326084] : [class_Orderings_Olinorder(_1326080), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326080), _1326082)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326080), _1326084)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326080, tc_HOL_Obool)), _1326082), _1326084) = c_Orderings_Obot__class_Obot(tc_fun(_1326080, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326080), c_Big__Operators_Olattice_OInf__fin(_1326080, c_Orderings_Oord__class_Omin(_1326080), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326080, tc_HOL_Obool)), _1326082), _1326084))), c_Big__Operators_Olattice_OInf__fin(_1326080, c_Orderings_Oord__class_Omin(_1326080), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326080, tc_HOL_Obool)), _1326082), _1326084))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326080), c_Big__Operators_Olattice_OInf__fin(_1326080, c_Orderings_Oord__class_Omin(_1326080), _1326082)), c_Big__Operators_Olattice_OInf__fin(_1326080, c_Orderings_Oord__class_Omin(_1326080), _1326084)))], (43703 ^ _773908) ^ [_1642975, _1642977] : [-(hAPP(c_Relation_OField(_1642975), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1642975, _1642975), tc_HOL_Obool), _1642977)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642975, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1642975, _1642975), tc_HOL_Obool), tc_fun(_1642975, tc_HOL_Obool), c_Relation_OField(_1642975)), _1642977)))], (7139 ^ _773908) ^ [_889480, _889482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889480), _889482)), _889482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12768 ^ _773908) ^ [_987911, _987913, _987915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987911), _987913)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987911), _987915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987913), _987915)))], (22823 ^ _773908) ^ [] : [-(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))))], (42806 ^ _773908) ^ [_1623358, _1623360, _1623362, _1623364, _1623366] : [_1623358 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1623360, _1623362, _1623358, _1623364), _1623366) = hAPP(c_Product__Type_OPair(_1623360, _1623362), _1623366))], (43992 ^ _773908) ^ [_1650138, _1650140, _1650142, _1650144] : [hBOOL(hAPP(c_Predicate_ODomainP(_1650138, _1650140, _1650142), _1650144)), -(hBOOL(hAPP(hAPP(_1650142, _1650144), 43995 ^ [_1650138, _1650140, _1650142, _1650144])))], (42638 ^ _773908) ^ [_1619587, _1619589] : [_1619587 = _1619589, -(hAPP(c_Code__Numeral_Oof__nat, _1619587) = hAPP(c_Code__Numeral_Oof__nat, _1619589))], (22141 ^ _773908) ^ [_1157086, _1157088, _1157090, _1157092] : [class_Fields_Olinordered__field(_1157086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157086), c_Groups_Ozero__class_Ozero(_1157086)), _1157088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157086), _1157090), _1157088)), _1157092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157086), _1157090), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157086), _1157092), _1157088))))], (200 ^ _773908) ^ [_776816, _776818, _776820, _776822, _776824, _776826, _776828, _776830, _776832, _776834, _776836, _776838] : [-(c_Equiv__Relations_Ocongruent2(_776836, _776832, _776828, _776824, _776820, _776816)), c_Equiv__Relations_Ocongruent2(_776838, _776834, _776830, _776826, _776822, _776818), _776838 = _776836, _776834 = _776832, _776830 = _776828, _776826 = _776824, _776822 = _776820, _776818 = _776816], (43077 ^ _773908) ^ [_1628732, _1628734, _1628736, _1628738, _1628740] : [c_List_Opartition(_1628732, _1628734, _1628736) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628732), tc_List_Olist(_1628732)), _1628738), _1628740), 43080 ^ _773908 : [(43087 ^ _773908) ^ [_1628994] : [hBOOL(hAPP(hAPP(c_member(_1628732), _1628994), hAPP(c_List_Oset(_1628732), _1628740))), hBOOL(hAPP(_1628734, _1628994))], (43081 ^ _773908) ^ [_1628885] : [hBOOL(hAPP(hAPP(c_member(_1628732), _1628885), hAPP(c_List_Oset(_1628732), _1628738))), -(hBOOL(hAPP(_1628734, _1628885)))]]], (38050 ^ _773908) ^ [_1497238, _1497240, _1497242] : [-(hAPP(hAPP(c_Set_Oinsert(_1497238), _1497240), _1497242) = hAPP(c_Set_OCollect(_1497238), hAPP(hAPP(c_COMBS(_1497238, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497238), c_fdisj), hAPP(hAPP(c_COMBC(_1497238, _1497238, tc_HOL_Obool), c_fequal), _1497240))), hAPP(hAPP(c_COMBC(_1497238, tc_fun(_1497238, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497238)), _1497242))))], (15579 ^ _773908) ^ [_1038579, _1038581, _1038583] : [class_Groups_Oordered__ab__group__add(_1038579), 15582 ^ _773908 : [(15589 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038579), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038579), _1038581), _1038583)), c_Groups_Ozero__class_Ozero(_1038579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038579), _1038581), _1038583)))], (15583 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038579), _1038581), _1038583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038579), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038579), _1038581), _1038583)), c_Groups_Ozero__class_Ozero(_1038579))))]]], (25483 ^ _773908) ^ [_1224819, _1224821] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1224819), hAPP(c_Nat_OSuc, _1224821)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1224821), 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)), _1224821)), _1224819))], (30908 ^ _773908) ^ [_1339987, _1339989, _1339991, _1339993, _1339995] : [class_Groups_Ocomm__monoid__mult(_1339987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339989), _1339991)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339989, _1339987), hAPP(hAPP(c_COMBS(_1339989, _1339987, _1339987), hAPP(hAPP(c_COMBB(_1339987, tc_fun(_1339987, _1339987), _1339989), c_Groups_Otimes__class_Otimes(_1339987)), _1339993)), _1339995)), _1339991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339987), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339989, _1339987), _1339993), _1339991)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339989, _1339987), _1339995), _1339991)))], (51738 ^ _773908) ^ [_1816614, _1816616] : [-(class_Enum_Oenum(tc_prod(_1816614, _1816616))), class_Enum_Oenum(_1816614), class_Enum_Oenum(_1816616)], (29537 ^ _773908) ^ [_1313259, _1313261] : [class_Orderings_Olinorder(_1313259), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313259), _1313261)), -(_1313261 = c_Orderings_Obot__class_Obot(tc_fun(_1313259, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1313259), c_Big__Operators_Olinorder__class_OMin(_1313259, _1313261)), _1313261)))], (44082 ^ _773908) ^ [_1652537] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652537, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1652537, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1652537, tc_HOL_Obool)))], (37708 ^ _773908) ^ [_1489428, _1489430, _1489432, _1489434, _1489436, _1489438, _1489440, _1489442] : [-(hAPP(c_Product__Type_Omap__pair(_1489428, _1489430, _1489432, _1489434, _1489436, _1489438), hAPP(hAPP(c_Product__Type_OPair(_1489428, _1489432), _1489440), _1489442)) = hAPP(hAPP(c_Product__Type_OPair(_1489430, _1489434), hAPP(_1489436, _1489440)), hAPP(_1489438, _1489442)))], (42271 ^ _773908) ^ [_1611252, _1611254, _1611256, _1611258, _1611260] : [-(hAPP(hAPP(c_List_Odrop(_1611252), _1611254), hAPP(hAPP(c_List_Omap(_1611256, _1611252), _1611258), _1611260)) = hAPP(hAPP(c_List_Omap(_1611256, _1611252), _1611258), hAPP(hAPP(c_List_Odrop(_1611256), _1611254), _1611260)))], (1124 ^ _773908) ^ [_790944, _790946] : [-(class_Lattices_Obounded__lattice(_790944)), _790946 = _790944, class_Lattices_Obounded__lattice(_790946)], (39987 ^ _773908) ^ [_1554805, _1554807, _1554809, _1554811] : [-(hAPP(hAPP(c_List_Onth(_1554805), hAPP(hAPP(c_List_Oappend(_1554805), _1554807), _1554809)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554805)), _1554807)), _1554811)) = hAPP(hAPP(c_List_Onth(_1554805), _1554809), _1554811))], (19825 ^ _773908) ^ [_1116039, _1116041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116039), _1116041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116039)), c_Int_OBit0(_1116041))))], (24547 ^ _773908) ^ [_1205734, _1205736, _1205738, _1205740] : [_1205738 = _1205740, -(hAPP(hAPP(c_COMBC(_1205734, tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_fun(_1205736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205736, tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_fun(_1205736, tc_HOL_Obool)), _1205734), c_COMBC(_1205736, tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205736, tc_prod(_1205734, _1205736)), tc_fun(_1205736, tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), _1205734), hAPP(c_COMBB(tc_prod(_1205734, _1205736), tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool), _1205736), c_member(tc_prod(_1205734, _1205736)))), c_Product__Type_OPair(_1205734, _1205736)))), _1205738) = hAPP(hAPP(c_COMBC(_1205734, tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_fun(_1205736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205736, tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_fun(_1205736, tc_HOL_Obool)), _1205734), c_COMBC(_1205736, tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1205736, tc_prod(_1205734, _1205736)), tc_fun(_1205736, tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool)), _1205734), hAPP(c_COMBB(tc_prod(_1205734, _1205736), tc_fun(tc_fun(tc_prod(_1205734, _1205736), tc_HOL_Obool), tc_HOL_Obool), _1205736), c_member(tc_prod(_1205734, _1205736)))), c_Product__Type_OPair(_1205734, _1205736)))), _1205740))], (8253 ^ _773908) ^ [_909788, _909790, _909792] : [class_Rings_Olinordered__semidom(_909788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909790), _909792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909788), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909788), _909790)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909788), _909792))))], (8163 ^ _773908) ^ [_907866, _907868, _907870, _907872] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907866, _907868)), _907870), _907872))), 8164 ^ _773908 : [(8171 ^ _773908) ^ [] : [hBOOL(hAPP(_907866, _907870)), 8174 ^ _773908 : [(8175 ^ _773908) ^ [_908085] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907868), _907870), _908085)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907866, _907868)), _908085), _907872))]]], (8165 ^ _773908) ^ [] : [_907872 = _907870, -(hBOOL(hAPP(_907866, _907870)))]]], (40975 ^ _773908) ^ [_1581140, _1581142] : [hAPP(c_List_Orotate1(_1581140), _1581142) = c_List_Olist_ONil(_1581140), -(_1581142 = c_List_Olist_ONil(_1581140))], (7815 ^ _773908) ^ [_901468, _901470, _901472, _901474] : [class_Rings_Ocomm__semiring__1(_901468), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901468), _901470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901468), _901472), _901474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901468), _901472), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901468), _901470), _901474)))], (14863 ^ _773908) ^ [_1025173, _1025175] : [-(_1025173 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025175), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025173), _1025175))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1025173, _1025175)))], (28853 ^ _773908) ^ [_1300989, _1300991, _1300993] : [class_Orderings_Olinorder(_1300989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300989), _1300991)), hBOOL(hAPP(hAPP(c_member(_1300989), _1300993), _1300991)), 28864 ^ _773908 : [(28871 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300989, tc_HOL_Obool)), _1300991), hAPP(hAPP(c_Set_Oinsert(_1300989), _1300993), c_Orderings_Obot__class_Obot(tc_fun(_1300989, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1300989, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1300989, _1300991) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300989), _1300993), c_Big__Operators_Olinorder__class_OMax(_1300989, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300989, tc_HOL_Obool)), _1300991), hAPP(hAPP(c_Set_Oinsert(_1300989), _1300993), c_Orderings_Obot__class_Obot(tc_fun(_1300989, tc_HOL_Obool)))))))], (28865 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300989, tc_HOL_Obool)), _1300991), hAPP(hAPP(c_Set_Oinsert(_1300989), _1300993), c_Orderings_Obot__class_Obot(tc_fun(_1300989, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1300989, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1300989, _1300991) = _1300993)]]], (6270 ^ _773908) ^ [_875608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _875608))))], (4472 ^ _773908) ^ [_841996, _841998, _842000, _842002, _842004, _842006] : [-(c_Predicate_Oconversep(_842006, _842002, _841998) = c_Predicate_Oconversep(_842004, _842000, _841996)), _842006 = _842004, _842002 = _842000, _841998 = _841996], (34147 ^ _773908) ^ [_1409596, _1409598, _1409600, _1409602, _1409604, _1409606, _1409608, _1409610] : [c_Finite__Set_Ofolding__image(_1409596, _1409598, _1409600, _1409602, _1409604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409598), _1409606)), -(hAPP(hAPP(_1409604, hAPP(hAPP(c_COMBS(_1409598, _1409596, _1409596), hAPP(hAPP(c_COMBB(_1409596, tc_fun(_1409596, _1409596), _1409598), _1409600), _1409608)), _1409610)), _1409606) = hAPP(hAPP(_1409600, hAPP(hAPP(_1409604, _1409608), _1409606)), hAPP(hAPP(_1409604, _1409610), _1409606)))], (9989 ^ _773908) ^ [_940028] : [class_Rings_Olinordered__semidom(_940028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940028), c_Groups_Oone__class_Oone(_940028)), c_Groups_Ozero__class_Ozero(_940028)))], (13781 ^ _773908) ^ [_1006028, _1006030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006028)), -(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, _1006030, _1006028))))], (4914 ^ _773908) ^ [_848899, _848901, _848903, _848905] : [-(c_List_Oupto(_848905, _848901) = c_List_Oupto(_848903, _848899)), _848905 = _848903, _848901 = _848899], (46760 ^ _773908) ^ [_1710759, _1710761] : [-(c_Transitive__Closure_Ortrancl(_1710759, c_Transitive__Closure_Ortrancl(_1710759, _1710761)) = c_Transitive__Closure_Ortrancl(_1710759, _1710761))], (7364 ^ _773908) ^ [_893012, _893014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893012), hAPP(c_Nat_OSuc, _893014)))), 7365 ^ _773908 : [(7368 ^ _773908) ^ [_893100] : [_893012 = hAPP(c_Nat_OSuc, _893100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893100), _893014))], (7366 ^ _773908) ^ [] : [_893012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (10169 ^ _773908) ^ [_942940, _942942, _942944] : [class_Orderings_Olinorder(_942940), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942940), _942942), _942944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942940), _942944), _942942)))], (45945 ^ _773908) ^ [_1692119, _1692121, _1692123] : [-(c_List_OdropWhile(_1692119, _1692121, _1692123) = hAPP(hAPP(c_List_Odrop(_1692119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692119)), c_List_OtakeWhile(_1692119, _1692121, _1692123))), _1692123))], (24699 ^ _773908) ^ [_1209322, _1209324, _1209326] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_1209322, _1209324)), _1209326), hAPP(hAPP(hAPP(c_Natural_Oupdate, _1209326), _1209322), hAPP(_1209324, _1209326)))))], (26309 ^ _773908) ^ [_1242222, _1242224, _1242226, _1242228, _1242230, _1242232] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1242228, _1242228)), hAPP(hAPP(c_Product__Type_OPair(_1242228, _1242228), hAPP(_1242232, _1242224)), hAPP(_1242232, _1242226))), _1242230)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1242222, _1242222)), hAPP(hAPP(c_Product__Type_OPair(_1242222, _1242222), _1242224), _1242226)), hAPP(hAPP(c_Relation_Oinv__image(_1242228, _1242222), _1242230), _1242232))))], (19531 ^ _773908) ^ [_1111004, _1111006] : [class_Int_Onumber__ring(_1111004), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111004), hAPP(c_Int_Onumber__class_Onumber__of(_1111004), c_Int_OBit1(c_Int_OPls))), _1111006) = _1111006)], (33274 ^ _773908) ^ [_1392004, _1392006, _1392008, _1392010] : [c_Fun_Oinj__on(_1392004, _1392006, _1392008, _1392010), 33277 ^ _773908 : [(33278 ^ _773908) ^ [_1392112] : [hBOOL(hAPP(hAPP(c_member(_1392004), _1392112), _1392010)), 33281 ^ _773908 : [(33282 ^ _773908) ^ [_1392214] : [hBOOL(hAPP(hAPP(c_member(_1392004), _1392214), _1392010)), hAPP(_1392008, _1392112) = hAPP(_1392008, _1392214), -(_1392112 = _1392214)]]]]], (42613 ^ _773908) ^ [_1619167, _1619169] : [hBOOL(hAPP(_1619167, c_Hilbert__Choice_OEps(_1619169, _1619167))), -(hBOOL(hAPP(_1619167, 42616 ^ [_1619167, _1619169])))], (7980 ^ _773908) ^ [_904603, _904605, _904607, _904609] : [c_Com_Ocom_OWhile(_904603, _904605) = c_Com_Ocom_OWhile(_904607, _904609), 7983 ^ _773908 : [(7986 ^ _773908) ^ [] : [-(_904605 = _904609)], (7984 ^ _773908) ^ [] : [-(_904603 = _904607)]]], (6576 ^ _773908) ^ [_880768, _880770, _880772, _880774] : [class_Orderings_Oorder(_880768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880768), _880770), _880772)), _880770 = _880774, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880768), _880774), _880772)))], (26940 ^ _773908) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (23185 ^ _773908) ^ [_1177161, _1177163] : [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(_1177163))), 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), _1177161)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1177161)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177163))))], (12562 ^ _773908) ^ [_984443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984443), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_984443 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19507 ^ _773908) ^ [_1110600, _1110602] : [c_Int_Oiszero(_1110600, hAPP(c_Int_Onumber__class_Onumber__of(_1110600), c_Int_OBit1(_1110602))), class_Int_Onumber__ring(_1110600), class_Int_Oring__char__0(_1110600)], (17881 ^ _773908) ^ [_1082638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082638)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082638))], (2796 ^ _773908) ^ [_815484, _815486, _815488, _815490] : [-(c_Divides_Odivmod__nat(_815490, _815486) = c_Divides_Odivmod__nat(_815488, _815484)), _815490 = _815488, _815486 = _815484], (49670 ^ _773908) ^ [_1776447, _1776449] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1776447), _1776449))), -(c_Lazy__Sequence_Osmall__lazy_H(_1776447, _1776449) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1776449), c_Lazy__Sequence_Osmall__lazy_H(_1776447, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1776449), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42804 ^ _773908) ^ [_1623259, _1623261, _1623263] : [-(c_Hilbert__Choice_OEps(tc_prod(_1623259, _1623261), hAPP(c_Product__Type_Oprod_Oprod__case(_1623259, _1623261, tc_HOL_Obool), _1623263)) = c_Hilbert__Choice_OEps(tc_prod(_1623259, _1623261), hAPP(hAPP(c_COMBS(tc_prod(_1623259, _1623261), _1623261, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1623259, tc_fun(_1623261, tc_HOL_Obool), tc_prod(_1623259, _1623261)), _1623263), c_Product__Type_Ofst(_1623259, _1623261))), c_Product__Type_Osnd(_1623259, _1623261))))], (39512 ^ _773908) ^ [_1541420, _1541422] : [-(_1541422 = c_List_Olist_ONil(_1541420)), -(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(_1541420)), _1541422))))], (43610 ^ _773908) ^ [_1640810, _1640812] : [-(c_Enum_Oenum__the(_1640810, _1640812) = c_HOL_OThe(_1640810, _1640812))], (4714 ^ _773908) ^ [_845799, _845801] : [_845801 = _845799, -(c_Lazy__Sequence_Osingle(_845801) = c_Lazy__Sequence_Osingle(_845799))], (20391 ^ _773908) ^ [_1125863, _1125865] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1125863), hAPP(c_Int_Onumber__class_Onumber__of(_1125863), _1125865)), 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(_1125863), hAPP(c_Int_Onumber__class_Onumber__of(_1125863), _1125865)), hAPP(c_Int_Onumber__class_Onumber__of(_1125863), _1125865))), class_Groups_Omonoid__mult(_1125863), class_Int_Onumber(_1125863)], (10707 ^ _773908) ^ [_951496, _951498, _951500] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951498), _951500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951496), _951498)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951496), _951500)))], (31554 ^ _773908) ^ [_1355273, _1355275, _1355277, _1355279, _1355281, _1355283] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355273, tc_fun(_1355275, tc_HOL_Obool)), _1355277), hAPP(hAPP(c_COMBC(_1355273, tc_fun(_1355279, tc_fun(_1355275, tc_HOL_Obool)), tc_fun(_1355275, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355279, tc_HOL_Obool), tc_fun(tc_fun(_1355279, tc_fun(_1355275, tc_HOL_Obool)), tc_fun(_1355275, tc_HOL_Obool)), _1355273), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355279, tc_fun(_1355275, tc_HOL_Obool))), _1355281)), _1355283)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355279, tc_fun(_1355275, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355273, tc_fun(_1355279, tc_HOL_Obool)), _1355277), _1355281)), _1355283))], (16827 ^ _773908) ^ [_1063092, _1063094, _1063096, _1063098] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063092), _1063094), _1063096)), hAPP(c_Int_Onumber__class_Onumber__of(_1063092), _1063098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063092), _1063094), hAPP(c_Int_Onumber__class_Onumber__of(_1063092), _1063098))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063092), _1063096), hAPP(c_Int_Onumber__class_Onumber__of(_1063092), _1063098)))), class_Int_Onumber(_1063092), class_Rings_Oring(_1063092)], (8601 ^ _773908) ^ [_916266, _916268, _916270] : [class_Rings_Oring(_916266), -(hAPP(c_Groups_Ouminus__class_Ouminus(_916266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916266), _916268), _916270)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916266), _916268), hAPP(c_Groups_Ouminus__class_Ouminus(_916266), _916270)))], (49412 ^ _773908) ^ [_1771493, _1771495, _1771497, _1771499] : [-(c_Lazy__Sequence_Oproduct(_1771493, _1771495, _1771497, _1771499) = hAPP(c_Lazy__Sequence_Obind(_1771493, tc_prod(_1771493, _1771495), _1771497), hAPP(hAPP(c_COMBB(tc_fun(_1771495, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1771493, _1771495))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1771493, _1771495)), _1771493), c_Lazy__Sequence_Obind(_1771495, tc_prod(_1771493, _1771495), _1771499)), hAPP(hAPP(c_COMBB(tc_fun(_1771495, tc_prod(_1771493, _1771495)), tc_fun(_1771495, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1771493, _1771495))), _1771493), hAPP(c_COMBB(tc_prod(_1771493, _1771495), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1771493, _1771495)), _1771495), c_Lazy__Sequence_Osingle(tc_prod(_1771493, _1771495)))), c_Product__Type_OPair(_1771493, _1771495)))))], (4026 ^ _773908) ^ [_834725, _834727, _834729, _834731, _834733, _834735] : [-(c_Nitpick_Otimes__frac(_834735, _834731, _834727) = c_Nitpick_Otimes__frac(_834733, _834729, _834725)), _834735 = _834733, _834731 = _834729, _834727 = _834725], (39921 ^ _773908) ^ [_1552869, _1552871, _1552873] : [39922 ^ _773908 : [(39923 ^ _773908) ^ [_1552958, _1552960] : [_1552871 = hAPP(hAPP(c_List_Olist_OCons(_1552869), _1552960), _1552958)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552869), tc_List_Olist(_1552869))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552869), tc_List_Olist(_1552869)), c_List_Olist_ONil(_1552869)), _1552871)), c_List_Olexord(_1552869, _1552873))))], (15701 ^ _773908) ^ [_1041036, _1041038] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041036), _1041038) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041036), _1041038)))], (46429 ^ _773908) ^ [_1702648, _1702650] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1702648, _1702648)), _1702650)), c_Wellfounded_Oacyclic(_1702648, _1702650), -(c_Wellfounded_Owf(_1702648, _1702650))], (3852 ^ _773908) ^ [_832010, _832012, _832014, _832016] : [-(c_Finite__Set_Ofold1(_832016, _832012) = c_Finite__Set_Ofold1(_832014, _832010)), _832016 = _832014, _832012 = _832010], (40571 ^ _773908) ^ [_1569025, _1569027, _1569029, _1569031, _1569033] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1569025, _1569027)), _1569029), hAPP(hAPP(c_List_Ozip(_1569025, _1569027), _1569031), _1569033)) = hAPP(hAPP(c_List_Ozip(_1569025, _1569027), hAPP(hAPP(c_List_Otake(_1569025), _1569029), _1569031)), hAPP(hAPP(c_List_Otake(_1569027), _1569029), _1569033)))], (14797 ^ _773908) ^ [_1024010, _1024012] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024010), _1024012) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1024012 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14806 ^ _773908 : [(14809 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024010), _1024012)))], (14807 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024010)))]], 14810 ^ _773908 : [(14813 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024012), _1024010)))], (14811 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024010), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15371 ^ _773908) ^ [_1034746, _1034748] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034746), _1034748) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034748), _1034746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1034746 = _1034748)], (10065 ^ _773908) ^ [_941288, _941290, _941292] : [class_Rings_Olinordered__idom(_941288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941288), c_Groups_Ozero__class_Ozero(_941288)), _941290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941288), c_Groups_Ozero__class_Ozero(_941288)), _941292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941288), _941292), c_Groups_Oone__class_Oone(_941288))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941288), _941290), _941292)), _941290)))], (39701 ^ _773908) ^ [_1546697, _1546699, _1546701] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1546697), tc_List_Olist(_1546697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1546697), tc_List_Olist(_1546697)), c_List_Olist_ONil(_1546697)), _1546699)), c_List_Olistrel(_1546697, _1546701))), -(_1546699 = c_List_Olist_ONil(_1546697))], (28674 ^ _773908) ^ [_1296161, _1296163, _1296165, _1296167] : [hBOOL(hAPP(hAPP(_1296165, _1296167), _1296163)), -(hBOOL(hAPP(hAPP(c_member(_1296161), _1296163), c_SetInterval_Oord_OgreaterThan(_1296161, _1296165, _1296167))))], (48519 ^ _773908) ^ [_1751824, _1751826, _1751828] : [class_Lattices_Olattice(_1751824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751824), _1751826)), -(hBOOL(hAPP(hAPP(c_member(_1751824), _1751828), _1751826))), -(c_Big__Operators_Olattice__class_OInf__fin(_1751824, hAPP(hAPP(c_Set_Oinsert(_1751824), _1751828), _1751826)) = hAPP(hAPP(c_Finite__Set_Ofold(_1751824, _1751824, c_Lattices_Osemilattice__inf__class_Oinf(_1751824)), _1751828), _1751826))], (49011 ^ _773908) ^ [_1762282, _1762284, _1762286, _1762288] : [class_Rings_Olinordered__semidom(_1762282), 49017 ^ _773908 : [(49020 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1762282), c_Groups_Ozero__class_Ozero(_1762282)), hAPP(_1762288, 49016 ^ [_1762282, _1762284, _1762286, _1762288])))], (49018 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762284), 49016 ^ [_1762282, _1762284, _1762286, _1762288]), _1762286)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1762282), c_Groups_Ozero__class_Ozero(_1762282)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1762284, _1762282), _1762288), _1762286))))], (19389 ^ _773908) ^ [_1108690] : [c_Int_OMin = _1108690, -(c_Int_OMin = c_Int_OBit1(_1108690))], (27276 ^ _773908) ^ [_1266520] : [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)), _1266520))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1266520)))], (43622 ^ _773908) ^ [_1641156, _1641158] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1641156), tc_fun(_1641156, tc_HOL_Obool), c_List_Oset(_1641156)), hAPP(c_List_Oset(tc_List_Olist(_1641156)), c_Enum_Osublists(_1641156, _1641158))) = hAPP(c_Set_OPow(_1641156), hAPP(c_List_Oset(_1641156), _1641158)))], (25319 ^ _773908) ^ [_1221290, _1221292, _1221294, _1221296] : [class_Orderings_Olinorder(_1221290), 25322 ^ _773908 : [(25323 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221290), _1221294), _1221296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), _1221294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), _1221296)))], (25333 ^ _773908) ^ [] : [25334 ^ _773908 : [(25337 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), _1221296))], (25335 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), _1221294))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221290), _1221292), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221290), _1221294), _1221296))))]]], (42183 ^ _773908) ^ [_1608669, _1608671, _1608673, _1608675, _1608677, _1608679] : [-(hAPP(c_Set_Ovimage(_1608669, _1608671, _1608673), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608675, tc_fun(_1608671, tc_HOL_Obool)), _1608677), _1608679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608675, tc_fun(_1608669, tc_HOL_Obool)), _1608677), hAPP(hAPP(c_COMBB(tc_fun(_1608671, tc_HOL_Obool), tc_fun(_1608669, tc_HOL_Obool), _1608675), c_Set_Ovimage(_1608669, _1608671, _1608673)), _1608679)))], (25545 ^ _773908) ^ [_1226222, _1226224] : [class_Orderings_Olinorder(_1226222), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1226222), _1226224), _1226224) = _1226224)], (41967 ^ _773908) ^ [_1602157, _1602159, _1602161, _1602163, _1602165, _1602167] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602157, tc_fun(_1602159, tc_fun(_1602161, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1602157, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_fun(_1602159, tc_fun(_1602161, tc_HOL_Obool)), _1602157), hAPP(c_COMBC(_1602159, tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_fun(_1602161, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602161, tc_fun(tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_fun(_1602161, tc_HOL_Obool)), _1602159), c_COMBC(_1602161, tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602161, tc_prod(_1602159, _1602161)), tc_fun(_1602161, tc_fun(tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_HOL_Obool)), _1602159), hAPP(c_COMBB(tc_prod(_1602159, _1602161), tc_fun(tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool), tc_HOL_Obool), _1602161), c_member(tc_prod(_1602159, _1602161)))), c_Product__Type_OPair(_1602159, _1602161))))), _1602163)), _1602165), _1602167)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602159, _1602161)), hAPP(hAPP(c_Product__Type_OPair(_1602159, _1602161), _1602165), _1602167)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602157, tc_fun(tc_prod(_1602159, _1602161), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1602157, tc_HOL_Obool))), _1602163))))], (33184 ^ _773908) ^ [_1390450] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1390450))))], (11517 ^ _773908) ^ [_966185, _966187, _966189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966185), _966187)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966185), _966189))), 11520 ^ _773908 : [(11523 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966187), _966189)))], (11521 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966185)))]]], (39156 ^ _773908) ^ [_1532534, _1532536, _1532538, _1532540, _1532542] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1532534), tc_List_Olist(_1532534))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1532534), tc_List_Olist(_1532534)), _1532536), _1532538)), hAPP(c_List_Olexn(_1532534, _1532540), _1532542))), 39159 ^ _773908 : [(39162 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532534)), _1532538) = _1532542)], (39160 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1532534)), _1532536) = _1532542)]]], (39094 ^ _773908) ^ [] : [-(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))))], (22861 ^ _773908) ^ [_1170413] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1170413)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1170413)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27354 ^ _773908) ^ [_1267802, _1267804, _1267806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267802), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267802, tc_HOL_Obool)), _1267804), _1267806))), 27357 ^ _773908 : [(27360 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267802), _1267806)))], (27358 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267802), _1267804)))]]], (24497 ^ _773908) ^ [_1204171, _1204173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204173), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204171), _1204173) = 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), _1204171), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204173)))))], (14979 ^ _773908) ^ [_1027532, _1027534, _1027536] : [hBOOL(hAPP(_1027532, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027534, _1027536))), 14982 ^ _773908 : [(14989 ^ _773908) ^ [] : [-(_1027536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14992 ^ _773908 : [(14993 ^ _773908) ^ [_1027780, _1027782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027780), _1027536)), _1027534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027536), _1027782)), _1027780), -(hBOOL(hAPP(_1027532, _1027780)))]]], (14983 ^ _773908) ^ [] : [_1027536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1027532, _1027534)))]]], (9869 ^ _773908) ^ [_938232, _938234, _938236] : [class_Orderings_Oorder(_938232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938232), _938234), _938236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938232), _938236), _938234)), -(_938234 = _938236)], (37520 ^ _773908) ^ [_1484037, _1484039, _1484041, _1484043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1484037, _1484039)), hAPP(hAPP(c_Product__Type_OSigma(_1484037, _1484039), _1484041), hAPP(c_COMBK(tc_fun(_1484039, tc_HOL_Obool), _1484037), _1484043)))), -(_1484041 = c_Orderings_Obot__class_Obot(tc_fun(_1484037, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1484039), _1484043)))], (51486 ^ _773908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (31457 ^ _773908) ^ [_1352714, _1352716, _1352718, _1352720, _1352722, _1352724] : [c_Equiv__Relations_Oequiv(_1352714, _1352716, _1352718), c_Equiv__Relations_Ocongruent(_1352714, tc_fun(_1352720, tc_HOL_Obool), _1352718, _1352722), hBOOL(hAPP(hAPP(c_member(_1352714), _1352724), _1352716)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1352714, tc_fun(_1352720, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1352714, _1352714, _1352718), hAPP(hAPP(c_Set_Oinsert(_1352714), _1352724), c_Orderings_Obot__class_Obot(tc_fun(_1352714, tc_HOL_Obool))))), _1352722) = hAPP(_1352722, _1352724))], (16451 ^ _773908) ^ [_1055956, _1055958, _1055960] : [class_Rings_Olinordered__idom(_1055956), -(hAPP(c_Groups_Oabs__class_Oabs(_1055956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055956), _1055958), _1055960)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055956), hAPP(c_Groups_Oabs__class_Oabs(_1055956), _1055958)), hAPP(c_Groups_Oabs__class_Oabs(_1055956), _1055960)))], (17183 ^ _773908) ^ [_1070308, _1070310, _1070312, _1070314] : [class_Rings_Olinordered__semidom(_1070308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070310), _1070312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070308), c_Groups_Ozero__class_Ozero(_1070308)), _1070314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070308), _1070314), c_Groups_Oone__class_Oone(_1070308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070308), hAPP(hAPP(c_Power_Opower__class_Opower(_1070308), _1070314), _1070312)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070308), _1070314), _1070310))))], (1634 ^ _773908) ^ [_797319, _797321] : [-(class_Rings_Olinordered__semiring(_797319)), _797321 = _797319, class_Rings_Olinordered__semiring(_797321)], (33394 ^ _773908) ^ [_1394230, _1394232, _1394234, _1394236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1394230), hAPP(c_Set_Oimage(_1394232, _1394230, _1394234), _1394236))), c_Fun_Oinj__on(_1394232, _1394230, _1394234, _1394236), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1394232), _1394236)))], (44802 ^ _773908) ^ [_1669137, _1669139, _1669141, _1669143] : [class_Groups_Ocomm__monoid__add(_1669137), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1669137), _1669139), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1669141, _1669143))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1669137), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1669137), _1669139), c_List_Oupt(_1669141, _1669143))))], (27820 ^ _773908) ^ [_1277512, _1277514, _1277516, _1277518] : [class_Lattices_Osemilattice__inf(_1277512), 27823 ^ _773908 : [(27832 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277512), _1277516), _1277518)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), _1277516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), _1277518))], (27824 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277512), _1277516), _1277518))), 27827 ^ _773908 : [(27830 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), _1277518)))], (27828 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277512), _1277514), _1277516)))]]]]], (34318 ^ _773908) ^ [] : [-(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)))], (3916 ^ _773908) ^ [_832976, _832978, _832980, _832982, _832984, _832986] : [-(c_List_Olinorder__class_Oinsort__key(_832986, _832982, _832978) = c_List_Olinorder__class_Oinsort__key(_832984, _832980, _832976)), _832986 = _832984, _832982 = _832980, _832978 = _832976], (51432 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (21747 ^ _773908) ^ [_1150288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150288)), -(c_Nat__Transfer_Ois__nat(_1150288))], (41482 ^ _773908) ^ [_1591032, _1591034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591032)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591034))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591032), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591034)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591032)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591032)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591034))))], (41816 ^ _773908) ^ [_1597690, _1597692, _1597694, _1597696, _1597698, _1597700] : [hBOOL(hAPP(hAPP(c_member(_1597690), _1597692), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597694, tc_fun(_1597690, tc_HOL_Obool)), _1597696), _1597698))), hBOOL(hAPP(hAPP(c_member(_1597694), _1597700), _1597696)), -(hBOOL(hAPP(hAPP(c_member(_1597690), _1597692), hAPP(_1597698, _1597700))))], (50733 ^ _773908) ^ [_1800164, _1800166, _1800168] : [-(c_Equiv__Relations_Oequiv(_1800164, _1800166, _1800168)), c_Relation_Orefl__on(_1800164, _1800166, _1800168), c_Relation_Osym(_1800164, _1800168), c_Relation_Otrans(_1800164, _1800168)], (11770 ^ _773908) ^ [_970541, _970543, _970545] : [class_Groups_Oordered__comm__monoid__add(_970541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970541), _970543), c_Groups_Ozero__class_Ozero(_970541))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970541), _970545), c_Groups_Ozero__class_Ozero(_970541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970541), _970543), _970545)), c_Groups_Ozero__class_Ozero(_970541))))], (27804 ^ _773908) ^ [_1277256, _1277258, _1277260] : [class_Lattices_Osemilattice__inf(_1277256), 27807 ^ _773908 : [(27814 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277256), _1277258), _1277260) = _1277258, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277256), _1277258), _1277260)))], (27808 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277256), _1277258), _1277260)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277256), _1277258), _1277260) = _1277258)]]], (37402 ^ _773908) ^ [_1480479, _1480481, _1480483, _1480485, _1480487, _1480489] : [class_Groups_Ocomm__monoid__mult(_1480479), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1480481, _1480479), hAPP(hAPP(c_COMBC(_1480481, tc_fun(_1480483, tc_HOL_Obool), _1480479), hAPP(hAPP(c_COMBB(tc_fun(_1480483, _1480479), tc_fun(tc_fun(_1480483, tc_HOL_Obool), _1480479), _1480481), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1480483, _1480479)), _1480485)), _1480487)), _1480489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1480481, _1480483), _1480479), hAPP(c_Product__Type_Oprod_Oprod__case(_1480481, _1480483, _1480479), _1480485)), hAPP(hAPP(c_Product__Type_OSigma(_1480481, _1480483), _1480489), hAPP(c_COMBK(tc_fun(_1480483, tc_HOL_Obool), _1480481), _1480487))))], (3490 ^ _773908) ^ [_826405, _826407, _826409, _826411, _826413, _826415] : [-(c_Divides_Odiv__class_Omod(_826415, _826411, _826407) = c_Divides_Odiv__class_Omod(_826413, _826409, _826405)), _826415 = _826413, _826411 = _826409, _826407 = _826405], (51678 ^ _773908) ^ [_1815846] : [-(class_Nat_Osize(tc_List_Olist(_1815846)))], (3140 ^ _773908) ^ [_820984, _820986] : [_820986 = _820984, -(c_Random_Orange(_820986) = c_Random_Orange(_820984))], (24697 ^ _773908) ^ [_1209276, _1209278, _1209280, _1209282] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_1209276, _1209278), _1209280, _1209282, hAPP(hAPP(hAPP(c_Natural_Oupdate, _1209280), _1209276), hAPP(_1209278, _1209280))))], (32071 ^ _773908) ^ [_1368531, _1368533, _1368535, _1368537, _1368539, _1368541, _1368543] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368531, tc_fun(_1368533, tc_fun(_1368535, tc_HOL_Obool))), _1368537), _1368539), _1368541), _1368543))), 32072 ^ _773908 : [(32073 ^ _773908) ^ [_1368616] : [hBOOL(hAPP(hAPP(c_member(_1368531), _1368616), _1368537)), hBOOL(hAPP(hAPP(hAPP(_1368539, _1368616), _1368541), _1368543))]]], (51278 ^ _773908) ^ [_1811747, _1811749] : [class_Lattices_Obounded__lattice(_1811747), -(class_Lattices_Obounded__lattice(tc_fun(_1811749, _1811747)))], (16985 ^ _773908) ^ [_1066427, _1066429, _1066431] : [class_Rings_Olinordered__idom(_1066427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066427), c_Groups_Ozero__class_Ozero(_1066427)), _1066429)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066427), hAPP(c_Groups_Oabs__class_Oabs(_1066427), _1066431)), _1066429) = hAPP(c_Groups_Oabs__class_Oabs(_1066427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066427), _1066431), _1066429)))], (38470 ^ _773908) ^ [_1513927, _1513929] : [-(hAPP(c_Fun_Oid(_1513927), _1513929) = _1513929)], (11473 ^ _773908) ^ [_965352, _965354] : [class_Rings_Olinordered__semidom(_965352), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965352), c_Groups_Ozero__class_Ozero(_965352)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_965352), _965354))))], (32173 ^ _773908) ^ [_1370498, _1370500, _1370502, _1370504] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1370498, _1370498)), hAPP(hAPP(c_Product__Type_OPair(_1370498, _1370498), _1370500), _1370502)), c_Relation_OId__on(_1370498, _1370504))), 32176 ^ _773908 : [(32179 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370498), _1370500), _1370504)))], (32177 ^ _773908) ^ [] : [-(_1370500 = _1370502)]]], (49388 ^ _773908) ^ [_1770487, _1770489, _1770491] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770487, _1770487, hAPP(hAPP(c_COMBB(tc_fun(_1770487, tc_HOL_Obool), tc_fun(_1770487, tc_HOL_Obool), _1770487), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1770487), c_fNot)), c_fequal)), _1770489), _1770491)), _1770489 = _1770491], (9583 ^ _773908) ^ [_933586, _933588, _933590] : [class_Rings_Olinordered__ring(_933586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933586), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933586), _933588), _933588)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933586), _933590), _933590))), c_Groups_Ozero__class_Ozero(_933586)))], (45521 ^ _773908) ^ [_1683270, _1683272] : [hBOOL(hAPP(c_List_Odistinct(_1683270), hAPP(c_List_Orev(_1683270), _1683272))), -(hBOOL(hAPP(c_List_Odistinct(_1683270), _1683272)))], (48319 ^ _773908) ^ [_1748011, _1748013, _1748015, _1748017] : [class_Lattices_Osemilattice__inf(_1748011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748011), _1748013)), hBOOL(hAPP(hAPP(c_member(_1748011), _1748015), _1748013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748011), hAPP(hAPP(c_Finite__Set_Ofold(_1748011, _1748011, c_Lattices_Osemilattice__inf__class_Oinf(_1748011)), _1748017), _1748013)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1748011), _1748015), _1748017))))], (46764 ^ _773908) ^ [_1710860, _1710862] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1710860, _1710860, _1710860), c_Transitive__Closure_Ortrancl(_1710860, _1710862)), c_Transitive__Closure_Ortrancl(_1710860, _1710862)) = c_Transitive__Closure_Ortrancl(_1710860, _1710862))], (27025 ^ _773908) ^ [_1260349, _1260351, _1260353] : [c_Relation_Ototal__on(_1260349, _1260351, _1260353), -(c_Relation_Ototal__on(_1260349, _1260351, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1260349, _1260349), tc_HOL_Obool)), _1260353), c_Relation_OId(_1260349))))], (16947 ^ _773908) ^ [_1065698, _1065700] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065698), _1065700)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1065698) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27298 ^ _773908) ^ [_1266831, _1266833] : [class_Finite__Set_Ofinite(_1266831), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266831), _1266833)))], (28638 ^ _773908) ^ [_1295426, _1295428, _1295430, _1295432] : [hBOOL(hAPP(hAPP(_1295430, _1295428), _1295432)), -(hBOOL(hAPP(hAPP(c_member(_1295426), _1295428), c_SetInterval_Oord_OatMost(_1295426, _1295430, _1295432))))], (31333 ^ _773908) ^ [_1349823, _1349825, _1349827] : [class_Orderings_Oorder(_1349823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349823), _1349825), _1349827)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1349823, _1349827, _1349825) = c_Orderings_Obot__class_Obot(tc_fun(_1349823, tc_HOL_Obool)))], (1962 ^ _773908) ^ [_802243, _802245, _802247, _802249, _802251, _802253, _802255, _802257] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_802257, _802253, _802249, _802245) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_802255, _802251, _802247, _802243)), _802257 = _802255, _802253 = _802251, _802249 = _802247, _802245 = _802243], (51644 ^ _773908) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (50878 ^ _773908) ^ [_1802994, _1802996, _1802998, _1803000] : [c_Fun_Oinj__on(_1802994, _1802996, _1802998, c_Orderings_Otop__class_Otop(tc_fun(_1802994, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1802996, _1802994, c_Hilbert__Choice_Oinv__into(_1802994, _1802996, c_Orderings_Otop__class_Otop(tc_fun(_1802994, tc_HOL_Obool)), _1802998)), hAPP(c_Set_Oimage(_1802994, _1802996, _1802998), _1803000)) = _1803000)], (32326 ^ _773908) ^ [_1373528, _1373530, _1373532] : [class_Lattices_Olattice(_1373528), hAPP(_1373530, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1373528), 32331 ^ [_1373528, _1373530, _1373532]), 32332 ^ [_1373528, _1373530, _1373532])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1373528), hAPP(_1373530, 32331 ^ [_1373528, _1373530, _1373532])), hAPP(_1373530, 32332 ^ [_1373528, _1373530, _1373532])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373528), _1373532)), -(_1373532 = c_Orderings_Obot__class_Obot(tc_fun(_1373528, tc_HOL_Obool))), -(hAPP(_1373530, c_Big__Operators_Olattice__class_OSup__fin(_1373528, _1373532)) = c_Big__Operators_Olattice__class_OSup__fin(_1373528, hAPP(c_Set_Oimage(_1373528, _1373528, _1373530), _1373532)))], (49376 ^ _773908) ^ [_1770247, _1770249, _1770251, _1770253, _1770255] : [hBOOL(hAPP(hAPP(_1770247, _1770249), _1770251)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770253, _1770255, _1770247), _1770251), _1770249)))], (31702 ^ _773908) ^ [_1358614, _1358616, _1358618, _1358620] : [-(_1358614 = c_Orderings_Obot__class_Obot(tc_fun(_1358616, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358616, tc_fun(_1358618, tc_HOL_Obool)), _1358614), hAPP(c_COMBK(tc_fun(_1358618, tc_HOL_Obool), _1358616), _1358620)) = _1358620)], (35006 ^ _773908) ^ [_1428273, _1428275, _1428277, _1428279] : [class_Orderings_Olinorder(_1428273), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428273, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1428273), _1428275)), c_SetInterval_Oord__class_OatLeastAtMost(_1428273, _1428277, _1428279)) = c_SetInterval_Oord__class_OatLeastAtMost(_1428273, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1428273), _1428275), _1428277), _1428279))], (39867 ^ _773908) ^ [_1551587, _1551589, _1551591] : [c_Relation_Orefl__on(_1551587, _1551589, _1551591), -(c_Relation_Orefl__on(tc_List_Olist(_1551587), c_List_Olists(_1551587, _1551589), c_List_Olistrel(_1551587, _1551591)))], (43697 ^ _773908) ^ [_1642828, _1642830, _1642832, _1642834, _1642836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1642828, _1642830)), hAPP(hAPP(c_Product__Type_OPair(_1642828, _1642830), _1642832), _1642834)), _1642836)), -(hBOOL(hAPP(hAPP(c_member(_1642828), _1642832), hAPP(c_Relation_ODomain(_1642828, _1642830), _1642836))))], (30155 ^ _773908) ^ [_1324741, _1324743, _1324745] : [class_Orderings_Olinorder(_1324741), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324741), _1324743)), hBOOL(hAPP(hAPP(c_member(_1324741), _1324745), _1324743)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324741), _1324745), c_Big__Operators_Olattice_OInf__fin(_1324741, c_Orderings_Oord__class_Omin(_1324741), _1324743)) = _1324745)], (41680 ^ _773908) ^ [_1595062, _1595064, _1595066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1595062), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595064)), _1595066))), -(c_List_Obutlast(_1595064, hAPP(hAPP(c_List_Otake(_1595064), _1595062), _1595066)) = hAPP(hAPP(c_List_Otake(_1595064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1595062), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1595066))], (40347 ^ _773908) ^ [_1563408, _1563410, _1563412, _1563414, _1563416] : [hBOOL(hAPP(hAPP(c_member(_1563408), _1563410), hAPP(c_List_Oset(_1563408), _1563412))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1563414), hAPP(_1563416, _1563410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1563414), c_List_Olist_Olist__size(_1563408, _1563416, _1563412))))], (3058 ^ _773908) ^ [_819693, _819695] : [_819695 = _819693, -(c_Groups_Oabs__class_Oabs(_819695) = c_Groups_Oabs__class_Oabs(_819693))], (51664 ^ _773908) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (28474 ^ _773908) ^ [_1292000, _1292002, _1292004, _1292006, _1292008, _1292010] : [c_Finite__Set_Ofolding(_1292000, _1292002, _1292004, _1292006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292000), _1292008)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292000), _1292010)), -(hAPP(c_Fun_Ocomp(_1292002, _1292002, _1292002, hAPP(_1292006, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292000, tc_HOL_Obool)), _1292008), _1292010))), hAPP(_1292006, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292000, tc_HOL_Obool)), _1292008), _1292010))) = hAPP(c_Fun_Ocomp(_1292002, _1292002, _1292002, hAPP(_1292006, _1292008)), hAPP(_1292006, _1292010)))], (51702 ^ _773908) ^ [_1816155] : [class_Finite__Set_Ofinite(_1816155), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1816155)))], (32139 ^ _773908) ^ [_1369744, _1369746, _1369748, _1369750] : [class_Orderings_Oorder(_1369744), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369744, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369744, _1369746, _1369748)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1369744, _1369748, _1369750)) = c_Orderings_Obot__class_Obot(tc_fun(_1369744, tc_HOL_Obool)))], (47078 ^ _773908) ^ [_1719117, _1719119, _1719121, _1719123, _1719125] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1719117, _1719117)), hAPP(hAPP(c_Product__Type_OPair(_1719117, _1719117), _1719119), _1719121)), c_Transitive__Closure_Ortrancl(_1719117, _1719123))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719117, _1719117)), hAPP(hAPP(c_Product__Type_OPair(_1719117, _1719117), _1719121), _1719125)), c_Transitive__Closure_Otrancl(_1719117, _1719123))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1719117, _1719117)), hAPP(hAPP(c_Product__Type_OPair(_1719117, _1719117), _1719119), _1719125)), c_Transitive__Closure_Otrancl(_1719117, _1719123))))], (46774 ^ _773908) ^ [_1711064, _1711066, _1711068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711064, _1711064), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1711064, _1711064), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1711064, _1711066)), c_Transitive__Closure_Ortrancl(_1711064, _1711068))), c_Transitive__Closure_Ortrancl(_1711064, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1711064, _1711064), tc_HOL_Obool)), _1711066), _1711068)))))], (38859 ^ _773908) ^ [_1524695, _1524697, _1524699] : [c_Wellfounded_Owf(_1524695, _1524697), hBOOL(hAPP(hAPP(c_member(tc_prod(_1524695, _1524695)), hAPP(hAPP(c_Product__Type_OPair(_1524695, _1524695), _1524699), _1524699)), _1524697))], (36141 ^ _773908) ^ [_1452332, _1452334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1452332, _1452334)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1452332, _1452334), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1452334), c_Orderings_Otop__class_Otop(tc_fun(_1452334, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1452332), c_Orderings_Otop__class_Otop(tc_fun(_1452332, tc_HOL_Obool)))))], (44638 ^ _773908) ^ [_1665952, _1665954, _1665956] : [-(c_List_Osublist(_1665952, _1665954, _1665956) = hAPP(hAPP(c_List_Omap(tc_prod(_1665952, tc_Nat_Onat), _1665952), c_Product__Type_Ofst(_1665952, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1665952, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1665952, 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(_1665952, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1665952, tc_Nat_Onat))), _1665956)), hAPP(hAPP(c_List_Ozip(_1665952, tc_Nat_Onat), _1665954), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665952)), _1665954))))))], (48305 ^ _773908) ^ [_1747744, _1747746, _1747748, _1747750] : [class_Lattices_Osemilattice__sup(_1747744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1747744), _1747746)), hBOOL(hAPP(hAPP(c_member(_1747744), _1747748), _1747746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747744), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1747744), _1747748), _1747750)), hAPP(hAPP(c_Finite__Set_Ofold(_1747744, _1747744, c_Lattices_Osemilattice__sup__class_Osup(_1747744)), _1747750), _1747746))))], (44533 ^ _773908) ^ [_1662271, _1662273] : [-(c_Random_Opick(_1662271, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1662271), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1662271, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1662271, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1662271)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1662273)) = c_Random_Opick(_1662271, _1662273))], (7281 ^ _773908) ^ [_891729, _891731] : [c_Com_Ocom_OAss(_891729, _891731) = c_Com_Ocom_OSKIP], (16004 ^ _773908) ^ [_1047352, _1047354, _1047356] : [-(hBOOL(hAPP(_1047352, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047354), _1047356)))), 16007 ^ _773908 : [(16010 ^ _773908) ^ [] : [hBOOL(hAPP(_1047352, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16008 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047354), _1047356)))]], 16012 ^ _773908 : [(16015 ^ _773908) ^ [] : [hBOOL(hAPP(_1047352, 16011 ^ [_1047352, _1047354, _1047356]))], (16013 ^ _773908) ^ [] : [-(_1047354 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047356), 16011 ^ [_1047352, _1047354, _1047356]))]]], (22209 ^ _773908) ^ [_1158386, _1158388, _1158390, _1158392] : [class_Fields_Olinordered__field__inverse__zero(_1158386), 22212 ^ _773908 : [(22213 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158386), _1158388), _1158390)), _1158392)), 22216 ^ _773908 : [(22223 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158390))), 22226 ^ _773908 : [(22233 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), _1158390), c_Groups_Ozero__class_Ozero(_1158386)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158392)))], (22227 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), _1158390), c_Groups_Ozero__class_Ozero(_1158386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158386), _1158392), _1158390)), _1158388)))]]], (22217 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), _1158388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158386), _1158392), _1158390))))]]], (22239 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158386), _1158388), _1158390)), _1158392))), 22242 ^ _773908 : [(22245 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), _1158388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158386), _1158392), _1158390)))], (22243 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158390)))]], 22246 ^ _773908 : [(22249 ^ _773908) ^ [] : [22250 ^ _773908 : [(22253 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158386), _1158392), _1158390)), _1158388))], (22251 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), _1158390), c_Groups_Ozero__class_Ozero(_1158386))))]], 22254 ^ _773908 : [(22257 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158392))], (22255 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), _1158390), c_Groups_Ozero__class_Ozero(_1158386)))]]], (22247 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158386), c_Groups_Ozero__class_Ozero(_1158386)), _1158390))]]]]], (45587 ^ _773908) ^ [_1684575, _1684577, _1684579, _1684581, _1684583] : [-(hAPP(c_List_Ofoldl(_1684575, _1684577, _1684579, _1684581), _1684583) = c_List_Ofoldr(_1684577, _1684575, hAPP(c_COMBC(_1684575, _1684577, _1684575), _1684579), hAPP(c_List_Orev(_1684577), _1684583), _1684581))], (13195 ^ _773908) ^ [_995430, _995432, _995434] : [13196 ^ _773908 : [(13199 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995430), _995434))], (13197 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995432)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995430), _995432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995434), _995432))))], (20001 ^ _773908) ^ [_1119064, _1119066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119064), _1119066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1119064)), c_Int_OBit0(_1119066))))], (20133 ^ _773908) ^ [_1121390, _1121392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121390), _1121392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121390)), c_Int_OBit0(_1121392))))], (19639 ^ _773908) ^ [_1112699, _1112701] : [class_Groups_Omonoid__mult(_1112699), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1112699), _1112701), 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(_1112699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112699), _1112701), _1112701)), _1112701))], (40523 ^ _773908) ^ [_1567923, _1567925, _1567927] : [_1567923 = c_List_Olist_ONil(_1567925), -(hAPP(c_List_Ohd(_1567925), hAPP(hAPP(c_List_Oappend(_1567925), _1567923), _1567927)) = hAPP(c_List_Ohd(_1567925), _1567927))], (16923 ^ _773908) ^ [_1065026, _1065028, _1065030] : [-(hAPP(hAPP(c_Set_Oinsert(_1065026), _1065028), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065026, tc_HOL_Obool)), _1065030), hAPP(hAPP(c_Set_Oinsert(_1065026), _1065028), c_Orderings_Obot__class_Obot(tc_fun(_1065026, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1065026), _1065028), _1065030))], (13504 ^ _773908) ^ [_1000792, _1000794, _1000796] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000792, tc_HOL_Obool)), _1000794) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000792, tc_HOL_Obool)), _1000796), -(_1000794 = _1000796)], (49121 ^ _773908) ^ [_1764450, _1764452, _1764454] : [c_List_Olist__all(_1764450, _1764454, _1764452), 49124 ^ _773908 : [(49125 ^ _773908) ^ [_1764531] : [hBOOL(hAPP(hAPP(c_member(_1764450), _1764531), hAPP(c_List_Oset(_1764450), _1764452))), -(hBOOL(hAPP(_1764454, _1764531)))]]], (48637 ^ _773908) ^ [_1753999] : [class_Orderings_Olinorder(_1753999), -(c_Finite__Set_Ofun__left__comm(_1753999, tc_List_Olist(_1753999), c_List_Olinorder__class_Oinsort__key(_1753999, _1753999, c_COMBI(_1753999))))], (13596 ^ _773908) ^ [_1002596, _1002598, _1002600, _1002602] : [class_Divides_Osemiring__div(_1002596), -(c_Divides_Odiv__class_Omod(_1002596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002596), _1002598), _1002600), _1002602) = c_Divides_Odiv__class_Omod(_1002596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002596), c_Divides_Odiv__class_Omod(_1002596, _1002598, _1002602)), _1002600), _1002602))], (38390 ^ _773908) ^ [_1510217, _1510219, _1510221] : [class_Orderings_Olinorder(_1510217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510217), _1510219)), -(_1510219 = c_Orderings_Obot__class_Obot(tc_fun(_1510217, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510217), _1510221)), -(_1510221 = c_Orderings_Obot__class_Obot(tc_fun(_1510217, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1510217), c_Big__Operators_Olattice_OInf__fin(_1510217, c_Orderings_Oord__class_Omin(_1510217), _1510219)), c_Big__Operators_Olattice_OInf__fin(_1510217, c_Orderings_Oord__class_Omin(_1510217), _1510221)) = c_Big__Operators_Olattice_OInf__fin(_1510217, c_Orderings_Oord__class_Omin(_1510217), hAPP(c_Set_OCollect(_1510217), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_HOL_Obool), tc_HOL_Obool, _1510217), c_HOL_OEx(_1510217)), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool)), tc_fun(_1510217, tc_HOL_Obool), _1510217), hAPP(c_COMBB(tc_fun(_1510217, tc_HOL_Obool), tc_HOL_Obool, _1510217), c_HOL_OEx(_1510217))), hAPP(hAPP(c_COMBC(_1510217, tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool)), tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_fun(tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool))), tc_fun(tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool)), tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool))), _1510217), c_COMBS(_1510217, tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_fun(_1510217, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1510217, tc_fun(tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool))), _1510217), hAPP(c_COMBB(tc_fun(_1510217, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool)), _1510217), c_COMBS(_1510217, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool)), tc_fun(_1510217, tc_fun(_1510217, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1510217), hAPP(c_COMBB(tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1510217), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510217), c_fconj))), hAPP(hAPP(c_COMBC(_1510217, tc_fun(_1510217, tc_fun(_1510217, _1510217)), tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1510217, _1510217), tc_fun(_1510217, tc_HOL_Obool)), tc_fun(tc_fun(_1510217, tc_fun(_1510217, _1510217)), tc_fun(_1510217, tc_fun(_1510217, tc_HOL_Obool))), _1510217), c_COMBB(tc_fun(_1510217, _1510217), tc_fun(_1510217, tc_HOL_Obool), _1510217)), hAPP(hAPP(c_COMBB(tc_fun(_1510217, tc_HOL_Obool), tc_fun(tc_fun(_1510217, _1510217), tc_fun(_1510217, tc_HOL_Obool)), _1510217), c_COMBB(_1510217, tc_HOL_Obool, _1510217)), c_fequal))), c_Orderings_Oord__class_Omax(_1510217)))))), hAPP(hAPP(c_COMBC(_1510217, tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1510217, tc_HOL_Obool), tc_fun(_1510217, tc_HOL_Obool)), _1510217), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1510217)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510217), c_fconj), hAPP(hAPP(c_COMBC(_1510217, tc_fun(_1510217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510217)), _1510219)))), hAPP(hAPP(c_COMBC(_1510217, tc_fun(_1510217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510217)), _1510221))))))))], (23221 ^ _773908) ^ [_1178072, _1178074] : [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), _1178072))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1178072))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1178072))), 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), _1178074))), c_COMBI(tc_Int_Oint))))], (25077 ^ _773908) ^ [_1216766, _1216768, _1216770, _1216772] : [class_Orderings_Olinorder(_1216766), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216766), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216766), _1216768), _1216770)), _1216772) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216766), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216766), _1216768), _1216772)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1216766), _1216770), _1216772)))], (38494 ^ _773908) ^ [_1514320, _1514322] : [-(hAPP(c_Set_Oimage(_1514320, _1514320, c_Fun_Oid(_1514320)), _1514322) = _1514322)], (42267 ^ _773908) ^ [_1611113, _1611115, _1611117, _1611119, _1611121] : [-(hAPP(hAPP(c_List_Otake(_1611113), _1611115), hAPP(hAPP(c_List_Omap(_1611117, _1611113), _1611119), _1611121)) = hAPP(hAPP(c_List_Omap(_1611117, _1611113), _1611119), hAPP(hAPP(c_List_Otake(_1611117), _1611115), _1611121)))], (32440 ^ _773908) ^ [_1375941, _1375943, _1375945] : [-(hAPP(c_Set_OPow(_1375941), hAPP(hAPP(c_Set_Oinsert(_1375941), _1375943), _1375945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1375941, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1375941), _1375945)), hAPP(c_Set_Oimage(tc_fun(_1375941, tc_HOL_Obool), tc_fun(_1375941, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1375941), _1375943)), hAPP(c_Set_OPow(_1375941), _1375945))))], (36406 ^ _773908) ^ [_1459130, _1459132] : [c_Equiv__Relations_Oequivp(_1459130, hAPP(hAPP(c_COMBC(_1459130, tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_fun(_1459130, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459130, tc_fun(tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_fun(_1459130, tc_HOL_Obool)), _1459130), c_COMBC(_1459130, tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459130, tc_prod(_1459130, _1459130)), tc_fun(_1459130, tc_fun(tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_HOL_Obool)), _1459130), hAPP(c_COMBB(tc_prod(_1459130, _1459130), tc_fun(tc_fun(tc_prod(_1459130, _1459130), tc_HOL_Obool), tc_HOL_Obool), _1459130), c_member(tc_prod(_1459130, _1459130)))), c_Product__Type_OPair(_1459130, _1459130)))), _1459132)), -(c_Equiv__Relations_Oequiv(_1459130, c_Orderings_Otop__class_Otop(tc_fun(_1459130, tc_HOL_Obool)), _1459132))], (36345 ^ _773908) ^ [_1457338, _1457340, _1457342, _1457344, _1457346] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1457338, _1457338, _1457340, _1457342, _1457344), _1457346)), -(hBOOL(hAPP(hAPP(c_member(_1457338), _1457342), _1457344))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1457338, _1457340, hAPP(hAPP(c_Set_Oinsert(_1457338), _1457342), _1457344)), _1457346)))], (26786 ^ _773908) ^ [_1256589, _1256591, _1256593, _1256595] : [-(c_Fun_Ofun__upd(_1256589, _1256591, _1256593, _1256595, hAPP(_1256593, _1256595)) = _1256593)], (25287 ^ _773908) ^ [_1220676] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1220676), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1220676)], (12200 ^ _773908) ^ [_978387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978387)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _978387)) = _978387)], (30951 ^ _773908) ^ [_1340957, _1340959, _1340961, _1340963, _1340965] : [class_Groups_Ocomm__monoid__mult(_1340957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340959), _1340961)), 30958 ^ _773908 : [(30965 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340959), _1340963), _1340961))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340959, _1340957), hAPP(hAPP(c_COMBC(_1340959, _1340957, _1340957), hAPP(hAPP(c_COMBS(_1340959, _1340957, tc_fun(_1340957, _1340957)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1340957, tc_fun(_1340957, _1340957)), _1340959), c_If(_1340957)), hAPP(c_fequal, _1340963))), _1340965)), c_Groups_Oone__class_Oone(_1340957))), _1340961) = c_Groups_Oone__class_Oone(_1340957))], (30959 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1340959), _1340963), _1340961)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340959, _1340957), hAPP(hAPP(c_COMBC(_1340959, _1340957, _1340957), hAPP(hAPP(c_COMBS(_1340959, _1340957, tc_fun(_1340957, _1340957)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1340957, tc_fun(_1340957, _1340957)), _1340959), c_If(_1340957)), hAPP(c_fequal, _1340963))), _1340965)), c_Groups_Oone__class_Oone(_1340957))), _1340961) = hAPP(_1340965, _1340963))]]], (51580 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (7617 ^ _773908) ^ [_897416, _897418, _897420, _897422, _897424, _897426] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_897416, _897418, _897420), _897422, _897424, _897426), 7622 ^ _773908 : [(7625 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_897418, _897422, _897424, _897426))], (7623 ^ _773908) ^ [] : [-(hBOOL(hAPP(_897416, _897422)))]], 7626 ^ _773908 : [(7629 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_897420, _897422, _897424, _897426))], (7627 ^ _773908) ^ [] : [hBOOL(hAPP(_897416, _897422))]]], (15779 ^ _773908) ^ [_1042480, _1042482, _1042484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042480), _1042482)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042484), _1042482)), _1042480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042482), _1042480)))], (41308 ^ _773908) ^ [_1587884, _1587886, _1587888] : [-(hAPP(c_List_Orotate(_1587884, _1587886), _1587888) = hAPP(c_List_Orotate(_1587884, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1587886, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587884)), _1587888))), _1587888))], (24173 ^ _773908) ^ [_1196486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1196486)), 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), _1196486)) = 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), _1196486))))))], (7901 ^ _773908) ^ [_903199, _903201, _903203, _903205] : [class_Orderings_Oorder(_903199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903199), hAPP(_903201, 7906 ^ [_903199, _903201, _903203, _903205])), hAPP(_903201, hAPP(c_Nat_OSuc, 7906 ^ [_903199, _903201, _903203, _903205])))), 7909 ^ _773908 : [(7916 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903203), _903205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903199), hAPP(_903201, _903203)), hAPP(_903201, _903205))))], (7910 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903199), hAPP(_903201, _903203)), hAPP(_903201, _903205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903203), _903205)))]]], (51748 ^ _773908) ^ [_1816743, _1816745] : [-(class_Nat_Osize(tc_prod(_1816743, _1816745)))], (4862 ^ _773908) ^ [_848055, _848057] : [_848057 = _848055, -(c_Nat_Osize__class_Osize(_848057) = c_Nat_Osize__class_Osize(_848055))], (16531 ^ _773908) ^ [_1057639, _1057641, _1057643] : [-(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, _1057639, _1057641)), _1057643), _1057641) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1057639), _1057643), _1057641))], (51564 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (36480 ^ _773908) ^ [_1460667, _1460669, _1460671, _1460673] : [c_Wellfounded_Omax__extp(_1460667, _1460669, _1460671, _1460673), 36483 ^ _773908 : [(36486 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1460667), _1460673)))], (36488 ^ _773908) ^ [] : [_1460673 = c_Orderings_Obot__class_Obot(tc_fun(_1460667, tc_HOL_Obool))], (36490 ^ _773908) ^ [_1460883] : [hBOOL(hAPP(hAPP(c_member(_1460667), _1460883), _1460671)), 36494 ^ _773908 : [(36497 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1460669, _1460883), 36493 ^ [_1460667, _1460669, _1460671, _1460673, _1460883])))], (36495 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460667), 36493 ^ [_1460667, _1460669, _1460671, _1460673, _1460883]), _1460673)))]]], (36484 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1460667), _1460671)))]]], (20305 ^ _773908) ^ [_1124388, _1124390] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124390))) = 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), _1124388), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124390))))], (22855 ^ _773908) ^ [_1170366, _1170368] : [-(_1170366 = _1170368), -(c_Random_Oinc__shift(_1170366, _1170368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1170368), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (31298 ^ _773908) ^ [_1348982, _1348984, _1348986, _1348988, _1348990] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1348982, _1348984, _1348986), _1348988), _1348990), c_Orderings_Obot__class_Obot(tc_fun(_1348984, tc_HOL_Obool))) = _1348990)], (8059 ^ _773908) ^ [_905939, _905941, _905943, _905945, _905947] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_905939, _905941), _905943, _905945, _905947), 8064 ^ _773908 : [(8067 ^ _773908) ^ [] : [hBOOL(hAPP(_905939, _905943))], (8065 ^ _773908) ^ [] : [-(_905947 = _905943)]], 8068 ^ _773908 : [(8074 ^ _773908) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_905939, _905941), 8070 ^ [_905939, _905941, _905943, _905945, _905947], _905945, _905947))], (8072 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_905941, _905943, _905945, 8070 ^ [_905939, _905941, _905943, _905945, _905947]))], (8069 ^ _773908) ^ [] : [-(hBOOL(hAPP(_905939, _905943)))]]], (40645 ^ _773908) ^ [_1570760, _1570762, _1570764, _1570766, _1570768, _1570770] : [-(hAPP(hAPP(c_List_Ozip(_1570760, _1570762), hAPP(hAPP(c_List_Olist_OCons(_1570760), _1570764), _1570766)), hAPP(hAPP(c_List_Olist_OCons(_1570762), _1570768), _1570770)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1570760, _1570762)), hAPP(hAPP(c_Product__Type_OPair(_1570760, _1570762), _1570764), _1570768)), hAPP(hAPP(c_List_Ozip(_1570760, _1570762), _1570766), _1570770)))], (5684 ^ _773908) ^ [_860826, _860828] : [_860828 = _860826, -(c_Orderings_Obot__class_Obot(_860828) = c_Orderings_Obot__class_Obot(_860826))], (51326 ^ _773908) ^ [_1812379, _1812381] : [class_Orderings_Opreorder(_1812379), -(class_Orderings_Opreorder(tc_fun(_1812381, _1812379)))], (30768 ^ _773908) ^ [_1337577, _1337579, _1337581, _1337583] : [class_Rings_Ocomm__semiring__1(_1337577), class_Rings_Ono__zero__divisors(_1337577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337579), _1337581)), 30779 ^ _773908 : [(30789 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337579, _1337577), _1337583), _1337581) = c_Groups_Ozero__class_Ozero(_1337577)), 30790 ^ _773908 : [(30791 ^ _773908) ^ [_1337955] : [hBOOL(hAPP(hAPP(c_member(_1337579), _1337955), _1337581)), hAPP(_1337583, _1337955) = c_Groups_Ozero__class_Ozero(_1337577)]]], (30780 ^ _773908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337579, _1337577), _1337583), _1337581) = c_Groups_Ozero__class_Ozero(_1337577), 30784 ^ _773908 : [(30787 ^ _773908) ^ [] : [-(hAPP(_1337583, 30783 ^ [_1337577, _1337579, _1337581, _1337583]) = c_Groups_Ozero__class_Ozero(_1337577))], (30785 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337579), 30783 ^ [_1337577, _1337579, _1337581, _1337583]), _1337581)))]]]]], (12148 ^ _773908) ^ [_977561] : [hAPP(c_Int_Onat, _977561) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977561), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26027 ^ _773908) ^ [_1235285, _1235287, _1235289, _1235291] : [class_Lattices_Osemilattice__sup(_1235285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235285), _1235287), _1235289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235285), _1235287), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1235285), _1235291), _1235289))))], (36289 ^ _773908) ^ [_1455364, _1455366, _1455368, _1455370, _1455372] : [class_Groups_Oab__semigroup__mult(_1455364), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1455364, _1455364, c_Groups_Otimes__class_Otimes(_1455364), _1455366, _1455368), _1455370)), -(hBOOL(hAPP(hAPP(c_member(_1455364), _1455366), _1455368))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1455364, _1455364, c_Groups_Otimes__class_Otimes(_1455364), _1455372, hAPP(hAPP(c_Set_Oinsert(_1455364), _1455366), _1455368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455364), _1455372), _1455370))))], (9157 ^ _773908) ^ [_925971, _925973, _925975, _925977] : [class_Rings_Olinordered__ring__strict(_925971), 9160 ^ _773908 : [(9175 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925971), _925973), _925975)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925971), _925973), _925977)))), 9176 ^ _773908 : [(9183 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925973), c_Groups_Ozero__class_Ozero(_925971))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925977), _925975))], (9177 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), c_Groups_Ozero__class_Ozero(_925971)), _925973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925975), _925977))]]], (9161 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925971), _925973), _925975)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925971), _925973), _925977))), 9166 ^ _773908 : [(9169 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925975), _925977)))], (9167 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), c_Groups_Ozero__class_Ozero(_925971)), _925973)))]], 9170 ^ _773908 : [(9173 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925977), _925975)))], (9171 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925971), _925973), c_Groups_Ozero__class_Ozero(_925971))))]]]]], (49346 ^ _773908) ^ [_1769628, _1769630, _1769632, _1769634] : [-(c_Predicate_Oconversep(_1769628, _1769630, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1769628, tc_fun(_1769630, tc_HOL_Obool))), _1769632), _1769634)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1769630, tc_fun(_1769628, tc_HOL_Obool))), c_Predicate_Oconversep(_1769628, _1769630, _1769632)), c_Predicate_Oconversep(_1769628, _1769630, _1769634)))], (26454 ^ _773908) ^ [_1247645, _1247647, _1247649, _1247651, _1247653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247645, tc_HOL_Obool)), _1247647), _1247649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247651, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1247645, _1247651, _1247653), _1247647)), hAPP(c_Set_Oimage(_1247645, _1247651, _1247653), _1247649))))], (14923 ^ _773908) ^ [_1026371, _1026373, _1026375] : [class_Divides_Osemiring__div(_1026371), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026371), _1026373), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026371), _1026375), _1026373))), c_Divides_Odiv__class_Omod(_1026371, _1026375, _1026373)) = _1026375)], (38033 ^ _773908) ^ [_1496826, _1496828] : [-(hBOOL(hAPP(_1496828, 38034 ^ [_1496826, _1496828]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1496826, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1496826), _1496828))], (37758 ^ _773908) ^ [_1491113, _1491115, _1491117] : [-(c_Relation_Orefl__on(_1491113, _1491115, _1491117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491113, _1491113), tc_HOL_Obool)), _1491117), hAPP(hAPP(c_Product__Type_OSigma(_1491113, _1491113), _1491115), hAPP(c_COMBK(tc_fun(_1491113, tc_HOL_Obool), _1491113), _1491115)))), 37764 ^ _773908 : [(37767 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491113, _1491113)), hAPP(hAPP(c_Product__Type_OPair(_1491113, _1491113), 37763 ^ [_1491113, _1491115, _1491117]), 37763 ^ [_1491113, _1491115, _1491117])), _1491117))], (37765 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491113), 37763 ^ [_1491113, _1491115, _1491117]), _1491115)))]]], (47851 ^ _773908) ^ [_1738098, _1738100, _1738102, _1738104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738100)), _1738102))), 47857 ^ _773908 : [(47860 ^ _773908) ^ [] : [hBOOL(hAPP(_1738104, 47856 ^ [_1738098, _1738100, _1738102, _1738104]))], (47858 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738100), 47856 ^ [_1738098, _1738100, _1738102, _1738104]), hAPP(c_List_Oset(_1738100), _1738102))))]], -(hBOOL(hAPP(_1738104, hAPP(hAPP(c_List_Onth(_1738100), _1738102), _1738098))))], (1424 ^ _773908) ^ [_794694, _794696] : [-(class_Lattices_Osemilattice__inf(_794694)), _794696 = _794694, class_Lattices_Osemilattice__inf(_794696)], (9841 ^ _773908) ^ [_937794, _937796, _937798, _937800] : [class_Orderings_Oord(_937794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937794), _937796), _937798)), _937798 = _937800, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937794), _937796), _937800)))], (41686 ^ _773908) ^ [_1595215] : [-(c_List_Obutlast(_1595215, c_List_Olist_ONil(_1595215)) = c_List_Olist_ONil(_1595215))], (31273 ^ _773908) ^ [_1348476, _1348478] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1348476, _1348478))))], (45393 ^ _773908) ^ [_1680388, _1680390, _1680392, _1680394, _1680396] : [class_Orderings_Olinorder(_1680388), c_Fun_Oinj__on(_1680390, _1680388, _1680392, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1680390, tc_HOL_Obool)), hAPP(c_List_Oset(_1680390), _1680394)), hAPP(c_List_Oset(_1680390), _1680396))), c_List_Olinorder__class_Osorted(_1680388, hAPP(hAPP(c_List_Omap(_1680390, _1680388), _1680392), _1680394)), hBOOL(hAPP(c_List_Odistinct(_1680388), hAPP(hAPP(c_List_Omap(_1680390, _1680388), _1680392), _1680394))), c_List_Olinorder__class_Osorted(_1680388, hAPP(hAPP(c_List_Omap(_1680390, _1680388), _1680392), _1680396)), hBOOL(hAPP(c_List_Odistinct(_1680388), hAPP(hAPP(c_List_Omap(_1680390, _1680388), _1680392), _1680396))), hAPP(c_List_Oset(_1680390), _1680394) = hAPP(c_List_Oset(_1680390), _1680396), -(_1680394 = _1680396)], (16423 ^ _773908) ^ [_1055438, _1055440] : [class_Groups_Oordered__ab__group__add__abs(_1055438), 16426 ^ _773908 : [(16433 ^ _773908) ^ [] : [_1055440 = c_Groups_Ozero__class_Ozero(_1055438), -(hAPP(c_Groups_Oabs__class_Oabs(_1055438), _1055440) = c_Groups_Ozero__class_Ozero(_1055438))], (16427 ^ _773908) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1055438), _1055440) = c_Groups_Ozero__class_Ozero(_1055438), -(_1055440 = c_Groups_Ozero__class_Ozero(_1055438))]]], (17557 ^ _773908) ^ [_1076939, _1076941, _1076943, _1076945] : [class_Groups_Omonoid__mult(_1076939), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076939), _1076941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076943), _1076945)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076939), hAPP(hAPP(c_Power_Opower__class_Opower(_1076939), _1076941), _1076943)), hAPP(hAPP(c_Power_Opower__class_Opower(_1076939), _1076941), _1076945)))], (2360 ^ _773908) ^ [_808458, _808460, _808462, _808464, _808466, _808468, _808470, _808472, _808474, _808476] : [-(c_Nitpick_Opair__box_Opair__box__rec(_808476, _808472, _808468, _808464, _808460) = c_Nitpick_Opair__box_Opair__box__rec(_808474, _808470, _808466, _808462, _808458)), _808476 = _808474, _808472 = _808470, _808468 = _808466, _808464 = _808462, _808460 = _808458], (38376 ^ _773908) ^ [_1509731, _1509733, _1509735] : [class_Lattices_Odistrib__lattice(_1509731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509731), _1509733)), -(_1509733 = c_Orderings_Obot__class_Obot(tc_fun(_1509731, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1509731), _1509735), c_Big__Operators_Olattice__class_OSup__fin(_1509731, _1509733)) = c_Big__Operators_Olattice__class_OSup__fin(_1509731, hAPP(c_Set_OCollect(_1509731), hAPP(hAPP(c_COMBB(tc_fun(_1509731, tc_HOL_Obool), tc_HOL_Obool, _1509731), c_HOL_OEx(_1509731)), hAPP(hAPP(c_COMBC(_1509731, tc_fun(_1509731, tc_HOL_Obool), tc_fun(_1509731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509731, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509731, tc_HOL_Obool), tc_fun(_1509731, tc_HOL_Obool)), _1509731), c_COMBS(_1509731, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509731, tc_HOL_Obool), tc_fun(_1509731, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509731), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509731), c_fconj)), hAPP(hAPP(c_COMBC(_1509731, tc_fun(_1509731, _1509731), tc_fun(_1509731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509731, tc_HOL_Obool), tc_fun(tc_fun(_1509731, _1509731), tc_fun(_1509731, tc_HOL_Obool)), _1509731), c_COMBB(_1509731, tc_HOL_Obool, _1509731)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1509731), _1509735))))), hAPP(hAPP(c_COMBC(_1509731, tc_fun(_1509731, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509731)), _1509733))))))], (26691 ^ _773908) ^ [_1254046, _1254048] : [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)), _1254046)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254046), _1254048)))], (42850 ^ _773908) ^ [] : [-(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))))], (41698 ^ _773908) ^ [_1595488, _1595490, _1595492] : [_1595488 = c_List_Olist_ONil(_1595490), -(c_List_Obutlast(_1595490, hAPP(hAPP(c_List_Olist_OCons(_1595490), _1595492), _1595488)) = c_List_Olist_ONil(_1595490))], (11449 ^ _773908) ^ [_964995, _964997] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964995), _964997) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11452 ^ _773908 : [(11455 ^ _773908) ^ [] : [-(_964997 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11453 ^ _773908) ^ [] : [-(_964995 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (37714 ^ _773908) ^ [_1489600, _1489602, _1489604, _1489606, _1489608, _1489610] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1489600, _1489602), _1489602, tc_prod(_1489604, _1489606), c_Product__Type_Osnd(_1489600, _1489602)), c_Product__Type_Omap__pair(_1489604, _1489600, _1489606, _1489602, _1489608, _1489610)) = hAPP(c_Fun_Ocomp(_1489606, _1489602, tc_prod(_1489604, _1489606), _1489610), c_Product__Type_Osnd(_1489604, _1489606)))], (6456 ^ _773908) ^ [_878797, _878799, _878801, _878803] : [class_Groups_Ocancel__semigroup__add(_878797), 6459 ^ _773908 : [(6466 ^ _773908) ^ [] : [_878801 = _878803, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878797), _878799), _878801) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878797), _878799), _878803))], (6460 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878797), _878799), _878801) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878797), _878799), _878803), -(_878801 = _878803)]]], (42531 ^ _773908) ^ [_1617301, _1617303, _1617305, _1617307] : [class_Groups_Ocomm__monoid__add(_1617301), 42534 ^ _773908 : [(42541 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1617303), _1617305))), -(c_Nitpick_Osetsum_H(_1617303, _1617301, _1617307, _1617305) = c_Groups_Ozero__class_Ozero(_1617301))], (42535 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1617303), _1617305)), -(c_Nitpick_Osetsum_H(_1617303, _1617301, _1617307, _1617305) = hAPP(c_List_Omonoid__add__class_Olistsum(_1617301), hAPP(hAPP(c_List_Omap(_1617303, _1617301), _1617307), c_Hilbert__Choice_OEps(tc_List_Olist(_1617303), hAPP(hAPP(c_COMBS(tc_List_Olist(_1617303), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1617303)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1617303), tc_fun(_1617303, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1617303, tc_HOL_Obool), tc_fun(tc_fun(_1617303, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1617303)), c_fequal), c_List_Oset(_1617303))), _1617305))), c_List_Odistinct(_1617303))))))]]], (10469 ^ _773908) ^ [_947336, _947338] : [class_Groups_Ocomm__monoid__mult(_947336), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947336), _947338), c_Groups_Oone__class_Oone(_947336)) = _947338)], (48361 ^ _773908) ^ [_1748812, _1748814] : [class_Complete__Lattice_Ocomplete__lattice(_1748812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748812), _1748814)), -(c_Complete__Lattice_OSup__class_OSup(_1748812, _1748814) = hAPP(hAPP(c_Finite__Set_Ofold(_1748812, _1748812, c_Lattices_Osemilattice__sup__class_Osup(_1748812)), c_Orderings_Obot__class_Obot(_1748812)), _1748814))], (13412 ^ _773908) ^ [_998984, _998986, _998988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998984, tc_HOL_Obool)), _998986), _998988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998984, tc_HOL_Obool)), _998988), _998986)), -(_998986 = _998988)], (51786 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (51023 ^ _773908) ^ [_1806376, _1806378, _1806380, _1806382, _1806384] : [c_Fun_Oinj__on(_1806376, _1806378, _1806380, c_Orderings_Otop__class_Otop(tc_fun(_1806376, tc_HOL_Obool))), 51029 ^ _773908 : [(51032 ^ _773908) ^ [] : [hBOOL(hAPP(_1806382, hAPP(c_Hilbert__Choice_Oinv__into(_1806376, _1806378, c_Orderings_Otop__class_Otop(tc_fun(_1806376, tc_HOL_Obool)), _1806380), 51028 ^ [_1806376, _1806378, _1806380, _1806382, _1806384])))], (51030 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806378), 51028 ^ [_1806376, _1806378, _1806380, _1806382, _1806384]), hAPP(c_Set_Oimage(_1806376, _1806378, _1806380), c_Orderings_Otop__class_Otop(tc_fun(_1806376, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1806382, _1806384)))], (27398 ^ _773908) ^ [_1268620, _1268622, _1268624, _1268626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268620, tc_HOL_Obool)), _1268622), hAPP(hAPP(c_Set_Oinsert(_1268620), _1268624), _1268626)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268620, tc_HOL_Obool)), _1268622), _1268626))))], (2076 ^ _773908) ^ [_804048, _804050] : [_804050 = _804048, -(c_HOL_Obool_Obool__size(_804050) = c_HOL_Obool_Obool__size(_804048))], (26135 ^ _773908) ^ [_1237664, _1237666] : [class_Lattices_Osemilattice__sup(_1237664), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237664), _1237666), _1237666) = _1237666)], (37259 ^ _773908) ^ [_1476696, _1476698, _1476700, _1476702] : [-(hBOOL(hAPP(hAPP(c_member(_1476696), _1476698), _1476700))), -(hAPP(c_Set_Ovimage(_1476702, _1476696, hAPP(c_COMBK(_1476696, _1476702), _1476698)), _1476700) = c_Orderings_Obot__class_Obot(tc_fun(_1476702, tc_HOL_Obool)))], (35394 ^ _773908) ^ [_1437154, _1437156, _1437158, _1437160] : [-(hBOOL(hAPP(hAPP(c_member(_1437154), _1437156), _1437158))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437154, tc_Nat_Onat), _1437160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1437154, tc_HOL_Obool)), _1437158), hAPP(hAPP(c_Set_Oinsert(_1437154), _1437156), c_Orderings_Obot__class_Obot(tc_fun(_1437154, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437154, tc_Nat_Onat), _1437160), _1437158))], (39803 ^ _773908) ^ [_1549900, _1549902, _1549904, _1549906, _1549908, _1549910] : [-(c_List_Olistrelp(_1549900, _1549902, hAPP(hAPP(c_List_Olist_OCons(_1549900), _1549904), _1549906), hAPP(hAPP(c_List_Olist_OCons(_1549900), _1549908), _1549910))), hBOOL(hAPP(hAPP(_1549902, _1549904), _1549908)), c_List_Olistrelp(_1549900, _1549902, _1549906, _1549910)], (12554 ^ _773908) ^ [_984281, _984283] : [_984283 = c_Orderings_Obot__class_Obot(tc_fun(_984281, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984281, tc_HOL_Obool)), _984283), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_984281, tc_HOL_Obool)), _984283))))], (40209 ^ _773908) ^ [_1560158, _1560160, _1560162, _1560164] : [-(hAPP(hAPP(c_List_Odrop(_1560158), _1560160), hAPP(hAPP(c_List_Odrop(_1560158), _1560162), _1560164)) = hAPP(hAPP(c_List_Odrop(_1560158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1560160), _1560162)), _1560164))], (28246 ^ _773908) ^ [_1286296, _1286298, _1286300, _1286302] : [class_Lattices_Odistrib__lattice(_1286296), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286296), _1286298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286296), _1286300), _1286302)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286296), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286296), _1286298), _1286300)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286296), _1286298), _1286302)))], (35879 ^ _773908) ^ [] : [-(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))], (17025 ^ _773908) ^ [_1067397, _1067399] : [class_Groups_Oordered__ab__group__add__abs(_1067397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067397), _1067399), c_Groups_Ozero__class_Ozero(_1067397))), -(hAPP(c_Groups_Oabs__class_Oabs(_1067397), _1067399) = hAPP(c_Groups_Ouminus__class_Ouminus(_1067397), _1067399))], (7401 ^ _773908) ^ [_893617, _893619, _893621] : [-(c_Nat_Onat_Onat__case(_893617, _893619, _893621, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _893619)], (46169 ^ _773908) ^ [_1697022, _1697024, _1697026, _1697028, _1697030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1697022, _1697024)), hAPP(_1697022, _1697026))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1697028, _1697028)), hAPP(hAPP(c_Product__Type_OPair(_1697028, _1697028), _1697024), _1697026)), c_List_Omeasures(_1697028, _1697030))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697028, _1697028)), hAPP(hAPP(c_Product__Type_OPair(_1697028, _1697028), _1697024), _1697026)), c_List_Omeasures(_1697028, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1697028, tc_Nat_Onat)), _1697022), _1697030)))))], (30561 ^ _773908) ^ [_1332890, _1332892, _1332894, _1332896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332890), _1332892)), hBOOL(hAPP(hAPP(c_member(_1332890), _1332894), _1332892)), hBOOL(hAPP(hAPP(c_member(_1332890), _1332896), _1332892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332890, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332890, tc_HOL_Obool)), _1332892), hAPP(hAPP(c_Set_Oinsert(_1332890), _1332894), c_Orderings_Obot__class_Obot(tc_fun(_1332890, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1332890), _1332896), c_Orderings_Obot__class_Obot(tc_fun(_1332890, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1332890), _1332892))))], (44323 ^ _773908) ^ [_1657544, _1657546, _1657548] : [hBOOL(hAPP(hAPP(c_member(_1657544), _1657546), hAPP(c_List_Oset(_1657544), _1657548))), -(c_List_Oinsert(_1657544, _1657546, _1657548) = _1657548)], (41221 ^ _773908) ^ [_1586115, _1586117, _1586119] : [hBOOL(hAPP(c_List_Odistinct(_1586115), hAPP(c_List_Orotate(_1586115, _1586117), _1586119))), -(hBOOL(hAPP(c_List_Odistinct(_1586115), _1586119)))], (20127 ^ _773908) ^ [_1121289, _1121291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121289)), c_Int_OBit0(_1121291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121289), _1121291)))], (27310 ^ _773908) ^ [_1266997] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266997), c_Orderings_Obot__class_Obot(tc_fun(_1266997, tc_HOL_Obool)))))], (44955 ^ _773908) ^ [_1672516, _1672518] : [c_List_Olist_ONil(_1672516) = c_List_Oremdups(_1672516, _1672518), -(_1672518 = c_List_Olist_ONil(_1672516))], (1744 ^ _773908) ^ [_798694, _798696] : [-(class_Rings_Ocomm__semiring(_798694)), _798696 = _798694, class_Rings_Ocomm__semiring(_798696)], (39362 ^ _773908) ^ [_1538478, _1538480, _1538482] : [_1538478 = hAPP(hAPP(c_List_Oappend(_1538480), _1538482), _1538478), -(_1538482 = c_List_Olist_ONil(_1538480))], (28897 ^ _773908) ^ [_1301788, _1301790] : [class_Lattices_Olattice(_1301788), -(c_Big__Operators_Olattice__class_OInf__fin(_1301788, hAPP(hAPP(c_Set_Oinsert(_1301788), _1301790), c_Orderings_Obot__class_Obot(tc_fun(_1301788, tc_HOL_Obool)))) = _1301790)], (28088 ^ _773908) ^ [_1282638, _1282640, _1282642, _1282644] : [class_Lattices_Osemilattice__inf(_1282638), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282638), _1282640), _1282642)), _1282644) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282638), _1282640), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282638), _1282642), _1282644)))], (25751 ^ _773908) ^ [_1230244, _1230246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230244, tc_HOL_Obool)), _1230246), c_Orderings_Obot__class_Obot(tc_fun(_1230244, tc_HOL_Obool))) = _1230246)], (51608 ^ _773908) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (17693 ^ _773908) ^ [_1079513, _1079515, _1079517, _1079519] : [class_Rings_Olinordered__semidom(_1079513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079513), c_Groups_Oone__class_Oone(_1079513)), _1079515)), 17700 ^ _773908 : [(17707 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1079517), _1079519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079513), hAPP(hAPP(c_Power_Opower__class_Opower(_1079513), _1079515), _1079517)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079513), _1079515), _1079519))))], (17701 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079513), hAPP(hAPP(c_Power_Opower__class_Opower(_1079513), _1079515), _1079517)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079513), _1079515), _1079519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1079517), _1079519)))]]], (19035 ^ _773908) ^ [_1102774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102774), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (942 ^ _773908) ^ [_788257, _788259, _788261, _788263] : [-(c_Predicate_Oreflp(_788261, _788257)), c_Predicate_Oreflp(_788263, _788259), _788263 = _788261, _788259 = _788257], (24149 ^ _773908) ^ [_1196000, _1196002, _1196004] : [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), _1196000), _1196002))), -(hBOOL(hAPP(hAPP(_1196004, _1196000), _1196002))), 24156 ^ _773908 : [(24159 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1196004, 24154 ^ [_1196000, _1196002, _1196004]), 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)))), 24155 ^ [_1196000, _1196002, _1196004])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24154 ^ [_1196000, _1196002, _1196004]), 24155 ^ [_1196000, _1196002, _1196004]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24155 ^ [_1196000, _1196002, _1196004]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24169 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1196004, 24154 ^ [_1196000, _1196002, _1196004]), 24155 ^ [_1196000, _1196002, _1196004]))], (24157 ^ _773908) ^ [] : [-(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), 24154 ^ [_1196000, _1196002, _1196004]), 24155 ^ [_1196000, _1196002, _1196004]))))]]], (12795 ^ _773908) ^ [_988427, _988429] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988429), _988427))))], (51169 ^ _773908) ^ [_1809717, _1809719, _1809721, _1809723] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1809717, _1809719, _1809721), c_Product__Type_Ocurry(_1809717, _1809719, _1809721, _1809723)) = _1809723)], (13750 ^ _773908) ^ [_1005511, _1005513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005511), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005511), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005513, _1005511))))], (8773 ^ _773908) ^ [_919054, _919056, _919058] : [class_Groups_Oordered__ab__group__add(_919054), 8776 ^ _773908 : [(8783 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919054), _919058), _919056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919054), hAPP(c_Groups_Ouminus__class_Ouminus(_919054), _919056)), hAPP(c_Groups_Ouminus__class_Ouminus(_919054), _919058))))], (8777 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919054), hAPP(c_Groups_Ouminus__class_Ouminus(_919054), _919056)), hAPP(c_Groups_Ouminus__class_Ouminus(_919054), _919058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919054), _919058), _919056)))]]], (7285 ^ _773908) ^ [_891837, _891839, _891841, _891843, _891845] : [c_Com_Ocom_OCall(_891837, _891839, _891841) = c_Com_Ocom_OSemi(_891843, _891845)], (45005 ^ _773908) ^ [_1673287, _1673289] : [hBOOL(hAPP(c_List_Odistinct(_1673287), _1673289)), -(c_List_Oremdups(_1673287, _1673289) = _1673289)], (1514 ^ _773908) ^ [_795819, _795821] : [-(class_Enum_Oenum(_795819)), _795821 = _795819, class_Enum_Oenum(_795821)], (31770 ^ _773908) ^ [_1360904, _1360906, _1360908, _1360910, _1360912, _1360914] : [class_Complete__Lattice_Ocomplete__lattice(_1360904), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360906, tc_fun(_1360908, _1360904)), _1360910), _1360912), _1360914) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360906, _1360904), _1360910), hAPP(hAPP(c_COMBC(_1360906, _1360908, _1360904), _1360912), _1360914)))], (2522 ^ _773908) ^ [_811145, _811147] : [_811147 = _811145, -(c_Natural_Oevalc(_811147) = c_Natural_Oevalc(_811145))], (34732 ^ _773908) ^ [_1422164, _1422166, _1422168, _1422170, _1422172] : [class_Groups_Ocomm__monoid__add(_1422164), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422166), _1422168)), 34739 ^ _773908 : [(34746 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422166), _1422170), _1422168))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422166, _1422164), hAPP(hAPP(c_COMBC(_1422166, _1422164, _1422164), hAPP(hAPP(c_COMBS(_1422166, _1422164, tc_fun(_1422164, _1422164)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422164, tc_fun(_1422164, _1422164)), _1422166), c_If(_1422164)), hAPP(c_fequal, _1422170))), _1422172)), c_Groups_Ozero__class_Ozero(_1422164))), _1422168) = c_Groups_Ozero__class_Ozero(_1422164))], (34740 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1422166), _1422170), _1422168)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422166, _1422164), hAPP(hAPP(c_COMBC(_1422166, _1422164, _1422164), hAPP(hAPP(c_COMBS(_1422166, _1422164, tc_fun(_1422164, _1422164)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422164, tc_fun(_1422164, _1422164)), _1422166), c_If(_1422164)), hAPP(c_fequal, _1422170))), _1422172)), c_Groups_Ozero__class_Ozero(_1422164))), _1422168) = hAPP(_1422172, _1422170))]]], (31657 ^ _773908) ^ [_1357599, _1357601, _1357603, _1357605, _1357607] : [-(hBOOL(hAPP(hAPP(c_member(_1357599), _1357601), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1357603, tc_fun(_1357599, tc_HOL_Obool)), _1357605), _1357607)))), 31658 ^ _773908 : [(31659 ^ _773908) ^ [_1357681] : [hBOOL(hAPP(hAPP(c_member(_1357603), _1357681), _1357605)), hBOOL(hAPP(hAPP(c_member(_1357599), _1357601), hAPP(_1357607, _1357681)))]]], (46911 ^ _773908) ^ [_1714486, _1714488, _1714490, _1714492, _1714494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714486), tc_List_Olist(_1714486))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714486), tc_List_Olist(_1714486)), _1714488), _1714490)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1714486), c_List_Olistrel1(_1714486, _1714492)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714486), tc_List_Olist(_1714486))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714486), tc_List_Olist(_1714486)), hAPP(hAPP(c_List_Olist_OCons(_1714486), _1714494), _1714488)), hAPP(hAPP(c_List_Olist_OCons(_1714486), _1714494), _1714490))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1714486), c_List_Olistrel1(_1714486, _1714492)))))], (7827 ^ _773908) ^ [_901720, _901722, _901724] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_901720, _901722, _901724)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901724)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14623 ^ _773908) ^ [_1021132, _1021134, _1021136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021132)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021132), _1021134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021132), _1021136)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021134), _1021136))], (43864 ^ _773908) ^ [_1646881, _1646883, _1646885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1646881, _1646883)), _1646885)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1646881), hAPP(c_Relation_ODomain(_1646881, _1646883), _1646885))))], (34157 ^ _773908) ^ [_1409857, _1409859, _1409861, _1409863, _1409865] : [c_Fun_Oinj__on(_1409857, _1409859, _1409861, _1409863), hBOOL(hAPP(hAPP(c_member(_1409857), _1409865), _1409863)), -(hAPP(c_Fun_Othe__inv__into(_1409857, _1409859, _1409863, _1409861), hAPP(_1409861, _1409865)) = _1409865)], (31752 ^ _773908) ^ [_1359926, _1359928, _1359930, _1359932, _1359934, _1359936] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359926, tc_fun(_1359928, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1359930, _1359926, _1359932), _1359934)), _1359936) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359930, tc_fun(_1359928, tc_HOL_Obool)), _1359934), hAPP(hAPP(c_COMBB(_1359926, tc_fun(_1359928, tc_HOL_Obool), _1359930), _1359936), _1359932)))], (10095 ^ _773908) ^ [_941802, _941804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _941802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _941804), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941802), _941804)))], (46941 ^ _773908) ^ [_1715362, _1715364, _1715366, _1715368] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715362), tc_List_Olist(_1715362))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715362), tc_List_Olist(_1715362)), _1715364), _1715366)), c_List_Olistrel1(_1715362, _1715368))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715362), tc_List_Olist(_1715362))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715362), tc_List_Olist(_1715362)), _1715364), _1715366)), c_List_Olistrel(_1715362, c_Transitive__Closure_Ortrancl(_1715362, _1715368)))))], (43817 ^ _773908) ^ [_1645614, _1645616, _1645618] : [hAPP(c_Relation_ODomain(_1645614, _1645616), _1645618) = c_Orderings_Obot__class_Obot(tc_fun(_1645614, tc_HOL_Obool)), -(_1645618 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1645614, _1645616), tc_HOL_Obool)))], (6590 ^ _773908) ^ [_880987, _880989, _880991, _880993] : [class_Orderings_Oord(_880987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880987), _880989), _880991)), _880991 = _880993, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880987), _880989), _880993)))], (31838 ^ _773908) ^ [_1362712, _1362714, _1362716, _1362718, _1362720] : [-(_1362712 = c_Orderings_Obot__class_Obot(tc_fun(_1362714, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362714, tc_fun(_1362716, tc_HOL_Obool)), _1362712), hAPP(hAPP(c_COMBB(tc_fun(_1362716, tc_HOL_Obool), tc_fun(_1362716, tc_HOL_Obool), _1362714), hAPP(c_Set_Oinsert(_1362716), _1362718)), _1362720)) = hAPP(hAPP(c_Set_Oinsert(_1362716), _1362718), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362714, tc_fun(_1362716, tc_HOL_Obool)), _1362712), _1362720)))], (11798 ^ _773908) ^ [_971051, _971053, _971055, _971057] : [class_Groups_Oordered__comm__monoid__add(_971051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971051), c_Groups_Ozero__class_Ozero(_971051)), _971053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971051), _971055), _971057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971051), _971055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971051), _971053), _971057))))], (50826 ^ _773908) ^ [_1801824, _1801826, _1801828] : [c_Fun_Oinj__on(_1801824, _1801826, _1801828, c_Orderings_Otop__class_Otop(tc_fun(_1801824, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1801826, _1801824, _1801824, c_Hilbert__Choice_Oinv__into(_1801824, _1801826, c_Orderings_Otop__class_Otop(tc_fun(_1801824, tc_HOL_Obool)), _1801828)), _1801828) = c_Fun_Oid(_1801824))], (27051 ^ _773908) ^ [_1261178, _1261180, _1261182] : [hBOOL(hAPP(hAPP(c_member(_1261178), _1261182), c_Wellfounded_Oacc(_1261178, _1261180))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1261178, hAPP(hAPP(c_COMBC(_1261178, tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_fun(_1261178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261178, tc_fun(tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_fun(_1261178, tc_HOL_Obool)), _1261178), c_COMBC(_1261178, tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261178, tc_prod(_1261178, _1261178)), tc_fun(_1261178, tc_fun(tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_HOL_Obool)), _1261178), hAPP(c_COMBB(tc_prod(_1261178, _1261178), tc_fun(tc_fun(tc_prod(_1261178, _1261178), tc_HOL_Obool), tc_HOL_Obool), _1261178), c_member(tc_prod(_1261178, _1261178)))), c_Product__Type_OPair(_1261178, _1261178)))), _1261180)), _1261182)))], (6028 ^ _773908) ^ [_870833, _870835, _870837, _870839] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870833)), _870835, _870837, _870839), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _870833), _870835, hAPP(c_Nat_OSuc, _870837), _870839))], (6408 ^ _773908) ^ [_877918, _877920, _877922, _877924] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_877918), 6411 ^ _773908 : [(6418 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877918), _877922), _877924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877918), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877918), _877920), _877922)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877918), _877920), _877924))))], (6412 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877918), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877918), _877920), _877922)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877918), _877920), _877924))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877918), _877922), _877924)))]]], (1224 ^ _773908) ^ [_792194, _792196] : [-(class_Rings_Olinordered__ring(_792194)), _792196 = _792194, class_Rings_Olinordered__ring(_792196)], (17279 ^ _773908) ^ [_1072061, _1072063] : [17280 ^ _773908 : [(17283 ^ _773908) ^ [] : [_1072061 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17281 ^ _773908) ^ [] : [_1072063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072061), _1072063) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26765 ^ _773908) ^ [_1255496, _1255498, _1255500, _1255502, _1255504] : [hBOOL(hAPP(hAPP(c_member(_1255496), _1255498), hAPP(c_Relation_OImage(_1255500, _1255496, _1255502), _1255504))), 26769 ^ _773908 : [(26772 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1255500), 26768 ^ [_1255496, _1255498, _1255500, _1255502, _1255504]), _1255504)))], (26770 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1255500, _1255496)), hAPP(hAPP(c_Product__Type_OPair(_1255500, _1255496), 26768 ^ [_1255496, _1255498, _1255500, _1255502, _1255504]), _1255498)), _1255502)))]]], (25489 ^ _773908) ^ [_1224993] : [class_Orderings_Olinorder(_1224993), -(c_Orderings_Oord_Omin(_1224993, hAPP(c_COMBC(_1224993, _1224993, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1224993))) = c_Orderings_Oord__class_Omax(_1224993))], (2282 ^ _773908) ^ [_807255, _807257, _807259, _807261] : [-(c_Com_Ocom_OWhile(_807261, _807257) = c_Com_Ocom_OWhile(_807259, _807255)), _807261 = _807259, _807257 = _807255], (13927 ^ _773908) ^ [_1008446, _1008448] : [class_Rings_Olinordered__idom(_1008446), 13930 ^ _773908 : [(13937 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008446), c_Groups_Ozero__class_Ozero(_1008446)), _1008448)), -(c_Groups_Osgn__class_Osgn(_1008446, _1008448) = c_Groups_Oone__class_Oone(_1008446))], (13931 ^ _773908) ^ [] : [c_Groups_Osgn__class_Osgn(_1008446, _1008448) = c_Groups_Oone__class_Oone(_1008446), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008446), c_Groups_Ozero__class_Ozero(_1008446)), _1008448)))]]], (33706 ^ _773908) ^ [_1400120, _1400122, _1400124, _1400126, _1400128, _1400130] : [c_Fun_Oinj__on(_1400120, _1400122, _1400124, _1400126), -(hBOOL(hAPP(hAPP(c_member(_1400122), _1400128), hAPP(c_Set_Oimage(_1400120, _1400122, _1400124), _1400126)))), -(c_Fun_Oinj__on(_1400120, _1400122, c_Fun_Ofun__upd(_1400120, _1400122, _1400124, _1400130, _1400128), _1400126))], (42796 ^ _773908) ^ [_1622940, _1622942, _1622944, _1622946, _1622948, _1622950, _1622952] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1622940, _1622942, _1622944, _1622946), _1622948), _1622950), _1622952) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622942, _1622944, _1622946), _1622950), hAPP(_1622948, _1622952)))], (31754 ^ _773908) ^ [_1360003, _1360005, _1360007, _1360009, _1360011] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360003, tc_fun(_1360005, tc_HOL_Obool)), _1360007), hAPP(hAPP(c_COMBS(_1360003, tc_fun(_1360005, tc_HOL_Obool), tc_fun(_1360005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360005, tc_HOL_Obool), tc_fun(tc_fun(_1360005, tc_HOL_Obool), tc_fun(_1360005, tc_HOL_Obool)), _1360003), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360005, tc_HOL_Obool))), _1360009)), _1360011)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360005, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360003, tc_fun(_1360005, tc_HOL_Obool)), _1360007), _1360009)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360003, tc_fun(_1360005, tc_HOL_Obool)), _1360007), _1360011)))], (37064 ^ _773908) ^ [_1472100, _1472102] : [class_Groups_Oab__semigroup__mult(_1472100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472100), _1472102)), -(_1472102 = c_Orderings_Obot__class_Obot(tc_fun(_1472100, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1472100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472100), 37077 ^ [_1472100, _1472102]), 37078 ^ [_1472100, _1472102])), hAPP(hAPP(c_Set_Oinsert(_1472100), 37077 ^ [_1472100, _1472102]), hAPP(hAPP(c_Set_Oinsert(_1472100), 37078 ^ [_1472100, _1472102]), c_Orderings_Obot__class_Obot(tc_fun(_1472100, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1472100), hAPP(c_Finite__Set_Ofold1(_1472100, c_Groups_Otimes__class_Otimes(_1472100)), _1472102)), _1472102)))], (27498 ^ _773908) ^ [_1271023, _1271025, _1271027, _1271029, _1271031, _1271033] : [c_Finite__Set_Ofolding__image__simple(_1271023, _1271025, _1271027, _1271029, _1271031, _1271033), -(hAPP(_1271033, c_Orderings_Obot__class_Obot(tc_fun(_1271025, tc_HOL_Obool))) = _1271029)], (39352 ^ _773908) ^ [_1538297, _1538299, _1538301] : [-(hAPP(hAPP(c_List_Oappend(_1538297), _1538299), _1538301) = c_List_Olist_ONil(_1538297)), _1538299 = c_List_Olist_ONil(_1538297), _1538301 = c_List_Olist_ONil(_1538297)], (31172 ^ _773908) ^ [_1346079, _1346081, _1346083, _1346085] : [c_Sum__Type_OPlus(_1346079, _1346081, _1346083, _1346085) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1346079, _1346081), tc_HOL_Obool)), 31175 ^ _773908 : [(31178 ^ _773908) ^ [] : [-(_1346085 = c_Orderings_Obot__class_Obot(tc_fun(_1346081, tc_HOL_Obool)))], (31176 ^ _773908) ^ [] : [-(_1346083 = c_Orderings_Obot__class_Obot(tc_fun(_1346079, tc_HOL_Obool)))]]], (7743 ^ _773908) ^ [_899775, _899777, _899779, _899781] : [c_Com_Ocom_OCond(_899775, _899777, _899779) = hAPP(c_Com_Ocom_OBODY, _899781)], (43290 ^ _773908) ^ [_1633676, _1633678, _1633680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633676, tc_HOL_Obool)), _1633678), _1633680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1633676), tc_HOL_Obool)), c_List_Olistsp(_1633676, _1633678)), c_List_Olistsp(_1633676, _1633680))))], (45189 ^ _773908) ^ [_1676431, _1676433, _1676435] : [class_Orderings_Olinorder(_1676431), 45192 ^ _773908 : [(45205 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1676431, hAPP(hAPP(c_List_Olist_OCons(_1676431), _1676433), _1676435))), c_List_Olinorder__class_Osorted(_1676431, _1676435), 45211 ^ _773908 : [(45214 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676431), _1676433), 45210 ^ [_1676431, _1676433, _1676435]))], (45212 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676431), 45210 ^ [_1676431, _1676433, _1676435]), hAPP(c_List_Oset(_1676431), _1676435))))]]], (45193 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1676431, hAPP(hAPP(c_List_Olist_OCons(_1676431), _1676433), _1676435)), 45196 ^ _773908 : [(45199 ^ _773908) ^ [_1676617] : [hBOOL(hAPP(hAPP(c_member(_1676431), _1676617), hAPP(c_List_Oset(_1676431), _1676435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676431), _1676433), _1676617)))], (45197 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1676431, _1676435))]]]]], (51784 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (26501 ^ _773908) ^ [_1248777, _1248779, _1248781, _1248783, _1248785] : [hBOOL(hAPP(hAPP(c_member(_1248777), _1248779), hAPP(c_Set_Oimage(_1248781, _1248777, _1248783), _1248785))), 26505 ^ _773908 : [(26508 ^ _773908) ^ [] : [-(_1248779 = hAPP(_1248783, 26504 ^ [_1248777, _1248779, _1248781, _1248783, _1248785]))], (26506 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248781), 26504 ^ [_1248777, _1248779, _1248781, _1248783, _1248785]), _1248785)))]]], (38426 ^ _773908) ^ [_1511832, _1511834, _1511836, _1511838] : [-(c_Nitpick_Oprod(_1511832, _1511834, _1511836, _1511838) = hAPP(c_Set_OCollect(tc_prod(_1511832, _1511834)), hAPP(c_Product__Type_Oprod_Oprod__case(_1511832, _1511834, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1511832, tc_fun(_1511834, tc_HOL_Obool), tc_fun(_1511834, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1511834, tc_HOL_Obool), tc_fun(_1511834, tc_HOL_Obool)), _1511832), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1511834)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511832), c_fconj), hAPP(hAPP(c_COMBC(_1511832, tc_fun(_1511832, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511832)), _1511836)))), hAPP(hAPP(c_COMBC(_1511834, tc_fun(_1511834, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511834)), _1511838)))))], (49344 ^ _773908) ^ [_1769573, _1769575, _1769577, _1769579, _1769581] : [-(c_Predicate_Oconversep(_1769573, _1769575, c_Predicate_Opred__comp(_1769573, _1769577, _1769575, _1769579, _1769581)) = c_Predicate_Opred__comp(_1769575, _1769577, _1769573, c_Predicate_Oconversep(_1769577, _1769575, _1769581), c_Predicate_Oconversep(_1769573, _1769577, _1769579)))], (39677 ^ _773908) ^ [_1545972] : [-(c_List_Olistset(_1545972, c_List_Olist_ONil(tc_fun(_1545972, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1545972)), c_List_Olist_ONil(_1545972)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1545972), tc_HOL_Obool))))], (32226 ^ _773908) ^ [_1371489, _1371491, _1371493] : [class_Orderings_Olinorder(_1371489), hAPP(_1371491, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371489), 32231 ^ [_1371489, _1371491, _1371493]), 32232 ^ [_1371489, _1371491, _1371493])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371489), hAPP(_1371491, 32231 ^ [_1371489, _1371491, _1371493])), hAPP(_1371491, 32232 ^ [_1371489, _1371491, _1371493])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371489), _1371493)), -(_1371493 = c_Orderings_Obot__class_Obot(tc_fun(_1371489, tc_HOL_Obool))), -(hAPP(_1371491, c_Big__Operators_Olattice_OSup__fin(_1371489, c_Orderings_Oord__class_Omax(_1371489), _1371493)) = c_Big__Operators_Olattice_OSup__fin(_1371489, c_Orderings_Oord__class_Omax(_1371489), hAPP(c_Set_Oimage(_1371489, _1371489, _1371491), _1371493)))], (36362 ^ _773908) ^ [_1457824, _1457826, _1457828, _1457830] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457824, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36363 ^ [_1457824, _1457826, _1457828, _1457830])), _1457826) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457824, 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), 36363 ^ [_1457824, _1457826, _1457828, _1457830]), _1457828))), _1457830), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457824, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1457826) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1457824, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1457830))], (20633 ^ _773908) ^ [_1130518] : [-(_1130518 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 20636 ^ _773908 : [(20643 ^ _773908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1130518, 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, _1130518) = 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), _1130518), 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)))], (20637 ^ _773908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1130518, 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, _1130518) = 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), _1130518), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (28326 ^ _773908) ^ [_1288316, _1288318, _1288320] : [class_Lattices_Oboolean__algebra(_1288316), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288316), _1288318), _1288320) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288316), _1288318), hAPP(c_Groups_Ouminus__class_Ouminus(_1288316), _1288320)))], (17233 ^ _773908) ^ [_1071247, _1071249, _1071251] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071247, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071247, tc_HOL_Obool)), _1071249), _1071251)), _1071251) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071247, tc_HOL_Obool)), _1071249), _1071251))], (50819 ^ _773908) ^ [_1801445, _1801447] : [c_Equiv__Relations_Opart__equivp(_1801445, _1801447), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1801445, tc_HOL_Obool)), 50822 ^ [_1801445, _1801447]), hAPP(hAPP(c_COMBB(tc_fun(_1801445, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1801445, tc_HOL_Obool)), c_HOL_OEx(_1801445)), hAPP(hAPP(c_COMBB(tc_fun(_1801445, tc_HOL_Obool), tc_fun(_1801445, tc_HOL_Obool), tc_fun(_1801445, tc_HOL_Obool)), hAPP(c_COMBS(_1801445, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801445), c_fconj), hAPP(hAPP(c_COMBS(_1801445, _1801445, tc_HOL_Obool), _1801447), c_COMBI(_1801445))))), hAPP(hAPP(c_COMBC(tc_fun(_1801445, tc_HOL_Obool), tc_fun(_1801445, tc_fun(_1801445, tc_HOL_Obool)), tc_fun(_1801445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1801445, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1801445, tc_fun(_1801445, tc_HOL_Obool)), tc_fun(_1801445, tc_HOL_Obool)), tc_fun(_1801445, tc_HOL_Obool)), c_COMBB(tc_fun(_1801445, tc_HOL_Obool), tc_HOL_Obool, _1801445)), c_fequal)), _1801447))))))], (40607 ^ _773908) ^ [_1569846, _1569848, _1569850, _1569852, _1569854, _1569856] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569846)), _1569848) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569850)), _1569852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569846)), _1569854) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569850)), _1569856), -(hAPP(hAPP(c_List_Ozip(_1569846, _1569850), hAPP(hAPP(c_List_Oappend(_1569846), _1569848), _1569854)), hAPP(hAPP(c_List_Oappend(_1569850), _1569852), _1569856)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1569846, _1569850)), hAPP(hAPP(c_List_Ozip(_1569846, _1569850), _1569848), _1569852)), hAPP(hAPP(c_List_Ozip(_1569846, _1569850), _1569854), _1569856)))], (14227 ^ _773908) ^ [_1014218, _1014220, _1014222] : [-(hBOOL(hAPP(_1014218, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1014220), _1014222)))), 14230 ^ _773908 : [(14233 ^ _773908) ^ [] : [hBOOL(hAPP(_1014218, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14231 ^ _773908) ^ [] : [-(_1014222 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14236 ^ _773908 : [(14237 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014222)))], (14243 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14239 ^ [_1014218, _1014220, _1014222]), _1014222)))], (14247 ^ _773908) ^ [] : [hBOOL(hAPP(_1014218, 14238 ^ [_1014218, _1014220, _1014222]))], (14245 ^ _773908) ^ [] : [-(_1014220 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014222), 14238 ^ [_1014218, _1014220, _1014222])), 14239 ^ [_1014218, _1014220, _1014222]))], (14241 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14239 ^ [_1014218, _1014220, _1014222])))]], 14248 ^ _773908 : [(14249 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014222), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14255 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14251 ^ [_1014218, _1014220, _1014222]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14259 ^ _773908) ^ [] : [hBOOL(hAPP(_1014218, 14250 ^ [_1014218, _1014220, _1014222]))], (14257 ^ _773908) ^ [] : [-(_1014220 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014222), 14250 ^ [_1014218, _1014220, _1014222])), 14251 ^ [_1014218, _1014220, _1014222]))], (14253 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014222), 14251 ^ [_1014218, _1014220, _1014222])))]]], (13063 ^ _773908) ^ [_993077, _993079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993077), _993079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993077)), _993079)))], (51506 ^ _773908) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (48481 ^ _773908) ^ [_1751171, _1751173, _1751175, _1751177] : [class_Complete__Lattice_Ocomplete__lattice(_1751171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751173), _1751175)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1751173, _1751171), _1751175), _1751177) = hAPP(hAPP(c_Finite__Set_Ofold(_1751173, _1751171, hAPP(hAPP(c_COMBB(_1751171, tc_fun(_1751171, _1751171), _1751173), c_Lattices_Osemilattice__inf__class_Oinf(_1751171)), _1751177)), c_Orderings_Otop__class_Otop(_1751171)), _1751175))], (46136 ^ _773908) ^ [_1696113, _1696115, _1696117, _1696119] : [-(c_List_Omaps(_1696113, _1696115, _1696117, _1696119) = c_List_Oconcat(_1696115, hAPP(hAPP(c_List_Omap(_1696113, tc_List_Olist(_1696115)), _1696117), _1696119)))], (49961 ^ _773908) ^ [_1782944, _1782946, _1782948, _1782950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1782944), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1782946, _1782948, _1782944, _1782950) = 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(_1782946)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1782946)))], (9525 ^ _773908) ^ [_932543, _932545, _932547] : [class_Rings_Oring__1(_932543), -(hAPP(c_Int_Oring__1__class_Oof__int(_932543), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _932545), _932547)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932543), hAPP(c_Int_Oring__1__class_Oof__int(_932543), _932545)), hAPP(c_Int_Oring__1__class_Oof__int(_932543), _932547)))], (7279 ^ _773908) ^ [_891689, _891691] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_891689, _891691)], (10723 ^ _773908) ^ [_951794, _951796] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951794), _951796))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _951794), _951796)), -(_951794 = _951796)], (39386 ^ _773908) ^ [_1538888, _1538890] : [-(hAPP(hAPP(c_List_Oappend(_1538888), _1538890), c_List_Olist_ONil(_1538888)) = _1538890)], (7515 ^ _773908) ^ [_895546, _895548, _895550, _895552, _895554, _895556] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_895546, _895548, _895550), _895552, _895554, _895556), 7520 ^ _773908 : [(7523 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_895548, _895552, _895554, _895556))], (7521 ^ _773908) ^ [] : [-(hBOOL(hAPP(_895546, _895552)))]], 7524 ^ _773908 : [(7527 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_895550, _895552, _895554, _895556))], (7525 ^ _773908) ^ [] : [hBOOL(hAPP(_895546, _895552))]]], (25095 ^ _773908) ^ [_1217243, _1217245, _1217247, _1217249] : [class_Orderings_Olinorder(_1217243), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217243), _1217245), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217243), _1217247), _1217249)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217243), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217243), _1217245), _1217247)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217243), _1217245), _1217249)))], (47345 ^ _773908) ^ [_1725458, _1725460] : [-(hAPP(c_Relation_Oconverse(_1725458, _1725458), c_Relation_OId__on(_1725458, _1725460)) = c_Relation_OId__on(_1725458, _1725460))], (3112 ^ _773908) ^ [_820534, _820536, _820538, _820540, _820542, _820544, _820546, _820548] : [-(c_Random_Oiterate(_820548, _820544, _820540, _820536) = c_Random_Oiterate(_820546, _820542, _820538, _820534)), _820548 = _820546, _820544 = _820542, _820540 = _820538, _820536 = _820534], (42175 ^ _773908) ^ [_1608290, _1608292, _1608294, _1608296, _1608298] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608290, tc_HOL_Obool)), _1608292), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608294, tc_fun(_1608290, tc_HOL_Obool)), _1608296), _1608298)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608294, tc_fun(_1608290, tc_HOL_Obool)), _1608296), hAPP(hAPP(c_COMBB(tc_fun(_1608290, tc_HOL_Obool), tc_fun(_1608290, tc_HOL_Obool), _1608294), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608290, tc_HOL_Obool)), _1608292)), _1608298)))], (41376 ^ _773908) ^ [_1589400, _1589402, _1589404, _1589406] : [-(_1589400 = c_List_Olist_ONil(_1589402)), 41379 ^ _773908 : [(41386 ^ _773908) ^ [] : [-(_1589404 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589402)), _1589400)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1589402, hAPP(hAPP(c_List_Olist__update(_1589402, _1589400), _1589404), _1589406)) = c_List_Olast(_1589402, _1589400))], (41380 ^ _773908) ^ [] : [_1589404 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589402)), _1589400)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1589402, hAPP(hAPP(c_List_Olist__update(_1589402, _1589400), _1589404), _1589406)) = _1589406)]]], (27057 ^ _773908) ^ [_1261525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1261525)), -(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))), _1261525)), c_FunDef_Omax__weak)))], (44611 ^ _773908) ^ [_1665216, _1665218, _1665220, _1665222] : [-(c_List_Otranspose(_1665216, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665218), tc_List_Olist(_1665216)), hAPP(c_List_Omap(_1665218, _1665216), _1665220)), _1665222)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665218), tc_List_Olist(_1665216)), hAPP(c_List_Omap(_1665218, _1665216), _1665220)), c_List_Otranspose(_1665218, _1665222)))], (22843 ^ _773908) ^ [_1170225, _1170227, _1170229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1170225), _1170227))), -(c_Random_Ominus__shift(_1170229, _1170225, _1170227) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1170225), _1170227))], (49576 ^ _773908) ^ [_1774512, _1774514, _1774516, _1774518] : [hBOOL(hAPP(hAPP(c_member(_1774512), _1774514), hAPP(c_List_Oset(_1774512), c_List_Oreplicate(_1774512, _1774516, _1774518)))), 49579 ^ _773908 : [(49582 ^ _773908) ^ [] : [_1774516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49580 ^ _773908) ^ [] : [-(_1774514 = _1774518)]]], (36907 ^ _773908) ^ [_1469222, _1469224, _1469226] : [class_Orderings_Olinorder(_1469222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469222), _1469224)), -(_1469224 = c_Orderings_Obot__class_Obot(tc_fun(_1469222, tc_HOL_Obool))), 36918 ^ _773908 : [(36919 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469222), _1469226), hAPP(c_Finite__Set_Ofold1(_1469222, c_Orderings_Oord__class_Omin(_1469222)), _1469224))), 36922 ^ _773908 : [(36923 ^ _773908) ^ [_1469515] : [hBOOL(hAPP(hAPP(c_member(_1469222), _1469515), _1469224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469222), _1469226), _1469515)))]]], (36929 ^ _773908) ^ [] : [36931 ^ _773908 : [(36934 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469222), _1469226), 36930 ^ [_1469222, _1469224, _1469226]))], (36932 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469222), 36930 ^ [_1469222, _1469224, _1469226]), _1469224)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469222), _1469226), hAPP(c_Finite__Set_Ofold1(_1469222, c_Orderings_Oord__class_Omin(_1469222)), _1469224))))]]], (874 ^ _773908) ^ [_787249, _787251, _787253, _787255, _787257, _787259] : [-(c_List_Olist__ex(_787257, _787253, _787249)), c_List_Olist__ex(_787259, _787255, _787251), _787259 = _787257, _787255 = _787253, _787251 = _787249], (47259 ^ _773908) ^ [_1723272, _1723274] : [-(c_Transitive__Closure_Ortrancl(_1723272, hAPP(c_Relation_Oconverse(_1723272, _1723272), _1723274)) = hAPP(c_Relation_Oconverse(_1723272, _1723272), c_Transitive__Closure_Ortrancl(_1723272, _1723274)))], (32058 ^ _773908) ^ [_1368221, _1368223] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1368221, _1368223))))], (1794 ^ _773908) ^ [_799319, _799321] : [-(class_Groups_Omonoid__mult(_799319)), _799321 = _799319, class_Groups_Omonoid__mult(_799321)], (9650 ^ _773908) ^ [_934730, _934732] : [class_Rings_Oring__1(_934730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934732)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_934730), hAPP(c_Int_Onat, _934732)) = hAPP(c_Int_Oring__1__class_Oof__int(_934730), _934732))], (31621 ^ _773908) ^ [_1356849, _1356851, _1356853, _1356855, _1356857] : [class_Complete__Lattice_Ocomplete__lattice(_1356849), class_Orderings_Olinorder(_1356849), 31628 ^ _773908 : [(31638 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356849), _1356851), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1356853, _1356849), _1356855), _1356857)))), 31639 ^ _773908 : [(31640 ^ _773908) ^ [_1357197] : [hBOOL(hAPP(hAPP(c_member(_1356853), _1357197), _1356855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356849), _1356851), hAPP(_1356857, _1357197)))]]], (31629 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356849), _1356851), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1356853, _1356849), _1356855), _1356857))), 31633 ^ _773908 : [(31636 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356849), _1356851), hAPP(_1356857, 31632 ^ [_1356849, _1356851, _1356853, _1356855, _1356857]))))], (31634 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356853), 31632 ^ [_1356849, _1356851, _1356853, _1356855, _1356857]), _1356855)))]]]]], (35753 ^ _773908) ^ [_1444884, _1444886, _1444888, _1444890, _1444892] : [class_Groups_Ocomm__monoid__add(_1444884), class_Groups_Ocomm__monoid__mult(_1444884), _1444886 = _1444888, c_Nat__Transfer_Onat__set(_1444888), 35771 ^ _773908 : [(35774 ^ _773908) ^ [] : [hAPP(_1444890, 35770 ^ [_1444884, _1444886, _1444888, _1444890, _1444892]) = hAPP(_1444892, 35770 ^ [_1444884, _1444886, _1444888, _1444890, _1444892])], (35772 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35770 ^ [_1444884, _1444886, _1444888, _1444890, _1444892])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1444884), _1444890), _1444886) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1444884), _1444892), _1444888))], (49079 ^ _773908) ^ [_1763654, _1763656, _1763658] : [c_List_Olist__all(_1763654, _1763656, _1763658), 49082 ^ _773908 : [(49083 ^ _773908) ^ [_1763735] : [hBOOL(hAPP(hAPP(c_member(_1763654), _1763735), hAPP(c_List_Oset(_1763654), _1763658))), -(hBOOL(hAPP(_1763656, _1763735)))]]], (13057 ^ _773908) ^ [_992978, _992980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992978)), _992980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992978), _992980)))], (12094 ^ _773908) ^ [_976674, _976676] : [class_Rings_Osemiring__1(_976674), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_976674), hAPP(c_Nat_OSuc, _976676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976674), c_Groups_Oone__class_Oone(_976674)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_976674), _976676)))], (23839 ^ _773908) ^ [_1190613, _1190615, _1190617, _1190619, _1190621, _1190623, _1190625] : [hBOOL(hAPP(hAPP(c_member(_1190613), _1190615), hAPP(hAPP(_1190617, _1190619), _1190621))), -(hBOOL(hAPP(hAPP(c_member(_1190613), _1190615), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1190623, _1190625, tc_fun(_1190613, tc_HOL_Obool)), _1190617), hAPP(hAPP(c_Product__Type_OPair(_1190623, _1190625), _1190619), _1190621)))))], (28556 ^ _773908) ^ [_1293742, _1293744, _1293746, _1293748, _1293750, _1293752, _1293754] : [c_Equiv__Relations_Oequiv(_1293742, _1293744, _1293746), hBOOL(hAPP(hAPP(c_member(tc_fun(_1293742, tc_HOL_Obool)), _1293748), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1293742), _1293744), _1293746))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1293742, tc_HOL_Obool)), _1293750), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1293742), _1293744), _1293746))), hBOOL(hAPP(hAPP(c_member(_1293742), _1293752), _1293748)), hBOOL(hAPP(hAPP(c_member(_1293742), _1293754), _1293750)), 28575 ^ _773908 : [(28582 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293742, _1293742)), hAPP(hAPP(c_Product__Type_OPair(_1293742, _1293742), _1293752), _1293754)), _1293746)), -(_1293748 = _1293750)], (28576 ^ _773908) ^ [] : [_1293748 = _1293750, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1293742, _1293742)), hAPP(hAPP(c_Product__Type_OPair(_1293742, _1293742), _1293752), _1293754)), _1293746)))]]], (43659 ^ _773908) ^ [_1642023, _1642025, _1642027, _1642029] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1642023)), _1642025), hAPP(c_List_Oset(tc_List_Olist(_1642023)), c_Enum_On__lists(_1642023, _1642027, _1642029)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642023)), _1642025) = _1642027)], (36219 ^ _773908) ^ [_1453761, _1453763, _1453765, _1453767, _1453769] : [c_Fun_Oinj__on(_1453761, _1453763, _1453765, c_Orderings_Otop__class_Otop(tc_fun(_1453761, tc_HOL_Obool))), 36222 ^ _773908 : [(36229 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1453761), _1453767), _1453769)), -(hBOOL(hAPP(hAPP(c_member(_1453763), hAPP(_1453765, _1453767)), hAPP(c_Set_Oimage(_1453761, _1453763, _1453765), _1453769))))], (36223 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1453763), hAPP(_1453765, _1453767)), hAPP(c_Set_Oimage(_1453761, _1453763, _1453765), _1453769))), -(hBOOL(hAPP(hAPP(c_member(_1453761), _1453767), _1453769)))]]], (10299 ^ _773908) ^ [_944808, _944810, _944812] : [class_Orderings_Oorder(_944808), -(_944810 = _944812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944808), _944812), _944810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944808), _944812), _944810)))], (42904 ^ _773908) ^ [_1625080] : [-(_1625080 = 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, _1625080)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1625080))))], (7491 ^ _773908) ^ [_895128, _895130, _895132] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_895128, _895130, _895132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _895130)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _895132))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29125 ^ _773908) ^ [_1305479, _1305481, _1305483] : [class_Orderings_Olinorder(_1305479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305479), _1305481)), -(_1305483 = c_Orderings_Obot__class_Obot(tc_fun(_1305479, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305479, tc_HOL_Obool)), _1305483), _1305481)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305479), c_Big__Operators_Olinorder__class_OMax(_1305479, _1305483)), c_Big__Operators_Olinorder__class_OMax(_1305479, _1305481)) = c_Big__Operators_Olinorder__class_OMax(_1305479, _1305481))], (42477 ^ _773908) ^ [_1616102, _1616104, _1616106, _1616108, _1616110] : [-(_1616102 = c_Orderings_Obot__class_Obot(tc_fun(_1616104, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616106, tc_HOL_Obool)), _1616108), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1616104, tc_fun(_1616106, tc_HOL_Obool)), _1616102), _1616110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616104, tc_fun(_1616106, tc_HOL_Obool)), _1616102), hAPP(hAPP(c_COMBB(tc_fun(_1616106, tc_HOL_Obool), tc_fun(_1616106, tc_HOL_Obool), _1616104), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616106, tc_HOL_Obool)), _1616108)), _1616110)))], (12837 ^ _773908) ^ [_989237, _989239] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989237), _989239), 12840 ^ _773908 : [(12843 ^ _773908) ^ [] : [-(_989239 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12841 ^ _773908) ^ [] : [-(_989237 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (50354 ^ _773908) ^ [_1793438, _1793440] : [-(c_Relation_Oantisym(_1793438, c_Relation_OId__on(_1793438, _1793440)))], (15853 ^ _773908) ^ [_1043909, _1043911, _1043913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043909), _1043911)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043911), _1043909)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043913), _1043909)), _1043911))], (3930 ^ _773908) ^ [_833197, _833199, _833201, _833203, _833205, _833207, _833209, _833211] : [-(c_List_Ofoldl(_833211, _833207, _833203, _833199) = c_List_Ofoldl(_833209, _833205, _833201, _833197)), _833211 = _833209, _833207 = _833205, _833203 = _833201, _833199 = _833197], (15321 ^ _773908) ^ [_1033713, _1033715, _1033717] : [class_Groups_Ogroup__add(_1033713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033713), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033713), _1033715), _1033717)), _1033717) = _1033715)], (37968 ^ _773908) ^ [_1495586, _1495588, _1495590] : [hBOOL(hAPP(hAPP(c_member(_1495586), _1495588), hAPP(c_Set_OCollect(_1495586), _1495590))), -(hBOOL(hAPP(_1495590, _1495588)))], (34203 ^ _773908) ^ [_1410726, _1410728, _1410730, _1410732, _1410734, _1410736, _1410738] : [c_Finite__Set_Ofolding__image(_1410726, _1410728, _1410730, _1410732, _1410734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410728), _1410736)), -(hAPP(hAPP(_1410734, _1410738), _1410736) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1410726, _1410728, _1410730), _1410738), _1410732), _1410736))], (47588 ^ _773908) ^ [_1731711, _1731713, _1731715, _1731717, _1731719] : [hAPP(hAPP(c_List_Olist_OCons(_1731711), _1731713), _1731715) = hAPP(c_List_Ofilter(_1731711, _1731717), _1731719), 47593 ^ _773908 : [(47602 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1731717, _1731713)))], (47604 ^ _773908) ^ [] : [-(_1731715 = hAPP(c_List_Ofilter(_1731711, _1731717), 47592 ^ [_1731711, _1731713, _1731715, _1731717, _1731719]))], (47596 ^ _773908) ^ [_1732025] : [hBOOL(hAPP(hAPP(c_member(_1731711), _1732025), hAPP(c_List_Oset(_1731711), 47591 ^ [_1731711, _1731713, _1731715, _1731717, _1731719]))), hBOOL(hAPP(_1731717, _1732025))], (47594 ^ _773908) ^ [] : [-(_1731719 = hAPP(hAPP(c_List_Oappend(_1731711), 47591 ^ [_1731711, _1731713, _1731715, _1731717, _1731719]), hAPP(hAPP(c_List_Olist_OCons(_1731711), _1731713), 47592 ^ [_1731711, _1731713, _1731715, _1731717, _1731719])))]]], (44835 ^ _773908) ^ [_1670168, _1670170, _1670172, _1670174] : [-(c_List_Ofoldr(_1670168, _1670170, _1670172, c_List_Olist_ONil(_1670168), _1670174) = _1670174)], (35975 ^ _773908) ^ [_1448952, _1448954, _1448956] : [class_Lattices_Obounded__lattice__top(_1448952), 35978 ^ _773908 : [(35987 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448952), _1448954), _1448956) = c_Orderings_Otop__class_Otop(_1448952)), _1448954 = c_Orderings_Otop__class_Otop(_1448952), _1448956 = c_Orderings_Otop__class_Otop(_1448952)], (35979 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448952), _1448954), _1448956) = c_Orderings_Otop__class_Otop(_1448952), 35982 ^ _773908 : [(35985 ^ _773908) ^ [] : [-(_1448956 = c_Orderings_Otop__class_Otop(_1448952))], (35983 ^ _773908) ^ [] : [-(_1448954 = c_Orderings_Otop__class_Otop(_1448952))]]]]], (13149 ^ _773908) ^ [_994600, _994602] : [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), _994600), _994602))), 13152 ^ _773908 : [(13155 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _994602)))], (13153 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _994600)))]]], (36759 ^ _773908) ^ [_1466576, _1466578] : [class_Orderings_Olinorder(_1466576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466576), _1466578)), -(c_Big__Operators_Olinorder__class_OMin(_1466576, _1466578) = hAPP(c_Finite__Set_Ofold1(_1466576, c_Orderings_Oord__class_Omin(_1466576)), _1466578))], (13552 ^ _773908) ^ [_1001630, _1001632, _1001634, _1001636] : [class_Divides_Osemiring__div(_1001630), -(c_Divides_Odiv__class_Omod(_1001630, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001630), _1001632), _1001634), _1001636) = c_Divides_Odiv__class_Omod(_1001630, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001630), c_Divides_Odiv__class_Omod(_1001630, _1001632, _1001636)), _1001634), _1001636))], (2986 ^ _773908) ^ [_818535, _818537, _818539, _818541] : [-(c_List_Olistset(_818541, _818537) = c_List_Olistset(_818539, _818535)), _818541 = _818539, _818537 = _818535], (16879 ^ _773908) ^ [_1064159, _1064161, _1064163] : [class_Int_Onumber__ring(_1064159), class_Rings_Olinordered__idom(_1064159), 16886 ^ _773908 : [(16893 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064161), _1064163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064159), hAPP(c_Int_Onumber__class_Onumber__of(_1064159), _1064161)), hAPP(c_Int_Onumber__class_Onumber__of(_1064159), _1064163))))], (16887 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064159), hAPP(c_Int_Onumber__class_Onumber__of(_1064159), _1064161)), hAPP(c_Int_Onumber__class_Onumber__of(_1064159), _1064163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064161), _1064163)))]]], (51302 ^ _773908) ^ [_1812063, _1812065] : [class_Lattices_Olattice(_1812063), -(class_Lattices_Osemilattice__sup(tc_fun(_1812065, _1812063)))], (7039 ^ _773908) ^ [_887925, _887927] : [7040 ^ _773908 : [(7041 ^ _773908) ^ [_887978] : [_887927 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887925), _887978))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887925), _887927)))], (18661 ^ _773908) ^ [_1096425, _1096427, _1096429, _1096431] : [hBOOL(hAPP(hAPP(c_member(_1096425), _1096427), _1096429)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096425, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1096425), _1096427), _1096431)), _1096429) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096425, tc_HOL_Obool)), _1096431), _1096429))], (5508 ^ _773908) ^ [_858182, _858184] : [_858184 = _858182, -(c_Fun_Oid(_858184) = c_Fun_Oid(_858182))], (44662 ^ _773908) ^ [_1666637, _1666639, _1666641] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1666637), c_List_Oupt(_1666639, _1666641)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666639), _1666637), _1666641))], (26745 ^ _773908) ^ [_1255001, _1255003, _1255005, _1255007] : [-(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), _1255001), _1255003)), 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), _1255005), _1255007)), 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), _1255001), _1255005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1255003), _1255007))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (34688 ^ _773908) ^ [_1421250, _1421252, _1421254, _1421256, _1421258] : [class_Groups_Ocomm__monoid__add(_1421250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421252), _1421254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421254), _1421256)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1421250), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421250), _1421258), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421252), _1421254))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421250), _1421258), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421254), _1421256))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421250), _1421258), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1421252), _1421256)))], (23191 ^ _773908) ^ [_1177327, _1177329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177327)), hAPP(c_Nat_OSuc, _1177329))), -(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(_1177327))), 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)), _1177329)))))], (30860 ^ _773908) ^ [_1339109, _1339111, _1339113, _1339115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1339109, _1339111)), c_Sum__Type_OPlus(_1339109, _1339111, _1339113, _1339115))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339109), _1339113)))], (1524 ^ _773908) ^ [_795944, _795946] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_795944)), _795946 = _795944, class_Groups_Oordered__cancel__ab__semigroup__add(_795946)], (37892 ^ _773908) ^ [_1493969] : [class_Lattices_Osemilattice__sup(_1493969), -(c_Finite__Set_Ofun__left__comm__idem(_1493969, _1493969, c_Lattices_Osemilattice__sup__class_Osup(_1493969)))], (15381 ^ _773908) ^ [_1034899] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034899), _1034899) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51616 ^ _773908) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (46798 ^ _773908) ^ [_1711620, _1711622, _1711624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711620, _1711620), tc_HOL_Obool)), _1711622), c_Transitive__Closure_Ortrancl(_1711620, _1711624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711620, _1711620), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1711620, _1711622)), c_Transitive__Closure_Ortrancl(_1711620, _1711624))))], (44947 ^ _773908) ^ [_1672394] : [-(c_List_Oremdups(_1672394, c_List_Olist_ONil(_1672394)) = c_List_Olist_ONil(_1672394))], (15413 ^ _773908) ^ [_1035441, _1035443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035441), _1035443)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035441, _1035443) = _1035441)], (13177 ^ _773908) ^ [_995073, _995075, _995077] : [13178 ^ _773908 : [(13181 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995075), _995077))], (13179 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995073)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995073), _995075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995073), _995077))))], (19371 ^ _773908) ^ [_1108410, _1108412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108410), _1108412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108410)), c_Int_OBit1(_1108412))))], (41245 ^ _773908) ^ [_1586553, _1586555] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1586553), _1586555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1586553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 41251 ^ _773908 : [(41254 ^ _773908) ^ [] : [41250 ^ [_1586553, _1586555] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41252 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 41250 ^ [_1586553, _1586555]), hAPP(c_List_Oset(tc_Nat_Onat), _1586555))))]]], (17325 ^ _773908) ^ [_1072787] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072787) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072787)))], (51296 ^ _773908) ^ [_1811984, _1811986] : [class_Lattices_Obounded__lattice(_1811984), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1811986, _1811984)))], (5592 ^ _773908) ^ [_859440, _859442] : [_859442 = _859440, -(tc_Lazy__Sequence_Olazy__sequence(_859442) = tc_Lazy__Sequence_Olazy__sequence(_859440))], (42790 ^ _773908) ^ [_1622781, _1622783, _1622785, _1622787, _1622789, _1622791, _1622793] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1622781, _1622783, _1622785, _1622787), _1622789), _1622791), _1622793) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622783, _1622785, _1622787), _1622791), hAPP(_1622789, _1622793)))], (26836 ^ _773908) ^ [_1257404, _1257406, _1257408, _1257410, _1257412, _1257414] : [_1257404 = _1257406, -(hAPP(c_Fun_Ofun__upd(_1257408, _1257410, _1257412, _1257406, _1257414), _1257404) = _1257414)], (17655 ^ _773908) ^ [_1078794, _1078796, _1078798] : [class_Rings_Olinordered__semidom(_1078794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078794), c_Groups_Oone__class_Oone(_1078794)), _1078796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078794), c_Groups_Oone__class_Oone(_1078794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078794), _1078796), hAPP(c_Nat_OSuc, _1078798)))))], (39137 ^ _773908) ^ [_1531625, _1531627] : [-(c_List_Olenlex(_1531625, _1531627) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1531625), tc_List_Olist(_1531625), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1531625), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), tc_List_Olist(_1531625)), c_COMBS(tc_List_Olist(_1531625), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1531625)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1531625)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1531625), tc_fun(tc_List_Olist(_1531625), tc_Nat_Onat), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1531625), tc_Nat_Onat), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), tc_List_Olist(_1531625)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1531625))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1531625)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1531625))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1531625)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1531625), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), tc_List_Olist(_1531625)), c_COMBS(tc_List_Olist(_1531625), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1531625)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1531625)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1531625), tc_fun(tc_List_Olist(_1531625), tc_Nat_Onat), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1531625), tc_Nat_Onat), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), tc_List_Olist(_1531625)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1531625))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1531625)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1531625))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1531625)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1531625), tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1531625), tc_HOL_Obool)), tc_List_Olist(_1531625)), c_COMBC(tc_List_Olist(_1531625), tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1531625), tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625))), tc_fun(tc_List_Olist(_1531625), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1531625)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1531625)), c_member(tc_prod(tc_List_Olist(_1531625), tc_List_Olist(_1531625))))), c_Product__Type_OPair(tc_List_Olist(_1531625), tc_List_Olist(_1531625))))), c_List_Olex(_1531625, _1531627)))))))], (32742 ^ _773908) ^ [_1381731] : [-(hAPP(c_Set_OPow(_1381731), c_Orderings_Obot__class_Obot(tc_fun(_1381731, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1381731, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1381731, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1381731, tc_HOL_Obool), tc_HOL_Obool))))], (4708 ^ _773908) ^ [_845714, _845716] : [_845716 = _845714, -(c_Lazy__Sequence_Oempty(_845716) = c_Lazy__Sequence_Oempty(_845714))], (48391 ^ _773908) ^ [_1749345, _1749347, _1749349] : [class_Lattices_Olattice(_1749345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749345), _1749347)), -(c_Big__Operators_Olattice__class_OSup__fin(_1749345, hAPP(hAPP(c_Set_Oinsert(_1749345), _1749349), _1749347)) = hAPP(hAPP(c_Finite__Set_Ofold(_1749345, _1749345, c_Lattices_Osemilattice__sup__class_Osup(_1749345)), _1749349), _1749347))], (38498 ^ _773908) ^ [_1514372] : [-(hAPP(c_Set_Oimage(_1514372, _1514372, c_Fun_Oid(_1514372)), c_Orderings_Otop__class_Otop(tc_fun(_1514372, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514372, tc_HOL_Obool)))], (4092 ^ _773908) ^ [_835720, _835722, _835724, _835726, _835728, _835730] : [-(c_Nitpick_Oplus__frac(_835730, _835726, _835722) = c_Nitpick_Oplus__frac(_835728, _835724, _835720)), _835730 = _835728, _835726 = _835724, _835722 = _835720], (20523 ^ _773908) ^ [_1128287, _1128289, _1128291] : [class_Rings_Olinordered__idom(_1128287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128287), c_Groups_Ozero__class_Ozero(_1128287)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128287), _1128289), 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)))), _1128291)))))], (23365 ^ _773908) ^ [_1180542, _1180544, _1180546, _1180548, _1180550] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1180542, _1180544, _1180546), _1180548), _1180550)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1180542, _1180544)), hAPP(hAPP(c_Product__Type_OPair(_1180542, _1180544), _1180548), _1180550)), _1180546)))], (42429 ^ _773908) ^ [_1614898, _1614900, _1614902, _1614904, _1614906] : [_1614898 = c_Orderings_Obot__class_Obot(tc_fun(_1614900, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1614902, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614900, tc_fun(_1614902, tc_HOL_Obool)), _1614898), _1614904)), _1614906) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1614902, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1614902, tc_HOL_Obool))), _1614906))], (51862 ^ _773908) ^ [_1817962, _1817964] : [_1817962 = _1817964, -(hBOOL(hAPP(hAPP(c_fequal, _1817962), _1817964)))], (7163 ^ _773908) ^ [_889775, _889777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889775), hAPP(c_Nat_OSuc, _889777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889775), _889777))), -(_889775 = _889777)], (21345 ^ _773908) ^ [_1142792, _1142794, _1142796] : [class_Fields_Olinordered__field(_1142792), -(_1142794 = c_Groups_Ozero__class_Ozero(_1142792)), -(hAPP(c_Groups_Oabs__class_Oabs(_1142792), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142792), _1142796), _1142794)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142792), hAPP(c_Groups_Oabs__class_Oabs(_1142792), _1142796)), hAPP(c_Groups_Oabs__class_Oabs(_1142792), _1142794)))], (50967 ^ _773908) ^ [_1805028, _1805030, _1805032, _1805034, _1805036] : [c_Fun_Oinj__on(_1805028, _1805030, _1805032, _1805034), hBOOL(hAPP(hAPP(c_member(_1805028), _1805036), _1805034)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1805028, _1805030, _1805034, _1805032), hAPP(_1805032, _1805036)) = _1805036)], (43624 ^ _773908) ^ [_1641215, _1641217, _1641219] : [-(hAPP(c_List_Oset(tc_List_Olist(_1641215)), c_Enum_On__lists(_1641215, _1641217, _1641219)) = hAPP(c_Set_OCollect(tc_List_Olist(_1641215)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1641215), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1641215)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1641215), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1641215)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1641215)))), _1641217))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1641215), tc_fun(_1641215, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1641215, tc_HOL_Obool), tc_fun(tc_fun(_1641215, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1641215)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1641215, tc_HOL_Obool))), c_List_Oset(_1641215))), hAPP(c_List_Oset(_1641215), _1641219)))))], (47180 ^ _773908) ^ [_1721461, _1721463, _1721465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721461, _1721461), tc_HOL_Obool)), _1721463), hAPP(hAPP(c_Product__Type_OSigma(_1721461, _1721461), _1721465), hAPP(c_COMBK(tc_fun(_1721461, tc_HOL_Obool), _1721461), _1721465)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721461, _1721461), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1721461, _1721463)), hAPP(hAPP(c_Product__Type_OSigma(_1721461, _1721461), _1721465), hAPP(c_COMBK(tc_fun(_1721461, tc_HOL_Obool), _1721461), _1721465)))))], (19917 ^ _773908) ^ [_1117617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117617), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1117617)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50211 ^ _773908) ^ [_1790592, _1790594] : [-(c_Relation_Otrans(_1790592, c_Transitive__Closure_Otrancl(_1790592, _1790594)))], (4608 ^ _773908) ^ [_844012, _844014] : [_844014 = _844012, -(c_If(_844014) = c_If(_844012))], (9622 ^ _773908) ^ [_934283, _934285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934283)), 9625 ^ _773908 : [(9632 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934283), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _934283)), _934285)))], (9626 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _934283)), _934285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934283), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934285))))]]], (11625 ^ _773908) ^ [_968106, _968108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _968106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _968108)), 11632 ^ _773908 : [(11639 ^ _773908) ^ [] : [_968106 = _968108, -(hAPP(c_Int_Onat, _968106) = hAPP(c_Int_Onat, _968108))], (11633 ^ _773908) ^ [] : [hAPP(c_Int_Onat, _968106) = hAPP(c_Int_Onat, _968108), -(_968106 = _968108)]]], (8851 ^ _773908) ^ [_920518, _920520] : [class_Rings_Ocomm__semiring__1(_920518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920518), c_Groups_Ozero__class_Ozero(_920518)), _920520) = c_Groups_Ozero__class_Ozero(_920518))], (23227 ^ _773908) ^ [_1178229, _1178231] : [-(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), _1178229)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1178229))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40185 ^ _773908) ^ [_1559660, _1559662] : [hAPP(c_List_Oset(_1559660), _1559662) = c_Orderings_Obot__class_Obot(tc_fun(_1559660, tc_HOL_Obool)), -(_1559662 = c_List_Olist_ONil(_1559660))], (5805 ^ _773908) ^ [_866055, _866057, _866059] : [hAPP(hAPP(c_Set_Oinsert(_866055), _866057), c_Orderings_Obot__class_Obot(tc_fun(_866055, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_866055), _866059), c_Orderings_Obot__class_Obot(tc_fun(_866055, tc_HOL_Obool))), -(_866057 = _866059)], (22899 ^ _773908) ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163] : [c_Nitpick_Ofold__graph_H(_1171151, _1171153, _1171155, _1171157, _1171159, hAPP(hAPP(_1171155, _1171161), _1171163)), 22904 ^ _773908 : [(22907 ^ _773908) ^ [] : [-(hAPP(hAPP(_1171155, _1171161), _1171163) = _1171157)], (22905 ^ _773908) ^ [] : [-(_1171159 = c_Orderings_Obot__class_Obot(tc_fun(_1171151, tc_HOL_Obool)))]], 22910 ^ _773908 : [(22915 ^ _773908) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1171151, _1171153, _1171155, _1171157, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171151, tc_HOL_Obool)), _1171159), hAPP(hAPP(c_Set_Oinsert(_1171151), 22908 ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163]), c_Orderings_Obot__class_Obot(tc_fun(_1171151, tc_HOL_Obool)))), 22909 ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163]))], (22913 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1171151), 22908 ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163]), _1171159)))], (22911 ^ _773908) ^ [] : [-(hAPP(hAPP(_1171155, _1171161), _1171163) = hAPP(hAPP(_1171155, 22908 ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163]), 22909 ^ [_1171151, _1171153, _1171155, _1171157, _1171159, _1171161, _1171163]))]]], (24685 ^ _773908) ^ [_1208950, _1208952] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1208950)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1208952)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1208952))), 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), _1208950)), c_Int_Onat)))))], (23135 ^ _773908) ^ [_1176034, _1176036] : [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(_1176036))), 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)), _1176034))))), -(hAPP(c_Nat_OSuc, _1176034) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176036))], (25761 ^ _773908) ^ [_1230421, _1230423] : [class_Lattices_Obounded__lattice__bot(_1230421), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1230421), _1230423), c_Orderings_Obot__class_Obot(_1230421)) = _1230423)], (51838 ^ _773908) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (24185 ^ _773908) ^ [_1196789, _1196791, _1196793, _1196795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1196795, _1196791)), hAPP(_1196795, _1196793))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1196789, _1196789)), hAPP(hAPP(c_Product__Type_OPair(_1196789, _1196789), _1196791), _1196793)), hAPP(c_Wellfounded_Omeasure(_1196789), _1196795))))], (49184 ^ _773908) ^ [_1765716, _1765718, _1765720, _1765722, _1765724, _1765726] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1765716, _1765718, _1765720), _1765722), hAPP(hAPP(c_Product__Type_OPair(_1765716, _1765718), _1765724), _1765726)) = hAPP(hAPP(_1765722, _1765724), _1765726))], (30876 ^ _773908) ^ [_1339420, _1339422, _1339424, _1339426] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1339420, _1339422)), c_Sum__Type_OPlus(_1339420, _1339422, _1339424, _1339426))), 30879 ^ _773908 : [(30882 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339422), _1339426)))], (30880 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339420), _1339424)))]]], (16411 ^ _773908) ^ [_1055248, _1055250] : [class_Groups_Oordered__ab__group__add__abs(_1055248), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055248), _1055250), hAPP(c_Groups_Oabs__class_Oabs(_1055248), _1055250))))], (43330 ^ _773908) ^ [_1634573, _1634575, _1634577, _1634579, _1634581] : [class_Orderings_Olinorder(_1634573), hBOOL(hAPP(c_List_Odistinct(_1634575), _1634577)), -(hBOOL(hAPP(c_List_Odistinct(_1634575), c_List_Olinorder__class_Oinsort__insert__key(_1634575, _1634573, _1634579, _1634581, _1634577))))], (2250 ^ _773908) ^ [_806733, _806735, _806737, _806739, _806741, _806743] : [-(c_Hoare__Mirabelle_Opeek__and(_806743, _806739, _806735) = c_Hoare__Mirabelle_Opeek__and(_806741, _806737, _806733)), _806743 = _806741, _806739 = _806737, _806735 = _806733], (20115 ^ _773908) ^ [_1121066, _1121068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1121066)), c_Int_OBit1(_1121068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121066), _1121068)))], (26536 ^ _773908) ^ [_1249557, _1249559, _1249561, _1249563] : [hAPP(c_Set_Oimage(_1249557, _1249559, _1249561), _1249563) = c_Orderings_Obot__class_Obot(tc_fun(_1249559, tc_HOL_Obool)), -(_1249563 = c_Orderings_Obot__class_Obot(tc_fun(_1249557, tc_HOL_Obool)))], (17333 ^ _773908) ^ [_1072948, _1072950] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072948)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072950)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1072950))))], (44174 ^ _773908) ^ [_1654225, _1654227, _1654229] : [class_Complete__Lattice_Ocomplete__lattice(_1654225), -(c_Complete__Lattice_OInf__class_OInf(_1654225, hAPP(hAPP(c_Set_Oinsert(_1654225), _1654227), _1654229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1654225), _1654227), c_Complete__Lattice_OInf__class_OInf(_1654225, _1654229)))], (42694 ^ _773908) ^ [] : [-(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))], (45218 ^ _773908) ^ [_1676956, _1676958, _1676960] : [class_Orderings_Olinorder(_1676956), 45221 ^ _773908 : [(45240 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1676956, hAPP(hAPP(c_List_Oappend(_1676956), _1676958), _1676960))), c_List_Olinorder__class_Osorted(_1676956, _1676958), c_List_Olinorder__class_Osorted(_1676956, _1676960), 45250 ^ _773908 : [(45256 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676956), 45249 ^ [_1676956, _1676958, _1676960]), 45252 ^ [_1676956, _1676958, _1676960]))], (45254 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676956), 45252 ^ [_1676956, _1676958, _1676960]), hAPP(c_List_Oset(_1676956), _1676960))))], (45251 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676956), 45249 ^ [_1676956, _1676958, _1676960]), hAPP(c_List_Oset(_1676956), _1676958))))]]], (45222 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1676956, hAPP(hAPP(c_List_Oappend(_1676956), _1676958), _1676960)), 45225 ^ _773908 : [(45230 ^ _773908) ^ [_1677192] : [hBOOL(hAPP(hAPP(c_member(_1676956), _1677192), hAPP(c_List_Oset(_1676956), _1676958))), 45233 ^ _773908 : [(45234 ^ _773908) ^ [_1677302] : [hBOOL(hAPP(hAPP(c_member(_1676956), _1677302), hAPP(c_List_Oset(_1676956), _1676960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676956), _1677192), _1677302)))]]], (45228 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1676956, _1676960))], (45226 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1676956, _1676958))]]]]], (42269 ^ _773908) ^ [_1611178, _1611180, _1611182, _1611184, _1611186] : [-(hAPP(hAPP(c_List_Omap(_1611178, _1611180), _1611182), hAPP(hAPP(c_List_Oappend(_1611178), _1611184), _1611186)) = hAPP(hAPP(c_List_Oappend(_1611180), hAPP(hAPP(c_List_Omap(_1611178, _1611180), _1611182), _1611184)), hAPP(hAPP(c_List_Omap(_1611178, _1611180), _1611182), _1611186)))], (37165 ^ _773908) ^ [_1474480, _1474482, _1474484, _1474486, _1474488, _1474490] : [-(hAPP(c_Set_Ovimage(_1474480, _1474482, _1474484), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474486, tc_fun(_1474482, tc_HOL_Obool)), _1474488), _1474490)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474486, tc_fun(_1474480, tc_HOL_Obool)), _1474488), hAPP(hAPP(c_COMBB(tc_fun(_1474482, tc_HOL_Obool), tc_fun(_1474480, tc_HOL_Obool), _1474486), c_Set_Ovimage(_1474480, _1474482, _1474484)), _1474490)))], (49973 ^ _773908) ^ [_1783454, _1783456, _1783458, _1783460, _1783462, _1783464, _1783466] : [hBOOL(hAPP(hAPP(_1783454, hAPP(c_Product__Type_Osnd(_1783456, _1783458), _1783460)), hAPP(c_Product__Type_Ofst(_1783456, _1783458), _1783460))), 49980 ^ _773908 : [(49983 ^ _773908) ^ [] : [hBOOL(hAPP(_1783462, hAPP(hAPP(_1783464, 49978 ^ [_1783454, _1783456, _1783458, _1783460, _1783462, _1783464, _1783466]), 49979 ^ [_1783454, _1783456, _1783458, _1783460, _1783462, _1783464, _1783466])))], (49981 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1783454, 49979 ^ [_1783454, _1783456, _1783458, _1783460, _1783462, _1783464, _1783466]), 49978 ^ [_1783454, _1783456, _1783458, _1783460, _1783462, _1783464, _1783466])))]], -(hBOOL(hAPP(_1783462, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1783456, _1783458, _1783466), _1783464), _1783460))))], (49009 ^ _773908) ^ [_1762247] : [-(c_Nitpick_Onum(_1762247) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1762247, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1762247)))], (11596 ^ _773908) ^ [_967597] : [11597 ^ _773908 : [(11598 ^ _773908) ^ [_967654] : [hBOOL(hAPP(_967597, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _967654)))]], 11600 ^ _773908 : [(11603 ^ _773908) ^ [] : [-(hBOOL(hAPP(_967597, 11599 ^ [_967597])))], (11601 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11599 ^ [_967597])))]]], (36669 ^ _773908) ^ [_1464805, _1464807] : [-(c_Set_Othe__elem(_1464805, _1464807) = c_HOL_OThe(_1464805, hAPP(hAPP(c_COMBB(tc_fun(_1464805, tc_HOL_Obool), tc_HOL_Obool, _1464805), hAPP(c_fequal, _1464807)), hAPP(hAPP(c_COMBC(_1464805, tc_fun(_1464805, tc_HOL_Obool), tc_fun(_1464805, tc_HOL_Obool)), c_Set_Oinsert(_1464805)), c_Orderings_Obot__class_Obot(tc_fun(_1464805, tc_HOL_Obool))))))], (6954 ^ _773908) ^ [_886455, _886457, _886459] : [class_Groups_Oordered__comm__monoid__add(_886455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886455), _886457), c_Groups_Ozero__class_Ozero(_886455))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886455), _886459), c_Groups_Ozero__class_Ozero(_886455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886455), _886457), _886459)), c_Groups_Ozero__class_Ozero(_886455))))], (45721 ^ _773908) ^ [_1687496, _1687498, _1687500, _1687502] : [hBOOL(hAPP(_1687496, _1687498)), -(c_List_OtakeWhile(_1687500, _1687496, hAPP(hAPP(c_List_Olist_OCons(_1687500), _1687498), _1687502)) = hAPP(hAPP(c_List_Olist_OCons(_1687500), _1687498), c_List_OtakeWhile(_1687500, _1687496, _1687502)))], (44778 ^ _773908) ^ [_1668630, _1668632] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1668630, _1668632) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1668630, hAPP(c_Nat_OSuc, _1668632))))], (36083 ^ _773908) ^ [_1450894] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450894, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1450894, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1450894, tc_HOL_Obool)))], (29733 ^ _773908) ^ [_1316583, _1316585] : [class_Groups_Olinordered__ab__group__add(_1316583), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316583), _1316585)), -(_1316585 = c_Orderings_Obot__class_Obot(tc_fun(_1316583, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1316583), c_Big__Operators_Olinorder__class_OMax(_1316583, _1316585)) = c_Big__Operators_Olinorder__class_OMin(_1316583, hAPP(c_Set_Oimage(_1316583, _1316583, c_Groups_Ouminus__class_Ouminus(_1316583)), _1316585)))], (35536 ^ _773908) ^ [_1440013, _1440015] : [class_Groups_Oordered__ab__group__add(_1440013), -(hAPP(c_Set_Oimage(_1440013, _1440013, c_Groups_Ouminus__class_Ouminus(_1440013)), hAPP(c_SetInterval_Oord__class_OlessThan(_1440013), _1440015)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440013), hAPP(c_Groups_Ouminus__class_Ouminus(_1440013), _1440015)))], (24747 ^ _773908) ^ [_1210421, _1210423, _1210425] : [class_Orderings_Olinorder(_1210421), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210421), _1210423), _1210425) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210421), _1210425), _1210423))], (3370 ^ _773908) ^ [_824507, _824509, _824511, _824513, _824515, _824517] : [-(c_List_Osublist(_824517, _824513, _824509) = c_List_Osublist(_824515, _824511, _824507)), _824517 = _824515, _824513 = _824511, _824509 = _824507], (34051 ^ _773908) ^ [_1407618, _1407620, _1407622] : [class_Orderings_Olinorder(_1407618), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407618), _1407620), _1407622)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407618, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1407618, _1407620), _1407622)), hAPP(hAPP(c_Set_Oinsert(_1407618), _1407622), c_Orderings_Obot__class_Obot(tc_fun(_1407618, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1407618, _1407620, _1407622))], (10579 ^ _773908) ^ [_949397, _949399, _949401] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949397), _949399) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949401), _949399), -(_949397 = _949401), -(_949399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21249 ^ _773908) ^ [_1141352, _1141354, _1141356, _1141358] : [class_Rings_Odivision__ring(_1141352), -(_1141354 = c_Groups_Ozero__class_Ozero(_1141352)), 21256 ^ _773908 : [(21263 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141352), _1141356), _1141354) = _1141358, -(_1141356 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141352), _1141358), _1141354))], (21257 ^ _773908) ^ [] : [_1141356 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141352), _1141358), _1141354), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141352), _1141356), _1141354) = _1141358)]]], (45097 ^ _773908) ^ [_1674937, _1674939, _1674941] : [class_Orderings_Olinorder(_1674937), -(c_List_Olinorder__class_Osorted(_1674937, hAPP(c_List_Ofilter(_1674937, hAPP(hAPP(c_COMBC(_1674937, _1674937, tc_HOL_Obool), c_fequal), hAPP(_1674939, _1674941))), _1674941)))], (46305 ^ _773908) ^ [_1700324, _1700326] : [c_Wellfounded_Owf(_1700324, _1700326), -(c_Wellfounded_OwfP(_1700324, hAPP(hAPP(c_COMBC(_1700324, tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_fun(_1700324, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700324, tc_fun(tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_fun(_1700324, tc_HOL_Obool)), _1700324), c_COMBC(_1700324, tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700324, tc_prod(_1700324, _1700324)), tc_fun(_1700324, tc_fun(tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_HOL_Obool)), _1700324), hAPP(c_COMBB(tc_prod(_1700324, _1700324), tc_fun(tc_fun(tc_prod(_1700324, _1700324), tc_HOL_Obool), tc_HOL_Obool), _1700324), c_member(tc_prod(_1700324, _1700324)))), c_Product__Type_OPair(_1700324, _1700324)))), _1700326)))], (22827 ^ _773908) ^ [_1169971, _1169973] : [-(c_FunDef_Ois__measure(_1169971, _1169973))], (44457 ^ _773908) ^ [_1660206, _1660208] : [-(c_List_OremoveAll(_1660206, _1660208) = c_List_Ofilter(_1660206, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1660206), c_fNot), hAPP(c_fequal, _1660208))))], (1374 ^ _773908) ^ [_794069, _794071] : [-(class_Orderings_Owellorder(_794069)), _794071 = _794069, class_Orderings_Owellorder(_794071)], (47347 ^ _773908) ^ [_1725495, _1725497, _1725499] : [-(hAPP(c_Relation_Oconverse(_1725495, _1725497), hAPP(c_Relation_Oconverse(_1725497, _1725495), _1725499)) = _1725499)], (42626 ^ _773908) ^ [_1619372, _1619374] : [-(c_Hilbert__Choice_OEps(_1619372, hAPP(hAPP(c_COMBC(_1619372, _1619372, tc_HOL_Obool), c_fequal), _1619374)) = _1619374)], (35410 ^ _773908) ^ [_1437538, _1437540, _1437542] : [class_Groups_Ocomm__monoid__add(_1437538), class_Groups_Ocomm__monoid__mult(_1437538), c_Nat__Transfer_Onat__set(_1437540), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1437538), _1437542), _1437540) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1437538), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1437538, tc_Nat_Onat), _1437542), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1437540)))], (16253 ^ _773908) ^ [_1052333, _1052335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052335)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1052335), _1052333)), _1052335) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1052335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052333), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51810 ^ _773908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (37052 ^ _773908) ^ [_1471864, _1471866, _1471868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471864, tc_HOL_Obool)), _1471866), hAPP(hAPP(c_Set_Oinsert(_1471864), _1471868), c_Orderings_Obot__class_Obot(tc_fun(_1471864, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1471864, _1471868, _1471866) = _1471868)], (35971 ^ _773908) ^ [_1448870, _1448872] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448870, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1448870, tc_HOL_Obool))), _1448872) = _1448872)], (3752 ^ _773908) ^ [_830512, _830514, _830516, _830518] : [-(c_List_Olistrel1(_830518, _830514) = c_List_Olistrel1(_830516, _830512)), _830518 = _830516, _830514 = _830512], (50771 ^ _773908) ^ [_1800700, _1800702] : [c_Predicate_Osymp(_1800700, _1800702), -(c_Relation_Osym(_1800700, hAPP(c_Set_OCollect(tc_prod(_1800700, _1800700)), hAPP(c_Product__Type_Oprod_Oprod__case(_1800700, _1800700, tc_HOL_Obool), _1800702))))], (27097 ^ _773908) ^ [_1262337, _1262339, _1262341] : [hBOOL(hAPP(hAPP(c_member(_1262337), _1262339), c_Wellfounded_Oacc(_1262337, _1262341))), 27100 ^ _773908 : [(27101 ^ _773908) ^ [_1262451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1262337, _1262337)), hAPP(hAPP(c_Product__Type_OPair(_1262337, _1262337), _1262451), _1262339)), _1262341)), -(hBOOL(hAPP(hAPP(c_member(_1262337), _1262451), c_Wellfounded_Oacc(_1262337, _1262341))))]]], (10643 ^ _773908) ^ [_950351, _950353, _950355] : [_950353 = _950355, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950351)), _950353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950351)), _950355))], (44281 ^ _773908) ^ [_1656787, _1656789] : [-(hAPP(c_List_OremoveAll(_1656787, _1656789), c_List_Olist_ONil(_1656787)) = c_List_Olist_ONil(_1656787))], (30575 ^ _773908) ^ [_1333245, _1333247, _1333249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333245), _1333247)), hBOOL(hAPP(hAPP(c_member(_1333245), _1333249), _1333247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333245, tc_HOL_Obool)), _1333247), hAPP(hAPP(c_Set_Oinsert(_1333245), _1333249), c_Orderings_Obot__class_Obot(tc_fun(_1333245, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1333245), _1333247))))], (9613 ^ _773908) ^ [_934142] : [-(c_Nat_Ofunpow(_934142) = c_Nat_Ocompow(_934142, _934142))], (28781 ^ _773908) ^ [_1299484, _1299486, _1299488, _1299490, _1299492, _1299494] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299484, tc_fun(_1299486, tc_HOL_Obool))), _1299488), _1299490), _1299492), _1299494)), -(hBOOL(hAPP(hAPP(_1299488, _1299492), _1299494)))], (33404 ^ _773908) ^ [_1394401, _1394403, _1394405, _1394407, _1394409] : [c_Fun_Oinj__on(_1394401, _1394403, _1394405, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1394401, tc_HOL_Obool)), _1394407), _1394409)), 33407 ^ _773908 : [(33414 ^ _773908) ^ [] : [_1394407 = _1394409, -(hAPP(c_Set_Oimage(_1394401, _1394403, _1394405), _1394407) = hAPP(c_Set_Oimage(_1394401, _1394403, _1394405), _1394409))], (33408 ^ _773908) ^ [] : [hAPP(c_Set_Oimage(_1394401, _1394403, _1394405), _1394407) = hAPP(c_Set_Oimage(_1394401, _1394403, _1394405), _1394409), -(_1394407 = _1394409)]]], (41478 ^ _773908) ^ [_1590939, _1590941] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1590939), _1590941) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1590939, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1590941), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (6736 ^ _773908) ^ [_883116, _883118, _883120] : [class_Orderings_Olinorder(_883116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883116), _883118), _883120))), -(_883118 = _883120), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883116), _883120), _883118)))], (18469 ^ _773908) ^ [_1092721, _1092723, _1092725, _1092727] : [hBOOL(hAPP(hAPP(c_member(_1092721), _1092723), _1092725)), -(hBOOL(hAPP(hAPP(c_member(_1092721), _1092723), hAPP(hAPP(c_Set_Oinsert(_1092721), _1092727), _1092725))))], (46766 ^ _773908) ^ [_1710904, _1710906] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1710904, _1710904, _1710904), _1710906), c_Transitive__Closure_Ortrancl(_1710904, _1710906)) = hAPP(hAPP(c_Relation_Orel__comp(_1710904, _1710904, _1710904), c_Transitive__Closure_Ortrancl(_1710904, _1710906)), _1710906))], (21269 ^ _773908) ^ [_1141680, _1141682, _1141684] : [class_Rings_Odivision__ring(_1141680), -(_1141682 = c_Groups_Ozero__class_Ozero(_1141680)), 21276 ^ _773908 : [(21283 ^ _773908) ^ [] : [_1141684 = _1141682, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141680), _1141684), _1141682) = c_Groups_Oone__class_Oone(_1141680))], (21277 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141680), _1141684), _1141682) = c_Groups_Oone__class_Oone(_1141680), -(_1141684 = _1141682)]]], (20299 ^ _773908) ^ [] : [-(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))))], (10395 ^ _773908) ^ [_946119, _946121, _946123, _946125] : [class_Orderings_Opreorder(_946119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946119), _946121), _946123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946119), _946123), _946125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946119), _946121), _946125)))], (48933 ^ _773908) ^ [_1760406, _1760408, _1760410] : [hBOOL(hAPP(hAPP(c_member(_1760406), _1760408), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1760406, tc_HOL_Obool), _1760410))), 48937 ^ _773908 : [(48940 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1760406, tc_HOL_Obool)), 48936 ^ [_1760406, _1760408, _1760410]), _1760410)))], (48938 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760406), _1760408), 48936 ^ [_1760406, _1760408, _1760410])))]]], (10945 ^ _773908) ^ [_955938, _955940, _955942] : [class_Groups_Oordered__comm__monoid__add(_955938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955938), c_Groups_Ozero__class_Ozero(_955938)), _955940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955938), c_Groups_Ozero__class_Ozero(_955938)), _955942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955938), c_Groups_Ozero__class_Ozero(_955938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955938), _955940), _955942))))], (19873 ^ _773908) ^ [_1116902] : [_1116902 = c_Int_OPls, -(c_Int_OBit0(_1116902) = c_Int_OPls)], (15189 ^ _773908) ^ [_1031418, _1031420, _1031422, _1031424, _1031426] : [class_Groups_Oab__group__add(_1031418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031418), _1031420), _1031422) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031418), _1031424), _1031426), 15196 ^ _773908 : [(15203 ^ _773908) ^ [] : [_1031424 = _1031426, -(_1031420 = _1031422)], (15197 ^ _773908) ^ [] : [_1031420 = _1031422, -(_1031424 = _1031426)]]], (25267 ^ _773908) ^ [_1220268, _1220270, _1220272, _1220274] : [class_Orderings_Olinorder(_1220268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220268), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220268), _1220270), _1220272)), _1220274)), 25274 ^ _773908 : [(25277 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220268), _1220272), _1220274)))], (25275 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220268), _1220270), _1220274)))]]], (33146 ^ _773908) ^ [_1389646, _1389648, _1389650] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1389646), _1389648))), 33149 ^ _773908 : [(33156 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1389650), _1389648))), -(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)), _1389646)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1389650), _1389648)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33150 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1389650), _1389648)), -(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)), _1389646)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1389650), _1389648)) = 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))))]]], (45872 ^ _773908) ^ [_1690653, _1690655, _1690657, _1690659] : [-(hBOOL(hAPP(_1690653, _1690655))), -(c_List_OdropWhile(_1690657, _1690653, hAPP(hAPP(c_List_Olist_OCons(_1690657), _1690655), _1690659)) = hAPP(hAPP(c_List_Olist_OCons(_1690657), _1690655), _1690659))], (33880 ^ _773908) ^ [_1403644, _1403646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1403644), _1403646)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403644), hAPP(c_Nat_OSuc, _1403646)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1403646), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403644), _1403646)))], (37668 ^ _773908) ^ [_1488335, _1488337, _1488339, _1488341, _1488343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488335, _1488337)), _1488339), hAPP(hAPP(c_Product__Type_OSigma(_1488335, _1488337), _1488341), _1488343))), 37672 ^ _773908 : [(37678 ^ _773908) ^ [] : [-(_1488339 = hAPP(hAPP(c_Product__Type_OPair(_1488335, _1488337), 37671 ^ [_1488335, _1488337, _1488339, _1488341, _1488343]), 37674 ^ [_1488335, _1488337, _1488339, _1488341, _1488343]))], (37676 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488337), 37674 ^ [_1488335, _1488337, _1488339, _1488341, _1488343]), hAPP(_1488343, 37671 ^ [_1488335, _1488337, _1488339, _1488341, _1488343]))))], (37673 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488335), 37671 ^ [_1488335, _1488337, _1488339, _1488341, _1488343]), _1488341)))]]], (51476 ^ _773908) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (9005 ^ _773908) ^ [_923403, _923405] : [class_Groups_Olinordered__ab__group__add(_923403), 9008 ^ _773908 : [(9015 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923403), c_Groups_Ozero__class_Ozero(_923403)), _923405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923403), hAPP(c_Groups_Ouminus__class_Ouminus(_923403), _923405)), _923405)))], (9009 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923403), hAPP(c_Groups_Ouminus__class_Ouminus(_923403), _923405)), _923405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923403), c_Groups_Ozero__class_Ozero(_923403)), _923405)))]]], (45087 ^ _773908) ^ [_1674750, _1674752, _1674754, _1674756, _1674758] : [class_Orderings_Olinorder(_1674750), c_List_Olinorder__class_Osorted(_1674750, hAPP(hAPP(c_List_Omap(_1674752, _1674750), _1674754), _1674756)), -(c_List_Olinorder__class_Osorted(_1674750, hAPP(hAPP(c_List_Omap(_1674752, _1674750), _1674754), c_List_Olinorder__class_Oinsort__insert__key(_1674752, _1674750, _1674754, _1674758, _1674756))))], (18423 ^ _773908) ^ [_1091911, _1091913, _1091915] : [_1091911 = c_Orderings_Obot__class_Obot(tc_fun(_1091913, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1091913), _1091915), _1091911))], (4614 ^ _773908) ^ [_844097, _844099, _844101, _844103, _844105, _844107] : [-(c_Lazy__Sequence_Obind(_844107, _844103, _844099) = c_Lazy__Sequence_Obind(_844105, _844101, _844097)), _844107 = _844105, _844103 = _844101, _844099 = _844097], (12714 ^ _773908) ^ [_986887, _986889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986887), _986889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986887), _986889)))], (13734 ^ _773908) ^ [_1005263, _1005265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005265)), -(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, _1005263, _1005265))))], (30331 ^ _773908) ^ [_1328257] : [c_Nat__Transfer_Onat__set(_1328257), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1328257) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1328257)))], (5628 ^ _773908) ^ [_859980, _859982, _859984, _859986, _859988, _859990] : [-(c_COMBC(_859990, _859986, _859982) = c_COMBC(_859988, _859984, _859980)), _859990 = _859988, _859986 = _859984, _859982 = _859980], (1394 ^ _773908) ^ [_794319, _794321] : [-(class_Lattices_Obounded__lattice__top(_794319)), _794321 = _794319, class_Lattices_Obounded__lattice__top(_794321)], (45778 ^ _773908) ^ [_1688574, _1688576, _1688578, _1688580, _1688582] : [-(hAPP(hAPP(c_List_Ozip(_1688574, _1688576), c_List_OtakeWhile(_1688574, _1688578, _1688580)), _1688582) = c_List_OtakeWhile(tc_prod(_1688574, _1688576), hAPP(c_Fun_Ocomp(_1688574, tc_HOL_Obool, tc_prod(_1688574, _1688576), _1688578), c_Product__Type_Ofst(_1688574, _1688576)), hAPP(hAPP(c_List_Ozip(_1688574, _1688576), _1688580), _1688582)))], (37090 ^ _773908) ^ [_1472787, _1472789, _1472791] : [class_Lattices_Oab__semigroup__idem__mult(_1472787), hAPP(_1472789, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472787), 37095 ^ [_1472787, _1472789, _1472791]), 37096 ^ [_1472787, _1472789, _1472791])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472787), hAPP(_1472789, 37095 ^ [_1472787, _1472789, _1472791])), hAPP(_1472789, 37096 ^ [_1472787, _1472789, _1472791])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472787), _1472791)), -(_1472791 = c_Orderings_Obot__class_Obot(tc_fun(_1472787, tc_HOL_Obool))), -(hAPP(_1472789, hAPP(c_Finite__Set_Ofold1(_1472787, c_Groups_Otimes__class_Otimes(_1472787)), _1472791)) = hAPP(c_Finite__Set_Ofold1(_1472787, c_Groups_Otimes__class_Otimes(_1472787)), hAPP(c_Set_Oimage(_1472787, _1472787, _1472789), _1472791)))], (44999 ^ _773908) ^ [_1673200, _1673202] : [c_List_Oremdups(_1673200, _1673202) = _1673202, -(hBOOL(hAPP(c_List_Odistinct(_1673200), _1673202)))], (3872 ^ _773908) ^ [_832308, _832310, _832312, _832314] : [-(c_Big__Operators_Olattice__class_OInf__fin(_832314, _832310) = c_Big__Operators_Olattice__class_OInf__fin(_832312, _832308)), _832314 = _832312, _832310 = _832308], (50231 ^ _773908) ^ [_1790935, _1790937, _1790939] : [c_Relation_Otrans(_1790935, _1790937), c_Relation_Otrans(_1790935, _1790939), -(c_Relation_Otrans(_1790935, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1790935, _1790935), tc_HOL_Obool)), _1790937), _1790939)))], (26051 ^ _773908) ^ [_1235728, _1235730, _1235732] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235728, tc_HOL_Obool)), _1235730), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235728, tc_HOL_Obool)), _1235730), _1235732)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235728, tc_HOL_Obool)), _1235730), _1235732))], (31760 ^ _773908) ^ [_1360303, _1360305, _1360307, _1360309, _1360311] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360303, tc_fun(_1360305, tc_HOL_Obool)), _1360307), hAPP(hAPP(c_COMBC(_1360303, tc_fun(_1360305, tc_HOL_Obool), tc_fun(_1360305, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360305, tc_HOL_Obool), tc_fun(tc_fun(_1360305, tc_HOL_Obool), tc_fun(_1360305, tc_HOL_Obool)), _1360303), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360305, tc_HOL_Obool))), _1360309)), _1360311)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360305, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360303, tc_fun(_1360305, tc_HOL_Obool)), _1360307), _1360309)), _1360311))], (40841 ^ _773908) ^ [_1576708, _1576710, _1576712, _1576714] : [c_Equiv__Relations_Ocongruent(_1576708, _1576710, _1576712, _1576714), 40844 ^ _773908 : [(40845 ^ _773908) ^ [_1576853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576708, _1576708)), _1576853), _1576712)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1576708, _1576708, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1576708, tc_fun(_1576708, _1576710), tc_fun(_1576708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576710, tc_HOL_Obool), tc_fun(tc_fun(_1576708, _1576710), tc_fun(_1576708, tc_HOL_Obool)), _1576708), c_COMBB(_1576710, tc_HOL_Obool, _1576708)), hAPP(hAPP(c_COMBB(_1576710, tc_fun(_1576710, tc_HOL_Obool), _1576708), c_fequal), _1576714))), _1576714)), _1576853)))]]], (49574 ^ _773908) ^ [_1774445, _1774447, _1774449] : [-(c_List_Oreplicate(_1774445, hAPP(c_Nat_OSuc, _1774447), _1774449) = hAPP(hAPP(c_List_Olist_OCons(_1774445), _1774449), c_List_Oreplicate(_1774445, _1774447, _1774449)))], (19995 ^ _773908) ^ [_1118963, _1118965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1118963)), c_Int_OBit0(_1118965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118963), _1118965)))], (29165 ^ _773908) ^ [_1306142, _1306144, _1306146] : [class_Orderings_Olinorder(_1306142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306142), _1306144)), -(_1306144 = c_Orderings_Obot__class_Obot(tc_fun(_1306142, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306142), _1306146)), -(_1306146 = c_Orderings_Obot__class_Obot(tc_fun(_1306142, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306142, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306142, tc_HOL_Obool)), _1306144), _1306146)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306142), c_Big__Operators_Olinorder__class_OMax(_1306142, _1306144)), c_Big__Operators_Olinorder__class_OMax(_1306142, _1306146)))], (20835 ^ _773908) ^ [_1134262, _1134264] : [c_Nat__Transfer_Ois__nat(_1134262), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1134262), _1134264)))], (3014 ^ _773908) ^ [_818985, _818987, _818989, _818991] : [-(c_Predicate_OPowp(_818991, _818987) = c_Predicate_OPowp(_818989, _818985)), _818991 = _818989, _818987 = _818985], (49446 ^ _773908) ^ [_1772094, _1772096] : [-(c_List_Oconcat(_1772094, c_List_Oreplicate(tc_List_Olist(_1772094), _1772096, c_List_Olist_ONil(_1772094))) = c_List_Olist_ONil(_1772094))], (36446 ^ _773908) ^ [_1460122, _1460124, _1460126] : [c_Equiv__Relations_Oequivp(_1460122, _1460124), -(hBOOL(hAPP(hAPP(_1460124, _1460126), _1460126)))], (46286 ^ _773908) ^ [_1699797, _1699799] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1699797, _1699799), 46287 ^ [_1699797, _1699799])), -(c_Wellfounded_OwfP(_1699797, _1699799))], (7117 ^ _773908) ^ [_889157, _889159] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _889157), hAPP(c_Nat_OSuc, _889159)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _889157), _889159)))], (28436 ^ _773908) ^ [_1291103, _1291105] : [c_Nat__Transfer_Onat__set(_1291103), c_Nat__Transfer_Onat__set(_1291105), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1291103), _1291105) = 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), _1291103)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1291105))))], (40199 ^ _773908) ^ [_1559897, _1559899, _1559901, _1559903] : [hBOOL(hAPP(hAPP(c_member(_1559897), _1559899), hAPP(c_List_Oset(_1559897), hAPP(hAPP(c_List_Odrop(_1559897), _1559901), _1559903)))), -(hBOOL(hAPP(hAPP(c_member(_1559897), _1559899), hAPP(c_List_Oset(_1559897), _1559903))))], (46720 ^ _773908) ^ [_1709688, _1709690, _1709692, _1709694, _1709696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1709688, _1709688)), hAPP(hAPP(c_Product__Type_OPair(_1709688, _1709688), _1709690), _1709692)), c_Transitive__Closure_Ortrancl(_1709688, _1709694))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1709688, _1709688)), hAPP(hAPP(c_Product__Type_OPair(_1709688, _1709688), _1709692), _1709696)), c_Transitive__Closure_Ortrancl(_1709688, _1709694))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1709688, _1709688)), hAPP(hAPP(c_Product__Type_OPair(_1709688, _1709688), _1709690), _1709696)), c_Transitive__Closure_Ortrancl(_1709688, _1709694))))], (50534 ^ _773908) ^ [_1796613, _1796615] : [50537 ^ _773908 : [(50540 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796613, _1796613)), hAPP(hAPP(c_Product__Type_OPair(_1796613, _1796613), 50536 ^ [_1796613, _1796615]), 50535 ^ [_1796613, _1796615])), _1796615))], (50538 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796613, _1796613)), hAPP(hAPP(c_Product__Type_OPair(_1796613, _1796613), 50535 ^ [_1796613, _1796615]), 50536 ^ [_1796613, _1796615])), _1796615)))]], -(c_Relation_Osym(_1796613, _1796615))], (158 ^ _773908) ^ [_776213, _776215, _776217, _776219, _776221, _776223, _776225, _776227] : [-(c_Finite__Set_Ofolding__idem(_776225, _776221, _776217, _776213)), c_Finite__Set_Ofolding__idem(_776227, _776223, _776219, _776215), _776227 = _776225, _776223 = _776221, _776219 = _776217, _776215 = _776213], (48952 ^ _773908) ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760851, _1760853)), _1760855), hAPP(hAPP(c_Relation_Orel__comp(_1760851, _1760857, _1760853), _1760859), _1760861))), 48958 ^ _773908 : [(48963 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760857, _1760853)), hAPP(hAPP(c_Product__Type_OPair(_1760857, _1760853), 48956 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861]), 48957 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861])), _1760861)))], (48961 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760851, _1760857)), hAPP(hAPP(c_Product__Type_OPair(_1760851, _1760857), 48955 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861]), 48956 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861])), _1760859)))], (48959 ^ _773908) ^ [] : [-(_1760855 = hAPP(hAPP(c_Product__Type_OPair(_1760851, _1760853), 48955 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861]), 48957 ^ [_1760851, _1760853, _1760855, _1760857, _1760859, _1760861]))]]], (40081 ^ _773908) ^ [_1557241, _1557243, _1557245, _1557247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1557241), _1557243)), -(hAPP(hAPP(c_List_Onth(_1557245), hAPP(hAPP(c_List_Otake(_1557245), _1557243), _1557247)), _1557241) = hAPP(hAPP(c_List_Onth(_1557245), _1557247), _1557241))], (27736 ^ _773908) ^ [_1275971, _1275973, _1275975, _1275977] : [hBOOL(hAPP(hAPP(c_member(_1275971), _1275973), _1275975)), hBOOL(hAPP(hAPP(c_member(_1275971), _1275973), _1275977)), -(hBOOL(hAPP(hAPP(c_member(_1275971), _1275973), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275971, tc_HOL_Obool)), _1275975), _1275977))))], (32614 ^ _773908) ^ [_1379124, _1379126, _1379128, _1379130, _1379132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379124, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1379126, _1379124, _1379128), _1379130)), _1379132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1379124, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1379126, tc_HOL_Obool), tc_fun(_1379124, tc_HOL_Obool), c_Set_Oimage(_1379126, _1379124, _1379128)), hAPP(c_Set_OPow(_1379126), _1379130))), hAPP(c_Set_OPow(_1379124), _1379132))))], (8583 ^ _773908) ^ [_915893, _915895, _915897] : [class_Rings_Ocomm__semiring__1(_915893), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915893), _915895), _915897) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915893), _915897), _915895))], (752 ^ _773908) ^ [_785426, _785428] : [-(class_Rings_Oinverse(_785426)), _785428 = _785426, class_Rings_Oinverse(_785428)], (1324 ^ _773908) ^ [_793444, _793446] : [-(class_Groups_Oabs__if(_793444)), _793446 = _793444, class_Groups_Oabs__if(_793446)], (14855 ^ _773908) ^ [_1024925, _1024927, _1024929] : [-(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), _1024925), _1024927)), _1024929)), _1024927) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1024929), _1024927))], (43667 ^ _773908) ^ [_1642211, _1642213, _1642215, _1642217] : [c_Fun_Oinj__on(_1642211, _1642213, _1642215, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642211, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1642211), tc_fun(_1642211, tc_HOL_Obool), c_List_Oset(_1642211)), _1642217))), -(c_Fun_Oinj__on(tc_List_Olist(_1642211), tc_List_Olist(_1642213), hAPP(c_List_Omap(_1642211, _1642213), _1642215), _1642217))], (36739 ^ _773908) ^ [_1466262, _1466264] : [class_Lattices_Olattice(_1466262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466262), _1466264)), -(c_Big__Operators_Olattice__class_OSup__fin(_1466262, _1466264) = hAPP(c_Finite__Set_Ofold1(_1466262, c_Lattices_Osemilattice__sup__class_Osup(_1466262)), _1466264))], (45784 ^ _773908) ^ [_1688726, _1688728, _1688730, _1688732, _1688734] : [hBOOL(hAPP(hAPP(c_member(_1688726), _1688728), hAPP(c_List_Oset(_1688726), _1688730))), -(hBOOL(hAPP(_1688732, _1688728))), -(c_List_OtakeWhile(_1688726, _1688732, hAPP(hAPP(c_List_Oappend(_1688726), _1688730), _1688734)) = c_List_OtakeWhile(_1688726, _1688732, _1688730))], (26599 ^ _773908) ^ [_1251047, _1251049, _1251051, _1251053, _1251055, _1251057] : [hBOOL(hAPP(hAPP(c_member(_1251047), _1251049), _1251051)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1251047, _1251053)), hAPP(hAPP(c_Product__Type_OPair(_1251047, _1251053), _1251049), _1251055)), _1251057)), -(hBOOL(hAPP(hAPP(c_member(_1251053), _1251055), hAPP(c_Relation_OImage(_1251047, _1251053, _1251057), _1251051))))], (42039 ^ _773908) ^ [_1604801, _1604803, _1604805, _1604807] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604801, tc_fun(_1604803, tc_HOL_Obool)), _1604805), _1604807) = c_Orderings_Otop__class_Otop(tc_fun(_1604803, tc_HOL_Obool)), 42042 ^ _773908 : [(42043 ^ _773908) ^ [_1604917] : [hBOOL(hAPP(hAPP(c_member(_1604801), _1604917), _1604805)), -(hAPP(_1604807, _1604917) = c_Orderings_Otop__class_Otop(tc_fun(_1604803, tc_HOL_Obool)))]]], (2574 ^ _773908) ^ [_811911, _811913, _811915, _811917, _811919, _811921] : [-(c_SetInterval_Oord_OatMost(_811921, _811917, _811913) = c_SetInterval_Oord_OatMost(_811919, _811915, _811911)), _811921 = _811919, _811917 = _811915, _811913 = _811911], (43745 ^ _773908) ^ [_1644153, _1644155, _1644157] : [class_Complete__Lattice_Ocomplete__lattice(_1644153), class_Orderings_Olinorder(_1644153), 43752 ^ _773908 : [(43762 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1644153), _1644155), c_Complete__Lattice_OSup__class_OSup(_1644153, _1644157)))), 43763 ^ _773908 : [(43764 ^ _773908) ^ [_1644459] : [hBOOL(hAPP(hAPP(c_member(_1644153), _1644459), _1644157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1644153), _1644155), _1644459))]]], (43753 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1644153), _1644155), c_Complete__Lattice_OSup__class_OSup(_1644153, _1644157))), 43757 ^ _773908 : [(43760 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1644153), _1644155), 43756 ^ [_1644153, _1644155, _1644157])))], (43758 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644153), 43756 ^ [_1644153, _1644155, _1644157]), _1644157)))]]]]], (16789 ^ _773908) ^ [_1062213, _1062215, _1062217, _1062219] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062213), hAPP(c_Int_Onumber__class_Onumber__of(_1062213), _1062215)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062213), _1062217), _1062219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062213), hAPP(c_Int_Onumber__class_Onumber__of(_1062213), _1062215)), _1062217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062213), hAPP(c_Int_Onumber__class_Onumber__of(_1062213), _1062215)), _1062219))), class_Int_Onumber(_1062213), class_Rings_Osemiring(_1062213)], (23081 ^ _773908) ^ [_1174899, _1174901] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1174899)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1174901)), hAPP(c_Int_Onat, _1174899)) = hAPP(c_Int_Onat, _1174901))], (26830 ^ _773908) ^ [_1257282, _1257284, _1257286, _1257288, _1257290] : [hAPP(_1257282, _1257284) = _1257286, -(c_Fun_Ofun__upd(_1257288, _1257290, _1257282, _1257284, _1257286) = _1257282)], (48441 ^ _773908) ^ [_1750276, _1750278, _1750280] : [class_Orderings_Olinorder(_1750276), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750276), _1750278)), -(c_Big__Operators_Olattice_OSup__fin(_1750276, c_Orderings_Oord__class_Omax(_1750276), hAPP(hAPP(c_Set_Oinsert(_1750276), _1750280), _1750278)) = hAPP(hAPP(c_Finite__Set_Ofold(_1750276, _1750276, c_Orderings_Oord__class_Omax(_1750276)), _1750280), _1750278))], (35060 ^ _773908) ^ [_1429444, _1429446, _1429448] : [class_Orderings_Oorder(_1429444), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429444, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1429444, _1429446, _1429448)), hAPP(c_SetInterval_Oord__class_OatLeast(_1429444), _1429448)) = c_Orderings_Obot__class_Obot(tc_fun(_1429444, tc_HOL_Obool)))], (51011 ^ _773908) ^ [_1806072, _1806074, _1806076] : [hAPP(c_Set_Oimage(_1806072, _1806074, _1806076), c_Orderings_Otop__class_Otop(tc_fun(_1806072, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1806074, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1806072, _1806074, _1806074, _1806076), c_Hilbert__Choice_Oinv__into(_1806072, _1806074, c_Orderings_Otop__class_Otop(tc_fun(_1806072, tc_HOL_Obool)), _1806076)) = c_Fun_Oid(_1806074))], (13666 ^ _773908) ^ [_1004085, _1004087] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1004085), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1004087)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004085, _1004087)))], (51602 ^ _773908) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (47192 ^ _773908) ^ [_1721813, _1721815] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1721813, _1721813)), hAPP(hAPP(c_Product__Type_OPair(_1721813, _1721813), 47193 ^ [_1721813, _1721815]), 47193 ^ [_1721813, _1721815])), c_Transitive__Closure_Otrancl(_1721813, _1721815)))), -(c_Wellfounded_Oacyclic(_1721813, _1721815))], (41856 ^ _773908) ^ [_1598528, _1598530, _1598532, _1598534, _1598536, _1598538, _1598540, _1598542] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598528, tc_fun(_1598530, tc_fun(_1598532, tc_HOL_Obool))), _1598534), _1598536), _1598538), _1598540)), -(hBOOL(hAPP(hAPP(hAPP(_1598536, _1598542), _1598538), _1598540))), hBOOL(hAPP(hAPP(c_member(_1598528), _1598542), _1598534))], (50723 ^ _773908) ^ [_1800035, _1800037, _1800039] : [c_Equiv__Relations_Oequiv(_1800035, _1800037, _1800039), 50726 ^ _773908 : [(50731 ^ _773908) ^ [] : [-(c_Relation_Otrans(_1800035, _1800039))], (50729 ^ _773908) ^ [] : [-(c_Relation_Osym(_1800035, _1800039))], (50727 ^ _773908) ^ [] : [-(c_Relation_Orefl__on(_1800035, _1800037, _1800039))]]], (8827 ^ _773908) ^ [_920022, _920024, _920026] : [class_Groups_Ogroup__add(_920022), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920022), _920024), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920022), hAPP(c_Groups_Ouminus__class_Ouminus(_920022), _920024)), _920026)) = _920026)], (40715 ^ _773908) ^ [_1572545, _1572547, _1572549, _1572551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572545, _1572545)), hAPP(hAPP(c_Product__Type_OPair(_1572545, _1572545), _1572547), _1572549)), hAPP(c_List_Oset(tc_prod(_1572545, _1572545)), hAPP(hAPP(c_List_Ozip(_1572545, _1572545), _1572551), _1572551)))), 40718 ^ _773908 : [(40721 ^ _773908) ^ [] : [-(_1572547 = _1572549)], (40719 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572545), _1572547), hAPP(c_List_Oset(_1572545), _1572551))))]]], (10313 ^ _773908) ^ [_945024, _945026, _945028] : [class_Orderings_Olinorder(_945024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945024), _945026), _945028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945024), _945028), _945026))], (12933 ^ _773908) ^ [_990775, _990777, _990779, _990781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990775, tc_HOL_Obool)), _990777), _990779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990775, tc_HOL_Obool)), _990779), _990781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990775, tc_HOL_Obool)), _990777), _990781)))], (26580 ^ _773908) ^ [_1250565, _1250567, _1250569, _1250571, _1250573] : [hBOOL(hAPP(hAPP(c_member(_1250565), _1250567), hAPP(c_Relation_OImage(_1250569, _1250565, _1250571), _1250573))), 26584 ^ _773908 : [(26587 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1250569, _1250565)), hAPP(hAPP(c_Product__Type_OPair(_1250569, _1250565), 26583 ^ [_1250565, _1250567, _1250569, _1250571, _1250573]), _1250567)), _1250571)))], (26585 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1250569), 26583 ^ [_1250565, _1250567, _1250569, _1250571, _1250573]), _1250573)))]]], (34772 ^ _773908) ^ [_1423212, _1423214, _1423216] : [class_Orderings_Oorder(_1423212), 34775 ^ _773908 : [(34782 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423212), _1423216), _1423214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423212, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1423212), _1423214)), hAPP(c_SetInterval_Oord__class_OatLeast(_1423212), _1423216))))], (34776 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423212, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1423212), _1423214)), hAPP(c_SetInterval_Oord__class_OatLeast(_1423212), _1423216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423212), _1423216), _1423214)))]]], (8567 ^ _773908) ^ [_915527, _915529] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _915527)), _915529) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _915527), _915529)))], (5214 ^ _773908) ^ [_853645, _853647, _853649, _853651] : [-(c_Relation_Oinv__image(_853651, _853647) = c_Relation_Oinv__image(_853649, _853645)), _853651 = _853649, _853647 = _853645], (47928 ^ _773908) ^ [_1739693, _1739695, _1739697] : [class_Orderings_Olinorder(_1739693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1739693), _1739695)), 47938 ^ _773908 : [(47941 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739693), 47937 ^ [_1739693, _1739695, _1739697]), _1739697))], (47939 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739693), 47937 ^ [_1739693, _1739695, _1739697]), _1739695)))]], hBOOL(hAPP(hAPP(c_member(_1739693), _1739697), _1739695)), -(c_Big__Operators_Olinorder__class_OMax(_1739693, _1739695) = _1739697)], (19739 ^ _773908) ^ [_1114270, _1114272] : [class_Int_Onumber__ring(_1114270), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114270), hAPP(c_Int_Onumber__class_Onumber__of(_1114270), _1114272)), c_Groups_Oone__class_Oone(_1114270)) = hAPP(c_Int_Onumber__class_Onumber__of(_1114270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114272), c_Int_OBit1(c_Int_OPls))))], (25851 ^ _773908) ^ [_1231951, _1231953, _1231955, _1231957] : [class_Lattices_Osemilattice__sup(_1231951), 25854 ^ _773908 : [(25863 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231951), _1231953), _1231955)), _1231957))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), _1231953), _1231957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), _1231955), _1231957))], (25855 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231951), _1231953), _1231955)), _1231957)), 25858 ^ _773908 : [(25861 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), _1231955), _1231957)))], (25859 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231951), _1231953), _1231957)))]]]]], (34638 ^ _773908) ^ [_1419909, _1419911, _1419913, _1419915, _1419917] : [class_Groups_Ocomm__monoid__add(_1419909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419911), _1419913)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419911, _1419909), hAPP(hAPP(c_COMBS(_1419911, _1419909, _1419909), hAPP(hAPP(c_COMBB(_1419909, tc_fun(_1419909, _1419909), _1419911), c_Groups_Oplus__class_Oplus(_1419909)), _1419915)), _1419917)), _1419913) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1419909), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419911, _1419909), _1419915), _1419913)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419911, _1419909), _1419917), _1419913)))], (38721 ^ _773908) ^ [] : [-(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)))))], (49610 ^ _773908) ^ [_1775110, _1775112, _1775114] : [-(_1775110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1775112), c_List_Oreplicate(_1775112, _1775110, _1775114)) = hAPP(hAPP(c_Set_Oinsert(_1775112), _1775114), c_Orderings_Obot__class_Obot(tc_fun(_1775112, tc_HOL_Obool))))], (44706 ^ _773908) ^ [_1667353, _1667355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667353), _1667355)), -(c_List_Oupt(_1667353, hAPP(c_Nat_OSuc, _1667355)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1667353, _1667355)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1667355), c_List_Olist_ONil(tc_Nat_Onat))))], (13576 ^ _773908) ^ [_1002178, _1002180, _1002182, _1002184, _1002186, _1002188] : [class_Divides_Osemiring__div(_1002178), c_Divides_Odiv__class_Omod(_1002178, _1002180, _1002182) = c_Divides_Odiv__class_Omod(_1002178, _1002184, _1002182), c_Divides_Odiv__class_Omod(_1002178, _1002186, _1002182) = c_Divides_Odiv__class_Omod(_1002178, _1002188, _1002182), -(c_Divides_Odiv__class_Omod(_1002178, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002178), _1002180), _1002186), _1002182) = c_Divides_Odiv__class_Omod(_1002178, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002178), _1002184), _1002188), _1002182))], (38753 ^ _773908) ^ [_1522459, _1522461] : [c_Wellfounded_Owf(_1522459, _1522461), -(c_Wellfounded_Owf(tc_fun(_1522459, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1522459, _1522461)))], (43626 ^ _773908) ^ [_1641360, _1641362, _1641364, _1641366, _1641368] : [43628 ^ _773908 : [(43631 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1641360, _1641362, tc_HOL_Obool), _1641368), 43627 ^ [_1641360, _1641362, _1641364, _1641366, _1641368]))], (43629 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641360, _1641362)), 43627 ^ [_1641360, _1641362, _1641364, _1641366, _1641368]), hAPP(c_List_Oset(tc_prod(_1641360, _1641362)), hAPP(hAPP(c_List_Ozip(_1641360, _1641362), _1641364), _1641366)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641360)), _1641364) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641362)), _1641366), -(c_List_Olist__all2(_1641360, _1641362, _1641368, _1641364, _1641366))], (38454 ^ _773908) ^ [_1513580, _1513582, _1513584] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1513580)), c_List_Osublist(_1513580, _1513582, _1513584)) = 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(_1513580)), _1513582)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1513584)))))], (20627 ^ _773908) ^ [_1130442] : [_1130442 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1130442) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23001 ^ _773908) ^ [_1173280, _1173282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173280)), _1173282)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173280), _1173282)))], (40141 ^ _773908) ^ [_1558513, _1558515, _1558517, _1558519] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1558513) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1558515), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1558513)), hAPP(hAPP(c_List_Olist_OCons(_1558515), _1558517), _1558519)) = hAPP(hAPP(c_List_Olist_OCons(_1558515), _1558517), hAPP(hAPP(c_List_Otake(_1558515), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1558513)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1558519)))], (43841 ^ _773908) ^ [_1646176, _1646178, _1646180] : [43843 ^ _773908 : [(43846 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646176, tc_HOL_Obool)), 43842 ^ [_1646176, _1646178, _1646180]), _1646180) = c_Orderings_Obot__class_Obot(tc_fun(_1646176, tc_HOL_Obool))], (43844 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1646176, tc_HOL_Obool)), 43842 ^ [_1646176, _1646178, _1646180]), _1646178)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646176, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646176, tc_HOL_Obool), _1646178)), _1646180) = c_Orderings_Obot__class_Obot(tc_fun(_1646176, tc_HOL_Obool)))], (48051 ^ _773908) ^ [_1742108, _1742110, _1742112] : [c_List_Olist__ex(_1742108, _1742110, hAPP(c_List_Orev(_1742108), _1742112)), -(c_List_Olist__ex(_1742108, _1742110, _1742112))], (46209 ^ _773908) ^ [_1698115, _1698117, _1698119, _1698121, _1698123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1698115, _1698117)), hAPP(_1698115, _1698119))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1698121, _1698121)), hAPP(hAPP(c_Product__Type_OPair(_1698121, _1698121), _1698117), _1698119)), c_List_Omeasures(_1698121, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1698121, tc_Nat_Onat)), _1698115), _1698123)))))], (36960 ^ _773908) ^ [_1470179, _1470181, _1470183] : [class_Orderings_Olinorder(_1470179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470179), _1470181)), -(_1470181 = c_Orderings_Obot__class_Obot(tc_fun(_1470179, tc_HOL_Obool))), 36971 ^ _773908 : [(36981 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470179), hAPP(c_Finite__Set_Ofold1(_1470179, c_Orderings_Oord__class_Omin(_1470179)), _1470181)), _1470183))), 36982 ^ _773908 : [(36983 ^ _773908) ^ [_1470568] : [hBOOL(hAPP(hAPP(c_member(_1470179), _1470568), _1470181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470179), _1470568), _1470183))]]], (36972 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470179), hAPP(c_Finite__Set_Ofold1(_1470179, c_Orderings_Oord__class_Omin(_1470179)), _1470181)), _1470183)), 36976 ^ _773908 : [(36979 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470179), 36975 ^ [_1470179, _1470181, _1470183]), _1470183)))], (36977 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470179), 36975 ^ [_1470179, _1470181, _1470183]), _1470181)))]]]]], (36031 ^ _773908) ^ [] : [-(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)))], (33002 ^ _773908) ^ [_1386817, _1386819, _1386821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386817)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386819), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1386821)), 33012 ^ _773908 : [(33018 ^ _773908) ^ [] : [-(_1386819 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33014 ^ [_1386817, _1386819, _1386821]), 33011 ^ [_1386817, _1386819, _1386821]))], (33016 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33014 ^ [_1386817, _1386819, _1386821]), _1386821)))], (33013 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33011 ^ [_1386817, _1386819, _1386821]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1386817))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386819), _1386817) = _1386819)], (49694 ^ _773908) ^ [_1776797, _1776799, _1776801] : [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), _1776797), _1776799))), -(hBOOL(hAPP(hAPP(_1776801, _1776797), _1776799))), 49701 ^ _773908 : [(49704 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 49699 ^ [_1776797, _1776799, _1776801]), 49700 ^ [_1776797, _1776799, _1776801]))), -(hBOOL(hAPP(hAPP(_1776801, 49699 ^ [_1776797, _1776799, _1776801]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 49700 ^ [_1776797, _1776799, _1776801]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49710 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1776801, 49699 ^ [_1776797, _1776799, _1776801]), 49700 ^ [_1776797, _1776799, _1776801]))], (49702 ^ _773908) ^ [] : [-(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), 49699 ^ [_1776797, _1776799, _1776801]), 49700 ^ [_1776797, _1776799, _1776801]))))]]], (46552 ^ _773908) ^ [_1705471, _1705473, _1705475, _1705477] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1705471, _1705473, _1705475, _1705477) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1705471, _1705473), _1705475), _1705477)))], (40747 ^ _773908) ^ [_1573472, _1573474, _1573476, _1573478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573472), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573474)), _1573476))), -(hBOOL(hAPP(hAPP(c_member(_1573474), _1573478), hAPP(c_List_Oset(_1573474), hAPP(hAPP(c_List_Olist__update(_1573474, _1573476), _1573472), _1573478)))))], (22995 ^ _773908) ^ [_1173128, _1173130, _1173132, _1173134, _1173136] : [class_Groups_Ominus(_1173128), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173130, _1173128)), _1173132), _1173134), _1173136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173128), hAPP(_1173132, _1173136)), hAPP(_1173134, _1173136)))], (26751 ^ _773908) ^ [_1255154] : [-(_1255154 = 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), 26748 ^ [_1255154]), 26749 ^ [_1255154])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (20041 ^ _773908) ^ [_1119819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1119819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1119819)))], (31397 ^ _773908) ^ [_1351232, _1351234, _1351236, _1351238] : [class_Groups_Ocomm__monoid__mult(_1351232), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351234), _1351236)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351234, _1351232), _1351238), _1351236) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351232, _1351234, c_Groups_Otimes__class_Otimes(_1351232)), _1351238), c_Groups_Oone__class_Oone(_1351232)), _1351236))], (42688 ^ _773908) ^ [_1620417, _1620419, _1620421, _1620423] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620417)), _1620419) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620421)), _1620423), -(hAPP(hAPP(c_List_Omap(tc_prod(_1620417, _1620421), _1620421), c_Product__Type_Osnd(_1620417, _1620421)), hAPP(hAPP(c_List_Ozip(_1620417, _1620421), _1620419), _1620423)) = _1620423)], (22889 ^ _773908) ^ [_1170945, _1170947, _1170949, _1170951] : [-(c_Nitpick_Ofold__graph_H(_1170945, _1170947, _1170949, _1170951, c_Orderings_Obot__class_Obot(tc_fun(_1170945, tc_HOL_Obool)), _1170951))], (40093 ^ _773908) ^ [_1557556, _1557558, _1557560] : [hAPP(hAPP(c_List_Otake(_1557556), _1557558), _1557560) = c_List_Olist_ONil(_1557556), -(_1557558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1557560 = c_List_Olist_ONil(_1557556))], (18007 ^ _773908) ^ [_1084499, _1084501] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1084499), hAPP(hAPP(c_Power_Opower__class_Opower(_1084499), hAPP(c_Int_Onumber__class_Onumber__of(_1084499), c_Int_OMin)), _1084501)) = c_Groups_Oone__class_Oone(_1084499)), class_Int_Onumber__ring(_1084499), class_Rings_Olinordered__idom(_1084499)], (50586 ^ _773908) ^ [_1797601, _1797603, _1797605, _1797607] : [c_Relation_Osym(_1797601, _1797603), -(c_Relation_Osym(_1797605, hAPP(hAPP(c_Relation_Oinv__image(_1797601, _1797605), _1797603), _1797607)))], (39843 ^ _773908) ^ [_1551070, _1551072, _1551074, _1551076] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551070)), hAPP(hAPP(c_List_Oappend(_1551070), _1551072), _1551074)), c_List_Olists(_1551070, _1551076))), 39846 ^ _773908 : [(39849 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551070)), _1551074), c_List_Olists(_1551070, _1551076))))], (39847 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1551070)), _1551072), c_List_Olists(_1551070, _1551076))))]]], (43368 ^ _773908) ^ [_1635337, _1635339, _1635341, _1635343, _1635345] : [c_List_Olist__all2(_1635337, _1635339, _1635341, _1635343, _1635345), 43371 ^ _773908 : [(43374 ^ _773908) ^ [_1635503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635337, _1635339)), _1635503), hAPP(c_List_Oset(tc_prod(_1635337, _1635339)), hAPP(hAPP(c_List_Ozip(_1635337, _1635339), _1635343), _1635345)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1635337, _1635339, tc_HOL_Obool), _1635341), _1635503)))], (43372 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635337)), _1635343) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635339)), _1635345))]]], (20783 ^ _773908) ^ [_1133526, _1133528, _1133530] : [class_Fields_Olinordered__field__inverse__zero(_1133526), -(hAPP(c_Groups_Oabs__class_Oabs(_1133526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133526), _1133528), _1133530)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133526), hAPP(c_Groups_Oabs__class_Oabs(_1133526), _1133528)), hAPP(c_Groups_Oabs__class_Oabs(_1133526), _1133530)))], (15505 ^ _773908) ^ [_1037084, _1037086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037084), _1037086)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1037086, _1037084) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037086), _1037084), _1037084))], (18603 ^ _773908) ^ [_1095190, _1095192, _1095194] : [hBOOL(hAPP(hAPP(c_member(_1095190), _1095192), hAPP(hAPP(c_Set_Oinsert(_1095190), _1095194), c_Orderings_Obot__class_Obot(tc_fun(_1095190, tc_HOL_Obool))))), -(_1095192 = _1095194)], (28668 ^ _773908) ^ [_1296052, _1296054, _1296056, _1296058] : [hBOOL(hAPP(hAPP(c_member(_1296052), _1296054), c_SetInterval_Oord_OgreaterThan(_1296052, _1296056, _1296058))), -(hBOOL(hAPP(hAPP(_1296056, _1296058), _1296054)))], (41266 ^ _773908) ^ [_1586959, _1586961, _1586963, _1586965] : [-(hAPP(c_List_Orotate(_1586959, _1586961), hAPP(c_List_Orotate(_1586959, _1586963), _1586965)) = hAPP(c_List_Orotate(_1586959, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1586961), _1586963)), _1586965))], (662 ^ _773908) ^ [_784025, _784027] : [-(class_Lattices_Oab__semigroup__idem__mult(_784025)), _784027 = _784025, class_Lattices_Oab__semigroup__idem__mult(_784027)], (23899 ^ _773908) ^ [_1191882, _1191884, _1191886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1191882, tc_fun(_1191882, tc_HOL_Obool))), _1191884), _1191886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1191882, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1191882, _1191886)), c_Wellfounded_Oaccp(_1191882, _1191884))))], (9589 ^ _773908) ^ [_933730, _933732, _933734] : [class_Rings_Olinordered__ring__strict(_933730), 9592 ^ _773908 : [(9593 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933730), c_Groups_Ozero__class_Ozero(_933730)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933730), _933732), _933732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933730), _933734), _933734)))), _933732 = c_Groups_Ozero__class_Ozero(_933730), _933734 = c_Groups_Ozero__class_Ozero(_933730)], (9603 ^ _773908) ^ [] : [9604 ^ _773908 : [(9607 ^ _773908) ^ [] : [-(_933734 = c_Groups_Ozero__class_Ozero(_933730))], (9605 ^ _773908) ^ [] : [-(_933732 = c_Groups_Ozero__class_Ozero(_933730))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933730), c_Groups_Ozero__class_Ozero(_933730)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933730), _933732), _933732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933730), _933734), _933734)))))]]], (4442 ^ _773908) ^ [_841541, _841543] : [_841543 = _841541, -(c_New__Random__Sequence_Opos__single(_841543) = c_New__Random__Sequence_Opos__single(_841541))], (11479 ^ _773908) ^ [_965455, _965457, _965459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965455), _965457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965459), _965455)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965459), _965457))))], (51588 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (46977 ^ _773908) ^ [_1716357, _1716359, _1716361, _1716363, _1716365] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1716357, _1716357)), hAPP(hAPP(c_Product__Type_OPair(_1716357, _1716357), _1716359), _1716361)), c_Transitive__Closure_Ortrancl(_1716357, _1716363))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1716357, _1716357), tc_HOL_Obool)), _1716363), hAPP(hAPP(c_Product__Type_OSigma(_1716357, _1716357), _1716365), hAPP(c_COMBK(tc_fun(_1716357, tc_HOL_Obool), _1716357), _1716365)))), -(_1716359 = _1716361), -(hBOOL(hAPP(hAPP(c_member(_1716357), _1716359), _1716365)))], (15773 ^ _773908) ^ [_1042343, _1042345, _1042347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042343), _1042345)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042345), _1042343)), _1042347) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042345), _1042347)), _1042343))], (36876 ^ _773908) ^ [_1468672, _1468674, _1468676] : [class_Orderings_Olinorder(_1468672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468672), _1468674)), -(_1468674 = c_Orderings_Obot__class_Obot(tc_fun(_1468672, tc_HOL_Obool))), 36887 ^ _773908 : [(36897 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468672), hAPP(c_Finite__Set_Ofold1(_1468672, c_Orderings_Oord__class_Omin(_1468672)), _1468674)), _1468676))), 36898 ^ _773908 : [(36899 ^ _773908) ^ [_1469061] : [hBOOL(hAPP(hAPP(c_member(_1468672), _1469061), _1468674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468672), _1469061), _1468676))]]], (36888 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468672), hAPP(c_Finite__Set_Ofold1(_1468672, c_Orderings_Oord__class_Omin(_1468672)), _1468674)), _1468676)), 36892 ^ _773908 : [(36895 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468672), 36891 ^ [_1468672, _1468674, _1468676]), _1468676)))], (36893 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1468672), 36891 ^ [_1468672, _1468674, _1468676]), _1468674)))]]]]], (20651 ^ _773908) ^ [_1130796, _1130798] : [class_Fields_Olinordered__field__inverse__zero(_1130796), class_Int_Onumber__ring(_1130796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130796), c_Groups_Ozero__class_Ozero(_1130796)), _1130798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130796), c_Groups_Ozero__class_Ozero(_1130796)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130796), _1130798), hAPP(c_Int_Onumber__class_Onumber__of(_1130796), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (31439 ^ _773908) ^ [_1352360, _1352362] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1352360), _1352362))), -(hAPP(c_Finite__Set_Ocard(_1352360), _1352362) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42381 ^ _773908) ^ [_1613553, _1613555] : [class_Groups_Oordered__ab__group__add__abs(_1613553), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613553), hAPP(c_Groups_Oabs__class_Oabs(_1613553), hAPP(c_List_Omonoid__add__class_Olistsum(_1613553), _1613555))), hAPP(c_List_Omonoid__add__class_Olistsum(_1613553), hAPP(hAPP(c_List_Omap(_1613553, _1613553), c_Groups_Oabs__class_Oabs(_1613553)), _1613555)))))], (24717 ^ _773908) ^ [_1209742, _1209744, _1209746, _1209748] : [class_Orderings_Olinorder(_1209742), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209742), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209742), _1209744), _1209746)), _1209748) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209742), _1209744), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209742), _1209746), _1209748)))], (7851 ^ _773908) ^ [_902130] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _902130)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27786 ^ _773908) ^ [_1276935, _1276937, _1276939] : [class_Lattices_Osemilattice__inf(_1276935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1276935), _1276937), _1276939)), _1276937)))], (50600 ^ _773908) ^ [_1797812, _1797814, _1797816, _1797818, _1797820] : [c_Equiv__Relations_Opart__equivp(_1797812, _1797814), hBOOL(hAPP(hAPP(_1797814, _1797816), _1797818)), hBOOL(hAPP(hAPP(_1797814, _1797818), _1797820)), -(hBOOL(hAPP(hAPP(_1797814, _1797816), _1797820)))], (2404 ^ _773908) ^ [_809236, _809238, _809240, _809242, _809244, _809246, _809248, _809250] : [-(c_Nitpick_Opair__box_OPairBox(_809250, _809246, _809242, _809238) = c_Nitpick_Opair__box_OPairBox(_809248, _809244, _809240, _809236)), _809250 = _809248, _809246 = _809244, _809242 = _809240, _809238 = _809236], (20649 ^ _773908) ^ [] : [-(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)))], (22805 ^ _773908) ^ [_1169723, _1169725] : [22806 ^ _773908 : [(22809 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1169725), _1169723))], (22807 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1169723), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1169723, _1169725) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (20315 ^ _773908) ^ [_1124584, _1124586, _1124588] : [class_Rings_Olinordered__semidom(_1124584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124584), hAPP(hAPP(c_Power_Opower__class_Opower(_1124584), _1124586), 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(_1124584), _1124588), 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(_1124584), c_Groups_Ozero__class_Ozero(_1124584)), _1124588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124584), _1124586), _1124588)))], (12236 ^ _773908) ^ [_978867, _978869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978867)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978869)))), 12239 ^ _773908 : [(12242 ^ _773908) ^ [] : [-(_978869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12240 ^ _773908) ^ [] : [-(_978867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41836 ^ _773908) ^ [_1598104, _1598106, _1598108, _1598110, _1598112, _1598114] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598104, tc_fun(_1598106, tc_HOL_Obool)), _1598108), _1598110), _1598112)), -(hBOOL(hAPP(hAPP(_1598110, _1598114), _1598112))), hBOOL(hAPP(hAPP(c_member(_1598104), _1598114), _1598108))], (40541 ^ _773908) ^ [_1568143, _1568145] : [-(_1568143 = c_List_Olist_ONil(_1568145)), -(hAPP(c_List_Ohd(_1568145), _1568143) = hAPP(hAPP(c_List_Onth(_1568145), _1568143), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4534 ^ _773908) ^ [_842919, _842921] : [_842921 = _842919, -(c_List_Odrop(_842921) = c_List_Odrop(_842919))], (13528 ^ _773908) ^ [_1001190, _1001192] : [class_Divides_Osemiring__div(_1001190), -(c_Divides_Odiv__class_Omod(_1001190, _1001192, _1001192) = c_Groups_Ozero__class_Ozero(_1001190))], (13167 ^ _773908) ^ [_994896, _994898, _994900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994896), _994898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994896), _994900))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _994896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994898), _994900)))], (44770 ^ _773908) ^ [_1668479, _1668481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668479), _1668481)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1668479, _1668481)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1668481), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (644 ^ _773908) ^ [_783756, _783758, _783760, _783762, _783764, _783766] : [-(c_Finite__Set_Ofun__left__comm__idem(_783764, _783760, _783756)), c_Finite__Set_Ofun__left__comm__idem(_783766, _783762, _783758), _783766 = _783764, _783762 = _783760, _783758 = _783756], (5124 ^ _773908) ^ [_852170, _852172, _852174, _852176, _852178, _852180, _852182, _852184, _852186, _852188, _852190, _852192] : [-(c_Partial__Function_Ofun__lub(_852192, _852188, _852184, _852180, _852176, _852172) = c_Partial__Function_Ofun__lub(_852190, _852186, _852182, _852178, _852174, _852170)), _852192 = _852190, _852188 = _852186, _852184 = _852182, _852180 = _852178, _852176 = _852174, _852172 = _852170], (8237 ^ _773908) ^ [_909526] : [class_Rings_Osemiring__1(_909526), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909526), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_909526))], (43955 ^ _773908) ^ [_1648909, _1648911] : [class_Complete__Lattice_Ocomplete__lattice(_1648909), -(c_Complete__Lattice_OSup__class_OSup(_1648909, hAPP(c_List_Oset(_1648909), _1648911)) = hAPP(c_List_Ofoldl(_1648909, _1648909, c_Lattices_Osemilattice__sup__class_Osup(_1648909), c_Orderings_Obot__class_Obot(_1648909)), _1648911))], (40693 ^ _773908) ^ [_1571830, _1571832, _1571834, _1571836, _1571838] : [-(hAPP(hAPP(c_List_Olist__update(_1571830, hAPP(hAPP(c_List_Olist_OCons(_1571830), _1571832), _1571834)), _1571836), _1571838) = c_Nat_Onat_Onat__case(tc_List_Olist(_1571830), hAPP(hAPP(c_List_Olist_OCons(_1571830), _1571838), _1571834), hAPP(hAPP(c_COMBB(tc_List_Olist(_1571830), tc_List_Olist(_1571830), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1571830), _1571832)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1571830, tc_List_Olist(_1571830)), c_List_Olist__update(_1571830, _1571834)), _1571838)), _1571836))], (18825 ^ _773908) ^ [_1099544] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099544), 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), _1099544)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1099544)))], (20815 ^ _773908) ^ [_1133996, _1133998] : [c_Nat__Transfer_Ois__nat(_1133996), c_Nat__Transfer_Ois__nat(_1133998), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133996, _1133998)))], (15425 ^ _773908) ^ [_1035587, _1035589] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035587), _1035589)), _1035589) = _1035587)], (24215 ^ _773908) ^ [_1197538, _1197540, _1197542] : [c_FunDef_Ois__measure(_1197538, _1197540), -(c_FunDef_Ois__measure(tc_prod(_1197542, _1197538), hAPP(hAPP(c_COMBB(_1197538, tc_Nat_Onat, tc_prod(_1197542, _1197538)), _1197540), c_Product__Type_Osnd(_1197542, _1197538))))], (3424 ^ _773908) ^ [_825340, _825342] : [_825342 = _825340, -(c_SetInterval_Oord__class_OatMost(_825342) = c_SetInterval_Oord__class_OatMost(_825340))], (32722 ^ _773908) ^ [_1381255, _1381257, _1381259, _1381261] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1381255, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381257, tc_fun(tc_fun(_1381255, tc_HOL_Obool), tc_HOL_Obool)), _1381259), hAPP(hAPP(c_COMBB(tc_fun(_1381255, tc_HOL_Obool), tc_fun(tc_fun(_1381255, tc_HOL_Obool), tc_HOL_Obool), _1381257), c_Set_OPow(_1381255)), _1381261))), hAPP(c_Set_OPow(_1381255), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381257, tc_fun(_1381255, tc_HOL_Obool)), _1381259), _1381261)))))], (16171 ^ _773908) ^ [_1050844, _1050846, _1050848, _1050850, _1050852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050844), _1050846)), 16174 ^ _773908 : [(16181 ^ _773908) ^ [] : [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), _1050846), _1050844)), _1050848)), _1050850)), _1050852)), -(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), _1050846), _1050848)), _1050850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050844), _1050848)), _1050852))))], (16175 ^ _773908) ^ [] : [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), _1050846), _1050848)), _1050850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050844), _1050848)), _1050852))), -(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), _1050846), _1050844)), _1050848)), _1050850)), _1050852)))]]], (7245 ^ _773908) ^ [_891037, _891039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891037), hAPP(c_Nat_OSuc, _891039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891037), _891039))), -(_891037 = _891039)], (36321 ^ _773908) ^ [_1456066, _1456068, _1456070, _1456072, _1456074, _1456076, _1456078] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1456066, _1456068, _1456070, _1456072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1456066, tc_HOL_Obool)), _1456074), hAPP(hAPP(c_Set_Oinsert(_1456066), _1456076), c_Orderings_Obot__class_Obot(tc_fun(_1456066, tc_HOL_Obool))))), _1456078)), hBOOL(hAPP(hAPP(c_member(_1456066), _1456076), _1456074)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1456066, _1456068, _1456070, _1456072, _1456074), hAPP(hAPP(_1456070, _1456076), _1456078))))], (47285 ^ _773908) ^ [_1723807, _1723809, _1723811, _1723813, _1723815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1723807, _1723809)), hAPP(hAPP(c_Product__Type_OPair(_1723807, _1723809), _1723811), _1723813)), hAPP(c_Relation_Oconverse(_1723809, _1723807), _1723815))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723809, _1723807)), hAPP(hAPP(c_Product__Type_OPair(_1723809, _1723807), _1723813), _1723811)), _1723815)))], (7747 ^ _773908) ^ [_899891, _899893, _899895, _899897, _899899] : [c_Com_Ocom_OLocal(_899891, _899893, _899895) = c_Com_Ocom_OAss(_899897, _899899)], (3088 ^ _773908) ^ [_820164, _820166, _820168, _820170, _820172, _820174] : [-(c_List_Olist_Olist__size(_820174, _820170, _820166) = c_List_Olist_Olist__size(_820172, _820168, _820164)), _820174 = _820172, _820170 = _820168, _820166 = _820164], (51426 ^ _773908) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (43860 ^ _773908) ^ [_1646767, _1646769, _1646771, _1646773] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646767, tc_fun(_1646769, tc_HOL_Obool)), _1646771), _1646773) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646769, tc_HOL_Obool), hAPP(c_Set_Oimage(_1646767, tc_fun(_1646769, tc_HOL_Obool), _1646773), _1646771)))], (17329 ^ _773908) ^ [_1072862, _1072864] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072862), _1072864)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1072862)), _1072864))], (14366 ^ _773908) ^ [_1016946, _1016948] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016946), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016948)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016946)), _1016948))], (50043 ^ _773908) ^ [_1785227, _1785229] : [-(hBOOL(hAPP(_1785229, 50050 ^ [_1785227, _1785229]))), 50044 ^ _773908 : [(50045 ^ _773908) ^ [_1785288] : [hBOOL(hAPP(hAPP(c_member(_1785227), _1785288), c_Orderings_Otop__class_Otop(tc_fun(_1785227, tc_HOL_Obool)))), hBOOL(hAPP(_1785229, _1785288))]]], (49560 ^ _773908) ^ [_1774162, _1774164, _1774166] : [-(_1774162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1774164), c_List_Oreplicate(_1774164, _1774162, _1774166)) = _1774166)], (49967 ^ _773908) ^ [_1783075, _1783077, _1783079, _1783081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1783075), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1783077, _1783079, _1783075, _1783081) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1783077, 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(_1783077)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1783079, _1783081)), 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(_1783077)))), 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(_1783077)))), 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(_1783077)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1783077, 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(_1783077)))), 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(_1783077)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1783077, _1783079, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1783075), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1783081))), 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(_1783077)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077)))), 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(_1783077)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1783077, 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(_1783077)))), 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(_1783077)))), 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(_1783077))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077)))), 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(_1783077)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077))))), tc_prod(_1783077, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1783077)), hAPP(hAPP(c_COMBB(_1783077, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1783077)))), tc_prod(_1783077, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1783077)), c_Product__Type_Ofst(_1783077, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (44776 ^ _773908) ^ [_1668590, _1668592] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1668590, _1668592)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1668590), hAPP(c_Nat_OSuc, _1668592)))], (44656 ^ _773908) ^ [_1666500, _1666502, _1666504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666500), _1666502)), _1666504)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1666502), c_List_Oupt(_1666500, _1666504)) = c_List_Oupt(_1666500, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666500), _1666502)))], (32025 ^ _773908) ^ [_1367345, _1367347, _1367349, _1367351, _1367353] : [class_Groups_Ocomm__monoid__mult(_1367345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367347), _1367349)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367347), _1367351)), 32039 ^ _773908 : [(32042 ^ _773908) ^ [] : [hAPP(_1367353, 32038 ^ [_1367345, _1367347, _1367349, _1367351, _1367353]) = c_Groups_Oone__class_Oone(_1367345)], (32040 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1367347), 32038 ^ [_1367345, _1367347, _1367349, _1367351, _1367353]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367347, tc_HOL_Obool)), _1367349), _1367351))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1367345, _1367347, c_Groups_Otimes__class_Otimes(_1367345)), _1367353), c_Groups_Oone__class_Oone(_1367345)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367347, tc_HOL_Obool)), _1367349), _1367351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367345), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1367345, _1367347, c_Groups_Otimes__class_Otimes(_1367345)), _1367353), c_Groups_Oone__class_Oone(_1367345)), _1367349)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1367345, _1367347, c_Groups_Otimes__class_Otimes(_1367345)), _1367353), c_Groups_Oone__class_Oone(_1367345)), _1367351)))], (5062 ^ _773908) ^ [_851247, _851249] : [_851249 = _851247, -(c_Random__Sequence_Osingle(_851249) = c_Random__Sequence_Osingle(_851247))], (37175 ^ _773908) ^ [_1474739, _1474741, _1474743, _1474745, _1474747] : [hBOOL(hAPP(hAPP(c_member(_1474739), _1474741), hAPP(c_Set_Ovimage(_1474739, _1474743, _1474745), _1474747))), -(hBOOL(hAPP(hAPP(c_member(_1474743), hAPP(_1474745, _1474741)), _1474747)))], (1404 ^ _773908) ^ [_794444, _794446] : [-(class_Lattices_Obounded__lattice__bot(_794444)), _794446 = _794444, class_Lattices_Obounded__lattice__bot(_794446)], (42201 ^ _773908) ^ [_1609231, _1609233, _1609235, _1609237, _1609239] : [class_Complete__Lattice_Ocomplete__lattice(_1609231), class_Orderings_Olinorder(_1609231), 42208 ^ _773908 : [(42218 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1609231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609233, _1609231), _1609235), _1609237)), _1609239))), 42219 ^ _773908 : [(42220 ^ _773908) ^ [_1609579] : [hBOOL(hAPP(hAPP(c_member(_1609233), _1609579), _1609235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1609231), hAPP(_1609237, _1609579)), _1609239))]]], (42209 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1609231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609233, _1609231), _1609235), _1609237)), _1609239)), 42213 ^ _773908 : [(42216 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1609231), hAPP(_1609237, 42212 ^ [_1609231, _1609233, _1609235, _1609237, _1609239])), _1609239)))], (42214 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609233), 42212 ^ [_1609231, _1609233, _1609235, _1609237, _1609239]), _1609235)))]]]]], (11267 ^ _773908) ^ [_961757, _961759, _961761, _961763, _961765] : [class_Rings_Oordered__semiring(_961757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961757), _961759), _961761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961757), _961763), _961765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961757), c_Groups_Ozero__class_Ozero(_961757)), _961761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961757), c_Groups_Ozero__class_Ozero(_961757)), _961763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961757), _961759), _961763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961757), _961761), _961765))))], (32568 ^ _773908) ^ [_1378330, _1378332, _1378334] : [class_Orderings_Oorder(_1378330), _1378332 = _1378334, -(c_SetInterval_Oord__class_OatLeastAtMost(_1378330, _1378332, _1378334) = hAPP(hAPP(c_Set_Oinsert(_1378330), _1378332), c_Orderings_Obot__class_Obot(tc_fun(_1378330, tc_HOL_Obool))))], (45533 ^ _773908) ^ [_1683489, _1683491] : [hAPP(c_List_Orev(_1683489), _1683491) = c_List_Olist_ONil(_1683489), -(_1683491 = c_List_Olist_ONil(_1683489))], (14039 ^ _773908) ^ [_1010547, _1010549, _1010551, _1010553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010549), _1010551)), -(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), _1010551), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010553, _1010547))), _1010549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010551), _1010547))))], (40129 ^ _773908) ^ [_1558295, _1558297, _1558299, _1558301] : [-(_1558295 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1558297), _1558295), hAPP(hAPP(c_List_Olist_OCons(_1558297), _1558299), _1558301)) = hAPP(hAPP(c_List_Olist_OCons(_1558297), _1558299), hAPP(hAPP(c_List_Otake(_1558297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1558295), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1558301)))], (10929 ^ _773908) ^ [_955655, _955657] : [class_Groups_Olinordered__ab__group__add(_955655), 10932 ^ _773908 : [(10939 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955655), _955657), c_Groups_Ozero__class_Ozero(_955655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955655), _955657), _955657)), c_Groups_Ozero__class_Ozero(_955655))))], (10933 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955655), _955657), _955657)), c_Groups_Ozero__class_Ozero(_955655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955655), _955657), c_Groups_Ozero__class_Ozero(_955655))))]]], (51780 ^ _773908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (21797 ^ _773908) ^ [_1151148, _1151150, _1151152, _1151154] : [class_Fields_Ofield__inverse__zero(_1151148), -(_1151150 = c_Groups_Ozero__class_Ozero(_1151148)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151148), _1151152), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151148), _1151154), _1151150)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151148), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151148), _1151154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151148), _1151152), _1151150))), _1151150))], (26747 ^ _773908) ^ [_1255102, _1255104] : [-(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), _1255102), _1255104)), 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), _1255102), _1255104))], (42650 ^ _773908) ^ [_1619747, _1619749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1619747)), hAPP(c_Code__Numeral_Oof__nat, _1619749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619747), _1619749)))], (29975 ^ _773908) ^ [_1321204, _1321206, _1321208] : [class_Orderings_Olinorder(_1321204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321204), _1321206)), -(_1321206 = c_Orderings_Obot__class_Obot(tc_fun(_1321204, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321204), _1321208)), -(_1321208 = c_Orderings_Obot__class_Obot(tc_fun(_1321204, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321204, tc_HOL_Obool)), _1321206), _1321208) = c_Orderings_Obot__class_Obot(tc_fun(_1321204, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1321204, c_Orderings_Oord__class_Omax(_1321204), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321204, tc_HOL_Obool)), _1321206), _1321208)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321204), c_Big__Operators_Olattice_OSup__fin(_1321204, c_Orderings_Oord__class_Omax(_1321204), _1321206)), c_Big__Operators_Olattice_OSup__fin(_1321204, c_Orderings_Oord__class_Omax(_1321204), _1321208)))], (50906 ^ _773908) ^ [_1803669, _1803671, _1803673] : [hAPP(_1803673, hAPP(c_Hilbert__Choice_Oinv__into(_1803669, _1803671, c_Orderings_Otop__class_Otop(tc_fun(_1803669, tc_HOL_Obool)), _1803673), 50907 ^ [_1803669, _1803671, _1803673])) = 50907 ^ [_1803669, _1803671, _1803673], -(hAPP(c_Set_Oimage(_1803669, _1803671, _1803673), c_Orderings_Otop__class_Otop(tc_fun(_1803669, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803671, tc_HOL_Obool)))], (6175 ^ _773908) ^ [_874025, _874027, _874029, _874031] : [c_Natural_Oevaln(_874025, _874027, _874029, _874031), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_874025), _874027), _874031)))], (11525 ^ _773908) ^ [_966334, _966336, _966338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966334), _966336)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966334), _966338)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966336), _966338))], (28172 ^ _773908) ^ [_1284380, _1284382, _1284384, _1284386] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284380, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284380, tc_HOL_Obool)), _1284382), _1284384)), _1284386) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284380, tc_HOL_Obool)), _1284382), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284380, tc_HOL_Obool)), _1284384), _1284386)))], (36107 ^ _773908) ^ [_1451359, _1451361, _1451363, _1451365, _1451367, _1451369, _1451371] : [-(hBOOL(hAPP(hAPP(c_member(_1451359), _1451361), _1451363))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1451359, _1451365, _1451367, _1451369, _1451363), _1451371)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1451359, _1451365, _1451367, _1451369, hAPP(hAPP(c_Set_Oinsert(_1451359), _1451361), _1451363)), hAPP(hAPP(_1451367, _1451361), _1451371))))], (9421 ^ _773908) ^ [_930844, _930846, _930848, _930850, _930852, _930854] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_930844), -(_930846 = c_Groups_Ozero__class_Ozero(_930844)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930844), _930848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930844), _930846), _930852)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930844), _930850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930844), _930846), _930854)), _930848 = _930850, -(_930852 = _930854)], (39065 ^ _773908) ^ [_1529538] : [-(hAPP(c_Relation_ORange(_1529538, _1529538), c_Relation_OId(_1529538)) = c_Orderings_Otop__class_Otop(tc_fun(_1529538, tc_HOL_Obool)))], (18121 ^ _773908) ^ [_1086412, _1086414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086412), _1086414)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1086412), _1086414) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36697 ^ _773908) ^ [_1465382, _1465384, _1465386] : [class_Orderings_Olinorder(_1465382), -(_1465384 = c_Orderings_Obot__class_Obot(tc_fun(_1465382, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465382, tc_HOL_Obool)), _1465384), _1465386)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465382), _1465386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465382), hAPP(c_Finite__Set_Ofold1(_1465382, c_Orderings_Oord__class_Omin(_1465382)), _1465386)), hAPP(c_Finite__Set_Ofold1(_1465382, c_Orderings_Oord__class_Omin(_1465382)), _1465384))))], (8513 ^ _773908) ^ [_914337, _914339, _914341, _914343, _914345] : [class_Rings_Ocomm__semiring__1(_914337), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), _914339), _914341)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), _914343), _914345)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), _914343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914337), _914339), _914341)), _914345)))], (20191 ^ _773908) ^ [_1122454] : [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), _1122454))), 20194 ^ _773908 : [(20197 ^ _773908) ^ [] : [-(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(_1122454)))))], (20195 ^ _773908) ^ [] : [-(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(_1122454)))))]]], (8109 ^ _773908) ^ [_906808, _906810, _906812, _906814] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_906808, _906810), _906812, _906814, _906812)), 8110 ^ _773908 : [(8113 ^ _773908) ^ [_906895] : [c_Natural_Oevaln(_906810, _906812, _906814, _906895), c_Natural_Oevaln(c_Com_Ocom_OWhile(_906808, _906810), _906895, _906814, _906812)], (8111 ^ _773908) ^ [] : [-(hBOOL(hAPP(_906808, _906812)))]]], (41688 ^ _773908) ^ [_1595245, _1595247, _1595249] : [-(hAPP(hAPP(c_List_Odrop(_1595245), _1595247), c_List_Obutlast(_1595245, _1595249)) = c_List_Obutlast(_1595245, hAPP(hAPP(c_List_Odrop(_1595245), _1595247), _1595249)))], (35865 ^ _773908) ^ [] : [-(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))))], (48877 ^ _773908) ^ [_1759187, _1759189, _1759191, _1759193, _1759195, _1759197, _1759199, _1759201] : [c_Finite__Set_Ofolding__image__simple__idem(_1759187, _1759189, _1759191, _1759193, _1759195, _1759197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1759189), _1759199)), -(hAPP(_1759197, hAPP(hAPP(c_Set_Oinsert(_1759189), _1759201), _1759199)) = hAPP(hAPP(_1759191, hAPP(_1759195, _1759201)), hAPP(_1759197, _1759199)))], (15611 ^ _773908) ^ [_1039259, _1039261, _1039263, _1039265, _1039267, _1039269] : [class_Rings_Oring(_1039259), 15614 ^ _773908 : [(15621 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039259), _1039261), _1039267)), _1039263)), _1039265) = _1039269, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), _1039261), _1039263)), _1039265) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), _1039267), _1039263)), _1039269))], (15615 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), _1039261), _1039263)), _1039265) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), _1039267), _1039263)), _1039269), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039259), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039259), _1039261), _1039267)), _1039263)), _1039265) = _1039269)]]], (30710 ^ _773908) ^ [_1336333, _1336335, _1336337, _1336339] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1336333), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336335, tc_Int_Oint), _1336337), _1336339)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336335, _1336333), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1336333, _1336335), c_Int_Oring__1__class_Oof__int(_1336333)), _1336337)), _1336339)), class_Groups_Ocomm__monoid__mult(_1336333), class_Rings_Oring__1(_1336333)], (37398 ^ _773908) ^ [_1480295, _1480297, _1480299] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1480295, _1480297), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1480295, _1480297), _1480299), hAPP(c_COMBK(tc_fun(_1480297, tc_HOL_Obool), _1480295), c_Orderings_Otop__class_Otop(tc_fun(_1480297, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1480295, _1480297), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1480295, tc_HOL_Obool)), _1480299)), hAPP(c_COMBK(tc_fun(_1480297, tc_HOL_Obool), _1480295), c_Orderings_Otop__class_Otop(tc_fun(_1480297, tc_HOL_Obool)))))], (39785 ^ _773908) ^ [_1549521, _1549523, _1549525, _1549527, _1549529, _1549531] : [hBOOL(hAPP(hAPP(_1549521, _1549523), _1549525)), c_List_Olistrelp(_1549527, _1549521, _1549529, _1549531), -(c_List_Olistrelp(_1549527, _1549521, hAPP(hAPP(c_List_Olist_OCons(_1549527), _1549523), _1549529), hAPP(hAPP(c_List_Olist_OCons(_1549527), _1549525), _1549531)))], (34464 ^ _773908) ^ [_1415624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415624)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415624) = 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, _1415624))))], (17019 ^ _773908) ^ [_1067176, _1067178, _1067180, _1067182, _1067184] : [class_Groups_Oordered__ab__group__add__abs(_1067176), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067176), hAPP(c_Groups_Oabs__class_Oabs(_1067176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067176), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067176), _1067178), _1067180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067176), _1067182), _1067184)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067176), hAPP(c_Groups_Oabs__class_Oabs(_1067176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067176), _1067178), _1067182))), hAPP(c_Groups_Oabs__class_Oabs(_1067176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067176), _1067180), _1067184))))))], (33554 ^ _773908) ^ [_1397173, _1397175, _1397177] : [class_Orderings_Oorder(_1397173), 33557 ^ _773908 : [(33564 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397173), _1397175), _1397177))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397173, _1397175), _1397177) = c_Orderings_Obot__class_Obot(tc_fun(_1397173, tc_HOL_Obool)))], (33558 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397173, _1397175), _1397177) = c_Orderings_Obot__class_Obot(tc_fun(_1397173, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397173), _1397175), _1397177))]]], (4148 ^ _773908) ^ [_836566, _836568, _836570, _836572] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_836572, _836568) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_836570, _836566)), _836572 = _836570, _836568 = _836566], (33642 ^ _773908) ^ [_1398762] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1398762) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1398762))], (41826 ^ _773908) ^ [_1597907, _1597909, _1597911, _1597913, _1597915, _1597917] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597907, tc_fun(_1597909, tc_HOL_Obool)), _1597911), _1597913), _1597915)), hBOOL(hAPP(hAPP(c_member(_1597907), _1597917), _1597911)), -(hBOOL(hAPP(hAPP(_1597913, _1597917), _1597915)))], (27966 ^ _773908) ^ [_1280167, _1280169, _1280171, _1280173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280167, tc_HOL_Obool)), _1280169), _1280171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280167, tc_HOL_Obool)), _1280169), _1280173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280167, tc_HOL_Obool)), _1280169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280167, tc_HOL_Obool)), _1280171), _1280173))))], (39030 ^ _773908) ^ [_1528523, _1528525, _1528527, _1528529] : [39032 ^ _773908 : [(39035 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1528525, hAPP(_1528527, 39031 ^ [_1528523, _1528525, _1528527, _1528529]))), hAPP(_1528525, 39031 ^ [_1528523, _1528525, _1528527, _1528529])))], (39033 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1528523, 39031 ^ [_1528523, _1528525, _1528527, _1528529])))]], -(c_Wellfounded_Owf(_1528529, hAPP(c_Set_OCollect(tc_prod(_1528529, _1528529)), hAPP(c_Product__Type_Oprod_Oprod__case(_1528529, _1528529, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1528529, tc_HOL_Obool), tc_fun(_1528529, tc_HOL_Obool), _1528529), hAPP(c_COMBS(_1528529, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528529), c_fconj), _1528523))), hAPP(hAPP(c_COMBC(_1528529, tc_fun(_1528529, _1528529), tc_fun(_1528529, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528529, tc_HOL_Obool), tc_fun(tc_fun(_1528529, _1528529), tc_fun(_1528529, tc_HOL_Obool)), _1528529), c_COMBB(_1528529, tc_HOL_Obool, _1528529)), c_fequal)), _1528527))))))], (42471 ^ _773908) ^ [_1615969, _1615971, _1615973, _1615975, _1615977] : [_1615969 = c_Orderings_Obot__class_Obot(tc_fun(_1615971, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615973, tc_HOL_Obool)), _1615975), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615971, tc_fun(_1615973, tc_HOL_Obool)), _1615969), _1615977)) = _1615975)], (23716 ^ _773908) ^ [_1188100, _1188102, _1188104, _1188106, _1188108, _1188110] : [hAPP(hAPP(c_Product__Type_OPair(_1188100, _1188102), _1188104), _1188106) = hAPP(hAPP(c_Product__Type_OPair(_1188100, _1188102), _1188108), _1188110), 23719 ^ _773908 : [(23722 ^ _773908) ^ [] : [-(_1188106 = _1188110)], (23720 ^ _773908) ^ [] : [-(_1188104 = _1188108)]]], (25385 ^ _773908) ^ [_1222431, _1222433, _1222435] : [class_Orderings_Olinorder(_1222431), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222431), _1222433), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222431), _1222433), _1222435)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222431), _1222433), _1222435))], (33983 ^ _773908) ^ [_1405907, _1405909, _1405911, _1405913] : [class_Orderings_Olinorder(_1405907), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405907, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1405907), _1405909)), c_SetInterval_Oord__class_OatLeastAtMost(_1405907, _1405911, _1405913)) = c_SetInterval_Oord__class_OatLeastAtMost(_1405907, _1405911, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1405907), _1405909), _1405913)))], (38412 ^ _773908) ^ [_1511334, _1511336, _1511338] : [class_Orderings_Olinorder(_1511334), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511334), _1511336)), -(_1511336 = c_Orderings_Obot__class_Obot(tc_fun(_1511334, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1511334), _1511338), c_Big__Operators_Olattice_OInf__fin(_1511334, c_Orderings_Oord__class_Omin(_1511334), _1511336)) = c_Big__Operators_Olattice_OInf__fin(_1511334, c_Orderings_Oord__class_Omin(_1511334), hAPP(c_Set_OCollect(_1511334), hAPP(hAPP(c_COMBB(tc_fun(_1511334, tc_HOL_Obool), tc_HOL_Obool, _1511334), c_HOL_OEx(_1511334)), hAPP(hAPP(c_COMBC(_1511334, tc_fun(_1511334, tc_HOL_Obool), tc_fun(_1511334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511334, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511334, tc_HOL_Obool), tc_fun(_1511334, tc_HOL_Obool)), _1511334), c_COMBS(_1511334, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511334, tc_HOL_Obool), tc_fun(_1511334, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511334), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511334), c_fconj)), hAPP(hAPP(c_COMBC(_1511334, tc_fun(_1511334, _1511334), tc_fun(_1511334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511334, tc_HOL_Obool), tc_fun(tc_fun(_1511334, _1511334), tc_fun(_1511334, tc_HOL_Obool)), _1511334), c_COMBB(_1511334, tc_HOL_Obool, _1511334)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1511334), _1511338))))), hAPP(hAPP(c_COMBC(_1511334, tc_fun(_1511334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511334)), _1511336))))))], (49348 ^ _773908) ^ [_1769697] : [-(c_Predicate_Oconversep(_1769697, _1769697, c_fequal) = c_fequal)], (32432 ^ _773908) ^ [_1375781, _1375783] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1375781, _1375783))))], (20753 ^ _773908) ^ [_1132885, _1132887] : [class_Rings_Odivision__ring(_1132885), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132885), _1132887), c_Groups_Oone__class_Oone(_1132885)) = _1132887)], (41959 ^ _773908) ^ [_1601560, _1601562, _1601564, _1601566, _1601568, _1601570] : [-(hAPP(hAPP(c_List_Ozip(_1601560, _1601562), hAPP(hAPP(c_List_Omap(_1601564, _1601560), _1601566), _1601568)), _1601570) = hAPP(hAPP(c_List_Omap(tc_prod(_1601564, _1601562), tc_prod(_1601560, _1601562)), hAPP(c_Product__Type_Oprod_Oprod__case(_1601564, _1601562, tc_prod(_1601560, _1601562)), hAPP(hAPP(c_COMBB(_1601560, tc_fun(_1601562, tc_prod(_1601560, _1601562)), _1601564), c_Product__Type_OPair(_1601560, _1601562)), _1601566))), hAPP(hAPP(c_List_Ozip(_1601564, _1601562), _1601568), _1601570)))], (1304 ^ _773908) ^ [_793194, _793196] : [-(class_Int_Onumber__ring(_793194)), _793196 = _793194, class_Int_Onumber__ring(_793196)], (4492 ^ _773908) ^ [_842302, _842304, _842306, _842308] : [-(c_List_Oconcat(_842308, _842304) = c_List_Oconcat(_842306, _842302)), _842308 = _842306, _842304 = _842302], (17297 ^ _773908) ^ [_1072386, _1072388] : [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), _1072386), _1072388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072386))), -(_1072388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16967 ^ _773908) ^ [_1066102, _1066104] : [class_Int_Onumber__ring(_1066102), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1066102), hAPP(c_Int_Onumber__class_Onumber__of(_1066102), _1066104)) = hAPP(c_Int_Onumber__class_Onumber__of(_1066102), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1066104)))], (50384 ^ _773908) ^ [_1793925, _1793927] : [c_Relation_Oantisym(_1793925, _1793927), 50387 ^ _773908 : [(50388 ^ _773908) ^ [_1794037, _1794039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1793925, _1793925)), hAPP(hAPP(c_Product__Type_OPair(_1793925, _1793925), _1794039), _1794037)), _1793927)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793925, _1793925)), hAPP(hAPP(c_Product__Type_OPair(_1793925, _1793925), _1794037), _1794039)), _1793927)), -(_1794039 = _1794037)]]], (51460 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (46511 ^ _773908) ^ [_1704506] : [-(_1704506 = hAPP(c_Int_OAbs__Integ, 46509 ^ [_1704506]))], (7045 ^ _773908) ^ [_888045, _888047] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888045), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _888047), _888045)))))], (13660 ^ _773908) ^ [_1003940, _1003942, _1003944] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003940), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003942, _1003944)), _1003944) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003940), _1003942), _1003944))], (23161 ^ _773908) ^ [_1176575, _1176577] : [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(_1176577))), 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), _1176575)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1176575)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176577))))], (44303 ^ _773908) ^ [_1657137, _1657139, _1657141] : [hBOOL(hAPP(c_List_Odistinct(_1657137), _1657139)), -(c_List_Oremove1(_1657137, _1657141, _1657139) = hAPP(c_List_OremoveAll(_1657137, _1657141), _1657139))], (34606 ^ _773908) ^ [_1419443, _1419445, _1419447] : [class_Groups_Ocomm__monoid__add(_1419443), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419445, _1419443), _1419447), c_Orderings_Obot__class_Obot(tc_fun(_1419445, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1419443))], (28222 ^ _773908) ^ [_1285612, _1285614, _1285616, _1285618] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285612, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285612, tc_HOL_Obool)), _1285614), _1285616)), _1285618) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285612, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285612, tc_HOL_Obool)), _1285614), _1285618)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285612, tc_HOL_Obool)), _1285616), _1285618)))], (51600 ^ _773908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (26562 ^ _773908) ^ [_1250152, _1250154, _1250156, _1250158] : [-(_1250152 = c_Orderings_Obot__class_Obot(tc_fun(_1250154, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1250154, _1250156, hAPP(c_COMBK(_1250156, _1250154), _1250158)), _1250152) = hAPP(hAPP(c_Set_Oinsert(_1250156), _1250158), c_Orderings_Obot__class_Obot(tc_fun(_1250156, tc_HOL_Obool))))], (51680 ^ _773908) ^ [_1815870, _1815872] : [-(class_Finite__Set_Ofinite(tc_sum(_1815870, _1815872))), class_Finite__Set_Ofinite(_1815870), class_Finite__Set_Ofinite(_1815872)], (43037 ^ _773908) ^ [_1627958, _1627960, _1627962, _1627964] : [-(hBOOL(hAPP(hAPP(c_member(_1627958), _1627960), hAPP(c_List_Oset(_1627958), _1627962)))), -(c_List_Oremove1(_1627958, _1627960, hAPP(hAPP(c_List_Oappend(_1627958), _1627962), _1627964)) = hAPP(hAPP(c_List_Oappend(_1627958), _1627962), c_List_Oremove1(_1627958, _1627960, _1627964)))], (1234 ^ _773908) ^ [_792319, _792321] : [-(class_Rings_Olinordered__idom(_792319)), _792321 = _792319, class_Rings_Olinordered__idom(_792321)], (9267 ^ _773908) ^ [_927978, _927980, _927982] : [class_Rings_Olinordered__semiring__strict(_927978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927978), c_Groups_Ozero__class_Ozero(_927978)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927978), _927980), _927982))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927978), c_Groups_Ozero__class_Ozero(_927978)), _927982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927978), c_Groups_Ozero__class_Ozero(_927978)), _927980)))], (23007 ^ _773908) ^ [_1173383, _1173385] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173383), _1173385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173383)), _1173385)))], (1554 ^ _773908) ^ [_796319, _796321] : [-(class_Groups_Olinordered__ab__semigroup__add(_796319)), _796321 = _796319, class_Groups_Olinordered__ab__semigroup__add(_796321)], (42946 ^ _773908) ^ [_1626082, _1626084, _1626086, _1626088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626084)), _1626086))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626084)), _1626088))), 42956 ^ _773908 : [(42959 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Onth(_1626084), _1626086), 42955 ^ [_1626082, _1626084, _1626086, _1626088]) = hAPP(hAPP(c_List_Onth(_1626084), _1626088), 42955 ^ [_1626082, _1626084, _1626086, _1626088])], (42957 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42955 ^ [_1626082, _1626084, _1626086, _1626088]), _1626082)))]], -(hAPP(hAPP(c_List_Otake(_1626084), _1626082), _1626086) = hAPP(hAPP(c_List_Otake(_1626084), _1626082), _1626088))], (19959 ^ _773908) ^ [_1118348, _1118350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1118348)), c_Int_OBit1(_1118350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118348), _1118350)))], (18475 ^ _773908) ^ [_1092846, _1092848, _1092850] : [hBOOL(hAPP(hAPP(c_member(_1092846), _1092848), _1092850)), -(hAPP(hAPP(c_Set_Oinsert(_1092846), _1092848), _1092850) = _1092850)], (2292 ^ _773908) ^ [_807404, _807406, _807408, _807410, _807412, _807414, _807416, _807418] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_807418, _807414, _807410, _807406) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_807416, _807412, _807408, _807404)), _807418 = _807416, _807414 = _807412, _807410 = _807408, _807406 = _807404], (40753 ^ _773908) ^ [_1573637, _1573639, _1573641, _1573643, _1573645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573637), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573639)), _1573641))), -(hAPP(hAPP(c_List_Olist__update(_1573639, hAPP(hAPP(c_List_Oappend(_1573639), _1573641), _1573643)), _1573637), _1573645) = hAPP(hAPP(c_List_Oappend(_1573639), hAPP(hAPP(c_List_Olist__update(_1573639, _1573641), _1573637), _1573645)), _1573643))], (31190 ^ _773908) ^ [_1346413, _1346415, _1346417, _1346419, _1346421] : [class_Groups_Ocomm__monoid__mult(_1346413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346415), _1346417)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346415), _1346419)), 31204 ^ _773908 : [(31207 ^ _773908) ^ [] : [hAPP(_1346421, 31203 ^ [_1346413, _1346415, _1346417, _1346419, _1346421]) = c_Groups_Oone__class_Oone(_1346413)], (31205 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346415), 31203 ^ [_1346413, _1346415, _1346417, _1346419, _1346421]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346415, tc_HOL_Obool)), _1346417), _1346419))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346415, _1346413), _1346421), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346415, tc_HOL_Obool)), _1346417), _1346419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346415, _1346413), _1346421), _1346417)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346415, _1346413), _1346421), _1346419)))], (50578 ^ _773908) ^ [_1797473, _1797475] : [-(c_Relation_Osym(_1797473, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1797473, _1797473), tc_HOL_Obool)), _1797475), hAPP(c_Relation_Oconverse(_1797473, _1797473), _1797475))))], (4508 ^ _773908) ^ [_842536, _842538, _842540, _842542] : [-(c_List_Ofilter(_842542, _842538) = c_List_Ofilter(_842540, _842536)), _842542 = _842540, _842538 = _842536], (35919 ^ _773908) ^ [_1447811] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1447811), c_Orderings_Otop__class_Otop(tc_fun(_1447811, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1447811)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1447811), tc_HOL_Obool)))))], (10503 ^ _773908) ^ [_947928, _947930, _947932, _947934] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947928), 10506 ^ _773908 : [(10513 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947928), _947932), _947934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947928), _947930), _947932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947928), _947930), _947934))))], (10507 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947928), _947930), _947932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947928), _947930), _947934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947928), _947932), _947934)))]]], (50554 ^ _773908) ^ [_1797106, _1797108] : [c_Relation_Osym(_1797106, hAPP(c_Relation_Oconverse(_1797106, _1797106), _1797108)), -(c_Relation_Osym(_1797106, _1797108))], (16555 ^ _773908) ^ [_1058025, _1058027] : [class_Int_Onumber__ring(_1058025), class_Rings_Olinordered__idom(_1058025), 16562 ^ _773908 : [(16569 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058025), hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027)), c_Groups_Ozero__class_Ozero(_1058025)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1058025), hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027)) = hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027))], (16563 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058025), hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027)), c_Groups_Ozero__class_Ozero(_1058025))), -(hAPP(c_Groups_Oabs__class_Oabs(_1058025), hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1058025), hAPP(c_Int_Onumber__class_Onumber__of(_1058025), _1058027)))]]], (16159 ^ _773908) ^ [_1050650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1050650)), -(_1050650 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050650), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (51095 ^ _773908) ^ [_1808144] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51091 ^ [_1808144]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36129 ^ _773908) ^ [_1452038, _1452040, _1452042, _1452044, _1452046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1452038), hAPP(c_Set_Oimage(_1452040, _1452038, _1452042), c_Orderings_Otop__class_Otop(tc_fun(_1452040, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1452044), hAPP(c_Set_Oimage(_1452040, _1452044, hAPP(hAPP(c_COMBB(_1452038, _1452044, _1452040), _1452046), _1452042)), c_Orderings_Otop__class_Otop(tc_fun(_1452040, tc_HOL_Obool))))))], (13845 ^ _773908) ^ [_1007088, _1007090] : [class_Rings_Olinordered__idom(_1007088), 13848 ^ _773908 : [(13855 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007088), c_Groups_Ozero__class_Ozero(_1007088)), _1007090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007088), c_Groups_Ozero__class_Ozero(_1007088)), c_Groups_Osgn__class_Osgn(_1007088, _1007090))))], (13849 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007088), c_Groups_Ozero__class_Ozero(_1007088)), c_Groups_Osgn__class_Osgn(_1007088, _1007090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007088), c_Groups_Ozero__class_Ozero(_1007088)), _1007090)))]]], (7049 ^ _773908) ^ [_888123, _888125] : [class_Groups_Omonoid__add(_888123), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888123), c_Groups_Ozero__class_Ozero(_888123)), _888125) = _888125)], (35913 ^ _773908) ^ [_1447696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1447696)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1447696), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447696), c_Orderings_Otop__class_Otop(tc_fun(_1447696, tc_HOL_Obool)))))], (32852 ^ _773908) ^ [_1383937, _1383939, _1383941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1383937, tc_HOL_Obool)), _1383939), _1383941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1383937, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1383937, _1383939)), c_Predicate_OPowp(_1383937, _1383941))))], (27882 ^ _773908) ^ [_1278572, _1278574, _1278576, _1278578] : [class_Lattices_Osemilattice__inf(_1278572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278572), _1278574), _1278576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278572), _1278574), _1278578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278572), _1278574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278572), _1278576), _1278578))))], (41416 ^ _773908) ^ [_1590046, _1590048, _1590050] : [-(_1590046 = c_List_Olist_ONil(_1590048)), -(c_List_Olast(_1590048, hAPP(hAPP(c_List_Olist_OCons(_1590048), _1590050), _1590046)) = c_List_Olast(_1590048, _1590046))], (26436 ^ _773908) ^ [_1247187, _1247189, _1247191] : [-(hAPP(c_Relation_OImage(_1247187, _1247189, _1247191), c_Orderings_Obot__class_Obot(tc_fun(_1247187, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1247189, tc_HOL_Obool)))], (27792 ^ _773908) ^ [_1277042, _1277044, _1277046] : [class_Lattices_Olattice(_1277042), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277042), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277042), _1277044), _1277046)), _1277046)))], (31892 ^ _773908) ^ [_1363998, _1364000, _1364002, _1364004, _1364006] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363998, tc_fun(_1364000, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1363998), _1364002), _1364004)), _1364006) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364000, tc_HOL_Obool)), hAPP(_1364006, _1364002)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363998, tc_fun(_1364000, tc_HOL_Obool)), _1364004), _1364006)))], (41584 ^ _773908) ^ [_1593064, _1593066, _1593068] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1593064)), _1593066), c_List_Olists(_1593064, _1593068)))), 41585 ^ _773908 : [(41588 ^ _773908) ^ [_1593192, _1593194] : [_1593066 = hAPP(hAPP(c_List_Olist_OCons(_1593064), _1593194), _1593192), hBOOL(hAPP(hAPP(c_member(_1593064), _1593194), _1593068)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1593064)), _1593192), c_List_Olists(_1593064, _1593068)))], (41586 ^ _773908) ^ [] : [_1593066 = c_List_Olist_ONil(_1593064)]]], (47996 ^ _773908) ^ [_1741187, _1741189, _1741191, _1741193] : [c_List_Olist__ex(_1741187, _1741189, hAPP(hAPP(c_List_Olist_OCons(_1741187), _1741191), _1741193)), -(hBOOL(hAPP(_1741189, _1741191))), -(c_List_Olist__ex(_1741187, _1741189, _1741193))], (45557 ^ _773908) ^ [_1683880] : [-(hAPP(c_List_Orev(_1683880), c_List_Olist_ONil(_1683880)) = c_List_Olist_ONil(_1683880))], (48826 ^ _773908) ^ [_1758034, _1758036] : [-(c_Wellfounded_Owf(_1758034, _1758036)), 48829 ^ _773908 : [(48832 ^ _773908) ^ [_1758254] : [hBOOL(hAPP(hAPP(c_member(_1758034), _1758254), 48827 ^ [_1758034, _1758036])), 48836 ^ _773908 : [(48839 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758034), 48835 ^ [_1758034, _1758036, _1758254]), 48827 ^ [_1758034, _1758036])))], (48837 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758034, _1758034)), hAPP(hAPP(c_Product__Type_OPair(_1758034, _1758034), 48835 ^ [_1758034, _1758036, _1758254]), _1758254)), _1758036)))]]], (48830 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758034), 48828 ^ [_1758034, _1758036]), 48827 ^ [_1758034, _1758036])))]]], (48605 ^ _773908) ^ [_1753427, _1753429, _1753431, _1753433, _1753435] : [c_Finite__Set_Ofun__left__comm(_1753427, _1753429, _1753431), -(c_Finite__Set_Ofun__left__comm(_1753433, _1753429, hAPP(hAPP(c_COMBB(_1753427, tc_fun(_1753429, _1753429), _1753433), _1753431), _1753435)))], (29205 ^ _773908) ^ [_1306728, _1306730, _1306732] : [class_Lattices_Olattice(_1306728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306728), _1306730)), -(hBOOL(hAPP(hAPP(c_member(_1306728), _1306732), _1306730))), -(_1306730 = c_Orderings_Obot__class_Obot(tc_fun(_1306728, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1306728, hAPP(hAPP(c_Set_Oinsert(_1306728), _1306732), _1306730)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1306728), _1306732), c_Big__Operators_Olattice__class_OInf__fin(_1306728, _1306730)))], (49906 ^ _773908) ^ [_1781975] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1781975)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1781975)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48887 ^ _773908) ^ [_1759402, _1759404, _1759406, _1759408, _1759410, _1759412, _1759414, _1759416] : [c_Finite__Set_Ofolding__image__simple__idem(_1759402, _1759404, _1759406, _1759408, _1759410, _1759412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1759404), _1759414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1759404, tc_HOL_Obool)), _1759416), _1759414)), -(hAPP(hAPP(_1759406, hAPP(_1759412, _1759416)), hAPP(_1759412, _1759414)) = hAPP(_1759412, _1759414))], (31832 ^ _773908) ^ [_1362549, _1362551, _1362553, _1362555, _1362557] : [_1362549 = c_Orderings_Obot__class_Obot(tc_fun(_1362551, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362551, tc_fun(_1362553, tc_HOL_Obool)), _1362549), hAPP(hAPP(c_COMBB(tc_fun(_1362553, tc_HOL_Obool), tc_fun(_1362553, tc_HOL_Obool), _1362551), hAPP(c_Set_Oinsert(_1362553), _1362555)), _1362557)) = c_Orderings_Obot__class_Obot(tc_fun(_1362553, tc_HOL_Obool)))], (17377 ^ _773908) ^ [_1073698, _1073700, _1073702] : [class_Rings_Oring__1__no__zero__divisors(_1073698), -(_1073700 = c_Groups_Ozero__class_Ozero(_1073698)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073698), _1073700), _1073702) = c_Groups_Ozero__class_Ozero(_1073698)], (50983 ^ _773908) ^ [_1805336, _1805338, _1805340, _1805342, _1805344] : [c_Fun_Oinj__on(_1805336, _1805338, _1805340, c_Orderings_Otop__class_Otop(tc_fun(_1805336, tc_HOL_Obool))), hAPP(_1805340, _1805342) = _1805344, -(hAPP(c_Hilbert__Choice_Oinv__into(_1805336, _1805338, c_Orderings_Otop__class_Otop(tc_fun(_1805336, tc_HOL_Obool)), _1805340), _1805344) = _1805342)], (16019 ^ _773908) ^ [_1047660, _1047662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047662), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047660), _1047662)))], (27240 ^ _773908) ^ [_1265942] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1265942)), -(_1265942 = 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))), _1265942)), c_FunDef_Omax__strict)))], (14639 ^ _773908) ^ [_1021422, _1021424, _1021426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021422), _1021424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021426), 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), _1021424), _1021426)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021422), _1021426))))], (51766 ^ _773908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (49692 ^ _773908) ^ [_1776765] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1776765) = c_Lazy__Sequence_Osmall__lazy_H(_1776765, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1776765)))], (12740 ^ _773908) ^ [_987357, _987359, _987361, _987363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987357), _987359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987361), _987363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987357), _987361)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987359), _987363))))], (40161 ^ _773908) ^ [_1559128, _1559130, _1559132] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559128, tc_HOL_Obool)), hAPP(c_List_Oset(_1559128), hAPP(hAPP(c_List_Otake(_1559128), _1559130), _1559132))), hAPP(c_List_Oset(_1559128), _1559132))))], (6672 ^ _773908) ^ [_882256, _882258, _882260] : [class_Orderings_Opreorder(_882256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882256), _882258), _882260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882256), _882260), _882258))], (40917 ^ _773908) ^ [_1579380, _1579382, _1579384, _1579386, _1579388] : [-(hAPP(hAPP(c_List_Ozip(_1579380, _1579382), hAPP(hAPP(c_List_Olist_OCons(_1579380), _1579384), _1579386)), _1579388) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1579380, _1579382)), _1579382, c_List_Olist_ONil(tc_prod(_1579380, _1579382)), hAPP(hAPP(c_COMBC(_1579382, tc_fun(tc_List_Olist(_1579382), tc_List_Olist(tc_prod(_1579380, _1579382))), tc_fun(tc_List_Olist(_1579382), tc_List_Olist(tc_prod(_1579380, _1579382)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1579380, _1579382)), tc_List_Olist(tc_prod(_1579380, _1579382))), tc_fun(tc_fun(tc_List_Olist(_1579382), tc_List_Olist(tc_prod(_1579380, _1579382))), tc_fun(tc_List_Olist(_1579382), tc_List_Olist(tc_prod(_1579380, _1579382)))), _1579382), c_COMBB(tc_List_Olist(tc_prod(_1579380, _1579382)), tc_List_Olist(tc_prod(_1579380, _1579382)), tc_List_Olist(_1579382))), hAPP(hAPP(c_COMBB(tc_prod(_1579380, _1579382), tc_fun(tc_List_Olist(tc_prod(_1579380, _1579382)), tc_List_Olist(tc_prod(_1579380, _1579382))), _1579382), c_List_Olist_OCons(tc_prod(_1579380, _1579382))), hAPP(c_Product__Type_OPair(_1579380, _1579382), _1579384)))), hAPP(c_List_Ozip(_1579380, _1579382), _1579386))), _1579388))], (39424 ^ _773908) ^ [_1539560, _1539562, _1539564, _1539566, _1539568] : [hAPP(hAPP(c_List_Oappend(_1539560), _1539562), hAPP(hAPP(c_List_Olist_OCons(_1539560), _1539564), c_List_Olist_ONil(_1539560))) = hAPP(hAPP(c_List_Oappend(_1539560), _1539566), hAPP(hAPP(c_List_Olist_OCons(_1539560), _1539568), c_List_Olist_ONil(_1539560))), 39427 ^ _773908 : [(39430 ^ _773908) ^ [] : [-(_1539564 = _1539568)], (39428 ^ _773908) ^ [] : [-(_1539562 = _1539566)]]], (45505 ^ _773908) ^ [_1682826, _1682828] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682826)), hAPP(c_List_Orev(_1682826), _1682828)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682826)), _1682828))], (33524 ^ _773908) ^ [_1396695, _1396697] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1396695), _1396697)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1396697), _1396695))], (23775 ^ _773908) ^ [_1189479, _1189481, _1189483] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1189479, _1189479)), hAPP(hAPP(c_Product__Type_OPair(_1189479, _1189479), _1189481), _1189481)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1189479, _1189479), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189483))))], (20061 ^ _773908) ^ [_1120151] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120151))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1120151)))))], (36799 ^ _773908) ^ [_1467216, _1467218, _1467220, _1467222, _1467224] : [-(hAPP(c_Fun_Othe__inv__into(_1467216, _1467218, _1467220, _1467222), _1467224) = c_HOL_OThe(_1467216, hAPP(hAPP(c_COMBS(_1467216, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467216), c_fconj), hAPP(hAPP(c_COMBC(_1467216, tc_fun(_1467216, tc_HOL_Obool), tc_HOL_Obool), c_member(_1467216)), _1467220))), hAPP(hAPP(c_COMBC(_1467216, _1467218, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1467218, tc_fun(_1467218, tc_HOL_Obool), _1467216), c_fequal), _1467222)), _1467224))))], (33306 ^ _773908) ^ [_1392781, _1392783, _1392785, _1392787, _1392789] : [c_Fun_Oinj__on(_1392781, _1392783, _1392785, _1392787), -(c_Fun_Oinj__on(_1392781, _1392783, _1392785, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392781, tc_HOL_Obool)), _1392787), _1392789)))], (6998 ^ _773908) ^ [_887248, _887250] : [class_Groups_Olinordered__ab__group__add(_887248), 7001 ^ _773908 : [(7008 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887248), c_Groups_Ozero__class_Ozero(_887248)), _887250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887248), c_Groups_Ozero__class_Ozero(_887248)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_887248), _887250), _887250))))], (7002 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887248), c_Groups_Ozero__class_Ozero(_887248)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_887248), _887250), _887250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887248), c_Groups_Ozero__class_Ozero(_887248)), _887250)))]]], (43639 ^ _773908) ^ [_1641699, _1641701, _1641703] : [hBOOL(hAPP(c_List_Odistinct(_1641699), _1641701)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1641699)), c_Enum_On__lists(_1641699, _1641703, _1641701))))], (19929 ^ _773908) ^ [_1117813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1117813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1117813))))], (45675 ^ _773908) ^ [_1686447, _1686449] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1686447), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1686447))), _1686449))), 45678 ^ _773908 : [(45685 ^ _773908) ^ [] : [-(_1686449 = c_List_Olist_ONil(tc_List_Olist(_1686447))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686447))), c_List_Otranspose(_1686447, _1686449)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686447)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1686447)), _1686449), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45679 ^ _773908) ^ [] : [_1686449 = c_List_Olist_ONil(tc_List_Olist(_1686447)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686447))), c_List_Otranspose(_1686447, _1686449)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11868 ^ _773908) ^ [_972336, _972338, _972340, _972342] : [class_Rings_Olinordered__semiring__strict(_972336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972336), _972338), _972340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972336), _972342), _972340))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972336), c_Groups_Ozero__class_Ozero(_972336)), _972340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972336), _972338), _972342)))], (40179 ^ _773908) ^ [_1559542, _1559544] : [_1559544 = c_List_Olist_ONil(_1559542), -(c_Orderings_Obot__class_Obot(tc_fun(_1559542, tc_HOL_Obool)) = hAPP(c_List_Oset(_1559542), _1559544))], (20093 ^ _773908) ^ [_1120623] : [-(c_Int_Osucc(c_Int_OBit0(_1120623)) = c_Int_OBit1(_1120623))], (6150 ^ _773908) ^ [_873597] : [hAPP(c_Nat_OSuc, _873597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33328 ^ _773908) ^ [_1393135, _1393137, _1393139, _1393141, _1393143] : [class_Orderings_Olinorder(_1393135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393135), _1393137), _1393139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393135), _1393141), _1393143)), 33339 ^ _773908 : [(33348 ^ _773908) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393135, _1393137), _1393139) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393135, _1393141), _1393143)), _1393137 = _1393141, _1393139 = _1393143], (33340 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393135, _1393137), _1393139) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393135, _1393141), _1393143), 33343 ^ _773908 : [(33346 ^ _773908) ^ [] : [-(_1393139 = _1393143)], (33344 ^ _773908) ^ [] : [-(_1393137 = _1393141)]]]]], (26665 ^ _773908) ^ [_1253303, _1253305, _1253307, _1253309] : [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), _1253303), _1253305)), 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), _1253307), _1253309)), 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), _1253303), _1253309)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253307), _1253305))))], (34436 ^ _773908) ^ [_1415099, _1415101, _1415103] : [class_Orderings_Olinorder(_1415099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415099), _1415101), _1415103)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415099, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1415099), _1415101)), c_SetInterval_Oord__class_OatLeastAtMost(_1415099, _1415101, _1415103)) = hAPP(c_SetInterval_Oord__class_OatMost(_1415099), _1415103))], (25361 ^ _773908) ^ [_1221997, _1221999] : [class_Orderings_Olinorder(_1221997), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221997), _1221999), _1221999) = _1221999)], (51372 ^ _773908) ^ [_1812982, _1812984] : [class_Groups_Ouminus(_1812982), -(class_Groups_Ouminus(tc_fun(_1812984, _1812982)))], (24689 ^ _773908) ^ [_1209067, _1209069, _1209071, _1209073, _1209075] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1209067, _1209069, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1209067)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1209067), hAPP(hAPP(c_COMBC(_1209067, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1209067), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1209071)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1209073)), _1209075))), c_Com_Ocom_OAss(_1209073, _1209075)), _1209071)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1209067), tc_HOL_Obool)))))], (26699 ^ _773908) ^ [_1254201, _1254203] : [_1254201 = _1254203, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254201) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254203))], (40851 ^ _773908) ^ [_1577084, _1577086, _1577088, _1577090] : [40853 ^ _773908 : [(40856 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1577084, _1577084, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1577084, tc_fun(_1577084, _1577086), tc_fun(_1577084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577086, tc_HOL_Obool), tc_fun(tc_fun(_1577084, _1577086), tc_fun(_1577084, tc_HOL_Obool)), _1577084), c_COMBB(_1577086, tc_HOL_Obool, _1577084)), hAPP(hAPP(c_COMBB(_1577086, tc_fun(_1577086, tc_HOL_Obool), _1577084), c_fequal), _1577090))), _1577090)), 40852 ^ [_1577084, _1577086, _1577088, _1577090]))], (40854 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577084, _1577084)), 40852 ^ [_1577084, _1577086, _1577088, _1577090]), _1577088)))]], -(c_Equiv__Relations_Ocongruent(_1577084, _1577086, _1577088, _1577090))], (25047 ^ _773908) ^ [_1215850, _1215852, _1215854, _1215856, _1215858, _1215860, _1215862, _1215864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1215850, _1215852), tc_prod(_1215850, _1215852))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1215850, _1215852), tc_prod(_1215850, _1215852)), hAPP(hAPP(c_Product__Type_OPair(_1215850, _1215852), _1215854), _1215856)), hAPP(hAPP(c_Product__Type_OPair(_1215850, _1215852), _1215858), _1215860))), c_Wellfounded_Olex__prod(_1215850, _1215852, _1215862, _1215864))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1215850, _1215850)), hAPP(hAPP(c_Product__Type_OPair(_1215850, _1215850), _1215854), _1215858)), _1215862))), 25054 ^ _773908 : [(25057 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1215852, _1215852)), hAPP(hAPP(c_Product__Type_OPair(_1215852, _1215852), _1215856), _1215860)), _1215864)))], (25055 ^ _773908) ^ [] : [-(_1215854 = _1215858)]]], (45143 ^ _773908) ^ [_1675735, _1675737] : [-(c_List_Oremdups(_1675735, c_List_Oremdups(_1675735, _1675737)) = c_List_Oremdups(_1675735, _1675737))], (11507 ^ _773908) ^ [_965984, _965986, _965988] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965984), _965986)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965988), _965986)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965984), _965988))], (34193 ^ _773908) ^ [_1410519, _1410521] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1410519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1410521), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1410519, _1410521))], (37771 ^ _773908) ^ [_1491462] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1491462), c_Int_OInteg)), -(_1491462 = hAPP(c_Int_ORep__Integ, 37774 ^ [_1491462]))], (40382 ^ _773908) ^ [_1564193, _1564195, _1564197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1564193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1564195)), _1564197))), -(hBOOL(hAPP(hAPP(c_member(_1564195), hAPP(hAPP(c_List_Onth(_1564195), _1564197), _1564193)), hAPP(c_List_Oset(_1564195), _1564197))))], (37722 ^ _773908) ^ [_1489926, _1489928, _1489930, _1489932, _1489934, _1489936, _1489938, _1489940, _1489942, _1489944] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1489926, _1489928), tc_prod(_1489930, _1489932), tc_prod(_1489934, _1489936), c_Product__Type_Omap__pair(_1489926, _1489930, _1489928, _1489932, _1489938, _1489940)), c_Product__Type_Omap__pair(_1489934, _1489926, _1489936, _1489928, _1489942, _1489944)) = c_Product__Type_Omap__pair(_1489934, _1489930, _1489936, _1489932, hAPP(c_Fun_Ocomp(_1489926, _1489930, _1489934, _1489938), _1489942), hAPP(c_Fun_Ocomp(_1489928, _1489932, _1489936, _1489940), _1489944)))], (22121 ^ _773908) ^ [_1156705, _1156707, _1156709, _1156711] : [class_Fields_Olinordered__field(_1156705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156705), _1156707), c_Groups_Ozero__class_Ozero(_1156705))), 22128 ^ _773908 : [(22135 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156705), _1156711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156705), _1156709), _1156707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156705), _1156709), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156705), _1156711), _1156707))))], (22129 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156705), _1156709), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156705), _1156711), _1156707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156705), _1156711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156705), _1156709), _1156707))))]]], (41278 ^ _773908) ^ [_1587249, _1587251, _1587253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1587249), _1587251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1587249), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1587251), _1587253))))], (15433 ^ _773908) ^ [_1035763, _1035765, _1035767] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035763), _1035765)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035767), _1035765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035763), _1035767))], (39609 ^ _773908) ^ [_1544048, _1544050, _1544052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544048), tc_List_Olist(_1544048))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544048), tc_List_Olist(_1544048)), _1544050), c_List_Olist_ONil(_1544048))), c_List_Olistrel1(_1544048, _1544052)))], (5224 ^ _773908) ^ [_853794, _853796, _853798, _853800] : [-(c_List_Olistrel(_853800, _853796) = c_List_Olistrel(_853798, _853794)), _853800 = _853798, _853796 = _853794], (49604 ^ _773908) ^ [_1775052, _1775054, _1775056] : [-(_1775052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1775054), c_List_Oreplicate(_1775054, _1775052, _1775056)) = hAPP(hAPP(c_Set_Oinsert(_1775054), _1775056), c_Orderings_Obot__class_Obot(tc_fun(_1775054, tc_HOL_Obool))))], (19089 ^ _773908) ^ [_1103650, _1103652] : [19090 ^ _773908 : [(19093 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103650), c_Int_OPls))], (19091 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103650), _1103652))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103650)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103652))))], (37898 ^ _773908) ^ [_1494048] : [class_Lattices_Osemilattice__inf(_1494048), -(c_Finite__Set_Ofun__left__comm__idem(_1494048, _1494048, c_Lattices_Osemilattice__inf__class_Oinf(_1494048)))], (51848 ^ _773908) ^ [_1817676, _1817678, _1817680, _1817682] : [-(hAPP(hAPP(c_COMBK(_1817676, _1817678), _1817680), _1817682) = _1817680)], (23708 ^ _773908) ^ [_1187922, _1187924, _1187926, _1187928, _1187930, _1187932] : [hAPP(hAPP(c_Product__Type_OPair(_1187922, _1187924), _1187926), _1187928) = hAPP(hAPP(c_Product__Type_OPair(_1187922, _1187924), _1187930), _1187932), 23711 ^ _773908 : [(23714 ^ _773908) ^ [] : [-(_1187928 = _1187932)], (23712 ^ _773908) ^ [] : [-(_1187926 = _1187930)]]], (19595 ^ _773908) ^ [_1111955, _1111957, _1111959] : [class_Rings_Osemiring__1(_1111955), hBOOL(hAPP(hAPP(c_member(_1111955), _1111957), c_Nat_Osemiring__1__class_ONats(_1111955))), hBOOL(hAPP(hAPP(c_member(_1111955), _1111959), c_Nat_Osemiring__1__class_ONats(_1111955))), -(hBOOL(hAPP(hAPP(c_member(_1111955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111955), _1111957), _1111959)), c_Nat_Osemiring__1__class_ONats(_1111955))))], (12917 ^ _773908) ^ [_990505, _990507, _990509, _990511] : [c_Hoare__Mirabelle_Ohoare__derivs(_990505, _990507, _990509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_990505), tc_HOL_Obool)), _990511), _990509)), -(c_Hoare__Mirabelle_Ohoare__derivs(_990505, _990507, _990511))], (20177 ^ _773908) ^ [_1122159] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1122159)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1122159)))], (43880 ^ _773908) ^ [_1647159, _1647161, _1647163] : [-(hAPP(c_Set_Oimage(tc_prod(_1647159, _1647161), _1647159, c_Product__Type_Ofst(_1647159, _1647161)), _1647163) = hAPP(c_Relation_ODomain(_1647159, _1647161), _1647163))], (43555 ^ _773908) ^ [_1639558, _1639560, _1639562, _1639564, _1639566] : [-(c_List_Olist__all2(_1639558, _1639560, _1639562, _1639564, _1639566)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639558)), _1639564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639560)), _1639566), 43561 ^ _773908 : [(43564 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1639562, hAPP(hAPP(c_List_Onth(_1639558), _1639564), 43560 ^ [_1639558, _1639560, _1639562, _1639564, _1639566])), hAPP(hAPP(c_List_Onth(_1639560), _1639566), 43560 ^ [_1639558, _1639560, _1639562, _1639564, _1639566])))], (43562 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43560 ^ [_1639558, _1639560, _1639562, _1639564, _1639566]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639558)), _1639564))))]]], (45183 ^ _773908) ^ [_1676316, _1676318, _1676320] : [hBOOL(hAPP(c_List_Odistinct(_1676316), _1676318)), -(c_List_Oremove1(_1676316, _1676320, c_List_Oremdups(_1676316, _1676318)) = c_List_Oremdups(_1676316, c_List_Oremove1(_1676316, _1676320, _1676318)))], (19647 ^ _773908) ^ [_1112840] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1112840))) = 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)))), _1112840))], (35895 ^ _773908) ^ [_1447404, _1447406] : [-(c_Sum__Type_OPlus(_1447404, _1447406, c_Orderings_Otop__class_Otop(tc_fun(_1447404, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1447406, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1447404, _1447406), tc_HOL_Obool)))], (29615 ^ _773908) ^ [_1314502, _1314504, _1314506] : [class_Orderings_Olinorder(_1314502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314502), _1314504)), -(_1314504 = c_Orderings_Obot__class_Obot(tc_fun(_1314502, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314502), _1314506)), -(_1314506 = c_Orderings_Obot__class_Obot(tc_fun(_1314502, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1314502, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314502, tc_HOL_Obool)), _1314504), _1314506)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314502), c_Big__Operators_Olinorder__class_OMin(_1314502, _1314504)), c_Big__Operators_Olinorder__class_OMin(_1314502, _1314506)))], (4424 ^ _773908) ^ [_841240, _841242, _841244, _841246, _841248, _841250, _841252, _841254] : [-(c_New__Random__Sequence_Opos__bind(_841254, _841250, _841246, _841242) = c_New__Random__Sequence_Opos__bind(_841252, _841248, _841244, _841240)), _841254 = _841252, _841250 = _841248, _841246 = _841244, _841242 = _841240], (8531 ^ _773908) ^ [_914834, _914836, _914838] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _914834), _914836)), _914838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _914834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _914836), _914838)))], (16153 ^ _773908) ^ [_1050604, _1050606] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050604), _1050606))), -(c_Nat__Transfer_Otsub(_1050606, _1050604) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19579 ^ _773908) ^ [_1111725] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1111725)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1111725)))], (41800 ^ _773908) ^ [_1597298, _1597300, _1597302, _1597304] : [class_Complete__Lattice_Ocomplete__lattice(_1597298), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597300, _1597298), hAPP(c_List_Oset(_1597300), _1597302)), _1597304) = hAPP(c_List_Ofoldl(_1597298, _1597300, hAPP(c_COMBC(_1597300, _1597298, _1597298), hAPP(hAPP(c_COMBB(_1597298, tc_fun(_1597298, _1597298), _1597300), c_Lattices_Osemilattice__inf__class_Oinf(_1597298)), _1597304)), c_Orderings_Otop__class_Otop(_1597298)), _1597302))], (1274 ^ _773908) ^ [_792819, _792821] : [-(class_Groups_Ogroup__add(_792819)), _792821 = _792819, class_Groups_Ogroup__add(_792821)], (23606 ^ _773908) ^ [_1185624, _1185626, _1185628, _1185630, _1185632, _1185634, _1185636] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185624, _1185626), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1185628), _1185630))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185632, _1185626), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1185634), _1185636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185626)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185624), _1185632), _1185626), 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), _1185628), _1185634)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185630), _1185636)), _1185626))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185630), _1185636), _1185626)))))], (47339 ^ _773908) ^ [_1725361, _1725363, _1725365] : [c_Relation_Ototal__on(_1725361, _1725363, _1725365), -(c_Relation_Ototal__on(_1725361, _1725363, hAPP(c_Relation_Oconverse(_1725361, _1725361), _1725365)))], (22875 ^ _773908) ^ [_1170739, _1170741] : [c_Code__Numeral_OSuc__code__numeral(_1170739) = c_Code__Numeral_OSuc__code__numeral(_1170741), -(_1170739 = _1170741)], (50452 ^ _773908) ^ [_1795285, _1795287] : [c_Predicate_Oreflp(_1795285, _1795287), c_Predicate_Osymp(_1795285, _1795287), c_Predicate_Otransp(_1795285, _1795287), -(c_Equiv__Relations_Oequivp(_1795285, _1795287))], (19965 ^ _773908) ^ [_1118449, _1118451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118449), _1118451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1118449)), c_Int_OBit1(_1118451))))], (40989 ^ _773908) ^ [_1581370, _1581372, _1581374, _1581376] : [-(hAPP(c_List_Orotate1(_1581370), c_List_Olist_ONil(_1581370)) = c_List_Olist_ONil(_1581370))], (32472 ^ _773908) ^ [_1376689, _1376691, _1376693] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1376689, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1376689, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1376689), _1376691)), hAPP(c_Set_OPow(_1376689), _1376693))), hAPP(c_Set_OPow(_1376689), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376689, tc_HOL_Obool)), _1376691), _1376693)))))], (1644 ^ _773908) ^ [_797444, _797446] : [-(class_Rings_Olinordered__semidom(_797444)), _797446 = _797444, class_Rings_Olinordered__semidom(_797446)], (33586 ^ _773908) ^ [_1397679, _1397681, _1397683, _1397685] : [class_Orderings_Olinorder(_1397679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397679), _1397681), _1397683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397679), _1397683), _1397685)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397679, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397679, _1397681), _1397683)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397679, _1397683), _1397685)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397679, _1397681), _1397685))], (49304 ^ _773908) ^ [_1768485, _1768487, _1768489, _1768491, _1768493] : [-(hAPP(c_New__DSequence_Opos__bind(_1768485, _1768487, _1768489, _1768491), _1768493) = hAPP(c_Lazy__Sequence_Obind(_1768485, _1768487, hAPP(_1768489, _1768493)), hAPP(hAPP(c_COMBC(_1768485, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1768487)), _1768491), _1768493)))], (1184 ^ _773908) ^ [_791694, _791696] : [-(class_Rings_Oring__no__zero__divisors(_791694)), _791696 = _791694, class_Rings_Oring__no__zero__divisors(_791696)], (32514 ^ _773908) ^ [_1377445, _1377447, _1377449] : [class_Orderings_Oorder(_1377445), 32517 ^ _773908 : [(32524 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377445), _1377447), _1377449))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1377445, _1377447, _1377449) = c_Orderings_Obot__class_Obot(tc_fun(_1377445, tc_HOL_Obool)))], (32518 ^ _773908) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1377445, _1377447, _1377449) = c_Orderings_Obot__class_Obot(tc_fun(_1377445, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377445), _1377447), _1377449))]]], (45609 ^ _773908) ^ [_1685063, _1685065] : [-(_1685063 = c_List_Olist_ONil(_1685065)), -(hAPP(c_List_Ohd(_1685065), hAPP(c_List_Orev(_1685065), _1685063)) = c_List_Olast(_1685065, _1685063))], (42566 ^ _773908) ^ [_1618184, _1618186, _1618188, _1618190, _1618192, _1618194, _1618196] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618184, tc_fun(_1618186, tc_fun(_1618188, tc_HOL_Obool))), _1618190), _1618192), _1618194), _1618196)), 42569 ^ _773908 : [(42570 ^ _773908) ^ [_1618312] : [hBOOL(hAPP(hAPP(c_member(_1618184), _1618312), _1618190)), -(hBOOL(hAPP(hAPP(hAPP(_1618192, _1618312), _1618194), _1618196)))]]], (39368 ^ _773908) ^ [_1538573, _1538575, _1538577] : [_1538577 = c_List_Olist_ONil(_1538575), -(_1538573 = hAPP(hAPP(c_List_Oappend(_1538575), _1538577), _1538573))], (38002 ^ _773908) ^ [_1496264, _1496266, _1496268] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496264), hAPP(c_Set_OCollect(_1496264), hAPP(hAPP(c_COMBS(_1496264, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496264), c_fdisj), _1496266)), _1496268))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496264), hAPP(c_Set_OCollect(_1496264), _1496266))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496264), hAPP(c_Set_OCollect(_1496264), _1496268)))], (4990 ^ _773908) ^ [_850105, _850107, _850109, _850111] : [-(c_Product__Type_Ofst(_850111, _850107) = c_Product__Type_Ofst(_850109, _850105)), _850111 = _850109, _850107 = _850105], (19029 ^ _773908) ^ [_1102687] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102687), c_Int_OPls)))], (50307 ^ _773908) ^ [_1792439, _1792441] : [50310 ^ _773908 : [(50316 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1792439, _1792439)), hAPP(hAPP(c_Product__Type_OPair(_1792439, _1792439), 50308 ^ [_1792439, _1792441]), 50312 ^ [_1792439, _1792441])), _1792441))], (50314 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1792439, _1792439)), hAPP(hAPP(c_Product__Type_OPair(_1792439, _1792439), 50309 ^ [_1792439, _1792441]), 50312 ^ [_1792439, _1792441])), _1792441)))], (50311 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1792439, _1792439)), hAPP(hAPP(c_Product__Type_OPair(_1792439, _1792439), 50308 ^ [_1792439, _1792441]), 50309 ^ [_1792439, _1792441])), _1792441)))]], -(c_Relation_Otrans(_1792439, _1792441))], (2762 ^ _773908) ^ [_814965, _814967, _814969, _814971] : [-(c_Nitpick_Onorm__frac(_814971, _814967) = c_Nitpick_Onorm__frac(_814969, _814965)), _814971 = _814969, _814967 = _814965], (33520 ^ _773908) ^ [_1396628, _1396630] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1396628), hAPP(c_Nat_OSuc, _1396630)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1396628, _1396630))], (25101 ^ _773908) ^ [_1217402, _1217404, _1217406] : [class_Orderings_Olinorder(_1217402), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217402), _1217404), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217402), _1217404), _1217406)) = _1217404)], (17775 ^ _773908) ^ [_1081103] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081103))), -(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), _1081103)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24837 ^ _773908) ^ [_1212005] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28805 ^ _773908) ^ [_1299977, _1299979, _1299981] : [class_Lattices_Olattice(_1299977), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299977), _1299979)), hBOOL(hAPP(hAPP(c_member(_1299977), _1299981), _1299979)), 28816 ^ _773908 : [(28823 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299977, tc_HOL_Obool)), _1299979), hAPP(hAPP(c_Set_Oinsert(_1299977), _1299981), c_Orderings_Obot__class_Obot(tc_fun(_1299977, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1299977, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1299977, _1299979) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299977), _1299981), c_Big__Operators_Olattice__class_OInf__fin(_1299977, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299977, tc_HOL_Obool)), _1299979), hAPP(hAPP(c_Set_Oinsert(_1299977), _1299981), c_Orderings_Obot__class_Obot(tc_fun(_1299977, tc_HOL_Obool)))))))], (28817 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299977, tc_HOL_Obool)), _1299979), hAPP(hAPP(c_Set_Oinsert(_1299977), _1299981), c_Orderings_Obot__class_Obot(tc_fun(_1299977, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1299977, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1299977, _1299979) = _1299981)]]], (43733 ^ _773908) ^ [_1643752, _1643754, _1643756, _1643758] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643752, tc_HOL_Obool), tc_fun(_1643754, tc_HOL_Obool)), _1643756), hAPP(hAPP(c_COMBC(tc_fun(_1643752, tc_HOL_Obool), tc_fun(_1643752, tc_fun(_1643754, tc_HOL_Obool)), tc_fun(_1643754, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1643752, tc_fun(_1643754, tc_HOL_Obool))), _1643758)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1643752, tc_fun(_1643754, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643752, tc_HOL_Obool), _1643756)), _1643758))], (8341 ^ _773908) ^ [_911352, _911354, _911356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _911352), _911354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911352), _911356)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911354), _911356))))], (47485 ^ _773908) ^ [_1728941, _1728943, _1728945, _1728947, _1728949] : [c_Relation_Osingle__valued(_1728941, _1728943, _1728945), c_Relation_Osingle__valued(_1728943, _1728947, _1728949), -(c_Relation_Osingle__valued(_1728941, _1728947, hAPP(hAPP(c_Relation_Orel__comp(_1728941, _1728943, _1728947), _1728945), _1728949)))], (51448 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (26729 ^ _773908) ^ [_1254728, _1254730] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254728)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254730))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1254728), _1254730)))], (36414 ^ _773908) ^ [_1459495, _1459497] : [c_Equiv__Relations_Oequivp(_1459495, _1459497), 36417 ^ _773908 : [(36424 ^ _773908) ^ [_1459688, _1459690] : [hAPP(_1459497, _1459690) = hAPP(_1459497, _1459688), -(hBOOL(hAPP(hAPP(_1459497, _1459690), _1459688)))], (36418 ^ _773908) ^ [_1459589, _1459591] : [hBOOL(hAPP(hAPP(_1459497, _1459591), _1459589)), -(hAPP(_1459497, _1459591) = hAPP(_1459497, _1459589))]]], (7741 ^ _773908) ^ [_899721, _899723, _899725, _899727] : [hAPP(c_Com_Ocom_OBODY, _899721) = c_Com_Ocom_OCond(_899723, _899725, _899727)], (49292 ^ _773908) ^ [_1768005, _1768007, _1768009, _1768011, _1768013, _1768015, _1768017] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1768005, _1768007, _1768009, _1768011, _1768013, _1768015, _1768017) = c_New__DSequence_Oneg__decr__bind(_1768005, _1768007, hAPP(hAPP(hAPP(_1768009, _1768013), _1768015), _1768017), hAPP(hAPP(c_COMBC(_1768005, 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(_1768007)))), hAPP(hAPP(c_COMBC(_1768005, 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(_1768007))))), hAPP(hAPP(c_COMBC(_1768005, 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(_1768007)))))), _1768011), _1768013)), _1768015)), _1768017)))], (51708 ^ _773908) ^ [_1816230] : [class_Enum_Oenum(_1816230), -(class_Enum_Oenum(tc_Option_Ooption(_1816230)))], (3746 ^ _773908) ^ [_830427, _830429] : [_830429 = _830427, -(c_Relation_OField(_830429) = c_Relation_OField(_830427))], (30137 ^ _773908) ^ [_1324409, _1324411, _1324413] : [class_Orderings_Olinorder(_1324409), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324409), _1324411)), -(_1324413 = c_Orderings_Obot__class_Obot(tc_fun(_1324409, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324409, tc_HOL_Obool)), _1324413), _1324411)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324409), c_Big__Operators_Olattice_OInf__fin(_1324409, c_Orderings_Oord__class_Omin(_1324409), _1324413)), c_Big__Operators_Olattice_OInf__fin(_1324409, c_Orderings_Oord__class_Omin(_1324409), _1324411)) = c_Big__Operators_Olattice_OInf__fin(_1324409, c_Orderings_Oord__class_Omin(_1324409), _1324411))], (12568 ^ _773908) ^ [_984524] : [_984524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984524), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32774 ^ _773908) ^ [_1382368, _1382370, _1382372] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1382368, tc_HOL_Obool)), _1382372), hAPP(c_Set_OPow(_1382368), _1382370))), -(hBOOL(hAPP(c_Predicate_OPowp(_1382368, hAPP(hAPP(c_COMBC(_1382368, tc_fun(_1382368, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382368)), _1382370)), _1382372)))], (26331 ^ _773908) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (38496 ^ _773908) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (28434 ^ _773908) ^ [_1291046, _1291048, _1291050] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1291046, tc_HOL_Obool)), _1291048), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1291046, tc_HOL_Obool)), _1291050)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291046, tc_HOL_Obool)), _1291048), _1291050))], (39733 ^ _773908) ^ [_1547517, _1547519, _1547521] : [-(c_List_Olistset(_1547517, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1547517, tc_HOL_Obool)), _1547519), _1547521)) = c_List_Oset__Cons(_1547517, _1547519, c_List_Olistset(_1547517, _1547521)))], (38745 ^ _773908) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (13360 ^ _773908) ^ [_998251] : [_998251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _998251) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4878 ^ _773908) ^ [_848289, _848291, _848293, _848295, _848297, _848299, _848301, _848303, _848305, _848307] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_848307, _848303, _848299, _848295, _848291) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_848305, _848301, _848297, _848293, _848289)), _848307 = _848305, _848303 = _848301, _848299 = _848297, _848295 = _848293, _848291 = _848289], (30355 ^ _773908) ^ [_1328592, _1328594] : [30356 ^ _773908 : [(30359 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1328592), _1328594)))], (30357 ^ _773908) ^ [] : [_1328594 = c_Orderings_Obot__class_Obot(tc_fun(_1328592, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1328592), _1328594) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (444 ^ _773908) ^ [_780752, _780754] : [-(c_Nat__Transfer_Onat__set(_780752)), _780754 = _780752, c_Nat__Transfer_Onat__set(_780754)], (1484 ^ _773908) ^ [_795444, _795446] : [-(class_Groups_Ouminus(_795444)), _795446 = _795444, class_Groups_Ouminus(_795446)], (42228 ^ _773908) ^ [_1609749, _1609751, _1609753, _1609755, _1609757, _1609759] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609749, tc_fun(_1609751, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609753, tc_fun(_1609749, tc_HOL_Obool)), _1609755), _1609757)), _1609759) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609753, tc_fun(_1609751, tc_HOL_Obool)), _1609755), hAPP(hAPP(c_COMBC(_1609753, tc_fun(_1609749, tc_fun(_1609751, tc_HOL_Obool)), tc_fun(_1609751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609749, tc_HOL_Obool), tc_fun(tc_fun(_1609749, tc_fun(_1609751, tc_HOL_Obool)), tc_fun(_1609751, tc_HOL_Obool)), _1609753), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609749, tc_fun(_1609751, tc_HOL_Obool))), _1609757)), _1609759)))], (19537 ^ _773908) ^ [_1111105] : [class_Int_Onumber__ring(_1111105), -(c_Groups_Oone__class_Oone(_1111105) = hAPP(c_Int_Onumber__class_Onumber__of(_1111105), c_Int_OBit1(c_Int_OPls)))], (38304 ^ _773908) ^ [_1506561, _1506563, _1506565] : [class_Groups_Olinordered__ab__semigroup__add(_1506561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506561), _1506563)), -(_1506563 = c_Orderings_Obot__class_Obot(tc_fun(_1506561, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1506561), _1506565), c_Big__Operators_Olinorder__class_OMax(_1506561, _1506563)) = c_Big__Operators_Olinorder__class_OMax(_1506561, hAPP(c_Set_OCollect(_1506561), hAPP(hAPP(c_COMBB(tc_fun(_1506561, tc_HOL_Obool), tc_HOL_Obool, _1506561), c_HOL_OEx(_1506561)), hAPP(hAPP(c_COMBC(_1506561, tc_fun(_1506561, tc_HOL_Obool), tc_fun(_1506561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506561, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506561, tc_HOL_Obool), tc_fun(_1506561, tc_HOL_Obool)), _1506561), c_COMBS(_1506561, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506561, tc_HOL_Obool), tc_fun(_1506561, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506561), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506561), c_fconj)), hAPP(hAPP(c_COMBC(_1506561, tc_fun(_1506561, _1506561), tc_fun(_1506561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506561, tc_HOL_Obool), tc_fun(tc_fun(_1506561, _1506561), tc_fun(_1506561, tc_HOL_Obool)), _1506561), c_COMBB(_1506561, tc_HOL_Obool, _1506561)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1506561), _1506565))))), hAPP(hAPP(c_COMBC(_1506561, tc_fun(_1506561, tc_HOL_Obool), tc_HOL_Obool), c_member(_1506561)), _1506563))))))], (4746 ^ _773908) ^ [_846267, _846269, _846271, _846273] : [-(c_Wellfounded_Oaccp(_846273, _846269) = c_Wellfounded_Oaccp(_846271, _846267)), _846273 = _846271, _846269 = _846267], (30599 ^ _773908) ^ [_1333758, _1333760, _1333762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333758), _1333760)), -(hAPP(c_Finite__Set_Ocard(_1333758), hAPP(hAPP(c_Set_Oinsert(_1333758), _1333762), _1333760)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1333758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333758, tc_HOL_Obool)), _1333760), hAPP(hAPP(c_Set_Oinsert(_1333758), _1333762), c_Orderings_Obot__class_Obot(tc_fun(_1333758, tc_HOL_Obool)))))))], (49720 ^ _773908) ^ [_1777600] : [-(c_Lazy__Sequence_Oyieldn(_1777600) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1777600), _1777600, c_Lazy__Sequence_Oyield(_1777600)))], (12502 ^ _773908) ^ [_983431] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983431), _983431)))], (37042 ^ _773908) ^ [_1471687, _1471689, _1471691, _1471693] : [c_Big__Operators_Osemilattice__big(_1471687, _1471689, _1471691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471687), _1471693)), -(hAPP(_1471691, _1471693) = hAPP(c_Finite__Set_Ofold1(_1471687, _1471689), _1471693))], (51290 ^ _773908) ^ [_1811905, _1811907] : [class_Lattices_Obounded__lattice(_1811905), -(class_Lattices_Obounded__lattice__top(tc_fun(_1811907, _1811905)))], (26510 ^ _773908) ^ [_1248961, _1248963, _1248965, _1248967, _1248969] : [-(hBOOL(hAPP(hAPP(c_member(_1248961), _1248963), hAPP(c_Set_Oimage(_1248965, _1248961, _1248967), _1248969)))), 26511 ^ _773908 : [(26512 ^ _773908) ^ [_1249031] : [hBOOL(hAPP(hAPP(c_member(_1248965), _1249031), _1248969)), _1248963 = hAPP(_1248967, _1249031)]]], (36159 ^ _773908) ^ [_1452591, _1452593, _1452595, _1452597] : [c_Fun_Oinj__on(_1452591, _1452593, _1452595, c_Orderings_Otop__class_Otop(tc_fun(_1452591, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1452591, tc_fun(_1452597, _1452593), hAPP(hAPP(c_COMBB(_1452593, tc_fun(_1452597, _1452593), _1452591), c_COMBK(_1452593, _1452597)), _1452595), c_Orderings_Otop__class_Otop(tc_fun(_1452591, tc_HOL_Obool))))], (28703 ^ _773908) ^ [_1297896, _1297898, _1297900, _1297902, _1297904, _1297906] : [hBOOL(hAPP(hAPP(c_member(_1297896), _1297898), c_SetInterval_Oord_OgreaterThanAtMost(_1297896, _1297900, _1297902, _1297904, _1297906))), 28706 ^ _773908 : [(28709 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1297900, _1297898), _1297906)))], (28707 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1297902, _1297904), _1297898)))]]], (6948 ^ _773908) ^ [_886334, _886336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886334), _886336)), _886336))], (49308 ^ _773908) ^ [_1768611, _1768613, _1768615, _1768617, _1768619] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1768611), _1768613), _1768615), _1768617), _1768619) = c_New__DSequence_Oneg__single(_1768611, _1768613))], (38048 ^ _773908) ^ [_1497153, _1497155, _1497157] : [-(hAPP(hAPP(c_Set_Oinsert(_1497153), _1497155), _1497157) = hAPP(c_Set_OCollect(_1497153), hAPP(hAPP(c_COMBS(_1497153, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497153), c_fdisj), hAPP(hAPP(c_COMBC(_1497153, _1497153, tc_HOL_Obool), c_fequal), _1497155))), hAPP(hAPP(c_COMBC(_1497153, tc_fun(_1497153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497153)), _1497157))))], (23480 ^ _773908) ^ [_1183314, _1183316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1183314), _1183316)), -(c_Divides_Odivmod__nat(_1183314, _1183316) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183314))], (49414 ^ _773908) ^ [_1771610, _1771612, _1771614] : [-(_1771610 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1771612), c_List_Oreplicate(_1771612, _1771610, _1771614)) = c_List_Oreplicate(_1771612, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1771610), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1771614))], (18923 ^ _773908) ^ [] : [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)], (20055 ^ _773908) ^ [_1120056] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1120056)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1120056))))], (12825 ^ _773908) ^ [_989005, _989007, _989009, _989011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989005), _989007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989009), _989011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989005), _989009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989007), _989011))))], (27126 ^ _773908) ^ [_1263109, _1263111, _1263113] : [c_Relation_Ototal__on(_1263109, _1263111, _1263113), 27129 ^ _773908 : [(27130 ^ _773908) ^ [_1263253] : [hBOOL(hAPP(hAPP(c_member(_1263109), _1263253), _1263111)), 27133 ^ _773908 : [(27134 ^ _773908) ^ [_1263393] : [hBOOL(hAPP(hAPP(c_member(_1263109), _1263393), _1263111)), -(_1263253 = _1263393), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263109, _1263109)), hAPP(hAPP(c_Product__Type_OPair(_1263109, _1263109), _1263253), _1263393)), _1263113))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263109, _1263109)), hAPP(hAPP(c_Product__Type_OPair(_1263109, _1263109), _1263393), _1263253)), _1263113)))]]]]], (51151 ^ _773908) ^ [_1809316, _1809318, _1809320, _1809322, _1809324] : [c_Fun_Obij__betw(_1809316, _1809318, _1809320, _1809322, _1809324), -(c_Fun_Obij__betw(_1809318, _1809316, c_Hilbert__Choice_Oinv__into(_1809316, _1809318, _1809322, _1809320), _1809324, _1809322))], (39139 ^ _773908) ^ [_1532181, _1532183] : [-(c_List_Olex(_1532181, _1532183) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1532181), tc_List_Olist(_1532181)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1532181, _1532183)))], (45603 ^ _773908) ^ [_1685016, _1685018] : [-(_1685016 = c_List_Olist_ONil(_1685018)), -(c_List_Olast(_1685018, hAPP(c_List_Orev(_1685018), _1685016)) = hAPP(c_List_Ohd(_1685018), _1685016))], (51408 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (42927 ^ _773908) ^ [_1625555, _1625557, _1625559, _1625561, _1625563, _1625565, _1625567, _1625569] : [c_Fun_Oinj__on(_1625555, _1625557, _1625559, _1625561), 42933 ^ _773908 : [(42936 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625555, tc_HOL_Obool)), hAPP(_1625567, 42932 ^ [_1625555, _1625557, _1625559, _1625561, _1625563, _1625565, _1625567, _1625569])), _1625561))], (42934 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625563), 42932 ^ [_1625555, _1625557, _1625559, _1625561, _1625563, _1625565, _1625567, _1625569]), _1625565)))]], hBOOL(hAPP(hAPP(c_member(_1625563), _1625569), _1625565)), -(hAPP(c_Set_Oimage(_1625555, _1625557, _1625559), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625563, tc_fun(_1625555, tc_HOL_Obool)), _1625565), _1625567)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625563, tc_fun(_1625557, tc_HOL_Obool)), _1625565), hAPP(hAPP(c_COMBB(tc_fun(_1625555, tc_HOL_Obool), tc_fun(_1625557, tc_HOL_Obool), _1625563), c_Set_Oimage(_1625555, _1625557, _1625559)), _1625567)))], (26233 ^ _773908) ^ [_1239747, _1239749, _1239751, _1239753] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239747, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1239747), _1239749), _1239751)), _1239753) = hAPP(hAPP(c_Set_Oinsert(_1239747), _1239749), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239747, tc_HOL_Obool)), _1239751), _1239753)))], (44861 ^ _773908) ^ [_1670867, _1670869] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670867)), c_List_Oremdups(_1670867, c_List_Oconcat(_1670867, _1670869))) = hAPP(c_Finite__Set_Ocard(_1670867), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1670867), tc_fun(_1670867, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1670867)), _1670869)), c_List_Oset(_1670867))))], (51776 ^ _773908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17999 ^ _773908) ^ [_1084374] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084374))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084374) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16769 ^ _773908) ^ [_1061886, _1061888, _1061890] : [class_Int_Onumber(_1061886), class_Orderings_Olinorder(_1061886), 16776 ^ _773908 : [(16783 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061886), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061890)), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061888)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061886), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061888)), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061890))))], (16777 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061886), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061888)), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061890))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061886), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061890)), hAPP(c_Int_Onumber__class_Onumber__of(_1061886), _1061888)))]]], (17411 ^ _773908) ^ [_1074381, _1074383, _1074385, _1074387] : [class_Groups_Omonoid__mult(_1074381), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1074381), _1074383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074385), _1074387)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074381), hAPP(hAPP(c_Power_Opower__class_Opower(_1074381), _1074383), _1074385)), _1074387))], (40593 ^ _773908) ^ [_1569574, _1569576, _1569578] : [-(hAPP(hAPP(c_List_Ozip(_1569574, _1569576), _1569578), c_List_Olist_ONil(_1569576)) = c_List_Olist_ONil(tc_prod(_1569574, _1569576)))], (34003 ^ _773908) ^ [_1406361, _1406363, _1406365] : [class_Orderings_Olinorder(_1406361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406361), _1406363), _1406365)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406361, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1406361), _1406363)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1406361, _1406363, _1406365)) = hAPP(c_SetInterval_Oord__class_OatMost(_1406361), _1406365))], (14859 ^ _773908) ^ [_1025039, _1025041, _1025043] : [-(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), _1025039), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025041), _1025039))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1025041, _1025039))), _1025043) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025041), _1025043))], (25557 ^ _773908) ^ [_1226414, _1226416, _1226418, _1226420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226414), _1226416)), -(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), _1226414), _1226418)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1226416), _1226420))), c_FunDef_Opair__less)))], (33292 ^ _773908) ^ [_1392389, _1392391, _1392393, _1392395] : [33294 ^ _773908 : [(33298 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392389), 33296 ^ [_1392389, _1392391, _1392393, _1392395]), _1392395)))], (33300 ^ _773908) ^ [] : [-(hAPP(_1392393, 33293 ^ [_1392389, _1392391, _1392393, _1392395]) = hAPP(_1392393, 33296 ^ [_1392389, _1392391, _1392393, _1392395]))], (33302 ^ _773908) ^ [] : [33293 ^ [_1392389, _1392391, _1392393, _1392395] = 33296 ^ [_1392389, _1392391, _1392393, _1392395]], (33295 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392389), 33293 ^ [_1392389, _1392391, _1392393, _1392395]), _1392395)))]], -(c_Fun_Oinj__on(_1392389, _1392391, _1392393, _1392395))], (31762 ^ _773908) ^ [_1360412, _1360414, _1360416, _1360418, _1360420] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360412, tc_HOL_Obool)), _1360414), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360416, tc_fun(_1360412, tc_HOL_Obool)), _1360418), _1360420)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360416, tc_fun(_1360412, tc_HOL_Obool)), _1360418), hAPP(hAPP(c_COMBB(tc_fun(_1360412, tc_HOL_Obool), tc_fun(_1360412, tc_HOL_Obool), _1360416), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360412, tc_HOL_Obool)), _1360414)), _1360420)))], (51654 ^ _773908) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (17867 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (48673 ^ _773908) ^ [_1754679, _1754681, _1754683, _1754685, _1754687, _1754689] : [c_Finite__Set_Ofun__left__comm(_1754679, _1754681, _1754683), hBOOL(hAPP(c_Finite__Set_Ofinite(_1754679), _1754685)), -(hBOOL(hAPP(hAPP(c_member(_1754679), _1754687), _1754685))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1754679, _1754681, _1754683), _1754689), hAPP(hAPP(c_Set_Oinsert(_1754679), _1754687), _1754685)) = hAPP(hAPP(c_Finite__Set_Ofold(_1754679, _1754681, _1754683), hAPP(hAPP(_1754683, _1754687), _1754689)), _1754685))], (29517 ^ _773908) ^ [_1312925, _1312927] : [class_Orderings_Olinorder(_1312925), -(c_Big__Operators_Olinorder__class_OMin(_1312925, hAPP(hAPP(c_Set_Oinsert(_1312925), _1312927), c_Orderings_Obot__class_Obot(tc_fun(_1312925, tc_HOL_Obool)))) = _1312927)], (11751 ^ _773908) ^ [_970193, _970195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _970193), _970195)), -(_970195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _970193), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11754 ^ [_970193, _970195])))], (50689 ^ _773908) ^ [_1799490, _1799492, _1799494] : [c_Relation_Osym(_1799490, _1799492), c_Relation_Osym(_1799490, _1799494), -(c_Relation_Osym(_1799490, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1799490, _1799490), tc_HOL_Obool)), _1799492), _1799494)))], (40653 ^ _773908) ^ [_1571022, _1571024, _1571026, _1571028, _1571030] : [-(hAPP(hAPP(c_List_Olist__update(_1571022, hAPP(hAPP(c_List_Oappend(_1571022), _1571024), hAPP(hAPP(c_List_Olist_OCons(_1571022), _1571026), _1571028))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571022)), _1571024)), _1571030) = hAPP(hAPP(c_List_Oappend(_1571022), _1571024), hAPP(hAPP(c_List_Olist_OCons(_1571022), _1571030), _1571028)))], (45719 ^ _773908) ^ [_1687416, _1687418, _1687420, _1687422, _1687424] : [-(c_List_OtakeWhile(_1687416, _1687418, hAPP(hAPP(c_List_Omap(_1687420, _1687416), _1687422), _1687424)) = hAPP(hAPP(c_List_Omap(_1687420, _1687416), _1687422), c_List_OtakeWhile(_1687420, hAPP(c_Fun_Ocomp(_1687416, tc_HOL_Obool, _1687420, _1687418), _1687422), _1687424)))], (6292 ^ _773908) ^ [_875894, _875896] : [hBOOL(hAPP(_875894, _875896)), 6298 ^ _773908 : [(6301 ^ _773908) ^ [] : [hBOOL(hAPP(_875894, 6297 ^ [_875894, _875896]))], (6299 ^ _773908) ^ [] : [-(hBOOL(hAPP(_875894, hAPP(c_Nat_OSuc, 6297 ^ [_875894, _875896]))))]], -(hBOOL(hAPP(_875894, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38428 ^ _773908) ^ [_1511960] : [-(c_Int_Oint__ge__less__than(_1511960) = 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), _1511960)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (49798 ^ _773908) ^ [_1779294, _1779296, _1779298] : [-(c_List_Olist__ex1(_1779294, _1779296, _1779298)), 49799 ^ _773908 : [(49800 ^ _773908) ^ [_1779388] : [hBOOL(hAPP(hAPP(c_member(_1779294), _1779388), hAPP(c_List_Oset(_1779294), _1779298))), hBOOL(hAPP(_1779296, _1779388)), 49808 ^ _773908 : [(49813 ^ _773908) ^ [] : [49807 ^ [_1779294, _1779296, _1779298, _1779388] = _1779388], (49811 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1779296, 49807 ^ [_1779294, _1779296, _1779298, _1779388])))], (49809 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779294), 49807 ^ [_1779294, _1779296, _1779298, _1779388]), hAPP(c_List_Oset(_1779294), _1779298))))]]]]], (37974 ^ _773908) ^ [_1495689, _1495691, _1495693] : [hBOOL(hAPP(_1495693, _1495691)), -(hBOOL(hAPP(hAPP(c_member(_1495689), _1495691), hAPP(c_Set_OCollect(_1495689), _1495693))))], (6004 ^ _773908) ^ [_870342, _870344, _870346] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _870342)), _870344), _870346)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870342))), _870344), _870346)))], (44387 ^ _773908) ^ [_1658815, _1658817, _1658819, _1658821, _1658823] : [-(hAPP(c_List_Ofilter(_1658815, _1658817), hAPP(hAPP(c_List_Omap(_1658819, _1658815), _1658821), _1658823)) = hAPP(hAPP(c_List_Omap(_1658819, _1658815), _1658821), hAPP(c_List_Ofilter(_1658819, hAPP(c_Fun_Ocomp(_1658815, tc_HOL_Obool, _1658819, _1658817), _1658821)), _1658823)))], (45782 ^ _773908) ^ [_1688698] : [-(c_List_Oreturn__list(_1688698) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1688698))], (6262 ^ _773908) ^ [_875480, _875482, _875484] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_875480, _875482, _875484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26788 ^ _773908) ^ [_1256627, _1256629] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1256627, _1256627)), hAPP(hAPP(c_Product__Type_OPair(_1256627, _1256627), _1256629), _1256629)), c_Relation_OId(_1256627))))], (7773 ^ _773908) ^ [_900650, _900652, _900654] : [c_Com_Ocom_OCond(_900650, _900652, _900654) = c_Com_Ocom_OSKIP], (42585 ^ _773908) ^ [_1618691, _1618693, _1618695] : [42586 ^ _773908 : [(42587 ^ _773908) ^ [_1618745] : [hBOOL(hAPP(_1618691, _1618745))]], _1618693 = c_Hilbert__Choice_OEps(_1618695, _1618691), -(hBOOL(hAPP(_1618691, _1618693)))], (6036 ^ _773908) ^ [_870992, _870994, _870996, _870998] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_870992, _870994)), _870996), _870998)), 6040 ^ _773908 : [(6043 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870994), 6039 ^ [_870992, _870994, _870996, _870998]), _870998)))], (6041 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870992), _870996), 6039 ^ [_870992, _870994, _870996, _870998])))]]], (48371 ^ _773908) ^ [_1748981, _1748983] : [class_Complete__Lattice_Ocomplete__lattice(_1748981), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748981), _1748983)), -(c_Complete__Lattice_OInf__class_OInf(_1748981, _1748983) = hAPP(hAPP(c_Finite__Set_Ofold(_1748981, _1748981, c_Lattices_Osemilattice__inf__class_Oinf(_1748981)), c_Orderings_Otop__class_Otop(_1748981)), _1748983))], (45625 ^ _773908) ^ [_1685420, _1685422, _1685424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685420), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685422)), _1685424))), -(hAPP(hAPP(c_List_Onth(_1685422), hAPP(c_List_Orev(_1685422), _1685424)), _1685420) = hAPP(hAPP(c_List_Onth(_1685422), _1685424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685422)), _1685424)), hAPP(c_Nat_OSuc, _1685420))))], (34788 ^ _773908) ^ [_1423504, _1423506, _1423508, _1423510] : [class_Rings_Osemiring__1(_1423504), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423506, _1423504), hAPP(c_COMBK(_1423504, _1423506), _1423508)), _1423510) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423504), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1423504), hAPP(c_Finite__Set_Ocard(_1423506), _1423510))), _1423508))], (42910 ^ _773908) ^ [_1625131, _1625133, _1625135, _1625137, _1625139] : [class_Groups_Omonoid__add(_1625131), class_Groups_Oordered__ab__semigroup__add(_1625131), 42920 ^ _773908 : [(42923 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625131), hAPP(_1625137, 42919 ^ [_1625131, _1625133, _1625135, _1625137, _1625139])), hAPP(_1625139, 42919 ^ [_1625131, _1625133, _1625135, _1625137, _1625139])))], (42921 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625133), 42919 ^ [_1625131, _1625133, _1625135, _1625137, _1625139]), hAPP(c_List_Oset(_1625133), _1625135))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625131), hAPP(c_List_Omonoid__add__class_Olistsum(_1625131), hAPP(hAPP(c_List_Omap(_1625133, _1625131), _1625137), _1625135))), hAPP(c_List_Omonoid__add__class_Olistsum(_1625131), hAPP(hAPP(c_List_Omap(_1625133, _1625131), _1625139), _1625135)))))], (15867 ^ _773908) ^ [_1044204, _1044206] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044204), _1044206)), _1044206) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044204), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044204, _1044206)))], (32478 ^ _773908) ^ [_1376869, _1376871, _1376873] : [-(hAPP(c_Set_OPow(_1376869), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376869, tc_HOL_Obool)), _1376871), _1376873)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1376869, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1376869), _1376871)), hAPP(c_Set_OPow(_1376869), _1376873)))], (12176 ^ _773908) ^ [_978013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978013)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _978013)) = _978013)], (19623 ^ _773908) ^ [_1112465] : [class_Rings_Osemiring__1(_1112465), -(hBOOL(hAPP(hAPP(c_member(_1112465), c_Groups_Oone__class_Oone(_1112465)), c_Nat_Osemiring__1__class_ONats(_1112465))))], (32492 ^ _773908) ^ [_1377145, _1377147] : [c_Nat__Transfer_Ois__nat(_1377145), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1377145, _1377147)))], (3812 ^ _773908) ^ [_831406, _831408] : [_831408 = _831406, -(c_Enum_Oenum__class_Oenum__all(_831408) = c_Enum_Oenum__class_Oenum__all(_831406))], (39164 ^ _773908) ^ [_1532737, _1532739, _1532741] : [-(hAPP(c_List_Olexn(_1532737, _1532739), hAPP(c_Nat_OSuc, _1532741)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1532737), tc_List_Olist(_1532737)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1532737, tc_List_Olist(_1532737)), tc_prod(_1532737, tc_List_Olist(_1532737))), tc_prod(tc_List_Olist(_1532737), tc_List_Olist(_1532737)), c_Product__Type_Omap__pair(tc_prod(_1532737, tc_List_Olist(_1532737)), tc_List_Olist(_1532737), tc_prod(_1532737, tc_List_Olist(_1532737)), tc_List_Olist(_1532737), hAPP(c_Product__Type_Oprod_Oprod__case(_1532737, tc_List_Olist(_1532737), tc_List_Olist(_1532737)), c_List_Olist_OCons(_1532737)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532737, tc_List_Olist(_1532737), tc_List_Olist(_1532737)), c_List_Olist_OCons(_1532737)))), c_Wellfounded_Olex__prod(_1532737, tc_List_Olist(_1532737), _1532739, hAPP(c_List_Olexn(_1532737, _1532739), _1532741)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1532737), tc_List_Olist(_1532737))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1532737), tc_List_Olist(_1532737), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1532737), tc_fun(tc_List_Olist(_1532737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1532737), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1532737), tc_HOL_Obool), tc_fun(tc_List_Olist(_1532737), tc_HOL_Obool)), tc_List_Olist(_1532737)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1532737))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1532737)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1532737), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1532737)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1532737)))), hAPP(c_Nat_OSuc, _1532741))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1532737), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1532737)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1532737)))), hAPP(c_Nat_OSuc, _1532741)))))))], (33716 ^ _773908) ^ [_1400268, _1400270, _1400272, _1400274, _1400276, _1400278] : [class_Groups_Ocomm__monoid__mult(_1400268), c_Fun_Oinj__on(_1400270, _1400272, _1400274, _1400276), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400272, _1400268), _1400278), hAPP(c_Set_Oimage(_1400270, _1400272, _1400274), _1400276)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400270, _1400268), hAPP(c_Fun_Ocomp(_1400272, _1400268, _1400270, _1400278), _1400274)), _1400276))], (28166 ^ _773908) ^ [_1284289, _1284291] : [class_Lattices_Osemilattice__inf(_1284289), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1284289), _1284291), _1284291) = _1284291)], (36151 ^ _773908) ^ [_1452492] : [class_Nat_Osemiring__char__0(_1452492), -(c_Fun_Oinj__on(tc_Nat_Onat, _1452492, c_Nat_Osemiring__1__class_Oof__nat(_1452492), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (20267 ^ _773908) ^ [_1123704, _1123706] : [class_Rings_Oring__1(_1123704), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123704), hAPP(c_Groups_Ouminus__class_Ouminus(_1123704), _1123706)), 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(_1123704), _1123706), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (282 ^ _773908) ^ [_778251, _778253] : [-(class_Fields_Ofield(_778251)), _778253 = _778251, class_Fields_Ofield(_778253)], (18847 ^ _773908) ^ [_1099855, _1099857] : [class_Int_Onumber__ring(_1099855), 18850 ^ _773908 : [(18857 ^ _773908) ^ [] : [c_Int_Oiszero(_1099855, hAPP(c_Int_Onumber__class_Onumber__of(_1099855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099857), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1099855), _1099857) = c_Groups_Ozero__class_Ozero(_1099855))], (18851 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1099855), _1099857) = c_Groups_Ozero__class_Ozero(_1099855), -(c_Int_Oiszero(_1099855, hAPP(c_Int_Onumber__class_Onumber__of(_1099855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099857), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (8595 ^ _773908) ^ [_916137, _916139, _916141] : [class_Rings_Oring(_916137), -(hAPP(c_Groups_Ouminus__class_Ouminus(_916137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916137), _916139), _916141)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916137), hAPP(c_Groups_Ouminus__class_Ouminus(_916137), _916139)), _916141))], (34990 ^ _773908) ^ [_1427943, _1427945, _1427947] : [class_Orderings_Olinorder(_1427943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427943), _1427945), _1427947)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427943, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1427943, _1427945), _1427947)), hAPP(c_SetInterval_Oord__class_OatLeast(_1427943), _1427947)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1427943), _1427945))], (16511 ^ _773908) ^ [_1057204, _1057206, _1057208, _1057210, _1057212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1057204, tc_HOL_Obool)), _1057206), _1057208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1057204, tc_HOL_Obool)), _1057210), _1057212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1057204, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057204, tc_HOL_Obool)), _1057206), _1057212)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057204, tc_HOL_Obool)), _1057208), _1057210))))], (15767 ^ _773908) ^ [_1042206, _1042208, _1042210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042206), _1042208)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042208), _1042210)), _1042206) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042208), _1042206)), _1042210))], (9615 ^ _773908) ^ [_934170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934170), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_934170 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 9618 ^ [_934170]))))], (5520 ^ _773908) ^ [_858352, _858354, _858356, _858358, _858360, _858362, _858364, _858366] : [-(c_Fun_Othe__inv__into(_858366, _858362, _858358, _858354) = c_Fun_Othe__inv__into(_858364, _858360, _858356, _858352)), _858366 = _858364, _858362 = _858360, _858358 = _858356, _858354 = _858352], (13658 ^ _773908) ^ [_1003913] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1003913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19567 ^ _773908) ^ [_1111582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1111582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1111582))))], (31427 ^ _773908) ^ [_1352091, _1352093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1352091), _1352093)), -(hAPP(c_Finite__Set_Ocard(_1352091), _1352093) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1352091, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1352091), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352093))], (8020 ^ _773908) ^ [_905199] : [_905199 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905199) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28046 ^ _773908) ^ [_1281790, _1281792, _1281794, _1281796] : [hBOOL(hAPP(hAPP(c_member(_1281790), _1281792), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281790, tc_HOL_Obool)), _1281794), _1281796))), 28049 ^ _773908 : [(28052 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281790), _1281792), _1281796)))], (28050 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281790), _1281792), _1281794)))]]], (24677 ^ _773908) ^ [_1208786, _1208788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1208786)), -(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(_1208786), _1208788))), _1208786)))], (16809 ^ _773908) ^ [_1062699, _1062701, _1062703] : [class_Rings_Ocomm__semiring__1(_1062699), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062699), _1062701), hAPP(c_Nat_OSuc, _1062703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062699), _1062701), hAPP(hAPP(c_Power_Opower__class_Opower(_1062699), _1062701), _1062703)))], (24249 ^ _773908) ^ [_1198127, _1198129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198127, _1198129) = 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), _1198127), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198129)))))], (50358 ^ _773908) ^ [_1793491, _1793493, _1793495, _1793497, _1793499] : [c_Predicate_Otransp(_1793491, _1793493), hBOOL(hAPP(hAPP(_1793493, _1793495), _1793497)), hBOOL(hAPP(hAPP(_1793493, _1793497), _1793499)), -(hBOOL(hAPP(hAPP(_1793493, _1793495), _1793499)))], (8379 ^ _773908) ^ [_912025] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912025) = _912025)], (32482 ^ _773908) ^ [_1376986, _1376988] : [c_Nat__Transfer_Ois__nat(_1376986), c_Nat__Transfer_Ois__nat(_1376988), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1376986, _1376988) = 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, _1376986), hAPP(c_Int_Onat, _1376988))))], (7111 ^ _773908) ^ [_889068, _889070] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _889068), _889070) = _889068, -(_889070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41300 ^ _773908) ^ [_1587664, _1587666, _1587668, _1587670, _1587672, _1587674] : [-(hAPP(c_List_Ofoldl(_1587664, _1587666, _1587668, _1587670), hAPP(hAPP(c_List_Oappend(_1587666), _1587672), _1587674)) = hAPP(c_List_Ofoldl(_1587664, _1587666, _1587668, hAPP(c_List_Ofoldl(_1587664, _1587666, _1587668, _1587670), _1587672)), _1587674))], (17917 ^ _773908) ^ [_1083146, _1083148] : [class_Int_Onumber__ring(_1083146), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083146), _1083148), hAPP(c_Int_Onumber__class_Onumber__of(_1083146), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083146), _1083148))], (30660 ^ _773908) ^ [_1335152, _1335154, _1335156, _1335158] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1335152, _1335156)), c_Sum__Type_OPlus(_1335152, _1335156, _1335154, _1335158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1335152), _1335154)), hAPP(c_Finite__Set_Ocard(_1335156), _1335158))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335152), _1335154)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335156), _1335158))], (25485 ^ _773908) ^ [_1224867, _1224869] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1224867)), _1224869) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1224867), 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), _1224867)), _1224869))], (12088 ^ _773908) ^ [_976531, _976533, _976535] : [class_Rings_Olinordered__ring(_976531), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976531), c_Groups_Ozero__class_Ozero(_976531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976531), _976533), _976533)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976531), _976535), _976535)))))], (1534 ^ _773908) ^ [_796069, _796071] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_796069)), _796071 = _796069, class_Groups_Oordered__ab__semigroup__add__imp__le(_796071)], (8891 ^ _773908) ^ [_921113, _921115, _921117] : [class_Rings_Ono__zero__divisors(_921113), -(_921115 = c_Groups_Ozero__class_Ozero(_921113)), -(_921117 = c_Groups_Ozero__class_Ozero(_921113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921113), _921115), _921117) = c_Groups_Ozero__class_Ozero(_921113)], (9561 ^ _773908) ^ [_933188, _933190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _933188)), hAPP(c_Int_Onat, _933190)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _933190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933188), _933190))], (25417 ^ _773908) ^ [_1223190, _1223192, _1223194, _1223196, _1223198, _1223200, _1223202] : [-(hAPP(c_Product__Type_Oapfst(_1223190, _1223192, _1223194, _1223196), hAPP(c_Product__Type_Oapfst(_1223198, _1223190, _1223194, _1223200), _1223202)) = hAPP(c_Product__Type_Oapfst(_1223198, _1223192, _1223194, hAPP(c_Fun_Ocomp(_1223190, _1223192, _1223198, _1223196), _1223200)), _1223202))], (44 ^ _773908) ^ [_774486, _774488] : [-(class_Rings_Odivision__ring(_774486)), _774488 = _774486, class_Rings_Odivision__ring(_774488)], (40471 ^ _773908) ^ [_1566494, _1566496, _1566498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1566494), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1566496)), _1566498))), -(hAPP(hAPP(c_List_Olist_OCons(_1566496), hAPP(hAPP(c_List_Onth(_1566496), _1566498), _1566494)), hAPP(hAPP(c_List_Odrop(_1566496), hAPP(c_Nat_OSuc, _1566494)), _1566498)) = hAPP(hAPP(c_List_Odrop(_1566496), _1566494), _1566498))], (23640 ^ _773908) ^ [_1186276, _1186278] : [-(_1186276 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23643 ^ _773908 : [(23650 ^ _773908) ^ [] : [-(_1186278 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1186276, _1186278) = 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, _1186278))), 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, _1186276)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1186278))), c_Divides_Opdivmod(_1186276, _1186278)), 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), _1186278))))), c_Divides_Opdivmod(_1186276, _1186278)))))], (23644 ^ _773908) ^ [] : [_1186278 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1186276, _1186278) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186276))]]], (41039 ^ _773908) ^ [_1582339] : [-(hAPP(c_List_Otl(_1582339), c_List_Olist_ONil(_1582339)) = c_List_Olist_ONil(_1582339))], (15627 ^ _773908) ^ [_1039656, _1039658] : [class_Groups_Ogroup__add(_1039656), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039656), c_Groups_Ozero__class_Ozero(_1039656)), _1039658) = hAPP(c_Groups_Ouminus__class_Ouminus(_1039656), _1039658))], (33868 ^ _773908) ^ [_1403365, _1403367, _1403369] : [class_Groups_Oordered__ab__group__add(_1403365), -(hAPP(c_Set_Oimage(_1403365, _1403365, c_Groups_Ouminus__class_Ouminus(_1403365)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1403365, _1403367), _1403369)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1403365, hAPP(c_Groups_Ouminus__class_Ouminus(_1403365), _1403369), hAPP(c_Groups_Ouminus__class_Ouminus(_1403365), _1403367)))], (36613 ^ _773908) ^ [_1463325, _1463327, _1463329, _1463331, _1463333, _1463335] : [c_Typedef_Otype__definition(_1463325, _1463327, _1463329, _1463331, _1463333), hBOOL(hAPP(hAPP(c_member(_1463327), _1463335), _1463333)), -(hAPP(_1463329, hAPP(_1463331, _1463335)) = _1463335)], (16165 ^ _773908) ^ [_1050747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1050747)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050747), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1050747)], (21549 ^ _773908) ^ [_1146616, _1146618, _1146620, _1146622] : [class_Fields_Olinordered__field(_1146616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146616), _1146618), c_Groups_Ozero__class_Ozero(_1146616))), 21556 ^ _773908 : [(21563 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146616), _1146622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146616), _1146620), _1146618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146616), _1146620), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146616), _1146622), _1146618))))], (21557 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146616), _1146620), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146616), _1146622), _1146618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146616), _1146622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146616), _1146620), _1146618))))]]], (19849 ^ _773908) ^ [_1116485, _1116487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116485), _1116487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116485)), c_Int_OBit0(_1116487))))], (39783 ^ _773908) ^ [_1549490, _1549492] : [-(c_List_Olistrelp(_1549490, _1549492, c_List_Olist_ONil(_1549490), c_List_Olist_ONil(_1549490)))], (7255 ^ _773908) ^ [_891155, _891157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _891155)), _891157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891155), _891157)))], (34039 ^ _773908) ^ [_1407079, _1407081, _1407083, _1407085] : [c_Fun_Oinj__on(_1407079, tc_fun(tc_fun(_1407079, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1407079, tc_fun(tc_prod(_1407079, _1407079), tc_HOL_Obool), tc_fun(tc_fun(_1407079, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407079, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1407079, _1407079), tc_HOL_Obool), tc_fun(tc_fun(_1407079, tc_HOL_Obool), tc_HOL_Obool)), _1407079), c_Equiv__Relations_Oquotient(_1407079)), hAPP(hAPP(c_COMBC(_1407079, tc_fun(_1407079, tc_HOL_Obool), tc_fun(_1407079, tc_HOL_Obool)), c_Set_Oinsert(_1407079)), c_Orderings_Obot__class_Obot(tc_fun(_1407079, tc_HOL_Obool))))), _1407081), _1407083), hBOOL(hAPP(hAPP(c_member(_1407079), _1407085), _1407083)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1407079, tc_HOL_Obool)), _1407083), hAPP(hAPP(c_Set_Oinsert(_1407079), _1407085), c_Orderings_Obot__class_Obot(tc_fun(_1407079, tc_HOL_Obool))))), _1407081) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1407079, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407079), _1407083), _1407081)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407079), hAPP(hAPP(c_Set_Oinsert(_1407079), _1407085), c_Orderings_Obot__class_Obot(tc_fun(_1407079, tc_HOL_Obool)))), _1407081)))], (36803 ^ _773908) ^ [_1467350, _1467352, _1467354] : [class_Lattices_Osemilattice__inf(_1467350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467350), _1467352)), hBOOL(hAPP(hAPP(c_member(_1467350), _1467354), _1467352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467350), hAPP(c_Finite__Set_Ofold1(_1467350, c_Lattices_Osemilattice__inf__class_Oinf(_1467350)), _1467352)), _1467354)))], (43427 ^ _773908) ^ [_1636641, _1636643, _1636645] : [c_List_Olist__all2(_1636645, _1636645, c_fequal, _1636641, _1636643), -(_1636641 = _1636643)], (1284 ^ _773908) ^ [_792944, _792946] : [-(class_Divides_Oring__div(_792944)), _792946 = _792944, class_Divides_Oring__div(_792946)], (47377 ^ _773908) ^ [_1726118, _1726120, _1726122, _1726124] : [-(hAPP(c_Relation_Oconverse(_1726118, _1726120), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1726118, _1726120), tc_HOL_Obool)), _1726122), _1726124)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1726120, _1726118), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1726118, _1726120), _1726122)), hAPP(c_Relation_Oconverse(_1726118, _1726120), _1726124)))], (33022 ^ _773908) ^ [_1387156, _1387158, _1387160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1387156)), 33025 ^ _773908 : [(33026 ^ _773908) ^ [_1387290] : [33028 ^ _773908 : [(33034 ^ _773908) ^ [] : [-(_1387290 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33030 ^ [_1387156, _1387158, _1387160, _1387290]), 33027 ^ [_1387156, _1387158, _1387160, _1387290]))], (33032 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33030 ^ [_1387156, _1387158, _1387160, _1387290]), _1387158)))], (33029 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33027 ^ [_1387156, _1387158, _1387160, _1387290]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1387156))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387290), _1387160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1387290), _1387156)), _1387160)))]]], (26452 ^ _773908) ^ [_1247571, _1247573, _1247575, _1247577, _1247579] : [-(hAPP(c_Relation_OImage(_1247571, _1247573, _1247575), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247571, tc_HOL_Obool)), _1247577), _1247579)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247573, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1247571, _1247573, _1247575), _1247577)), hAPP(c_Relation_OImage(_1247571, _1247573, _1247575), _1247579)))], (27644 ^ _773908) ^ [_1274056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1274056)), 27648 ^ _773908 : [(27649 ^ _773908) ^ [_1274136] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1274136), _1274056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1274136), 27647 ^ [_1274056])))]]], (51017 ^ _773908) ^ [_1806221, _1806223, _1806225] : [hAPP(c_Fun_Ocomp(_1806221, _1806223, _1806223, _1806225), c_Hilbert__Choice_Oinv__into(_1806221, _1806223, c_Orderings_Otop__class_Otop(tc_fun(_1806221, tc_HOL_Obool)), _1806225)) = c_Fun_Oid(_1806223), -(hAPP(c_Set_Oimage(_1806221, _1806223, _1806225), c_Orderings_Otop__class_Otop(tc_fun(_1806221, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1806223, tc_HOL_Obool)))], (48775 ^ _773908) ^ [_1756772, _1756774, _1756776, _1756778] : [class_Lattices_Osemilattice__inf(_1756772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1756772), _1756774)), 48785 ^ _773908 : [(48788 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756772), _1756776), 48784 ^ [_1756772, _1756774, _1756776, _1756778]))], (48786 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756772), 48784 ^ [_1756772, _1756774, _1756776, _1756778]), _1756774)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756772), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1756772), _1756776), _1756778)), hAPP(hAPP(c_Finite__Set_Ofold(_1756772, _1756772, c_Lattices_Osemilattice__inf__class_Oinf(_1756772)), _1756778), _1756774))))], (26141 ^ _773908) ^ [_1237755, _1237757] : [class_Lattices_Osemilattice__sup(_1237755), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237755), _1237757), _1237757) = _1237757)], (8053 ^ _773908) ^ [_905791, _905793, _905795] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905791)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _905793)), _905795)) = 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), _905791), _905793))), _905795))], (45011 ^ _773908) ^ [_1673380, _1673382] : [hBOOL(hAPP(c_List_Odistinct(_1673380), _1673382)), -(c_List_Oremdups(_1673380, _1673382) = _1673382)], (14360 ^ _773908) ^ [_1016806, _1016808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016806, _1016808)), _1016806)))], (34019 ^ _773908) ^ [_1406683, _1406685, _1406687] : [class_Orderings_Oorder(_1406683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406683, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1406683), _1406685)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1406683, _1406685, _1406687)) = c_Orderings_Obot__class_Obot(tc_fun(_1406683, tc_HOL_Obool)))], (38675 ^ _773908) ^ [_1521135, _1521137, _1521139, _1521141] : [-(c_List_Osublist(_1521135, hAPP(hAPP(c_List_Oappend(_1521135), _1521137), _1521139), _1521141) = hAPP(hAPP(c_List_Oappend(_1521135), c_List_Osublist(_1521135, _1521137, _1521141)), c_List_Osublist(_1521135, _1521139, 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(_1521135)), _1521137)))), _1521141)))))], (4158 ^ _773908) ^ [_836715, _836717] : [_836717 = _836715, -(c_Nat_Osemiring__1__class_Oof__nat(_836717) = c_Nat_Osemiring__1__class_Oof__nat(_836715))], (47956 ^ _773908) ^ [_1740284, _1740286, _1740288] : [c_List_Olist__ex(_1740284, _1740286, _1740288), 47960 ^ _773908 : [(47963 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1740286, hAPP(hAPP(c_List_Onth(_1740284), _1740288), 47959 ^ [_1740284, _1740286, _1740288]))))], (47961 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47959 ^ [_1740284, _1740286, _1740288]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740284)), _1740288))))]]], (3222 ^ _773908) ^ [_822221, _822223, _822225, _822227] : [-(c_Enum_Osublists(_822227, _822223) = c_Enum_Osublists(_822225, _822221)), _822227 = _822225, _822223 = _822221], (34356 ^ _773908) ^ [_1413547, _1413549, _1413551] : [class_Orderings_Olinorder(_1413547), 34359 ^ _773908 : [(34366 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413547), _1413549), _1413551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1413547, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413547), _1413549)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413547), _1413551))))], (34360 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1413547, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413547), _1413549)), hAPP(c_SetInterval_Oord__class_OlessThan(_1413547), _1413551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413547), _1413549), _1413551)))]]], (9897 ^ _773908) ^ [_938678, _938680, _938682] : [class_Orderings_Oorder(_938678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938678), _938680), _938682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938678), _938682), _938680)), -(_938682 = _938680)], (50096 ^ _773908) ^ [_1787055, _1787057, _1787059, _1787061] : [class_Complete__Lattice_Ocomplete__lattice(_1787055), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1787057, _1787055), _1787059), _1787061) = c_Complete__Lattice_OSup__class_OSup(_1787055, hAPP(c_Set_OCollect(_1787055), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool), tc_HOL_Obool, _1787055), c_HOL_OEx(tc_fun(_1787057, _1787055))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool), tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool), _1787055), hAPP(c_COMBS(tc_fun(_1787057, _1787055), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1787057, _1787055)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1787057, _1787055), tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1787057, _1787055))), _1787059)))), hAPP(hAPP(c_COMBC(_1787055, tc_fun(tc_fun(_1787057, _1787055), _1787055), tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1787055, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1787057, _1787055), _1787055), tc_fun(tc_fun(_1787057, _1787055), tc_HOL_Obool)), _1787055), c_COMBB(_1787055, tc_HOL_Obool, tc_fun(_1787057, _1787055))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1787057, _1787055), _1787057, _1787055), c_COMBI(tc_fun(_1787057, _1787055))), _1787061)))))))], (5572 ^ _773908) ^ [_859142, _859144, _859146, _859148] : [-(tc_Nitpick_Opair__box(_859148, _859144) = tc_Nitpick_Opair__box(_859146, _859142)), _859148 = _859146, _859144 = _859142], (10409 ^ _773908) ^ [_946352, _946354, _946356, _946358] : [class_Orderings_Oorder(_946352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946352), _946354), _946356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946352), _946358), _946354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946352), _946358), _946356)))], (13989 ^ _773908) ^ [_1009588, _1009590, _1009592] : [-(hBOOL(hAPP(_1009588, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1009590, _1009592)))), 13992 ^ _773908 : [(13995 ^ _773908) ^ [] : [hBOOL(hAPP(_1009588, _1009590))], (13993 ^ _773908) ^ [] : [-(_1009592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13998 ^ _773908 : [(13999 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009592)))], (14005 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14001 ^ [_1009588, _1009590, _1009592]), _1009592)))], (14009 ^ _773908) ^ [] : [hBOOL(hAPP(_1009588, 14001 ^ [_1009588, _1009590, _1009592]))], (14007 ^ _773908) ^ [] : [-(_1009590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009592), 14000 ^ [_1009588, _1009590, _1009592])), 14001 ^ [_1009588, _1009590, _1009592]))], (14003 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14001 ^ [_1009588, _1009590, _1009592])))]], 14010 ^ _773908 : [(14011 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009592), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14017 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14013 ^ [_1009588, _1009590, _1009592]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14021 ^ _773908) ^ [] : [hBOOL(hAPP(_1009588, 14013 ^ [_1009588, _1009590, _1009592]))], (14019 ^ _773908) ^ [] : [-(_1009590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009592), 14012 ^ [_1009588, _1009590, _1009592])), 14013 ^ [_1009588, _1009590, _1009592]))], (14015 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009592), 14013 ^ [_1009588, _1009590, _1009592])))]]], (42319 ^ _773908) ^ [_1612230, _1612232, _1612234, _1612236, _1612238] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1612230), tc_List_Olist(_1612232), tc_List_Olist(_1612234), hAPP(c_List_Omap(_1612230, _1612232), _1612236)), hAPP(c_List_Omap(_1612234, _1612230), _1612238)) = hAPP(c_List_Omap(_1612234, _1612232), hAPP(c_Fun_Ocomp(_1612230, _1612232, _1612234, _1612236), _1612238)))], (6924 ^ _773908) ^ [_885987, _885989, _885991] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885987), _885989)), _885991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885989), _885991)))], (12907 ^ _773908) ^ [_990340, _990342, _990344, _990346] : [c_Hoare__Mirabelle_Ohoare__derivs(_990340, _990342, _990344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_990340), tc_HOL_Obool)), _990342), _990346)), -(c_Hoare__Mirabelle_Ohoare__derivs(_990340, _990346, _990344))], (42993 ^ _773908) ^ [_1627173, _1627175, _1627177, _1627179] : [-(_1627173 = _1627175), -(c_List_Oremove1(_1627177, _1627173, hAPP(hAPP(c_List_Olist_OCons(_1627177), _1627175), _1627179)) = hAPP(hAPP(c_List_Olist_OCons(_1627177), _1627175), c_List_Oremove1(_1627177, _1627173, _1627179)))], (10137 ^ _773908) ^ [_942522, _942524, _942526] : [class_Orderings_Olinorder(_942522), 10140 ^ _773908 : [(10147 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942522), _942526), _942524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942522), _942524), _942526))], (10141 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942522), _942524), _942526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942522), _942526), _942524)))]]], (15109 ^ _773908) ^ [_1029841, _1029843] : [-(_1029841 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15112 ^ _773908 : [(15119 ^ _773908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029843, _1029841) = 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), _1029843)), _1029841) = 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), _1029843), _1029841))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15113 ^ _773908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029843, _1029841) = 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), _1029843)), _1029841) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029843), _1029841)))]]], (7998 ^ _773908) ^ [_904869, _904871, _904873] : [class_Nat_Osemiring__char__0(_904869), 8001 ^ _773908 : [(8008 ^ _773908) ^ [] : [_904871 = _904873, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904869), _904871) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904869), _904873))], (8002 ^ _773908) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904869), _904871) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904869), _904873), -(_904871 = _904873)]]], (3326 ^ _773908) ^ [_823823, _823825, _823827, _823829] : [-(c_Random_Opick(_823829, _823825) = c_Random_Opick(_823827, _823823)), _823829 = _823827, _823825 = _823823], (46144 ^ _773908) ^ [_1696305, _1696307] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1696305)), _1696307)), 46150 ^ _773908 : [(46153 ^ _773908) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1696305), 46149 ^ [_1696305, _1696307]))], (46151 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1696305)), 46149 ^ [_1696305, _1696307]), hAPP(c_List_Oset(tc_List_Olist(_1696305)), _1696307))))]], 46157 ^ _773908 : [(46161 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1696305)), 46159 ^ [_1696305, _1696307]), hAPP(c_List_Oset(tc_List_Olist(_1696305)), _1696307))))], (46163 ^ _773908) ^ [] : [46156 ^ [_1696305, _1696307] = 46159 ^ [_1696305, _1696307]], (46165 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1696305, tc_HOL_Obool)), hAPP(c_List_Oset(_1696305), 46156 ^ [_1696305, _1696307])), hAPP(c_List_Oset(_1696305), 46159 ^ [_1696305, _1696307])) = c_Orderings_Obot__class_Obot(tc_fun(_1696305, tc_HOL_Obool))], (46158 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1696305)), 46156 ^ [_1696305, _1696307]), hAPP(c_List_Oset(tc_List_Olist(_1696305)), _1696307))))]], -(hBOOL(hAPP(c_List_Odistinct(_1696305), c_List_Oconcat(_1696305, _1696307))))], (47058 ^ _773908) ^ [_1718577, _1718579, _1718581, _1718583, _1718585] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1718577, _1718577)), hAPP(hAPP(c_Product__Type_OPair(_1718577, _1718577), _1718579), _1718581)), c_Transitive__Closure_Ortrancl(_1718577, _1718583))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1718577, _1718577)), hAPP(hAPP(c_Product__Type_OPair(_1718577, _1718577), _1718581), _1718585)), _1718583)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718577, _1718577)), hAPP(hAPP(c_Product__Type_OPair(_1718577, _1718577), _1718579), _1718585)), c_Transitive__Closure_Otrancl(_1718577, _1718583))))], (36117 ^ _773908) ^ [_1451594, _1451596, _1451598, _1451600] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451594, tc_fun(_1451596, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451594, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451596, tc_HOL_Obool), tc_fun(_1451596, tc_HOL_Obool), _1451594), hAPP(c_COMBC(_1451596, tc_fun(_1451596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451596))), _1451598)), _1451600)), -(hBOOL(hAPP(hAPP(c_member(_1451596), _1451600), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451594, tc_fun(_1451596, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451594, tc_HOL_Obool))), _1451598))))], (43858 ^ _773908) ^ [_1646731] : [-(hAPP(c_Relation_ODomain(_1646731, _1646731), c_Relation_OId(_1646731)) = c_Orderings_Otop__class_Otop(tc_fun(_1646731, tc_HOL_Obool)))], (38996 ^ _773908) ^ [_1527844, _1527846, _1527848, _1527850] : [c_FunDef_Oreduction__pair(_1527844, _1527846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool)), _1527848), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool), tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool)), _1527846))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool)), _1527850), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool), tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool)), _1527846))), c_Wellfounded_Owf(_1527844, _1527850), -(c_Wellfounded_Owf(_1527844, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527844, _1527844), tc_HOL_Obool)), _1527848), _1527850)))], (47150 ^ _773908) ^ [_1720654, _1720656, _1720658, _1720660, _1720662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1720654, _1720654)), hAPP(hAPP(c_Product__Type_OPair(_1720654, _1720654), _1720656), _1720658)), _1720660)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1720654, _1720654)), hAPP(hAPP(c_Product__Type_OPair(_1720654, _1720654), _1720658), _1720662)), c_Transitive__Closure_Otrancl(_1720654, _1720660))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1720654, _1720654)), hAPP(hAPP(c_Product__Type_OPair(_1720654, _1720654), _1720656), _1720662)), c_Transitive__Closure_Otrancl(_1720654, _1720660))))], (48901 ^ _773908) ^ [_1759685, _1759687] : [-(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)))), _1759685)) = 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)))), _1759687))), 48903 ^ _773908 : [(48906 ^ _773908) ^ [] : [48907 ^ _773908 : [(48910 ^ _773908) ^ [] : [hBOOL(hAPP(_1759687, 48902 ^ [_1759685, _1759687]))], (48908 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1759685, 48902 ^ [_1759685, _1759687])))]], 48911 ^ _773908 : [(48914 ^ _773908) ^ [] : [hBOOL(hAPP(_1759685, 48902 ^ [_1759685, _1759687]))], (48912 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1759687, 48902 ^ [_1759685, _1759687])))]]], (48904 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 48902 ^ [_1759685, _1759687])))]]], (28688 ^ _773908) ^ [_1296978, _1296980, _1296982, _1296984, _1296986, _1296988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1296978, _1296980)), hAPP(hAPP(c_Product__Type_OPair(_1296978, _1296980), _1296986), _1296988)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool)), _1296982), _1296984))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296978, tc_fun(_1296980, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1296978, tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_fun(_1296980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296980, tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_fun(_1296980, tc_HOL_Obool)), _1296978), c_COMBC(_1296980, tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296980, tc_prod(_1296978, _1296980)), tc_fun(_1296980, tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), _1296978), hAPP(c_COMBB(tc_prod(_1296978, _1296980), tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool), _1296980), c_member(tc_prod(_1296978, _1296980)))), c_Product__Type_OPair(_1296978, _1296980)))), _1296982)), hAPP(hAPP(c_COMBC(_1296978, tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_fun(_1296980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296980, tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_fun(_1296980, tc_HOL_Obool)), _1296978), c_COMBC(_1296980, tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296980, tc_prod(_1296978, _1296980)), tc_fun(_1296980, tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool)), _1296978), hAPP(c_COMBB(tc_prod(_1296978, _1296980), tc_fun(tc_fun(tc_prod(_1296978, _1296980), tc_HOL_Obool), tc_HOL_Obool), _1296980), c_member(tc_prod(_1296978, _1296980)))), c_Product__Type_OPair(_1296978, _1296980)))), _1296984)), _1296986), _1296988)))], (38510 ^ _773908) ^ [_1514598, _1514600, _1514602, _1514604] : [-(c_Product__Type_Oapsnd(_1514598, _1514600, _1514602, _1514604) = c_Product__Type_Omap__pair(_1514602, _1514602, _1514598, _1514600, c_Fun_Oid(_1514602), _1514604))], (7922 ^ _773908) ^ [_903617, _903619, _903621, _903623, _903625, _903627] : [hBOOL(hAPP(_903617, _903619)), c_Natural_Oevaln(_903621, _903619, _903623, _903625), c_Natural_Oevaln(c_Com_Ocom_OWhile(_903617, _903621), _903625, _903623, _903627), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_903617, _903621), _903619, _903623, _903627))], (35933 ^ _773908) ^ [_1448112, _1448114] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1448112, _1448114)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1448112, _1448114), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448112), c_Orderings_Otop__class_Otop(tc_fun(_1448112, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448114), c_Orderings_Otop__class_Otop(tc_fun(_1448114, tc_HOL_Obool))))], (31739 ^ _773908) ^ [_1359502, _1359504, _1359506, _1359508, _1359510] : [31741 ^ _773908 : [(31744 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359502, tc_HOL_Obool)), hAPP(_1359508, 31740 ^ [_1359502, _1359504, _1359506, _1359508, _1359510])), _1359510))], (31742 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359504), 31740 ^ [_1359502, _1359504, _1359506, _1359508, _1359510]), _1359506)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359502, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359504, tc_fun(_1359502, tc_HOL_Obool)), _1359506), _1359508)), _1359510)))], (49755 ^ _773908) ^ [_1778355, _1778357, _1778359, _1778361] : [49756 ^ _773908 : [(49759 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1778355), _1778359), _1778361))], (49757 ^ _773908) ^ [] : [_1778357 = _1778361]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1778355), hAPP(hAPP(c_List_Olist_OCons(_1778355), _1778357), _1778359)), _1778361)))], (36101 ^ _773908) ^ [_1451213, _1451215] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451213, tc_HOL_Obool)), _1451215), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451213, tc_HOL_Obool)), _1451215)) = c_Orderings_Otop__class_Otop(tc_fun(_1451213, tc_HOL_Obool)))], (2334 ^ _773908) ^ [_808075, _808077] : [_808077 = _808075, -(c_Hoare__Mirabelle_OMGT(_808077) = c_Hoare__Mirabelle_OMGT(_808075))], (4122 ^ _773908) ^ [_836175, _836177] : [_836177 = _836175, -(c_Nitpick_Onum(_836177) = c_Nitpick_Onum(_836175))], (38609 ^ _773908) ^ [_1517880, _1517882, _1517884, _1517886] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517880, _1517880), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1517882), _1517884)), _1517886) = hAPP(hAPP(c_Relation_Orel__comp(_1517880, _1517880, _1517880), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517880, _1517880), tc_HOL_Obool), _1517882), _1517886)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517880, _1517880), tc_HOL_Obool), _1517884), _1517886)))], (39981 ^ _773908) ^ [_1554634, _1554636, _1554638, _1554640] : [-(hAPP(hAPP(c_List_Onth(_1554634), hAPP(hAPP(c_List_Olist_OCons(_1554634), _1554636), _1554638)), hAPP(c_Nat_OSuc, _1554640)) = hAPP(hAPP(c_List_Onth(_1554634), _1554638), _1554640))], (46873 ^ _773908) ^ [_1713602, _1713604, _1713606, _1713608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713602, _1713602)), hAPP(hAPP(c_Product__Type_OPair(_1713602, _1713602), _1713604), _1713606)), c_Transitive__Closure_Ortrancl(_1713602, _1713608))), hBOOL(hAPP(hAPP(c_member(_1713602), _1713606), c_Wellfounded_Oacc(_1713602, _1713608))), -(hBOOL(hAPP(hAPP(c_member(_1713602), _1713604), c_Wellfounded_Oacc(_1713602, _1713608))))], (26321 ^ _773908) ^ [_1242514, _1242516, _1242518, _1242520, _1242522] : [26324 ^ _773908 : [(26327 ^ _773908) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1242516, _1242518, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1242516)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1242516), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1242516), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 26323 ^ [_1242514, _1242516, _1242518, _1242520, _1242522]))), _1242520), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1242516), hAPP(_1242522, 26322 ^ [_1242514, _1242516, _1242518, _1242520, _1242522])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1242516), tc_HOL_Obool))))], (26325 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1242514, 26322 ^ [_1242514, _1242516, _1242518, _1242520, _1242522]), 26323 ^ [_1242514, _1242516, _1242518, _1242520, _1242522])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1242516, _1242518, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1242516)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1242516), _1242514), _1242520), _1242522)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1242516), tc_HOL_Obool)))))], (45880 ^ _773908) ^ [_1690750, _1690752, _1690754] : [hBOOL(hAPP(c_List_Odistinct(_1690750), _1690752)), -(hBOOL(hAPP(c_List_Odistinct(_1690750), c_List_OdropWhile(_1690750, _1690754, _1690752))))], (32388 ^ _773908) ^ [_1374833, _1374835] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1374833), _1374835)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1374833, tc_HOL_Obool)), hAPP(c_Set_OPow(_1374833), _1374835)) = 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(_1374833), _1374835)))], (14406 ^ _773908) ^ [_1017656, _1017658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017656), _1017658)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017656), _1017658) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15023 ^ _773908) ^ [_1028374, _1028376, _1028378, _1028380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1028374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028376), _1028378)), -(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), _1028378), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028380, _1028374))), _1028376)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028378), _1028374))))], (41780 ^ _773908) ^ [_1596990, _1596992, _1596994, _1596996] : [-(hAPP(hAPP(c_List_Oappend(_1596990), _1596992), hAPP(hAPP(c_List_Olist_OCons(_1596990), _1596994), c_List_Olist_ONil(_1596990))) = _1596996), -(_1596996 = c_List_Olist_ONil(_1596990)), c_List_Obutlast(_1596990, _1596996) = _1596992, c_List_Olast(_1596990, _1596996) = _1596994], (47291 ^ _773908) ^ [_1723978, _1723980, _1723982, _1723984, _1723986] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1723978, _1723980)), hAPP(hAPP(c_Product__Type_OPair(_1723978, _1723980), _1723982), _1723984)), _1723986)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723980, _1723978)), hAPP(hAPP(c_Product__Type_OPair(_1723980, _1723978), _1723984), _1723982)), hAPP(c_Relation_Oconverse(_1723978, _1723980), _1723986))))], (17097 ^ _773908) ^ [_1068582, _1068584, _1068586] : [class_Int_Onumber__ring(_1068582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068582), hAPP(c_Groups_Ouminus__class_Ouminus(_1068582), hAPP(c_Int_Onumber__class_Onumber__of(_1068582), _1068584))), _1068586) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068582), hAPP(c_Int_Onumber__class_Onumber__of(_1068582), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068584))), _1068586))], (28532 ^ _773908) ^ [_1293215, _1293217, _1293219, _1293221, _1293223] : [c_Finite__Set_Ofolding__one(_1293215, _1293217, _1293219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293215), _1293221)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293215), _1293223)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293215, tc_HOL_Obool)), _1293221), _1293223) = c_Orderings_Obot__class_Obot(tc_fun(_1293215, tc_HOL_Obool))), -(hAPP(hAPP(_1293217, hAPP(_1293219, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293215, tc_HOL_Obool)), _1293221), _1293223))), hAPP(_1293219, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293215, tc_HOL_Obool)), _1293221), _1293223))) = hAPP(hAPP(_1293217, hAPP(_1293219, _1293221)), hAPP(_1293219, _1293223)))], (24759 ^ _773908) ^ [_1210639, _1210641] : [class_Orderings_Olinorder(_1210639), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210639), _1210641), _1210641) = _1210641)], (42706 ^ _773908) ^ [_1620824, _1620826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620824), _1620826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1620824)), hAPP(c_Code__Numeral_Oof__nat, _1620826))))], (47094 ^ _773908) ^ [_1719499, _1719501] : [-(c_Transitive__Closure_Otrancl(_1719499, _1719501) = hAPP(hAPP(c_Relation_Orel__comp(_1719499, _1719499, _1719499), _1719501), c_Transitive__Closure_Ortrancl(_1719499, _1719501)))], (9329 ^ _773908) ^ [_929124, _929126, _929128, _929130] : [class_Rings_Olinordered__semiring__strict(_929124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929124), _929126), _929128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929124), c_Groups_Ozero__class_Ozero(_929124)), _929130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929124), _929126), _929130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929124), _929128), _929130))))], (32730 ^ _773908) ^ [_1381477, _1381479, _1381481, _1381483] : [class_Orderings_Oorder(_1381477), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381477, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1381477, _1381479, _1381481)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1381477, _1381481, _1381483)) = c_Orderings_Obot__class_Obot(tc_fun(_1381477, tc_HOL_Obool)))], (17499 ^ _773908) ^ [_1075905, _1075907, _1075909] : [class_Rings_Olinordered__semidom(_1075905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075905), c_Groups_Oone__class_Oone(_1075905)), _1075907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075905), c_Groups_Oone__class_Oone(_1075905)), hAPP(hAPP(c_Power_Opower__class_Opower(_1075905), _1075907), _1075909))))], (5674 ^ _773908) ^ [_860677, _860679, _860681, _860683] : [-(hAPP(_860683, _860679) = hAPP(_860681, _860677)), _860683 = _860681, _860679 = _860677], (26481 ^ _773908) ^ [_1248333, _1248335] : [-(hAPP(c_Set_Oimage(_1248333, _1248333, c_COMBI(_1248333)), _1248335) = _1248335)], (49186 ^ _773908) ^ [_1765792, _1765794, _1765796] : [c_List_Olist__ex1(_1765792, _1765794, _1765796), 49190 ^ _773908 : [(49195 ^ _773908) ^ [_1766038] : [-(_1766038 = 49189 ^ [_1765792, _1765794, _1765796]), hBOOL(hAPP(hAPP(c_member(_1765792), _1766038), hAPP(c_List_Oset(_1765792), _1765796))), hBOOL(hAPP(_1765794, _1766038))], (49193 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1765794, 49189 ^ [_1765792, _1765794, _1765796])))], (49191 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765792), 49189 ^ [_1765792, _1765794, _1765796]), hAPP(c_List_Oset(_1765792), _1765796))))]]], (2098 ^ _773908) ^ [_804367, _804369, _804371, _804373] : [-(c_SMT_Oz3mod(_804373, _804369) = c_SMT_Oz3mod(_804371, _804367)), _804373 = _804371, _804369 = _804367], (37720 ^ _773908) ^ [_1489831, _1489833, _1489835, _1489837, _1489839, _1489841, _1489843, _1489845, _1489847, _1489849] : [-(c_Product__Type_Omap__pair(_1489831, _1489833, _1489835, _1489837, hAPP(c_Fun_Ocomp(_1489839, _1489833, _1489831, _1489841), _1489843), hAPP(c_Fun_Ocomp(_1489845, _1489837, _1489835, _1489847), _1489849)) = hAPP(c_Fun_Ocomp(tc_prod(_1489839, _1489845), tc_prod(_1489833, _1489837), tc_prod(_1489831, _1489835), c_Product__Type_Omap__pair(_1489839, _1489833, _1489845, _1489837, _1489841, _1489847)), c_Product__Type_Omap__pair(_1489831, _1489839, _1489835, _1489845, _1489843, _1489849)))], (690 ^ _773908) ^ [_784419, _784421, _784423, _784425, _784427, _784429] : [-(c_Finite__Set_Ofun__left__comm(_784427, _784423, _784419)), c_Finite__Set_Ofun__left__comm(_784429, _784425, _784421), _784429 = _784427, _784425 = _784423, _784421 = _784419], (30363 ^ _773908) ^ [_1328736, _1328738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1328736), _1328738))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1328736), _1328738)))], (28662 ^ _773908) ^ [_1295916, _1295918, _1295920, _1295922] : [hBOOL(hAPP(hAPP(_1295920, _1295918), _1295922)), -(hBOOL(hAPP(hAPP(c_member(_1295916), _1295918), c_SetInterval_Oord_OlessThan(_1295916, _1295920, _1295922))))], (44188 ^ _773908) ^ [_1654601, _1654603, _1654605, _1654607, _1654609] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654601, tc_fun(_1654603, tc_HOL_Obool)), _1654605), hAPP(hAPP(c_COMBS(_1654601, tc_fun(_1654603, tc_HOL_Obool), tc_fun(_1654603, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654603, tc_HOL_Obool), tc_fun(tc_fun(_1654603, tc_HOL_Obool), tc_fun(_1654603, tc_HOL_Obool)), _1654601), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654603, tc_HOL_Obool))), _1654607)), _1654609)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654603, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654603, tc_HOL_Obool), hAPP(c_Set_Oimage(_1654601, tc_fun(_1654603, tc_HOL_Obool), _1654607), _1654605))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654603, tc_HOL_Obool), hAPP(c_Set_Oimage(_1654601, tc_fun(_1654603, tc_HOL_Obool), _1654609), _1654605))))], (11812 ^ _773908) ^ [_971304, _971306, _971308, _971310] : [class_Groups_Oordered__comm__monoid__add(_971304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971304), c_Groups_Ozero__class_Ozero(_971304)), _971306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971304), _971308), _971310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971304), _971308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971304), _971306), _971310))))], (27946 ^ _773908) ^ [_1279743, _1279745, _1279747, _1279749] : [class_Lattices_Osemilattice__inf(_1279743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279743), _1279745), _1279747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279743), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1279743), _1279745), _1279749)), _1279747)))], (33062 ^ _773908) ^ [_1387972, _1387974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1387972)), 33071 ^ _773908 : [(33074 ^ _773908) ^ [] : [hBOOL(hAPP(_1387974, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33067 ^ [_1387972, _1387974]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 33068 ^ [_1387972, _1387974]), _1387972))))], (33072 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1387974, 33067 ^ [_1387972, _1387974])))]], 33075 ^ _773908 : [(33078 ^ _773908) ^ [] : [hBOOL(hAPP(_1387974, 33067 ^ [_1387972, _1387974]))], (33076 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1387974, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33067 ^ [_1387972, _1387974]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 33068 ^ [_1387972, _1387974]), _1387972)))))]], 33079 ^ _773908 : [(33089 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1387974, 33096 ^ [_1387972, _1387974]))), 33090 ^ _773908 : [(33091 ^ _773908) ^ [_1388519] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1388519), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1387972))), hBOOL(hAPP(_1387974, _1388519))]]], (33080 ^ _773908) ^ [] : [33081 ^ _773908 : [(33082 ^ _773908) ^ [_1388404] : [hBOOL(hAPP(_1387974, _1388404))]], 33084 ^ _773908 : [(33087 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1387974, 33083 ^ [_1387972, _1387974])))], (33085 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33083 ^ [_1387972, _1387974]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1387972))))]]]]], (44973 ^ _773908) ^ [_1672798, _1672800] : [_1672800 = c_List_Olist_ONil(_1672798), -(c_List_Oremdups(_1672798, _1672800) = c_List_Olist_ONil(_1672798))], (9211 ^ _773908) ^ [_926958, _926960, _926962] : [class_Rings_Olinordered__semiring__strict(_926958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926958), c_Groups_Ozero__class_Ozero(_926958)), _926960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926958), c_Groups_Ozero__class_Ozero(_926958)), _926962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926958), c_Groups_Ozero__class_Ozero(_926958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926958), _926960), _926962))))], (24419 ^ _773908) ^ [_1202722, _1202724, _1202726, _1202728] : [hBOOL(hAPP(_1202722, _1202724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202726, tc_HOL_Obool)), _1202722), _1202728)), -(hBOOL(hAPP(_1202728, _1202724)))], (51510 ^ _773908) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (5889 ^ _773908) ^ [_868139] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _868139)], (44349 ^ _773908) ^ [_1657976, _1657978] : [-(c_List_Oinsert(_1657976, _1657978, c_List_Olist_ONil(_1657976)) = hAPP(hAPP(c_List_Olist_OCons(_1657976), _1657978), c_List_Olist_ONil(_1657976)))], (2038 ^ _773908) ^ [_803457, _803459, _803461, _803463, _803465, _803467] : [-(c_Com_Ocom_OCall(_803467, _803463, _803459) = c_Com_Ocom_OCall(_803465, _803461, _803457)), _803467 = _803465, _803463 = _803461, _803459 = _803457], (2012 ^ _773908) ^ [_803066, _803068] : [_803068 = _803066, -(c_Com_Ocom_Ocom__size(_803068) = c_Com_Ocom_Ocom__size(_803066))], (31043 ^ _773908) ^ [_1343065, _1343067, _1343069, _1343071, _1343073] : [class_Groups_Ocomm__monoid__mult(_1343065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343067), _1343069)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343067), _1343071)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343065), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343067, _1343065), _1343073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343067, tc_HOL_Obool)), _1343069), _1343071))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343067, _1343065), _1343073), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343067, tc_HOL_Obool)), _1343069), _1343071))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343065), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343067, _1343065), _1343073), _1343069)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343067, _1343065), _1343073), _1343071)))], (1020 ^ _773908) ^ [_789374, _789376, _789378, _789380] : [-(c_Relation_Osym(_789378, _789374)), c_Relation_Osym(_789380, _789376), _789380 = _789378, _789376 = _789374], (15633 ^ _773908) ^ [_1039761, _1039763, _1039765] : [class_Rings_Ocomm__ring__1(_1039761), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039761), _1039763), _1039765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039761), _1039763), hAPP(c_Groups_Ouminus__class_Ouminus(_1039761), _1039765)))], (15485 ^ _773908) ^ [_1036691, _1036693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036691), _1036693)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036693), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036693), _1036691)) = _1036691)], (47703 ^ _773908) ^ [_1735062, _1735064, _1735066, _1735068] : [class_Groups_Ocomm__monoid__mult(_1735062), hBOOL(hAPP(c_Finite__Set_Ofinite(_1735064), _1735066)), 47713 ^ _773908 : [(47716 ^ _773908) ^ [] : [hAPP(_1735068, 47712 ^ [_1735062, _1735064, _1735066, _1735068]) = c_Groups_Oone__class_Oone(_1735062)], (47714 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735064), 47712 ^ [_1735062, _1735064, _1735066, _1735068]), _1735066)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1735062, _1735064, c_Groups_Otimes__class_Otimes(_1735062)), _1735068), c_Groups_Oone__class_Oone(_1735062)), _1735066) = c_Groups_Oone__class_Oone(_1735062))], (40089 ^ _773908) ^ [_1557444, _1557446, _1557448, _1557450] : [-(hAPP(hAPP(c_List_Otake(_1557444), _1557446), hAPP(hAPP(c_List_Otake(_1557444), _1557448), _1557450)) = hAPP(hAPP(c_List_Otake(_1557444), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1557446), _1557448)), _1557450))], (23490 ^ _773908) ^ [_1183501, _1183503, _1183505, _1183507] : [-(hAPP(c_Nat_Onat_Onat__rec(_1183501, _1183503, _1183505), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1183507)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1183501), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1183507))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183501, _1183501), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1183501, tc_fun(_1183501, _1183501)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1183501, tc_fun(_1183501, _1183501)), tc_Int_Oint), c_If(_1183501)), c_Nat__Numeral_Oneg)), _1183503)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183501, _1183501), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1183501, _1183501), tc_Int_Oint), _1183505), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1183501, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1183501, _1183503, _1183505)), c_Int_Onat)))))], (12602 ^ _773908) ^ [_985161, _985163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985161), hAPP(c_Nat_OSuc, _985163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985161), _985163))), -(_985161 = hAPP(c_Nat_OSuc, _985163))], (47246 ^ _773908) ^ [_1723018, _1723020, _1723022] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1723018, _1723018), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1723018, _1723018), _1723020)), c_Transitive__Closure_Ortrancl(_1723018, _1723020)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1723018, _1723018), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723018, _1723018)), hAPP(hAPP(c_Product__Type_OPair(_1723018, _1723018), _1723022), _1723022)), c_Transitive__Closure_Otrancl(_1723018, _1723020)))], (11245 ^ _773908) ^ [_961334, _961336, _961338, _961340, _961342] : [class_Rings_Oordered__semiring(_961334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961334), _961336), _961338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961334), _961340), _961342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961334), c_Groups_Ozero__class_Ozero(_961334)), _961336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961334), c_Groups_Ozero__class_Ozero(_961334)), _961340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961334), _961336), _961340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961334), _961338), _961342))))], (38130 ^ _773908) ^ [_1499243, _1499245, _1499247, _1499249, _1499251, _1499253, _1499255] : [class_Groups_Ocomm__monoid__add(_1499243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499245), _1499247)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499249), _1499251)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499245, _1499243), hAPP(hAPP(c_COMBS(_1499245, tc_fun(_1499249, tc_HOL_Obool), _1499243), hAPP(hAPP(c_COMBB(tc_fun(_1499249, _1499243), tc_fun(tc_fun(_1499249, tc_HOL_Obool), _1499243), _1499245), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499249, _1499243)), _1499253)), hAPP(hAPP(c_COMBB(tc_fun(_1499249, tc_HOL_Obool), tc_fun(_1499249, tc_HOL_Obool), _1499245), c_Set_OCollect(_1499249)), hAPP(hAPP(c_COMBB(tc_fun(_1499249, tc_HOL_Obool), tc_fun(_1499249, tc_HOL_Obool), _1499245), hAPP(c_COMBS(_1499249, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499249), c_fconj), hAPP(hAPP(c_COMBC(_1499249, tc_fun(_1499249, tc_HOL_Obool), tc_HOL_Obool), c_member(_1499249)), _1499251)))), _1499255)))), _1499247) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499249, _1499243), hAPP(hAPP(c_COMBS(_1499249, tc_fun(_1499245, tc_HOL_Obool), _1499243), hAPP(hAPP(c_COMBB(tc_fun(_1499245, _1499243), tc_fun(tc_fun(_1499245, tc_HOL_Obool), _1499243), _1499249), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499245, _1499243)), hAPP(c_COMBC(_1499245, _1499249, _1499243), _1499253))), hAPP(hAPP(c_COMBB(tc_fun(_1499245, tc_HOL_Obool), tc_fun(_1499245, tc_HOL_Obool), _1499249), c_Set_OCollect(_1499245)), hAPP(hAPP(c_COMBB(tc_fun(_1499245, tc_HOL_Obool), tc_fun(_1499245, tc_HOL_Obool), _1499249), hAPP(c_COMBS(_1499245, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499245), c_fconj), hAPP(hAPP(c_COMBC(_1499245, tc_fun(_1499245, tc_HOL_Obool), tc_HOL_Obool), c_member(_1499245)), _1499247)))), hAPP(c_COMBC(_1499245, _1499249, tc_HOL_Obool), _1499255))))), _1499251))], (48279 ^ _773908) ^ [_1747175, _1747177, _1747179, _1747181, _1747183] : [class_Complete__Lattice_Ocomplete__lattice(_1747175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1747177), _1747179)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1747175), _1747181), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1747177, _1747175), _1747179), _1747183)) = hAPP(hAPP(c_Finite__Set_Ofold(_1747177, _1747175, hAPP(hAPP(c_COMBB(_1747175, tc_fun(_1747175, _1747175), _1747177), c_Lattices_Osemilattice__inf__class_Oinf(_1747175)), _1747183)), _1747181), _1747179))], (50213 ^ _773908) ^ [_1790620, _1790622] : [c_Relation_Otrans(_1790620, _1790622), -(c_Transitive__Closure_Otrancl(_1790620, _1790622) = _1790622)], (8028 ^ _773908) ^ [_905315, _905317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _905315), _905317)), -(_905317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _905315), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8031 ^ [_905315, _905317]))))], (19843 ^ _773908) ^ [_1116384, _1116386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116384)), c_Int_OBit0(_1116386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116384), _1116386)))], (26213 ^ _773908) ^ [_1239263, _1239265, _1239267, _1239269] : [class_Lattices_Osemilattice__sup(_1239263), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239263), _1239265), _1239267)), _1239269) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239263), _1239265), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239263), _1239267), _1239269)))], (16399 ^ _773908) ^ [_1055043, _1055045] : [-(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), _1055043)), _1055045))))], (38524 ^ _773908) ^ [_1514877, _1514879, _1514881, _1514883] : [class_Groups_Ocomm__monoid__mult(_1514877), c_Fun_Oinj__on(_1514879, _1514877, _1514881, _1514883), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514879, _1514877), _1514881), _1514883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514877, _1514877), c_Fun_Oid(_1514877)), hAPP(c_Set_Oimage(_1514879, _1514877, _1514881), _1514883)))], (41716 ^ _773908) ^ [_1595772, _1595774, _1595776] : [-(_1595772 = c_List_Olist_ONil(_1595774)), -(c_List_Obutlast(_1595774, hAPP(hAPP(c_List_Oappend(_1595774), _1595776), _1595772)) = hAPP(hAPP(c_List_Oappend(_1595774), _1595776), c_List_Obutlast(_1595774, _1595772)))], (30605 ^ _773908) ^ [_1333935, _1333937, _1333939] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333935), _1333937)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333935), _1333939)), 30615 ^ _773908 : [(30618 ^ _773908) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30616 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333935), 30614 ^ [_1333935, _1333937, _1333939]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333935, tc_HOL_Obool)), _1333937), _1333939))))]], -(hAPP(c_Finite__Set_Ocard(_1333935), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333935, tc_HOL_Obool)), _1333937), _1333939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333935), _1333937)), hAPP(c_Finite__Set_Ocard(_1333935), _1333939)))], (25403 ^ _773908) ^ [_1222842, _1222844, _1222846, _1222848] : [class_Orderings_Olinorder(_1222842), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222842), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222842), _1222844), _1222846)), _1222848) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222842), _1222844), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222842), _1222846), _1222848)))], (50241 ^ _773908) ^ [_1791096] : [-(c_Relation_Otrans(tc_fun(_1791096, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1791096)))], (47787 ^ _773908) ^ [_1736499, _1736501, _1736503] : [class_Enum_Oenum(_1736499), class_Enum_Oenum(_1736501), 47794 ^ _773908 : [(47801 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736501), hAPP(hAPP(c_COMBB(tc_fun(_1736499, tc_HOL_Obool), tc_HOL_Obool, _1736501), c_Enum_Oenum__class_Oenum__all(_1736499)), hAPP(hAPP(c_COMBB(tc_fun(_1736499, tc_prod(_1736501, _1736499)), tc_fun(_1736499, tc_HOL_Obool), _1736501), hAPP(c_COMBB(tc_prod(_1736501, _1736499), tc_HOL_Obool, _1736499), _1736503)), c_Product__Type_OPair(_1736501, _1736499))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1736501, _1736499)), _1736503)))], (47795 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1736501, _1736499)), _1736503)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736501), hAPP(hAPP(c_COMBB(tc_fun(_1736499, tc_HOL_Obool), tc_HOL_Obool, _1736501), c_Enum_Oenum__class_Oenum__all(_1736499)), hAPP(hAPP(c_COMBB(tc_fun(_1736499, tc_prod(_1736501, _1736499)), tc_fun(_1736499, tc_HOL_Obool), _1736501), hAPP(c_COMBB(tc_prod(_1736501, _1736499), tc_HOL_Obool, _1736499), _1736503)), c_Product__Type_OPair(_1736501, _1736499))))))]]], (37548 ^ _773908) ^ [_1484623, _1484625, _1484627, _1484629] : [-(_1484623 = c_Orderings_Obot__class_Obot(tc_fun(_1484625, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1484625, _1484627), _1484627, c_Product__Type_Osnd(_1484625, _1484627)), hAPP(hAPP(c_Product__Type_OSigma(_1484625, _1484627), _1484623), hAPP(c_COMBK(tc_fun(_1484627, tc_HOL_Obool), _1484625), _1484629))) = _1484629)], (43665 ^ _773908) ^ [_1642158, _1642160, _1642162] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1642158))), c_Enum_On__lists(_1642158, _1642160, _1642162)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642158)), _1642162)), _1642160))], (45317 ^ _773908) ^ [_1678875, _1678877] : [class_Orderings_Olinorder(_1678875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1678875), _1678877)), 45324 ^ _773908 : [(45329 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1678875), c_List_Olinorder__class_Osorted__list__of__set(_1678875, _1678877))))], (45327 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1678875, c_List_Olinorder__class_Osorted__list__of__set(_1678875, _1678877)))], (45325 ^ _773908) ^ [] : [-(hAPP(c_List_Oset(_1678875), c_List_Olinorder__class_Osorted__list__of__set(_1678875, _1678877)) = _1678877)]]], (30459 ^ _773908) ^ [_1330502, _1330504, _1330506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330502), _1330504)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330502), _1330506)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330502), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330502, tc_HOL_Obool)), _1330504), _1330506))), hAPP(c_Finite__Set_Ocard(_1330502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330502, tc_HOL_Obool)), _1330504), _1330506))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330502), _1330504)), hAPP(c_Finite__Set_Ocard(_1330502), _1330506)))], (48223 ^ _773908) ^ [_1745913, _1745915, _1745917] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1745913), _1745915)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1745913, tc_HOL_Obool)), _1745915), _1745917) = hAPP(hAPP(c_Finite__Set_Ofold(_1745913, tc_fun(_1745913, tc_HOL_Obool), c_Set_Oinsert(_1745913)), _1745917), _1745915))], (41027 ^ _773908) ^ [_1582082, _1582084, _1582086] : [hBOOL(hAPP(c_List_Odistinct(_1582082), _1582084)), -(hBOOL(hAPP(c_List_Odistinct(_1582082), hAPP(hAPP(c_List_Odrop(_1582082), _1582086), _1582084))))], (49141 ^ _773908) ^ [_1764854, _1764856, _1764858] : [49143 ^ _773908 : [(49146 ^ _773908) ^ [] : [hBOOL(hAPP(_1764856, 49142 ^ [_1764854, _1764856, _1764858]))], (49144 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764854), 49142 ^ [_1764854, _1764856, _1764858]), hAPP(c_List_Oset(_1764854), _1764858))))]], -(c_List_Olist__all(_1764854, _1764856, _1764858))], (41606 ^ _773908) ^ [_1593563] : [class_Groups_Omonoid__add(_1593563), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1593563), c_List_Olist_ONil(_1593563)) = c_Groups_Ozero__class_Ozero(_1593563))], (40367 ^ _773908) ^ [_1563852, _1563854, _1563856] : [40369 ^ _773908 : [(40372 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1563852), 40368 ^ [_1563852, _1563854, _1563856]), _1563856))], (40370 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1563852), 40368 ^ [_1563852, _1563854, _1563856]), hAPP(c_List_Oset(_1563852), _1563854))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1563852)), _1563854), c_List_Olists(_1563852, _1563856))))], (47385 ^ _773908) ^ [_1726328, _1726330, _1726332, _1726334, _1726336] : [-(hAPP(c_Relation_Oconverse(_1726328, _1726330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1726332, tc_fun(tc_prod(_1726328, _1726330), tc_HOL_Obool)), _1726334), _1726336)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1726332, tc_fun(tc_prod(_1726330, _1726328), tc_HOL_Obool)), _1726334), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1726328, _1726330), tc_HOL_Obool), tc_fun(tc_prod(_1726330, _1726328), tc_HOL_Obool), _1726332), c_Relation_Oconverse(_1726328, _1726330)), _1726336)))], (24007 ^ _773908) ^ [_1193319, _1193321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193321)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193319, _1193321), c_Divides_OposDivAlg(_1193319, _1193321))))], (43823 ^ _773908) ^ [_1645727, _1645729, _1645731] : [_1645731 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1645727, _1645729), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1645727, _1645729), _1645731) = c_Orderings_Obot__class_Obot(tc_fun(_1645727, tc_HOL_Obool)))], (44887 ^ _773908) ^ [_1671389, _1671391] : [-(hBOOL(hAPP(c_List_Odistinct(_1671389), c_List_Oremdups(_1671389, _1671391))))], (5767 ^ _773908) ^ [_865227, _865229, _865231, _865233, _865235, _865237] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_865227, _865229, _865231, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_865227), _865233), _865235), _865237)) = hAPP(hAPP(hAPP(_865231, _865233), _865235), _865237))], (28106 ^ _773908) ^ [_1283067, _1283069, _1283071, _1283073] : [class_Lattices_Osemilattice__inf(_1283067), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283067), _1283069), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283067), _1283071), _1283073)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283067), _1283071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283067), _1283069), _1283073)))], (16847 ^ _773908) ^ [_1063578, _1063580, _1063582] : [class_Int_Onumber__ring(_1063578), class_Rings_Olinordered__idom(_1063578), 16854 ^ _773908 : [(16861 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1063580), _1063582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063578), hAPP(c_Int_Onumber__class_Onumber__of(_1063578), _1063580)), hAPP(c_Int_Onumber__class_Onumber__of(_1063578), _1063582))))], (16855 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063578), hAPP(c_Int_Onumber__class_Onumber__of(_1063578), _1063580)), hAPP(c_Int_Onumber__class_Onumber__of(_1063578), _1063582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1063580), _1063582)))]]], (49552 ^ _773908) ^ [_1774074, _1774076, _1774078, _1774080] : [-(hAPP(hAPP(c_List_Odrop(_1774074), _1774076), c_List_Oreplicate(_1774074, _1774078, _1774080)) = c_List_Oreplicate(_1774074, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1774078), _1774076), _1774080))], (24835 ^ _773908) ^ [_1211976] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1211976), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23155 ^ _773908) ^ [_1176430, _1176432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1176430)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176432))), -(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(_1176432))), 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), _1176430)), c_Int_Onat))))))], (26025 ^ _773908) ^ [_1235237, _1235239, _1235241] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1235237, tc_HOL_Obool)), _1235239), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235237, tc_HOL_Obool)), _1235239), _1235241))))], (48979 ^ _773908) ^ [_1761624, _1761626] : [-(c_Nitpick_Oinverse__frac(_1761624, _1761626) = hAPP(hAPP(c_Nitpick_Ofrac(_1761624), hAPP(c_Nitpick_Odenom(_1761624), _1761626)), hAPP(c_Nitpick_Onum(_1761624), _1761626)))], (36452 ^ _773908) ^ [_1460211, _1460213, _1460215, _1460217] : [c_Equiv__Relations_Oequivp(_1460211, _1460213), hBOOL(hAPP(hAPP(_1460213, _1460215), _1460217)), -(hBOOL(hAPP(hAPP(_1460213, _1460217), _1460215)))], (40999 ^ _773908) ^ [_1581574, _1581576] : [-(_1581574 = c_List_Olist_ONil(_1581576)), -(hAPP(c_List_Orotate1(_1581576), _1581574) = hAPP(hAPP(c_List_Oappend(_1581576), hAPP(c_List_Otl(_1581576), _1581574)), hAPP(hAPP(c_List_Olist_OCons(_1581576), hAPP(c_List_Ohd(_1581576), _1581574)), c_List_Olist_ONil(_1581576))))], (34109 ^ _773908) ^ [_1408770, _1408772, _1408774, _1408776, _1408778, _1408780, _1408782, _1408784] : [c_Finite__Set_Ofolding__image(_1408770, _1408772, _1408774, _1408776, _1408778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408772), _1408780)), c_Fun_Oinj__on(_1408772, _1408772, _1408782, _1408780), -(hAPP(hAPP(_1408778, _1408784), hAPP(c_Set_Oimage(_1408772, _1408772, _1408782), _1408780)) = hAPP(hAPP(_1408778, hAPP(c_Fun_Ocomp(_1408772, _1408770, _1408772, _1408784), _1408782)), _1408780))], (26469 ^ _773908) ^ [_1248024, _1248026, _1248028, _1248030, _1248032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248024, tc_HOL_Obool)), _1248026), hAPP(c_Set_Oimage(_1248028, _1248024, _1248030), _1248032)))), 26470 ^ _773908 : [(26471 ^ _773908) ^ [_1248104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248028, tc_HOL_Obool)), _1248104), _1248032)), _1248026 = hAPP(c_Set_Oimage(_1248028, _1248024, _1248030), _1248104)]]], (43888 ^ _773908) ^ [_1647298, _1647300] : [class_Complete__Lattice_Ocomplete__lattice(_1647298), -(c_Complete__Lattice_OSup__class_OSup(_1647298, hAPP(hAPP(c_Set_Oinsert(_1647298), _1647300), c_Orderings_Obot__class_Obot(tc_fun(_1647298, tc_HOL_Obool)))) = _1647300)], (36476 ^ _773908) ^ [_1460597] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1460597)), c_Int_OInteg)))], (14815 ^ _773908) ^ [_1024241, _1024243] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024241), _1024243) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14816 ^ _773908 : [(14825 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024241), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024243), _1024241))], (14819 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024241), _1024243))], (14817 ^ _773908) ^ [] : [_1024243 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (51578 ^ _773908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (49739 ^ _773908) ^ [_1778081, _1778083, _1778085] : [hBOOL(hAPP(hAPP(c_member(_1778081), _1778085), hAPP(c_List_Oset(_1778081), _1778083))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1778081), _1778083), _1778085)))], (40159 ^ _773908) ^ [_1559094, _1559096] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559094), hAPP(c_List_Oset(_1559094), _1559096))))], (31552 ^ _773908) ^ [_1355154, _1355156, _1355158, _1355160, _1355162, _1355164] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355154, tc_fun(_1355156, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355158, tc_fun(_1355154, tc_HOL_Obool)), _1355160), _1355162)), _1355164) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355158, tc_fun(_1355156, tc_HOL_Obool)), _1355160), hAPP(hAPP(c_COMBC(_1355158, tc_fun(_1355154, tc_fun(_1355156, tc_HOL_Obool)), tc_fun(_1355156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355154, tc_HOL_Obool), tc_fun(tc_fun(_1355154, tc_fun(_1355156, tc_HOL_Obool)), tc_fun(_1355156, tc_HOL_Obool)), _1355158), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355154, tc_fun(_1355156, tc_HOL_Obool))), _1355162)), _1355164)))], (17665 ^ _773908) ^ [_1078983, _1078985, _1078987, _1078989] : [class_Rings_Olinordered__semidom(_1078983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078985), _1078987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078983), c_Groups_Oone__class_Oone(_1078983)), _1078989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078983), hAPP(hAPP(c_Power_Opower__class_Opower(_1078983), _1078989), _1078985)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078983), _1078989), _1078987))))], (29865 ^ _773908) ^ [_1319161, _1319163, _1319165] : [class_Orderings_Olinorder(_1319161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319161), _1319163)), -(_1319165 = c_Orderings_Obot__class_Obot(tc_fun(_1319161, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319161, tc_HOL_Obool)), _1319165), _1319163)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1319161), c_Big__Operators_Olattice_OSup__fin(_1319161, c_Orderings_Oord__class_Omax(_1319161), _1319165)), c_Big__Operators_Olattice_OSup__fin(_1319161, c_Orderings_Oord__class_Omax(_1319161), _1319163)) = c_Big__Operators_Olattice_OSup__fin(_1319161, c_Orderings_Oord__class_Omax(_1319161), _1319163))], (3212 ^ _773908) ^ [_822072, _822074, _822076, _822078] : [-(c_Enum_Oenum__the(_822078, _822074) = c_Enum_Oenum__the(_822076, _822072)), _822078 = _822076, _822074 = _822072], (15519 ^ _773908) ^ [_1037427, _1037429, _1037431] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037427), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1037429, _1037431)), _1037431) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037427), _1037429), _1037431))], (19767 ^ _773908) ^ [_1114919, _1114921] : [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), _1114919))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1114921)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1114919))) = 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), _1114921), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114919)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21325 ^ _773908) ^ [_1142466, _1142468, _1142470] : [class_Rings_Odivision__ring(_1142466), -(_1142468 = c_Groups_Ozero__class_Ozero(_1142466)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1142466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142466), _1142470), _1142468)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142466), _1142470), hAPP(c_Groups_Ouminus__class_Ouminus(_1142466), _1142468)))], (24081 ^ _773908) ^ [_1194676, _1194678, _1194680, _1194682, _1194684] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1194676, _1194678), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1194680), _1194682))), -(_1194678 = 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), _1194684), _1194676), _1194678), 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), _1194684), _1194680)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194684), _1194682)), _1194678))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194684), _1194682), _1194678)))))], (33140 ^ _773908) ^ [_1389494, _1389496, _1389498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1389494), _1389496)), -(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)), _1389494)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1389498), _1389496)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1389498), _1389494)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1389496), _1389494)))], (13614 ^ _773908) ^ [_1003017, _1003019, _1003021, _1003023] : [class_Divides_Osemiring__div(_1003017), -(c_Divides_Odiv__class_Omod(_1003017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003017), _1003019), _1003021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003017), _1003023), _1003021)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003017), c_Divides_Odiv__class_Omod(_1003017, _1003019, _1003023)), _1003021))], (50931 ^ _773908) ^ [_1804312, _1804314, _1804316, _1804318, _1804320] : [hBOOL(hAPP(hAPP(c_member(_1804312), _1804314), hAPP(c_Set_Oimage(_1804316, _1804312, _1804318), _1804320))), -(hBOOL(hAPP(hAPP(c_member(_1804316), hAPP(c_Hilbert__Choice_Oinv__into(_1804316, _1804312, _1804320, _1804318), _1804314)), _1804320)))], (11733 ^ _773908) ^ [_969911, _969913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _969911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _969913), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _969911), _969913))), -(_969911 = _969913)], (17057 ^ _773908) ^ [_1067915, _1067917] : [class_Groups_Oordered__ab__group__add__abs(_1067915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067915), _1067917), c_Groups_Ozero__class_Ozero(_1067915))), -(hAPP(c_Groups_Oabs__class_Oabs(_1067915), _1067917) = hAPP(c_Groups_Ouminus__class_Ouminus(_1067915), _1067917))], (23065 ^ _773908) ^ [_1174440] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1174440)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174440)), 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))))], (6272 ^ _773908) ^ [_875632] : [-(_875632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_875632 = hAPP(c_Nat_OSuc, 6275 ^ [_875632]))], (33436 ^ _773908) ^ [_1394986, _1394988, _1394990, _1394992, _1394994, _1394996] : [c_Fun_Oinj__on(_1394986, _1394988, _1394990, _1394992), c_Fun_Oinj__on(_1394988, _1394994, _1394996, hAPP(c_Set_Oimage(_1394986, _1394988, _1394990), _1394992)), -(c_Fun_Oinj__on(_1394986, _1394994, hAPP(c_Fun_Ocomp(_1394988, _1394994, _1394986, _1394996), _1394990), _1394992))], (9644 ^ _773908) ^ [_934639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _934639)), -(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, _934639))))], (50476 ^ _773908) ^ [_1795638, _1795640] : [c_Equiv__Relations_Oequivp(_1795638, _1795640), 50479 ^ _773908 : [(50484 ^ _773908) ^ [] : [-(c_Predicate_Otransp(_1795638, _1795640))], (50482 ^ _773908) ^ [] : [-(c_Predicate_Osymp(_1795638, _1795640))], (50480 ^ _773908) ^ [] : [-(c_Predicate_Oreflp(_1795638, _1795640))]]], (17335 ^ _773908) ^ [_1073006, _1073008] : [_1073006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1073008), _1073006) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51526 ^ _773908) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (12308 ^ _773908) ^ [_979968, _979970] : [-(_979968 = hAPP(c_Int_Onat, _979970)), 12311 ^ _773908 : [(12314 ^ _773908) ^ [] : [_979970 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _979968)], (12312 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979970)))]], 12315 ^ _773908 : [(12318 ^ _773908) ^ [] : [_979968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12316 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979970))]]], (37530 ^ _773908) ^ [_1484216, _1484218, _1484220, _1484222] : [_1484216 = c_Orderings_Obot__class_Obot(tc_fun(_1484218, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1484220, _1484218), _1484220, c_Product__Type_Ofst(_1484220, _1484218)), hAPP(hAPP(c_Product__Type_OSigma(_1484220, _1484218), _1484222), hAPP(c_COMBK(tc_fun(_1484218, tc_HOL_Obool), _1484220), _1484216))) = c_Orderings_Obot__class_Obot(tc_fun(_1484220, tc_HOL_Obool)))], (42263 ^ _773908) ^ [_1610949, _1610951, _1610953, _1610955] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1610949, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610951, tc_fun(_1610949, tc_HOL_Obool)), _1610953), _1610955)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1610951, tc_fun(_1610949, tc_HOL_Obool)), _1610953), hAPP(hAPP(c_COMBB(tc_fun(_1610949, tc_HOL_Obool), tc_fun(_1610949, tc_HOL_Obool), _1610951), c_Groups_Ouminus__class_Ouminus(tc_fun(_1610949, tc_HOL_Obool))), _1610955)))], (42265 ^ _773908) ^ [_1611031, _1611033, _1611035, _1611037] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1611031, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611033, tc_fun(_1611031, tc_HOL_Obool)), _1611035), _1611037)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611033, tc_fun(_1611031, tc_HOL_Obool)), _1611035), hAPP(hAPP(c_COMBB(tc_fun(_1611031, tc_HOL_Obool), tc_fun(_1611031, tc_HOL_Obool), _1611033), c_Groups_Ouminus__class_Ouminus(tc_fun(_1611031, tc_HOL_Obool))), _1611037)))], (37149 ^ _773908) ^ [_1474128, _1474130] : [-(hAPP(c_Set_Ovimage(_1474128, _1474128, c_COMBI(_1474128)), _1474130) = _1474130)], (25799 ^ _773908) ^ [_1230972, _1230974] : [class_Lattices_Olattice(_1230972), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1230972), _1230974), _1230974) = _1230974)], (24603 ^ _773908) ^ [_1207435, _1207437] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207435), _1207437) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1207435, _1207437)))], (20665 ^ _773908) ^ [_1131037, _1131039] : [class_Fields_Olinordered__field__inverse__zero(_1131037), class_Int_Onumber__ring(_1131037), 20672 ^ _773908 : [(20679 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131037), c_Groups_Ozero__class_Ozero(_1131037)), _1131039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131037), c_Groups_Ozero__class_Ozero(_1131037)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131037), _1131039), hAPP(c_Int_Onumber__class_Onumber__of(_1131037), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20673 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131037), c_Groups_Ozero__class_Ozero(_1131037)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131037), _1131039), hAPP(c_Int_Onumber__class_Onumber__of(_1131037), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131037), c_Groups_Ozero__class_Ozero(_1131037)), _1131039)))]]], (13308 ^ _773908) ^ [_997421, _997423] : [class_Groups_Osgn__if(_997421), 13311 ^ _773908 : [(13318 ^ _773908) ^ [] : [-(_997423 = c_Groups_Ozero__class_Ozero(_997421)), 13321 ^ _773908 : [(13328 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997421), c_Groups_Ozero__class_Ozero(_997421)), _997423))), -(c_Groups_Osgn__class_Osgn(_997421, _997423) = hAPP(c_Groups_Ouminus__class_Ouminus(_997421), c_Groups_Oone__class_Oone(_997421)))], (13322 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997421), c_Groups_Ozero__class_Ozero(_997421)), _997423)), -(c_Groups_Osgn__class_Osgn(_997421, _997423) = c_Groups_Oone__class_Oone(_997421))]]], (13312 ^ _773908) ^ [] : [_997423 = c_Groups_Ozero__class_Ozero(_997421), -(c_Groups_Osgn__class_Osgn(_997421, _997423) = c_Groups_Ozero__class_Ozero(_997421))]]], (18629 ^ _773908) ^ [_1095739, _1095741, _1095743, _1095745] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095739, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1095739), _1095741), _1095743)), _1095745))), hBOOL(hAPP(hAPP(c_member(_1095739), _1095741), _1095745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095739, tc_HOL_Obool)), _1095743), _1095745))], (44792 ^ _773908) ^ [_1668910] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1668910) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1668910))))], (17315 ^ _773908) ^ [_1072629] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072629) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1072629))], (40921 ^ _773908) ^ [_1579808, _1579810, _1579812] : [40923 ^ _773908 : [(40926 ^ _773908) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1579808, hAPP(c_Nat_OSuc, _1579812), 40922 ^ [_1579808, _1579810, _1579812])], (40924 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1579808)), 40922 ^ [_1579808, _1579810, _1579812]), _1579810)))]], 40927 ^ _773908 : [(40928 ^ _773908) ^ [_1579981] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1579808)), _1579981), _1579810)), -(c_Hoare__Mirabelle_Otriple__valid(_1579808, _1579812, _1579981))]]], (35424 ^ _773908) ^ [_1437783, _1437785, _1437787] : [-(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), _1437783)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1437785))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1437787))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1437787), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1437783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1437783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1437787), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1437785)))))], (40311 ^ _773908) ^ [_1562589, _1562591, _1562593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562589)), _1562591)), _1562593)), -(hAPP(hAPP(c_List_Odrop(_1562589), _1562593), _1562591) = c_List_Olist_ONil(_1562589))], (13434 ^ _773908) ^ [_999473, _999475, _999477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999473, tc_HOL_Obool)), _999477), _999475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999473, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999473, tc_HOL_Obool)), _999475)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999473, tc_HOL_Obool)), _999477))))], (34470 ^ _773908) ^ [_1415727, _1415729, _1415731] : [-(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), _1415727)), 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))), _1415729))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1415731))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1415731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415727), 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), _1415731), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1415729)))))], (45583 ^ _773908) ^ [_1684460, _1684462, _1684464] : [-(hAPP(c_List_Orev(_1684460), hAPP(hAPP(c_List_Oappend(_1684460), _1684462), _1684464)) = hAPP(hAPP(c_List_Oappend(_1684460), hAPP(c_List_Orev(_1684460), _1684464)), hAPP(c_List_Orev(_1684460), _1684462)))], (41402 ^ _773908) ^ [_1589848, _1589850] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1589848, _1589850)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1589848, _1589850))], (51115 ^ _773908) ^ [_1808442, _1808444, _1808446, _1808448] : [c_Fun_Obij__betw(_1808442, _1808444, _1808446, c_Orderings_Otop__class_Otop(tc_fun(_1808442, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808444, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1808442, _1808444, _1808446), hAPP(c_Set_OCollect(_1808442), _1808448)) = hAPP(c_Set_OCollect(_1808444), hAPP(hAPP(c_COMBB(_1808442, tc_HOL_Obool, _1808444), _1808448), c_Hilbert__Choice_Oinv__into(_1808442, _1808444, c_Orderings_Otop__class_Otop(tc_fun(_1808442, tc_HOL_Obool)), _1808446))))], (9722 ^ _773908) ^ [_935898, _935900] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935898), _935900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935900), _935898))], (17935 ^ _773908) ^ [_1083451] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1083451), hAPP(c_Int_Onumber__class_Onumber__of(_1083451), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1083451)), class_Int_Onumber__ring(_1083451), class_Rings_Olinordered__idom(_1083451)], (21493 ^ _773908) ^ [_1145517, _1145519, _1145521, _1145523] : [class_Fields_Olinordered__field(_1145517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145517), _1145519), _1145521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145517), _1145523), c_Groups_Ozero__class_Ozero(_1145517))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145517), c_Groups_Ozero__class_Ozero(_1145517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145517), _1145519), _1145521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145517), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145517), _1145523), _1145519)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145517), _1145523), _1145521))))], (1164 ^ _773908) ^ [_791444, _791446] : [-(class_Rings_Oring__1__no__zero__divisors(_791444)), _791446 = _791444, class_Rings_Oring__1__no__zero__divisors(_791446)], (9253 ^ _773908) ^ [_927723, _927725, _927727] : [class_Rings_Olinordered__semiring__strict(_927723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927723), c_Groups_Ozero__class_Ozero(_927723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927723), _927725), _927727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927723), c_Groups_Ozero__class_Ozero(_927723)), _927725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927723), c_Groups_Ozero__class_Ozero(_927723)), _927727)))], (35520 ^ _773908) ^ [_1439691, _1439693, _1439695] : [class_Orderings_Oorder(_1439691), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439691, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1439691, _1439693, _1439695)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439691), _1439695)) = c_Orderings_Obot__class_Obot(tc_fun(_1439691, tc_HOL_Obool)))], (31375 ^ _773908) ^ [_1350801, _1350803, _1350805, _1350807, _1350809] : [class_Orderings_Olinorder(_1350801), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350801, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1350801, _1350803, _1350805)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1350801, _1350807, _1350809)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1350801, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350801), _1350803), _1350807), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1350801), _1350805), _1350809)))], (38583 ^ _773908) ^ [_1517104, _1517106, _1517108] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517104, _1517106, _1517106), _1517108), c_Relation_OId(_1517106)) = _1517108)], (48199 ^ _773908) ^ [_1745370, _1745372, _1745374, _1745376] : [-(hAPP(c_Finite__Set_Ofold__image(_1745370, _1745372, _1745374), _1745376) = c_Finite__Set_Ofold(_1745372, _1745370, hAPP(hAPP(c_COMBB(_1745370, tc_fun(_1745370, _1745370), _1745372), _1745374), _1745376)))], (41692 ^ _773908) ^ [_1595343, _1595345, _1595347] : [hBOOL(hAPP(hAPP(c_member(_1595343), _1595345), hAPP(c_List_Oset(_1595343), c_List_Obutlast(_1595343, _1595347)))), -(hBOOL(hAPP(hAPP(c_member(_1595343), _1595345), hAPP(c_List_Oset(_1595343), _1595347))))], (28993 ^ _773908) ^ [_1303337, _1303339, _1303341] : [class_Orderings_Olinorder(_1303337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303337), _1303339)), hBOOL(hAPP(hAPP(c_member(_1303337), _1303341), _1303339)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1303337), _1303341), c_Big__Operators_Olinorder__class_OMax(_1303337, _1303339)) = c_Big__Operators_Olinorder__class_OMax(_1303337, _1303339))], (51906 ^ _773908) ^ [_1818517, _1818519] : [hBOOL(_1818517), -(hBOOL(hAPP(hAPP(c_fdisj, _1818517), _1818519)))], (35839 ^ _773908) ^ [_1446444, _1446446, _1446448, _1446450, _1446452] : [c_Fun_Oinj__on(_1446444, _1446446, _1446448, c_Orderings_Otop__class_Otop(tc_fun(_1446444, tc_HOL_Obool))), hAPP(_1446448, _1446450) = hAPP(_1446448, _1446452), -(_1446450 = _1446452)], (47423 ^ _773908) ^ [_1727580, _1727582, _1727584] : [c_Relation_Orefl__on(_1727580, _1727582, _1727584), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1727580, _1727580), tc_HOL_Obool)), _1727584), hAPP(hAPP(c_Relation_Orel__comp(_1727580, _1727580, _1727580), hAPP(c_Relation_Oconverse(_1727580, _1727580), _1727584)), _1727584))))], (33182 ^ _773908) ^ [_1390417, _1390419] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1390417), _1390419))))], (28228 ^ _773908) ^ [_1285919, _1285921, _1285923] : [class_Lattices_Olattice(_1285919), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1285919), _1285921), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285919), _1285921), _1285923)) = _1285921)], (8607 ^ _773908) ^ [_916395, _916397] : [class_Rings_Oring__1(_916395), -(hAPP(c_Int_Oring__1__class_Oof__int(_916395), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _916397)) = hAPP(c_Groups_Ouminus__class_Ouminus(_916395), hAPP(c_Int_Oring__1__class_Oof__int(_916395), _916397)))], (37655 ^ _773908) ^ [_1487998, _1488000, _1488002, _1488004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487998), _1488000)), 37661 ^ _773908 : [(37664 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488002), hAPP(_1488004, 37660 ^ [_1487998, _1488000, _1488002, _1488004])))], (37662 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487998), 37660 ^ [_1487998, _1488000, _1488002, _1488004]), _1488000)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1487998, _1488002)), hAPP(hAPP(c_Product__Type_OSigma(_1487998, _1488002), _1488000), _1488004)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487998, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1488002, tc_HOL_Obool), tc_Nat_Onat, _1487998), c_Finite__Set_Ocard(_1488002)), _1488004)), _1488000))], (13366 ^ _773908) ^ [_998327] : [-(_998327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13369 ^ _773908 : [(13376 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998327))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _998327) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13370 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998327)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _998327) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (15645 ^ _773908) ^ [_1039999, _1040001, _1040003] : [class_Groups_Oab__group__add(_1039999), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039999), _1040001), _1040003) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039999), _1040001), hAPP(c_Groups_Ouminus__class_Ouminus(_1039999), _1040003)))], (47110 ^ _773908) ^ [_1719813] : [-(c_Transitive__Closure_Otrancl(_1719813, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1719813, _1719813), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1719813, _1719813), tc_HOL_Obool)))], (8392 ^ _773908) ^ [_912199, _912201] : [class_Rings_Olinordered__idom(_912199), 8395 ^ _773908 : [(8402 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912201), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912199), hAPP(c_Int_Oring__1__class_Oof__int(_912199), _912201)), c_Groups_Ozero__class_Ozero(_912199))))], (8396 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912199), hAPP(c_Int_Oring__1__class_Oof__int(_912199), _912201)), c_Groups_Ozero__class_Ozero(_912199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912201), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23590 ^ _773908) ^ [_1185309, _1185311, _1185313, _1185315] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185309, _1185311), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1185313), _1185315))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1185309, _1185311) = _1185315)], (13805 ^ _773908) ^ [_1006409, _1006411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006409), 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, _1006411, _1006409)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48072 ^ _773908) ^ [_1742474, _1742476, _1742478, _1742480, _1742482, _1742484, _1742486, _1742488] : [class_Groups_Ocomm__monoid__add(_1742474), class_Orderings_Oord(_1742476), _1742478 = _1742480, _1742482 = _1742484, 48090 ^ _773908 : [(48095 ^ _773908) ^ [] : [hAPP(_1742486, 48089 ^ [_1742474, _1742476, _1742478, _1742480, _1742482, _1742484, _1742486, _1742488]) = hAPP(_1742488, 48089 ^ [_1742474, _1742476, _1742478, _1742480, _1742482, _1742484, _1742486, _1742488])], (48093 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1742476), 48089 ^ [_1742474, _1742476, _1742478, _1742480, _1742482, _1742484, _1742486, _1742488]), _1742484)))], (48091 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1742476), _1742480), 48089 ^ [_1742474, _1742476, _1742478, _1742480, _1742482, _1742484, _1742486, _1742488])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1742476, _1742474), _1742486), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1742476, _1742478), _1742482)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1742476, _1742474), _1742488), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1742476, _1742480), _1742484)))], (51822 ^ _773908) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (24393 ^ _773908) ^ [_1202081, _1202083, _1202085, _1202087, _1202089, _1202091, _1202093] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1202081, _1202083, _1202085), hAPP(c_Fun_Ocomp(_1202087, tc_fun(_1202083, _1202085), _1202081, _1202089), _1202091)), _1202093) = hAPP(hAPP(_1202089, hAPP(_1202091, hAPP(c_Product__Type_Ofst(_1202081, _1202083), _1202093))), hAPP(c_Product__Type_Osnd(_1202081, _1202083), _1202093)))], (49779 ^ _773908) ^ [_1778861, _1778863, _1778865] : [c_List_Olist__ex1(_1778861, _1778863, _1778865), 49783 ^ _773908 : [(49788 ^ _773908) ^ [_1779107] : [-(_1779107 = 49782 ^ [_1778861, _1778863, _1778865]), hBOOL(hAPP(hAPP(c_member(_1778861), _1779107), hAPP(c_List_Oset(_1778861), _1778865))), hBOOL(hAPP(_1778863, _1779107))], (49786 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1778863, 49782 ^ [_1778861, _1778863, _1778865])))], (49784 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778861), 49782 ^ [_1778861, _1778863, _1778865]), hAPP(c_List_Oset(_1778861), _1778865))))]]], (51474 ^ _773908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51636 ^ _773908) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (1704 ^ _773908) ^ [_798194, _798196] : [-(class_Groups_Ocomm__monoid__add(_798194)), _798196 = _798194, class_Groups_Ocomm__monoid__add(_798196)], (37554 ^ _773908) ^ [_1484701, _1484703, _1484705, _1484707, _1484709, _1484711] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484701, _1484703), hAPP(hAPP(c_Set_Oinsert(_1484701), _1484705), _1484707)), hAPP(c_COMBK(tc_fun(_1484703, tc_HOL_Obool), _1484701), hAPP(hAPP(c_Set_Oinsert(_1484703), _1484709), _1484711))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1484701, _1484703)), hAPP(hAPP(c_Product__Type_OPair(_1484701, _1484703), _1484705), _1484709)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1484701, _1484703), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484701, _1484703), _1484707), hAPP(c_COMBK(tc_fun(_1484703, tc_HOL_Obool), _1484701), hAPP(hAPP(c_Set_Oinsert(_1484703), _1484709), _1484711)))), hAPP(hAPP(c_Product__Type_OSigma(_1484701, _1484703), hAPP(hAPP(c_Set_Oinsert(_1484701), _1484705), _1484707)), hAPP(c_COMBK(tc_fun(_1484703, tc_HOL_Obool), _1484701), _1484711)))))], (23486 ^ _773908) ^ [_1183413, _1183415] : [-(c_Divides_Odivmod__nat(_1183413, _1183415) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1183413), _1183415)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1183413, _1183415)))], (19379 ^ _773908) ^ [_1108560] : [c_Int_OBit1(_1108560) = c_Int_OPls], (42105 ^ _773908) ^ [_1606288, _1606290, _1606292, _1606294] : [_1606288 = c_Orderings_Obot__class_Obot(tc_fun(_1606290, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606290, tc_fun(_1606292, tc_HOL_Obool)), _1606288), hAPP(c_COMBK(tc_fun(_1606292, tc_HOL_Obool), _1606290), _1606294)) = c_Orderings_Otop__class_Otop(tc_fun(_1606292, tc_HOL_Obool)))], (18143 ^ _773908) ^ [_1086771] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086771))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086771)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (39695 ^ _773908) ^ [_1546550, _1546552, _1546554] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1546550), tc_List_Olist(_1546550))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1546550), tc_List_Olist(_1546550)), _1546552), c_List_Olist_ONil(_1546550))), c_List_Olistrel(_1546550, _1546554))), -(_1546552 = c_List_Olist_ONil(_1546550))], (42712 ^ _773908) ^ [_1620935, _1620937] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1620935)), hAPP(c_Code__Numeral_Oof__nat, _1620937)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620935), _1620937)))], (23455 ^ _773908) ^ [_1182669, _1182671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1182669, _1182669)), hAPP(hAPP(c_Product__Type_OPair(_1182669, _1182669), 23456 ^ [_1182669, _1182671]), 23456 ^ [_1182669, _1182671])), _1182671)), -(c_Nitpick_Orefl_H(_1182669, _1182671))], (28148 ^ _773908) ^ [_1283980, _1283982, _1283984] : [class_Lattices_Olattice(_1283980), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283980), _1283982), _1283984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283980), _1283984), _1283982))], (7451 ^ _773908) ^ [_894502, _894504] : [class_Rings_Ocomm__semiring__1(_894502), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894502), _894504), c_Groups_Ozero__class_Ozero(_894502)) = _894504)], (29597 ^ _773908) ^ [_1314188, _1314190, _1314192] : [class_Orderings_Olinorder(_1314188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314188), _1314190)), -(_1314192 = c_Orderings_Obot__class_Obot(tc_fun(_1314188, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314188, tc_HOL_Obool)), _1314192), _1314190)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314188), c_Big__Operators_Olinorder__class_OMin(_1314188, _1314192)), c_Big__Operators_Olinorder__class_OMin(_1314188, _1314190)) = c_Big__Operators_Olinorder__class_OMin(_1314188, _1314190))], (33312 ^ _773908) ^ [_1392894, _1392896, _1392898] : [class_Orderings_Olinorder(_1392894), 33315 ^ _773908 : [(33322 ^ _773908) ^ [] : [_1392896 = _1392898, -(hAPP(c_SetInterval_Oord__class_OatMost(_1392894), _1392896) = hAPP(c_SetInterval_Oord__class_OatMost(_1392894), _1392898))], (33316 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1392894), _1392896) = hAPP(c_SetInterval_Oord__class_OatMost(_1392894), _1392898), -(_1392896 = _1392898)]]], (25807 ^ _773908) ^ [_1231147, _1231149, _1231151] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231147, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1231147, tc_HOL_Obool)), _1231149), _1231151)), _1231151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1231147, tc_HOL_Obool)), _1231149), _1231151))], (43953 ^ _773908) ^ [_1648841, _1648843, _1648845] : [-(hAPP(c_Relation_ODomain(_1648841, _1648843), hAPP(c_Set_OCollect(tc_prod(_1648841, _1648843)), hAPP(c_Product__Type_Oprod_Oprod__case(_1648841, _1648843, tc_HOL_Obool), _1648845))) = hAPP(c_Set_OCollect(_1648841), hAPP(hAPP(c_COMBB(tc_fun(_1648843, tc_HOL_Obool), tc_HOL_Obool, _1648841), c_HOL_OEx(_1648843)), _1648845)))], (31471 ^ _773908) ^ [_1353015, _1353017, _1353019, _1353021, _1353023, _1353025, _1353027, _1353029, _1353031, _1353033] : [c_Equiv__Relations_Oequiv(_1353015, _1353017, _1353019), c_Equiv__Relations_Oequiv(_1353021, _1353023, _1353025), c_Equiv__Relations_Ocongruent2(_1353015, _1353021, tc_fun(_1353027, tc_HOL_Obool), _1353019, _1353025, _1353029), hBOOL(hAPP(hAPP(c_member(_1353015), _1353031), _1353017)), hBOOL(hAPP(hAPP(c_member(_1353021), _1353033), _1353023)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353015, tc_fun(_1353027, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1353015, _1353015, _1353019), hAPP(hAPP(c_Set_Oinsert(_1353015), _1353031), c_Orderings_Obot__class_Obot(tc_fun(_1353015, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1353021, tc_fun(_1353027, tc_HOL_Obool)), tc_fun(_1353027, tc_HOL_Obool), _1353015), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353021, tc_fun(_1353027, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1353021, _1353021, _1353025), hAPP(hAPP(c_Set_Oinsert(_1353021), _1353033), c_Orderings_Obot__class_Obot(tc_fun(_1353021, tc_HOL_Obool)))))), _1353029)) = hAPP(hAPP(_1353029, _1353031), _1353033))], (23111 ^ _773908) ^ [_1175411, _1175413, _1175415, _1175417] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1175411, _1175413)), c_Nitpick_Opair__box_OPairBox(_1175411, _1175413, _1175415, _1175417)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9662 ^ _773908) ^ [_934930, _934932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934932)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _934930), _934932)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _934930)), hAPP(c_Int_Onat, _934932)))], (16489 ^ _773908) ^ [_1056725, _1056727] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056725, tc_HOL_Obool)), _1056727), c_Orderings_Obot__class_Obot(tc_fun(_1056725, tc_HOL_Obool))) = _1056727)], (31818 ^ _773908) ^ [_1362216, _1362218, _1362220, _1362222, _1362224] : [_1362216 = c_Orderings_Obot__class_Obot(tc_fun(_1362218, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1362220), _1362222), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362218, tc_fun(_1362220, tc_HOL_Obool)), _1362216), _1362224)) = hAPP(hAPP(c_Set_Oinsert(_1362220), _1362222), c_Orderings_Obot__class_Obot(tc_fun(_1362220, tc_HOL_Obool))))], (32306 ^ _773908) ^ [_1373125, _1373127, _1373129] : [class_Lattices_Olattice(_1373125), hAPP(_1373127, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373125), 32311 ^ [_1373125, _1373127, _1373129]), 32312 ^ [_1373125, _1373127, _1373129])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373125), hAPP(_1373127, 32311 ^ [_1373125, _1373127, _1373129])), hAPP(_1373127, 32312 ^ [_1373125, _1373127, _1373129])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373125), _1373129)), -(_1373129 = c_Orderings_Obot__class_Obot(tc_fun(_1373125, tc_HOL_Obool))), -(hAPP(_1373127, c_Big__Operators_Olattice__class_OInf__fin(_1373125, _1373129)) = c_Big__Operators_Olattice__class_OInf__fin(_1373125, hAPP(c_Set_Oimage(_1373125, _1373125, _1373127), _1373129)))], (45585 ^ _773908) ^ [_1684518, _1684520, _1684522, _1684524, _1684526] : [-(c_List_Ofoldr(_1684518, _1684520, _1684522, _1684524, _1684526) = hAPP(c_List_Ofoldl(_1684520, _1684518, hAPP(c_COMBC(_1684518, _1684520, _1684520), _1684522), _1684526), hAPP(c_List_Orev(_1684518), _1684524)))], (7831 ^ _773908) ^ [_901803, _901805] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_901803, _901805)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_901805)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16873 ^ _773908) ^ [_1064004, _1064006, _1064008, _1064010] : [class_Rings_Ocomm__semiring__1(_1064004), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064004), hAPP(hAPP(c_Power_Opower__class_Opower(_1064004), _1064006), _1064008)), hAPP(hAPP(c_Power_Opower__class_Opower(_1064004), _1064006), _1064010)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1064004), _1064006), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064008), _1064010)))], (30375 ^ _773908) ^ [_1328968, _1328970, _1328972] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1328968), _1328970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328968, tc_HOL_Obool)), _1328972), _1328970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1328968), _1328972)), hAPP(c_Finite__Set_Ocard(_1328968), _1328970))))], (1774 ^ _773908) ^ [_799069, _799071] : [-(class_Orderings_Opreorder(_799069)), _799071 = _799069, class_Orderings_Opreorder(_799071)], (22787 ^ _773908) ^ [_1169516, _1169518] : [_1169516 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1169516, _1169518) = _1169518)], (45133 ^ _773908) ^ [_1675598, _1675600] : [class_Orderings_Olinorder(_1675598), c_List_Olinorder__class_Osorted(_1675598, _1675600), -(c_List_Olinorder__class_Osorted(_1675598, hAPP(c_List_Otl(_1675598), _1675600)))], (43673 ^ _773908) ^ [_1642360, _1642362, _1642364] : [c_Wellfounded_Owf(_1642360, _1642362), c_Wellfounded_Owf(_1642360, _1642364), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642360, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1642360, _1642360), _1642362)), hAPP(c_Relation_ORange(_1642360, _1642360), _1642364)) = c_Orderings_Obot__class_Obot(tc_fun(_1642360, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1642360, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1642360, _1642360), tc_HOL_Obool)), _1642362), _1642364)))], (1504 ^ _773908) ^ [_795694, _795696] : [-(class_Finite__Set_Ofinite(_795694)), _795696 = _795694, class_Finite__Set_Ofinite(_795696)], (13895 ^ _773908) ^ [_1007904, _1007906, _1007908, _1007910] : [class_Groups_Ouminus(_1007904), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007906, _1007904)), _1007908), _1007910) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007904), hAPP(_1007908, _1007910)))], (51818 ^ _773908) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (46343 ^ _773908) ^ [_1701266, _1701268, _1701270] : [c_Wellfounded_Oacyclic(_1701266, _1701268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1701266, _1701266), tc_HOL_Obool)), _1701270), _1701268)), -(c_Wellfounded_Oacyclic(_1701266, _1701270))], (50838 ^ _773908) ^ [_1802088, _1802090, _1802092] : [c_Fun_Oinj__on(_1802088, _1802090, _1802092, c_Orderings_Otop__class_Otop(tc_fun(_1802088, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1802090, _1802088, _1802088, c_Hilbert__Choice_Oinv__into(_1802088, _1802090, c_Orderings_Otop__class_Otop(tc_fun(_1802088, tc_HOL_Obool)), _1802092)), _1802092) = c_Fun_Oid(_1802088))], (51632 ^ _773908) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (37412 ^ _773908) ^ [_1480949, _1480951, _1480953, _1480955, _1480957] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1480949, _1480951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480949, tc_HOL_Obool)), _1480953), _1480955)), _1480957) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480949, _1480951), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1480949, _1480951), _1480953), _1480957)), hAPP(hAPP(c_Product__Type_OSigma(_1480949, _1480951), _1480955), _1480957)))], (49061 ^ _773908) ^ [_1763350, _1763352, _1763354, _1763356] : [c_List_Olist__all(_1763350, _1763352, hAPP(hAPP(c_List_Oappend(_1763350), _1763354), _1763356)), 49064 ^ _773908 : [(49067 ^ _773908) ^ [] : [-(c_List_Olist__all(_1763350, _1763352, _1763356))], (49065 ^ _773908) ^ [] : [-(c_List_Olist__all(_1763350, _1763352, _1763354))]]], (32804 ^ _773908) ^ [_1383003, _1383005, _1383007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1383003)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1383005), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1383007)), 32811 ^ _773908 : [(32812 ^ _773908) ^ [_1383211] : [32814 ^ _773908 : [(32820 ^ _773908) ^ [] : [-(_1383211 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32816 ^ [_1383003, _1383005, _1383007, _1383211]), 32813 ^ [_1383003, _1383005, _1383007, _1383211]))], (32818 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32816 ^ [_1383003, _1383005, _1383007, _1383211]), _1383007)))], (32815 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32813 ^ [_1383003, _1383005, _1383007, _1383211]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1383003))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383211), _1383005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1383211), _1383003)), _1383005)))]]], (18985 ^ _773908) ^ [_1101915, _1101917] : [class_Int_Onumber__ring(_1101915), -(hBOOL(hAPP(hAPP(c_member(_1101915), hAPP(c_Int_Onumber__class_Onumber__of(_1101915), _1101917)), c_Int_Oring__1__class_OInts(_1101915))))], (7711 ^ _773908) ^ [_899152, _899154, _899156, _899158, _899160] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_899152, _899154, _899156)), _899158), _899160)), 7716 ^ _773908 : [(7719 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899154), _899158), _899160)))], (7717 ^ _773908) ^ [] : [-(hBOOL(hAPP(_899152, _899158)))]], 7720 ^ _773908 : [(7723 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899156), _899158), _899160)))], (7721 ^ _773908) ^ [] : [hBOOL(hAPP(_899152, _899158))]]], (27518 ^ _773908) ^ [_1271457, _1271459, _1271461, _1271463, _1271465, _1271467] : [c_Finite__Set_Ofolding(_1271457, _1271459, _1271461, _1271463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271457), _1271465)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271457), _1271467)), -(hAPP(c_Fun_Ocomp(_1271459, _1271459, _1271459, hAPP(_1271463, _1271467)), hAPP(_1271463, _1271465)) = hAPP(c_Fun_Ocomp(_1271459, _1271459, _1271459, hAPP(_1271463, _1271465)), hAPP(_1271463, _1271467)))], (8199 ^ _773908) ^ [_908665, _908667, _908669, _908671, _908673] : [c_Com_Ocom_OWhile(_908665, _908667) = c_Com_Ocom_OCall(_908669, _908671, _908673)], (20257 ^ _773908) ^ [_1123540] : [-(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)))), _1123540) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1123540)))], (51494 ^ _773908) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12969 ^ _773908) ^ [_991434, _991436, _991438] : [12970 ^ _773908 : [(12973 ^ _773908) ^ [] : [_991436 = _991438], (12971 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991434, tc_HOL_Obool)), _991436), _991438))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991434, tc_HOL_Obool)), _991436), _991438)))], (50108 ^ _773908) ^ [_1787941, _1787943, _1787945, _1787947] : [class_Complete__Lattice_Ocomplete__lattice(_1787941), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1787943, _1787941), _1787945), _1787947) = c_Complete__Lattice_OInf__class_OInf(_1787941, hAPP(c_Set_OCollect(_1787941), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool), tc_HOL_Obool, _1787941), c_HOL_OEx(tc_fun(_1787943, _1787941))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool), tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool), _1787941), hAPP(c_COMBS(tc_fun(_1787943, _1787941), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1787943, _1787941)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1787943, _1787941), tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1787943, _1787941))), _1787945)))), hAPP(hAPP(c_COMBC(_1787941, tc_fun(tc_fun(_1787943, _1787941), _1787941), tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1787941, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1787943, _1787941), _1787941), tc_fun(tc_fun(_1787943, _1787941), tc_HOL_Obool)), _1787941), c_COMBB(_1787941, tc_HOL_Obool, tc_fun(_1787943, _1787941))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1787943, _1787941), _1787943, _1787941), c_COMBI(tc_fun(_1787943, _1787941))), _1787947)))))))], (47495 ^ _773908) ^ [_1729108] : [-(c_Relation_Osingle__valued(_1729108, _1729108, c_Relation_OId(_1729108)))], (10863 ^ _773908) ^ [_954350] : [class_Rings_Olinordered__semidom(_954350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954350), c_Groups_Oone__class_Oone(_954350)), c_Groups_Ozero__class_Ozero(_954350)))], (48147 ^ _773908) ^ [_1744381, _1744383, _1744385] : [48148 ^ _773908 : [(48149 ^ _773908) ^ [_1744458, _1744460] : [_1744385 = hAPP(hAPP(c_List_Oappend(_1744381), _1744460), hAPP(hAPP(c_List_Olist_OCons(_1744381), _1744383), _1744458))]], -(hBOOL(hAPP(hAPP(c_member(_1744381), _1744383), hAPP(c_List_Oset(_1744381), _1744385))))], (28739 ^ _773908) ^ [_1298639, _1298641, _1298643, _1298645, _1298647] : [hBOOL(hAPP(hAPP(c_member(_1298639), _1298641), c_SetInterval_Oord_OgreaterThanLessThan(_1298639, _1298643, _1298645, _1298647))), 28742 ^ _773908 : [(28745 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298643, _1298641), _1298647)))], (28743 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298643, _1298645), _1298641)))]]], (26207 ^ _773908) ^ [_1239120, _1239122, _1239124, _1239126] : [class_Lattices_Olattice(_1239120), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239120), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239120), _1239122), _1239124)), _1239126) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239120), _1239122), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239120), _1239124), _1239126)))], (11840 ^ _773908) ^ [_971812, _971814, _971816] : [class_Groups_Oordered__comm__monoid__add(_971812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971812), c_Groups_Ozero__class_Ozero(_971812)), _971814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971812), c_Groups_Ozero__class_Ozero(_971812)), _971816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971812), c_Groups_Ozero__class_Ozero(_971812)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971812), _971814), _971816))))], (31570 ^ _773908) ^ [_1355729, _1355731, _1355733, _1355735, _1355737, _1355739] : [c_Equiv__Relations_Ocongruent(_1355729, _1355731, _1355733, _1355735), hBOOL(hAPP(hAPP(c_member(tc_prod(_1355729, _1355729)), hAPP(hAPP(c_Product__Type_OPair(_1355729, _1355729), _1355737), _1355739)), _1355733)), -(hAPP(_1355735, _1355737) = hAPP(_1355735, _1355739))], (45595 ^ _773908) ^ [_1684802, _1684804, _1684806, _1684808] : [_1684804 = hAPP(hAPP(c_List_Oappend(_1684802), hAPP(c_List_Orev(_1684802), _1684808)), hAPP(hAPP(c_List_Olist_OCons(_1684802), _1684806), c_List_Olist_ONil(_1684802))), -(hAPP(c_List_Orev(_1684802), _1684804) = hAPP(hAPP(c_List_Olist_OCons(_1684802), _1684806), _1684808))], (42744 ^ _773908) ^ [_1621682] : [-(_1621682 = 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)), _1621682)))], (12995 ^ _773908) ^ [_991938, _991940, _991942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991938, tc_HOL_Obool)), _991940), hAPP(hAPP(c_Set_Oinsert(_991938), _991942), c_Orderings_Obot__class_Obot(tc_fun(_991938, tc_HOL_Obool))))), -(_991940 = c_Orderings_Obot__class_Obot(tc_fun(_991938, tc_HOL_Obool))), -(_991940 = hAPP(hAPP(c_Set_Oinsert(_991938), _991942), c_Orderings_Obot__class_Obot(tc_fun(_991938, tc_HOL_Obool))))], (39061 ^ _773908) ^ [_1529422, _1529424] : [-(hAPP(c_Relation_ORange(_1529422, _1529424), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529422, _1529424), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1529424, tc_HOL_Obool)))], (36567 ^ _773908) ^ [_1462548, _1462550, _1462552, _1462554, _1462556, _1462558, _1462560] : [c_Typedef_Otype__definition(_1462548, _1462550, _1462552, _1462554, _1462556), 36570 ^ _773908 : [(36577 ^ _773908) ^ [] : [_1462558 = _1462560, -(hAPP(_1462552, _1462558) = hAPP(_1462552, _1462560))], (36571 ^ _773908) ^ [] : [hAPP(_1462552, _1462558) = hAPP(_1462552, _1462560), -(_1462558 = _1462560)]]], (20047 ^ _773908) ^ [_1119902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1119902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1119902))))], (13670 ^ _773908) ^ [_1004169, _1004171] : [class_Rings_Olinordered__idom(_1004169), 13673 ^ _773908 : [(13680 ^ _773908) ^ [] : [_1004171 = c_Groups_Ozero__class_Ozero(_1004169), -(c_Groups_Osgn__class_Osgn(_1004169, _1004171) = c_Groups_Ozero__class_Ozero(_1004169))], (13674 ^ _773908) ^ [] : [c_Groups_Osgn__class_Osgn(_1004169, _1004171) = c_Groups_Ozero__class_Ozero(_1004169), -(_1004171 = c_Groups_Ozero__class_Ozero(_1004169))]]], (15135 ^ _773908) ^ [_1030300, _1030302, _1030304] : [class_Divides_Osemiring__div(_1030300), -(_1030302 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030300), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030300), _1030302), _1030304)), _1030304)), c_Divides_Odiv__class_Omod(_1030300, _1030302, _1030304)))], (24207 ^ _773908) ^ [_1197329, _1197331, _1197333, _1197335, _1197337, _1197339] : [hAPP(_1197335, hAPP(c_Product__Type_Osnd(_1197333, _1197329), _1197337)) = hAPP(_1197339, hAPP(c_Product__Type_Osnd(_1197333, _1197329), _1197337)), -(hAPP(c_Product__Type_Oapsnd(_1197329, _1197331, _1197333, _1197335), _1197337) = hAPP(c_Product__Type_Oapsnd(_1197329, _1197331, _1197333, _1197339), _1197337))], (17787 ^ _773908) ^ [_1081254] : [class_Power_Opower(_1081254), -(c_Power_Opower__class_Opower(_1081254) = c_Power_Opower_Opower(_1081254, c_Groups_Oone__class_Oone(_1081254), c_Groups_Otimes__class_Otimes(_1081254)))], (23702 ^ _773908) ^ [_1187779, _1187781, _1187783, _1187785] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1187779, _1187779)), hAPP(hAPP(c_Product__Type_OPair(_1187779, _1187779), _1187781), _1187783)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1187779, _1187779), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1187785))), -(_1187781 = _1187783)], (24977 ^ _773908) ^ [_1214498, _1214500, _1214502] : [class_Orderings_Olinorder(_1214498), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214498), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214498), _1214500), _1214502)), _1214502)))], (41330 ^ _773908) ^ [_1588318, _1588320, _1588322] : [class_Lattices_Olattice(_1588318), -(c_Big__Operators_Olattice__class_OSup__fin(_1588318, hAPP(c_List_Oset(_1588318), hAPP(hAPP(c_List_Olist_OCons(_1588318), _1588320), _1588322))) = hAPP(c_List_Ofoldl(_1588318, _1588318, c_Lattices_Osemilattice__sup__class_Osup(_1588318), _1588320), _1588322))], (51566 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (45565 ^ _773908) ^ [_1684055, _1684057, _1684059] : [_1684057 = hAPP(hAPP(c_List_Olist_OCons(_1684055), _1684059), c_List_Olist_ONil(_1684055)), -(hAPP(c_List_Orev(_1684055), _1684057) = hAPP(hAPP(c_List_Olist_OCons(_1684055), _1684059), c_List_Olist_ONil(_1684055)))], (50866 ^ _773908) ^ [_1802704, _1802706, _1802708] : [c_Fun_Oinj__on(_1802704, _1802706, _1802708, c_Orderings_Otop__class_Otop(tc_fun(_1802704, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1802706, _1802704, c_Hilbert__Choice_Oinv__into(_1802704, _1802706, c_Orderings_Otop__class_Otop(tc_fun(_1802704, tc_HOL_Obool)), _1802708)), c_Orderings_Otop__class_Otop(tc_fun(_1802706, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802704, tc_HOL_Obool)))], (35869 ^ _773908) ^ [_1446958] : [-(hAPP(c_Set_OPow(_1446958), c_Orderings_Otop__class_Otop(tc_fun(_1446958, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1446958, tc_HOL_Obool), tc_HOL_Obool)))], (10597 ^ _773908) ^ [_949670, _949672, _949674] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949670), _949672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949670), _949674), -(_949672 = _949674), -(_949670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13143 ^ _773908) ^ [] : [-(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)))], (51610 ^ _773908) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (18621 ^ _773908) ^ [_1095566, _1095568, _1095570, _1095572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095566, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1095566), _1095568), _1095570)), _1095572)), 18624 ^ _773908 : [(18627 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095566, tc_HOL_Obool)), _1095570), _1095572)))], (18625 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1095566), _1095568), _1095572)))]]], (8683 ^ _773908) ^ [_917690, _917692] : [class_Rings_Oring__1(_917690), 8686 ^ _773908 : [(8693 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917692), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_917690), _917692) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917690), hAPP(c_Int_Onat, _917692)))], (8687 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917692), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_917690), _917692) = hAPP(c_Groups_Ouminus__class_Ouminus(_917690), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917690), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _917692)))))]]], (33100 ^ _773908) ^ [_1388666, _1388668, _1388670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1388666)), 33103 ^ _773908 : [(33104 ^ _773908) ^ [_1388800] : [33106 ^ _773908 : [(33112 ^ _773908) ^ [] : [-(_1388800 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33108 ^ [_1388666, _1388668, _1388670, _1388800]), 33105 ^ [_1388666, _1388668, _1388670, _1388800]))], (33110 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33108 ^ [_1388666, _1388668, _1388670, _1388800]), _1388668)))], (33107 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33105 ^ [_1388666, _1388668, _1388670, _1388800]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1388666))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388800), _1388670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1388800), _1388666)), _1388670)))]]], (39985 ^ _773908) ^ [_1554745, _1554747, _1554749, _1554751] : [-(hAPP(hAPP(c_List_Onth(_1554745), hAPP(hAPP(c_List_Oappend(_1554745), _1554747), hAPP(hAPP(c_List_Olist_OCons(_1554745), _1554749), _1554751))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554745)), _1554747)) = _1554749)], (7753 ^ _773908) ^ [_900071, _900073, _900075, _900077, _900079, _900081] : [c_Com_Ocom_OCall(_900071, _900073, _900075) = c_Com_Ocom_OLocal(_900077, _900079, _900081)], (18691 ^ _773908) ^ [_1096962, _1096964, _1096966] : [-(hBOOL(hAPP(hAPP(c_member(_1096962), _1096964), _1096966))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096962, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1096962), _1096964), _1096966)), hAPP(hAPP(c_Set_Oinsert(_1096962), _1096964), c_Orderings_Obot__class_Obot(tc_fun(_1096962, tc_HOL_Obool)))) = _1096966)], (50265 ^ _773908) ^ [_1791450, _1791452] : [-(c_Relation_Otrans(_1791450, c_Transitive__Closure_Ortrancl(_1791450, _1791452)))], (37536 ^ _773908) ^ [_1484373, _1484375, _1484377, _1484379] : [-(_1484373 = c_Orderings_Obot__class_Obot(tc_fun(_1484375, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1484377, _1484375), _1484377, c_Product__Type_Ofst(_1484377, _1484375)), hAPP(hAPP(c_Product__Type_OSigma(_1484377, _1484375), _1484379), hAPP(c_COMBK(tc_fun(_1484375, tc_HOL_Obool), _1484377), _1484373))) = _1484379)], (27318 ^ _773908) ^ [_1267154, _1267156, _1267158] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267154), _1267158)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267154), hAPP(hAPP(c_Set_Oinsert(_1267154), _1267156), _1267158))))], (34316 ^ _773908) ^ [_1412870] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1412870) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412870))], (3336 ^ _773908) ^ [_823972, _823974, _823976, _823978] : [-(c_Random_Oselect__weight(_823978, _823974) = c_Random_Oselect__weight(_823976, _823972)), _823978 = _823976, _823974 = _823972], (6076 ^ _773908) ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710] : [c_Hoare__Mirabelle_Ohoare__derivs(_871698, _871700, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871698)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871698), _871702), _871704), _871706)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871698), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_871698, _871700, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871698)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871698), _871708), _871704), _871710)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871698), tc_HOL_Obool))))), 6083 ^ _773908 : [(6087 ^ _773908) ^ [_872172] : [hBOOL(hAPP(hAPP(_871702, _872172), 6082 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710])), -(hBOOL(hAPP(hAPP(_871706, _872172), 6085 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710])))], (6093 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_871710, 6081 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710]), 6085 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710]))], (6084 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_871708, 6081 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710]), 6082 ^ [_871698, _871700, _871702, _871704, _871706, _871708, _871710])))]]], (23462 ^ _773908) ^ [_1182836, _1182838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1182836), _1182838)), -(c_Divides_Odivmod__nat(_1182838, _1182836) = 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), _1182838), _1182836)), _1182836))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1182838), _1182836), _1182836)))], (48457 ^ _773908) ^ [_1750734, _1750736, _1750738, _1750740, _1750742] : [c_Finite__Set_Ofolding__one(_1750734, _1750736, _1750738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750734), _1750740)), -(hBOOL(hAPP(hAPP(c_member(_1750734), _1750742), _1750740))), -(hAPP(_1750738, hAPP(hAPP(c_Set_Oinsert(_1750734), _1750742), _1750740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1750734, _1750734, _1750736), _1750742), _1750740))], (42762 ^ _773908) ^ [_1621939, _1621941, _1621943, _1621945] : [class_Groups_Ocomm__monoid__add(_1621939), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1621939), _1621941), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1621943, _1621945))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1621939), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1621939), _1621941), c_List_Oupto(_1621943, _1621945))))], (34618 ^ _773908) ^ [_1419661, _1419663, _1419665, _1419667] : [class_Groups_Ocomm__monoid__add(_1419661), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1419663), _1419665))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419663, _1419661), _1419667), _1419665) = c_Groups_Ozero__class_Ozero(_1419661))], (46586 ^ _773908) ^ [_1706417, _1706419, _1706421, _1706423, _1706425, _1706427] : [hBOOL(hAPP(hAPP(c_member(_1706417), _1706419), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1706421, _1706423, tc_fun(_1706417, tc_HOL_Obool)), _1706425), _1706427))), 46591 ^ _773908 : [(46594 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706417), _1706419), hAPP(hAPP(_1706425, 46589 ^ [_1706417, _1706419, _1706421, _1706423, _1706425, _1706427]), 46590 ^ [_1706417, _1706419, _1706421, _1706423, _1706425, _1706427]))))], (46592 ^ _773908) ^ [] : [-(_1706427 = hAPP(hAPP(c_Product__Type_OPair(_1706421, _1706423), 46589 ^ [_1706417, _1706419, _1706421, _1706423, _1706425, _1706427]), 46590 ^ [_1706417, _1706419, _1706421, _1706423, _1706425, _1706427]))]]], (6618 ^ _773908) ^ [_881425, _881427, _881429, _881431] : [class_Orderings_Oord(_881425), _881427 = _881429, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881425), _881429), _881431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881425), _881427), _881431)))], (43743 ^ _773908) ^ [_1644119, _1644121] : [-(hAPP(c_Relation_ODomain(_1644119, _1644119), c_Relation_OId__on(_1644119, _1644121)) = _1644121)], (26617 ^ _773908) ^ [_1251462, _1251464, _1251466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1251462, _1251462), tc_HOL_Obool)), _1251464), _1251466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251462, tc_HOL_Obool)), hAPP(c_Relation_OField(_1251462), _1251464)), hAPP(c_Relation_OField(_1251462), _1251466))))], (15087 ^ _773908) ^ [_1029514, _1029516] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029514))), -(c_SMT_Oz3div(_1029516, _1029514) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029516), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029514))))], (27664 ^ _773908) ^ [_1274434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1274434)), 27668 ^ _773908 : [(27669 ^ _773908) ^ [_1274514] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1274514), _1274434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1274514), 27667 ^ [_1274434])))]]], (25883 ^ _773908) ^ [_1232510, _1232512, _1232514, _1232516] : [class_Lattices_Osemilattice__sup(_1232510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232510), _1232512), _1232514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232510), _1232512), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1232510), _1232516), _1232514))))], (51544 ^ _773908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (28094 ^ _773908) ^ [_1282781, _1282783, _1282785, _1282787] : [class_Lattices_Olattice(_1282781), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282781), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282781), _1282783), _1282785)), _1282787) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282781), _1282783), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282781), _1282785), _1282787)))], (27334 ^ _773908) ^ [_1267436, _1267438, _1267440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267436), _1267438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267436, tc_HOL_Obool)), _1267440), _1267438)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267436), _1267440)))], (17719 ^ _773908) ^ [_1080009, _1080011, _1080013, _1080015] : [class_Rings_Olinordered__semidom(_1080009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1080011), _1080013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080009), c_Groups_Oone__class_Oone(_1080009)), _1080015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080009), hAPP(hAPP(c_Power_Opower__class_Opower(_1080009), _1080015), _1080011)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080009), _1080015), _1080013))))], (7749 ^ _773908) ^ [_899950, _899952, _899954, _899956, _899958] : [c_Com_Ocom_OLocal(_899950, _899952, _899954) = c_Com_Ocom_OSemi(_899956, _899958)], (39418 ^ _773908) ^ [_1539439, _1539441] : [_1539441 = c_List_Olist_ONil(_1539439), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1539439)), _1539441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51464 ^ _773908) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (27718 ^ _773908) ^ [_1275655, _1275657, _1275659, _1275661] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275655, tc_HOL_Obool)), _1275657), _1275659), _1275661)), 27721 ^ _773908 : [(27724 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1275659, _1275661)))], (27722 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1275657, _1275661)))]]], (5422 ^ _773908) ^ [_856803, _856805, _856807, _856809, _856811, _856813, _856815, _856817] : [-(c_Fun_Ocomp(_856817, _856813, _856809, _856805) = c_Fun_Ocomp(_856815, _856811, _856807, _856803)), _856817 = _856815, _856813 = _856811, _856809 = _856807, _856805 = _856803], (27250 ^ _773908) ^ [_1266052, _1266054, _1266056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266052), _1266054)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266052), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266052, tc_HOL_Obool)), _1266054), _1266056))))], (6215 ^ _773908) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15333 ^ _773908) ^ [_1033931, _1033933, _1033935] : [class_Groups_Oab__group__add(_1033931), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1033931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033931), _1033933), _1033935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033931), _1033935), _1033933))], (48057 ^ _773908) ^ [_1742197, _1742199, _1742201] : [c_List_Olist__ex(_1742197, _1742199, _1742201), -(c_List_Olist__ex(_1742197, _1742199, hAPP(c_List_Orev(_1742197), _1742201)))], (6190 ^ _773908) ^ [_874302, _874304, _874306, _874308, _874310] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_874302, _874304), _874306, _874308, _874310)), 6191 ^ _773908 : [(6192 ^ _773908) ^ [_874357] : [c_Natural_Oevaln(_874302, _874306, _874308, _874357), c_Natural_Oevaln(_874304, _874357, _874308, _874310)]]], (7014 ^ _773908) ^ [_887546, _887548] : [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), _887546), _887548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887548)))], (26096 ^ _773908) ^ [_1236778, _1236780, _1236782, _1236784] : [26098 ^ _773908 : [(26101 ^ _773908) ^ [] : [hBOOL(hAPP(_1236784, 26097 ^ [_1236778, _1236780, _1236782, _1236784]))], (26099 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1236778), 26097 ^ [_1236778, _1236780, _1236782, _1236784]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1236778, tc_HOL_Obool)), _1236780), _1236782))))]], 26102 ^ _773908 : [(26109 ^ _773908) ^ [_1237095] : [hBOOL(hAPP(hAPP(c_member(_1236778), _1237095), _1236782)), -(hBOOL(hAPP(_1236784, _1237095)))], (26103 ^ _773908) ^ [_1236998] : [hBOOL(hAPP(hAPP(c_member(_1236778), _1236998), _1236780)), -(hBOOL(hAPP(_1236784, _1236998)))]]], (38589 ^ _773908) ^ [_1517257, _1517259, _1517261, _1517263] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517257, _1517259, _1517261), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517257, _1517259), tc_HOL_Obool))), _1517263) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517257, _1517261), tc_HOL_Obool)))], (47263 ^ _773908) ^ [_1723358, _1723360] : [c_Wellfounded_Owf(_1723358, hAPP(c_Relation_Oconverse(_1723358, _1723358), _1723360)), -(c_Wellfounded_Owf(_1723358, hAPP(c_Relation_Oconverse(_1723358, _1723358), c_Transitive__Closure_Otrancl(_1723358, _1723360))))], (35274 ^ _773908) ^ [_1434597, _1434599, _1434601] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434597, tc_Nat_Onat), _1434599), _1434601)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434597, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1434597), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1434599)), _1434601))], (2132 ^ _773908) ^ [_804886, _804888] : [_804888 = _804886, -(c_Int_Oring__1__class_OInts(_804888) = c_Int_Oring__1__class_OInts(_804886))], (38146 ^ _773908) ^ [_1500084, _1500086, _1500088, _1500090] : [_1500084 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1500086, _1500088), 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)), _1500090))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500086), _1500084)))], (2052 ^ _773908) ^ [_803678, _803680, _803682, _803684] : [-(c_Com_Ocom_OSemi(_803684, _803680) = c_Com_Ocom_OSemi(_803682, _803678)), _803684 = _803682, _803680 = _803678], (42788 ^ _773908) ^ [_1622654, _1622656, _1622658, _1622660, _1622662, _1622664, _1622666, _1622668, _1622670] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1622654, _1622656, _1622658, _1622660), hAPP(hAPP(c_Product__Type_Oscomp(_1622654, _1622662, _1622664, tc_prod(_1622656, _1622658)), _1622666), _1622668)), _1622670) = hAPP(hAPP(c_Product__Type_Oscomp(_1622654, _1622662, _1622664, _1622660), _1622666), hAPP(hAPP(c_COMBC(_1622662, tc_fun(_1622656, tc_fun(_1622658, _1622660)), tc_fun(_1622664, _1622660)), hAPP(hAPP(c_COMBB(tc_fun(_1622664, tc_prod(_1622656, _1622658)), tc_fun(tc_fun(_1622656, tc_fun(_1622658, _1622660)), tc_fun(_1622664, _1622660)), _1622662), c_Product__Type_Oscomp(_1622664, _1622656, _1622658, _1622660)), _1622668)), _1622670)))], (38747 ^ _773908) ^ [_1522356, _1522358, _1522360] : [c_Wellfounded_Owf(_1522356, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1522356, _1522356), tc_HOL_Obool), _1522358), _1522360)), -(c_Wellfounded_Owf(_1522356, _1522360))], (24723 ^ _773908) ^ [_1209885, _1209887, _1209889, _1209891] : [class_Orderings_Olinorder(_1209885), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209885), _1209887), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209885), _1209889), _1209891)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209885), _1209889), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209885), _1209887), _1209891)))], (41205 ^ _773908) ^ [_1585871, _1585873] : [class_Lattices_Oab__semigroup__idem__mult(_1585871), -(_1585873 = c_List_Olist_ONil(_1585871)), -(hAPP(c_Finite__Set_Ofold1(_1585871, c_Groups_Otimes__class_Otimes(_1585871)), hAPP(c_List_Oset(_1585871), _1585873)) = hAPP(c_List_Ofoldl(_1585871, _1585871, c_Groups_Otimes__class_Otimes(_1585871), hAPP(c_List_Ohd(_1585871), _1585873)), hAPP(c_List_Otl(_1585871), _1585873)))], (34868 ^ _773908) ^ [_1425208, _1425210, _1425212, _1425214, _1425216] : [class_Groups_Ocomm__monoid__add(_1425208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425210), _1425212)), c_Fun_Oinj__on(_1425210, _1425210, _1425214, _1425212), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425210, _1425208), _1425216), hAPP(c_Set_Oimage(_1425210, _1425210, _1425214), _1425212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425210, _1425208), hAPP(c_Fun_Ocomp(_1425210, _1425208, _1425210, _1425216), _1425214)), _1425212))], (16031 ^ _773908) ^ [_1047876, _1047878, _1047880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047876), _1047878)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047878), _1047876))), _1047880) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1047878)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047876), _1047880)))], (49515 ^ _773908) ^ [_1773324, _1773326, _1773328, _1773330] : [49516 ^ _773908 : [(49519 ^ _773908) ^ [] : [_1773326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49517 ^ _773908) ^ [] : [hBOOL(hAPP(_1773330, _1773328))]], 49520 ^ _773908 : [(49521 ^ _773908) ^ [_1773449] : [hBOOL(hAPP(hAPP(c_member(_1773324), _1773449), hAPP(c_List_Oset(_1773324), c_List_Oreplicate(_1773324, _1773326, _1773328)))), -(hBOOL(hAPP(_1773330, _1773449)))]]], (24929 ^ _773908) ^ [_1213683, _1213685, _1213687, _1213689] : [class_Orderings_Olinorder(_1213683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213683), _1213685), _1213687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213683), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213683), _1213685), _1213689)), _1213687)))], (17851 ^ _773908) ^ [_1082289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082289)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1082289) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1082289), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5350 ^ _773908) ^ [_855653, _855655] : [_855655 = _855653, -(c_Groups_Ozero__class_Ozero(_855655) = c_Groups_Ozero__class_Ozero(_855653))], (8805 ^ _773908) ^ [_919620, _919622, _919624] : [class_Groups_Oordered__ab__group__add(_919620), 8808 ^ _773908 : [(8815 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919620), _919624), hAPP(c_Groups_Ouminus__class_Ouminus(_919620), _919622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919620), _919622), hAPP(c_Groups_Ouminus__class_Ouminus(_919620), _919624))))], (8809 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919620), _919622), hAPP(c_Groups_Ouminus__class_Ouminus(_919620), _919624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919620), _919624), hAPP(c_Groups_Ouminus__class_Ouminus(_919620), _919622))))]]], (38910 ^ _773908) ^ [_1525721, _1525723, _1525725] : [c_Wellfounded_Owf(_1525721, _1525723), -(hBOOL(hAPP(hAPP(c_member(_1525721), _1525725), c_Wellfounded_Oacc(_1525721, _1525723))))], (15059 ^ _773908) ^ [_1029028, _1029030, _1029032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029028)), 15062 ^ _773908 : [(15063 ^ _773908) ^ [] : [-(_1029030 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029032), _1029028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029028), _1029030)), _1029032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029028), hAPP(c_Nat_OSuc, _1029030))))], (15073 ^ _773908) ^ [] : [_1029030 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029032), _1029028), 15076 ^ _773908 : [(15079 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029028), hAPP(c_Nat_OSuc, _1029030)))))], (15077 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029028), _1029030)), _1029032)))]]]]], (35190 ^ _773908) ^ [_1432761, _1432763, _1432765, _1432767, _1432769] : [class_Groups_Oordered__comm__monoid__add(_1432761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432763), _1432765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432763, tc_HOL_Obool)), _1432767), _1432765)), 35204 ^ _773908 : [(35207 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432761), c_Groups_Ozero__class_Ozero(_1432761)), hAPP(_1432769, 35203 ^ [_1432761, _1432763, _1432765, _1432767, _1432769])))], (35205 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432763), 35203 ^ [_1432761, _1432763, _1432765, _1432767, _1432769]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1432763, tc_HOL_Obool)), _1432765), _1432767))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432761), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1432763, _1432761), _1432769), _1432767)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1432763, _1432761), _1432769), _1432765))))], (8297 ^ _773908) ^ [_910564, _910566, _910568, _910570, _910572, _910574, _910576] : [hAPP(c_Fun_Ocomp(_910564, _910566, _910568, _910570), _910572) = _910574, -(hAPP(_910570, hAPP(_910572, _910576)) = hAPP(_910574, _910576))], (18325 ^ _773908) ^ [_1090346, _1090348, _1090350, _1090352] : [hBOOL(hAPP(hAPP(c_member(_1090346), _1090348), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090346, tc_HOL_Obool)), _1090350), _1090352))), 18328 ^ _773908 : [(18331 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1090346), _1090348), _1090352))], (18329 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1090346), _1090348), _1090350)))]]], (34237 ^ _773908) ^ [_1411409, _1411411, _1411413, _1411415, _1411417, _1411419, _1411421, _1411423] : [class_Groups_Ocomm__monoid__mult(_1411409), c_Fun_Oinj__on(_1411411, _1411413, _1411415, _1411417), _1411419 = hAPP(c_Set_Oimage(_1411411, _1411413, _1411415), _1411417), 34251 ^ _773908 : [(34254 ^ _773908) ^ [] : [hAPP(_1411421, 34250 ^ [_1411409, _1411411, _1411413, _1411415, _1411417, _1411419, _1411421, _1411423]) = hAPP(hAPP(c_Fun_Ocomp(_1411413, _1411409, _1411411, _1411423), _1411415), 34250 ^ [_1411409, _1411411, _1411413, _1411415, _1411417, _1411419, _1411421, _1411423])], (34252 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411411), 34250 ^ [_1411409, _1411411, _1411413, _1411415, _1411417, _1411419, _1411421, _1411423]), _1411417)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411413, _1411409), _1411423), _1411419) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411411, _1411409), _1411421), _1411417))], (26177 ^ _773908) ^ [_1238423, _1238425, _1238427] : [class_Lattices_Osemilattice__sup(_1238423), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238423), _1238425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238423), _1238425), _1238427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238423), _1238425), _1238427))], (8219 ^ _773908) ^ [_909246] : [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), _909246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _909246)))], (3574 ^ _773908) ^ [_827717, _827719, _827721, _827723] : [-(c_List_Olinorder__class_Osorted__list__of__set(_827723, _827719) = c_List_Olinorder__class_Osorted__list__of__set(_827721, _827717)), _827723 = _827721, _827719 = _827717], (38875 ^ _773908) ^ [_1525027, _1525029, _1525031, _1525033] : [c_Wellfounded_Owf(_1525027, _1525029), hBOOL(hAPP(hAPP(c_member(tc_prod(_1525027, _1525027)), hAPP(hAPP(c_Product__Type_OPair(_1525027, _1525027), _1525031), _1525033)), _1525029)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1525027, _1525027)), hAPP(hAPP(c_Product__Type_OPair(_1525027, _1525027), _1525033), _1525031)), _1525029))], (24395 ^ _773908) ^ [_1202158, _1202160, _1202162, _1202164, _1202166] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1202158, _1202160, _1202162), _1202164), _1202166) = hAPP(hAPP(_1202164, hAPP(c_Product__Type_Ofst(_1202158, _1202160), _1202166)), hAPP(c_Product__Type_Osnd(_1202158, _1202160), _1202166)))], (40215 ^ _773908) ^ [_1560303, _1560305, _1560307, _1560309] : [-(hAPP(hAPP(c_List_Odrop(_1560303), _1560305), hAPP(hAPP(c_List_Olist_OCons(_1560303), _1560307), _1560309)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1560303), hAPP(hAPP(c_List_Olist_OCons(_1560303), _1560307), _1560309), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1560303), tc_List_Olist(_1560303)), c_List_Odrop(_1560303)), _1560309), _1560305))], (49180 ^ _773908) ^ [_1765641, _1765643, _1765645] : [-(c_Product__Type_Ointernal__split(_1765641, _1765643, _1765645) = c_Product__Type_Oprod_Oprod__case(_1765641, _1765643, _1765645))], (44897 ^ _773908) ^ [_1671563, _1671565] : [class_Orderings_Olinorder(_1671563), -(_1671565 = c_List_Olist_ONil(_1671563)), c_List_Olinorder__class_Osorted(_1671563, _1671565), -(c_List_Olinorder__class_Osorted(_1671563, c_List_Obutlast(_1671563, _1671565)))], (38897 ^ _773908) ^ [_1525486, _1525488] : [c_Wellfounded_Owf(_1525486, _1525488), 38900 ^ _773908 : [(38901 ^ _773908) ^ [_1525555] : [-(hBOOL(hAPP(hAPP(c_member(_1525486), _1525555), c_Wellfounded_Oacc(_1525486, _1525488))))]]], (44640 ^ _773908) ^ [_1666055, _1666057, _1666059, _1666061] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1666055, tc_Nat_Onat), _1666055), c_Product__Type_Ofst(_1666055, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1666055, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1666055, 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(_1666055, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1666055, tc_Nat_Onat))), _1666057)), hAPP(hAPP(c_List_Ozip(_1666055, tc_Nat_Onat), _1666059), c_List_Oupt(_1666061, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666061), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666055)), _1666059)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1666055, tc_Nat_Onat), _1666055), c_Product__Type_Ofst(_1666055, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1666055, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1666055, 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(_1666055, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1666055, 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(_1666055, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1666055, tc_Nat_Onat))), _1666061))), _1666057)), hAPP(hAPP(c_List_Ozip(_1666055, tc_Nat_Onat), _1666059), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666055)), _1666059))))))], (6051 ^ _773908) ^ [_871282, _871284] : [hAPP(c_Nat_OSuc, _871282) = hAPP(c_Nat_OSuc, _871284), -(_871282 = _871284)], (8424 ^ _773908) ^ [_912714, _912716, _912718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912714), _912716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _912718)), -(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), _912718)), _912714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _912718)), _912716))))], (20217 ^ _773908) ^ [_1122934, _1122936] : [class_Rings_Oring__1__no__zero__divisors(_1122934), 20220 ^ _773908 : [(20227 ^ _773908) ^ [] : [_1122936 = c_Groups_Ozero__class_Ozero(_1122934), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1122934), _1122936), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1122934))], (20221 ^ _773908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1122934), _1122936), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1122934), -(_1122936 = c_Groups_Ozero__class_Ozero(_1122934))]]], (39049 ^ _773908) ^ [_1529190, _1529192, _1529194] : [hAPP(c_Relation_ORange(_1529190, _1529192), _1529194) = c_Orderings_Obot__class_Obot(tc_fun(_1529192, tc_HOL_Obool)), -(_1529194 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529190, _1529192), tc_HOL_Obool)))], (26047 ^ _773908) ^ [_1235643, _1235645] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235643, tc_HOL_Obool)), _1235645), _1235645) = _1235645)], (15841 ^ _773908) ^ [_1043665, _1043667, _1043669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043665), _1043667)), _1043669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043669), _1043667))))], (42866 ^ _773908) ^ [_1624380] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1624380)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1624380))], (34322 ^ _773908) ^ [_1412949] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412949)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1412949), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412949)))], (36157 ^ _773908) ^ [] : [-(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)))], (40743 ^ _773908) ^ [_1573258, _1573260, _1573262, _1573264, _1573266] : [-(hAPP(hAPP(c_List_Ozip(_1573258, _1573260), _1573262), hAPP(hAPP(c_List_Oappend(_1573260), _1573264), _1573266)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1573258, _1573260)), hAPP(hAPP(c_List_Ozip(_1573258, _1573260), hAPP(hAPP(c_List_Otake(_1573258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573260)), _1573264)), _1573262)), _1573264)), hAPP(hAPP(c_List_Ozip(_1573258, _1573260), hAPP(hAPP(c_List_Odrop(_1573258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573260)), _1573264)), _1573262)), _1573266)))], (12182 ^ _773908) ^ [_978119, _978121] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _978119) = _978121, 12185 ^ _773908 : [(12188 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978121)))], (12186 ^ _773908) ^ [] : [-(_978119 = hAPP(c_Int_Onat, _978121))]]], (51820 ^ _773908) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (42177 ^ _773908) ^ [_1608380, _1608382, _1608384, _1608386, _1608388] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608380, tc_HOL_Obool)), _1608382), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608384, tc_fun(_1608380, tc_HOL_Obool)), _1608386), _1608388)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608384, tc_fun(_1608380, tc_HOL_Obool)), _1608386), hAPP(hAPP(c_COMBB(tc_fun(_1608380, tc_HOL_Obool), tc_fun(_1608380, tc_HOL_Obool), _1608384), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608380, tc_HOL_Obool)), _1608382)), _1608388)))], (39073 ^ _773908) ^ [_1529687, _1529689, _1529691] : [-(hAPP(c_Set_Oimage(tc_prod(_1529687, _1529689), _1529689, c_Product__Type_Osnd(_1529687, _1529689)), _1529691) = hAPP(c_Relation_ORange(_1529687, _1529689), _1529691))], (1076 ^ _773908) ^ [_790146, _790148, _790150, _790152, _790154, _790156, _790158, _790160] : [-(c_Fun_Oinj__on(_790158, _790154, _790150, _790146)), c_Fun_Oinj__on(_790160, _790156, _790152, _790148), _790160 = _790158, _790156 = _790154, _790152 = _790150, _790148 = _790146], (37574 ^ _773908) ^ [_1485549, _1485551, _1485553, _1485555] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485549, _1485551), _1485553), _1485555) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485549, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), _1485553), hAPP(hAPP(c_COMBS(_1485549, tc_fun(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485551, tc_HOL_Obool), tc_fun(tc_fun(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), _1485549), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), _1485555)), hAPP(hAPP(c_COMBC(_1485549, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1485551, tc_fun(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), _1485549), c_COMBC(_1485551, tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1485551, tc_prod(_1485549, _1485551)), tc_fun(_1485551, tc_fun(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))), _1485549), hAPP(c_COMBB(tc_prod(_1485549, _1485551), tc_fun(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool), tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), _1485551), c_Set_Oinsert(tc_prod(_1485549, _1485551)))), c_Product__Type_OPair(_1485549, _1485551)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool))))))], (19645 ^ _773908) ^ [] : [-(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))))))], (44503 ^ _773908) ^ [_1661212, _1661214, _1661216, _1661218] : [-(hAPP(hAPP(c_List_Omap(_1661212, _1661214), _1661216), c_List_Oconcat(_1661212, _1661218)) = c_List_Oconcat(_1661214, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661212), tc_List_Olist(_1661214)), hAPP(c_List_Omap(_1661212, _1661214), _1661216)), _1661218)))], (45131 ^ _773908) ^ [_1675570, _1675572] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1675570, _1675572)))], (38076 ^ _773908) ^ [_1497946, _1497948] : [-(hAPP(c_Set_OCollect(_1497946), hAPP(hAPP(c_COMBC(_1497946, _1497946, tc_HOL_Obool), c_fequal), _1497948)) = hAPP(hAPP(c_Set_Oinsert(_1497946), _1497948), c_Orderings_Obot__class_Obot(tc_fun(_1497946, tc_HOL_Obool))))], (42465 ^ _773908) ^ [_1615820, _1615822, _1615824] : [c_Fun_Oinj__on(tc_List_Olist(_1615820), tc_List_Olist(_1615822), hAPP(c_List_Omap(_1615820, _1615822), _1615824), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1615820), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1615820, _1615822, _1615824, c_Orderings_Otop__class_Otop(tc_fun(_1615820, tc_HOL_Obool))))], (6251 ^ _773908) ^ [_875274, _875276, _875278] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_875274), _875276), _875278)), -(c_Natural_Oevaln(_875274, _875276, 6254 ^ [_875274, _875276, _875278], _875278))], (9439 ^ _773908) ^ [_931182] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _931182)), _931182) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40617 ^ _773908) ^ [_1570155, _1570157, _1570159] : [-(hAPP(hAPP(c_List_Olist__update(_1570155, _1570157), _1570159), hAPP(hAPP(c_List_Onth(_1570155), _1570157), _1570159)) = _1570157)], (24765 ^ _773908) ^ [_1210730, _1210732, _1210734, _1210736] : [class_Orderings_Olinorder(_1210730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210730), _1210732), _1210734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210730), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210730), _1210732), _1210736)), _1210734)))], (47000 ^ _773908) ^ [_1717171, _1717173, _1717175, _1717177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717171, _1717171)), hAPP(hAPP(c_Product__Type_OPair(_1717171, _1717171), _1717173), _1717175)), _1717177)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1717171, _1717171)), hAPP(hAPP(c_Product__Type_OPair(_1717171, _1717171), _1717173), _1717175)), c_Transitive__Closure_Otrancl(_1717171, _1717177))))], (39939 ^ _773908) ^ [_1553482, _1553484, _1553486, _1553488] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1553482), tc_List_Olist(_1553482))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1553482), tc_List_Olist(_1553482)), _1553484), _1553486)), c_List_Olistrel(_1553482, _1553488)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553482)), _1553484) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553482)), _1553486), 39945 ^ _773908 : [(39948 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553482, _1553482)), hAPP(hAPP(c_Product__Type_OPair(_1553482, _1553482), hAPP(hAPP(c_List_Onth(_1553482), _1553484), 39944 ^ [_1553482, _1553484, _1553486, _1553488])), hAPP(hAPP(c_List_Onth(_1553482), _1553486), 39944 ^ [_1553482, _1553484, _1553486, _1553488]))), _1553488))], (39946 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39944 ^ [_1553482, _1553484, _1553486, _1553488]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553482)), _1553484))))]]], (25297 ^ _773908) ^ [_1220910, _1220912, _1220914, _1220916] : [class_Orderings_Olinorder(_1220910), 25300 ^ _773908 : [(25309 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220910), _1220912), _1220914)), _1220916))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), _1220912), _1220916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), _1220914), _1220916))], (25301 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220910), _1220912), _1220914)), _1220916)), 25304 ^ _773908 : [(25307 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), _1220914), _1220916)))], (25305 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220910), _1220912), _1220916)))]]]]], (41612 ^ _773908) ^ [_1593654, _1593656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1593654), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1593656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1593656), _1593654)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1593656))))], (24379 ^ _773908) ^ [_1201771, _1201773, _1201775, _1201777, _1201779] : [-(hAPP(c_Product__Type_Ofst(_1201771, _1201773), hAPP(c_Product__Type_Oapsnd(_1201775, _1201773, _1201771, _1201777), _1201779)) = hAPP(c_Product__Type_Ofst(_1201771, _1201775), _1201779))], (7863 ^ _773908) ^ [_902521, _902523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902521), _902523)), -(_902523 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902521), 7866 ^ [_902521, _902523])))], (22801 ^ _773908) ^ [] : [-(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))], (50614 ^ _773908) ^ [_1798041, _1798043, _1798045, _1798047] : [c_Equiv__Relations_Opart__equivp(_1798041, _1798043), hBOOL(hAPP(hAPP(_1798043, _1798045), _1798047)), -(hBOOL(hAPP(hAPP(_1798043, _1798047), _1798045)))], (17117 ^ _773908) ^ [_1069098, _1069100, _1069102, _1069104] : [class_Rings_Olinordered__semidom(_1069098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069098), _1069100), _1069102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069098), c_Groups_Ozero__class_Ozero(_1069098)), _1069100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069098), hAPP(hAPP(c_Power_Opower__class_Opower(_1069098), _1069100), _1069104)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069098), _1069102), _1069104))))], (50279 ^ _773908) ^ [_1791669, _1791671, _1791673, _1791675, _1791677] : [c_Relation_Otrans(_1791669, _1791671), hBOOL(hAPP(hAPP(c_member(tc_prod(_1791669, _1791669)), hAPP(hAPP(c_Product__Type_OPair(_1791669, _1791669), _1791673), _1791675)), _1791671)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1791669, _1791669)), hAPP(hAPP(c_Product__Type_OPair(_1791669, _1791669), _1791675), _1791677)), _1791671)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791669, _1791669)), hAPP(hAPP(c_Product__Type_OPair(_1791669, _1791669), _1791673), _1791677)), _1791671)))], (38891 ^ _773908) ^ [_1525359, _1525361, _1525363] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1525359)), hAPP(hAPP(c_List_Oappend(_1525359), _1525361), _1525363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1525359)), _1525361)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1525359)), _1525363)))], (15719 ^ _773908) ^ [_1041369, _1041371, _1041373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041369), _1041373)), _1041371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041369), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041371), _1041373))))], (17539 ^ _773908) ^ [_1076582, _1076584, _1076586] : [class_Power_Opower(_1076582), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076582), _1076584), hAPP(c_Nat_OSuc, _1076586)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076582), _1076584), hAPP(hAPP(c_Power_Opower__class_Opower(_1076582), _1076584), _1076586)))], (44335 ^ _773908) ^ [_1657713, _1657715, _1657717] : [hBOOL(hAPP(c_List_Odistinct(_1657713), _1657715)), -(hBOOL(hAPP(c_List_Odistinct(_1657713), c_List_Oinsert(_1657713, _1657717, _1657715))))], (16475 ^ _773908) ^ [_1056420, _1056422, _1056424, _1056426] : [class_Rings_Ocomm__semiring__1(_1056420), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1056420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056420), _1056422), _1056424)), _1056426) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056420), hAPP(hAPP(c_Power_Opower__class_Opower(_1056420), _1056422), _1056426)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056420), _1056424), _1056426)))], (51770 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (17997 ^ _773908) ^ [_1084342] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1084342), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1084342))], (40759 ^ _773908) ^ [_1573806, _1573808, _1573810, _1573812, _1573814] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573808)), _1573810)))), -(hAPP(hAPP(c_List_Olist__update(_1573808, hAPP(hAPP(c_List_Oappend(_1573808), _1573810), _1573812)), _1573806), _1573814) = hAPP(hAPP(c_List_Oappend(_1573808), _1573810), hAPP(hAPP(c_List_Olist__update(_1573808, _1573812), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1573806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573808)), _1573810))), _1573814)))], (38679 ^ _773908) ^ [_1521232, _1521234, _1521236, _1521238, _1521240, _1521242, _1521244, _1521246] : [hBOOL(hAPP(hAPP(_1521232, _1521234), _1521236)), hBOOL(hAPP(hAPP(_1521238, _1521236), _1521240)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1521242, _1521244, _1521246, _1521232, _1521238), _1521234), _1521240)))], (33874 ^ _773908) ^ [_1403500, _1403502, _1403504] : [class_Groups_Oordered__ab__group__add(_1403500), -(hAPP(c_Set_Oimage(_1403500, _1403500, c_Groups_Ouminus__class_Ouminus(_1403500)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1403500, _1403502, _1403504)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1403500, hAPP(c_Groups_Ouminus__class_Ouminus(_1403500), _1403504)), hAPP(c_Groups_Ouminus__class_Ouminus(_1403500), _1403502)))], (21879 ^ _773908) ^ [_1152539, _1152541, _1152543, _1152545] : [class_Fields_Ofield__inverse__zero(_1152539), class_Int_Onumber(_1152539), 21886 ^ _773908 : [(21887 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152539), _1152541), _1152543) = hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545), 21890 ^ _773908 : [(21897 ^ _773908) ^ [] : [_1152543 = c_Groups_Ozero__class_Ozero(_1152539), -(hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545) = c_Groups_Ozero__class_Ozero(_1152539))], (21891 ^ _773908) ^ [] : [-(_1152543 = c_Groups_Ozero__class_Ozero(_1152539)), -(_1152541 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152539), hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545)), _1152543))]]], (21903 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152539), _1152541), _1152543) = hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545)), 21906 ^ _773908 : [(21909 ^ _773908) ^ [] : [_1152541 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152539), hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545)), _1152543)], (21907 ^ _773908) ^ [] : [_1152543 = c_Groups_Ozero__class_Ozero(_1152539)]], 21910 ^ _773908 : [(21913 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1152539), _1152545) = c_Groups_Ozero__class_Ozero(_1152539)], (21911 ^ _773908) ^ [] : [-(_1152543 = c_Groups_Ozero__class_Ozero(_1152539))]]]]], (40633 ^ _773908) ^ [_1570461, _1570463, _1570465, _1570467, _1570469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570461, tc_HOL_Obool)), hAPP(c_List_Oset(_1570461), _1570463)), _1570465)), hBOOL(hAPP(hAPP(c_member(_1570461), _1570467), _1570465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570461, tc_HOL_Obool)), hAPP(c_List_Oset(_1570461), hAPP(hAPP(c_List_Olist__update(_1570461, _1570463), _1570469), _1570467))), _1570465)))], (48857 ^ _773908) ^ [_1758803, _1758805, _1758807, _1758809, _1758811, _1758813, _1758815] : [c_Finite__Set_Ofolding__image__simple__idem(_1758803, _1758805, _1758807, _1758809, _1758811, _1758813), -(hAPP(hAPP(_1758807, _1758815), _1758815) = _1758815)], (32768 ^ _773908) ^ [_1382223, _1382225, _1382227] : [hBOOL(hAPP(c_Predicate_OPowp(_1382223, hAPP(hAPP(c_COMBC(_1382223, tc_fun(_1382223, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382223)), _1382225)), _1382227)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382223, tc_HOL_Obool)), _1382227), hAPP(c_Set_OPow(_1382223), _1382225))))], (6097 ^ _773908) ^ [_872493, _872495, _872497, _872499, _872501] : [c_Hoare__Mirabelle_Otriple__valid(_872493, _872495, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872493), _872497), _872499), _872501)), 6100 ^ _773908 : [(6101 ^ _773908) ^ [_872614, _872616] : [hBOOL(hAPP(hAPP(_872497, _872616), _872614)), 6104 ^ _773908 : [(6105 ^ _773908) ^ [_872704] : [c_Natural_Oevaln(_872499, _872614, _872495, _872704), -(hBOOL(hAPP(hAPP(_872501, _872616), _872704)))]]]]], (31648 ^ _773908) ^ [_1357391, _1357393, _1357395, _1357397, _1357399] : [hBOOL(hAPP(hAPP(c_member(_1357391), _1357393), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1357395, tc_fun(_1357391, tc_HOL_Obool)), _1357397), _1357399))), 31652 ^ _773908 : [(31655 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357391), _1357393), hAPP(_1357399, 31651 ^ [_1357391, _1357393, _1357395, _1357397, _1357399]))))], (31653 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357395), 31651 ^ [_1357391, _1357393, _1357395, _1357397, _1357399]), _1357397)))]]], (15829 ^ _773908) ^ [_1043413, _1043415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043413), _1043415)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043415), _1043413)) = _1043415)], (47365 ^ _773908) ^ [_1725908, _1725910, _1725912] : [c_Relation_Orefl__on(_1725908, _1725910, _1725912), -(c_Relation_Orefl__on(_1725908, _1725910, hAPP(c_Relation_Oconverse(_1725908, _1725908), _1725912)))], (14502 ^ _773908) ^ [_1019117, _1019119] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019117, _1019119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1019117 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019119), 14505 ^ [_1019117, _1019119]))], (51418 ^ _773908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (17947 ^ _773908) ^ [_1083638, _1083640] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083638), _1083640) = c_Groups_Oone__class_Oone(tc_Int_Oint), 17952 ^ _773908 : [(17955 ^ _773908) ^ [] : [-(_1083640 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17953 ^ _773908) ^ [] : [-(_1083638 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 17956 ^ _773908 : [(17959 ^ _773908) ^ [] : [-(_1083640 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (17957 ^ _773908) ^ [] : [-(_1083638 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (46396 ^ _773908) ^ [_1702184, _1702186] : [class_Enum_Oenum(_1702184), 46399 ^ _773908 : [(46406 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1702184), _1702186)), -(hBOOL(hAPP(_1702186, 46409 ^ [_1702184, _1702186])))], (46400 ^ _773908) ^ [] : [46401 ^ _773908 : [(46402 ^ _773908) ^ [_1702286] : [hBOOL(hAPP(_1702186, _1702286))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1702184), _1702186)))]]], (39589 ^ _773908) ^ [_1543404, _1543406, _1543408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543404, _1543404), tc_HOL_Obool)), _1543406), _1543408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1543404), tc_List_Olist(_1543404)), tc_HOL_Obool)), c_List_Olistrel1(_1543404, _1543406)), c_List_Olistrel1(_1543404, _1543408))))], (23285 ^ _773908) ^ [_1179301, _1179303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179301)), 23288 ^ _773908 : [(23295 ^ _773908) ^ [] : [-(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), _1179303), _1179301)))), -(c_Divides_OnegDivAlg(_1179303, _1179301) = hAPP(c_Divides_Oadjust(_1179301), c_Divides_OnegDivAlg(_1179303, 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)))), _1179301))))], (23289 ^ _773908) ^ [] : [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), _1179303), _1179301))), -(c_Divides_OnegDivAlg(_1179303, _1179301) = 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), _1179303), _1179301)))]]], (15427 ^ _773908) ^ [_1035624, _1035626] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035624), _1035626)), _1035624) = _1035626)], (22961 ^ _773908) ^ [_1172498] : [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), _1172498))), 22964 ^ _773908 : [(22971 ^ _773908) ^ [] : [-(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), _1172498))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172498)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172498)), 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), _1172498)))))], (22965 ^ _773908) ^ [] : [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), _1172498)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172498)) = 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), _1172498))))]]], (3070 ^ _773908) ^ [_819863, _819865, _819867, _819869, _819871, _819873, _819875, _819877] : [-(c_Nitpick_Osetsum_H(_819877, _819873, _819869, _819865) = c_Nitpick_Osetsum_H(_819875, _819871, _819867, _819863)), _819877 = _819875, _819873 = _819871, _819869 = _819867, _819865 = _819863], (31067 ^ _773908) ^ [_1343695, _1343697, _1343699, _1343701, _1343703] : [class_Groups_Ocomm__monoid__mult(_1343695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343697), _1343699)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343697), _1343701)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343697, tc_HOL_Obool)), _1343699), _1343701) = c_Orderings_Obot__class_Obot(tc_fun(_1343697, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343697, _1343695), _1343703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343697, tc_HOL_Obool)), _1343699), _1343701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343695), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343697, _1343695), _1343703), _1343699)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343697, _1343695), _1343703), _1343701)))], (34199 ^ _773908) ^ [_1410642, _1410644] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1410642), _1410644)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1410644), _1410642)))], (6111 ^ _773908) ^ [_872811, _872813, _872815, _872817, _872819] : [6114 ^ _773908 : [(6120 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_872819, 6112 ^ [_872811, _872813, _872815, _872817, _872819]), 6116 ^ [_872811, _872813, _872815, _872817, _872819]))], (6118 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_872817, 6113 ^ [_872811, _872813, _872815, _872817, _872819], _872813, 6116 ^ [_872811, _872813, _872815, _872817, _872819]))], (6115 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_872815, 6112 ^ [_872811, _872813, _872815, _872817, _872819]), 6113 ^ [_872811, _872813, _872815, _872817, _872819])))]], -(c_Hoare__Mirabelle_Otriple__valid(_872811, _872813, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872811), _872815), _872817), _872819)))], (16677 ^ _773908) ^ [_1060126, _1060128, _1060130] : [class_Groups_Oordered__ab__group__add__abs(_1060126), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060126), hAPP(c_Groups_Oabs__class_Oabs(_1060126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060126), hAPP(c_Groups_Oabs__class_Oabs(_1060126), _1060128)), hAPP(c_Groups_Oabs__class_Oabs(_1060126), _1060130)))), hAPP(c_Groups_Oabs__class_Oabs(_1060126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060126), _1060128), _1060130)))))], (45709 ^ _773908) ^ [_1687277, _1687279, _1687281] : [class_Orderings_Olinorder(_1687277), c_List_Olinorder__class_Osorted(_1687277, _1687279), -(c_List_Olinorder__class_Osorted(_1687277, c_List_OtakeWhile(_1687277, _1687281, _1687279)))], (44410 ^ _773908) ^ [_1659279, _1659281] : [-(hAPP(c_List_Ofilter(_1659279, _1659281), c_List_Olist_ONil(_1659279)) = c_List_Olist_ONil(_1659279))], (39745 ^ _773908) ^ [_1547921, _1547923, _1547925, _1547927] : [c_List_Olistrelp(_1547921, hAPP(hAPP(c_COMBC(_1547921, tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_fun(_1547921, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547921, tc_fun(tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_fun(_1547921, tc_HOL_Obool)), _1547921), c_COMBC(_1547921, tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547921, tc_prod(_1547921, _1547921)), tc_fun(_1547921, tc_fun(tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_HOL_Obool)), _1547921), hAPP(c_COMBB(tc_prod(_1547921, _1547921), tc_fun(tc_fun(tc_prod(_1547921, _1547921), tc_HOL_Obool), tc_HOL_Obool), _1547921), c_member(tc_prod(_1547921, _1547921)))), c_Product__Type_OPair(_1547921, _1547921)))), _1547923), _1547925, _1547927), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1547921), tc_List_Olist(_1547921))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1547921), tc_List_Olist(_1547921)), _1547925), _1547927)), c_List_Olistrel(_1547921, _1547923))))], (16326 ^ _773908) ^ [_1053783] : [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), _1053783))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1053783) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1053783)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (40885 ^ _773908) ^ [_1578120, _1578122, _1578124] : [c_Relation_Orefl__on(_1578120, _1578122, _1578124), 40888 ^ _773908 : [(40895 ^ _773908) ^ [_1578604] : [hBOOL(hAPP(hAPP(c_member(_1578120), _1578604), _1578122)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578120, _1578120)), hAPP(hAPP(c_Product__Type_OPair(_1578120, _1578120), _1578604), _1578604)), _1578124)))], (40889 ^ _773908) ^ [_1578331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578120, _1578120)), _1578331), _1578124)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1578120, _1578120, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1578120, tc_fun(_1578120, tc_HOL_Obool), tc_fun(_1578120, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578120, tc_HOL_Obool), tc_fun(_1578120, tc_HOL_Obool)), _1578120), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578120)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578120), c_fconj), hAPP(hAPP(c_COMBC(_1578120, tc_fun(_1578120, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578120)), _1578122)))), hAPP(hAPP(c_COMBC(_1578120, tc_fun(_1578120, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578120)), _1578122))), _1578331)))]]], (37946 ^ _773908) ^ [_1494895, _1494897, _1494899] : [37947 ^ _773908 : [(37950 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1494895), hAPP(c_Set_OCollect(_1494895), _1494899)))], (37948 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1494895), hAPP(c_Set_OCollect(_1494895), _1494897)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494895), hAPP(c_Set_OCollect(_1494895), hAPP(hAPP(c_COMBS(_1494895, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1494895), c_fconj), _1494897)), _1494899)))))], (25873 ^ _773908) ^ [_1232331, _1232333, _1232335, _1232337] : [class_Lattices_Osemilattice__sup(_1232331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232331), _1232333), _1232335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232331), _1232333), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1232331), _1232335), _1232337))))], (5322 ^ _773908) ^ [_855249, _855251] : [_855251 = _855249, -(c_Groups_Oone__class_Oone(_855251) = c_Groups_Oone__class_Oone(_855249))], (42111 ^ _773908) ^ [_1606425, _1606427, _1606429, _1606431] : [-(_1606425 = c_Orderings_Obot__class_Obot(tc_fun(_1606427, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606427, tc_fun(_1606429, tc_HOL_Obool)), _1606425), hAPP(c_COMBK(tc_fun(_1606429, tc_HOL_Obool), _1606427), _1606431)) = _1606431)], (4 ^ _773908) ^ [_773958, _773960] : [_773960 = _773958, -(_773958 = _773960)], (3536 ^ _773908) ^ [_827164, _827166, _827168, _827170] : [-(c_List_Otranspose(_827170, _827166) = c_List_Otranspose(_827168, _827164)), _827170 = _827168, _827166 = _827164], (51111 ^ _773908) ^ [_1808358] : [-(c_Quickcheck_Obeyond(_1808358, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (44412 ^ _773908) ^ [_1659329, _1659331, _1659333, _1659335] : [hBOOL(hAPP(_1659329, _1659331)), -(hAPP(c_List_Ofilter(_1659333, _1659329), hAPP(hAPP(c_List_Olist_OCons(_1659333), _1659331), _1659335)) = hAPP(hAPP(c_List_Olist_OCons(_1659333), _1659331), hAPP(c_List_Ofilter(_1659333, _1659329), _1659335)))], (15533 ^ _773908) ^ [_1037732, _1037734, _1037736] : [hBOOL(hAPP(_1037732, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037734), _1037736)))), 15536 ^ _773908 : [(15543 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037734), _1037736)), -(hBOOL(hAPP(_1037732, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15537 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037736), _1037734)), -(hBOOL(hAPP(_1037732, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037734)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037736)))))]]], (34408 ^ _773908) ^ [_1414571, _1414573, _1414575] : [class_Orderings_Oorder(_1414571), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414571, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1414571), _1414573)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1414571, _1414573), _1414575)) = c_Orderings_Obot__class_Obot(tc_fun(_1414571, tc_HOL_Obool)))], (24323 ^ _773908) ^ [_1200569, _1200571, _1200573, _1200575] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1200569, tc_fun(_1200571, tc_HOL_Obool))), _1200573), _1200575)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1200569, _1200571)), hAPP(hAPP(c_Product__Type_OPair(_1200569, _1200571), _1200573), _1200575)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1200569, _1200571), tc_HOL_Obool)))))], (26971 ^ _773908) ^ [_1259561] : [-(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)), _1259561)))], (23405 ^ _773908) ^ [_1181259, _1181261] : [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), _1181259))), 23408 ^ _773908 : [(23415 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181261)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181259)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181261), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181259)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181259)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181261), 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), _1181259)))))], (23409 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181261)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181259))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181261), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1181259)) = 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), _1181261)))]]], (46140 ^ _773908) ^ [_1696197, _1696199, _1696201, _1696203, _1696205] : [-(c_List_Omaps(_1696197, _1696199, _1696201, hAPP(hAPP(c_List_Olist_OCons(_1696197), _1696203), _1696205)) = hAPP(hAPP(c_List_Oappend(_1696199), hAPP(_1696201, _1696203)), c_List_Omaps(_1696197, _1696199, _1696201, _1696205)))], (27586 ^ _773908) ^ [_1272799, _1272801, _1272803, _1272805, _1272807] : [c_Finite__Set_Ofolding__one(_1272799, _1272801, _1272803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272799), _1272805)), -(hBOOL(hAPP(hAPP(c_member(_1272799), _1272807), _1272805))), -(_1272805 = c_Orderings_Obot__class_Obot(tc_fun(_1272799, tc_HOL_Obool))), -(hAPP(_1272803, hAPP(hAPP(c_Set_Oinsert(_1272799), _1272807), _1272805)) = hAPP(hAPP(_1272801, _1272807), hAPP(_1272803, _1272805)))], (41324 ^ _773908) ^ [_1588209, _1588211] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1588209), hAPP(c_List_Oset(tc_Nat_Onat), _1588211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1588209), 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)), _1588211))))], (21637 ^ _773908) ^ [_1148297, _1148299, _1148301, _1148303] : [class_Fields_Olinordered__field__inverse__zero(_1148297), 21640 ^ _773908 : [(21641 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148297), _1148299), _1148301)), _1148303)), 21644 ^ _773908 : [(21651 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148301))), 21654 ^ _773908 : [(21661 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148301), c_Groups_Ozero__class_Ozero(_1148297)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148303)))], (21655 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148301), c_Groups_Ozero__class_Ozero(_1148297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148297), _1148303), _1148301)), _1148299)))]]], (21645 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148297), _1148303), _1148301))))]]], (21667 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148297), _1148299), _1148301)), _1148303))), 21670 ^ _773908 : [(21673 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148297), _1148303), _1148301)))], (21671 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148301)))]], 21674 ^ _773908 : [(21677 ^ _773908) ^ [] : [21678 ^ _773908 : [(21681 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148297), _1148303), _1148301)), _1148299))], (21679 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148301), c_Groups_Ozero__class_Ozero(_1148297))))]], 21682 ^ _773908 : [(21685 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148303))], (21683 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), _1148301), c_Groups_Ozero__class_Ozero(_1148297)))]]], (21675 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148297), c_Groups_Ozero__class_Ozero(_1148297)), _1148301))]]]]], (23949 ^ _773908) ^ [_1192578, _1192580, _1192582] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192578), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192580)), _1192582)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192578, _1192580), hAPP(c_Divides_OnegateSnd, _1192582))))], (10 ^ _773908) ^ [_774031, _774033, _774035] : [-(_774035 = _774031), _774035 = _774033, _774033 = _774031], (19041 ^ _773908) ^ [_1102879] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102879), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102879), c_Int_OPls)))], (17597 ^ _773908) ^ [_1077783, _1077785, _1077787, _1077789] : [class_Rings_Olinordered__semidom(_1077783), hAPP(hAPP(c_Power_Opower__class_Opower(_1077783), _1077785), hAPP(c_Nat_OSuc, _1077787)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1077783), _1077789), hAPP(c_Nat_OSuc, _1077787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077783), c_Groups_Ozero__class_Ozero(_1077783)), _1077785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077783), c_Groups_Ozero__class_Ozero(_1077783)), _1077789)), -(_1077785 = _1077789)], (20685 ^ _773908) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (14330 ^ _773908) ^ [_1016121, _1016123, _1016125] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016121), _1016123)), _1016125) = 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), _1016121), _1016125)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016123), _1016125))), 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, _1016121, _1016125)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016123, _1016125))), _1016125)))], (31768 ^ _773908) ^ [_1360701, _1360703, _1360705, _1360707, _1360709, _1360711, _1360713] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360701, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360703, tc_fun(_1360701, tc_HOL_Obool)), _1360705), _1360707)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360709, tc_fun(_1360701, tc_HOL_Obool)), _1360711), _1360713)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360703, tc_fun(_1360701, tc_HOL_Obool)), _1360705), hAPP(hAPP(c_COMBB(tc_fun(_1360709, tc_fun(_1360701, tc_HOL_Obool)), tc_fun(_1360701, tc_HOL_Obool), _1360703), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360709, tc_fun(_1360701, tc_HOL_Obool)), _1360711)), hAPP(hAPP(c_COMBC(_1360703, tc_fun(_1360709, tc_fun(_1360701, tc_HOL_Obool)), tc_fun(_1360709, tc_fun(_1360701, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1360701, tc_HOL_Obool), tc_fun(_1360701, tc_HOL_Obool)), tc_fun(tc_fun(_1360709, tc_fun(_1360701, tc_HOL_Obool)), tc_fun(_1360709, tc_fun(_1360701, tc_HOL_Obool))), _1360703), c_COMBB(tc_fun(_1360701, tc_HOL_Obool), tc_fun(_1360701, tc_HOL_Obool), _1360709)), hAPP(hAPP(c_COMBB(tc_fun(_1360701, tc_HOL_Obool), tc_fun(tc_fun(_1360701, tc_HOL_Obool), tc_fun(_1360701, tc_HOL_Obool)), _1360703), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360701, tc_HOL_Obool))), _1360707))), _1360713))))], (20 ^ _773908) ^ [_774168, _774170, _774172, _774174] : [-(c_Int_Oiszero(_774172, _774168)), c_Int_Oiszero(_774174, _774170), _774174 = _774172, _774170 = _774168], (8121 ^ _773908) ^ [_907046, _907048, _907050] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907046, _907048)), _907050), _907050)), hBOOL(hAPP(_907046, _907050)), 8129 ^ _773908 : [(8132 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_907046, _907048)), 8128 ^ [_907046, _907048, _907050]), _907050)))], (8130 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_907048), _907050), 8128 ^ [_907046, _907048, _907050])))]]], (35158 ^ _773908) ^ [_1431920, _1431922, _1431924] : [class_Fields_Ofield(_1431920), -(_1431922 = c_Groups_Oone__class_Oone(_1431920)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1431920), hAPP(c_Power_Opower__class_Opower(_1431920), _1431922)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1431924)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1431920), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431920), hAPP(hAPP(c_Power_Opower__class_Opower(_1431920), _1431922), _1431924)), c_Groups_Oone__class_Oone(_1431920))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431920), _1431922), c_Groups_Oone__class_Oone(_1431920))))], (51231 ^ _773908) ^ [_1810947, _1810949, _1810951, _1810953] : [c_Fun_Obij__betw(_1810947, _1810949, _1810951, c_Orderings_Obot__class_Obot(tc_fun(_1810947, tc_HOL_Obool)), _1810953), -(_1810953 = c_Orderings_Obot__class_Obot(tc_fun(_1810949, tc_HOL_Obool)))], (19007 ^ _773908) ^ [_1102286, _1102288] : [class_Rings_Oring__1(_1102286), -(hBOOL(hAPP(hAPP(c_member(_1102286), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102286), _1102288)), c_Int_Oring__1__class_OInts(_1102286))))], (46215 ^ _773908) ^ [_1698285, _1698287, _1698289, _1698291] : [-(_1698285 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1698287, tc_HOL_Obool), tc_HOL_Obool))), 46221 ^ _773908 : [(46224 ^ _773908) ^ [] : [c_Fun_Oinj__on(_1698287, _1698289, _1698291, 46220 ^ [_1698285, _1698287, _1698289, _1698291])], (46222 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1698287, tc_HOL_Obool)), 46220 ^ [_1698285, _1698287, _1698289, _1698291]), _1698285)))]], -(c_Fun_Oinj__on(_1698287, _1698289, _1698291, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1698287, tc_HOL_Obool), _1698285)))], (8839 ^ _773908) ^ [_920280, _920282, _920284] : [class_Groups_Oab__group__add(_920280), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920280), _920282), _920284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920280), hAPP(c_Groups_Ouminus__class_Ouminus(_920280), _920282)), hAPP(c_Groups_Ouminus__class_Ouminus(_920280), _920284)))], (16953 ^ _773908) ^ [_1065799, _1065801, _1065803] : [class_Int_Onumber__ring(_1065799), -(hAPP(c_Int_Onumber__class_Onumber__of(_1065799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1065801), _1065803)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065799), hAPP(c_Int_Onumber__class_Onumber__of(_1065799), _1065801)), hAPP(c_Int_Onumber__class_Onumber__of(_1065799), _1065803)))], (51700 ^ _773908) ^ [_1816128, _1816130] : [-(class_Nat_Osize(tc_sum(_1816128, _1816130)))], (46317 ^ _773908) ^ [_1700746, _1700748, _1700750, _1700752] : [class_Orderings_Oorder(_1700746), class_Enum_Oenum(_1700748), 46324 ^ _773908 : [(46333 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1700748, _1700746)), _1700750), _1700752))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1700748, _1700746)), _1700750), _1700752)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1700748), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1700748), c_fNot), hAPP(hAPP(c_COMBS(_1700748, _1700746, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1700746, tc_fun(_1700746, tc_HOL_Obool), _1700748), c_fequal), _1700750)), _1700752))))], (46325 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1700748, _1700746)), _1700750), _1700752)), 46328 ^ _773908 : [(46331 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1700748), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1700748), c_fNot), hAPP(hAPP(c_COMBS(_1700748, _1700746, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1700746, tc_fun(_1700746, tc_HOL_Obool), _1700748), c_fequal), _1700750)), _1700752)))))], (46329 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1700748, _1700746)), _1700750), _1700752)))]]]]], (14521 ^ _773908) ^ [_1019422, _1019424, _1019426] : [-(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), _1019422), _1019424)), _1019426), _1019424) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019426, _1019424))], (42117 ^ _773908) ^ [_1606493, _1606495, _1606497, _1606499, _1606501] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606493, tc_fun(_1606495, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606493, tc_HOL_Obool)), _1606497), _1606499)), _1606501) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606495, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606493, tc_fun(_1606495, tc_HOL_Obool)), _1606497), _1606501)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606493, tc_fun(_1606495, tc_HOL_Obool)), _1606499), _1606501)))], (37736 ^ _773908) ^ [_1490445, _1490447, _1490449, _1490451, _1490453, _1490455, _1490457, _1490459] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490445, _1490447)), _1490449), hAPP(c_Set_Oimage(tc_prod(_1490451, _1490453), tc_prod(_1490445, _1490447), c_Product__Type_Omap__pair(_1490451, _1490445, _1490453, _1490447, _1490455, _1490457)), _1490459))), 37741 ^ _773908 : [(37744 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490451, _1490453)), hAPP(hAPP(c_Product__Type_OPair(_1490451, _1490453), 37739 ^ [_1490445, _1490447, _1490449, _1490451, _1490453, _1490455, _1490457, _1490459]), 37740 ^ [_1490445, _1490447, _1490449, _1490451, _1490453, _1490455, _1490457, _1490459])), _1490459)))], (37742 ^ _773908) ^ [] : [-(_1490449 = hAPP(hAPP(c_Product__Type_OPair(_1490445, _1490447), hAPP(_1490455, 37739 ^ [_1490445, _1490447, _1490449, _1490451, _1490453, _1490455, _1490457, _1490459])), hAPP(_1490457, 37740 ^ [_1490445, _1490447, _1490449, _1490451, _1490453, _1490455, _1490457, _1490459])))]]], (21529 ^ _773908) ^ [_1146235, _1146237, _1146239, _1146241] : [class_Fields_Olinordered__field(_1146235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146235), _1146237), c_Groups_Ozero__class_Ozero(_1146235))), 21536 ^ _773908 : [(21543 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146235), _1146241), _1146237)), _1146239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146235), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146235), _1146239), _1146237)), _1146241)))], (21537 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146235), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146235), _1146239), _1146237)), _1146241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146235), _1146241), _1146237)), _1146239)))]]], (43380 ^ _773908) ^ [_1635662, _1635664, _1635666, _1635668, _1635670] : [-(c_List_Olist__all2(_1635662, _1635664, _1635666, _1635668, _1635670)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635662)), _1635668) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635664)), _1635670), 43386 ^ _773908 : [(43389 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1635662, _1635664, tc_HOL_Obool), _1635666), 43385 ^ [_1635662, _1635664, _1635666, _1635668, _1635670]))], (43387 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635662, _1635664)), 43385 ^ [_1635662, _1635664, _1635666, _1635668, _1635670]), hAPP(c_List_Oset(tc_prod(_1635662, _1635664)), hAPP(hAPP(c_List_Ozip(_1635662, _1635664), _1635668), _1635670)))))]]], (39751 ^ _773908) ^ [_1548298, _1548300, _1548302, _1548304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1548298), tc_List_Olist(_1548298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1548298), tc_List_Olist(_1548298)), _1548302), _1548304)), c_List_Olistrel(_1548298, _1548300))), -(c_List_Olistrelp(_1548298, hAPP(hAPP(c_COMBC(_1548298, tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_fun(_1548298, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548298, tc_fun(tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_fun(_1548298, tc_HOL_Obool)), _1548298), c_COMBC(_1548298, tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548298, tc_prod(_1548298, _1548298)), tc_fun(_1548298, tc_fun(tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_HOL_Obool)), _1548298), hAPP(c_COMBB(tc_prod(_1548298, _1548298), tc_fun(tc_fun(tc_prod(_1548298, _1548298), tc_HOL_Obool), tc_HOL_Obool), _1548298), c_member(tc_prod(_1548298, _1548298)))), c_Product__Type_OPair(_1548298, _1548298)))), _1548300), _1548302, _1548304))], (3762 ^ _773908) ^ [_830661, _830663, _830665, _830667] : [-(c_Relation_ORange(_830667, _830663) = c_Relation_ORange(_830665, _830661)), _830667 = _830665, _830663 = _830661], (8225 ^ _773908) ^ [_909331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _909331)), -(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), _909331))))], (26824 ^ _773908) ^ [_1257226, _1257228, _1257230, _1257232, _1257234, _1257236] : [-(_1257226 = _1257228), -(hAPP(c_Fun_Ofun__upd(_1257230, _1257232, _1257234, _1257228, _1257236), _1257226) = hAPP(_1257234, _1257226))], (19475 ^ _773908) ^ [_1110060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1110060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1110060))))], (30698 ^ _773908) ^ [_1336069, _1336071, _1336073, _1336075] : [class_Fields_Olinordered__field(_1336069), -(hAPP(c_Groups_Oabs__class_Oabs(_1336069), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336071, _1336069), _1336073), _1336075)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336071, _1336069), hAPP(hAPP(c_COMBB(_1336069, _1336069, _1336071), c_Groups_Oabs__class_Oabs(_1336069)), _1336073)), _1336075))], (18867 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (44072 ^ _773908) ^ [_1652199, _1652201, _1652203] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652199, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1652199, tc_HOL_Obool)), _1652201), _1652203)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652199, tc_HOL_Obool)), _1652201), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652199, tc_HOL_Obool), _1652203)))], (48213 ^ _773908) ^ [_1745690, _1745692, _1745694, _1745696] : [class_Lattices_Osemilattice__sup(_1745690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745690), _1745692)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1745690, _1745690, c_Lattices_Osemilattice__sup__class_Osup(_1745690)), _1745694), hAPP(hAPP(c_Set_Oinsert(_1745690), _1745696), _1745692)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1745690), _1745696), hAPP(hAPP(c_Finite__Set_Ofold(_1745690, _1745690, c_Lattices_Osemilattice__sup__class_Osup(_1745690)), _1745694), _1745692)))], (49314 ^ _773908) ^ [_1768812, _1768814, _1768816, _1768818] : [-(c_New__Random__Sequence_Opos__map(_1768812, _1768814, _1768816, _1768818) = c_New__Random__Sequence_Opos__bind(_1768812, _1768814, _1768818, hAPP(c_Fun_Ocomp(_1768814, 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(_1768814))))), _1768812, c_New__Random__Sequence_Opos__single(_1768814)), _1768816)))], (18915 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (17265 ^ _773908) ^ [_1071887] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071887)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071887)))], (37408 ^ _773908) ^ [_1480724, _1480726, _1480728, _1480730, _1480732] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1480724, _1480726), _1480728), hAPP(hAPP(c_COMBS(_1480724, tc_fun(_1480726, tc_HOL_Obool), tc_fun(_1480726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480726, tc_HOL_Obool), tc_fun(tc_fun(_1480726, tc_HOL_Obool), tc_fun(_1480726, tc_HOL_Obool)), _1480724), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480726, tc_HOL_Obool))), _1480730)), _1480732)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480724, _1480726), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1480724, _1480726), _1480728), _1480730)), hAPP(hAPP(c_Product__Type_OSigma(_1480724, _1480726), _1480728), _1480732)))], (51760 ^ _773908) ^ [_1816860] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1816860)))], (36555 ^ _773908) ^ [_1462324, _1462326, _1462328, _1462330, _1462332] : [c_Typedef_Otype__definition(_1462324, _1462326, _1462328, _1462330, _1462332), -(hAPP(c_Set_Oimage(_1462326, _1462324, _1462330), _1462332) = c_Orderings_Otop__class_Otop(tc_fun(_1462324, tc_HOL_Obool)))], (7942 ^ _773908) ^ [_903889, _903891, _903893] : [-(hBOOL(hAPP(_903889, _903891))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_903889, _903893)), _903891), _903891)))], (14719 ^ _773908) ^ [_1022772, _1022774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022774), 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), _1022772), _1022774)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4128 ^ _773908) ^ [_836260, _836262] : [_836262 = _836260, -(c_Nitpick_ORep__Frac(_836262) = c_Nitpick_ORep__Frac(_836260))], (16417 ^ _773908) ^ [_1055347] : [class_Groups_Oordered__ab__group__add__abs(_1055347), -(hAPP(c_Groups_Oabs__class_Oabs(_1055347), c_Groups_Ozero__class_Ozero(_1055347)) = c_Groups_Ozero__class_Ozero(_1055347))], (47497 ^ _773908) ^ [_1729134, _1729136, _1729138, _1729140, _1729142, _1729144] : [c_Relation_Osingle__valued(_1729134, _1729136, _1729138), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729134, _1729136)), hAPP(hAPP(c_Product__Type_OPair(_1729134, _1729136), _1729140), _1729142)), _1729138)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729134, _1729136)), hAPP(hAPP(c_Product__Type_OPair(_1729134, _1729136), _1729140), _1729144)), _1729138)), -(_1729142 = _1729144)], (51648 ^ _773908) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (4838 ^ _773908) ^ [_847685, _847687, _847689, _847691] : [-(c_HOL_OThe(_847691, _847687) = c_HOL_OThe(_847689, _847685)), _847691 = _847689, _847687 = _847685], (20121 ^ _773908) ^ [_1121167, _1121169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121167), _1121169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1121167)), c_Int_OBit1(_1121169))))], (44363 ^ _773908) ^ [_1658376, _1658378, _1658380] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658376)), hAPP(c_List_Ofilter(_1658376, _1658378), _1658380))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658376)), hAPP(c_List_Ofilter(_1658376, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1658376), c_fNot), _1658378)), _1658380))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658376)), _1658380))], (40517 ^ _773908) ^ [_1567853, _1567855, _1567857] : [-(_1567853 = c_List_Olist_ONil(_1567855)), -(hAPP(c_List_Ohd(_1567855), hAPP(hAPP(c_List_Oappend(_1567855), _1567853), _1567857)) = hAPP(c_List_Ohd(_1567855), _1567853))], (8303 ^ _773908) ^ [_910685, _910687, _910689, _910691, _910693, _910695, _910697, _910699, _910701] : [hAPP(c_Fun_Ocomp(_910685, _910687, _910689, _910691), _910693) = hAPP(c_Fun_Ocomp(_910695, _910687, _910689, _910697), _910699), -(hAPP(_910691, hAPP(_910693, _910701)) = hAPP(_910697, hAPP(_910699, _910701)))], (46770 ^ _773908) ^ [_1710991, _1710993] : [-(c_Relation_Orefl__on(_1710991, c_Orderings_Otop__class_Otop(tc_fun(_1710991, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1710991, _1710993)))], (39075 ^ _773908) ^ [_1529754, _1529756, _1529758, _1529760] : [hBOOL(hAPP(hAPP(c_member(_1529754), _1529756), hAPP(c_Relation_ORange(_1529758, _1529754), _1529760))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529758, _1529754)), hAPP(hAPP(c_Product__Type_OPair(_1529758, _1529754), 39078 ^ [_1529754, _1529756, _1529758, _1529760]), _1529756)), _1529760)))], (41227 ^ _773908) ^ [_1586218, _1586220, _1586222] : [hBOOL(hAPP(c_List_Odistinct(_1586218), _1586222)), -(hBOOL(hAPP(c_List_Odistinct(_1586218), hAPP(c_List_Orotate(_1586218, _1586220), _1586222))))], (30319 ^ _773908) ^ [_1327996, _1327998, _1328000] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327996), _1327998)), hBOOL(hAPP(hAPP(c_member(_1327996), _1328000), _1327998)), -(hAPP(c_Finite__Set_Ocard(_1327996), _1327998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1327996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327996, tc_HOL_Obool)), _1327998), hAPP(hAPP(c_Set_Oinsert(_1327996), _1328000), c_Orderings_Obot__class_Obot(tc_fun(_1327996, tc_HOL_Obool)))))))], (14629 ^ _773908) ^ [_1021263, _1021265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1021263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021265), _1021263)), _1021265)))], (19779 ^ _773908) ^ [_1115148, _1115150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115148), 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)))), _1115150))), 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)))), _1115148)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115150), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1115148))], (11309 ^ _773908) ^ [_962556, _962558, _962560] : [class_Rings_Oordered__cancel__semiring(_962556), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962556), _962558), _962560)), c_Groups_Ozero__class_Ozero(_962556)))), 11314 ^ _773908 : [(11321 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962556), _962558), c_Groups_Ozero__class_Ozero(_962556))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962556), c_Groups_Ozero__class_Ozero(_962556)), _962560))], (11315 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962556), c_Groups_Ozero__class_Ozero(_962556)), _962558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962556), _962560), c_Groups_Ozero__class_Ozero(_962556)))]]], (26384 ^ _773908) ^ [_1245748, _1245750, _1245752, _1245754, _1245756, _1245758] : [c_Hoare__Mirabelle_Ohoare__derivs(_1245748, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1245748), tc_HOL_Obool)), _1245750), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1245748), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748))), hAPP(hAPP(c_COMBB(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1245748)), _1245752)), c_Com_Ocom_OBODY)), _1245754)), _1245756)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1245748), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748))), hAPP(hAPP(c_COMBB(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1245748, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1245748))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1245748)), _1245752)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1245754)), _1245756)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1245758), _1245756)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1245748, _1245750, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1245748)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1245748), hAPP(_1245752, _1245758)), hAPP(c_Com_Ocom_OBODY, _1245758)), hAPP(_1245754, _1245758))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1245748), tc_HOL_Obool)))))], (36625 ^ _773908) ^ [_1463554, _1463556, _1463558, _1463560, _1463562] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1463554, _1463556, hAPP(hAPP(c_Set_Oinsert(_1463554), _1463558), _1463560)), _1463562)), 36630 ^ _773908 : [(36635 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463554), 36628 ^ [_1463554, _1463556, _1463558, _1463560, _1463562]), 36629 ^ [_1463554, _1463556, _1463558, _1463560, _1463562]))], (36633 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1463554, _1463554, _1463556, 36628 ^ [_1463554, _1463556, _1463558, _1463560, _1463562], 36629 ^ [_1463554, _1463556, _1463558, _1463560, _1463562]), _1463562)))], (36631 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1463554), _1463558), _1463560) = hAPP(hAPP(c_Set_Oinsert(_1463554), 36628 ^ [_1463554, _1463556, _1463558, _1463560, _1463562]), 36629 ^ [_1463554, _1463556, _1463558, _1463560, _1463562]))]]], (28338 ^ _773908) ^ [_1288574, _1288576, _1288578] : [class_Lattices_Oboolean__algebra(_1288574), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1288574), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288574), _1288576), _1288578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288574), hAPP(c_Groups_Ouminus__class_Ouminus(_1288574), _1288576)), hAPP(c_Groups_Ouminus__class_Ouminus(_1288574), _1288578)))], (28028 ^ _773908) ^ [_1281408, _1281410] : [class_Lattices_Obounded__lattice__bot(_1281408), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1281408), c_Orderings_Obot__class_Obot(_1281408)), _1281410) = c_Orderings_Obot__class_Obot(_1281408))], (44295 ^ _773908) ^ [_1657022, _1657024, _1657026, _1657028] : [-(hAPP(c_List_OremoveAll(_1657022, _1657024), hAPP(hAPP(c_List_Oappend(_1657022), _1657026), _1657028)) = hAPP(hAPP(c_List_Oappend(_1657022), hAPP(c_List_OremoveAll(_1657022, _1657024), _1657026)), hAPP(c_List_OremoveAll(_1657022, _1657024), _1657028)))], (590 ^ _773908) ^ [_782941, _782943, _782945, _782947] : [-(c_List_Olinorder__class_Osorted(_782945, _782941)), c_List_Olinorder__class_Osorted(_782947, _782943), _782947 = _782945, _782943 = _782941], (35211 ^ _773908) ^ [_1433247, _1433249, _1433251, _1433253, _1433255] : [class_Groups_Oordered__ab__semigroup__add(_1433247), class_Rings_Osemiring__1(_1433247), 35221 ^ _773908 : [(35224 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433247), hAPP(_1433253, 35220 ^ [_1433247, _1433249, _1433251, _1433253, _1433255])), _1433255))], (35222 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433249), 35220 ^ [_1433247, _1433249, _1433251, _1433253, _1433255]), _1433251)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433247), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433249, _1433247), _1433253), _1433251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433247), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1433247), hAPP(c_Finite__Set_Ocard(_1433249), _1433251))), _1433255))))], (51205 ^ _773908) ^ [_1810503, _1810505, _1810507, _1810509, _1810511] : [c_Fun_Obij__betw(_1810503, _1810505, _1810507, _1810509, _1810511), -(c_Fun_Oinj__on(_1810503, _1810505, _1810507, _1810509))], (38245 ^ _773908) ^ [_1504247] : [-(c_Relation_OId(_1504247) = hAPP(c_Set_OCollect(tc_prod(_1504247, _1504247)), hAPP(hAPP(c_COMBB(tc_fun(_1504247, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1504247, _1504247)), c_HOL_OEx(_1504247)), hAPP(hAPP(c_COMBC(tc_prod(_1504247, _1504247), tc_fun(_1504247, tc_prod(_1504247, _1504247)), tc_fun(_1504247, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_fun(tc_fun(_1504247, tc_prod(_1504247, _1504247)), tc_fun(_1504247, tc_HOL_Obool)), tc_prod(_1504247, _1504247)), c_COMBB(tc_prod(_1504247, _1504247), tc_HOL_Obool, _1504247)), c_fequal)), hAPP(hAPP(c_COMBS(_1504247, _1504247, tc_prod(_1504247, _1504247)), c_Product__Type_OPair(_1504247, _1504247)), c_COMBI(_1504247))))))], (28368 ^ _773908) ^ [_1289216, _1289218, _1289220, _1289222] : [hBOOL(hAPP(hAPP(c_member(_1289216), _1289218), _1289220)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289216, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1289216), _1289218), _1289222)), _1289220) = hAPP(hAPP(c_Set_Oinsert(_1289216), _1289218), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289216, tc_HOL_Obool)), _1289222), _1289220)))], (21821 ^ _773908) ^ [_1151573, _1151575, _1151577, _1151579] : [class_Fields_Ofield(_1151573), -(_1151575 = c_Groups_Ozero__class_Ozero(_1151573)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151573), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151573), _1151577), _1151575)), _1151579) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151573), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151573), _1151577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151573), _1151575), _1151579))), _1151575))], (19581 ^ _773908) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (51308 ^ _773908) ^ [_1812142, _1812144] : [class_Lattices_Olattice(_1812142), -(class_Lattices_Osemilattice__inf(tc_fun(_1812144, _1812142)))], (35228 ^ _773908) ^ [_1433637, _1433639, _1433641, _1433643, _1433645] : [class_Groups_Ocomm__monoid__add(_1433637), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433639), _1433641)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433639), _1433643)), 35242 ^ _773908 : [(35245 ^ _773908) ^ [] : [hAPP(_1433645, 35241 ^ [_1433637, _1433639, _1433641, _1433643, _1433645]) = c_Groups_Ozero__class_Ozero(_1433637)], (35243 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433639), 35241 ^ [_1433637, _1433639, _1433641, _1433643, _1433645]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433639, tc_HOL_Obool)), _1433641), _1433643))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433639, _1433637), _1433645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1433639, tc_HOL_Obool)), _1433641), _1433643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433637), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433639, _1433637), _1433645), _1433641)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433639, _1433637), _1433645), _1433643)))], (36033 ^ _773908) ^ [_1449881, _1449883] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1449881, tc_HOL_Obool)), _1449883), c_Orderings_Otop__class_Otop(tc_fun(_1449881, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1449881, tc_HOL_Obool)))], (40563 ^ _773908) ^ [_1568585, _1568587, _1568589, _1568591] : [-(hAPP(c_List_Oset(tc_prod(_1568585, _1568587)), hAPP(hAPP(c_List_Ozip(_1568585, _1568587), _1568589), _1568591)) = hAPP(c_Set_OCollect(tc_prod(_1568585, _1568587)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1568585, _1568587)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1568585, _1568587), 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(_1568585, _1568587)), 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(_1568585, _1568587)), 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(_1568585, _1568587), tc_fun(tc_Nat_Onat, tc_prod(_1568585, _1568587)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1568585, _1568587), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1568585, _1568587)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1568585, _1568587)), c_COMBB(tc_prod(_1568585, _1568587), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1568587, tc_prod(_1568585, _1568587)), hAPP(hAPP(c_COMBB(_1568585, tc_fun(_1568587, tc_prod(_1568585, _1568587)), tc_Nat_Onat), c_Product__Type_OPair(_1568585, _1568587)), hAPP(c_List_Onth(_1568585), _1568589))), hAPP(c_List_Onth(_1568587), _1568591)))))), 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(_1568585)), _1568589)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1568587)), _1568591)))))))], (20275 ^ _773908) ^ [_1123856] : [-(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)))), _1123856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123856), _1123856))], (6200 ^ _773908) ^ [_874484, _874486] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _874484, _874486, _874484))], (25653 ^ _773908) ^ [_1228377] : [-(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)), _1228377), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (28650 ^ _773908) ^ [_1295671, _1295673, _1295675, _1295677] : [hBOOL(hAPP(hAPP(_1295675, _1295677), _1295673)), -(hBOOL(hAPP(hAPP(c_member(_1295671), _1295673), c_SetInterval_Oord_OatLeast(_1295671, _1295675, _1295677))))], (20145 ^ _773908) ^ [_1121613, _1121615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121613), _1121615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121613)), c_Int_OBit0(_1121615))))], (38885 ^ _773908) ^ [_1525241, _1525243, _1525245] : [c_Wellfounded_Owf(_1525241, _1525243), hBOOL(hAPP(hAPP(c_member(tc_prod(_1525241, _1525241)), hAPP(hAPP(c_Product__Type_OPair(_1525241, _1525241), _1525245), _1525245)), _1525243))], (43463 ^ _773908) ^ [_1637378, _1637380, _1637382, _1637384, _1637386, _1637388, _1637390] : [-(c_List_Olist__all2(_1637378, _1637380, _1637382, hAPP(hAPP(c_List_Olist_OCons(_1637378), _1637384), _1637386), hAPP(hAPP(c_List_Olist_OCons(_1637380), _1637388), _1637390))), hBOOL(hAPP(hAPP(_1637382, _1637384), _1637388)), c_List_Olist__all2(_1637378, _1637380, _1637382, _1637386, _1637390)], (13185 ^ _773908) ^ [_995253, _995255, _995257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995253), _995255)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995257), _995255))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995253), _995257)))], (42832 ^ _773908) ^ [_1623837, _1623839] : [hAPP(c_Code__Numeral_Onat__of, _1623837) = hAPP(c_Code__Numeral_Onat__of, _1623839), -(_1623837 = _1623839)], (39110 ^ _773908) ^ [_1531161, _1531163, _1531165, _1531167, _1531169] : [hBOOL(hAPP(hAPP(_1531161, _1531163), _1531165)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1531167, _1531169, _1531161), _1531165)))], (7235 ^ _773908) ^ [_890868, _890870, _890872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890868), _890870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890870), _890872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890868)), _890872)))], (47405 ^ _773908) ^ [_1726975, _1726977, _1726979, _1726981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1726975, _1726975)), hAPP(hAPP(c_Product__Type_OPair(_1726975, _1726975), _1726977), _1726979)), c_Transitive__Closure_Otrancl(_1726975, hAPP(c_Relation_Oconverse(_1726975, _1726975), _1726981)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1726975, _1726975)), hAPP(hAPP(c_Product__Type_OPair(_1726975, _1726975), _1726977), _1726979)), hAPP(c_Relation_Oconverse(_1726975, _1726975), c_Transitive__Closure_Otrancl(_1726975, _1726981)))))], (20937 ^ _773908) ^ [_1136065, _1136067, _1136069, _1136071] : [class_Fields_Olinordered__field(_1136065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136065), _1136067), _1136069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136065), _1136071), c_Groups_Ozero__class_Ozero(_1136065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136065), _1136069), _1136071)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136065), _1136067), _1136071))))], (39520 ^ _773908) ^ [_1541558, _1541560, _1541562] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1541558), tc_List_Olist(_1541558))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1541558), tc_List_Olist(_1541558)), c_List_Olist_ONil(_1541558)), _1541560)), c_List_Olex(_1541558, _1541562)))], (20583 ^ _773908) ^ [_1129574, _1129576, _1129578] : [class_Rings_Olinordered__idom(_1129574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129574), c_Groups_Ozero__class_Ozero(_1129574)), hAPP(hAPP(c_Power_Opower__class_Opower(_1129574), _1129576), 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)))), _1129578))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129574), c_Groups_Ozero__class_Ozero(_1129574)), _1129576)))], (47333 ^ _773908) ^ [_1725270, _1725272, _1725274] : [c_Relation_Ototal__on(_1725270, _1725272, hAPP(c_Relation_Oconverse(_1725270, _1725270), _1725274)), -(c_Relation_Ototal__on(_1725270, _1725272, _1725274))], (27192 ^ _773908) ^ [_1264780, _1264782, _1264784, _1264786, _1264788] : [c_Equiv__Relations_Oequiv(_1264780, _1264782, _1264784), hBOOL(hAPP(hAPP(c_member(_1264780), _1264786), _1264782)), hBOOL(hAPP(hAPP(c_member(_1264780), _1264788), _1264782)), 27203 ^ _773908 : [(27210 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1264780, _1264780)), hAPP(hAPP(c_Product__Type_OPair(_1264780, _1264780), _1264786), _1264788)), _1264784)), -(hAPP(c_Relation_OImage(_1264780, _1264780, _1264784), hAPP(hAPP(c_Set_Oinsert(_1264780), _1264786), c_Orderings_Obot__class_Obot(tc_fun(_1264780, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1264780, _1264780, _1264784), hAPP(hAPP(c_Set_Oinsert(_1264780), _1264788), c_Orderings_Obot__class_Obot(tc_fun(_1264780, tc_HOL_Obool)))))], (27204 ^ _773908) ^ [] : [hAPP(c_Relation_OImage(_1264780, _1264780, _1264784), hAPP(hAPP(c_Set_Oinsert(_1264780), _1264786), c_Orderings_Obot__class_Obot(tc_fun(_1264780, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1264780, _1264780, _1264784), hAPP(hAPP(c_Set_Oinsert(_1264780), _1264788), c_Orderings_Obot__class_Obot(tc_fun(_1264780, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1264780, _1264780)), hAPP(hAPP(c_Product__Type_OPair(_1264780, _1264780), _1264786), _1264788)), _1264784)))]]], (24343 ^ _773908) ^ [_1201070, _1201072, _1201074, _1201076, _1201078] : [hAPP(c_Product__Type_Ofst(_1201070, _1201072), hAPP(hAPP(c_Product__Type_OPair(_1201070, _1201072), _1201074), _1201076)) = _1201078, -(_1201074 = _1201078)], (47449 ^ _773908) ^ [_1728053, _1728055, _1728057] : [-(hAPP(c_Relation_Oconverse(_1728053, _1728055), _1728057) = hAPP(c_Set_OCollect(tc_prod(_1728055, _1728053)), hAPP(c_Product__Type_Oprod_Oprod__case(_1728055, _1728053, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1728055, tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_fun(_1728053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1728053, tc_fun(tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_fun(_1728053, tc_HOL_Obool)), _1728055), c_COMBC(_1728053, tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1728053, tc_prod(_1728053, _1728055)), tc_fun(_1728053, tc_fun(tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_HOL_Obool)), _1728055), hAPP(c_COMBB(tc_prod(_1728053, _1728055), tc_fun(tc_fun(tc_prod(_1728053, _1728055), tc_HOL_Obool), tc_HOL_Obool), _1728053), c_member(tc_prod(_1728053, _1728055)))), hAPP(c_COMBC(_1728053, _1728055, tc_prod(_1728053, _1728055)), c_Product__Type_OPair(_1728053, _1728055))))), _1728057))))], (15879 ^ _773908) ^ [_1044450, _1044452] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044450), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044452)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044450), _1044452)))], (35893 ^ _773908) ^ [_1447371] : [c_Orderings_Otop__class_Otop(tc_fun(_1447371, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1447371, tc_HOL_Obool))], (23777 ^ _773908) ^ [_1189537, _1189539, _1189541, _1189543, _1189545, _1189547] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1189537, _1189539, _1189541, _1189543, c_Nitpick_Opair__box_OPairBox(_1189537, _1189539, _1189545, _1189547)) = hAPP(hAPP(_1189543, _1189545), _1189547))], (23063 ^ _773908) ^ [_1174395, _1174397] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174395), hAPP(c_Nat_OSuc, _1174397)) = 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), _1174395), _1174397)))], (13157 ^ _773908) ^ [_994723, _994725] : [-(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), _994723), _994725)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _994723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _994725))], (16143 ^ _773908) ^ [_1050402, _1050404] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050402, _1050404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1050402), _1050404)), _1050404)))], (32456 ^ _773908) ^ [_1376296, _1376298, _1376300] : [-(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)), _1376296)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1376298, _1376300)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1376298), _1376296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1376300), _1376296)))], (37587 ^ _773908) ^ [_1486060, _1486062, _1486064, _1486066] : [-(c_Fun_Oinj__on(_1486060, tc_prod(_1486062, _1486060), 37585 ^ [_1486060, _1486062, _1486064, _1486066], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486062, tc_fun(_1486060, tc_HOL_Obool)), _1486064), _1486066)))], (51894 ^ _773908) ^ [_1818343, _1818345] : [hBOOL(hAPP(hAPP(c_fconj, _1818343), _1818345)), -(hBOOL(_1818343))], (17989 ^ _773908) ^ [_1084189, _1084191, _1084193, _1084195, _1084197] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1084189, _1084191, _1084193), _1084195), hAPP(c_Nat_OSuc, _1084197)) = hAPP(hAPP(_1084193, _1084195), hAPP(hAPP(c_Power_Opower_Opower(_1084189, _1084191, _1084193), _1084195), _1084197)))], (1764 ^ _773908) ^ [_798944, _798946] : [-(class_Rings_Ozero__neq__one(_798944)), _798946 = _798944, class_Rings_Ozero__neq__one(_798946)], (49069 ^ _773908) ^ [_1763475, _1763477, _1763479, _1763481] : [-(c_List_Olist__all(_1763475, _1763477, hAPP(hAPP(c_List_Oappend(_1763475), _1763479), _1763481))), c_List_Olist__all(_1763475, _1763477, _1763479), c_List_Olist__all(_1763475, _1763477, _1763481)], (12100 ^ _773908) ^ [_976795, _976797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _976795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _976797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976797), _976795))))], (45691 ^ _773908) ^ [_1686757, _1686759, _1686761] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1686757), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1686757))), _1686759))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686761), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686757))), _1686759))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686757))), hAPP(c_List_Ofilter(tc_List_Olist(_1686757), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1686757)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686761)), c_Nat_Osize__class_Osize(tc_List_Olist(_1686757)))), c_List_Otranspose(_1686757, _1686759))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686757)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1686757)), _1686759), _1686761)))], (8408 ^ _773908) ^ [_912461, _912463] : [class_Rings_Olinordered__idom(_912461), 8411 ^ _773908 : [(8418 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912461), c_Groups_Ozero__class_Ozero(_912461)), hAPP(c_Int_Oring__1__class_Oof__int(_912461), _912463))))], (8412 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912461), c_Groups_Ozero__class_Ozero(_912461)), hAPP(c_Int_Oring__1__class_Oof__int(_912461), _912463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912463)))]]], (14368 ^ _773908) ^ [_1016989, _1016991] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016989)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016991)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016989), _1016991))], (37690 ^ _773908) ^ [_1488922, _1488924, _1488926, _1488928, _1488930, _1488932, _1488934, _1488936] : [c_Fun_Oinj__on(_1488922, _1488924, _1488926, _1488928), c_Fun_Oinj__on(_1488930, _1488932, _1488934, _1488936), -(c_Fun_Oinj__on(tc_prod(_1488922, _1488930), tc_prod(_1488924, _1488932), c_Product__Type_Omap__pair(_1488922, _1488924, _1488930, _1488932, _1488926, _1488934), hAPP(hAPP(c_Product__Type_OSigma(_1488922, _1488930), _1488928), hAPP(c_COMBK(tc_fun(_1488930, tc_HOL_Obool), _1488922), _1488936))))], (41516 ^ _773908) ^ [_1591573] : [c_List_Onat__list(_1591573), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1591573)))], (20021 ^ _773908) ^ [_1119437, _1119439] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1119437)), c_Int_OBit1(_1119439)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1119437), _1119439)))], (19757 ^ _773908) ^ [_1114661, _1114663] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1114661), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1114663)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1114661), 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)))), _1114663)))], (5044 ^ _773908) ^ [_850946, _850948, _850950, _850952, _850954, _850956, _850958, _850960] : [-(c_Random__Sequence_Obind(_850960, _850956, _850952, _850948) = c_Random__Sequence_Obind(_850958, _850954, _850950, _850946)), _850960 = _850958, _850956 = _850954, _850952 = _850950, _850948 = _850946], (41292 ^ _773908) ^ [_1587516, _1587518, _1587520] : [_1587520 = c_List_Olist_ONil(_1587516), -(hAPP(c_List_Orotate(_1587516, _1587518), _1587520) = c_List_Olist_ONil(_1587516))], (51504 ^ _773908) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (39552 ^ _773908) ^ [_1542376, _1542378, _1542380, _1542382, _1542384, _1542386] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1542376), tc_List_Olist(_1542376))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1542376), tc_List_Olist(_1542376)), hAPP(hAPP(c_List_Oappend(_1542376), _1542378), hAPP(hAPP(c_List_Olist_OCons(_1542376), _1542380), c_List_Olist_ONil(_1542376)))), hAPP(hAPP(c_List_Oappend(_1542376), _1542382), hAPP(hAPP(c_List_Olist_OCons(_1542376), _1542384), c_List_Olist_ONil(_1542376))))), c_List_Olistrel1(_1542376, _1542386)))), 39553 ^ _773908 : [(39560 ^ _773908) ^ [] : [_1542378 = _1542382, hBOOL(hAPP(hAPP(c_member(tc_prod(_1542376, _1542376)), hAPP(hAPP(c_Product__Type_OPair(_1542376, _1542376), _1542380), _1542384)), _1542386))], (39554 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1542376), tc_List_Olist(_1542376))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1542376), tc_List_Olist(_1542376)), _1542378), _1542382)), c_List_Olistrel1(_1542376, _1542386))), _1542380 = _1542384]]], (25039 ^ _773908) ^ [_1215638, _1215640, _1215642, _1215644, _1215646] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1215638, _1215640, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1215638)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1215638), hAPP(hAPP(c_COMBC(_1215638, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1215638), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1215642)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1215644)), _1215646))), c_Com_Ocom_OAss(_1215644, _1215646)), _1215642)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1215638), tc_HOL_Obool)))))], (37157 ^ _773908) ^ [_1474293, _1474295, _1474297, _1474299, _1474301] : [hBOOL(hAPP(_1474299, hAPP(_1474297, _1474301))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1474293, _1474295, _1474297), _1474299), _1474301)))], (41989 ^ _773908) ^ [_1603411, _1603413, _1603415, _1603417, _1603419] : [41991 ^ _773908 : [(41994 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603411, tc_HOL_Obool)), _1603413), hAPP(_1603419, 41990 ^ [_1603411, _1603413, _1603415, _1603417, _1603419])))], (41992 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603415), 41990 ^ [_1603411, _1603413, _1603415, _1603417, _1603419]), _1603417)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603411, tc_HOL_Obool)), _1603413), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603415, tc_fun(_1603411, tc_HOL_Obool)), _1603417), _1603419))))], (8096 ^ _773908) ^ [_906594, _906596, _906598, _906600] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_906594, _906596), _906598, _906600, _906598), hBOOL(hAPP(_906594, _906598)), 8104 ^ _773908 : [(8107 ^ _773908) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_906594, _906596), 8103 ^ [_906594, _906596, _906598, _906600], _906600, _906598))], (8105 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_906596, _906598, _906600, 8103 ^ [_906594, _906596, _906598, _906600]))]]], (40565 ^ _773908) ^ [_1568810, _1568812, _1568814, _1568816, _1568818, _1568820] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1568810, _1568812), hAPP(hAPP(c_List_Ozip(_1568810, _1568812), _1568814), _1568816)), _1568818), _1568820) = hAPP(hAPP(c_List_Ozip(_1568810, _1568812), hAPP(hAPP(c_List_Olist__update(_1568810, _1568814), _1568818), hAPP(c_Product__Type_Ofst(_1568810, _1568812), _1568820))), hAPP(hAPP(c_List_Olist__update(_1568812, _1568816), _1568818), hAPP(c_Product__Type_Osnd(_1568810, _1568812), _1568820))))], (41624 ^ _773908) ^ [_1593904, _1593906, _1593908] : [class_Groups_Omonoid__add(_1593904), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1593904), hAPP(hAPP(c_List_Oappend(_1593904), _1593906), _1593908)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1593904), hAPP(c_List_Omonoid__add__class_Olistsum(_1593904), _1593906)), hAPP(c_List_Omonoid__add__class_Olistsum(_1593904), _1593908)))], (38729 ^ _773908) ^ [_1522072, _1522074, _1522076] : [c_Wellfounded_Owf(_1522072, _1522074), -(c_Wellfounded_Owf(_1522072, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522072, _1522072), tc_HOL_Obool)), _1522074), _1522076)))], (16487 ^ _773908) ^ [_1056684, _1056686] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056684, tc_HOL_Obool)), _1056686), _1056686) = c_Orderings_Obot__class_Obot(tc_fun(_1056684, tc_HOL_Obool)))], (18689 ^ _773908) ^ [_1096935] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096935), c_Int_OMin) = c_Int_Opred(_1096935))], (47355 ^ _773908) ^ [_1725683, _1725685, _1725687, _1725689, _1725691] : [-(hAPP(c_Relation_Oconverse(_1725683, _1725685), hAPP(hAPP(c_Relation_Orel__comp(_1725683, _1725687, _1725685), _1725689), _1725691)) = hAPP(hAPP(c_Relation_Orel__comp(_1725685, _1725687, _1725683), hAPP(c_Relation_Oconverse(_1725687, _1725685), _1725691)), hAPP(c_Relation_Oconverse(_1725683, _1725687), _1725689)))], (34600 ^ _773908) ^ [_1419242, _1419244, _1419246, _1419248, _1419250] : [class_Groups_Oab__group__add(_1419242), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419244, _1419242), hAPP(hAPP(c_COMBS(_1419244, _1419242, _1419242), hAPP(hAPP(c_COMBB(_1419242, tc_fun(_1419242, _1419242), _1419244), c_Groups_Ominus__class_Ominus(_1419242)), _1419246)), _1419248)), _1419250) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1419242), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419244, _1419242), _1419246), _1419250)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419244, _1419242), _1419248), _1419250)))], (14334 ^ _773908) ^ [_1016250, _1016252] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016250), _1016252)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016250)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016252)))], (30928 ^ _773908) ^ [_1340521, _1340523, _1340525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1340521), _1340523)), 30931 ^ _773908 : [(30932 ^ _773908) ^ [] : [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(_1340521, tc_Nat_Onat), _1340525), _1340523))), 30935 ^ _773908 : [(30936 ^ _773908) ^ [_1340689] : [hBOOL(hAPP(hAPP(c_member(_1340521), _1340689), _1340523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1340525, _1340689))))]]], (30942 ^ _773908) ^ [] : [30944 ^ _773908 : [(30947 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1340525, 30943 ^ [_1340521, _1340523, _1340525])))], (30945 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340521), 30943 ^ [_1340521, _1340523, _1340525]), _1340523)))]], -(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(_1340521, tc_Nat_Onat), _1340525), _1340523))))]]], (37964 ^ _773908) ^ [_1495467, _1495469, _1495471, _1495473] : [-(hAPP(c_Set_Ovimage(_1495467, _1495469, _1495471), hAPP(c_Set_OCollect(_1495469), _1495473)) = hAPP(c_Set_OCollect(_1495467), hAPP(hAPP(c_COMBB(_1495469, tc_HOL_Obool, _1495467), _1495473), _1495471)))], (14364 ^ _773908) ^ [_1016893, _1016895, _1016897] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016893), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016895, _1016897)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016893), _1016895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016893), _1016897)))], (50925 ^ _773908) ^ [_1804179, _1804181, _1804183, _1804185, _1804187] : [hBOOL(hAPP(hAPP(c_member(_1804179), _1804181), hAPP(c_Set_Oimage(_1804183, _1804179, _1804185), _1804187))), -(hAPP(_1804185, hAPP(c_Hilbert__Choice_Oinv__into(_1804183, _1804179, _1804187, _1804185), _1804181)) = _1804181)], (28118 ^ _773908) ^ [_1283353, _1283355, _1283357, _1283359] : [class_Lattices_Osemilattice__inf(_1283353), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283353), _1283355), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283353), _1283357), _1283359)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283353), _1283357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283353), _1283355), _1283359)))], (30045 ^ _773908) ^ [_1322621, _1322623] : [class_Orderings_Olinorder(_1322621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322621), _1322623)), -(_1322623 = c_Orderings_Obot__class_Obot(tc_fun(_1322621, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322621), c_Big__Operators_Olattice_OInf__fin(_1322621, c_Orderings_Oord__class_Omin(_1322621), _1322623)), c_Big__Operators_Olattice_OSup__fin(_1322621, c_Orderings_Oord__class_Omax(_1322621), _1322623))))], (14336 ^ _773908) ^ [_1016296, _1016298, _1016300] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016296, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016298), _1016300)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016298), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016296), _1016298), _1016300))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016296, _1016298)))], (762 ^ _773908) ^ [_785551, _785553, _785555, _785557, _785559, _785561] : [-(c_Nitpick_Oless__frac(_785559, _785555, _785551)), c_Nitpick_Oless__frac(_785561, _785557, _785553), _785561 = _785559, _785557 = _785555, _785553 = _785551], (18877 ^ _773908) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (3654 ^ _773908) ^ [_828987, _828989] : [_828989 = _828987, -(c_Enum_Oenum__class_Oenum__ex(_828989) = c_Enum_Oenum__class_Oenum__ex(_828987))], (42143 ^ _773908) ^ [_1607261, _1607263, _1607265, _1607267, _1607269] : [_1607261 = c_Orderings_Obot__class_Obot(tc_fun(_1607263, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607265, tc_HOL_Obool)), _1607267), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607263, tc_fun(_1607265, tc_HOL_Obool)), _1607261), _1607269)) = _1607267)], (35360 ^ _773908) ^ [_1436323, _1436325] : [hAPP(_1436323, 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), _1436323), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436325)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1436323), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1436325)))], (41440 ^ _773908) ^ [_1590374, _1590376, _1590378] : [-(_1590374 = c_List_Olist_ONil(_1590376)), -(c_List_Olast(_1590376, hAPP(hAPP(c_List_Oappend(_1590376), _1590378), _1590374)) = c_List_Olast(_1590376, _1590374))], (45286 ^ _773908) ^ [_1678304, _1678306] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678304)), c_List_Oremdups(_1678304, _1678306)) = hAPP(c_Finite__Set_Ocard(_1678304), hAPP(c_List_Oset(_1678304), _1678306)))], (31550 ^ _773908) ^ [_1355035, _1355037, _1355039, _1355041, _1355043, _1355045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355035, tc_fun(_1355037, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355039, tc_fun(_1355035, tc_HOL_Obool)), _1355041), _1355043)), _1355045) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355039, tc_fun(_1355037, tc_HOL_Obool)), _1355041), hAPP(hAPP(c_COMBC(_1355039, tc_fun(_1355035, tc_fun(_1355037, tc_HOL_Obool)), tc_fun(_1355037, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355035, tc_HOL_Obool), tc_fun(tc_fun(_1355035, tc_fun(_1355037, tc_HOL_Obool)), tc_fun(_1355037, tc_HOL_Obool)), _1355039), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355035, tc_fun(_1355037, tc_HOL_Obool))), _1355043)), _1355045)))], (6169 ^ _773908) ^ [_873913, _873915, _873917] : [6170 ^ _773908 : [(6171 ^ _773908) ^ [_873963] : [c_Natural_Oevaln(_873913, _873915, _873963, _873917)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_873913), _873915), _873917)))], (1584 ^ _773908) ^ [_796694, _796696] : [-(class_Groups_Oordered__comm__monoid__add(_796694)), _796696 = _796694, class_Groups_Oordered__comm__monoid__add(_796696)], (23884 ^ _773908) ^ [_1191545, _1191547, _1191549] : [23886 ^ _773908 : [(23889 ^ _773908) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1191545, _1191547), 23885 ^ [_1191545, _1191547, _1191549]))], (23887 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1191547, 23885 ^ [_1191545, _1191547, _1191549]), _1191549)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1191545, _1191547), _1191549)))], (40934 ^ _773908) ^ [_1580088, _1580090, _1580092, _1580094, _1580096, _1580098] : [-(hAPP(c_List_Olist_Olist__case(_1580088, _1580090, _1580092, _1580094), hAPP(hAPP(c_List_Olist_OCons(_1580090), _1580096), _1580098)) = hAPP(hAPP(_1580094, _1580096), _1580098))], (50219 ^ _773908) ^ [_1790703, _1790705] : [c_Relation_Otrans(_1790703, _1790705), -(c_Relation_Otrans(_1790703, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1790703, _1790703), tc_HOL_Obool)), _1790705), c_Relation_OId(_1790703))))], (13907 ^ _773908) ^ [_1008116, _1008118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1008116), _1008118)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008116, _1008118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1008116), _1008118))], (24391 ^ _773908) ^ [_1202033, _1202035, _1202037] : [-(hAPP(hAPP(c_Product__Type_OPair(_1202033, _1202035), hAPP(c_Product__Type_Ofst(_1202033, _1202035), _1202037)), hAPP(c_Product__Type_Osnd(_1202033, _1202035), _1202037)) = _1202037)], (16351 ^ _773908) ^ [_1054301, _1054303, _1054305] : [class_Int_Onumber__ring(_1054301), class_Int_Oring__char__0(_1054301), 16358 ^ _773908 : [(16365 ^ _773908) ^ [] : [_1054303 = _1054305, -(hAPP(c_Int_Onumber__class_Onumber__of(_1054301), _1054303) = hAPP(c_Int_Onumber__class_Onumber__of(_1054301), _1054305))], (16359 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054301), _1054303) = hAPP(c_Int_Onumber__class_Onumber__of(_1054301), _1054305), -(_1054303 = _1054305)]]], (45619 ^ _773908) ^ [_1685215, _1685217, _1685219] : [-(hAPP(c_List_Orev(_1685215), hAPP(hAPP(c_List_Otake(_1685215), _1685217), _1685219)) = hAPP(hAPP(c_List_Odrop(_1685215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685215)), _1685219)), _1685217)), hAPP(c_List_Orev(_1685215), _1685219)))], (4628 ^ _773908) ^ [_844318, _844320, _844322, _844324, _844326, _844328, _844330, _844332, _844334, _844336] : [-(c_Predicate_Opred__comp(_844336, _844332, _844328, _844324, _844320) = c_Predicate_Opred__comp(_844334, _844330, _844326, _844322, _844318)), _844336 = _844334, _844332 = _844330, _844328 = _844326, _844324 = _844322, _844320 = _844318], (11784 ^ _773908) ^ [_970796, _970798, _970800] : [class_Groups_Oordered__comm__monoid__add(_970796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970796), _970798), c_Groups_Ozero__class_Ozero(_970796))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970796), _970800), c_Groups_Ozero__class_Ozero(_970796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970796), _970798), _970800)), c_Groups_Ozero__class_Ozero(_970796))))], (46093 ^ _773908) ^ [_1695244, _1695246] : [class_Orderings_Olinorder(_1695244), 46096 ^ _773908 : [(46117 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1695244, _1695246)), 46118 ^ _773908 : [(46121 ^ _773908) ^ [_1695804, _1695806] : [_1695246 = hAPP(hAPP(c_List_Olist_OCons(_1695244), _1695804), _1695806), 46127 ^ _773908 : [(46130 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695244), _1695804), 46126 ^ [_1695244, _1695246, _1695804, _1695806]))], (46128 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695244), 46126 ^ [_1695244, _1695246, _1695804, _1695806]), hAPP(c_List_Oset(_1695244), _1695806))))]], c_List_Olinorder__class_Osorted(_1695244, _1695806)], (46119 ^ _773908) ^ [] : [_1695246 = c_List_Olist_ONil(_1695244)]]], (46097 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1695244, _1695246), -(_1695246 = c_List_Olist_ONil(_1695244)), 46106 ^ _773908 : [(46109 ^ _773908) ^ [_1695578] : [hBOOL(hAPP(hAPP(c_member(_1695244), _1695578), hAPP(c_List_Oset(_1695244), 46104 ^ [_1695244, _1695246]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695244), 46105 ^ [_1695244, _1695246]), _1695578)))], (46115 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1695244, 46104 ^ [_1695244, _1695246]))], (46107 ^ _773908) ^ [] : [-(_1695246 = hAPP(hAPP(c_List_Olist_OCons(_1695244), 46105 ^ [_1695244, _1695246]), 46104 ^ [_1695244, _1695246]))]]]]], (42987 ^ _773908) ^ [_1627074, _1627076, _1627078, _1627080] : [_1627074 = _1627076, -(c_List_Oremove1(_1627078, _1627074, hAPP(hAPP(c_List_Olist_OCons(_1627078), _1627076), _1627080)) = _1627080)], (41618 ^ _773908) ^ [_1593775, _1593777, _1593779] : [class_Groups_Omonoid__add(_1593775), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1593775), hAPP(hAPP(c_List_Olist_OCons(_1593775), _1593777), _1593779)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1593775), _1593777), hAPP(c_List_Omonoid__add__class_Olistsum(_1593775), _1593779)))], (4740 ^ _773908) ^ [_846182, _846184] : [_846184 = _846182, -(c_Groups_Ouminus__class_Ouminus(_846184) = c_Groups_Ouminus__class_Ouminus(_846182))], (30169 ^ _773908) ^ [_1324976, _1324978, _1324980] : [class_Orderings_Olinorder(_1324976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324976), _1324978)), -(_1324978 = c_Orderings_Obot__class_Obot(tc_fun(_1324976, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324976), _1324980)), -(_1324980 = c_Orderings_Obot__class_Obot(tc_fun(_1324976, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1324976, c_Orderings_Oord__class_Omin(_1324976), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324976, tc_HOL_Obool)), _1324978), _1324980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324976), c_Big__Operators_Olattice_OInf__fin(_1324976, c_Orderings_Oord__class_Omin(_1324976), _1324978)), c_Big__Operators_Olattice_OInf__fin(_1324976, c_Orderings_Oord__class_Omin(_1324976), _1324980)))], (36789 ^ _773908) ^ [_1467053, _1467055] : [class_Orderings_Olinorder(_1467053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467053), _1467055)), -(c_Big__Operators_Olattice_OSup__fin(_1467053, c_Orderings_Oord__class_Omax(_1467053), _1467055) = hAPP(c_Finite__Set_Ofold1(_1467053, c_Orderings_Oord__class_Omax(_1467053)), _1467055))], (47297 ^ _773908) ^ [_1724173, _1724175, _1724177, _1724179, _1724181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1724173, _1724175)), hAPP(hAPP(c_Product__Type_OPair(_1724173, _1724175), _1724177), _1724179)), hAPP(c_Relation_Oconverse(_1724175, _1724173), _1724181))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1724175, _1724173)), hAPP(hAPP(c_Product__Type_OPair(_1724175, _1724173), _1724179), _1724177)), _1724181)))], (45739 ^ _773908) ^ [_1687745, _1687747] : [-(c_List_OtakeWhile(_1687745, _1687747, c_List_Olist_ONil(_1687745)) = c_List_Olist_ONil(_1687745))], (27019 ^ _773908) ^ [_1260238, _1260240, _1260242] : [c_Relation_Ototal__on(_1260238, _1260240, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1260238, _1260238), tc_HOL_Obool)), _1260242), c_Relation_OId(_1260238))), -(c_Relation_Ototal__on(_1260238, _1260240, _1260242))], (14861 ^ _773908) ^ [_1025100, _1025102, _1025104] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025100), _1025102)), _1025104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025100), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025102), _1025104))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025100), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1025102, _1025104))), _1025104)))], (24401 ^ _773908) ^ [_1202289, _1202291, _1202293, _1202295, _1202297, _1202299] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1202289, _1202291), _1202291, _1202293), hAPP(hAPP(c_COMBB(_1202295, tc_fun(_1202291, _1202293), tc_prod(_1202289, _1202291)), _1202297), hAPP(hAPP(c_COMBB(_1202289, _1202295, tc_prod(_1202289, _1202291)), _1202299), c_Product__Type_Ofst(_1202289, _1202291)))), c_Product__Type_Osnd(_1202289, _1202291)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1202289, _1202291, _1202293), hAPP(hAPP(c_COMBB(_1202295, tc_fun(_1202291, _1202293), _1202289), _1202297), _1202299)))], (7757 ^ _773908) ^ [_900192, _900194, _900196] : [c_Com_Ocom_OLocal(_900192, _900194, _900196) = c_Com_Ocom_OSKIP], (40501 ^ _773908) ^ [_1567410, _1567412, _1567414] : [-(hAPP(c_List_Oset(_1567410), c_List_Osublist(_1567410, _1567412, _1567414)) = hAPP(c_Set_OCollect(_1567410), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1567410), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1567410, 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)), _1567410), 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)), _1567410), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1567410, tc_fun(tc_Nat_Onat, _1567410), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567410, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1567410), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1567410), c_COMBB(_1567410, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1567410), _1567412))))), 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(_1567410)), _1567412)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1567414))))))], (25481 ^ _773908) ^ [_1224752, _1224754, _1224756, _1224758, _1224760, _1224762, _1224764] : [-(hAPP(c_Product__Type_Oapsnd(_1224752, _1224754, _1224756, _1224758), hAPP(c_Product__Type_Oapfst(_1224760, _1224756, _1224752, _1224762), _1224764)) = hAPP(c_Product__Type_Oapfst(_1224760, _1224756, _1224754, _1224762), hAPP(c_Product__Type_Oapsnd(_1224752, _1224754, _1224760, _1224758), _1224764)))], (32978 ^ _773908) ^ [_1386345, _1386347, _1386349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386345)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1386347), _1386349)), 32985 ^ _773908 : [(32986 ^ _773908) ^ [_1386541] : [32988 ^ _773908 : [(32994 ^ _773908) ^ [] : [-(_1386541 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32990 ^ [_1386345, _1386347, _1386349, _1386541]), 32987 ^ [_1386345, _1386347, _1386349, _1386541]))], (32992 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32990 ^ [_1386345, _1386347, _1386349, _1386541]), _1386349)))], (32989 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32987 ^ [_1386345, _1386347, _1386349, _1386541]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1386345))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386541), _1386347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386541), _1386345)), _1386347)))]]], (4082 ^ _773908) ^ [_835571, _835573, _835575, _835577] : [-(c_Nitpick_OAbs__Frac(_835577, _835573) = c_Nitpick_OAbs__Frac(_835575, _835571)), _835577 = _835575, _835573 = _835571], (19909 ^ _773908) ^ [_1117485] : [c_Int_OMin = c_Int_OBit0(_1117485)], (4010 ^ _773908) ^ [_834491, _834493, _834495, _834497] : [-(c_Nitpick_Oint__lcm(_834497, _834493) = c_Nitpick_Oint__lcm(_834495, _834491)), _834497 = _834495, _834493 = _834491], (49448 ^ _773908) ^ [_1772147, _1772149, _1772151, _1772153] : [hBOOL(hAPP(_1772147, _1772149)), -(hAPP(c_List_Ofilter(_1772151, _1772147), c_List_Oreplicate(_1772151, _1772153, _1772149)) = c_List_Oreplicate(_1772151, _1772153, _1772149))], (27410 ^ _773908) ^ [_1268950, _1268952, _1268954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1268950, tc_HOL_Obool), tc_fun(_1268950, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1268950, tc_HOL_Obool), tc_fun(_1268950, tc_HOL_Obool)), _1268952), _1268954)), c_Wellfounded_Ofinite__psubset(_1268950))), 27413 ^ _773908 : [(27416 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268950), _1268954)))], (27414 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1268950, tc_HOL_Obool)), _1268952), _1268954)))]]], (29781 ^ _773908) ^ [_1317508, _1317510, _1317512, _1317514, _1317516, _1317518] : [c_Finite__Set_Ofolding__idem(_1317508, _1317510, _1317512, _1317514), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317508), _1317516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317508, tc_HOL_Obool)), _1317518), _1317516)), -(hAPP(c_Fun_Ocomp(_1317510, _1317510, _1317510, hAPP(_1317514, _1317516)), hAPP(_1317514, _1317518)) = hAPP(_1317514, _1317516))], (7275 ^ _773908) ^ [_891589, _891591, _891593, _891595] : [c_Com_Ocom_OAss(_891589, _891591) = c_Com_Ocom_OSemi(_891593, _891595)], (29261 ^ _773908) ^ [_1307672, _1307674, _1307676] : [class_Lattices_Olattice(_1307672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307672), _1307674)), 29268 ^ _773908 : [(29275 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307672, tc_HOL_Obool)), _1307674), hAPP(hAPP(c_Set_Oinsert(_1307672), _1307676), c_Orderings_Obot__class_Obot(tc_fun(_1307672, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307672, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1307672, hAPP(hAPP(c_Set_Oinsert(_1307672), _1307676), _1307674)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1307672), _1307676), c_Big__Operators_Olattice__class_OInf__fin(_1307672, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307672, tc_HOL_Obool)), _1307674), hAPP(hAPP(c_Set_Oinsert(_1307672), _1307676), c_Orderings_Obot__class_Obot(tc_fun(_1307672, tc_HOL_Obool)))))))], (29269 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307672, tc_HOL_Obool)), _1307674), hAPP(hAPP(c_Set_Oinsert(_1307672), _1307676), c_Orderings_Obot__class_Obot(tc_fun(_1307672, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307672, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1307672, hAPP(hAPP(c_Set_Oinsert(_1307672), _1307676), _1307674)) = _1307676)]]], (48153 ^ _773908) ^ [_1744541, _1744543, _1744545] : [class_Orderings_Olinorder(_1744541), hBOOL(hAPP(c_Finite__Set_Ofinite(_1744541), _1744543)), -(hBOOL(hAPP(hAPP(c_member(_1744541), _1744545), _1744543))), -(c_Big__Operators_Olattice_OSup__fin(_1744541, c_Orderings_Oord__class_Omax(_1744541), hAPP(hAPP(c_Set_Oinsert(_1744541), _1744545), _1744543)) = hAPP(hAPP(c_Finite__Set_Ofold(_1744541, _1744541, c_Orderings_Oord__class_Omax(_1744541)), _1744545), _1744543))], (42648 ^ _773908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (31029 ^ _773908) ^ [_1342704, _1342706, _1342708, _1342710, _1342712] : [class_Groups_Ocomm__monoid__mult(_1342704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342706), _1342708)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342706), _1342710)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342704), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342706, _1342704), _1342712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342706, tc_HOL_Obool)), _1342708), _1342710))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342706, _1342704), _1342712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342706, tc_HOL_Obool)), _1342708), _1342710))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342704), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342706, _1342704), _1342712), _1342708)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342706, _1342704), _1342712), _1342710)))], (30740 ^ _773908) ^ [_1337056, _1337058, _1337060] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1337056), _1337058), _1337060) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1337056), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1337056, tc_Int_Oint), _1337058), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1337060))), class_Groups_Ocomm__monoid__add(_1337056), class_Groups_Ocomm__monoid__mult(_1337056)], (12378 ^ _773908) ^ [_981122, _981124, _981126, _981128, _981130] : [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), _981122), _981124)), _981126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _981122), _981128)), _981130))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981126), _981122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981130), _981122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981124), _981128)))], (14171 ^ _773908) ^ [_1013093, _1013095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1013093, _1013095))))], (18889 ^ _773908) ^ [_1100437] : [class_Int_Onumber__ring(_1100437), -(hAPP(c_Int_Onumber__class_Onumber__of(_1100437), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1100437))], (45467 ^ _773908) ^ [_1682141, _1682143, _1682145, _1682147, _1682149] : [c_List_Olist__all2(_1682141, _1682143, _1682145, _1682147, _1682149), -(c_List_Olist__all2(_1682141, _1682143, _1682145, hAPP(c_List_Orev(_1682141), _1682147), hAPP(c_List_Orev(_1682143), _1682149)))], (39530 ^ _773908) ^ [_1541828, _1541830, _1541832] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1541828))), -(c_List_Osublist(_1541830, hAPP(hAPP(c_List_Olist_OCons(_1541830), _1541832), c_List_Olist_ONil(_1541830)), _1541828) = c_List_Olist_ONil(_1541830))], (19323 ^ _773908) ^ [_1107538, _1107540] : [_1107538 = _1107540, -(c_Int_OBit1(_1107538) = c_Int_OBit1(_1107540))], (30866 ^ _773908) ^ [_1339222, _1339224, _1339226, _1339228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339222), _1339224)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339226), _1339228)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1339222, _1339226)), c_Sum__Type_OPlus(_1339222, _1339226, _1339224, _1339228))))], (43071 ^ _773908) ^ [_1628639] : [class_Orderings_Olinorder(_1628639), -(c_List_Olinorder__class_Osorted__list__of__set(_1628639, c_Orderings_Obot__class_Obot(tc_fun(_1628639, tc_HOL_Obool))) = c_List_Olist_ONil(_1628639))], (37022 ^ _773908) ^ [_1471307, _1471309, _1471311] : [-(c_HOL_OThe(tc_prod(_1471307, _1471309), hAPP(c_Product__Type_Oprod_Oprod__case(_1471307, _1471309, tc_HOL_Obool), _1471311)) = c_HOL_OThe(tc_prod(_1471307, _1471309), hAPP(hAPP(c_COMBS(tc_prod(_1471307, _1471309), _1471309, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1471307, tc_fun(_1471309, tc_HOL_Obool), tc_prod(_1471307, _1471309)), _1471311), c_Product__Type_Ofst(_1471307, _1471309))), c_Product__Type_Osnd(_1471307, _1471309))))], (32632 ^ _773908) ^ [_1379595, _1379597, _1379599] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1379595, tc_HOL_Obool)), _1379597), hAPP(c_Set_OPow(_1379595), _1379599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379595, tc_HOL_Obool)), _1379597), _1379599)))], (10745 ^ _773908) ^ [_952188, _952190, _952192, _952194, _952196, _952198] : [class_Rings_Olinordered__semiring__1(_952188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952188), _952190), _952192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952188), _952194), _952192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952188), c_Groups_Ozero__class_Ozero(_952188)), _952196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952188), c_Groups_Ozero__class_Ozero(_952188)), _952198)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952188), _952196), _952198) = c_Groups_Oone__class_Oone(_952188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952188), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952188), _952196), _952190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952188), _952198), _952194))), _952192)))], (41914 ^ _773908) ^ [_1600159, _1600161, _1600163, _1600165, _1600167, _1600169, _1600171] : [hAPP(hAPP(c_List_Omap(_1600159, _1600161), _1600163), _1600165) = hAPP(hAPP(c_List_Omap(_1600167, _1600161), _1600169), _1600171), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600159)), _1600165) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600167)), _1600171))], (14370 ^ _773908) ^ [_1017032, _1017034] : [class_Divides_Osemiring__div(_1017032), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1017032), c_Groups_Ozero__class_Ozero(_1017032)), _1017034) = c_Groups_Ozero__class_Ozero(_1017032))], (5775 ^ _773908) ^ [_865477, _865479, _865481, _865483, _865485] : [hAPP(hAPP(c_Set_Oinsert(_865477), _865479), hAPP(hAPP(c_Set_Oinsert(_865477), _865481), c_Orderings_Obot__class_Obot(tc_fun(_865477, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_865477), _865483), hAPP(hAPP(c_Set_Oinsert(_865477), _865485), c_Orderings_Obot__class_Obot(tc_fun(_865477, tc_HOL_Obool)))), 5780 ^ _773908 : [(5783 ^ _773908) ^ [] : [-(_865481 = _865485)], (5781 ^ _773908) ^ [] : [-(_865479 = _865483)]], 5784 ^ _773908 : [(5787 ^ _773908) ^ [] : [-(_865481 = _865483)], (5785 ^ _773908) ^ [] : [-(_865479 = _865485)]]], (15521 ^ _773908) ^ [_1037478, _1037480, _1037482] : [-(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, _1037478, _1037480)), _1037482), _1037480) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037478), _1037482), _1037480))], (37253 ^ _773908) ^ [_1476571, _1476573, _1476575, _1476577] : [hBOOL(hAPP(hAPP(c_member(_1476571), _1476573), _1476575)), -(hAPP(c_Set_Ovimage(_1476577, _1476571, hAPP(c_COMBK(_1476571, _1476577), _1476573)), _1476575) = c_Orderings_Otop__class_Otop(tc_fun(_1476577, tc_HOL_Obool)))], (51249 ^ _773908) ^ [_1811270, _1811272, _1811274, _1811276, _1811278] : [c_Fun_Obij__betw(_1811270, _1811272, _1811274, _1811276, _1811278), -(c_Fun_Obij__betw(_1811272, _1811270, c_Fun_Othe__inv__into(_1811270, _1811272, _1811276, _1811274), _1811278, _1811276))], (21777 ^ _773908) ^ [_1150792, _1150794, _1150796, _1150798] : [class_Fields_Ofield__inverse__zero(_1150792), -(_1150794 = c_Groups_Ozero__class_Ozero(_1150792)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150792), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150792), _1150796), _1150794)), _1150798) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150792), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150792), _1150796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150792), _1150798), _1150794))), _1150794))], (15563 ^ _773908) ^ [_1038296, _1038298, _1038300] : [class_Groups_Oordered__ab__group__add(_1038296), 15566 ^ _773908 : [(15573 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038296), _1038298), _1038300)), c_Groups_Ozero__class_Ozero(_1038296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038296), _1038298), _1038300)))], (15567 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038296), _1038298), _1038300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038296), _1038298), _1038300)), c_Groups_Ozero__class_Ozero(_1038296))))]]], (38806 ^ _773908) ^ [_1523552, _1523554, _1523556, _1523558] : [hAPP(hAPP(c_List_Oappend(_1523552), _1523554), _1523556) = hAPP(hAPP(c_List_Oappend(_1523552), _1523554), _1523558), -(_1523556 = _1523558)], (25835 ^ _773908) ^ [_1231695, _1231697, _1231699] : [class_Lattices_Osemilattice__sup(_1231695), 25838 ^ _773908 : [(25845 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231695), _1231697), _1231699) = _1231699, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231695), _1231697), _1231699)))], (25839 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231695), _1231697), _1231699)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231695), _1231697), _1231699) = _1231699)]]], (34752 ^ _773908) ^ [_1422674, _1422676, _1422678, _1422680, _1422682] : [class_Groups_Ocomm__monoid__add(_1422674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422676), _1422678)), 34759 ^ _773908 : [(34766 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422676), _1422680), _1422678))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422676, _1422674), hAPP(hAPP(c_COMBC(_1422676, _1422674, _1422674), hAPP(hAPP(c_COMBS(_1422676, _1422674, tc_fun(_1422674, _1422674)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422674, tc_fun(_1422674, _1422674)), _1422676), c_If(_1422674)), hAPP(hAPP(c_COMBC(_1422676, _1422676, tc_HOL_Obool), c_fequal), _1422680))), _1422682)), c_Groups_Ozero__class_Ozero(_1422674))), _1422678) = c_Groups_Ozero__class_Ozero(_1422674))], (34760 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1422676), _1422680), _1422678)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422676, _1422674), hAPP(hAPP(c_COMBC(_1422676, _1422674, _1422674), hAPP(hAPP(c_COMBS(_1422676, _1422674, tc_fun(_1422674, _1422674)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422674, tc_fun(_1422674, _1422674)), _1422676), c_If(_1422674)), hAPP(hAPP(c_COMBC(_1422676, _1422676, tc_HOL_Obool), c_fequal), _1422680))), _1422682)), c_Groups_Ozero__class_Ozero(_1422674))), _1422678) = hAPP(_1422682, _1422680))]]], (43001 ^ _773908) ^ [_1627268, _1627270, _1627272] : [-(hBOOL(hAPP(hAPP(c_member(_1627268), _1627270), hAPP(c_List_Oset(_1627268), _1627272)))), -(c_List_Oremove1(_1627268, _1627270, _1627272) = _1627272)], (29655 ^ _773908) ^ [_1315088, _1315090, _1315092] : [class_Orderings_Olinorder(_1315088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315088), _1315090)), 29662 ^ _773908 : [(29669 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315088, tc_HOL_Obool)), _1315090), hAPP(hAPP(c_Set_Oinsert(_1315088), _1315092), c_Orderings_Obot__class_Obot(tc_fun(_1315088, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1315088, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1315088, hAPP(hAPP(c_Set_Oinsert(_1315088), _1315092), _1315090)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315088), _1315092), c_Big__Operators_Olinorder__class_OMin(_1315088, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315088, tc_HOL_Obool)), _1315090), hAPP(hAPP(c_Set_Oinsert(_1315088), _1315092), c_Orderings_Obot__class_Obot(tc_fun(_1315088, tc_HOL_Obool)))))))], (29663 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315088, tc_HOL_Obool)), _1315090), hAPP(hAPP(c_Set_Oinsert(_1315088), _1315092), c_Orderings_Obot__class_Obot(tc_fun(_1315088, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1315088, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1315088, hAPP(hAPP(c_Set_Oinsert(_1315088), _1315092), _1315090)) = _1315092)]]], (31856 ^ _773908) ^ [_1363110, _1363112, _1363114, _1363116, _1363118] : [_1363110 = c_Orderings_Obot__class_Obot(tc_fun(_1363112, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363114, tc_HOL_Obool)), _1363116), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363112, tc_fun(_1363114, tc_HOL_Obool)), _1363110), _1363118)) = _1363116)], (42662 ^ _773908) ^ [_1619963, _1619965] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1619963), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1619965), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 42669 ^ _773908 : [(42676 ^ _773908) ^ [] : [_1619963 = _1619965, -(hAPP(c_Code__Numeral_Oof__nat, _1619963) = hAPP(c_Code__Numeral_Oof__nat, _1619965))], (42670 ^ _773908) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1619963) = hAPP(c_Code__Numeral_Oof__nat, _1619965), -(_1619963 = _1619965)]]], (14519 ^ _773908) ^ [_1019387, _1019389] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019387, _1019389)), _1019389) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48259 ^ _773908) ^ [_1746721, _1746723, _1746725, _1746727, _1746729, _1746731] : [c_Finite__Set_Ofun__left__comm__idem(_1746721, _1746723, _1746725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1746721), _1746727)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1746721, _1746723, _1746725), _1746729), hAPP(hAPP(c_Set_Oinsert(_1746721), _1746731), _1746727)) = hAPP(hAPP(c_Finite__Set_Ofold(_1746721, _1746723, _1746725), hAPP(hAPP(_1746725, _1746731), _1746729)), _1746727))], (6604 ^ _773908) ^ [_881206, _881208, _881210, _881212] : [class_Orderings_Oorder(_881206), _881208 = _881210, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881206), _881212), _881210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881206), _881212), _881208)))], (39314 ^ _773908) ^ [_1537623, _1537625, _1537627] : [_1537623 = _1537625, -(_1537623 = hAPP(hAPP(c_List_Oappend(_1537627), c_List_Olist_ONil(_1537627)), _1537625))], (49598 ^ _773908) ^ [_1774951, _1774953, _1774955] : [_1774951 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1774953), c_List_Oreplicate(_1774953, _1774951, _1774955)) = c_Orderings_Obot__class_Obot(tc_fun(_1774953, tc_HOL_Obool)))], (42179 ^ _773908) ^ [_1608470, _1608472, _1608474, _1608476, _1608478] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608470, tc_fun(_1608472, tc_HOL_Obool)), _1608474), hAPP(hAPP(c_COMBC(_1608470, tc_fun(_1608472, tc_HOL_Obool), tc_fun(_1608472, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608472, tc_HOL_Obool), tc_fun(tc_fun(_1608472, tc_HOL_Obool), tc_fun(_1608472, tc_HOL_Obool)), _1608470), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608472, tc_HOL_Obool))), _1608476)), _1608478)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608472, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608470, tc_fun(_1608472, tc_HOL_Obool)), _1608474), _1608476)), _1608478))], (2926 ^ _773908) ^ [_817531, _817533, _817535, _817537] : [-(c_List_Olenlex(_817537, _817533) = c_List_Olenlex(_817535, _817531)), _817537 = _817535, _817533 = _817531], (48491 ^ _773908) ^ [_1751386, _1751388, _1751390] : [class_Groups_Oab__semigroup__mult(_1751386), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751386), _1751388)), -(hBOOL(hAPP(hAPP(c_member(_1751386), _1751390), _1751388))), -(hAPP(c_Finite__Set_Ofold1(_1751386, c_Groups_Otimes__class_Otimes(_1751386)), hAPP(hAPP(c_Set_Oinsert(_1751386), _1751390), _1751388)) = hAPP(hAPP(c_Finite__Set_Ofold(_1751386, _1751386, c_Groups_Otimes__class_Otimes(_1751386)), _1751390), _1751388))], (17347 ^ _773908) ^ [_1073166, _1073168] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1073166) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073168), 17350 ^ _773908 : [(17353 ^ _773908) ^ [] : [-(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), _1073168))))], (17351 ^ _773908) ^ [] : [-(_1073166 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1073168)))]]], (27708 ^ _773908) ^ [_1275354, _1275356, _1275358, _1275360, _1275362, _1275364] : [c_Equiv__Relations_Oequiv(_1275354, _1275356, _1275358), hBOOL(hAPP(hAPP(c_member(_1275354), _1275360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1275354, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1275354, _1275354, _1275358), hAPP(hAPP(c_Set_Oinsert(_1275354), _1275362), c_Orderings_Obot__class_Obot(tc_fun(_1275354, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1275354, _1275354, _1275358), hAPP(hAPP(c_Set_Oinsert(_1275354), _1275364), c_Orderings_Obot__class_Obot(tc_fun(_1275354, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1275354, _1275354)), hAPP(hAPP(c_Product__Type_OPair(_1275354, _1275354), _1275362), _1275364)), _1275358)))], (2018 ^ _773908) ^ [_803151, _803153] : [_803153 = _803151, -(c_Nat_Onat_Onat__size(_803153) = c_Nat_Onat_Onat__size(_803151))], (6264 ^ _773908) ^ [_875514, _875516, _875518] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_875514, _875516, _875518)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5088 ^ _773908) ^ [_851638, _851640] : [_851640 = _851638, -(c_Set_OBex(_851640) = c_Set_OBex(_851638))], (7219 ^ _773908) ^ [_890641, _890643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890641), _890643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890641), hAPP(c_Nat_OSuc, _890643))))], (30551 ^ _773908) ^ [_1332661, _1332663, _1332665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332661), _1332663)), hBOOL(hAPP(hAPP(c_member(_1332661), _1332665), _1332663)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1332661), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332661, tc_HOL_Obool)), _1332663), hAPP(hAPP(c_Set_Oinsert(_1332661), _1332665), c_Orderings_Obot__class_Obot(tc_fun(_1332661, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1332661), _1332663))], (14525 ^ _773908) ^ [_1019552, _1019554] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019552), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019554)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019552, _1019554)))], (22865 ^ _773908) ^ [_1170485, _1170487, _1170489, _1170491, _1170493, _1170495, _1170497] : [hBOOL(hAPP(hAPP(c_member(_1170485), _1170487), _1170489)), c_Nitpick_Ofold__graph_H(_1170485, _1170491, _1170493, _1170495, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1170485, tc_HOL_Obool)), _1170489), hAPP(hAPP(c_Set_Oinsert(_1170485), _1170487), c_Orderings_Obot__class_Obot(tc_fun(_1170485, tc_HOL_Obool)))), _1170497), -(c_Nitpick_Ofold__graph_H(_1170485, _1170491, _1170493, _1170495, _1170489, hAPP(hAPP(_1170493, _1170487), _1170497)))], (26556 ^ _773908) ^ [_1250031, _1250033, _1250035, _1250037] : [_1250031 = c_Orderings_Obot__class_Obot(tc_fun(_1250033, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1250033, _1250035, hAPP(c_COMBK(_1250035, _1250033), _1250037)), _1250031) = c_Orderings_Obot__class_Obot(tc_fun(_1250035, tc_HOL_Obool)))], (29345 ^ _773908) ^ [_1309437, _1309439, _1309441] : [class_Lattices_Olattice(_1309437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309437), _1309439)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309437), _1309441)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309437, tc_HOL_Obool)), _1309439), _1309441) = c_Orderings_Obot__class_Obot(tc_fun(_1309437, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309437), c_Big__Operators_Olattice__class_OInf__fin(_1309437, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309437, tc_HOL_Obool)), _1309439), _1309441))), c_Big__Operators_Olattice__class_OInf__fin(_1309437, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309437, tc_HOL_Obool)), _1309439), _1309441))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309437), c_Big__Operators_Olattice__class_OInf__fin(_1309437, _1309439)), c_Big__Operators_Olattice__class_OInf__fin(_1309437, _1309441)))], (28302 ^ _773908) ^ [_1287760, _1287762, _1287764, _1287766] : [class_Lattices_Olattice(_1287760), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287760), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287760), _1287762), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1287760), _1287764), _1287766))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1287760), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287760), _1287762), _1287764)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287760), _1287762), _1287766)))))], (37440 ^ _773908) ^ [_1481846, _1481848, _1481850, _1481852, _1481854] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1481846, _1481848), _1481850), hAPP(hAPP(c_COMBS(_1481846, tc_fun(_1481848, tc_HOL_Obool), tc_fun(_1481848, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481848, tc_HOL_Obool), tc_fun(tc_fun(_1481848, tc_HOL_Obool), tc_fun(_1481848, tc_HOL_Obool)), _1481846), c_Groups_Ominus__class_Ominus(tc_fun(_1481848, tc_HOL_Obool))), _1481852)), _1481854)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1481846, _1481848), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1481846, _1481848), _1481850), _1481852)), hAPP(hAPP(c_Product__Type_OSigma(_1481846, _1481848), _1481850), _1481854)))], (15807 ^ _773908) ^ [_1042987, _1042989, _1042991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042987), _1042989)), 15810 ^ _773908 : [(15817 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042991), _1042987)), _1042989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042989), _1042987))))], (15811 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042989), _1042987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042991), _1042987)), _1042989)))]]], (32648 ^ _773908) ^ [_1379888, _1379890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379888), hAPP(c_Nat_OSuc, _1379890))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1379888, hAPP(c_Nat_OSuc, _1379890)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379890)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1379888, _1379890)))], (14617 ^ _773908) ^ [_1021027, _1021029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021027)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021027), _1021029)), _1021027) = _1021029)], (28729 ^ _773908) ^ [_1298422, _1298424, _1298426, _1298428, _1298430, _1298432] : [-(hBOOL(hAPP(hAPP(c_member(_1298422), _1298424), c_SetInterval_Oord_OatLeastLessThan(_1298422, _1298426, _1298428, _1298430, _1298432)))), hBOOL(hAPP(hAPP(_1298426, _1298430), _1298424)), hBOOL(hAPP(hAPP(_1298428, _1298424), _1298432))], (38052 ^ _773908) ^ [_1497323, _1497325, _1497327] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1497323, tc_HOL_Obool)), _1497325), _1497327) = hAPP(c_Set_OCollect(_1497323), hAPP(hAPP(c_COMBS(_1497323, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497323), c_fdisj), hAPP(hAPP(c_COMBC(_1497323, tc_fun(_1497323, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497323)), _1497325))), hAPP(hAPP(c_COMBC(_1497323, tc_fun(_1497323, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497323)), _1497327))))], (30720 ^ _773908) ^ [_1336536, _1336538, _1336540] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336536, tc_Nat_Onat), _1336538), _1336540)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336536, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1336536), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1336538)), _1336540))], (28979 ^ _773908) ^ [_1303108, _1303110, _1303112] : [class_Lattices_Olattice(_1303108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303108), _1303110)), hBOOL(hAPP(hAPP(c_member(_1303108), _1303112), _1303110)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303108), _1303112), c_Big__Operators_Olattice__class_OSup__fin(_1303108, _1303110)) = _1303112)], (23588 ^ _773908) ^ [_1185276, _1185278] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1185276, _1185278), c_Divides_Odivmod__nat(_1185276, _1185278))))], (35272 ^ _773908) ^ [_1434552, _1434554] : [-(hAPP(c_Finite__Set_Ocard(_1434552), _1434554) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434552, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1434552), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1434554))], (50544 ^ _773908) ^ [_1796878, _1796880, _1796882, _1796884] : [c_Relation_Osym(_1796878, _1796880), hBOOL(hAPP(hAPP(c_member(tc_prod(_1796878, _1796878)), hAPP(hAPP(c_Product__Type_OPair(_1796878, _1796878), _1796882), _1796884)), _1796880)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796878, _1796878)), hAPP(hAPP(c_Product__Type_OPair(_1796878, _1796878), _1796884), _1796882)), _1796880)))], (18705 ^ _773908) ^ [_1097227] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1097227), c_Int_OMin) = c_Int_Osucc(_1097227))], (15639 ^ _773908) ^ [_1039880, _1039882, _1039884] : [class_Groups_Ogroup__add(_1039880), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039880), _1039882), _1039884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039880), _1039882), hAPP(c_Groups_Ouminus__class_Ouminus(_1039880), _1039884)))], (22897 ^ _773908) ^ [_1171090] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1171090)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1171090)], (20025 ^ _773908) ^ [_1119513, _1119515] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1119513)), c_Int_OBit0(_1119515)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1119513), _1119515)))], (14404 ^ _773908) ^ [_1017627] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017627), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1017627)], (13716 ^ _773908) ^ [_1004946, _1004948, _1004950, _1004952] : [class_Divides_Osemiring__div(_1004946), -(c_Divides_Odiv__class_Omod(_1004946, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004946), _1004948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004946), _1004950), _1004952)), _1004952) = c_Divides_Odiv__class_Omod(_1004946, _1004948, _1004952))], (43925 ^ _773908) ^ [_1648231, _1648233, _1648235] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648231, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648231, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1648231, tc_HOL_Obool), tc_HOL_Obool)), _1648233), _1648235))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648231, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648231, tc_HOL_Obool), _1648233)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648231, tc_HOL_Obool), _1648235)))))], (26615 ^ _773908) ^ [_1251421] : [-(hAPP(c_Relation_OField(_1251421), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1251421, _1251421), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1251421, tc_HOL_Obool)))], (38707 ^ _773908) ^ [_1521710, _1521712] : [-(c_Wellfounded_Owf(_1521710, hAPP(c_Wellfounded_Omeasure(_1521710), _1521712)))], (2936 ^ _773908) ^ [_817680, _817682, _817684, _817686, _817688, _817690, _817692, _817694, _817696, _817698, _817700, _817702] : [-(c_Product__Type_Omap__pair(_817702, _817698, _817694, _817690, _817686, _817682) = c_Product__Type_Omap__pair(_817700, _817696, _817692, _817688, _817684, _817680)), _817702 = _817700, _817698 = _817696, _817694 = _817692, _817690 = _817688, _817686 = _817684, _817682 = _817680], (6063 ^ _773908) ^ [_871467] : [hAPP(c_Nat_OSuc, _871467) = _871467], (28076 ^ _773908) ^ [_1282364, _1282366, _1282368, _1282370, _1282372] : [class_Lattices_Olattice(_1282364), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1282366, _1282364)), _1282368), _1282370), _1282372) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282364), hAPP(_1282368, _1282372)), hAPP(_1282370, _1282372)))], (44275 ^ _773908) ^ [_1656680, _1656682, _1656684] : [hBOOL(hAPP(c_List_Odistinct(_1656680), _1656682)), -(hBOOL(hAPP(c_List_Odistinct(_1656680), hAPP(c_List_OremoveAll(_1656680, _1656684), _1656682))))], (41302 ^ _773908) ^ [_1587729, _1587731, _1587733, _1587735, _1587737, _1587739] : [-(hAPP(c_List_Ofoldl(_1587729, _1587731, _1587733, _1587735), hAPP(hAPP(c_List_Olist_OCons(_1587731), _1587737), _1587739)) = hAPP(c_List_Ofoldl(_1587729, _1587731, _1587733, hAPP(hAPP(_1587733, _1587735), _1587737)), _1587739))], (23478 ^ _773908) ^ [_1183285] : [-(c_Divides_Odivmod__nat(_1183285, 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)), _1183285))], (31057 ^ _773908) ^ [_1343426, _1343428, _1343430, _1343432, _1343434] : [class_Groups_Ocomm__monoid__mult(_1343426), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343428), _1343430)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343428, _1343426), _1343432), hAPP(hAPP(c_Set_Oinsert(_1343428), _1343434), _1343430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343426), hAPP(_1343432, _1343434)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343428, _1343426), _1343432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343428, tc_HOL_Obool)), _1343430), hAPP(hAPP(c_Set_Oinsert(_1343428), _1343434), c_Orderings_Obot__class_Obot(tc_fun(_1343428, tc_HOL_Obool)))))))], (43308 ^ _773908) ^ [_1634113, _1634115, _1634117] : [-(c_List_Olistsp(_1634113, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1634113, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1634113, tc_fun(_1634113, tc_HOL_Obool), tc_HOL_Obool), c_member(_1634113)), _1634115)), hAPP(hAPP(c_COMBC(_1634113, tc_fun(_1634113, tc_HOL_Obool), tc_HOL_Obool), c_member(_1634113)), _1634117))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1634113), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634113), tc_fun(tc_List_Olist(_1634113), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1634113))), c_List_Olists(_1634113, _1634115))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634113), tc_fun(tc_List_Olist(_1634113), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1634113))), c_List_Olists(_1634113, _1634117))))], (22939 ^ _773908) ^ [_1172164, _1172166] : [_1172164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1172166, _1172164) = _1172166)], (51366 ^ _773908) ^ [_1812903, _1812905] : [class_Orderings_Obot(_1812903), -(class_Orderings_Obot(tc_fun(_1812905, _1812903)))], (13502 ^ _773908) ^ [_1000733, _1000735] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000733, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000733, tc_HOL_Obool)), _1000735)) = _1000735)], (30515 ^ _773908) ^ [_1331862, _1331864, _1331866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331862), _1331864)), -(hAPP(c_Finite__Set_Ocard(_1331862), hAPP(hAPP(c_Set_Oinsert(_1331862), _1331866), _1331864)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1331862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331862, tc_HOL_Obool)), _1331864), hAPP(hAPP(c_Set_Oinsert(_1331862), _1331866), c_Orderings_Obot__class_Obot(tc_fun(_1331862, tc_HOL_Obool)))))))], (41310 ^ _773908) ^ [_1587934, _1587936, _1587938] : [-(hAPP(c_List_Orotate(_1587934, hAPP(c_Nat_OSuc, _1587936)), _1587938) = hAPP(c_List_Orotate1(_1587934), hAPP(c_List_Orotate(_1587934, _1587936), _1587938)))], (23749 ^ _773908) ^ [_1188769, _1188771, _1188773, _1188775, _1188777, _1188779] : [_1188769 = _1188771, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188773, _1188775, _1188777), _1188779), _1188769) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188773, _1188775, _1188777), _1188779), _1188771))], (7677 ^ _773908) ^ [_898463, _898465, _898467, _898469] : [hAPP(c_Com_Ocom_OBODY, _898463) = c_Com_Ocom_OLocal(_898465, _898467, _898469)], (9682 ^ _773908) ^ [_935303, _935305] : [hAPP(c_Int_Onat, _935303) = _935305, 9685 ^ _773908 : [(9692 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935303))), -(_935305 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9686 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935303)), -(_935303 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935305))]]], (49300 ^ _773908) ^ [_1768326, _1768328, _1768330, _1768332] : [-(c_New__Random__Sequence_Opos__empty(_1768326, _1768328, _1768330, _1768332) = c_New__DSequence_Opos__empty(_1768326))], (51514 ^ _773908) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (47525 ^ _773908) ^ [_1729809, _1729811, _1729813] : [47528 ^ _773908 : [(47534 ^ _773908) ^ [] : [47527 ^ [_1729809, _1729811, _1729813] = 47530 ^ [_1729809, _1729811, _1729813]], (47532 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729809, _1729811)), hAPP(hAPP(c_Product__Type_OPair(_1729809, _1729811), 47526 ^ [_1729809, _1729811, _1729813]), 47530 ^ [_1729809, _1729811, _1729813])), _1729813)))], (47529 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729809, _1729811)), hAPP(hAPP(c_Product__Type_OPair(_1729809, _1729811), 47526 ^ [_1729809, _1729811, _1729813]), 47527 ^ [_1729809, _1729811, _1729813])), _1729813)))]], -(c_Relation_Osingle__valued(_1729809, _1729811, _1729813))], (15929 ^ _773908) ^ [_1045810, _1045812, _1045814, _1045816, _1045818, _1045820] : [class_Rings_Oordered__ring(_1045810), 15932 ^ _773908 : [(15939 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045810), _1045816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045810), _1045818), _1045812)), _1045814)), _1045820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), _1045812), _1045814)), _1045816)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), _1045818), _1045814)), _1045820))))], (15933 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), _1045812), _1045814)), _1045816)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), _1045818), _1045814)), _1045820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045810), _1045816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045810), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045810), _1045818), _1045812)), _1045814)), _1045820))))]]], (47411 ^ _773908) ^ [_1727192, _1727194, _1727196, _1727198, _1727200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1727192, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1727194, _1727192, _1727196), _1727198)), _1727200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1727194, tc_HOL_Obool)), _1727198), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1727194, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1727192, _1727194, hAPP(c_Relation_Oconverse(_1727194, _1727192), _1727196)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1727192, tc_HOL_Obool)), _1727200))))))], (33484 ^ _773908) ^ [_1395910, _1395912] : [33486 ^ _773908 : [(33489 ^ _773908) ^ [] : [hBOOL(hAPP(_1395912, 33485 ^ [_1395910, _1395912]))], (33487 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33485 ^ [_1395910, _1395912]), _1395910)))]], 33490 ^ _773908 : [(33491 ^ _773908) ^ [_1396060] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1396060), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1395910))), -(hBOOL(hAPP(_1395912, _1396060)))]]], (17393 ^ _773908) ^ [_1073998, _1074000, _1074002, _1074004] : [class_Groups_Ocomm__monoid__mult(_1073998), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1073998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073998), _1074000), _1074002)), _1074004) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073998), hAPP(hAPP(c_Power_Opower__class_Opower(_1073998), _1074000), _1074004)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073998), _1074002), _1074004)))], (46596 ^ _773908) ^ [_1706686, _1706688] : [class_Orderings_Olinorder(_1706686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1706686), _1706688)), 46604 ^ _773908 : [(46607 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1706686, 46603 ^ [_1706686, _1706688]))], (46609 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706686), 46603 ^ [_1706686, _1706688])))], (46611 ^ _773908) ^ [_1707012] : [-(_1707012 = 46603 ^ [_1706686, _1706688]), hAPP(c_List_Oset(_1706686), _1707012) = _1706688, c_List_Olinorder__class_Osorted(_1706686, _1707012), hBOOL(hAPP(c_List_Odistinct(_1706686), _1707012))], (46605 ^ _773908) ^ [] : [-(hAPP(c_List_Oset(_1706686), 46603 ^ [_1706686, _1706688]) = _1706688)]]], (27164 ^ _773908) ^ [_1264180, _1264182, _1264184, _1264186, _1264188] : [c_Equiv__Relations_Oequiv(_1264180, _1264182, _1264184), 27167 ^ _773908 : [(27178 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1264180, _1264180)), hAPP(hAPP(c_Product__Type_OPair(_1264180, _1264180), _1264186), _1264188)), _1264184))), hAPP(c_Relation_OImage(_1264180, _1264180, _1264184), hAPP(hAPP(c_Set_Oinsert(_1264180), _1264186), c_Orderings_Obot__class_Obot(tc_fun(_1264180, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1264180, _1264180, _1264184), hAPP(hAPP(c_Set_Oinsert(_1264180), _1264188), c_Orderings_Obot__class_Obot(tc_fun(_1264180, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1264180), _1264186), _1264182)), hBOOL(hAPP(hAPP(c_member(_1264180), _1264188), _1264182))], (27168 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1264180, _1264180)), hAPP(hAPP(c_Product__Type_OPair(_1264180, _1264180), _1264186), _1264188)), _1264184)), 27171 ^ _773908 : [(27176 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264180), _1264188), _1264182)))], (27174 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264180), _1264186), _1264182)))], (27172 ^ _773908) ^ [] : [-(hAPP(c_Relation_OImage(_1264180, _1264180, _1264184), hAPP(hAPP(c_Set_Oinsert(_1264180), _1264186), c_Orderings_Obot__class_Obot(tc_fun(_1264180, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1264180, _1264180, _1264184), hAPP(hAPP(c_Set_Oinsert(_1264180), _1264188), c_Orderings_Obot__class_Obot(tc_fun(_1264180, tc_HOL_Obool)))))]]]]], (49440 ^ _773908) ^ [_1772001, _1772003, _1772005] : [_1772003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1772001, _1772003, _1772005) = c_List_Olist_ONil(_1772001))], (44030 ^ _773908) ^ [_1651129, _1651131] : [class_Complete__Lattice_Ocomplete__lattice(_1651129), -(c_Complete__Lattice_OSup__class_OSup(_1651129, _1651131) = c_Complete__Lattice_OInf__class_OInf(_1651129, hAPP(c_Set_OCollect(_1651129), hAPP(hAPP(c_COMBB(tc_fun(_1651129, tc_HOL_Obool), tc_HOL_Obool, _1651129), c_HOL_OAll(_1651129)), hAPP(hAPP(c_COMBB(tc_fun(_1651129, tc_HOL_Obool), tc_fun(_1651129, tc_HOL_Obool), _1651129), hAPP(c_COMBS(_1651129, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1651129), c_fimplies), hAPP(hAPP(c_COMBC(_1651129, tc_fun(_1651129, tc_HOL_Obool), tc_HOL_Obool), c_member(_1651129)), _1651131)))), hAPP(c_COMBC(_1651129, _1651129, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1651129)))))))], (45375 ^ _773908) ^ [_1680061, _1680063, _1680065, _1680067] : [class_Orderings_Olinorder(_1680061), c_List_Olinorder__class_Osorted(_1680061, _1680063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680065), _1680067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680067), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680061)), _1680063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680061), hAPP(hAPP(c_List_Onth(_1680061), _1680063), _1680065)), hAPP(hAPP(c_List_Onth(_1680061), _1680063), _1680067))))], (27466 ^ _773908) ^ [_1270209, _1270211, _1270213, _1270215, _1270217, _1270219, _1270221, _1270223] : [c_Finite__Set_Ofolding__image__simple(_1270209, _1270211, _1270213, _1270215, _1270217, _1270219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270211), _1270221)), hBOOL(hAPP(hAPP(c_member(_1270211), _1270223), _1270221)), -(hAPP(_1270219, _1270221) = hAPP(hAPP(_1270213, hAPP(_1270217, _1270223)), hAPP(_1270219, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270211, tc_HOL_Obool)), _1270221), hAPP(hAPP(c_Set_Oinsert(_1270211), _1270223), c_Orderings_Obot__class_Obot(tc_fun(_1270211, tc_HOL_Obool)))))))], (20729 ^ _773908) ^ [_1132247, _1132249, _1132251, _1132253] : [class_Rings_Odivision__ring(_1132247), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132247), _1132249), _1132251)), _1132253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132247), _1132249), _1132253)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132247), _1132251), _1132253)))], (27798 ^ _773908) ^ [_1277149, _1277151, _1277153] : [class_Lattices_Osemilattice__inf(_1277149), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277149), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277149), _1277151), _1277153)), _1277153)))], (10697 ^ _773908) ^ [_951317, _951319, _951321] : [class_Groups_Oordered__ab__group__add(_951317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951317), _951319), _951321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951317), hAPP(c_Groups_Ouminus__class_Ouminus(_951317), _951321)), hAPP(c_Groups_Ouminus__class_Ouminus(_951317), _951319))))], (13051 ^ _773908) ^ [_992860, _992862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992860), _992862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992860), hAPP(c_Nat_OSuc, _992862))))], (11581 ^ _773908) ^ [_967359] : [-(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), _967359))))], (22813 ^ _773908) ^ [_1169858, _1169860] : [-(c_Random_Olog(_1169858, _1169860) = 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(_1169858, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1169860), _1169858)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1169858), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1169860), _1169858)))], (43923 ^ _773908) ^ [_1648160, _1648162, _1648164, _1648166, _1648168] : [-(hAPP(c_Relation_ODomain(_1648160, _1648162), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1648160, _1648162)), hAPP(hAPP(c_Product__Type_OPair(_1648160, _1648162), _1648164), _1648166)), _1648168)) = hAPP(hAPP(c_Set_Oinsert(_1648160), _1648164), hAPP(c_Relation_ODomain(_1648160, _1648162), _1648168)))], (40293 ^ _773908) ^ [_1562164, _1562166, _1562168, _1562170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1562164), _1562166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562168, tc_HOL_Obool)), hAPP(c_List_Oset(_1562168), hAPP(hAPP(c_List_Otake(_1562168), _1562164), _1562170))), hAPP(c_List_Oset(_1562168), hAPP(hAPP(c_List_Otake(_1562168), _1562166), _1562170)))))], (36817 ^ _773908) ^ [_1467587, _1467589, _1467591] : [class_Lattices_Osemilattice__inf(_1467587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467587), _1467589)), -(_1467589 = c_Orderings_Obot__class_Obot(tc_fun(_1467587, tc_HOL_Obool))), 36828 ^ _773908 : [(36829 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467587), _1467591), hAPP(c_Finite__Set_Ofold1(_1467587, c_Lattices_Osemilattice__inf__class_Oinf(_1467587)), _1467589))), 36832 ^ _773908 : [(36833 ^ _773908) ^ [_1467880] : [hBOOL(hAPP(hAPP(c_member(_1467587), _1467880), _1467589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467587), _1467591), _1467880)))]]], (36839 ^ _773908) ^ [] : [36841 ^ _773908 : [(36844 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467587), _1467591), 36840 ^ [_1467587, _1467589, _1467591]))], (36842 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1467587), 36840 ^ [_1467587, _1467589, _1467591]), _1467589)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467587), _1467591), hAPP(c_Finite__Set_Ofold1(_1467587, c_Lattices_Osemilattice__inf__class_Oinf(_1467587)), _1467589))))]]], (34908 ^ _773908) ^ [_1425950, _1425952, _1425954] : [class_Groups_Ocomm__monoid__add(_1425950), hAPP(_1425952, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1425950), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1425950), _1425952), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1425954)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1425950), _1425952), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425954)))], (38430 ^ _773908) ^ [_1512006] : [-(c_Int_Oint__ge__less__than2(_1512006) = 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), _1512006)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (49486 ^ _773908) ^ [_1772787, _1772789, _1772791, _1772793, _1772795] : [-(c_List_Oreplicate(_1772787, _1772789, _1772791) = c_List_Oreplicate(_1772787, _1772793, _1772795)), _1772789 = _1772793, 49491 ^ _773908 : [(49494 ^ _773908) ^ [] : [_1772791 = _1772795], (49492 ^ _773908) ^ [] : [_1772789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (40121 ^ _773908) ^ [_1558116, _1558118, _1558120] : [-(hAPP(hAPP(c_List_Otake(_1558116), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1558116), _1558118), _1558120)) = hAPP(hAPP(c_List_Olist_OCons(_1558116), _1558118), c_List_Olist_ONil(_1558116)))], (51191 ^ _773908) ^ [_1810198, _1810200, _1810202, _1810204, _1810206, _1810208, _1810210] : [c_Fun_Obij__betw(_1810198, _1810200, _1810202, _1810204, _1810206), c_Fun_Obij__betw(_1810198, _1810200, _1810202, _1810208, _1810210), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1810200, tc_HOL_Obool)), _1810206), _1810210) = c_Orderings_Obot__class_Obot(tc_fun(_1810200, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1810198, _1810200, _1810202, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1810198, tc_HOL_Obool)), _1810204), _1810208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1810200, tc_HOL_Obool)), _1810206), _1810210)))], (51950 ^ _773908) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))], (50560 ^ _773908) ^ [_1797191, _1797193] : [c_Relation_Osym(_1797191, _1797193), -(c_Relation_Osym(_1797191, hAPP(c_Relation_Oconverse(_1797191, _1797191), _1797193)))], (6864 ^ _773908) ^ [_885019, _885021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885019), _885021)), _885019 = _885021], (27388 ^ _773908) ^ [_1268408, _1268410, _1268412, _1268414, _1268416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268408), _1268410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268412, tc_HOL_Obool)), _1268414), hAPP(c_Set_Oimage(_1268408, _1268412, _1268416), _1268410))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268412), _1268414)))], (51520 ^ _773908) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (6314 ^ _773908) ^ [_876198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876198), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (40217 ^ _773908) ^ [_1560379, _1560381, _1560383, _1560385] : [-(hAPP(hAPP(c_List_Odrop(_1560379), hAPP(c_Nat_OSuc, _1560381)), hAPP(hAPP(c_List_Olist_OCons(_1560379), _1560383), _1560385)) = hAPP(hAPP(c_List_Odrop(_1560379), _1560381), _1560385))], (40251 ^ _773908) ^ [_1561157, _1561159, _1561161, _1561163] : [-(hBOOL(hAPP(hAPP(c_member(_1561157), _1561159), hAPP(c_List_Oset(_1561157), _1561161)))), hBOOL(hAPP(hAPP(c_member(_1561157), _1561159), hAPP(c_List_Oset(_1561157), c_List_Osublist(_1561157, _1561161, _1561163))))], (12162 ^ _773908) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20255 ^ _773908) ^ [] : [-(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))))))], (5771 ^ _773908) ^ [_865358, _865360, _865362] : [c_Orderings_Obot__class_Obot(tc_fun(_865358, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_865358), _865360), _865362)], (1754 ^ _773908) ^ [_798819, _798821] : [-(class_Nat_Osemiring__char__0(_798819)), _798821 = _798819, class_Nat_Osemiring__char__0(_798821)], (6152 ^ _773908) ^ [_873632] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _873632)], (42595 ^ _773908) ^ [_1618851, _1618853, _1618855] : [hBOOL(hAPP(_1618851, _1618853)), -(hBOOL(hAPP(_1618851, c_Hilbert__Choice_OEps(_1618855, _1618851))))], (13608 ^ _773908) ^ [_1002874, _1002876, _1002878, _1002880] : [class_Divides_Osemiring__div(_1002874), -(c_Divides_Odiv__class_Omod(_1002874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002874), _1002876), _1002878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002874), _1002876), _1002880)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002874), _1002876), c_Divides_Odiv__class_Omod(_1002874, _1002878, _1002880)))], (1354 ^ _773908) ^ [_793819, _793821] : [-(class_Rings_Oidom(_793819)), _793821 = _793819, class_Rings_Oidom(_793821)], (35883 ^ _773908) ^ [_1447169, _1447171, _1447173, _1447175] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1447169, _1447171, _1447173, _1447175, c_Orderings_Obot__class_Obot(tc_fun(_1447169, tc_HOL_Obool))), _1447175)))], (6510 ^ _773908) ^ [_879738, _879740, _879742, _879744] : [-(c_Com_Ocom_OAss(_879738, _879740) = c_Com_Ocom_OAss(_879742, _879744)), _879738 = _879742, _879740 = _879744], (5502 ^ _773908) ^ [_858097, _858099] : [_858099 = _858097, -(c_Lattices_Osemilattice__sup__class_Osup(_858099) = c_Lattices_Osemilattice__sup__class_Osup(_858097))], (10857 ^ _773908) ^ [_954255] : [class_Rings_Olinordered__semidom(_954255), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954255), c_Groups_Ozero__class_Ozero(_954255)), c_Groups_Oone__class_Oone(_954255))))], (41920 ^ _773908) ^ [_1600310, _1600312, _1600314, _1600316] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600310)), hAPP(hAPP(c_List_Omap(_1600312, _1600310), _1600314), _1600316)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600312)), _1600316))], (24243 ^ _773908) ^ [_1198010] : [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), _1198010))), -(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), _1198010)) = 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), _1198010))))], (16723 ^ _773908) ^ [_1061082, _1061084, _1061086] : [class_Groups_Oordered__ab__group__add__abs(_1061082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061082), _1061084), _1061086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061082), hAPP(c_Groups_Ouminus__class_Ouminus(_1061082), _1061084)), _1061086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061082), hAPP(c_Groups_Oabs__class_Oabs(_1061082), _1061084)), _1061086)))], (38020 ^ _773908) ^ [_1496646, _1496648] : [-(hBOOL(hAPP(_1496648, 38021 ^ [_1496646, _1496648]))), -(hAPP(c_Set_OCollect(_1496646), _1496648) = c_Orderings_Obot__class_Obot(tc_fun(_1496646, tc_HOL_Obool)))], (24857 ^ _773908) ^ [_1212413, _1212415, _1212417, _1212419, _1212421] : [class_Orderings_Olinorder(_1212413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212413), _1212415), _1212417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212413), _1212419), _1212421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212413), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212413), _1212415), _1212419)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212413), _1212417), _1212421))))], (37700 ^ _773908) ^ [_1489149, _1489151, _1489153, _1489155, _1489157, _1489159, _1489161, _1489163, _1489165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1489149, _1489151)), hAPP(hAPP(c_Product__Type_OPair(_1489149, _1489151), _1489153), _1489155)), _1489157)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1489159, _1489161)), hAPP(hAPP(c_Product__Type_OPair(_1489159, _1489161), hAPP(_1489163, _1489153)), hAPP(_1489165, _1489155))), hAPP(c_Set_Oimage(tc_prod(_1489149, _1489151), tc_prod(_1489159, _1489161), c_Product__Type_Omap__pair(_1489149, _1489159, _1489151, _1489161, _1489163, _1489165)), _1489157))))], (21479 ^ _773908) ^ [_1145262, _1145264, _1145266] : [class_Fields_Olinordered__field(_1145262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145262), c_Groups_Ozero__class_Ozero(_1145262)), _1145264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145262), c_Groups_Ozero__class_Ozero(_1145262)), _1145266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145262), c_Groups_Ozero__class_Ozero(_1145262)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145262), _1145264), _1145266))))], (8365 ^ _773908) ^ [_911766, _911768] : [_911766 = _911768, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911766) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911768))], (39504 ^ _773908) ^ [_1541280, _1541282] : [-(c_List_Osublist(_1541280, _1541282, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1541280))], (37591 ^ _773908) ^ [_1486200, _1486202, _1486204, _1486206, _1486208, _1486210] : [class_Groups_Ocomm__monoid__mult(_1486200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486202), _1486204)), 37601 ^ _773908 : [(37604 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486206), hAPP(_1486208, 37600 ^ [_1486200, _1486202, _1486204, _1486206, _1486208, _1486210])))], (37602 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486202), 37600 ^ [_1486200, _1486202, _1486204, _1486206, _1486208, _1486210]), _1486204)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1486200, _1486202, c_Groups_Otimes__class_Otimes(_1486200)), hAPP(hAPP(c_COMBS(_1486202, tc_fun(_1486206, tc_HOL_Obool), _1486200), hAPP(hAPP(c_COMBC(_1486202, _1486200, tc_fun(tc_fun(_1486206, tc_HOL_Obool), _1486200)), hAPP(hAPP(c_COMBB(tc_fun(_1486206, _1486200), tc_fun(_1486200, tc_fun(tc_fun(_1486206, tc_HOL_Obool), _1486200)), _1486202), c_Finite__Set_Ofold__image(_1486200, _1486206, c_Groups_Otimes__class_Otimes(_1486200))), _1486210)), c_Groups_Oone__class_Oone(_1486200))), _1486208)), c_Groups_Oone__class_Oone(_1486200)), _1486204) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1486200, tc_prod(_1486202, _1486206), c_Groups_Otimes__class_Otimes(_1486200)), hAPP(c_Product__Type_Oprod_Oprod__case(_1486202, _1486206, _1486200), _1486210)), c_Groups_Oone__class_Oone(_1486200)), hAPP(hAPP(c_Product__Type_OSigma(_1486202, _1486206), _1486204), _1486208)))], (19807 ^ _773908) ^ [_1115755, _1115757] : [c_Int_OBit0(_1115755) = c_Int_OBit0(_1115757), -(_1115755 = _1115757)], (8757 ^ _773908) ^ [_918828, _918830] : [class_Groups_Olinordered__ab__group__add(_918828), 8760 ^ _773908 : [(8767 ^ _773908) ^ [] : [_918830 = c_Groups_Ozero__class_Ozero(_918828), -(hAPP(c_Groups_Ouminus__class_Ouminus(_918828), _918830) = _918830)], (8761 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_918828), _918830) = _918830, -(_918830 = c_Groups_Ozero__class_Ozero(_918828))]]], (45846 ^ _773908) ^ [_1690091, _1690093, _1690095] : [hBOOL(hAPP(c_List_Odistinct(_1690091), _1690093)), hBOOL(hAPP(hAPP(c_member(_1690091), _1690095), hAPP(c_List_Oset(_1690091), _1690093))), -(c_List_OdropWhile(_1690091, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1690091), c_fNot), hAPP(hAPP(c_COMBC(_1690091, _1690091, tc_HOL_Obool), c_fequal), _1690095)), hAPP(c_List_Orev(_1690091), _1690093)) = hAPP(hAPP(c_List_Olist_OCons(_1690091), _1690095), hAPP(c_List_Orev(_1690091), c_List_OtakeWhile(_1690091, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1690091), c_fNot), hAPP(hAPP(c_COMBC(_1690091, _1690091, tc_HOL_Obool), c_fequal), _1690095)), _1690093))))], (44023 ^ _773908) ^ [_1650964, _1650966, _1650968, _1650970] : [hBOOL(hAPP(hAPP(c_member(_1650964), _1650966), hAPP(c_Relation_ODomain(_1650964, _1650968), _1650970))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650964, _1650968)), hAPP(hAPP(c_Product__Type_OPair(_1650964, _1650968), _1650966), 44026 ^ [_1650964, _1650966, _1650968, _1650970])), _1650970)))], (7419 ^ _773908) ^ [_893932, _893934, _893936, _893938] : [class_Rings_Olinordered__semidom(_893932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893932), c_Groups_Ozero__class_Ozero(_893932)), _893934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893932), _893936), _893938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893932), _893936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893932), _893934), _893938))))], (39893 ^ _773908) ^ [_1552136] : [-(c_List_Olists(_1552136, c_Orderings_Obot__class_Obot(tc_fun(_1552136, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1552136)), c_List_Olist_ONil(_1552136)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1552136), tc_HOL_Obool))))], (26973 ^ _773908) ^ [_1259586, _1259588] : [c_Nat__Transfer_Onat__set(_1259586), c_Nat__Transfer_Onat__set(_1259588), 26980 ^ _773908 : [(26987 ^ _773908) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259586) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259588), -(_1259586 = _1259588)], (26981 ^ _773908) ^ [] : [_1259586 = _1259588, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259586) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259588))]]], (24369 ^ _773908) ^ [_1201584, _1201586, _1201588, _1201590] : [-(_1201584 = _1201586), hAPP(c_Product__Type_Ofst(_1201588, _1201590), _1201584) = hAPP(c_Product__Type_Ofst(_1201588, _1201590), _1201586), hAPP(c_Product__Type_Osnd(_1201588, _1201590), _1201584) = hAPP(c_Product__Type_Osnd(_1201588, _1201590), _1201586)], (34181 ^ _773908) ^ [_1410283, _1410285, _1410287, _1410289] : [c_Fun_Oinj__on(_1410283, _1410285, _1410287, _1410289), -(c_Fun_Oinj__on(_1410285, _1410283, c_Fun_Othe__inv__into(_1410283, _1410285, _1410289, _1410287), hAPP(c_Set_Oimage(_1410283, _1410285, _1410287), _1410289)))], (37778 ^ _773908) ^ [_1491567, _1491569] : [-(c_Relation_Orefl__on(_1491567, _1491569, c_Relation_OId__on(_1491567, _1491569)))], (50249 ^ _773908) ^ [_1791211, _1791213] : [-(c_Relation_Otrans(_1791211, c_Relation_OId__on(_1791211, _1791213)))], (3036 ^ _773908) ^ [_819304, _819306, _819308, _819310, _819312, _819314, _819316, _819318, _819320, _819322] : [-(c_Fun_Ofun__upd(_819322, _819318, _819314, _819310, _819306) = c_Fun_Ofun__upd(_819320, _819316, _819312, _819308, _819304)), _819322 = _819320, _819318 = _819316, _819314 = _819312, _819310 = _819308, _819306 = _819304], (12797 ^ _773908) ^ [_988463, _988465, _988467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988463), _988465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988465), _988467))))], (16125 ^ _773908) ^ [_1050182, _1050184] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050182, _1050184) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050182, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050184)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050182, _1050184)), _1050184))], (13466 ^ _773908) ^ [_1000094, _1000096, _1000098] : [_1000094 = _1000096, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000098, tc_HOL_Obool)), _1000096), _1000094)))], (26671 ^ _773908) ^ [_1253496, _1253498, _1253500, _1253502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253496), _1253502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253500), _1253498))), -(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), _1253496), _1253498)), 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), _1253500), _1253502)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (51612 ^ _773908) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (45999 ^ _773908) ^ [_1693386, _1693388] : [class_Orderings_Olinorder(_1693386), -(c_List_Olinorder__class_Osorted(_1693386, c_List_Olinorder__class_Osort__key(_1693386, _1693386, c_COMBI(_1693386), _1693388)))], (40249 ^ _773908) ^ [_1561107, _1561109, _1561111] : [-(hAPP(hAPP(c_List_Oappend(_1561107), hAPP(hAPP(c_List_Otake(_1561107), _1561109), _1561111)), hAPP(hAPP(c_List_Odrop(_1561107), _1561109), _1561111)) = _1561111)], (38042 ^ _773908) ^ [_1496922, _1496924, _1496926] : [-(hAPP(hAPP(c_Set_Oinsert(_1496922), _1496924), hAPP(c_Set_OCollect(_1496922), _1496926)) = hAPP(c_Set_OCollect(_1496922), hAPP(hAPP(c_COMBS(_1496922, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496922), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496922), c_fNot), hAPP(hAPP(c_COMBC(_1496922, _1496922, tc_HOL_Obool), c_fequal), _1496924)))), _1496926)))], (28396 ^ _773908) ^ [_1289857, _1289859, _1289861] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289857, tc_HOL_Obool)), _1289859), _1289861) = c_Orderings_Obot__class_Obot(tc_fun(_1289857, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289857, tc_HOL_Obool)), _1289859), _1289861) = _1289859)], (7879 ^ _773908) ^ [_902786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902786)), -(_902786 = hAPP(c_Nat_OSuc, 7882 ^ [_902786]))], (26548 ^ _773908) ^ [_1249785, _1249787, _1249789, _1249791, _1249793] : [hBOOL(hAPP(hAPP(c_member(_1249785), _1249787), _1249789)), -(hAPP(hAPP(c_Set_Oinsert(_1249791), hAPP(_1249793, _1249787)), hAPP(c_Set_Oimage(_1249785, _1249791, _1249793), _1249789)) = hAPP(c_Set_Oimage(_1249785, _1249791, _1249793), _1249789))], (37352 ^ _773908) ^ [_1479143, _1479145, _1479147, _1479149, _1479151, _1479153] : [hBOOL(hAPP(hAPP(c_member(_1479143), _1479145), _1479147)), 37355 ^ _773908 : [(37362 ^ _773908) ^ [] : [_1479151 = _1479153, -(hAPP(hAPP(c_Product__Type_OSigma(_1479149, _1479143), _1479151), hAPP(c_COMBK(tc_fun(_1479143, tc_HOL_Obool), _1479149), _1479147)) = hAPP(hAPP(c_Product__Type_OSigma(_1479149, _1479143), _1479153), hAPP(c_COMBK(tc_fun(_1479143, tc_HOL_Obool), _1479149), _1479147)))], (37356 ^ _773908) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1479149, _1479143), _1479151), hAPP(c_COMBK(tc_fun(_1479143, tc_HOL_Obool), _1479149), _1479147)) = hAPP(hAPP(c_Product__Type_OSigma(_1479149, _1479143), _1479153), hAPP(c_COMBK(tc_fun(_1479143, tc_HOL_Obool), _1479149), _1479147)), -(_1479151 = _1479153)]]], (42826 ^ _773908) ^ [_1623731, _1623733] : [_1623731 = _1623733, -(hAPP(c_Code__Numeral_Onat__of, _1623731) = hAPP(c_Code__Numeral_Onat__of, _1623733))], (37466 ^ _773908) ^ [_1482676, _1482678, _1482680, _1482682, _1482684, _1482686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482676, _1482678)), hAPP(hAPP(c_Product__Type_OPair(_1482676, _1482678), _1482680), _1482682)), hAPP(hAPP(c_Product__Type_OSigma(_1482676, _1482678), _1482684), _1482686))), -(hBOOL(hAPP(hAPP(c_member(_1482676), _1482680), _1482684)))], (2816 ^ _773908) ^ [_815782, _815784, _815786, _815788, _815790, _815792] : [-(c_Partial__Function_Oflat__lub(_815792, _815788, _815784) = c_Partial__Function_Oflat__lub(_815790, _815786, _815782)), _815792 = _815790, _815788 = _815786, _815784 = _815782], (1834 ^ _773908) ^ [_799819, _799821] : [-(class_Rings_Omult__zero(_799819)), _799821 = _799819, class_Rings_Omult__zero(_799821)], (42171 ^ _773908) ^ [_1607978, _1607980, _1607982, _1607984, _1607986, _1607988, _1607990] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607978, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607980, tc_fun(_1607978, tc_HOL_Obool)), _1607982), _1607984)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607986, tc_fun(_1607978, tc_HOL_Obool)), _1607988), _1607990)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607980, tc_fun(_1607978, tc_HOL_Obool)), _1607982), hAPP(hAPP(c_COMBB(tc_fun(_1607986, tc_fun(_1607978, tc_HOL_Obool)), tc_fun(_1607978, tc_HOL_Obool), _1607980), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607986, tc_fun(_1607978, tc_HOL_Obool)), _1607988)), hAPP(hAPP(c_COMBC(_1607980, tc_fun(_1607986, tc_fun(_1607978, tc_HOL_Obool)), tc_fun(_1607986, tc_fun(_1607978, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1607978, tc_HOL_Obool), tc_fun(_1607978, tc_HOL_Obool)), tc_fun(tc_fun(_1607986, tc_fun(_1607978, tc_HOL_Obool)), tc_fun(_1607986, tc_fun(_1607978, tc_HOL_Obool))), _1607980), c_COMBB(tc_fun(_1607978, tc_HOL_Obool), tc_fun(_1607978, tc_HOL_Obool), _1607986)), hAPP(hAPP(c_COMBB(tc_fun(_1607978, tc_HOL_Obool), tc_fun(tc_fun(_1607978, tc_HOL_Obool), tc_fun(_1607978, tc_HOL_Obool)), _1607980), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607978, tc_HOL_Obool))), _1607984))), _1607990))))], (25195 ^ _773908) ^ [_1218998, _1219000, _1219002, _1219004] : [class_Orderings_Olinorder(_1218998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218998), _1219000), _1219002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218998), _1219000), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218998), _1219004), _1219002))))], (35867 ^ _773908) ^ [_1446886, _1446888, _1446890, _1446892, _1446894] : [-(hAPP(c_Set_Oimage(_1446886, _1446888, hAPP(hAPP(c_COMBB(_1446890, _1446888, _1446886), _1446892), _1446894)), c_Orderings_Otop__class_Otop(tc_fun(_1446886, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1446890, _1446888, _1446892), hAPP(c_Set_Oimage(_1446886, _1446890, _1446894), c_Orderings_Otop__class_Otop(tc_fun(_1446886, tc_HOL_Obool)))))], (23033 ^ _773908) ^ [_1173867, _1173869, _1173871, _1173873, _1173875] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1173867, _1173869, _1173871), _1173873), _1173875))), hBOOL(hAPP(hAPP(_1173869, _1173873), _1173875)), hBOOL(hAPP(_1173871, _1173875))], (49382 ^ _773908) ^ [_1770358, _1770360, _1770362, _1770364, _1770366] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770358, _1770360, _1770362), _1770364), _1770366)), -(hBOOL(hAPP(hAPP(_1770362, _1770366), _1770364)))], (43107 ^ _773908) ^ [_1629820, _1629822, _1629824, _1629826] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1629820)), _1629822), c_List_Olists(_1629820, _1629824))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1629820)), _1629822), c_List_Olists(_1629820, _1629826))), -(hBOOL(hAPP(c_List_Olistsp(_1629820, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1629820, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1629820, tc_fun(_1629820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1629820)), _1629824)), hAPP(hAPP(c_COMBC(_1629820, tc_fun(_1629820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1629820)), _1629826))), _1629822)))], (36379 ^ _773908) ^ [_1458314, _1458316, _1458318, _1458320] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1458314, _1458316, hAPP(hAPP(c_Set_Oinsert(_1458314), _1458318), c_Orderings_Obot__class_Obot(tc_fun(_1458314, tc_HOL_Obool)))), _1458320)), -(_1458318 = _1458320)], (18271 ^ _773908) ^ [_1089384, _1089386, _1089388, _1089390] : [_1089384 = _1089386, 18276 ^ _773908 : [(18279 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089388), _1089390), _1089386)))], (18277 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089388), _1089390), _1089384)))]], 18280 ^ _773908 : [(18283 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1089388), _1089390), _1089386))], (18281 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1089388), _1089390), _1089384))]]], (29389 ^ _773908) ^ [_1310262, _1310264, _1310266] : [class_Orderings_Olinorder(_1310262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310262), _1310264)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310262), _1310266)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310262, tc_HOL_Obool)), _1310264), _1310266) = c_Orderings_Obot__class_Obot(tc_fun(_1310262, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310262), c_Big__Operators_Olinorder__class_OMax(_1310262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310262, tc_HOL_Obool)), _1310264), _1310266))), c_Big__Operators_Olinorder__class_OMax(_1310262, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310262, tc_HOL_Obool)), _1310264), _1310266))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310262), c_Big__Operators_Olinorder__class_OMax(_1310262, _1310264)), c_Big__Operators_Olinorder__class_OMax(_1310262, _1310266)))], (17905 ^ _773908) ^ [_1082993] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082993))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1082993)) = _1082993)], (42307 ^ _773908) ^ [_1612110, _1612112, _1612114, _1612116] : [-(_1612110 = c_List_Olist_ONil(_1612112)), -(hAPP(c_List_Ohd(_1612114), hAPP(hAPP(c_List_Omap(_1612112, _1612114), _1612116), _1612110)) = hAPP(_1612116, hAPP(c_List_Ohd(_1612112), _1612110)))], (7759 ^ _773908) ^ [_900238, _900240, _900242] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_900238, _900240, _900242)], (21157 ^ _773908) ^ [_1139791, _1139793, _1139795, _1139797] : [class_Fields_Ofield__inverse__zero(_1139791), -(_1139793 = c_Groups_Ozero__class_Ozero(_1139791)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139791), _1139795), _1139793)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139791), _1139797), _1139793)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139791), _1139795), _1139797))], (39047 ^ _773908) ^ [_1529138, _1529140] : [-(hAPP(c_Relation_ORange(_1529138, _1529138), c_Relation_OId__on(_1529138, _1529140)) = _1529140)], (47006 ^ _773908) ^ [_1717334, _1717336, _1717338, _1717340] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717334, _1717334)), hAPP(hAPP(c_Product__Type_OPair(_1717334, _1717334), _1717336), _1717338)), c_Transitive__Closure_Otrancl(_1717334, _1717340))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1717334, _1717334)), hAPP(hAPP(c_Product__Type_OPair(_1717334, _1717334), _1717336), _1717338)), c_Transitive__Closure_Ortrancl(_1717334, _1717340))))], (40376 ^ _773908) ^ [_1564072, _1564074, _1564076] : [hBOOL(hAPP(hAPP(c_member(_1564072), _1564074), hAPP(c_List_Oset(_1564072), _1564076))), -(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(_1564072)), _1564076))))], (13093 ^ _773908) ^ [_993620] : [-(hAPP(c_Nat_OSuc, _993620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993620), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43737 ^ _773908) ^ [_1643932, _1643934, _1643936] : [-(hAPP(c_Relation_ODomain(_1643932, _1643934), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1643932, _1643934), tc_HOL_Obool), _1643936)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1643932, _1643934), tc_HOL_Obool), tc_fun(_1643932, tc_HOL_Obool)), _1643936), c_Relation_ODomain(_1643932, _1643934)))], (33700 ^ _773908) ^ [_1399990, _1399992, _1399994, _1399996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1399990), hAPP(c_Set_Oimage(_1399992, _1399990, _1399994), _1399996))), hAPP(c_Finite__Set_Ocard(_1399992), _1399996))), c_Fun_Oinj__on(_1399992, _1399990, _1399994, _1399996)], (31245 ^ _773908) ^ [_1347836, _1347838, _1347840, _1347842, _1347844] : [class_Groups_Ocomm__monoid__mult(_1347836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347838), _1347840)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347838), _1347842)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1347838, tc_HOL_Obool)), _1347840), _1347842) = c_Orderings_Obot__class_Obot(tc_fun(_1347838, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1347836, _1347838, c_Groups_Otimes__class_Otimes(_1347836)), _1347844), c_Groups_Oone__class_Oone(_1347836)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1347838, tc_HOL_Obool)), _1347840), _1347842)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347836), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1347836, _1347838, c_Groups_Otimes__class_Otimes(_1347836)), _1347844), c_Groups_Oone__class_Oone(_1347836)), _1347840)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1347836, _1347838, c_Groups_Otimes__class_Otimes(_1347836)), _1347844), c_Groups_Oone__class_Oone(_1347836)), _1347842)))], (40280 ^ _773908) ^ [_1561845, _1561847, _1561849] : [40282 ^ _773908 : [(40285 ^ _773908) ^ [] : [hBOOL(hAPP(_1561849, hAPP(hAPP(c_List_Onth(_1561845), _1561847), 40281 ^ [_1561845, _1561847, _1561849])))], (40283 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40281 ^ [_1561845, _1561847, _1561849]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561845)), _1561847))))]], 40286 ^ _773908 : [(40287 ^ _773908) ^ [_1562047] : [hBOOL(hAPP(hAPP(c_member(_1561845), _1562047), hAPP(c_List_Oset(_1561845), _1561847))), -(hBOOL(hAPP(_1561849, _1562047)))]]], (13496 ^ _773908) ^ [_1000640, _1000642] : [class_Rings_Olinordered__idom(_1000640), -(c_Groups_Osgn__class_Osgn(_1000640, c_Groups_Osgn__class_Osgn(_1000640, _1000642)) = c_Groups_Osgn__class_Osgn(_1000640, _1000642))], (35000 ^ _773908) ^ [_1428142, _1428144, _1428146] : [class_Orderings_Oorder(_1428142), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428142, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1428142, _1428144), _1428146)), hAPP(c_SetInterval_Oord__class_OatLeast(_1428142), _1428146)) = c_Orderings_Obot__class_Obot(tc_fun(_1428142, tc_HOL_Obool)))], (20165 ^ _773908) ^ [_1121963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1121963)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121963), c_Int_OMin)))], (1214 ^ _773908) ^ [_792069, _792071] : [-(class_Rings_Oordered__ring__abs(_792069)), _792071 = _792069, class_Rings_Oordered__ring__abs(_792071)], (17263 ^ _773908) ^ [_1071841, _1071843] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071841)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071843)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1071841), _1071843)))], (23943 ^ _773908) ^ [_1192539] : [-(_1192539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1192539), 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)))))], (39538 ^ _773908) ^ [_1541966, _1541968, _1541970, _1541972, _1541974, _1541976] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1541966), tc_List_Olist(_1541966))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1541966), tc_List_Olist(_1541966)), hAPP(hAPP(c_List_Oappend(_1541966), _1541968), hAPP(hAPP(c_List_Olist_OCons(_1541966), _1541970), c_List_Olist_ONil(_1541966)))), hAPP(hAPP(c_List_Oappend(_1541966), _1541972), hAPP(hAPP(c_List_Olist_OCons(_1541966), _1541974), c_List_Olist_ONil(_1541966))))), c_List_Olistrel1(_1541966, _1541976))), 39543 ^ _773908 : [(39546 ^ _773908) ^ [] : [-(_1541970 = _1541974)], (39544 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1541966), tc_List_Olist(_1541966))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1541966), tc_List_Olist(_1541966)), _1541968), _1541972)), c_List_Olistrel1(_1541966, _1541976))))]], 39547 ^ _773908 : [(39550 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541966, _1541966)), hAPP(hAPP(c_Product__Type_OPair(_1541966, _1541966), _1541970), _1541974)), _1541976)))], (39548 ^ _773908) ^ [] : [-(_1541968 = _1541972)]]], (51093 ^ _773908) ^ [_1808116] : [-(_1808116 = hAPP(c_Code__Numeral_Oof__nat, 51091 ^ [_1808116]))], (29363 ^ _773908) ^ [_1309785, _1309787, _1309789] : [class_Lattices_Olattice(_1309785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309785), _1309787)), -(_1309787 = c_Orderings_Obot__class_Obot(tc_fun(_1309785, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309785), _1309789)), -(_1309789 = c_Orderings_Obot__class_Obot(tc_fun(_1309785, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309785, tc_HOL_Obool)), _1309787), _1309789) = c_Orderings_Obot__class_Obot(tc_fun(_1309785, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1309785, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309785, tc_HOL_Obool)), _1309787), _1309789)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309785), c_Big__Operators_Olattice__class_OInf__fin(_1309785, _1309787)), c_Big__Operators_Olattice__class_OInf__fin(_1309785, _1309789)))], (46817 ^ _773908) ^ [_1712096, _1712098, _1712100] : [46818 ^ _773908 : [(46819 ^ _773908) ^ [_1712172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712096, _1712096)), _1712098), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1712096, _1712096), tc_HOL_Obool), _1712172), _1712100)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1712096, _1712096)), _1712098), c_Transitive__Closure_Ortrancl(_1712096, _1712100))))], (28180 ^ _773908) ^ [_1284635, _1284637] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284635, tc_HOL_Obool)), _1284637), _1284637) = _1284637)], (14539 ^ _773908) ^ [_1019798, _1019800, _1019802, _1019804] : [class_Divides_Osemiring__div(_1019798), -(_1019800 = c_Groups_Ozero__class_Ozero(_1019798)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019798), _1019802), _1019800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019798), _1019804), _1019800)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019798), _1019802), _1019804))], (26753 ^ _773908) ^ [_1255226, _1255228, _1255230, _1255232, _1255234, _1255236] : [hBOOL(hAPP(hAPP(c_member(_1255226), _1255228), _1255230)), -(hAPP(c_Set_Oimage(_1255226, _1255232, c_Fun_Ofun__upd(_1255226, _1255232, _1255234, _1255228, _1255236)), _1255230) = hAPP(hAPP(c_Set_Oinsert(_1255232), _1255236), hAPP(c_Set_Oimage(_1255226, _1255232, _1255234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255226, tc_HOL_Obool)), _1255230), hAPP(hAPP(c_Set_Oinsert(_1255226), _1255228), c_Orderings_Obot__class_Obot(tc_fun(_1255226, tc_HOL_Obool)))))))], (45990 ^ _773908) ^ [_1693265, _1693267, _1693269] : [45992 ^ _773908 : [(45995 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1693267, 45991 ^ [_1693265, _1693267, _1693269])))], (45993 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1693265), 45991 ^ [_1693265, _1693267, _1693269]), hAPP(c_List_Oset(_1693265), c_List_OdropWhile(_1693265, _1693267, _1693269)))))]], -(c_List_OtakeWhile(_1693265, _1693267, _1693269) = hAPP(c_List_Ofilter(_1693265, _1693267), _1693269))], (2150 ^ _773908) ^ [_805141, _805143, _805145, _805147] : [-(c_Nat__Transfer_Otsub(_805147, _805143) = c_Nat__Transfer_Otsub(_805145, _805141)), _805147 = _805145, _805143 = _805141], (7047 ^ _773908) ^ [_888084, _888086] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888084), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _888084), _888086)))))], (46762 ^ _773908) ^ [_1710793, _1710795, _1710797] : [-(c_Transitive__Closure_Ortrancl(_1710793, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1710793, _1710793), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1710793, _1710795)), c_Transitive__Closure_Ortrancl(_1710793, _1710797))) = c_Transitive__Closure_Ortrancl(_1710793, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1710793, _1710793), tc_HOL_Obool)), _1710795), _1710797)))], (9113 ^ _773908) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19317 ^ _773908) ^ [_1107457, _1107459] : [c_Int_OBit1(_1107457) = c_Int_OBit1(_1107459), -(_1107457 = _1107459)], (108 ^ _773908) ^ [_775474, _775476, _775478, _775480] : [-(c_FunDef_Ois__measure(_775478, _775474)), c_FunDef_Ois__measure(_775480, _775476), _775480 = _775478, _775476 = _775474], (43831 ^ _773908) ^ [_1645908, _1645910, _1645912] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645908, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645908, tc_HOL_Obool), _1645910)), _1645912) = c_Orderings_Obot__class_Obot(tc_fun(_1645908, tc_HOL_Obool)), 43834 ^ _773908 : [(43835 ^ _773908) ^ [_1646043] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1645908, tc_HOL_Obool)), _1646043), _1645910)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1645908, tc_HOL_Obool)), _1646043), _1645912) = c_Orderings_Obot__class_Obot(tc_fun(_1645908, tc_HOL_Obool)))]]], (41806 ^ _773908) ^ [_1597469, _1597471, _1597473, _1597475, _1597477, _1597479] : [hBOOL(hAPP(hAPP(c_member(_1597469), _1597471), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597473, tc_fun(_1597469, tc_HOL_Obool)), _1597475), _1597477))), -(hBOOL(hAPP(hAPP(c_member(_1597469), _1597471), hAPP(_1597477, _1597479)))), hBOOL(hAPP(hAPP(c_member(_1597473), _1597479), _1597475))], (33212 ^ _773908) ^ [_1390931, _1390933, _1390935, _1390937, _1390939, _1390941] : [c_Fun_Oinj__on(_1390931, _1390933, _1390935, _1390937), hAPP(_1390935, _1390939) = hAPP(_1390935, _1390941), hBOOL(hAPP(hAPP(c_member(_1390931), _1390939), _1390937)), hBOOL(hAPP(hAPP(c_member(_1390931), _1390941), _1390937)), -(_1390939 = _1390941)], (50442 ^ _773908) ^ [_1795154, _1795156] : [c_Equiv__Relations_Oequivp(_1795154, _1795156), 50445 ^ _773908 : [(50450 ^ _773908) ^ [] : [-(c_Predicate_Otransp(_1795154, _1795156))], (50448 ^ _773908) ^ [] : [-(c_Predicate_Osymp(_1795154, _1795156))], (50446 ^ _773908) ^ [] : [-(c_Predicate_Oreflp(_1795154, _1795156))]]], (44389 ^ _773908) ^ [_1658884, _1658886, _1658888] : [-(hAPP(c_List_Ofilter(_1658884, _1658886), c_List_Oconcat(_1658884, _1658888)) = c_List_Oconcat(_1658884, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1658884), tc_List_Olist(_1658884)), c_List_Ofilter(_1658884, _1658886)), _1658888)))], (26005 ^ _773908) ^ [_1234810, _1234812, _1234814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234810, tc_HOL_Obool)), _1234812), _1234814)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234810, tc_HOL_Obool)), _1234812), _1234814) = _1234814)], (18175 ^ _773908) ^ [_1087364, _1087366, _1087368] : [18177 ^ _773908 : [(18180 ^ _773908) ^ [] : [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(_1087366, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18176 ^ [_1087364, _1087366, _1087368]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1087366, 18176 ^ [_1087364, _1087366, _1087368])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18178 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18176 ^ [_1087364, _1087366, _1087368]), _1087364)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1087366, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1087368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087368), hAPP(_1087366, _1087364))), 18190 ^ _773908 : [(18193 ^ _773908) ^ [] : [-(hAPP(_1087366, 18189 ^ [_1087364, _1087366, _1087368]) = _1087368)], (18191 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18189 ^ [_1087364, _1087366, _1087368]), _1087364)))]]], (43606 ^ _773908) ^ [_1640693, _1640695, _1640697, _1640699] : [-(hAPP(c_List_Oset(tc_prod(_1640693, _1640695)), c_Enum_Oproduct(_1640693, _1640695, _1640697, _1640699)) = hAPP(hAPP(c_Product__Type_OSigma(_1640693, _1640695), hAPP(c_List_Oset(_1640693), _1640697)), hAPP(c_COMBK(tc_fun(_1640695, tc_HOL_Obool), _1640693), hAPP(c_List_Oset(_1640695), _1640699))))], (45878 ^ _773908) ^ [_1690717, _1690719] : [-(c_List_OdropWhile(_1690717, _1690719, c_List_Olist_ONil(_1690717)) = c_List_Olist_ONil(_1690717))], (18819 ^ _773908) ^ [_1099453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099453), 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), _1099453)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18871 ^ _773908) ^ [_1100200] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100200), c_Int_OPls) = _1100200)], (25071 ^ _773908) ^ [_1216550, _1216552] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1216550)), hAPP(c_Nat_OSuc, _1216552)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1216550))), 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, _1216552))), 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)), _1216552)))))], (42898 ^ _773908) ^ [_1624950, _1624952] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1624950), _1624952) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624950)), hAPP(c_Code__Numeral_Onat__of, _1624952))))], (28550 ^ _773908) ^ [_1293571, _1293573, _1293575, _1293577] : [hBOOL(hAPP(hAPP(c_member(_1293571), _1293573), _1293575)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1293571, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1293571, _1293571, _1293577), hAPP(hAPP(c_Set_Oinsert(_1293571), _1293573), c_Orderings_Obot__class_Obot(tc_fun(_1293571, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1293571), _1293575), _1293577))))], (51546 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (504 ^ _773908) ^ [_781640, _781642] : [-(c_Nitpick_Ounknown(_781640)), _781642 = _781640, c_Nitpick_Ounknown(_781642)], (50374 ^ _773908) ^ [_1793751, _1793753, _1793755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1793751, _1793751), tc_HOL_Obool)), _1793753), _1793755)), c_Relation_Oantisym(_1793751, _1793755), -(c_Relation_Oantisym(_1793751, _1793753))], (14905 ^ _773908) ^ [_1025904, _1025906, _1025908, _1025910] : [class_Divides_Osemiring__div(_1025904), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025904), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025904), _1025906), _1025908)), _1025908)), c_Divides_Odiv__class_Omod(_1025904, _1025906, _1025908))), _1025910) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025904), _1025906), _1025910))], (40509 ^ _773908) ^ [_1567614, _1567616, _1567618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567614), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1567616)), _1567618))), -(hAPP(hAPP(c_List_Oappend(_1567616), hAPP(hAPP(c_List_Otake(_1567616), _1567614), _1567618)), hAPP(hAPP(c_List_Olist_OCons(_1567616), hAPP(c_List_Ohd(_1567616), hAPP(hAPP(c_List_Odrop(_1567616), _1567614), _1567618))), c_List_Olist_ONil(_1567616))) = hAPP(hAPP(c_List_Otake(_1567616), hAPP(c_Nat_OSuc, _1567614)), _1567618))], (9724 ^ _773908) ^ [_935935, _935937, _935939, _935941] : [class_Orderings_Oord(_935935), 9727 ^ _773908 : [(9734 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935935), hAPP(_935939, 9735 ^ [_935935, _935937, _935939, _935941])), hAPP(_935941, 9735 ^ [_935935, _935937, _935939, _935941]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935937, _935935)), _935939), _935941)))], (9728 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935937, _935935)), _935939), _935941)), 9731 ^ _773908 : [(9732 ^ _773908) ^ [_936092] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935935), hAPP(_935939, _936092)), hAPP(_935941, _936092))))]]]]], (48589 ^ _773908) ^ [_1753015, _1753017, _1753019, _1753021, _1753023, _1753025] : [c_Finite__Set_Ofun__left__comm(_1753015, _1753017, _1753019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1753015), _1753021)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1753015, _1753017, _1753019), _1753023), hAPP(hAPP(c_Set_Oinsert(_1753015), _1753025), _1753021)) = hAPP(hAPP(_1753019, _1753025), hAPP(hAPP(c_Finite__Set_Ofold(_1753015, _1753017, _1753019), _1753023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1753015, tc_HOL_Obool)), _1753021), hAPP(hAPP(c_Set_Oinsert(_1753015), _1753025), c_Orderings_Obot__class_Obot(tc_fun(_1753015, tc_HOL_Obool)))))))], (39781 ^ _773908) ^ [_1549459, _1549461] : [-(c_List_Olistrelp(_1549459, _1549461, c_List_Olist_ONil(_1549459), c_List_Olist_ONil(_1549459)))], (41434 ^ _773908) ^ [_1590322, _1590324, _1590326] : [-(_1590322 = c_List_Olist_ONil(_1590324)), -(c_List_Olast(_1590324, hAPP(hAPP(c_List_Oappend(_1590324), _1590326), _1590322)) = c_List_Olast(_1590324, _1590322))], (7761 ^ _773908) ^ [_900290, _900292, _900294, _900296, _900298] : [c_Com_Ocom_OAss(_900290, _900292) = c_Com_Ocom_OCond(_900294, _900296, _900298)], (8329 ^ _773908) ^ [_911272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911272)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14165 ^ _773908) ^ [_1012938, _1012940, _1012942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012938)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012940, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012942), _1012938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012942), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012940), _1012942), _1012938))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012940, _1012942)))], (7870 ^ _773908) ^ [_902638, _902640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902638), _902640)), 7874 ^ _773908 : [(7877 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902638), 7873 ^ [_902638, _902640]) = _902640)], (7875 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7873 ^ [_902638, _902640])))]]], (10437 ^ _773908) ^ [_946818, _946820, _946822, _946824] : [class_Orderings_Oorder(_946818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946818), _946820), _946822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946818), _946824), _946820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946818), _946824), _946822)))], (11071 ^ _773908) ^ [_958124, _958126, _958128] : [class_Rings_Olinordered__ring__strict(_958124), 11074 ^ _773908 : [(11089 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958124), _958126), _958128)), c_Groups_Ozero__class_Ozero(_958124)))), 11090 ^ _773908 : [(11097 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), _958126), c_Groups_Ozero__class_Ozero(_958124))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), c_Groups_Ozero__class_Ozero(_958124)), _958128))], (11091 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), c_Groups_Ozero__class_Ozero(_958124)), _958126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), _958128), c_Groups_Ozero__class_Ozero(_958124)))]]], (11075 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958124), _958126), _958128)), c_Groups_Ozero__class_Ozero(_958124))), 11080 ^ _773908 : [(11083 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), _958128), c_Groups_Ozero__class_Ozero(_958124))))], (11081 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), c_Groups_Ozero__class_Ozero(_958124)), _958126)))]], 11084 ^ _773908 : [(11087 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), c_Groups_Ozero__class_Ozero(_958124)), _958128)))], (11085 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958124), _958126), c_Groups_Ozero__class_Ozero(_958124))))]]]]], (19419 ^ _773908) ^ [_1109159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1109159))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1109159)))], (34167 ^ _773908) ^ [_1410038, _1410040, _1410042, _1410044, _1410046, _1410048] : [c_Fun_Oinj__on(_1410038, _1410040, _1410042, _1410044), hAPP(_1410042, _1410046) = _1410048, hBOOL(hAPP(hAPP(c_member(_1410038), _1410046), _1410044)), -(hAPP(c_Fun_Othe__inv__into(_1410038, _1410040, _1410044, _1410042), _1410048) = _1410046)], (49640 ^ _773908) ^ [_1775880, _1775882, _1775884, _1775886] : [-(c_Lazy__Sequence_Oappend(_1775880, c_Lazy__Sequence_Olazy__sequence_OInsert(_1775880, _1775882, _1775884), _1775886) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1775880, _1775882, c_Lazy__Sequence_Oappend(_1775880, _1775884, _1775886)))], (18395 ^ _773908) ^ [_1091514, _1091516] : [-(hBOOL(hAPP(hAPP(c_member(_1091514), 18396 ^ [_1091514, _1091516]), _1091516))), -(_1091516 = c_Orderings_Obot__class_Obot(tc_fun(_1091514, tc_HOL_Obool)))], (7751 ^ _773908) ^ [_900009, _900011, _900013, _900015, _900017] : [c_Com_Ocom_OSemi(_900009, _900011) = c_Com_Ocom_OLocal(_900013, _900015, _900017)], (4956 ^ _773908) ^ [_849570, _849572, _849574, _849576, _849578, _849580, _849582, _849584] : [-(c_Random__Sequence_ORandom(_849584, _849580, _849576, _849572) = c_Random__Sequence_ORandom(_849582, _849578, _849574, _849570)), _849584 = _849582, _849580 = _849578, _849576 = _849574, _849572 = _849570], (44589 ^ _773908) ^ [_1664320, _1664322, _1664324, _1664326] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1664320)), c_List_Otranspose__rel(_1664320)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664320)), hAPP(hAPP(c_List_Olist_OCons(_1664320), _1664322), _1664324)), _1664326))), -(c_List_Otranspose(_1664320, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664320)), hAPP(hAPP(c_List_Olist_OCons(_1664320), _1664322), _1664324)), _1664326)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664320)), hAPP(hAPP(c_List_Olist_OCons(_1664320), _1664322), c_List_Oconcat(_1664320, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1664320), tc_List_Olist(_1664320)), c_List_Olist_Olist__case(tc_List_Olist(_1664320), _1664320, c_List_Olist_ONil(_1664320), hAPP(hAPP(c_COMBB(tc_List_Olist(_1664320), tc_fun(tc_List_Olist(_1664320), tc_List_Olist(_1664320)), _1664320), c_COMBK(tc_List_Olist(_1664320), tc_List_Olist(_1664320))), hAPP(hAPP(c_COMBC(_1664320, tc_List_Olist(_1664320), tc_List_Olist(_1664320)), c_List_Olist_OCons(_1664320)), c_List_Olist_ONil(_1664320))))), _1664326)))), c_List_Otranspose(_1664320, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1664320)), _1664324), c_List_Oconcat(tc_List_Olist(_1664320), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1664320), tc_List_Olist(tc_List_Olist(_1664320))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1664320)), _1664320, c_List_Olist_ONil(tc_List_Olist(_1664320)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1664320), tc_List_Olist(tc_List_Olist(_1664320))), _1664320), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664320), tc_List_Olist(tc_List_Olist(_1664320)), tc_List_Olist(tc_List_Olist(_1664320))), c_List_Olist_OCons(tc_List_Olist(_1664320))), c_List_Olist_ONil(tc_List_Olist(_1664320)))))), _1664326))))))], (35276 ^ _773908) ^ [_1434655, _1434657, _1434659] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1434655), _1434657)), 35279 ^ _773908 : [(35299 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434655, tc_Nat_Onat), _1434659), _1434657) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 35300 ^ _773908 : [(35301 ^ _773908) ^ [_1435136] : [hBOOL(hAPP(hAPP(c_member(_1434655), _1435136), _1434657)), hAPP(_1434659, _1435136) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35309 ^ _773908 : [(35314 ^ _773908) ^ [] : [hAPP(_1434659, 35308 ^ [_1434655, _1434657, _1434659, _1435136]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35312 ^ _773908) ^ [] : [_1435136 = 35308 ^ [_1434655, _1434657, _1434659, _1435136]], (35310 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434655), 35308 ^ [_1434655, _1434657, _1434659, _1435136]), _1434657)))]]]]], (35280 ^ _773908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434655, tc_Nat_Onat), _1434659), _1434657) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35284 ^ _773908 : [(35289 ^ _773908) ^ [_1434975] : [hBOOL(hAPP(hAPP(c_member(_1434655), _1434975), _1434657)), -(35283 ^ [_1434655, _1434657, _1434659] = _1434975), -(hAPP(_1434659, _1434975) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35287 ^ _773908) ^ [] : [-(hAPP(_1434659, 35283 ^ [_1434655, _1434657, _1434659]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35285 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434655), 35283 ^ [_1434655, _1434657, _1434659]), _1434657)))]]]]], (5150 ^ _773908) ^ [_852655, _852657, _852659, _852661, _852663, _852665, _852667, _852669] : [-(c_Wellfounded_Olex__prod(_852669, _852665, _852661, _852657) = c_Wellfounded_Olex__prod(_852667, _852663, _852659, _852655)), _852669 = _852667, _852665 = _852663, _852661 = _852659, _852657 = _852655], (22887 ^ _773908) ^ [_1170907, _1170909, _1170911, _1170913] : [-(c_Nitpick_Ofold__graph_H(_1170907, _1170909, _1170911, _1170913, c_Orderings_Obot__class_Obot(tc_fun(_1170907, tc_HOL_Obool)), _1170913))], (44537 ^ _773908) ^ [_1662397, _1662399, _1662401] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1662397, tc_HOL_Obool)), hAPP(c_List_Oset(_1662397), _1662399)), hAPP(hAPP(c_Set_Oinsert(_1662397), _1662401), c_Orderings_Obot__class_Obot(tc_fun(_1662397, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1662397), hAPP(c_List_Ofilter(_1662397, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1662397), c_fNot), hAPP(hAPP(c_COMBC(_1662397, _1662397, tc_HOL_Obool), c_fequal), _1662401))), _1662399)))], (27655 ^ _773908) ^ [_1274243] : [27657 ^ _773908 : [(27660 ^ _773908) ^ [_1274353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27656 ^ [_1274243, _1274353]), _1274353))], (27658 ^ _773908) ^ [_1274319] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27656 ^ [_1274243, _1274319]), _1274243)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1274243)))], (45749 ^ _773908) ^ [_1687931, _1687933, _1687935, _1687937] : [hBOOL(hAPP(hAPP(c_member(_1687931), _1687933), hAPP(c_List_Oset(_1687931), c_List_OtakeWhile(_1687931, _1687935, _1687937)))), 45752 ^ _773908 : [(45755 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1687935, _1687933)))], (45753 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1687931), _1687933), hAPP(c_List_Oset(_1687931), _1687937))))]]], (40597 ^ _773908) ^ [_1569656, _1569658, _1569660, _1569662, _1569664, _1569666] : [-(_1569656 = _1569658), -(hAPP(hAPP(c_List_Olist__update(_1569660, hAPP(hAPP(c_List_Olist__update(_1569660, _1569662), _1569656), _1569664)), _1569658), _1569666) = hAPP(hAPP(c_List_Olist__update(_1569660, hAPP(hAPP(c_List_Olist__update(_1569660, _1569662), _1569658), _1569666)), _1569656), _1569664))], (18265 ^ _773908) ^ [_1089287] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089287) = 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(_1089287)))))], (46643 ^ _773908) ^ [_1707659, _1707661, _1707663, _1707665, _1707667] : [class_Orderings_Olinorder(_1707659), 46649 ^ _773908 : [(46652 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707659), hAPP(_1707665, _1707667)), hAPP(_1707665, 46648 ^ [_1707659, _1707661, _1707663, _1707665, _1707667])))], (46650 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1707661), 46648 ^ [_1707659, _1707661, _1707663, _1707665, _1707667]), hAPP(c_List_Oset(_1707661), _1707663))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707661, _1707659, _1707665), _1707667), _1707663) = hAPP(hAPP(c_List_Olist_OCons(_1707661), _1707667), _1707663))], (14517 ^ _773908) ^ [_1019358] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019358, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1019358)], (19353 ^ _773908) ^ [_1108086, _1108088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108086)), c_Int_OBit1(_1108088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108086), _1108088)))], (44355 ^ _773908) ^ [_1658217, _1658219, _1658221] : [hBOOL(hAPP(c_List_Odistinct(_1658217), _1658219)), -(hBOOL(hAPP(c_List_Odistinct(_1658217), hAPP(c_List_Ofilter(_1658217, _1658221), _1658219))))], (41374 ^ _773908) ^ [_1589354, _1589356] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1589354, _1589356) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1589354), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1589356), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45743 ^ _773908) ^ [_1687828, _1687830, _1687832] : [hBOOL(hAPP(c_List_Odistinct(_1687828), _1687830)), -(hBOOL(hAPP(c_List_Odistinct(_1687828), c_List_OtakeWhile(_1687828, _1687832, _1687830))))], (19935 ^ _773908) ^ [_1117914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1117914)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117914), c_Int_OPls)))], (23734 ^ _773908) ^ [_1188444, _1188446, _1188448] : [hBOOL(hAPP(_1188444, 23735 ^ [_1188444, _1188446, _1188448])), 23738 ^ _773908 : [(23739 ^ _773908) ^ [_1188555, _1188557] : [-(hBOOL(hAPP(_1188444, hAPP(hAPP(c_Product__Type_OPair(_1188446, _1188448), _1188557), _1188555))))]]], (37133 ^ _773908) ^ [_1473664, _1473666, _1473668, _1473670, _1473672] : [-(hAPP(c_Set_Ovimage(_1473664, _1473666, _1473668), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473666, tc_HOL_Obool)), _1473670), _1473672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473664, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473664, _1473666, _1473668), _1473670)), hAPP(c_Set_Ovimage(_1473664, _1473666, _1473668), _1473672)))], (48347 ^ _773908) ^ [_1748545, _1748547, _1748549, _1748551] : [class_Orderings_Olinorder(_1748545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748545), _1748547)), hBOOL(hAPP(hAPP(c_member(_1748545), _1748549), _1748547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748545), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1748545), _1748549), _1748551)), hAPP(hAPP(c_Finite__Set_Ofold(_1748545, _1748545, c_Orderings_Oord__class_Omax(_1748545)), _1748551), _1748547))))], (27982 ^ _773908) ^ [_1280507, _1280509, _1280511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280507, tc_HOL_Obool)), _1280509), _1280511)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280507, tc_HOL_Obool)), _1280509), _1280511) = _1280509)], (16043 ^ _773908) ^ [_1048174, _1048176, _1048178, _1048180, _1048182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048174), _1048176)), 16046 ^ _773908 : [(16053 ^ _773908) ^ [] : [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), _1048176), _1048174)), _1048178)), _1048180)), _1048182)), -(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), _1048176), _1048178)), _1048180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048174), _1048178)), _1048182))))], (16047 ^ _773908) ^ [] : [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), _1048176), _1048178)), _1048180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048174), _1048178)), _1048182))), -(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), _1048176), _1048174)), _1048178)), _1048180)), _1048182)))]]], (45280 ^ _773908) ^ [_1678230, _1678232, _1678234] : [-(hBOOL(hAPP(hAPP(c_member(_1678230), _1678232), hAPP(c_List_Oset(_1678230), _1678234)))), -(c_List_Oremdups(_1678230, hAPP(hAPP(c_List_Olist_OCons(_1678230), _1678232), _1678234)) = hAPP(hAPP(c_List_Olist_OCons(_1678230), _1678232), c_List_Oremdups(_1678230, _1678234)))], (31263 ^ _773908) ^ [_1348279, _1348281, _1348283, _1348285, _1348287, _1348289] : [hBOOL(hAPP(hAPP(c_member(_1348279), _1348281), _1348283)), hBOOL(hAPP(hAPP(_1348285, _1348281), _1348287)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1348279, tc_fun(_1348289, tc_HOL_Obool)), _1348283), _1348285), _1348287)))], (7388 ^ _773908) ^ [_893426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893426)), -(_893426 = hAPP(c_Nat_OSuc, 7391 ^ [_893426]))], (26303 ^ _773908) ^ [_1242035, _1242037, _1242039, _1242041, _1242043, _1242045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1242035, _1242035)), hAPP(hAPP(c_Product__Type_OPair(_1242035, _1242035), _1242037), _1242039)), hAPP(hAPP(c_Relation_Oinv__image(_1242041, _1242035), _1242043), _1242045))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1242041, _1242041)), hAPP(hAPP(c_Product__Type_OPair(_1242041, _1242041), hAPP(_1242045, _1242037)), hAPP(_1242045, _1242039))), _1242043)))], (10743 ^ _773908) ^ [_952126, _952128, _952130, _952132] : [-(hAPP(hAPP(c_Nat_Ocompow(_952126, _952126), _952128), hAPP(hAPP(c_Nat_Ocompow(_952126, _952126), _952130), _952132)) = hAPP(hAPP(c_Nat_Ocompow(_952126, _952126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952130), _952128)), _952132))], (23724 ^ _773908) ^ [_1188243, _1188245, _1188247, _1188249, _1188251, _1188253] : [-(hAPP(hAPP(c_Product__Type_OPair(_1188243, _1188245), _1188247), _1188249) = hAPP(hAPP(c_Product__Type_OPair(_1188243, _1188245), _1188251), _1188253)), _1188247 = _1188251, _1188249 = _1188253], (24125 ^ _773908) ^ [_1195505, _1195507, _1195509] : [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), _1195505), _1195507))), -(hBOOL(hAPP(hAPP(_1195509, _1195505), _1195507))), 24132 ^ _773908 : [(24135 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1195509, 24130 ^ [_1195505, _1195507, _1195509]), 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)))), 24131 ^ [_1195505, _1195507, _1195509])))), -(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), 24130 ^ [_1195505, _1195507, _1195509]), 24131 ^ [_1195505, _1195507, _1195509])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24131 ^ [_1195505, _1195507, _1195509]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24145 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1195509, 24130 ^ [_1195505, _1195507, _1195509]), 24131 ^ [_1195505, _1195507, _1195509]))], (24133 ^ _773908) ^ [] : [-(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), 24130 ^ [_1195505, _1195507, _1195509]), 24131 ^ [_1195505, _1195507, _1195509]))))]]], (17839 ^ _773908) ^ [_1082120, _1082122] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082120))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082120)), _1082122) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082122))], (46179 ^ _773908) ^ [_1697295, _1697297] : [-(c_Wellfounded_Owf(_1697295, c_List_Omeasures(_1697295, _1697297)))], (42259 ^ _773908) ^ [_1610765, _1610767, _1610769, _1610771, _1610773] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610765, tc_HOL_Obool)), _1610767), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610769, tc_fun(_1610765, tc_HOL_Obool)), _1610771), _1610773)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1610769, tc_fun(_1610765, tc_HOL_Obool)), _1610771), hAPP(hAPP(c_COMBB(tc_fun(_1610765, tc_HOL_Obool), tc_fun(_1610765, tc_HOL_Obool), _1610769), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610765, tc_HOL_Obool)), _1610767)), _1610773)))], (25059 ^ _773908) ^ [_1216175, _1216177, _1216179, _1216181, _1216183, _1216185, _1216187, _1216189] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1216175, _1216177), tc_prod(_1216175, _1216177))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1216175, _1216177), tc_prod(_1216175, _1216177)), hAPP(hAPP(c_Product__Type_OPair(_1216175, _1216177), _1216179), _1216181)), hAPP(hAPP(c_Product__Type_OPair(_1216175, _1216177), _1216183), _1216185))), c_Wellfounded_Olex__prod(_1216175, _1216177, _1216187, _1216189)))), 25060 ^ _773908 : [(25063 ^ _773908) ^ [] : [_1216179 = _1216183, hBOOL(hAPP(hAPP(c_member(tc_prod(_1216177, _1216177)), hAPP(hAPP(c_Product__Type_OPair(_1216177, _1216177), _1216181), _1216185)), _1216189))], (25061 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1216175, _1216175)), hAPP(hAPP(c_Product__Type_OPair(_1216175, _1216175), _1216179), _1216183)), _1216187))]]], (47606 ^ _773908) ^ [_1732229, _1732231, _1732233, _1732235, _1732237] : [-(hAPP(hAPP(c_List_Olist_OCons(_1732229), _1732231), _1732233) = hAPP(c_List_Ofilter(_1732229, _1732235), _1732237)), 47607 ^ _773908 : [(47608 ^ _773908) ^ [_1732357, _1732359] : [_1732237 = hAPP(hAPP(c_List_Oappend(_1732229), _1732359), hAPP(hAPP(c_List_Olist_OCons(_1732229), _1732231), _1732357)), 47614 ^ _773908 : [(47617 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1732235, 47613 ^ [_1732229, _1732231, _1732233, _1732235, _1732237, _1732357, _1732359])))], (47615 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732229), 47613 ^ [_1732229, _1732231, _1732233, _1732235, _1732237, _1732357, _1732359]), hAPP(c_List_Oset(_1732229), _1732359))))]], hBOOL(hAPP(_1732235, _1732231)), _1732233 = hAPP(c_List_Ofilter(_1732229, _1732235), _1732357)]]], (41955 ^ _773908) ^ [_1601325, _1601327] : [-(hAPP(hAPP(c_List_Ozip(_1601325, _1601325), _1601327), _1601327) = hAPP(hAPP(c_List_Omap(_1601325, tc_prod(_1601325, _1601325)), hAPP(hAPP(c_COMBS(_1601325, _1601325, tc_prod(_1601325, _1601325)), c_Product__Type_OPair(_1601325, _1601325)), c_COMBI(_1601325))), _1601327))], (4810 ^ _773908) ^ [_847281, _847283] : [_847283 = _847281, -(c_List_Olist_OCons(_847283) = c_List_Olist_OCons(_847281))], (32430 ^ _773908) ^ [_1375750, _1375752] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1375750, _1375752))))], (5821 ^ _773908) ^ [_866395, _866397, _866399, _866401, _866403, _866405] : [c_Hoare__Mirabelle_Ohoare__derivs(_866395, _866397, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866395)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866395), _866399), _866401), _866403)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866395), tc_HOL_Obool)))), 5828 ^ _773908 : [(5831 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_866405, 5826 ^ [_866395, _866397, _866399, _866401, _866403, _866405]), 5827 ^ [_866395, _866397, _866399, _866401, _866403, _866405]))], (5829 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_866403, 5826 ^ [_866395, _866397, _866399, _866401, _866403, _866405]), 5827 ^ [_866395, _866397, _866399, _866401, _866403, _866405])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_866395, _866397, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866395)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866395), _866399), _866401), _866405)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866395), tc_HOL_Obool)))))], (19941 ^ _773908) ^ [_1118009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118009), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1118009)), c_Int_OPls)))], (39819 ^ _773908) ^ [_1550238, _1550240, _1550242, _1550244, _1550246] : [-(_1550238 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1550240, _1550242, _1550244), _1550238), _1550246) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1550242), _1550240), tc_prod(_1550242, _1550240), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1550242), _1550240), c_List_Olist_ONil(_1550242)), _1550246), hAPP(c_Product__Type_Oprod_Oprod__case(_1550242, _1550240, tc_prod(tc_List_Olist(_1550242), _1550240)), hAPP(hAPP(c_COMBC(_1550242, tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240)), tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1550242), _1550240), tc_prod(tc_List_Olist(_1550242), _1550240)), tc_fun(tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240)), tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240))), _1550242), c_COMBB(tc_prod(tc_List_Olist(_1550242), _1550240), tc_prod(tc_List_Olist(_1550242), _1550240), _1550240)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1550242), tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240))), tc_fun(tc_prod(tc_List_Olist(_1550242), _1550240), tc_prod(tc_List_Olist(_1550242), _1550240)), _1550242), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1550242), _1550240, tc_prod(tc_List_Olist(_1550242), _1550240))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1550242), tc_List_Olist(_1550242)), tc_fun(tc_List_Olist(_1550242), tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240))), _1550242), hAPP(c_COMBB(tc_List_Olist(_1550242), tc_fun(_1550240, tc_prod(tc_List_Olist(_1550242), _1550240)), tc_List_Olist(_1550242)), c_Product__Type_OPair(tc_List_Olist(_1550242), _1550240))), c_List_Olist_OCons(_1550242))))), hAPP(c_Lazy__Sequence_Oanamorph(_1550240, _1550242, _1550244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1550238), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1550244, _1550246)))], (37794 ^ _773908) ^ [_1491861, _1491863, _1491865, _1491867, _1491869] : [c_Relation_Orefl__on(_1491861, _1491863, _1491865), c_Relation_Orefl__on(_1491861, _1491867, _1491869), -(c_Relation_Orefl__on(_1491861, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491861, tc_HOL_Obool)), _1491863), _1491867), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1491861, _1491861), tc_HOL_Obool)), _1491865), _1491869)))], (39579 ^ _773908) ^ [_1543163, _1543165, _1543167, _1543169] : [hBOOL(hAPP(hAPP(c_member(_1543163), _1543165), c_Wellfounded_Oacc(_1543163, _1543167))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1543163)), _1543169), c_Wellfounded_Oacc(tc_List_Olist(_1543163), c_List_Olistrel1(_1543163, _1543167)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1543163)), hAPP(hAPP(c_List_Olist_OCons(_1543163), _1543165), _1543169)), c_Wellfounded_Oacc(tc_List_Olist(_1543163), c_List_Olistrel1(_1543163, _1543167)))))], (4540 ^ _773908) ^ [_843004, _843006, _843008, _843010] : [-(c_List_Olast(_843010, _843006) = c_List_Olast(_843008, _843004)), _843010 = _843008, _843006 = _843004], (42882 ^ _773908) ^ [_1624661] : [-(hAPP(c_Code__Numeral_Onat__of, _1624661) = c_Code__Numeral_Onat__of__aux(_1624661, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23377 ^ _773908) ^ [_1180818] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1180818) = 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)))], (23067 ^ _773908) ^ [_1174477, _1174479, _1174481] : [class_Int_Onumber__ring(_1174477), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1174477), _1174479), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1174481))) = hAPP(hAPP(c_HOL_OLet(_1174477, _1174477), hAPP(hAPP(c_Power_Opower__class_Opower(_1174477), _1174479), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174481))), hAPP(hAPP(c_COMBS(_1174477, _1174477, _1174477), c_Groups_Otimes__class_Otimes(_1174477)), c_COMBI(_1174477))))], (22849 ^ _773908) ^ [_1170289, _1170291] : [_1170289 = _1170291, -(c_Random_Oinc__shift(_1170289, _1170291) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (43721 ^ _773908) ^ [_1643401, _1643403, _1643405] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643401, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1643401, tc_HOL_Obool)), _1643403), _1643405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1643401, tc_HOL_Obool)), _1643403), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643401, tc_HOL_Obool), _1643405)))], (44269 ^ _773908) ^ [_1656501, _1656503, _1656505, _1656507, _1656509] : [c_Fun_Oinj__on(_1656501, _1656503, _1656505, hAPP(hAPP(c_Set_Oinsert(_1656501), _1656507), hAPP(c_List_Oset(_1656501), _1656509))), -(hAPP(hAPP(c_List_Omap(_1656501, _1656503), _1656505), hAPP(c_List_OremoveAll(_1656501, _1656507), _1656509)) = hAPP(c_List_OremoveAll(_1656503, hAPP(_1656505, _1656507)), hAPP(hAPP(c_List_Omap(_1656501, _1656503), _1656505), _1656509)))], (25479 ^ _773908) ^ [_1224709, _1224711] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224709), _1224711)), _1224711) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1224709), _1224711))], (16625 ^ _773908) ^ [_1059188, _1059190] : [class_Groups_Oordered__ab__group__add__abs(_1059188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059188), c_Groups_Ozero__class_Ozero(_1059188)), _1059190)), -(hAPP(c_Groups_Oabs__class_Oabs(_1059188), _1059190) = _1059190)], (47138 ^ _773908) ^ [_1720338, _1720340] : [-(c_Transitive__Closure_Otrancl(_1720338, _1720340) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1720338, _1720338), tc_HOL_Obool)), _1720340), hAPP(hAPP(c_Relation_Orel__comp(_1720338, _1720338, _1720338), c_Transitive__Closure_Otrancl(_1720338, _1720340)), _1720340)))], (13119 ^ _773908) ^ [_994084, _994086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994084)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994084), _994086)))], (7283 ^ _773908) ^ [_891778, _891780, _891782, _891784, _891786] : [c_Com_Ocom_OSemi(_891778, _891780) = c_Com_Ocom_OCall(_891782, _891784, _891786)], (21511 ^ _773908) ^ [_1145876, _1145878, _1145880, _1145882] : [class_Fields_Olinordered__field(_1145876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145876), _1145878), _1145880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145876), c_Groups_Ozero__class_Ozero(_1145876)), _1145882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145876), c_Groups_Ozero__class_Ozero(_1145876)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145876), _1145880), _1145878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145876), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145876), _1145882), _1145880)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145876), _1145882), _1145878))))], (23602 ^ _773908) ^ [_1185535, _1185537] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185535), _1185537)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185535), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1185537)))], (6344 ^ _773908) ^ [_876756, _876758, _876760, _876762] : [class_Groups_Ocancel__semigroup__add(_876756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876756), _876758), _876760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876756), _876762), _876760), -(_876758 = _876762)], (48249 ^ _773908) ^ [_1746498, _1746500, _1746502, _1746504, _1746506, _1746508] : [c_Finite__Set_Ofun__left__comm__idem(_1746498, _1746500, _1746502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1746498), _1746504)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1746498, _1746500, _1746502), _1746506), hAPP(hAPP(c_Set_Oinsert(_1746498), _1746508), _1746504)) = hAPP(hAPP(_1746502, _1746508), hAPP(hAPP(c_Finite__Set_Ofold(_1746498, _1746500, _1746502), _1746506), _1746504)))], (17067 ^ _773908) ^ [_1068092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068092)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1068092 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47685 ^ _773908) ^ [_1734597, _1734599, _1734601] : [-(hBOOL(hAPP(hAPP(c_member(_1734597), _1734599), c_Wellfounded_Oacc(_1734597, _1734601)))), 47689 ^ _773908 : [(47692 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1734597), 47688 ^ [_1734597, _1734599, _1734601]), c_Wellfounded_Oacc(_1734597, _1734601)))], (47690 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734597, _1734597)), hAPP(hAPP(c_Product__Type_OPair(_1734597, _1734597), 47688 ^ [_1734597, _1734599, _1734601]), _1734599)), _1734601)))]]], (43933 ^ _773908) ^ [_1648528, _1648530, _1648532] : [class_Complete__Lattice_Ocomplete__lattice(_1648528), -(c_Complete__Lattice_OSup__class_OSup(_1648528, hAPP(hAPP(c_Set_Oinsert(_1648528), _1648530), hAPP(hAPP(c_Set_Oinsert(_1648528), _1648532), c_Orderings_Obot__class_Obot(tc_fun(_1648528, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1648528), _1648530), _1648532))], (43616 ^ _773908) ^ [_1641019, _1641021] : [hBOOL(hAPP(c_List_Odistinct(_1641019), _1641021)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1641019, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1641019), tc_fun(_1641019, tc_HOL_Obool)), c_List_Oset(_1641019)), c_Enum_Osublists(_1641019, _1641021)))))], (19261 ^ _773908) ^ [_1106456, _1106458] : [class_Int_Onumber__ring(_1106456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1106458)), -(hBOOL(hAPP(hAPP(c_member(_1106456), hAPP(c_Int_Onumber__class_Onumber__of(_1106456), _1106458)), c_Nat_Osemiring__1__class_ONats(_1106456))))], (20261 ^ _773908) ^ [_1123607] : [class_Rings_Osemiring__1(_1123607), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123607), c_Groups_Oone__class_Oone(_1123607)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1123607))], (13698 ^ _773908) ^ [_1004609, _1004611, _1004613] : [class_Divides_Osemiring__div(_1004609), -(c_Divides_Odiv__class_Omod(_1004609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004609), _1004611), _1004613), _1004613) = c_Groups_Ozero__class_Ozero(_1004609))], (4116 ^ _773908) ^ [_836090, _836092] : [_836092 = _836090, -(c_Nitpick_Odenom(_836092) = c_Nitpick_Odenom(_836090))], (18929 ^ _773908) ^ [_1100954] : [class_Int_Onumber__ring(_1100954), -(c_Int_Oiszero(_1100954, hAPP(c_Int_Onumber__class_Onumber__of(_1100954), c_Int_OPls)))], (23803 ^ _773908) ^ [_1189984, _1189986, _1189988, _1189990, _1189992] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189984, _1189986), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189988), _1189990))), -(_1189986 = 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)), _1189992)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189984, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189986), _1189992)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1189988), _1189992)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189986), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189988, _1189992))), _1189990)))))], (26347 ^ _773908) ^ [_1244319] : [-(c_Wellfounded_Omeasure(_1244319) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1244319), c_Wellfounded_Oless__than))], (13241 ^ _773908) ^ [_996226, _996228, _996230] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996226), _996228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996226), _996230), -(_996226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_996228 = _996230)], (7151 ^ _773908) ^ [_889609, _889611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889609), _889611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889611), hAPP(c_Nat_OSuc, _889609))))], (7271 ^ _773908) ^ [_891481, _891483, _891485, _891487] : [c_Com_Ocom_OCall(_891481, _891483, _891485) = hAPP(c_Com_Ocom_OBODY, _891487)], (34141 ^ _773908) ^ [_1409480, _1409482] : [-(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)), _1409480), _1409482))], (23093 ^ _773908) ^ [_1175068, _1175070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175068), 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)), _1175070)), -(c_Divides_OnegDivAlg(_1175068, _1175070) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1175068), _1175070)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175068, _1175070)))], (18785 ^ _773908) ^ [_1098951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098951), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098951)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45447 ^ _773908) ^ [_1681721, _1681723] : [-(c_Fun_Oinj__on(tc_List_Olist(_1681721), tc_List_Olist(_1681721), c_List_Orev(_1681721), _1681723))], (32081 ^ _773908) ^ [_1368784, _1368786] : [-(c_Relation_OId__on(_1368784, _1368786) = hAPP(c_Product__Type_Oprod_Oprod__case(_1368784, _1368784, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1368784, tc_HOL_Obool, tc_fun(_1368784, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368784, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1368784, tc_HOL_Obool)), _1368784), c_COMBC(_1368784, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368784, tc_HOL_Obool), tc_fun(_1368784, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1368784), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1368784), c_fconj)), c_fequal))), _1368786)))], (26858 ^ _773908) ^ [_1257794, _1257796, _1257798] : [_1257796 = _1257798, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1257794, _1257794)), hAPP(hAPP(c_Product__Type_OPair(_1257794, _1257794), _1257796), _1257798)), c_Relation_OId(_1257794))))], (30339 ^ _773908) ^ [_1328377, _1328379] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1328377), _1328379))), -(hAPP(c_Finite__Set_Ocard(_1328377), _1328379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13334 ^ _773908) ^ [_997818, _997820] : [class_Rings_Olinordered__idom(_997818), 13337 ^ _773908 : [(13344 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997818), _997820), c_Groups_Ozero__class_Ozero(_997818))), -(c_Groups_Osgn__class_Osgn(_997818, _997820) = hAPP(c_Groups_Ouminus__class_Ouminus(_997818), c_Groups_Oone__class_Oone(_997818)))], (13338 ^ _773908) ^ [] : [c_Groups_Osgn__class_Osgn(_997818, _997820) = hAPP(c_Groups_Ouminus__class_Ouminus(_997818), c_Groups_Oone__class_Oone(_997818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997818), _997820), c_Groups_Ozero__class_Ozero(_997818))))]]], (41963 ^ _773908) ^ [_1601807, _1601809, _1601811, _1601813, _1601815, _1601817, _1601819, _1601821] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1601807, _1601809), _1601811), _1601813), hAPP(hAPP(c_List_Ozip(_1601807, _1601809), _1601815), hAPP(hAPP(c_List_Omap(_1601817, _1601809), _1601819), _1601821))) = hAPP(hAPP(c_List_Omap(tc_prod(_1601807, _1601817), _1601811), hAPP(c_Product__Type_Oprod_Oprod__case(_1601807, _1601817, _1601811), hAPP(hAPP(c_COMBB(tc_fun(_1601817, tc_prod(_1601807, _1601809)), tc_fun(_1601817, _1601811), _1601807), hAPP(c_COMBB(tc_prod(_1601807, _1601809), _1601811, _1601817), _1601813)), hAPP(hAPP(c_COMBC(_1601807, tc_fun(_1601817, _1601809), tc_fun(_1601817, tc_prod(_1601807, _1601809))), hAPP(hAPP(c_COMBB(tc_fun(_1601809, tc_prod(_1601807, _1601809)), tc_fun(tc_fun(_1601817, _1601809), tc_fun(_1601817, tc_prod(_1601807, _1601809))), _1601807), c_COMBB(_1601809, tc_prod(_1601807, _1601809), _1601817)), c_Product__Type_OPair(_1601807, _1601809))), _1601819)))), hAPP(hAPP(c_List_Ozip(_1601807, _1601817), _1601815), _1601821)))], (26697 ^ _773908) ^ [_1254157] : [-(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)), _1254157)) = _1254157)], (51548 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (50436 ^ _773908) ^ [_1795071, _1795073] : [c_Wellfounded_Oacyclic(_1795071, _1795073), -(c_Relation_Oantisym(_1795071, c_Transitive__Closure_Ortrancl(_1795071, _1795073)))], (25673 ^ _773908) ^ [] : [-(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)))))], (42277 ^ _773908) ^ [_1611479, _1611481, _1611483, _1611485, _1611487] : [-(hAPP(c_List_Orotate(_1611479, _1611481), hAPP(hAPP(c_List_Omap(_1611483, _1611479), _1611485), _1611487)) = hAPP(hAPP(c_List_Omap(_1611483, _1611479), _1611485), hAPP(c_List_Orotate(_1611483, _1611481), _1611487)))], (51434 ^ _773908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (6930 ^ _773908) ^ [_886135, _886137] : [-(_886135 = _886137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886135), _886137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886137), _886135)))], (41055 ^ _773908) ^ [_1582614, _1582616, _1582618] : [hBOOL(hAPP(c_List_Odistinct(_1582614), _1582616)), -(hBOOL(hAPP(c_List_Odistinct(_1582614), c_List_Osublist(_1582614, _1582616, _1582618))))], (51844 ^ _773908) ^ [_1817622] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1817622)))], (2092 ^ _773908) ^ [_804282, _804284] : [_804284 = _804282, -(c_Nat_Ofunpow(_804284) = c_Nat_Ofunpow(_804282))], (51840 ^ _773908) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (28428 ^ _773908) ^ [_1290843, _1290845, _1290847] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290843, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290843, tc_HOL_Obool)), _1290845), _1290847)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290843, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290843, tc_HOL_Obool)), _1290845)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290843, tc_HOL_Obool)), _1290847)))], (27372 ^ _773908) ^ [_1268130, _1268132, _1268134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268130), _1268132)), 27375 ^ _773908 : [(27382 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268130), _1268134)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268130, tc_HOL_Obool)), _1268134), _1268132))))], (27376 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1268130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268130, tc_HOL_Obool)), _1268134), _1268132))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1268130), _1268134)))]]], (45455 ^ _773908) ^ [_1681889, _1681891, _1681893, _1681895, _1681897] : [c_List_Olist__all2(_1681889, _1681891, _1681893, _1681895, hAPP(c_List_Orev(_1681891), _1681897)), -(c_List_Olist__all2(_1681889, _1681891, _1681893, hAPP(c_List_Orev(_1681889), _1681895), _1681897))], (40603 ^ _773908) ^ [_1569736, _1569738, _1569740, _1569742, _1569744] : [-(hAPP(hAPP(c_List_Olist__update(_1569736, hAPP(hAPP(c_List_Olist__update(_1569736, _1569738), _1569740), _1569742)), _1569740), _1569744) = hAPP(hAPP(c_List_Olist__update(_1569736, _1569738), _1569740), _1569744))], (51556 ^ _773908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (33230 ^ _773908) ^ [_1391240, _1391242, _1391244, _1391246, _1391248, _1391250] : [c_Fun_Oinj__on(_1391240, _1391242, _1391244, _1391246), hBOOL(hAPP(hAPP(c_member(_1391240), _1391248), _1391246)), hBOOL(hAPP(hAPP(c_member(_1391240), _1391250), _1391246)), 33241 ^ _773908 : [(33248 ^ _773908) ^ [] : [_1391248 = _1391250, -(hAPP(_1391244, _1391248) = hAPP(_1391244, _1391250))], (33242 ^ _773908) ^ [] : [hAPP(_1391244, _1391248) = hAPP(_1391244, _1391250), -(_1391248 = _1391250)]]], (41081 ^ _773908) ^ [_1583077, _1583079, _1583081] : [-(hAPP(hAPP(c_List_Odrop(_1583077), hAPP(c_Nat_OSuc, _1583079)), _1583081) = hAPP(hAPP(c_List_Odrop(_1583077), _1583079), hAPP(c_List_Otl(_1583077), _1583081)))], (25829 ^ _773908) ^ [_1231588, _1231590, _1231592] : [class_Lattices_Osemilattice__sup(_1231588), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231588), _1231590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231588), _1231592), _1231590))))], (50919 ^ _773908) ^ [_1804016, _1804018, _1804020, _1804022] : [hAPP(c_Set_Oimage(_1804016, _1804018, _1804020), c_Orderings_Otop__class_Otop(tc_fun(_1804016, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804018, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1804016, _1804018, _1804020), hAPP(c_Set_Oimage(_1804018, _1804016, c_Hilbert__Choice_Oinv__into(_1804016, _1804018, c_Orderings_Otop__class_Otop(tc_fun(_1804016, tc_HOL_Obool)), _1804020)), _1804022)) = _1804022)], (43999 ^ _773908) ^ [_1650253, _1650255, _1650257, _1650259] : [44000 ^ _773908 : [(44001 ^ _773908) ^ [_1650307] : [hBOOL(hAPP(hAPP(_1650257, _1650259), _1650307))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1650253, _1650255, _1650257), _1650259)))], (47213 ^ _773908) ^ [_1722252, _1722254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722252, _1722252), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1722252, _1722254)), hAPP(hAPP(c_Product__Type_OSigma(_1722252, _1722252), hAPP(c_Relation_OField(_1722252), _1722254)), hAPP(c_COMBK(tc_fun(_1722252, tc_HOL_Obool), _1722252), hAPP(c_Relation_OField(_1722252), _1722254))))))], (6279 ^ _773908) ^ [_875674, _875676] : [hBOOL(hAPP(_875674, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6285 ^ _773908 : [(6288 ^ _773908) ^ [] : [hBOOL(hAPP(_875674, hAPP(c_Nat_OSuc, 6284 ^ [_875674, _875676])))], (6286 ^ _773908) ^ [] : [-(hBOOL(hAPP(_875674, 6284 ^ [_875674, _875676])))]], -(hBOOL(hAPP(_875674, _875676)))], (41965 ^ _773908) ^ [_1601988, _1601990, _1601992, _1601994, _1601996, _1601998] : [-(hAPP(hAPP(c_List_Ozip(_1601988, _1601990), _1601992), hAPP(hAPP(c_List_Omap(_1601994, _1601990), _1601996), _1601998)) = hAPP(hAPP(c_List_Omap(tc_prod(_1601988, _1601994), tc_prod(_1601988, _1601990)), hAPP(c_Product__Type_Oprod_Oprod__case(_1601988, _1601994, tc_prod(_1601988, _1601990)), hAPP(hAPP(c_COMBC(_1601988, tc_fun(_1601994, _1601990), tc_fun(_1601994, tc_prod(_1601988, _1601990))), hAPP(hAPP(c_COMBB(tc_fun(_1601990, tc_prod(_1601988, _1601990)), tc_fun(tc_fun(_1601994, _1601990), tc_fun(_1601994, tc_prod(_1601988, _1601990))), _1601988), c_COMBB(_1601990, tc_prod(_1601988, _1601990), _1601994)), c_Product__Type_OPair(_1601988, _1601990))), _1601996))), hAPP(hAPP(c_List_Ozip(_1601988, _1601994), _1601992), _1601998)))], (1884 ^ _773908) ^ [_800444, _800446] : [-(class_Power_Opower(_800444)), _800446 = _800444, class_Power_Opower(_800446)], (10353 ^ _773908) ^ [_945599, _945601, _945603] : [class_Orderings_Oorder(_945599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945599), _945601), _945603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945599), _945601), _945603))), -(_945601 = _945603)], (30405 ^ _773908) ^ [_1329537, _1329539, _1329541] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329537), _1329539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1329537, tc_HOL_Obool)), _1329541), _1329539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329537), _1329541)), hAPP(c_Finite__Set_Ocard(_1329537), _1329539))))], (9003 ^ _773908) ^ [_923371] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923371)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923371))], (45497 ^ _773908) ^ [_1682690, _1682692, _1682694] : [_1682692 = hAPP(c_List_Orev(_1682690), _1682694), -(hAPP(c_List_Orev(_1682690), _1682692) = _1682694)], (50721 ^ _773908) ^ [_1799972, _1799974] : [-(c_Relation_Osym(_1799972, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1799972, _1799972), tc_HOL_Obool)), _1799974), hAPP(c_Relation_Oconverse(_1799972, _1799972), _1799974))))], (31542 ^ _773908) ^ [_1354785, _1354787] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1354785, _1354787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1354787), hAPP(c_Nat_OSuc, _1354785)))], (5094 ^ _773908) ^ [_851723, _851725, _851727, _851729] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_851729, _851725) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_851727, _851723)), _851729 = _851727, _851725 = _851723], (51442 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (34518 ^ _773908) ^ [_1416924, _1416926, _1416928] : [class_Orderings_Olinorder(_1416924), 34521 ^ _773908 : [(34528 ^ _773908) ^ [] : [_1416926 = _1416928, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1416924), _1416926) = hAPP(c_SetInterval_Oord__class_OatLeast(_1416924), _1416928))], (34522 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1416924), _1416926) = hAPP(c_SetInterval_Oord__class_OatLeast(_1416924), _1416928), -(_1416926 = _1416928)]]], (18655 ^ _773908) ^ [_1096255, _1096257, _1096259, _1096261] : [hBOOL(hAPP(hAPP(c_member(_1096255), _1096257), _1096259)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096255, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1096255), _1096257), _1096261)), _1096259) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096255, tc_HOL_Obool)), _1096261), _1096259))], (36283 ^ _773908) ^ [_1455169, _1455171, _1455173, _1455175] : [hAPP(c_Set_Oimage(_1455169, _1455171, _1455173), c_Orderings_Otop__class_Otop(tc_fun(_1455169, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1455171, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455171, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1455171, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1455169, _1455171, _1455173), _1455175))), hAPP(c_Set_Oimage(_1455169, _1455171, _1455173), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1455169, tc_HOL_Obool)), _1455175)))))], (27282 ^ _773908) ^ [_1266611] : [c_Nat__Transfer_Onat__set(_1266611), 27285 ^ _773908 : [(27292 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1266611))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1266611)))], (27286 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1266611)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1266611))))]]], (23025 ^ _773908) ^ [_1173730, _1173732, _1173734, _1173736, _1173738] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1173730, _1173732, _1173734), _1173736), _1173738)), 23028 ^ _773908 : [(23031 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1173734, _1173738)))], (23029 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1173732, _1173736), _1173738)))]]], (6870 ^ _773908) ^ [_885107, _885109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885107), _885109)), _885109 = _885107], (46463 ^ _773908) ^ [_1703102, _1703104, _1703106, _1703108, _1703110, _1703112] : [-(_1703102 = c_Orderings_Obot__class_Obot(tc_fun(_1703104, tc_HOL_Obool))), 46469 ^ _773908 : [(46472 ^ _773908) ^ [] : [c_Fun_Oinj__on(_1703106, _1703108, _1703110, hAPP(_1703112, 46468 ^ [_1703102, _1703104, _1703106, _1703108, _1703110, _1703112]))], (46470 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703104), 46468 ^ [_1703102, _1703104, _1703106, _1703108, _1703110, _1703112]), _1703102)))]], -(c_Fun_Oinj__on(_1703106, _1703108, _1703110, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1703104, tc_fun(_1703106, tc_HOL_Obool)), _1703102), _1703112)))], (20565 ^ _773908) ^ [_1129167] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1129167, 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, _1129167, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (42293 ^ _773908) ^ [_1611841, _1611843, _1611845] : [-(hAPP(hAPP(c_List_Omap(_1611841, _1611843), _1611845), c_List_Olist_ONil(_1611841)) = c_List_Olist_ONil(_1611843))], (23558 ^ _773908) ^ [_1184704] : [-(c_Hoare__Mirabelle_OMGT(_1184704) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1184704), c_Natural_Oevalc(_1184704)))], (35072 ^ _773908) ^ [_1429694, _1429696] : [class_Groups_Oordered__ab__group__add(_1429694), -(hAPP(c_Set_Oimage(_1429694, _1429694, c_Groups_Ouminus__class_Ouminus(_1429694)), hAPP(c_SetInterval_Oord__class_OatLeast(_1429694), _1429696)) = hAPP(c_SetInterval_Oord__class_OatMost(_1429694), hAPP(c_Groups_Ouminus__class_Ouminus(_1429694), _1429696)))], (51812 ^ _773908) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (16401 ^ _773908) ^ [_1055079, _1055081, _1055083] : [class_Groups_Oordered__ab__group__add__abs(_1055079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055079), hAPP(c_Groups_Oabs__class_Oabs(_1055079), _1055081)), _1055083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055079), _1055081), _1055083)))], (43310 ^ _773908) ^ [_1634245, _1634247, _1634249, _1634251, _1634253] : [class_Orderings_Olinorder(_1634245), -(hBOOL(hAPP(hAPP(c_member(_1634245), hAPP(_1634247, _1634249)), hAPP(c_Set_Oimage(_1634251, _1634245, _1634247), hAPP(c_List_Oset(_1634251), _1634253))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1634251, _1634245, _1634247, _1634249, _1634253) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1634251, _1634245, _1634247), _1634249), _1634253))], (28178 ^ _773908) ^ [_1284586, _1284588, _1284590] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284586, tc_HOL_Obool)), _1284588), _1284590) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284586, tc_HOL_Obool)), _1284590), _1284588))], (8371 ^ _773908) ^ [_911857, _911859, _911861] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911857), _911859)), _911861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911859), _911861)))], (32910 ^ _773908) ^ [_1385084, _1385086, _1385088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385084)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385086), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1385088)), 32920 ^ _773908 : [(32926 ^ _773908) ^ [] : [-(_1385086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32922 ^ [_1385084, _1385086, _1385088]), 32919 ^ [_1385084, _1385086, _1385088]))], (32924 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32922 ^ [_1385084, _1385086, _1385088]), _1385088)))], (32921 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32919 ^ [_1385084, _1385086, _1385088]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1385084))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385086), _1385084) = _1385086)], (18873 ^ _773908) ^ [_1100229] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1100229) = c_Int_OPls)], (47965 ^ _773908) ^ [_1740454, _1740456, _1740458] : [-(c_List_Olist__ex(_1740454, _1740456, _1740458)), 47966 ^ _773908 : [(47967 ^ _773908) ^ [_1740519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740519), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740454)), _1740458))), hBOOL(hAPP(_1740456, hAPP(hAPP(c_List_Onth(_1740454), _1740458), _1740519)))]]], (33989 ^ _773908) ^ [_1406050, _1406052, _1406054, _1406056, _1406058, _1406060, _1406062] : [class_Groups_Oab__semigroup__mult(_1406050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406052), _1406054)), c_Fun_Oinj__on(_1406052, _1406056, _1406058, _1406054), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406050, _1406056, c_Groups_Otimes__class_Otimes(_1406050)), _1406060), _1406062), hAPP(c_Set_Oimage(_1406052, _1406056, _1406058), _1406054)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406050, _1406052, c_Groups_Otimes__class_Otimes(_1406050)), hAPP(c_Fun_Ocomp(_1406056, _1406050, _1406052, _1406060), _1406058)), _1406062), _1406054))], (16187 ^ _773908) ^ [_1051235, _1051237, _1051239, _1051241, _1051243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051235), _1051237)), 16190 ^ _773908 : [(16197 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051241), 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), _1051237), _1051235)), _1051239)), _1051243))), -(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), _1051235), _1051239)), _1051241)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051237), _1051239)), _1051243))))], (16191 ^ _773908) ^ [] : [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), _1051235), _1051239)), _1051241)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051237), _1051239)), _1051243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051241), 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), _1051237), _1051235)), _1051239)), _1051243))))]]], (33446 ^ _773908) ^ [_1395173, _1395175, _1395177, _1395179, _1395181, _1395183] : [c_Fun_Oinj__on(_1395173, _1395175, hAPP(c_Fun_Ocomp(_1395177, _1395175, _1395173, _1395179), _1395181), _1395183), -(c_Fun_Oinj__on(_1395177, _1395175, _1395179, hAPP(c_Set_Oimage(_1395173, _1395177, _1395181), _1395183)))], (17551 ^ _773908) ^ [_1076844, _1076846] : [class_Power_Opower(_1076844), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076844), _1076846), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1076844))], (4790 ^ _773908) ^ [_846975, _846977, _846979, _846981, _846983, _846985] : [-(c_Lazy__Sequence_Oanamorph(_846985, _846981, _846977) = c_Lazy__Sequence_Oanamorph(_846983, _846979, _846975)), _846985 = _846983, _846981 = _846979, _846977 = _846975], (26165 ^ _773908) ^ [_1238173, _1238175, _1238177] : [class_Lattices_Osemilattice__sup(_1238173), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238173), _1238175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238173), _1238175), _1238177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238173), _1238175), _1238177))], (46782 ^ _773908) ^ [_1711274, _1711276, _1711278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711274, _1711274), tc_HOL_Obool)), _1711276), _1711278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711274, _1711274), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1711274, _1711276)), c_Transitive__Closure_Ortrancl(_1711274, _1711278))))], (18639 ^ _773908) ^ [_1095947, _1095949, _1095951, _1095953] : [-(hBOOL(hAPP(hAPP(c_member(_1095947), _1095949), _1095951))), 18642 ^ _773908 : [(18649 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095947, tc_HOL_Obool)), _1095951), _1095953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095947, tc_HOL_Obool)), _1095951), hAPP(hAPP(c_Set_Oinsert(_1095947), _1095949), _1095953))))], (18643 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095947, tc_HOL_Obool)), _1095951), hAPP(hAPP(c_Set_Oinsert(_1095947), _1095949), _1095953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095947, tc_HOL_Obool)), _1095951), _1095953)))]]], (43829 ^ _773908) ^ [_1645846, _1645848] : [-(hAPP(c_Relation_ODomain(_1645846, _1645848), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1645846, _1645848), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1645846, tc_HOL_Obool)))], (31302 ^ _773908) ^ [_1349115, _1349117, _1349119, _1349121, _1349123, _1349125] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349115, tc_fun(_1349117, tc_HOL_Obool)), _1349119), hAPP(c_Fun_Ocomp(_1349121, tc_fun(_1349117, tc_HOL_Obool), _1349115, _1349123), _1349125)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349121, tc_fun(_1349117, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1349115, _1349121, _1349125), _1349119)), _1349123))], (45345 ^ _773908) ^ [_1679337, _1679339] : [class_Orderings_Olinorder(_1679337), 45348 ^ _773908 : [(45349 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1679337, _1679339), 45352 ^ _773908 : [(45353 ^ _773908) ^ [_1679508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679508), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679337)), _1679339))), 45356 ^ _773908 : [(45357 ^ _773908) ^ [_1679625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679625), _1679508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1679337), hAPP(hAPP(c_List_Onth(_1679337), _1679339), _1679625)), hAPP(hAPP(c_List_Onth(_1679337), _1679339), _1679508))))]]]]], (45363 ^ _773908) ^ [] : [45365 ^ _773908 : [(45371 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1679337), hAPP(hAPP(c_List_Onth(_1679337), _1679339), 45367 ^ [_1679337, _1679339])), hAPP(hAPP(c_List_Onth(_1679337), _1679339), 45364 ^ [_1679337, _1679339])))], (45369 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45367 ^ [_1679337, _1679339]), 45364 ^ [_1679337, _1679339])))], (45366 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45364 ^ [_1679337, _1679339]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679337)), _1679339))))]], -(c_List_Olinorder__class_Osorted(_1679337, _1679339))]]], (26774 ^ _773908) ^ [_1255741, _1255743, _1255745, _1255747] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255741, tc_fun(_1255741, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1255741, tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_fun(_1255741, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1255741, tc_fun(tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_fun(_1255741, tc_HOL_Obool)), _1255741), c_COMBC(_1255741, tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1255741, tc_prod(_1255741, _1255741)), tc_fun(_1255741, tc_fun(tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_HOL_Obool)), _1255741), hAPP(c_COMBB(tc_prod(_1255741, _1255741), tc_fun(tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool), tc_HOL_Obool), _1255741), c_member(tc_prod(_1255741, _1255741)))), c_Product__Type_OPair(_1255741, _1255741)))), _1255743)), c_fequal), _1255745), _1255747)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1255741, _1255741)), hAPP(hAPP(c_Product__Type_OPair(_1255741, _1255741), _1255745), _1255747)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1255741, _1255741), tc_HOL_Obool)), _1255743), c_Relation_OId(_1255741)))))], (39166 ^ _773908) ^ [_1533049, _1533051, _1533053, _1533055] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533049), tc_List_Olist(_1533049))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533049), tc_List_Olist(_1533049)), _1533051), _1533053)), c_List_Olex(_1533049, _1533055))), 39169 ^ _773908 : [(39172 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533049)), _1533051) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533049)), _1533053))], (39170 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533049), tc_List_Olist(_1533049))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533049), tc_List_Olist(_1533049)), _1533051), _1533053)), c_List_Olexord(_1533049, _1533055))))]]], (17201 ^ _773908) ^ [_1070647, _1070649, _1070651, _1070653] : [class_Rings_Olinordered__semidom(_1070647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070649), _1070651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070647), c_Groups_Ozero__class_Ozero(_1070647)), _1070653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070647), _1070653), c_Groups_Oone__class_Oone(_1070647))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070647), hAPP(hAPP(c_Power_Opower__class_Opower(_1070647), _1070653), _1070651)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070647), _1070653), _1070649))))], (4386 ^ _773908) ^ [_840641, _840643, _840645, _840647] : [-(c_New__DSequence_Oneg__single(_840647, _840643) = c_New__DSequence_Oneg__single(_840645, _840641)), _840647 = _840645, _840643 = _840641], (27842 ^ _773908) ^ [_1277892, _1277894, _1277896, _1277898] : [class_Lattices_Osemilattice__inf(_1277892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277892), _1277894), _1277896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277892), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1277892), _1277894), _1277898)), _1277896)))], (2890 ^ _773908) ^ [_816991, _816993, _816995, _816997] : [-(c_Wellfounded_Omin__ext(_816997, _816993) = c_Wellfounded_Omin__ext(_816995, _816991)), _816997 = _816995, _816993 = _816991], (19189 ^ _773908) ^ [_1105246, _1105248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105246), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105246)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105248)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105248))], (19609 ^ _773908) ^ [_1112210, _1112212, _1112214] : [class_Rings_Osemiring__1(_1112210), hBOOL(hAPP(hAPP(c_member(_1112210), _1112212), c_Nat_Osemiring__1__class_ONats(_1112210))), hBOOL(hAPP(hAPP(c_member(_1112210), _1112214), c_Nat_Osemiring__1__class_ONats(_1112210))), -(hBOOL(hAPP(hAPP(c_member(_1112210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112210), _1112212), _1112214)), c_Nat_Osemiring__1__class_ONats(_1112210))))], (51482 ^ _773908) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (20205 ^ _773908) ^ [_1122710, _1122712] : [class_Int_Onumber__ring(_1122710), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122710), _1122712), hAPP(c_Int_Onumber__class_Onumber__of(_1122710), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122710), _1122712), _1122712))], (41888 ^ _773908) ^ [_1599345, _1599347, _1599349] : [class_Groups_Omonoid__add(_1599345), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1599345), hAPP(hAPP(c_List_Omap(_1599347, _1599345), hAPP(c_COMBK(_1599345, _1599347), c_Groups_Ozero__class_Ozero(_1599345))), _1599349)) = c_Groups_Ozero__class_Ozero(_1599345))], (38833 ^ _773908) ^ [_1524131, _1524133, _1524135, _1524137, _1524139] : [-(hAPP(hAPP(c_List_Oappend(_1524131), _1524133), _1524135) = hAPP(hAPP(c_List_Oappend(_1524131), _1524137), _1524139)), 38834 ^ _773908 : [(38841 ^ _773908) ^ [_1524355] : [hAPP(hAPP(c_List_Oappend(_1524131), _1524133), _1524355) = _1524137, _1524135 = hAPP(hAPP(c_List_Oappend(_1524131), _1524355), _1524139)], (38835 ^ _773908) ^ [_1524243] : [_1524133 = hAPP(hAPP(c_List_Oappend(_1524131), _1524137), _1524243), hAPP(hAPP(c_List_Oappend(_1524131), _1524243), _1524135) = _1524139]]], (2478 ^ _773908) ^ [_810367, _810369, _810371, _810373, _810375, _810377, _810379, _810381, _810383, _810385] : [-(c_Product__Type_Oprod_Oprod__size(_810385, _810381, _810377, _810373, _810369) = c_Product__Type_Oprod_Oprod__size(_810383, _810379, _810375, _810371, _810367)), _810385 = _810383, _810381 = _810379, _810377 = _810375, _810373 = _810371, _810369 = _810367], (11133 ^ _773908) ^ [_959224, _959226, _959228] : [class_Rings_Oordered__cancel__semiring(_959224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959224), c_Groups_Ozero__class_Ozero(_959224)), _959226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959224), _959228), c_Groups_Ozero__class_Ozero(_959224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959224), _959228), _959226)), c_Groups_Ozero__class_Ozero(_959224))))], (38903 ^ _773908) ^ [_1525588, _1525590] : [hBOOL(hAPP(hAPP(c_member(_1525588), 38904 ^ [_1525588, _1525590]), c_Wellfounded_Oacc(_1525588, _1525590))), -(c_Wellfounded_Owf(_1525588, _1525590))], (34938 ^ _773908) ^ [_1426597, _1426599, _1426601, _1426603, _1426605] : [class_Groups_Ocomm__monoid__add(_1426597), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426599), _1426601)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426599, _1426597), _1426603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426599, tc_HOL_Obool)), _1426601), _1426605)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426599, _1426597), hAPP(hAPP(c_COMBC(_1426599, _1426597, _1426597), hAPP(hAPP(c_COMBS(_1426599, _1426597, tc_fun(_1426597, _1426597)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426597, tc_fun(_1426597, _1426597)), _1426599), c_If(_1426597)), hAPP(hAPP(c_COMBC(_1426599, tc_fun(_1426599, tc_HOL_Obool), tc_HOL_Obool), c_member(_1426599)), _1426605))), _1426603)), c_Groups_Ozero__class_Ozero(_1426597))), _1426601))], (45274 ^ _773908) ^ [_1678105, _1678107, _1678109] : [hBOOL(hAPP(hAPP(c_member(_1678105), _1678107), hAPP(c_List_Oset(_1678105), _1678109))), -(c_List_Oremdups(_1678105, hAPP(hAPP(c_List_Olist_OCons(_1678105), _1678107), _1678109)) = c_List_Oremdups(_1678105, _1678109))], (13728 ^ _773908) ^ [_1005164, _1005166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005164, _1005166)), _1005164)))], (49466 ^ _773908) ^ [_1772456, _1772458, _1772460] : [-(c_List_Oreplicate(_1772456, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772456)), hAPP(c_List_Ofilter(_1772456, hAPP(c_fequal, _1772458)), _1772460)), _1772458) = hAPP(c_List_Ofilter(_1772456, hAPP(c_fequal, _1772458)), _1772460))], (8929 ^ _773908) ^ [_921711, _921713, _921715, _921717, _921719] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_921711), 8932 ^ _773908 : [(8933 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921713), _921717)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921715), _921719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921713), _921719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921715), _921717)), -(_921713 = _921715), -(_921717 = _921719)], (8943 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921713), _921717)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921715), _921719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921713), _921719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921711), _921715), _921717))), 8946 ^ _773908 : [(8949 ^ _773908) ^ [] : [_921717 = _921719], (8947 ^ _773908) ^ [] : [_921713 = _921715]]]]], (40062 ^ _773908) ^ [_1556755, _1556757, _1556759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1556755), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556757)), _1556759))), -(hAPP(hAPP(c_List_Otake(_1556757), hAPP(c_Nat_OSuc, _1556755)), _1556759) = hAPP(hAPP(c_List_Oappend(_1556757), hAPP(hAPP(c_List_Otake(_1556757), _1556755), _1556759)), hAPP(hAPP(c_List_Olist_OCons(_1556757), hAPP(hAPP(c_List_Onth(_1556757), _1556759), _1556755)), c_List_Olist_ONil(_1556757))))], (48139 ^ _773908) ^ [_1744222, _1744224, _1744226] : [hBOOL(hAPP(hAPP(c_member(_1744222), _1744224), hAPP(c_List_Oset(_1744222), _1744226))), -(_1744226 = hAPP(hAPP(c_List_Oappend(_1744222), 48142 ^ [_1744222, _1744224, _1744226]), hAPP(hAPP(c_List_Olist_OCons(_1744222), _1744224), 48143 ^ [_1744222, _1744224, _1744226])))], (40317 ^ _773908) ^ [_1562712, _1562714, _1562716, _1562718] : [-(hAPP(hAPP(c_List_Odrop(_1562712), _1562714), hAPP(hAPP(c_List_Oappend(_1562712), _1562716), _1562718)) = hAPP(hAPP(c_List_Oappend(_1562712), hAPP(hAPP(c_List_Odrop(_1562712), _1562714), _1562716)), hAPP(hAPP(c_List_Odrop(_1562712), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1562714), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562712)), _1562716))), _1562718)))], (44632 ^ _773908) ^ [_1665709, _1665711, _1665713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665709), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1665711))), c_List_Otranspose(_1665711, _1665713)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1665711)), c_List_Otranspose(_1665711, _1665713)), _1665709) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665711), _1665711), hAPP(hAPP(c_COMBC(tc_List_Olist(_1665711), tc_Nat_Onat, _1665711), c_List_Onth(_1665711)), _1665709)), hAPP(c_List_Ofilter(tc_List_Olist(_1665711), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1665711)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665709)), c_Nat_Osize__class_Osize(tc_List_Olist(_1665711)))), _1665713)))], (10809 ^ _773908) ^ [_953361, _953363] : [class_Rings_Olinordered__idom(_953361), 10812 ^ _773908 : [(10819 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _953363), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953361), hAPP(c_Int_Oring__1__class_Oof__int(_953361), _953363)), c_Groups_Ozero__class_Ozero(_953361))))], (10813 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953361), hAPP(c_Int_Oring__1__class_Oof__int(_953361), _953363)), c_Groups_Ozero__class_Ozero(_953361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _953363), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15657 ^ _773908) ^ [_1040252, _1040254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040252), _1040254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040252), _1040254)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31696 ^ _773908) ^ [_1358477, _1358479, _1358481, _1358483] : [_1358477 = c_Orderings_Obot__class_Obot(tc_fun(_1358479, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358479, tc_fun(_1358481, tc_HOL_Obool)), _1358477), hAPP(c_COMBK(tc_fun(_1358481, tc_HOL_Obool), _1358479), _1358483)) = c_Orderings_Obot__class_Obot(tc_fun(_1358481, tc_HOL_Obool)))], (23781 ^ _773908) ^ [_1189637, _1189639] : [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), _1189637), _1189639))), 23784 ^ _773908 : [(23793 ^ _773908) ^ [] : [-(c_Divides_OnegDivAlg(_1189637, _1189639) = hAPP(c_Divides_Oadjust(_1189639), c_Divides_OnegDivAlg(_1189637, 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)))), _1189639)))), -(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), _1189637), _1189639)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1189639), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23785 ^ _773908) ^ [] : [23786 ^ _773908 : [(23789 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1189639), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23787 ^ _773908) ^ [] : [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), _1189637), _1189639)))]], -(c_Divides_OnegDivAlg(_1189637, _1189639) = 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), _1189637), _1189639)))]]], (27852 ^ _773908) ^ [_1278071, _1278073, _1278075, _1278077] : [class_Lattices_Osemilattice__inf(_1278071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278071), _1278073), _1278075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278071), _1278077), _1278073)), _1278075)))], (9461 ^ _773908) ^ [_931546, _931548, _931550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _931546), _931548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _931550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931550), _931546)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931550), _931548))))], (44184 ^ _773908) ^ [_1654460, _1654462, _1654464] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654460, tc_HOL_Obool)), _1654462), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654460, tc_HOL_Obool), _1654464)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1654460, tc_HOL_Obool), tc_fun(_1654460, tc_HOL_Obool)), _1654464), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654460, tc_HOL_Obool)), _1654462)))], (31243 ^ _773908) ^ [_1347680, _1347682, _1347684] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1347680), _1347682), _1347684) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1347680, tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool)), _1347682), hAPP(hAPP(c_COMBC(_1347680, tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347680, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool)), _1347680), c_Set_Oinsert(tc_fun(_1347680, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1347680, tc_HOL_Obool), tc_fun(_1347680, tc_HOL_Obool), _1347680), c_Relation_OImage(_1347680, _1347680, _1347684)), hAPP(hAPP(c_COMBC(_1347680, tc_fun(_1347680, tc_HOL_Obool), tc_fun(_1347680, tc_HOL_Obool)), c_Set_Oinsert(_1347680)), c_Orderings_Obot__class_Obot(tc_fun(_1347680, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1347680, tc_HOL_Obool), tc_HOL_Obool)))))], (40245 ^ _773908) ^ [_1560985, _1560987, _1560989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1560985, tc_HOL_Obool)), hAPP(c_List_Oset(_1560985), hAPP(hAPP(c_List_Odrop(_1560985), _1560987), _1560989))), hAPP(c_List_Oset(_1560985), _1560989))))], (28064 ^ _773908) ^ [_1282160, _1282162, _1282164, _1282166] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1282160, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1282160), _1282162), _1282164)), hAPP(hAPP(c_Set_Oinsert(_1282160), _1282162), _1282166)) = hAPP(hAPP(c_Set_Oinsert(_1282160), _1282162), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1282160, tc_HOL_Obool)), _1282164), _1282166)))], (51870 ^ _773908) ^ [] : [-(hBOOL(c_fTrue))], (38460 ^ _773908) ^ [_1513712, _1513714, _1513716] : [-(hAPP(c_Fun_Ocomp(_1513712, _1513714, _1513712, _1513716), c_Fun_Oid(_1513712)) = _1513716)], (18243 ^ _773908) ^ [_1088901, _1088903, _1088905] : [class_Int_Onumber__ring(_1088901), 18246 ^ _773908 : [(18253 ^ _773908) ^ [] : [c_Int_Oiszero(_1088901, hAPP(c_Int_Onumber__class_Onumber__of(_1088901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088903), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088905)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088901), _1088903) = hAPP(c_Int_Onumber__class_Onumber__of(_1088901), _1088905))], (18247 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1088901), _1088903) = hAPP(c_Int_Onumber__class_Onumber__of(_1088901), _1088905), -(c_Int_Oiszero(_1088901, hAPP(c_Int_Onumber__class_Onumber__of(_1088901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088903), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088905)))))]]], (27262 ^ _773908) ^ [_1266280, _1266282, _1266284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266280), _1266282)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266280), hAPP(hAPP(c_Set_Oinsert(_1266280), _1266284), _1266282))))], (37151 ^ _773908) ^ [_1474186, _1474188, _1474190, _1474192, _1474194] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1474186, _1474188, _1474190), _1474192), _1474194)), -(hBOOL(hAPP(_1474192, hAPP(_1474190, _1474194))))], (12787 ^ _773908) ^ [_988277, _988279] : [12788 ^ _773908 : [(12789 ^ _773908) ^ [_988327] : [_988279 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988277), _988327)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988277), _988279)))], (13075 ^ _773908) ^ [_993296, _993298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993296), _993298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993296), hAPP(c_Nat_OSuc, _993298))))], (5835 ^ _773908) ^ [_866824, _866826, _866828, _866830, _866832, _866834] : [c_Hoare__Mirabelle_Ohoare__derivs(_866824, _866826, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866824)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866824), _866828), _866830), _866832)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866824), tc_HOL_Obool)))), 5842 ^ _773908 : [(5845 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_866828, 5840 ^ [_866824, _866826, _866828, _866830, _866832, _866834]), 5841 ^ [_866824, _866826, _866828, _866830, _866832, _866834]))], (5843 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_866834, 5840 ^ [_866824, _866826, _866828, _866830, _866832, _866834]), 5841 ^ [_866824, _866826, _866828, _866830, _866832, _866834])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_866824, _866826, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866824)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866824), _866834), _866830), _866832)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866824), tc_HOL_Obool)))))], (17261 ^ _773908) ^ [_1071795, _1071797] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071795)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071797)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071795), _1071797)))], (19899 ^ _773908) ^ [_1117282, _1117284] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1117282)), c_Int_OBit0(_1117284)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117282), _1117284)))], (13203 ^ _773908) ^ [_995592, _995594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995594)), 13210 ^ _773908 : [(13217 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _995592), _995594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _995592)), hAPP(c_Int_Onat, _995594))))], (13211 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _995592)), hAPP(c_Int_Onat, _995594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _995592), _995594)))]]], (37836 ^ _773908) ^ [_1492686, _1492688, _1492690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492686, _1492686), tc_HOL_Obool)), _1492688), hAPP(hAPP(c_Product__Type_OSigma(_1492686, _1492686), _1492690), hAPP(c_COMBK(tc_fun(_1492686, tc_HOL_Obool), _1492686), _1492690)))), 37842 ^ _773908 : [(37845 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492686, _1492686)), hAPP(hAPP(c_Product__Type_OPair(_1492686, _1492686), 37841 ^ [_1492686, _1492688, _1492690]), 37841 ^ [_1492686, _1492688, _1492690])), _1492688))], (37843 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492686), 37841 ^ [_1492686, _1492688, _1492690]), _1492690)))]], -(c_Relation_Orefl__on(_1492686, _1492690, _1492688))], (19983 ^ _773908) ^ [_1118776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1118776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1118776)))], (5881 ^ _773908) ^ [_867974, _867976] : [-(c_Set_Othe__elem(_867974, hAPP(hAPP(c_Set_Oinsert(_867974), _867976), c_Orderings_Obot__class_Obot(tc_fun(_867974, tc_HOL_Obool)))) = _867976)], (12835 ^ _773908) ^ [_989196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _989196) = _989196)], (38605 ^ _773908) ^ [_1517725, _1517727, _1517729, _1517731, _1517733, _1517735] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517725, _1517727, _1517729), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517725, _1517727), tc_HOL_Obool)), _1517731), _1517733)), _1517735) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517725, _1517729), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517725, _1517727, _1517729), _1517731), _1517735)), hAPP(hAPP(c_Relation_Orel__comp(_1517725, _1517727, _1517729), _1517733), _1517735)))], (23203 ^ _773908) ^ [_1177587, _1177589, _1177591, _1177593, _1177595] : [-(c_Nat_Onat_Onat__case(_1177587, _1177589, _1177591, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177593)), _1177595)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1177587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1177593))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1177587, _1177587), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1177587, tc_fun(_1177587, _1177587)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1177587, tc_fun(_1177587, _1177587)), tc_Int_Oint), c_If(_1177587)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1177587, _1177589, _1177591, _1177595))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1177587, tc_Int_Oint), _1177591), 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)), _1177595)))))], (4924 ^ _773908) ^ [_849048, _849050, _849052, _849054, _849056, _849058] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_849058, _849054, _849050) = c_SetInterval_Oord__class_OatLeastAtMost(_849056, _849052, _849048)), _849058 = _849056, _849054 = _849052, _849050 = _849048], (45757 ^ _773908) ^ [_1688116, _1688118, _1688120] : [c_List_OtakeWhile(_1688116, _1688118, _1688120) = _1688120, 45760 ^ _773908 : [(45761 ^ _773908) ^ [_1688203] : [hBOOL(hAPP(hAPP(c_member(_1688116), _1688203), hAPP(c_List_Oset(_1688116), _1688120))), -(hBOOL(hAPP(_1688118, _1688203)))]]], (24213 ^ _773908) ^ [_1197484, _1197486, _1197488] : [-(hAPP(c_Product__Type_Osnd(_1197484, _1197486), _1197488) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1197484, _1197486, _1197486), hAPP(c_COMBK(tc_fun(_1197486, _1197486), _1197484), c_COMBI(_1197486))), _1197488))], (42495 ^ _773908) ^ [_1616457, _1616459, _1616461, _1616463] : [class_Groups_Ocomm__monoid__add(_1616457), hBOOL(hAPP(c_List_Odistinct(_1616459), _1616461)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616457), hAPP(hAPP(c_List_Omap(_1616459, _1616457), _1616463), _1616461)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1616459, _1616457), _1616463), hAPP(c_List_Oset(_1616459), _1616461)))], (47215 ^ _773908) ^ [_1722339, _1722341, _1722343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1722339, _1722339)), _1722341), c_Transitive__Closure_Otrancl(_1722339, _1722343))), 47219 ^ _773908 : [(47222 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1722339, _1722339)), _1722341), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1722339, _1722339), tc_HOL_Obool), 47218 ^ [_1722339, _1722341, _1722343]), _1722343))))], (47220 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 47218 ^ [_1722339, _1722341, _1722343])))]]], (27746 ^ _773908) ^ [_1276172, _1276174, _1276176, _1276178] : [hBOOL(hAPP(hAPP(c_member(_1276172), _1276174), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1276172, tc_HOL_Obool)), _1276176), _1276178))), 27749 ^ _773908 : [(27752 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276172), _1276174), _1276178)))], (27750 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276172), _1276174), _1276176)))]]], (38948 ^ _773908) ^ [_1526674, _1526676, _1526678] : [c_Wellfounded_Owf(_1526674, _1526676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1526674, tc_HOL_Obool)), _1526678), hAPP(c_Relation_OImage(_1526674, _1526674, _1526676), _1526678))), -(_1526678 = c_Orderings_Obot__class_Obot(tc_fun(_1526674, tc_HOL_Obool)))], (28040 ^ _773908) ^ [_1281638, _1281640, _1281642, _1281644] : [hBOOL(hAPP(hAPP(c_member(_1281638), _1281640), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281638, tc_HOL_Obool)), _1281642), _1281644))), -(hBOOL(hAPP(hAPP(c_member(_1281638), _1281640), _1281642)))], (26219 ^ _773908) ^ [_1239406, _1239408, _1239410, _1239412, _1239414] : [class_Lattices_Olattice(_1239406), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239408, _1239406)), _1239410), _1239412), _1239414) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1239406), hAPP(_1239410, _1239414)), hAPP(_1239412, _1239414)))], (50183 ^ _773908) ^ [_1789829, _1789831, _1789833, _1789835, _1789837, _1789839] : [-(c_Partial__Function_Ofun__lub(_1789829, _1789831, _1789833, _1789835, _1789837, _1789839) = hAPP(_1789835, hAPP(c_Set_OCollect(_1789829), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool), tc_HOL_Obool, _1789829), c_HOL_OEx(tc_fun(_1789833, _1789829))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool), tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool), _1789829), hAPP(c_COMBS(tc_fun(_1789833, _1789829), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1789833, _1789829)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1789833, _1789829), tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1789833, _1789829))), _1789837)))), hAPP(hAPP(c_COMBC(_1789829, tc_fun(tc_fun(_1789833, _1789829), _1789829), tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1789829, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1789833, _1789829), _1789829), tc_fun(tc_fun(_1789833, _1789829), tc_HOL_Obool)), _1789829), c_COMBB(_1789829, tc_HOL_Obool, tc_fun(_1789833, _1789829))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1789833, _1789829), _1789833, _1789829), c_COMBI(tc_fun(_1789833, _1789829))), _1789839)))))))], (42161 ^ _773908) ^ [_1607653, _1607655, _1607657, _1607659, _1607661] : [-(_1607653 = c_Orderings_Obot__class_Obot(tc_fun(_1607655, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607657, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607655, tc_fun(_1607657, tc_HOL_Obool)), _1607653), _1607659)), _1607661) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607655, tc_fun(_1607657, tc_HOL_Obool)), _1607653), hAPP(hAPP(c_COMBC(_1607655, tc_fun(_1607657, tc_HOL_Obool), tc_fun(_1607657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1607657, tc_HOL_Obool), tc_fun(tc_fun(_1607657, tc_HOL_Obool), tc_fun(_1607657, tc_HOL_Obool)), _1607655), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607657, tc_HOL_Obool))), _1607659)), _1607661)))], (1804 ^ _773908) ^ [_799444, _799446] : [-(class_Groups_Omonoid__add(_799444)), _799446 = _799444, class_Groups_Omonoid__add(_799446)], (30831 ^ _773908) ^ [_1338576, _1338578, _1338580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338576), _1338578)), 30834 ^ _773908 : [(30835 ^ _773908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338576, tc_Nat_Onat), _1338580), _1338578) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 30838 ^ _773908 : [(30839 ^ _773908) ^ [_1338738] : [hBOOL(hAPP(hAPP(c_member(_1338576), _1338738), _1338578)), -(hAPP(_1338580, _1338738) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (30845 ^ _773908) ^ [] : [30847 ^ _773908 : [(30850 ^ _773908) ^ [] : [hAPP(_1338580, 30846 ^ [_1338576, _1338578, _1338580]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (30848 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338576), 30846 ^ [_1338576, _1338578, _1338580]), _1338578)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338576, tc_Nat_Onat), _1338580), _1338578) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (38104 ^ _773908) ^ [_1498615, _1498617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1498615), hAPP(c_Set_OCollect(_1498615), _1498617))), 38107 ^ _773908 : [(38114 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1498615), c_Orderings_Otop__class_Otop(tc_fun(_1498615, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498615), hAPP(c_Set_OCollect(_1498615), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498615), c_fNot), _1498617)))))], (38108 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1498615), hAPP(c_Set_OCollect(_1498615), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498615), c_fNot), _1498617)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498615), c_Orderings_Otop__class_Otop(tc_fun(_1498615, tc_HOL_Obool)))))]]], (11854 ^ _773908) ^ [_972067, _972069, _972071, _972073] : [class_Rings_Olinordered__semiring__strict(_972067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972067), _972069), _972071)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972067), _972069), _972073))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972067), c_Groups_Ozero__class_Ozero(_972067)), _972069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972067), _972071), _972073)))], (28402 ^ _773908) ^ [_1290011, _1290013, _1290015, _1290017] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290011, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290011, tc_HOL_Obool)), _1290013), _1290015)), _1290017) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290011, tc_HOL_Obool)), _1290013), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290011, tc_HOL_Obool)), _1290015), _1290017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290011, tc_HOL_Obool)), _1290017), _1290013)))], (4164 ^ _773908) ^ [_836800, _836802] : [_836802 = _836800, -(c_Lazy__Sequence_Ohit__bound(_836802) = c_Lazy__Sequence_Ohit__bound(_836800))], (42119 ^ _773908) ^ [_1606582, _1606584, _1606586, _1606588, _1606590, _1606592] : [hBOOL(hAPP(hAPP(c_member(_1606582), _1606584), _1606586)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606582, tc_fun(_1606588, tc_HOL_Obool)), _1606586), hAPP(hAPP(c_COMBB(tc_fun(_1606588, tc_HOL_Obool), tc_fun(_1606588, tc_HOL_Obool), _1606582), hAPP(c_Set_Oinsert(_1606588), _1606590)), _1606592)) = hAPP(hAPP(c_Set_Oinsert(_1606588), _1606590), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606582, tc_fun(_1606588, tc_HOL_Obool)), _1606586), _1606592)))], (17085 ^ _773908) ^ [_1068447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068447), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1068447) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068447))], (48969 ^ _773908) ^ [_1761431, _1761433, _1761435] : [-(c_Nitpick_Oof__frac(_1761433, _1761431, _1761435) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1761431), hAPP(c_Int_Oring__1__class_Oof__int(_1761431), hAPP(c_Nitpick_Onum(_1761433), _1761435))), hAPP(c_Int_Oring__1__class_Oof__int(_1761431), hAPP(c_Nitpick_Odenom(_1761433), _1761435)))), class_Rings_Oinverse(_1761431), class_Rings_Oring__1(_1761431)], (19023 ^ _773908) ^ [_1102572, _1102574] : [class_Rings_Oring__1(_1102572), -(hBOOL(hAPP(hAPP(c_member(_1102572), hAPP(c_Int_Oring__1__class_Oof__int(_1102572), _1102574)), c_Int_Oring__1__class_OInts(_1102572))))], (23173 ^ _773908) ^ [_1176868, _1176870] : [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(_1176868))), 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)), _1176870)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176868)), hAPP(c_Nat_OSuc, _1176870))))], (2340 ^ _773908) ^ [_808160, _808162, _808164, _808166] : [-(c_Groups_Osgn__class_Osgn(_808166, _808162) = c_Groups_Osgn__class_Osgn(_808164, _808160)), _808166 = _808164, _808162 = _808160], (36623 ^ _773908) ^ [_1463502] : [-(c_Nitpick_Ozero__frac(_1463502) = c_Nitpick_OAbs__Frac(_1463502, 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))))], (37824 ^ _773908) ^ [_1492444, _1492446, _1492448, _1492450, _1492452] : [c_Relation_Orefl__on(_1492444, _1492446, _1492448), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492444, _1492444)), hAPP(hAPP(c_Product__Type_OPair(_1492444, _1492444), _1492450), _1492452)), _1492448)), -(hBOOL(hAPP(hAPP(c_member(_1492444), _1492452), _1492446)))], (8213 ^ _773908) ^ [_909007, _909009, _909011, _909013, _909015] : [c_Hoare__Mirabelle_Ohoare__derivs(_909007, _909009, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909007)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909007), c_Hoare__Mirabelle_Opeek__and(_909007, _909011, _909013)), _909015), _909011)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909007), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_909007, _909009, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909007)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909007), _909011), c_Com_Ocom_OWhile(_909013, _909015)), c_Hoare__Mirabelle_Opeek__and(_909007, _909011, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _909013)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909007), tc_HOL_Obool)))))], (49043 ^ _773908) ^ [_1763039, _1763041, _1763043, _1763045] : [c_List_Olist__all(_1763039, _1763041, hAPP(hAPP(c_List_Olist_OCons(_1763039), _1763043), _1763045)), 49046 ^ _773908 : [(49049 ^ _773908) ^ [] : [-(c_List_Olist__all(_1763039, _1763041, _1763045))], (49047 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1763041, _1763043)))]]], (11553 ^ _773908) ^ [_966828, _966830, _966832] : [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, _966828)), _966830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966828)), _966832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966830), _966832)))], (39344 ^ _773908) ^ [_1538168, _1538170, _1538172] : [hAPP(hAPP(c_List_Oappend(_1538168), _1538170), _1538172) = c_List_Olist_ONil(_1538168), 39347 ^ _773908 : [(39350 ^ _773908) ^ [] : [-(_1538172 = c_List_Olist_ONil(_1538168))], (39348 ^ _773908) ^ [] : [-(_1538170 = c_List_Olist_ONil(_1538168))]]], (49910 ^ _773908) ^ [_1782040, _1782042, _1782044, _1782046] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1782040, _1782042, _1782044, _1782046, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1782042)) = _1782044)], (44527 ^ _773908) ^ [_1662010, _1662012, _1662014] : [-(c_List_Oconcat(_1662010, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1662010)), _1662012), _1662014)) = hAPP(hAPP(c_List_Oappend(_1662010), c_List_Oconcat(_1662010, _1662012)), c_List_Oconcat(_1662010, _1662014)))], (18481 ^ _773908) ^ [_1092955, _1092957, _1092959, _1092961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1092955, tc_HOL_Obool)), _1092957), _1092959)), hBOOL(hAPP(hAPP(c_member(_1092955), _1092961), _1092957)), -(hBOOL(hAPP(hAPP(c_member(_1092955), _1092961), _1092959)))], (49302 ^ _773908) ^ [_1768362, _1768364, _1768366, _1768368, _1768370, _1768372, _1768374] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1768362, _1768364, _1768366, _1768368), _1768370), _1768372), _1768374) = c_New__DSequence_Oneg__bind(_1768362, _1768364, hAPP(hAPP(hAPP(_1768366, _1768370), _1768372), _1768374), hAPP(hAPP(c_COMBC(_1768362, 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(_1768364)))), hAPP(hAPP(c_COMBC(_1768362, 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(_1768364))))), hAPP(hAPP(c_COMBC(_1768362, 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(_1768364)))))), _1768368), _1768370)), _1768372)), _1768374)))], (44925 ^ _773908) ^ [_1672008, _1672010, _1672012, _1672014] : [class_Orderings_Olinorder(_1672008), 44928 ^ _773908 : [(44937 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1672008, hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672010), hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672012), _1672014)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1672008), _1672010), _1672012)), c_List_Olinorder__class_Osorted(_1672008, hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672012), _1672014))], (44929 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1672008, hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672010), hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672012), _1672014))), 44932 ^ _773908 : [(44935 ^ _773908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1672008, hAPP(hAPP(c_List_Olist_OCons(_1672008), _1672012), _1672014)))], (44933 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1672008), _1672010), _1672012)))]]]]], (144 ^ _773908) ^ [_776020, _776022, _776024, _776026] : [-(c_Relation_Oirrefl(_776024, _776020)), c_Relation_Oirrefl(_776026, _776022), _776026 = _776024, _776022 = _776020], (45449 ^ _773908) ^ [_1681778, _1681780, _1681782, _1681784, _1681786] : [c_List_Olist__all2(_1681778, _1681780, _1681782, hAPP(c_List_Orev(_1681778), _1681784), _1681786), -(c_List_Olist__all2(_1681778, _1681780, _1681782, _1681784, hAPP(c_List_Orev(_1681780), _1681786)))], (12845 ^ _773908) ^ [_989348, _989350] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989348), _989350)), _989348 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _989350 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (18927 ^ _773908) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (47572 ^ _773908) ^ [_1731128, _1731130, _1731132, _1731134, _1731136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1731128, _1731128)), hAPP(hAPP(c_Product__Type_OPair(_1731128, _1731128), _1731130), _1731132)), c_Transitive__Closure_Ortrancl(_1731128, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1731128, _1731128), tc_HOL_Obool)), _1731134), _1731136)))), 47578 ^ _773908 : [(47584 ^ _773908) ^ [] : [47577 ^ [_1731128, _1731130, _1731132, _1731134, _1731136] = 47580 ^ [_1731128, _1731130, _1731132, _1731134, _1731136]], (47582 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731128, _1731128)), hAPP(hAPP(c_Product__Type_OPair(_1731128, _1731128), 47577 ^ [_1731128, _1731130, _1731132, _1731134, _1731136]), 47580 ^ [_1731128, _1731130, _1731132, _1731134, _1731136])), _1731136)))], (47579 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731128, _1731128)), hAPP(hAPP(c_Product__Type_OPair(_1731128, _1731128), _1731130), 47577 ^ [_1731128, _1731130, _1731132, _1731134, _1731136])), c_Transitive__Closure_Ortrancl(_1731128, _1731134))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731128, _1731128)), hAPP(hAPP(c_Product__Type_OPair(_1731128, _1731128), _1731130), _1731132)), c_Transitive__Closure_Ortrancl(_1731128, _1731134))))], (50715 ^ _773908) ^ [_1799889, _1799891] : [c_Relation_Osym(_1799889, _1799891), -(c_Relation_Osym(_1799889, c_Transitive__Closure_Otrancl(_1799889, _1799891)))], (33196 ^ _773908) ^ [_1390653, _1390655, _1390657, _1390659, _1390661] : [c_Fun_Oinj__on(_1390653, _1390655, _1390657, _1390659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390653, tc_HOL_Obool)), _1390661), _1390659)), -(c_Fun_Oinj__on(_1390653, _1390655, _1390657, _1390661))], (32434 ^ _773908) ^ [_1375812, _1375814, _1375816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375812, tc_HOL_Obool)), _1375814), _1375816)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1375812, tc_HOL_Obool)), _1375814), hAPP(c_Set_OPow(_1375812), _1375816))))], (7529 ^ _773908) ^ [_895788, _895790, _895792, _895794, _895796] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_895788, _895790, _895792)), _895794), _895796)), 7534 ^ _773908 : [(7537 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895790), _895794), _895796)))], (7535 ^ _773908) ^ [] : [-(hBOOL(hAPP(_895788, _895794)))]], 7538 ^ _773908 : [(7541 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895792), _895794), _895796)))], (7539 ^ _773908) ^ [] : [hBOOL(hAPP(_895788, _895794))]]], (37432 ^ _773908) ^ [_1481479, _1481481, _1481483, _1481485, _1481487] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1481479, _1481481), _1481483), hAPP(hAPP(c_COMBS(_1481479, tc_fun(_1481481, tc_HOL_Obool), tc_fun(_1481481, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481481, tc_HOL_Obool), tc_fun(tc_fun(_1481481, tc_HOL_Obool), tc_fun(_1481481, tc_HOL_Obool)), _1481479), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481481, tc_HOL_Obool))), _1481485)), _1481487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1481479, _1481481), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1481479, _1481481), _1481483), _1481485)), hAPP(hAPP(c_Product__Type_OSigma(_1481479, _1481481), _1481483), _1481487)))], (25521 ^ _773908) ^ [_1225689, _1225691, _1225693, _1225695, _1225697] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1225689, _1225689)), hAPP(hAPP(c_Product__Type_OPair(_1225689, _1225689), _1225691), _1225693)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1225689, _1225689), tc_HOL_Obool), _1225695), _1225697))), 25526 ^ _773908 : [(25529 ^ _773908) ^ [] : [-(_1225691 = _1225693)], (25527 ^ _773908) ^ [] : [-(_1225695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25532 ^ _773908 : [(25537 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1225689, _1225689)), hAPP(hAPP(c_Product__Type_OPair(_1225689, _1225689), 25530 ^ [_1225689, _1225691, _1225693, _1225695, _1225697]), _1225693)), _1225697)))], (25535 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1225689, _1225689)), hAPP(hAPP(c_Product__Type_OPair(_1225689, _1225689), _1225691), 25530 ^ [_1225689, _1225691, _1225693, _1225695, _1225697])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1225689, _1225689), tc_HOL_Obool), 25531 ^ [_1225689, _1225691, _1225693, _1225695, _1225697]), _1225697))))], (25533 ^ _773908) ^ [] : [-(_1225695 = hAPP(c_Nat_OSuc, 25531 ^ [_1225689, _1225691, _1225693, _1225695, _1225697]))]]], (25473 ^ _773908) ^ [_1224570, _1224572, _1224574] : [class_Groups_Olinordered__ab__group__add(_1224570), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1224570), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224570), _1224572), _1224574)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224570), hAPP(c_Groups_Ouminus__class_Ouminus(_1224570), _1224572)), hAPP(c_Groups_Ouminus__class_Ouminus(_1224570), _1224574)))], (43268 ^ _773908) ^ [_1633274, _1633276, _1633278, _1633280, _1633282] : [class_Orderings_Olinorder(_1633274), 43271 ^ _773908 : [(43280 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1633276), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1633276, _1633274, _1633278), _1633280), _1633282)))), -(hBOOL(hAPP(hAPP(c_member(_1633276), _1633280), hAPP(c_List_Oset(_1633276), _1633282)))), hBOOL(hAPP(c_List_Odistinct(_1633276), _1633282))], (43272 ^ _773908) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1633276), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1633276, _1633274, _1633278), _1633280), _1633282))), 43275 ^ _773908 : [(43278 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1633276), _1633282)))], (43276 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1633276), _1633280), hAPP(c_List_Oset(_1633276), _1633282)))]]]]], (5983 ^ _773908) ^ [_869900, _869902, _869904, _869906] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_869900, _869902)), _869904), _869906)), 5987 ^ _773908 : [(5990 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869902), 5986 ^ [_869900, _869902, _869904, _869906]), _869906)))], (5988 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869900), _869904), 5986 ^ [_869900, _869902, _869904, _869906])))]]], (28314 ^ _773908) ^ [_1288106, _1288108] : [class_Lattices_Oboolean__algebra(_1288106), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288106), _1288108), hAPP(c_Groups_Ouminus__class_Ouminus(_1288106), _1288108)) = c_Orderings_Obot__class_Obot(_1288106))], (44289 ^ _773908) ^ [_1656952, _1656954, _1656956, _1656958] : [-(_1656952 = _1656954), -(hAPP(c_List_OremoveAll(_1656956, _1656952), hAPP(hAPP(c_List_Olist_OCons(_1656956), _1656954), _1656958)) = hAPP(hAPP(c_List_Olist_OCons(_1656956), _1656954), hAPP(c_List_OremoveAll(_1656956, _1656952), _1656958)))], (22863 ^ _773908) ^ [_1170450] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1170450)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1170450)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45181 ^ _773908) ^ [_1676288, _1676290] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1676288, _1676290)))], (12590 ^ _773908) ^ [_984995, _984997] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984995), _984997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984997)), _984995)))], (15913 ^ _773908) ^ [_1045371, _1045373, _1045375, _1045377, _1045379, _1045381] : [class_Rings_Oordered__ring(_1045371), 15916 ^ _773908 : [(15923 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045371), _1045373), _1045379)), _1045375)), _1045377)), _1045381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), _1045373), _1045375)), _1045377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), _1045379), _1045375)), _1045381))))], (15917 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), _1045373), _1045375)), _1045377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), _1045379), _1045375)), _1045381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045371), _1045373), _1045379)), _1045375)), _1045377)), _1045381)))]]], (51404 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (16137 ^ _773908) ^ [_1050343, _1050345] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050343, _1050345) = 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), _1050343), _1050345) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050345), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050343, _1050345)))], (9660 ^ _773908) ^ [_934896] : [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, _934896)))))], (2468 ^ _773908) ^ [_810218, _810220, _810222, _810224] : [-(c_Divides_OposDivAlg(_810224, _810220) = c_Divides_OposDivAlg(_810222, _810218)), _810224 = _810222, _810220 = _810218], (20035 ^ _773908) ^ [_1119706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119706), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1119706)), c_Int_OMin)))], (44505 ^ _773908) ^ [_1661275, _1661277] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661275)), c_List_Oconcat(_1661275, _1661277)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661275), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1661275))), _1661277)))], (34223 ^ _773908) ^ [_1411122, _1411124, _1411126, _1411128, _1411130, _1411132] : [c_Fun_Oinj__on(_1411122, _1411124, _1411126, _1411128), hBOOL(hAPP(hAPP(c_member(_1411124), _1411130), hAPP(c_Set_Oimage(_1411122, _1411124, _1411126), _1411128))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411122, tc_HOL_Obool)), _1411128), _1411132)), -(hBOOL(hAPP(hAPP(c_member(_1411122), hAPP(c_Fun_Othe__inv__into(_1411122, _1411124, _1411128, _1411126), _1411130)), _1411132)))], (7131 ^ _773908) ^ [_889361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _889361)), _889361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44513 ^ _773908) ^ [_1661637, _1661639] : [-(hAPP(c_List_Oset(_1661637), c_List_Oconcat(_1661637, _1661639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1661637), tc_fun(_1661637, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1661637)), _1661639)), c_List_Oset(_1661637)))], (12120 ^ _773908) ^ [_977113, _977115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _977113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _977115)), -(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), _977115), _977113))))], (8589 ^ _773908) ^ [_916002, _916004, _916006] : [class_Rings_Oring__1(_916002), -(hAPP(c_Int_Oring__1__class_Oof__int(_916002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _916004), _916006)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916002), hAPP(c_Int_Oring__1__class_Oof__int(_916002), _916004)), hAPP(c_Int_Oring__1__class_Oof__int(_916002), _916006)))], (12811 ^ _773908) ^ [_988719] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988719), _988719)))))], (42423 ^ _773908) ^ [_1614772, _1614774, _1614776, _1614778, _1614780] : [-(_1614772 = c_Orderings_Obot__class_Obot(tc_fun(_1614774, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614774, tc_fun(_1614776, tc_HOL_Obool)), _1614772), hAPP(hAPP(c_COMBB(tc_fun(_1614776, tc_HOL_Obool), tc_fun(_1614776, tc_HOL_Obool), _1614774), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614776, tc_HOL_Obool)), _1614778)), _1614780)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614776, tc_HOL_Obool)), _1614778), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614774, tc_fun(_1614776, tc_HOL_Obool)), _1614772), _1614780)))], (21583 ^ _773908) ^ [_1147266, _1147268, _1147270, _1147272] : [class_Fields_Olinordered__field(_1147266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147266), c_Groups_Ozero__class_Ozero(_1147266)), _1147268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147266), _1147270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147266), _1147272), _1147268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147266), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147266), _1147270), _1147268)), _1147272)))], (27031 ^ _773908) ^ [_1260466, _1260468, _1260470, _1260472, _1260474] : [c_Equiv__Relations_Oequiv(_1260466, _1260468, _1260470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260466, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1260466, _1260466, _1260470), hAPP(hAPP(c_Set_Oinsert(_1260466), _1260472), c_Orderings_Obot__class_Obot(tc_fun(_1260466, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1260466, _1260466, _1260470), hAPP(hAPP(c_Set_Oinsert(_1260466), _1260474), c_Orderings_Obot__class_Obot(tc_fun(_1260466, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1260466), _1260472), _1260468)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1260466, _1260466)), hAPP(hAPP(c_Product__Type_OPair(_1260466, _1260466), _1260474), _1260472)), _1260470)))], (3712 ^ _773908) ^ [_829900, _829902, _829904, _829906, _829908, _829910] : [-(c_List_OdropWhile(_829910, _829906, _829902) = c_List_OdropWhile(_829908, _829904, _829900)), _829910 = _829908, _829906 = _829904, _829902 = _829900], (8211 ^ _773908) ^ [_908979, _908981] : [c_Com_Ocom_OWhile(_908979, _908981) = c_Com_Ocom_OSKIP], (19947 ^ _773908) ^ [_1118125, _1118127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1118125)), c_Int_OBit1(_1118127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118125), _1118127)))], (22043 ^ _773908) ^ [_1155276, _1155278] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155276), _1155278), hAPP(c_Int_Onumber__class_Onumber__of(_1155276), c_Int_OBit1(c_Int_OPls))) = _1155278), class_Fields_Ofield(_1155276), class_Int_Onumber__ring(_1155276)], (41428 ^ _773908) ^ [_1590217, _1590219, _1590221] : [_1590217 = c_List_Olist_ONil(_1590219), -(c_List_Olast(_1590219, hAPP(hAPP(c_List_Oappend(_1590219), _1590221), _1590217)) = c_List_Olast(_1590219, _1590221))], (19445 ^ _773908) ^ [_1109585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1109585)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109585), c_Int_OMin)))], (34416 ^ _773908) ^ [_1414740, _1414742] : [class_Orderings_Olinorder(_1414740), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414740, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1414740), _1414742)), hAPP(hAPP(c_Set_Oinsert(_1414740), _1414742), c_Orderings_Obot__class_Obot(tc_fun(_1414740, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1414740), _1414742))], (47511 ^ _773908) ^ [_1729435, _1729437, _1729439] : [c_Relation_Osingle__valued(_1729435, _1729437, _1729439), 47514 ^ _773908 : [(47515 ^ _773908) ^ [_1729556, _1729558] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729435, _1729437)), hAPP(hAPP(c_Product__Type_OPair(_1729435, _1729437), _1729558), _1729556)), _1729439)), 47518 ^ _773908 : [(47519 ^ _773908) ^ [_1729682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729435, _1729437)), hAPP(hAPP(c_Product__Type_OPair(_1729435, _1729437), _1729558), _1729682)), _1729439)), -(_1729556 = _1729682)]]]]], (20363 ^ _773908) ^ [_1125378, _1125380] : [class_Rings_Olinordered__idom(_1125378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125378), hAPP(hAPP(c_Power_Opower__class_Opower(_1125378), _1125380), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1125378)))], (40219 ^ _773908) ^ [_1560435, _1560437, _1560439, _1560441] : [hBOOL(hAPP(hAPP(c_member(_1560435), _1560437), hAPP(c_List_Oset(_1560435), hAPP(hAPP(c_List_Olist_OCons(_1560435), _1560439), _1560441)))), -(_1560437 = _1560439), -(hBOOL(hAPP(hAPP(c_member(_1560435), _1560437), hAPP(c_List_Oset(_1560435), _1560441))))], (18917 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (10777 ^ _773908) ^ [_952806, _952808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952806)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _952806), _952808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _952806)), hAPP(c_Int_Onat, _952808)))], (51754 ^ _773908) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (31756 ^ _773908) ^ [_1360124, _1360126, _1360128, _1360130, _1360132] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360124, tc_fun(_1360126, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360124, tc_HOL_Obool)), _1360128), _1360130)), _1360132) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360126, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360124, tc_fun(_1360126, tc_HOL_Obool)), _1360128), _1360132)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360124, tc_fun(_1360126, tc_HOL_Obool)), _1360130), _1360132)))], (1714 ^ _773908) ^ [_798319, _798321] : [-(class_Rings_Ocomm__semiring__1(_798319)), _798321 = _798319, class_Rings_Ocomm__semiring__1(_798321)], (16899 ^ _773908) ^ [_1064490, _1064492, _1064494] : [class_Int_Onumber__ring(_1064490), -(hAPP(c_Int_Onumber__class_Onumber__of(_1064490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1064492), _1064494)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064490), hAPP(c_Int_Onumber__class_Onumber__of(_1064490), _1064492)), hAPP(c_Int_Onumber__class_Onumber__of(_1064490), _1064494)))], (24807 ^ _773908) ^ [_1211468, _1211470, _1211472, _1211474] : [class_Orderings_Olinorder(_1211468), 24810 ^ _773908 : [(24811 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211468), _1211470), _1211472)), _1211474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), _1211470), _1211474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), _1211472), _1211474)))], (24821 ^ _773908) ^ [] : [24822 ^ _773908 : [(24825 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), _1211472), _1211474))], (24823 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), _1211470), _1211474))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211468), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211468), _1211470), _1211472)), _1211474)))]]], (46264 ^ _773908) ^ [_1699442, _1699444, _1699446] : [c_Wellfounded_OwfP(_1699442, _1699444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1699442, tc_fun(_1699442, tc_HOL_Obool))), _1699446), _1699444)), -(c_Wellfounded_OwfP(_1699442, _1699446))], (31304 ^ _773908) ^ [_1349214, _1349216, _1349218, _1349220, _1349222] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349214, tc_fun(_1349216, tc_HOL_Obool)), _1349218), _1349220), _1349222)), 31308 ^ _773908 : [(31311 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1349220, 31307 ^ [_1349214, _1349216, _1349218, _1349220, _1349222]), _1349222)))], (31309 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349214), 31307 ^ [_1349214, _1349216, _1349218, _1349220, _1349222]), _1349218)))]]], (21993 ^ _773908) ^ [_1154339, _1154341, _1154343] : [class_Fields_Olinordered__field(_1154339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154339), _1154341), _1154343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154339), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154339), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154339), _1154341), _1154343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154339), c_Groups_Oone__class_Oone(_1154339)), c_Groups_Oone__class_Oone(_1154339)))), _1154343)))], (7886 ^ _773908) ^ [_902881, _902883, _902885, _902887] : [class_Orderings_Oorder(_902881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902881), hAPP(_902883, 7891 ^ [_902881, _902883, _902885, _902887])), hAPP(_902883, hAPP(c_Nat_OSuc, 7891 ^ [_902881, _902883, _902885, _902887])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902885), _902887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902881), hAPP(_902883, _902885)), hAPP(_902883, _902887))))], (26735 ^ _773908) ^ [] : [-(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))))], (29473 ^ _773908) ^ [_1311975, _1311977] : [class_Lattices_Olattice(_1311975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311975), _1311977)), -(_1311977 = c_Orderings_Obot__class_Obot(tc_fun(_1311975, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1311975), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1311975), 29486 ^ [_1311975, _1311977]), 29487 ^ [_1311975, _1311977])), hAPP(hAPP(c_Set_Oinsert(_1311975), 29486 ^ [_1311975, _1311977]), hAPP(hAPP(c_Set_Oinsert(_1311975), 29487 ^ [_1311975, _1311977]), c_Orderings_Obot__class_Obot(tc_fun(_1311975, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1311975), c_Big__Operators_Olattice__class_OSup__fin(_1311975, _1311977)), _1311977)))], (35949 ^ _773908) ^ [_1448434, _1448436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448434), c_Orderings_Otop__class_Otop(tc_fun(_1448434, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448436), c_Orderings_Otop__class_Otop(tc_fun(_1448436, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1448434, _1448436)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1448434, _1448436), tc_HOL_Obool)))))], (51642 ^ _773908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (45017 ^ _773908) ^ [_1673471, _1673473, _1673475] : [class_Orderings_Olinorder(_1673471), c_List_Olinorder__class_Osorted(_1673471, _1673473), hBOOL(hAPP(c_List_Odistinct(_1673471), _1673473)), c_List_Olinorder__class_Osorted(_1673471, _1673475), hBOOL(hAPP(c_List_Odistinct(_1673471), _1673475)), hAPP(c_List_Oset(_1673471), _1673473) = hAPP(c_List_Oset(_1673471), _1673475), -(_1673473 = _1673475)], (15389 ^ _773908) ^ [_1035040, _1035042] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035040)), hAPP(c_Nat_OSuc, _1035042)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035040), _1035042))], (46808 ^ _773908) ^ [_1711872, _1711874] : [-(c_Transitive__Closure_Ortrancl(_1711872, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1711872, _1711872), tc_HOL_Obool)), _1711874), c_Relation_OId(_1711872))) = c_Transitive__Closure_Ortrancl(_1711872, _1711874))], (6888 ^ _773908) ^ [_885299, _885301, _885303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885299), _885301)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885299), _885303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885301), _885303)))], (8377 ^ _773908) ^ [_911996] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911996), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _911996)], (44459 ^ _773908) ^ [_1660250] : [-(c_List_Oconcat(_1660250, c_List_Olist_ONil(tc_List_Olist(_1660250))) = c_List_Olist_ONil(_1660250))], (23073 ^ _773908) ^ [_1174648, _1174650] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1174648), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1174650))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1174648), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174650))), 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))))], (23363 ^ _773908) ^ [_1180457] : [-(c_Divides_Oadjust(_1180457) = 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)), _1180457))))), 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)), _1180457))))), 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))))))))], (7821 ^ _773908) ^ [_901611, _901613, _901615] : [class_Rings_Ocomm__semiring__1(_901611), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901611), _901613), _901615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901611), _901615), _901613))], (40872 ^ _773908) ^ [_1577788, _1577790, _1577792] : [-(_1577788 = _1577790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577792)), _1577788) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577792)), _1577790), 40878 ^ _773908 : [(40881 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1577792, _1577792, tc_HOL_Obool), c_fequal), 40877 ^ [_1577788, _1577790, _1577792]))], (40879 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577792, _1577792)), 40877 ^ [_1577788, _1577790, _1577792]), hAPP(c_List_Oset(tc_prod(_1577792, _1577792)), hAPP(hAPP(c_List_Ozip(_1577792, _1577792), _1577788), _1577790)))))]]], (33844 ^ _773908) ^ [_1402785, _1402787, _1402789, _1402791] : [class_Orderings_Oorder(_1402785), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402785, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402785, _1402787), _1402789)), c_SetInterval_Oord__class_OatLeastAtMost(_1402785, _1402789, _1402791)) = c_Orderings_Obot__class_Obot(tc_fun(_1402785, tc_HOL_Obool)))], (43182 ^ _773908) ^ [_1631501, _1631503, _1631505] : [-(c_List_Olistsp(_1631501, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1631501, tc_HOL_Obool)), _1631503), _1631505)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1631501), tc_HOL_Obool)), c_List_Olistsp(_1631501, _1631503)), c_List_Olistsp(_1631501, _1631505)))], (42973 ^ _773908) ^ [_1626748, _1626750, _1626752] : [hBOOL(hAPP(c_List_Odistinct(_1626748), _1626750)), -(hAPP(c_List_Oset(_1626748), c_List_Oremove1(_1626748, _1626752, _1626750)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626748, tc_HOL_Obool)), hAPP(c_List_Oset(_1626748), _1626750)), hAPP(hAPP(c_Set_Oinsert(_1626748), _1626752), c_Orderings_Obot__class_Obot(tc_fun(_1626748, tc_HOL_Obool)))))], (21917 ^ _773908) ^ [_1153134, _1153136, _1153138, _1153140] : [class_Fields_Ofield__inverse__zero(_1153134), class_Int_Onumber(_1153134), 21924 ^ _773908 : [(21925 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153134), _1153138), _1153140), 21928 ^ _773908 : [(21935 ^ _773908) ^ [] : [_1153140 = c_Groups_Ozero__class_Ozero(_1153134), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136) = c_Groups_Ozero__class_Ozero(_1153134))], (21929 ^ _773908) ^ [] : [-(_1153140 = c_Groups_Ozero__class_Ozero(_1153134)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153134), hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136)), _1153140) = _1153138)]]], (21941 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153134), _1153138), _1153140)), 21944 ^ _773908 : [(21947 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153134), hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136)), _1153140) = _1153138], (21945 ^ _773908) ^ [] : [_1153140 = c_Groups_Ozero__class_Ozero(_1153134)]], 21948 ^ _773908 : [(21951 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1153134), _1153136) = c_Groups_Ozero__class_Ozero(_1153134)], (21949 ^ _773908) ^ [] : [-(_1153140 = c_Groups_Ozero__class_Ozero(_1153134))]]]]], (3244 ^ _773908) ^ [_822540, _822542, _822544, _822546, _822548, _822550] : [-(c_Set_Ovimage(_822550, _822546, _822542) = c_Set_Ovimage(_822548, _822544, _822540)), _822550 = _822548, _822546 = _822544, _822542 = _822540], (45767 ^ _773908) ^ [_1688312, _1688314, _1688316] : [45769 ^ _773908 : [(45772 ^ _773908) ^ [] : [hBOOL(hAPP(_1688314, 45768 ^ [_1688312, _1688314, _1688316]))], (45770 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1688312), 45768 ^ [_1688312, _1688314, _1688316]), hAPP(c_List_Oset(_1688312), _1688316))))]], -(c_List_OtakeWhile(_1688312, _1688314, _1688316) = _1688316)], (28430 ^ _773908) ^ [_1290916, _1290918, _1290920] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290916, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290916, tc_HOL_Obool)), _1290918), _1290920)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290916, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290916, tc_HOL_Obool)), _1290918)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290916, tc_HOL_Obool)), _1290920)))], (2528 ^ _773908) ^ [_811230, _811232, _811234, _811236] : [-(c_Com_Ocom_OAss(_811236, _811232) = c_Com_Ocom_OAss(_811234, _811230)), _811236 = _811234, _811232 = _811230], (2866 ^ _773908) ^ [_816605, _816607, _816609, _816611, _816613, _816615, _816617, _816619] : [-(c_Product__Type_Oapsnd(_816619, _816615, _816611, _816607) = c_Product__Type_Oapsnd(_816617, _816613, _816609, _816605)), _816619 = _816617, _816615 = _816613, _816611 = _816609, _816607 = _816605], (43479 ^ _773908) ^ [_1637695, _1637697, _1637699, _1637701] : [_1637701 = c_List_Olist_ONil(_1637697), -(c_List_Olist__all2(_1637695, _1637697, _1637699, c_List_Olist_ONil(_1637695), _1637701))], (11826 ^ _773908) ^ [_971557, _971559, _971561] : [class_Groups_Oordered__comm__monoid__add(_971557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971557), c_Groups_Ozero__class_Ozero(_971557)), _971559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971557), c_Groups_Ozero__class_Ozero(_971557)), _971561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971557), c_Groups_Ozero__class_Ozero(_971557)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971557), _971559), _971561))))], (39248 ^ _773908) ^ [_1535174, _1535176, _1535178, _1535180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535174)), _1535176)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1535174)), _1535178))), _1535176 = hAPP(hAPP(c_List_Olist_OCons(_1535174), _1535180), _1535178)], (10113 ^ _773908) ^ [_942138, _942140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942138), _942140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _942138), c_Groups_Oone__class_Oone(tc_Int_Oint))), _942140)))], (51832 ^ _773908) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (49007 ^ _773908) ^ [_1762212] : [-(c_Nitpick_Odenom(_1762212) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1762212, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1762212)))], (20593 ^ _773908) ^ [_1129769, _1129771, _1129773] : [class_Rings_Olinordered__idom(_1129769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129769), _1129771), c_Groups_Ozero__class_Ozero(_1129769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129769), hAPP(hAPP(c_Power_Opower__class_Opower(_1129769), _1129771), 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)))), _1129773)))), c_Groups_Ozero__class_Ozero(_1129769))))], (46311 ^ _773908) ^ [_1700639, _1700641] : [c_Wellfounded_OwfP(_1700639, _1700641), -(c_Wellfounded_Oacyclic(_1700639, hAPP(c_Set_OCollect(tc_prod(_1700639, _1700639)), hAPP(c_Product__Type_Oprod_Oprod__case(_1700639, _1700639, tc_HOL_Obool), _1700641))))], (1384 ^ _773908) ^ [_794194, _794196] : [-(class_Complete__Lattice_Ocomplete__lattice(_794194)), _794196 = _794194, class_Complete__Lattice_Ocomplete__lattice(_794196)], (47907 ^ _773908) ^ [_1739321, _1739323, _1739325] : [class_Orderings_Olinorder(_1739321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1739321), _1739323)), 47917 ^ _773908 : [(47920 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739321), _1739325), 47916 ^ [_1739321, _1739323, _1739325]))], (47918 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739321), 47916 ^ [_1739321, _1739323, _1739325]), _1739323)))]], hBOOL(hAPP(hAPP(c_member(_1739321), _1739325), _1739323)), -(c_Big__Operators_Olinorder__class_OMin(_1739321, _1739323) = _1739325)], (45043 ^ _773908) ^ [_1673854, _1673856, _1673858, _1673860, _1673862] : [class_Orderings_Olinorder(_1673854), c_List_Olinorder__class_Osorted(_1673854, hAPP(hAPP(c_List_Omap(_1673856, _1673854), _1673858), _1673860)), -(c_List_Olinorder__class_Osorted(_1673854, hAPP(hAPP(c_List_Omap(_1673856, _1673854), _1673858), hAPP(c_List_Ofilter(_1673856, _1673862), _1673860))))], (43739 ^ _773908) ^ [_1643995, _1643997, _1643999, _1644001] : [-(hAPP(c_Set_Ovimage(_1643995, _1643997, _1643999), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643997, tc_HOL_Obool), _1644001)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643997, tc_HOL_Obool), tc_fun(_1643995, tc_HOL_Obool)), _1644001), c_Set_Ovimage(_1643995, _1643997, _1643999)))], (32046 ^ _773908) ^ [_1367888, _1367890] : [-(c_Relation_OId__on(_1367888, _1367890) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1367888, tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool)), _1367890), hAPP(hAPP(c_COMBC(_1367888, tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool), tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1367888, _1367888), tc_fun(tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool), tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool)), _1367888), c_Set_Oinsert(tc_prod(_1367888, _1367888))), hAPP(hAPP(c_COMBS(_1367888, _1367888, tc_prod(_1367888, _1367888)), c_Product__Type_OPair(_1367888, _1367888)), c_COMBI(_1367888)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1367888, _1367888), tc_HOL_Obool)))))], (37380 ^ _773908) ^ [_1479940, _1479942, _1479944, _1479946] : [hAPP(hAPP(c_Product__Type_OSigma(_1479940, _1479942), _1479944), hAPP(c_COMBK(tc_fun(_1479942, tc_HOL_Obool), _1479940), _1479946)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479940, _1479942), tc_HOL_Obool)), -(_1479944 = c_Orderings_Obot__class_Obot(tc_fun(_1479940, tc_HOL_Obool))), -(_1479946 = c_Orderings_Obot__class_Obot(tc_fun(_1479942, tc_HOL_Obool)))], (47160 ^ _773908) ^ [_1720921, _1720923, _1720925, _1720927, _1720929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1720921, _1720921)), hAPP(hAPP(c_Product__Type_OPair(_1720921, _1720921), _1720923), _1720925)), c_Transitive__Closure_Otrancl(_1720921, _1720927))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1720921, _1720921)), hAPP(hAPP(c_Product__Type_OPair(_1720921, _1720921), _1720925), _1720929)), _1720927)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1720921, _1720921)), hAPP(hAPP(c_Product__Type_OPair(_1720921, _1720921), _1720923), _1720929)), c_Transitive__Closure_Otrancl(_1720921, _1720927))))], (37638 ^ _773908) ^ [_1487521, _1487523, _1487525, _1487527, _1487529, _1487531] : [class_Groups_Ocomm__monoid__add(_1487521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487523), _1487525)), 37648 ^ _773908 : [(37651 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487527), hAPP(_1487529, 37647 ^ [_1487521, _1487523, _1487525, _1487527, _1487529, _1487531])))], (37649 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487523), 37647 ^ [_1487521, _1487523, _1487525, _1487527, _1487529, _1487531]), _1487525)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487523, _1487521), hAPP(hAPP(c_COMBS(_1487523, tc_fun(_1487527, tc_HOL_Obool), _1487521), hAPP(hAPP(c_COMBB(tc_fun(_1487527, _1487521), tc_fun(tc_fun(_1487527, tc_HOL_Obool), _1487521), _1487523), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487527, _1487521)), _1487531)), _1487529)), _1487525) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1487523, _1487527), _1487521), hAPP(c_Product__Type_Oprod_Oprod__case(_1487523, _1487527, _1487521), _1487531)), hAPP(hAPP(c_Product__Type_OSigma(_1487523, _1487527), _1487525), _1487529)))], (38928 ^ _773908) ^ [_1526150, _1526152, _1526154] : [c_Wellfounded_Owf(_1526150, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526150, _1526150), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526150, _1526150), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1526150, _1526150, _1526150), _1526152), _1526152)), hAPP(hAPP(c_Relation_Orel__comp(_1526150, _1526150, _1526150), _1526154), _1526152))), _1526154)), -(c_Wellfounded_Owf(_1526150, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526150, _1526150), tc_HOL_Obool)), _1526152), _1526154)))], (37123 ^ _773908) ^ [_1473471, _1473473, _1473475, _1473477, _1473479, _1473481] : [hAPP(_1473471, _1473473) = _1473475, hBOOL(hAPP(hAPP(c_member(_1473477), _1473475), _1473479)), -(hBOOL(hAPP(hAPP(c_member(_1473481), _1473473), hAPP(c_Set_Ovimage(_1473481, _1473477, _1473471), _1473479))))], (41710 ^ _773908) ^ [_1595667, _1595669, _1595671] : [_1595667 = c_List_Olist_ONil(_1595669), -(c_List_Obutlast(_1595669, hAPP(hAPP(c_List_Oappend(_1595669), _1595671), _1595667)) = c_List_Obutlast(_1595669, _1595671))], (35506 ^ _773908) ^ [_1439437, _1439439] : [class_Orderings_Olinorder(_1439437), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1439437, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1439437), _1439439)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439437), _1439439))], (44042 ^ _773908) ^ [_1651597, _1651599] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1651597), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651597, tc_HOL_Obool), _1651599)))), 44043 ^ _773908 : [(44044 ^ _773908) ^ [_1651661] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1651597, tc_HOL_Obool)), _1651661), _1651599)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1651597), _1651661))]]], (18099 ^ _773908) ^ [_1086122] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086122)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086122)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086122))], (43509 ^ _773908) ^ [_1638345, _1638347, _1638349, _1638351, _1638353, _1638355, _1638357] : [c_List_Olist__all2(_1638345, _1638347, _1638349, _1638351, hAPP(hAPP(c_List_Omap(_1638353, _1638347), _1638355), _1638357)), -(c_List_Olist__all2(_1638345, _1638353, hAPP(hAPP(c_COMBC(_1638345, tc_fun(_1638353, _1638347), tc_fun(_1638353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638347, tc_HOL_Obool), tc_fun(tc_fun(_1638353, _1638347), tc_fun(_1638353, tc_HOL_Obool)), _1638345), c_COMBB(_1638347, tc_HOL_Obool, _1638353)), _1638349)), _1638355), _1638351, _1638357))], (43013 ^ _773908) ^ [_1627444, _1627446, _1627448, _1627450] : [-(_1627444 = _1627446), 43016 ^ _773908 : [(43023 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1627448), _1627444), hAPP(c_List_Oset(_1627448), _1627450))), -(hBOOL(hAPP(hAPP(c_member(_1627448), _1627444), hAPP(c_List_Oset(_1627448), c_List_Oremove1(_1627448, _1627446, _1627450)))))], (43017 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1627448), _1627444), hAPP(c_List_Oset(_1627448), c_List_Oremove1(_1627448, _1627446, _1627450)))), -(hBOOL(hAPP(hAPP(c_member(_1627448), _1627444), hAPP(c_List_Oset(_1627448), _1627450))))]]], (13722 ^ _773908) ^ [_1005073, _1005075] : [class_Divides_Osemiring__div(_1005073), -(c_Divides_Odiv__class_Omod(_1005073, _1005075, c_Groups_Oone__class_Oone(_1005073)) = c_Groups_Ozero__class_Ozero(_1005073))], (37235 ^ _773908) ^ [_1476186, _1476188, _1476190, _1476192] : [-(hAPP(c_Set_Oimage(_1476186, _1476188, _1476190), hAPP(c_Set_Ovimage(_1476186, _1476188, _1476190), _1476192)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476188, tc_HOL_Obool)), _1476192), hAPP(c_Set_Oimage(_1476186, _1476188, _1476190), c_Orderings_Otop__class_Otop(tc_fun(_1476186, tc_HOL_Obool)))))], (41600 ^ _773908) ^ [_1593430, _1593432] : [class_Groups_Ocomm__monoid__add(_1593430), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1593430), _1593432) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1593430), hAPP(c_List_Onth(_1593430), _1593432)), 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(_1593430)), _1593432))))], (51572 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (43870 ^ _773908) ^ [_1646994, _1646996, _1646998] : [class_Complete__Lattice_Ocomplete__lattice(_1646994), hBOOL(hAPP(hAPP(c_member(_1646994), _1646996), _1646998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1646994), _1646996), c_Complete__Lattice_OSup__class_OSup(_1646994, _1646998))))], (1174 ^ _773908) ^ [_791569, _791571] : [-(class_Rings_Olinordered__ring__strict(_791569)), _791571 = _791569, class_Rings_Olinordered__ring__strict(_791571)], (28656 ^ _773908) ^ [_1295807, _1295809, _1295811, _1295813] : [hBOOL(hAPP(hAPP(c_member(_1295807), _1295809), c_SetInterval_Oord_OlessThan(_1295807, _1295811, _1295813))), -(hBOOL(hAPP(hAPP(_1295811, _1295809), _1295813)))], (23103 ^ _773908) ^ [_1175249] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1175249) = 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), _1175249), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (22803 ^ _773908) ^ [_1169682, _1169684, _1169686] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1169682, _1169684, _1169686, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1169684)], (19335 ^ _773908) ^ [_1107741, _1107743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107741), _1107743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107741)), c_Int_OBit1(_1107743))))], (39147 ^ _773908) ^ [_1532326, _1532328, _1532330, _1532332] : [hBOOL(hAPP(hAPP(c_member(_1532326), _1532328), hAPP(c_Relation_ORange(_1532330, _1532326), _1532332))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532330, _1532326)), hAPP(hAPP(c_Product__Type_OPair(_1532330, _1532326), 39150 ^ [_1532326, _1532328, _1532330, _1532332]), _1532328)), _1532332)))], (30585 ^ _773908) ^ [_1333478, _1333480, _1333482, _1333484] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333478), _1333480)), hBOOL(hAPP(hAPP(c_member(_1333478), _1333482), _1333480)), -(hBOOL(hAPP(hAPP(c_member(_1333478), _1333482), _1333484))), -(hAPP(c_Finite__Set_Ocard(_1333478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333478, tc_HOL_Obool)), _1333480), hAPP(hAPP(c_Set_Oinsert(_1333478), _1333482), _1333484))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333478, tc_HOL_Obool)), _1333480), _1333484))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49428 ^ _773908) ^ [_1771803, _1771805, _1771807] : [_1771805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1771803) = c_List_Oreplicate(_1771803, _1771805, _1771807))], (41318 ^ _773908) ^ [_1588094, _1588096, _1588098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588094)), _1588096)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1588094, _1588098), _1588096) = _1588096)], (39396 ^ _773908) ^ [_1539070, _1539072, _1539074] : [-(c_List_Olist_ONil(_1539070) = hAPP(hAPP(c_List_Oappend(_1539070), _1539072), _1539074)), _1539072 = c_List_Olist_ONil(_1539070), _1539074 = c_List_Olist_ONil(_1539070)], (39116 ^ _773908) ^ [_1531266, _1531268] : [c_Wellfounded_Owf(_1531266, _1531268), -(c_Wellfounded_Owf(tc_List_Olist(_1531266), c_List_Olex(_1531266, _1531268)))], (46853 ^ _773908) ^ [_1713197, _1713199] : [-(c_Transitive__Closure_Ortrancl(_1713197, _1713199) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1713197, _1713197), tc_HOL_Obool)), c_Relation_OId(_1713197)), hAPP(hAPP(c_Relation_Orel__comp(_1713197, _1713197, _1713197), c_Transitive__Closure_Ortrancl(_1713197, _1713199)), _1713199)))], (16037 ^ _773908) ^ [_1048025, _1048027, _1048029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048025), _1048027)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048029), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048027), _1048025))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048029), _1048025)), hAPP(c_Nat_OSuc, _1048027)))], (45733 ^ _773908) ^ [_1687677, _1687679, _1687681, _1687683, _1687685] : [-(hBOOL(hAPP(_1687677, _1687679))), -(c_List_OtakeWhile(_1687681, _1687677, hAPP(hAPP(c_List_Oappend(_1687681), _1687683), hAPP(hAPP(c_List_Olist_OCons(_1687681), _1687679), _1687685))) = c_List_OtakeWhile(_1687681, _1687677, _1687683))], (22895 ^ _773908) ^ [_1171051, _1171053, _1171055, _1171057] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1171051, _1171053, _1171055, c_Code__Numeral_OSuc__code__numeral(_1171057)) = hAPP(_1171055, _1171057))], (31999 ^ _773908) ^ [_1366919, _1366921] : [_1366919 = _1366921, -(hAPP(c_Int_ORep__Integ, _1366919) = hAPP(c_Int_ORep__Integ, _1366921))], (29325 ^ _773908) ^ [_1308967, _1308969, _1308971] : [class_Orderings_Olinorder(_1308967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308967), _1308969)), 29332 ^ _773908 : [(29339 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308967, tc_HOL_Obool)), _1308969), hAPP(hAPP(c_Set_Oinsert(_1308967), _1308971), c_Orderings_Obot__class_Obot(tc_fun(_1308967, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308967, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308967, hAPP(hAPP(c_Set_Oinsert(_1308967), _1308971), _1308969)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308967), _1308971), c_Big__Operators_Olinorder__class_OMax(_1308967, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308967, tc_HOL_Obool)), _1308969), hAPP(hAPP(c_Set_Oinsert(_1308967), _1308971), c_Orderings_Obot__class_Obot(tc_fun(_1308967, tc_HOL_Obool)))))))], (29333 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308967, tc_HOL_Obool)), _1308969), hAPP(hAPP(c_Set_Oinsert(_1308967), _1308971), c_Orderings_Obot__class_Obot(tc_fun(_1308967, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308967, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1308967, hAPP(hAPP(c_Set_Oinsert(_1308967), _1308971), _1308969)) = _1308971)]]], (51762 ^ _773908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51512 ^ _773908) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (14865 ^ _773908) ^ [_1025220, _1025222, _1025224, _1025226] : [class_Divides_Osemiring__div(_1025220), -(_1025222 = c_Groups_Ozero__class_Ozero(_1025220)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025220), _1025224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025220), _1025222), _1025226))), _1025222) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025220), _1025226), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025220), _1025224), _1025222)))], (8279 ^ _773908) ^ [_910240, _910242, _910244] : [class_Rings_Osemiring__1(_910240), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_910240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _910242), _910244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910240), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_910240), _910242)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_910240), _910244)))], (38072 ^ _773908) ^ [_1497807, _1497809, _1497811] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497807, tc_HOL_Obool)), _1497809), _1497811) = hAPP(c_Set_OCollect(_1497807), hAPP(hAPP(c_COMBS(_1497807, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497807), c_fconj), hAPP(hAPP(c_COMBC(_1497807, tc_fun(_1497807, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497807)), _1497809))), hAPP(hAPP(c_COMBC(_1497807, tc_fun(_1497807, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497807)), _1497811))))], (18529 ^ _773908) ^ [_1093912, _1093914, _1093916, _1093918] : [hBOOL(hAPP(hAPP(c_member(_1093912), _1093914), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093912, tc_HOL_Obool)), _1093916), _1093918))), -(hBOOL(hAPP(hAPP(c_member(_1093912), _1093914), _1093916)))], (44843 ^ _773908) ^ [_1670318, _1670320, _1670322, _1670324, _1670326, _1670328, _1670330] : [-(c_List_Ofoldr(_1670318, _1670320, _1670322, hAPP(hAPP(c_List_Omap(_1670324, _1670318), _1670326), _1670328), _1670330) = c_List_Ofoldr(_1670324, _1670320, hAPP(c_Fun_Ocomp(_1670318, tc_fun(_1670320, _1670320), _1670324, _1670322), _1670326), _1670328, _1670330))], (36499 ^ _773908) ^ [_1461067, _1461069, _1461071, _1461073] : [-(c_Wellfounded_Omax__extp(_1461067, _1461069, _1461071, _1461073)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461067), _1461071)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461067), _1461073)), -(_1461073 = c_Orderings_Obot__class_Obot(tc_fun(_1461067, tc_HOL_Obool))), 36513 ^ _773908 : [(36516 ^ _773908) ^ [_1461412] : [hBOOL(hAPP(hAPP(c_member(_1461067), _1461412), _1461073)), hBOOL(hAPP(hAPP(_1461069, 36512 ^ [_1461067, _1461069, _1461071, _1461073]), _1461412))], (36514 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461067), 36512 ^ [_1461067, _1461069, _1461071, _1461073]), _1461071)))]]], (10047 ^ _773908) ^ [_940965, _940967, _940969] : [class_Rings_Olinordered__idom(_940965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940965), c_Groups_Ozero__class_Ozero(_940965)), _940967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940965), c_Groups_Ozero__class_Ozero(_940965)), _940969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940965), _940969), c_Groups_Oone__class_Oone(_940965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940965), _940969), _940967)), _940967)))], (49460 ^ _773908) ^ [_1772310, _1772312, _1772314, _1772316] : [-(hAPP(hAPP(c_List_Omap(_1772310, _1772312), hAPP(c_COMBK(_1772312, _1772310), _1772314)), _1772316) = c_List_Oreplicate(_1772312, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772310)), _1772316), _1772314))], (7123 ^ _773908) ^ [_889295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889295), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33358 ^ _773908) ^ [_1393616, _1393618, _1393620, _1393622, _1393624] : [class_Orderings_Olinorder(_1393616), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393616, _1393618), _1393620) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1393616, _1393622), _1393624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393616), _1393618), _1393620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393616), _1393622), _1393624)), -(_1393618 = _1393622)], (44168 ^ _773908) ^ [_1654132] : [class_Complete__Lattice_Ocomplete__lattice(_1654132), -(c_Complete__Lattice_OInf__class_OInf(_1654132, c_Orderings_Otop__class_Otop(tc_fun(_1654132, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1654132))], (31300 ^ _773908) ^ [_1349031, _1349033, _1349035, _1349037, _1349039, _1349041] : [-(hAPP(c_Relation_OImage(_1349031, _1349033, _1349035), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349037, tc_fun(_1349031, tc_HOL_Obool)), _1349039), _1349041)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1349037, tc_fun(_1349033, tc_HOL_Obool)), _1349039), hAPP(hAPP(c_COMBB(tc_fun(_1349031, tc_HOL_Obool), tc_fun(_1349033, tc_HOL_Obool), _1349037), c_Relation_OImage(_1349031, _1349033, _1349035)), _1349041)))], (38474 ^ _773908) ^ [_1513987, _1513989] : [-(c_Product__Type_Oapsnd(_1513987, _1513987, _1513989, c_Fun_Oid(_1513987)) = c_Fun_Oid(tc_prod(_1513989, _1513987)))], (49995 ^ _773908) ^ [_1784176, _1784178, _1784180] : [-(c_List_Olist__ex(_1784176, _1784180, _1784178)), 49996 ^ _773908 : [(49997 ^ _773908) ^ [_1784233] : [hBOOL(hAPP(hAPP(c_member(_1784176), _1784233), hAPP(c_List_Oset(_1784176), _1784178))), hBOOL(hAPP(_1784180, _1784233))]]], (23141 ^ _773908) ^ [_1176163, _1176165, _1176167, _1176169] : [-(c_Nat_Onat_Onat__case(_1176163, _1176165, _1176167, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176169)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1176163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1176169))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1176163, _1176163), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1176163, tc_fun(_1176163, _1176163)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1176163, tc_fun(_1176163, _1176163)), tc_Int_Oint), c_If(_1176163)), c_Nat__Numeral_Oneg)), _1176165)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1176163, tc_Int_Oint), _1176167), c_Int_Onat))))], (7055 ^ _773908) ^ [_888218, _888220] : [class_Groups_Ocomm__monoid__add(_888218), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_888218), c_Groups_Ozero__class_Ozero(_888218)), _888220) = _888220)], (21385 ^ _773908) ^ [_1143483, _1143485, _1143487] : [class_Fields_Olinordered__field(_1143483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143483), _1143485), c_Groups_Ozero__class_Ozero(_1143483))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143483), c_Groups_Ozero__class_Ozero(_1143483)), _1143487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143483), _1143485), _1143487)), c_Groups_Ozero__class_Ozero(_1143483))))], (16081 ^ _773908) ^ [_1049127, _1049129, _1049131, _1049133, _1049135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049127), _1049129)), 16084 ^ _773908 : [(16091 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049133), 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), _1049129), _1049127)), _1049131)), _1049135))), -(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), _1049127), _1049131)), _1049133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049129), _1049131)), _1049135))))], (16085 ^ _773908) ^ [] : [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), _1049127), _1049131)), _1049133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049129), _1049131)), _1049135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049133), 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), _1049129), _1049127)), _1049131)), _1049135))))]]], (33810 ^ _773908) ^ [_1402080, _1402082, _1402084, _1402086] : [class_Orderings_Olinorder(_1402080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402080), _1402082), _1402084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402080), _1402084), _1402086)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402080, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402080, _1402082), _1402084)), c_SetInterval_Oord__class_OatLeastAtMost(_1402080, _1402084, _1402086)) = c_SetInterval_Oord__class_OatLeastAtMost(_1402080, _1402082, _1402086))], (19575 ^ _773908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (6124 ^ _773908) ^ [_873192, _873194, _873196, _873198, _873200, _873202] : [c_Natural_Oevaln(_873192, _873194, _873196, _873198), c_Natural_Oevaln(_873200, _873198, _873196, _873202), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_873192, _873200), _873194, _873196, _873202))], (15215 ^ _773908) ^ [_1031866, _1031868, _1031870, _1031872, _1031874] : [class_Groups_Ominus(_1031866), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031868, _1031866)), _1031870), _1031872), _1031874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031866), hAPP(_1031870, _1031874)), hAPP(_1031872, _1031874)))], (32454 ^ _773908) ^ [_1376254, _1376256] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1376254, _1376256) = 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), _1376254), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1376256))))], (6538 ^ _773908) ^ [_880142, _880144, _880146] : [class_Orderings_Opreorder(_880142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880142), _880144), _880146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880142), _880146), _880144))], (34800 ^ _773908) ^ [_1423808, _1423810] : [class_Orderings_Olinorder(_1423808), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423808, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1423808), _1423810)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1423808), _1423810))], (26195 ^ _773908) ^ [_1238834, _1238836, _1238838, _1238840] : [class_Lattices_Osemilattice__sup(_1238834), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238834), _1238836), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238834), _1238838), _1238840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238834), _1238838), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238834), _1238836), _1238840)))], (31361 ^ _773908) ^ [_1350523, _1350525, _1350527, _1350529, _1350531, _1350533] : [class_Groups_Oab__semigroup__mult(_1350523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350525), _1350527)), -(hBOOL(hAPP(hAPP(c_member(_1350525), _1350529), _1350527))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350523, _1350525, c_Groups_Otimes__class_Otimes(_1350523)), _1350531), _1350533), hAPP(hAPP(c_Set_Oinsert(_1350525), _1350529), _1350527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350523), hAPP(_1350531, _1350529)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350523, _1350525, c_Groups_Otimes__class_Otimes(_1350523)), _1350531), _1350533), _1350527)))], (45433 ^ _773908) ^ [_1681298, _1681300, _1681302, _1681304] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1681298), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1681298))), _1681300))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681302), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1681298))), c_List_Otranspose(_1681298, _1681300)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681304), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1681298))), hAPP(c_List_Ofilter(tc_List_Olist(_1681298), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1681298)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681302)), c_Nat_Osize__class_Osize(tc_List_Olist(_1681298)))), _1681300)))), -(hAPP(hAPP(c_List_Onth(_1681298), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1681298)), c_List_Otranspose(_1681298, _1681300)), _1681302)), _1681304) = hAPP(hAPP(c_List_Onth(_1681298), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1681298)), _1681300), _1681304)), _1681302))], (16905 ^ _773908) ^ [_1064625, _1064627, _1064629] : [class_Int_Onumber__ring(_1064625), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064625), hAPP(c_Int_Onumber__class_Onumber__of(_1064625), _1064627)), hAPP(c_Int_Onumber__class_Onumber__of(_1064625), _1064629)) = hAPP(c_Int_Onumber__class_Onumber__of(_1064625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1064627), _1064629)))], (12953 ^ _773908) ^ [_991169, _991171, _991173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991169, tc_HOL_Obool)), _991171), _991173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991169, tc_HOL_Obool)), _991171), _991173)))], (2118 ^ _773908) ^ [_804665, _804667, _804669, _804671, _804673, _804675] : [-(c_Power_Opower_Opower(_804675, _804671, _804667) = c_Power_Opower_Opower(_804673, _804669, _804665)), _804675 = _804673, _804671 = _804669, _804667 = _804665], (47654 ^ _773908) ^ [_1733687, _1733689, _1733691, _1733693, _1733695, _1733697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1733687, tc_HOL_Obool)), _1733689), _1733691)), 47660 ^ _773908 : [(47663 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1733693, tc_HOL_Obool)), hAPP(_1733695, 47659 ^ [_1733687, _1733689, _1733691, _1733693, _1733695, _1733697])), hAPP(_1733697, 47659 ^ [_1733687, _1733689, _1733691, _1733693, _1733695, _1733697])))], (47661 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733687), 47659 ^ [_1733687, _1733689, _1733691, _1733693, _1733695, _1733697]), _1733689)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1733687, _1733693), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1733687, _1733693), _1733689), _1733695)), hAPP(hAPP(c_Product__Type_OSigma(_1733687, _1733693), _1733691), _1733697))))], (44186 ^ _773908) ^ [_1654527, _1654529, _1654531] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654527, tc_HOL_Obool)), _1654529), _1654531) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654527, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1654527, tc_HOL_Obool)), _1654529), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1654527, tc_HOL_Obool)), _1654531), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1654527, tc_HOL_Obool), tc_HOL_Obool))))))], (31748 ^ _773908) ^ [_1359765, _1359767, _1359769, _1359771, _1359773, _1359775] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359765, tc_fun(_1359767, tc_HOL_Obool)), _1359769), hAPP(hAPP(c_COMBB(_1359771, tc_fun(_1359767, tc_HOL_Obool), _1359765), _1359773), _1359775)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359771, tc_fun(_1359767, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1359765, _1359771, _1359775), _1359769)), _1359773))], (23051 ^ _773908) ^ [_1174196, _1174198, _1174200, _1174202, _1174204, _1174206] : [-(c_Nitpick_Opair__box_OPairBox(_1174196, _1174198, _1174200, _1174202) = c_Nitpick_Opair__box_OPairBox(_1174196, _1174198, _1174204, _1174206)), _1174200 = _1174204, _1174202 = _1174206], (7936 ^ _773908) ^ [_903846, _903848, _903850, _903852] : [-(hBOOL(hAPP(_903846, _903848))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_903846, _903850), _903848, _903852, _903848))], (42351 ^ _773908) ^ [_1612955, _1612957, _1612959, _1612961, _1612963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612955), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612957)), _1612959))), -(hAPP(hAPP(c_List_Onth(_1612961), hAPP(hAPP(c_List_Omap(_1612957, _1612961), _1612963), _1612959)), _1612955) = hAPP(_1612963, hAPP(hAPP(c_List_Onth(_1612957), _1612959), _1612955)))], (2310 ^ _773908) ^ [_807705, _807707, _807709, _807711] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_807711, _807707) = c_Code__Numeral_Odiv__mod__code__numeral(_807709, _807705)), _807711 = _807709, _807707 = _807705], (50794 ^ _773908) ^ [_1801079, _1801081] : [-(c_Equiv__Relations_Opart__equivp(_1801079, _1801081)), 50797 ^ _773908 : [(50798 ^ _773908) ^ [_1801156] : [hBOOL(hAPP(hAPP(_1801081, _1801156), _1801156))]], c_Predicate_Osymp(_1801079, _1801081), c_Predicate_Otransp(_1801079, _1801081)], (23628 ^ _773908) ^ [_1186139, _1186141] : [-(_1186139 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1186141, _1186139) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1186141), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1186139)))], (51420 ^ _773908) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (44509 ^ _773908) ^ [_1661480, _1661482, _1661484] : [-(hAPP(c_List_Oset(_1661480), hAPP(c_List_Ofilter(_1661480, _1661482), _1661484)) = hAPP(c_Set_OCollect(_1661480), hAPP(hAPP(c_COMBS(_1661480, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1661480), c_fconj), hAPP(hAPP(c_COMBC(_1661480, tc_fun(_1661480, tc_HOL_Obool), tc_HOL_Obool), c_member(_1661480)), hAPP(c_List_Oset(_1661480), _1661484)))), _1661482)))], (51806 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (24671 ^ _773908) ^ [_1208635, _1208637, _1208639, _1208641, _1208643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1208635, _1208637)), hAPP(_1208635, _1208639))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1208641, _1208641)), hAPP(hAPP(c_Product__Type_OPair(_1208641, _1208641), _1208637), _1208639)), c_Wellfounded_Omlex__prod(_1208641, _1208635, _1208643))))], (28234 ^ _773908) ^ [_1286028, _1286030, _1286032] : [class_Lattices_Olattice(_1286028), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286028), _1286030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286028), _1286030), _1286032)) = _1286030)], (36549 ^ _773908) ^ [_1462211, _1462213, _1462215, _1462217, _1462219] : [c_Typedef_Otype__definition(_1462211, _1462213, _1462215, _1462217, _1462219), -(hAPP(c_Set_Oimage(_1462211, _1462213, _1462215), c_Orderings_Otop__class_Otop(tc_fun(_1462211, tc_HOL_Obool))) = _1462219)], (514 ^ _773908) ^ [_781765, _781767, _781769, _781771] : [-(c_Wellfounded_OwfP(_781769, _781765)), c_Wellfounded_OwfP(_781771, _781767), _781771 = _781769, _781767 = _781765], (8373 ^ _773908) ^ [_911908, _911910, _911912] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911910), _911912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911908), _911912)))], (4448 ^ _773908) ^ [_841626, _841628, _841630, _841632, _841634, _841636] : [-(c_List_Osplice(_841636, _841632, _841628) = c_List_Osplice(_841634, _841630, _841626)), _841636 = _841634, _841632 = _841630, _841628 = _841626], (39408 ^ _773908) ^ [_1539268, _1539270] : [-(c_List_Osublist(_1539268, c_List_Olist_ONil(_1539268), _1539270) = c_List_Olist_ONil(_1539268))], (46528 ^ _773908) ^ [_1704856, _1704858] : [46530 ^ _773908 : [(46533 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1704858), 46529 ^ [_1704856, _1704858]))], (46531 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46529 ^ [_1704856, _1704858]), _1704856)))]], -(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)), _1704858), _1704856))], (18919 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (50185 ^ _773908) ^ [_1790042, _1790044, _1790046, _1790048, _1790050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1790042), tc_List_Olist(_1790042))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1790042), tc_List_Olist(_1790042)), _1790044), _1790046)), c_List_Olexord(_1790042, _1790048))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1790042), tc_List_Olist(_1790042))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1790042), tc_List_Olist(_1790042)), _1790046), _1790050)), c_List_Olexord(_1790042, _1790048))), c_Relation_Otrans(_1790042, _1790048), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1790042), tc_List_Olist(_1790042))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1790042), tc_List_Olist(_1790042)), _1790044), _1790050)), c_List_Olexord(_1790042, _1790048))))], (20307 ^ _773908) ^ [_1124440] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1124440), _1124440)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1124440)], (26049 ^ _773908) ^ [_1235679, _1235681, _1235683] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235679, tc_HOL_Obool)), _1235681), _1235683) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235679, tc_HOL_Obool)), _1235683), _1235681))], (780 ^ _773908) ^ [_785820, _785822, _785824, _785826, _785828, _785830] : [-(c_Nitpick_Oless__eq__frac(_785828, _785824, _785820)), c_Nitpick_Oless__eq__frac(_785830, _785826, _785822), _785830 = _785828, _785826 = _785824, _785822 = _785820], (43651 ^ _773908) ^ [_1641930, _1641932] : [-(_1641930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1641932, _1641930, c_List_Olist_ONil(_1641932)) = c_List_Olist_ONil(tc_List_Olist(_1641932)))], (6022 ^ _773908) ^ [_870724, _870726, _870728, _870730] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _870724), _870726, hAPP(c_Nat_OSuc, _870728), _870730), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870724)), _870726, _870728, _870730))], (51470 ^ _773908) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (37265 ^ _773908) ^ [_1476763, _1476765, _1476767, _1476769] : [-(hAPP(c_Set_Ovimage(_1476763, _1476765, _1476767), _1476769) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476765, tc_fun(_1476763, tc_HOL_Obool)), _1476769), hAPP(hAPP(c_COMBB(tc_fun(_1476765, tc_HOL_Obool), tc_fun(_1476763, tc_HOL_Obool), _1476765), c_Set_Ovimage(_1476763, _1476765, _1476767)), hAPP(hAPP(c_COMBC(_1476765, tc_fun(_1476765, tc_HOL_Obool), tc_fun(_1476765, tc_HOL_Obool)), c_Set_Oinsert(_1476765)), c_Orderings_Obot__class_Obot(tc_fun(_1476765, tc_HOL_Obool))))))], (48599 ^ _773908) ^ [_1753286, _1753288, _1753290, _1753292, _1753294] : [c_Finite__Set_Ofun__left__comm(_1753286, _1753288, _1753290), -(hAPP(c_Fun_Ocomp(_1753288, _1753288, _1753288, hAPP(_1753290, _1753292)), hAPP(_1753290, _1753294)) = hAPP(c_Fun_Ocomp(_1753288, _1753288, _1753288, hAPP(_1753290, _1753294)), hAPP(_1753290, _1753292)))], (6952 ^ _773908) ^ [_886427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886427), _886427))], (21361 ^ _773908) ^ [_1143099, _1143101] : [c_Nat__Transfer_Ois__nat(_1143099), c_Nat__Transfer_Ois__nat(_1143101), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1143099, _1143101)))], (9751 ^ _773908) ^ [_936399, _936401, _936403] : [class_Orderings_Oorder(_936399), 9754 ^ _773908 : [(9763 ^ _773908) ^ [] : [-(_936401 = _936403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936399), _936401), _936403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936399), _936403), _936401))], (9755 ^ _773908) ^ [] : [_936401 = _936403, 9758 ^ _773908 : [(9761 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936399), _936403), _936401)))], (9759 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936399), _936401), _936403)))]]]]], (45507 ^ _773908) ^ [_1682870, _1682872, _1682874, _1682876] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682870)), _1682872) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682874)), _1682876), -(hAPP(hAPP(c_List_Ozip(_1682870, _1682874), hAPP(c_List_Orev(_1682870), _1682872)), hAPP(c_List_Orev(_1682874), _1682876)) = hAPP(c_List_Orev(tc_prod(_1682870, _1682874)), hAPP(hAPP(c_List_Ozip(_1682870, _1682874), _1682872), _1682876)))], (28210 ^ _773908) ^ [_1285119, _1285121, _1285123, _1285125] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285119, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285119, tc_HOL_Obool)), _1285121), _1285123)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285119, tc_HOL_Obool)), _1285125), _1285123)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285119, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285119, tc_HOL_Obool)), _1285121), _1285123)), _1285125))], (33894 ^ _773908) ^ [_1403861, _1403863, _1403865, _1403867, _1403869] : [c_Fun_Oinj__on(_1403861, _1403863, _1403865, hAPP(hAPP(c_Set_Oinsert(_1403861), _1403867), _1403869)), 33897 ^ _773908 : [(33900 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1403863), hAPP(_1403865, _1403867)), hAPP(c_Set_Oimage(_1403861, _1403863, _1403865), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403861, tc_HOL_Obool)), _1403869), hAPP(hAPP(c_Set_Oinsert(_1403861), _1403867), c_Orderings_Obot__class_Obot(tc_fun(_1403861, tc_HOL_Obool)))))))], (33898 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1403861, _1403863, _1403865, _1403869))]]], (9793 ^ _773908) ^ [_937056, _937058, _937060] : [class_Orderings_Oorder(_937056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), _937058), _937060)), 9800 ^ _773908 : [(9807 ^ _773908) ^ [] : [_937060 = _937058, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), _937060), _937058)))], (9801 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), _937060), _937058)), -(_937060 = _937058)]]], (40163 ^ _773908) ^ [_1559183, _1559185, _1559187, _1559189] : [-(hAPP(hAPP(c_List_Otake(_1559183), _1559185), hAPP(hAPP(c_List_Odrop(_1559183), _1559187), _1559189)) = hAPP(hAPP(c_List_Odrop(_1559183), _1559187), hAPP(hAPP(c_List_Otake(_1559183), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1559185), _1559187)), _1559189)))], (34300 ^ _773908) ^ [_1412629, _1412631, _1412633] : [class_Orderings_Olinorder(_1412629), 34303 ^ _773908 : [(34310 ^ _773908) ^ [] : [_1412631 = _1412633, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1412629), _1412631) = hAPP(c_SetInterval_Oord__class_OlessThan(_1412629), _1412633))], (34304 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1412629), _1412631) = hAPP(c_SetInterval_Oord__class_OlessThan(_1412629), _1412633), -(_1412631 = _1412633)]]], (50326 ^ _773908) ^ [_1792977, _1792979] : [c_Relation_Otrans(_1792977, hAPP(c_Set_OCollect(tc_prod(_1792977, _1792977)), hAPP(c_Product__Type_Oprod_Oprod__case(_1792977, _1792977, tc_HOL_Obool), _1792979))), -(c_Predicate_Otransp(_1792977, _1792979))], (6204 ^ _773908) ^ [_874557, _874559, _874561, _874563] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_874557)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874557), _874559), _874561), _874563)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44369 ^ _773908) ^ [_1658562, _1658564, _1658566, _1658568] : [-(hBOOL(hAPP(_1658562, _1658564))), -(c_List_Oremove1(_1658566, _1658564, hAPP(c_List_Ofilter(_1658566, _1658562), _1658568)) = hAPP(c_List_Ofilter(_1658566, _1658562), _1658568))], (39536 ^ _773908) ^ [_1541886, _1541888, _1541890] : [-(c_Random_Oselect__weight(_1541886, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1541886)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1541886), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1541888)), _1541890)) = c_Random_Oselect__weight(_1541886, _1541890))], (7125 ^ _773908) ^ [_889329] : [-(_889329 = 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)), _889329)))], (15757 ^ _773908) ^ [_1042019, _1042021, _1042023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042019), _1042021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042023), _1042019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042019), _1042023)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042021), _1042023))))], (42181 ^ _773908) ^ [_1608579, _1608581, _1608583, _1608585, _1608587] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608579, tc_fun(_1608581, tc_HOL_Obool)), _1608583), hAPP(hAPP(c_COMBB(tc_fun(_1608581, tc_HOL_Obool), tc_fun(_1608581, tc_HOL_Obool), _1608579), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608581, tc_HOL_Obool)), _1608585)), _1608587)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608581, tc_HOL_Obool)), _1608585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608579, tc_fun(_1608581, tc_HOL_Obool)), _1608583), _1608587)))], (46829 ^ _773908) ^ [_1712411, _1712413] : [-(c_Transitive__Closure_Ortrancl(_1712411, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1712411, _1712411), tc_HOL_Obool)), _1712413), c_Relation_OId(_1712411))) = c_Transitive__Closure_Ortrancl(_1712411, _1712413))], (16231 ^ _773908) ^ [_1052031, _1052033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052033), _1052031))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1052033), _1052031) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052033), _1052031)), _1052031)))], (21421 ^ _773908) ^ [_1144161, _1144163, _1144165, _1144167, _1144169] : [class_Fields_Olinordered__field(_1144161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144161), c_Groups_Ozero__class_Ozero(_1144161)), _1144163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144161), _1144163), _1144165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144161), c_Groups_Ozero__class_Ozero(_1144161)), _1144167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144161), _1144167), _1144169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144161), _1144163), _1144169)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144161), _1144165), _1144167))))], (40117 ^ _773908) ^ [_1557992, _1557994, _1557996] : [-(c_List_Osublist(_1557992, _1557994, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1557996)) = hAPP(hAPP(c_List_Otake(_1557992), _1557996), _1557994))], (14527 ^ _773908) ^ [_1019594, _1019596] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019594, _1019596)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019594), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019596)))], (51454 ^ _773908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (7681 ^ _773908) ^ [_898577, _898579, _898581, _898583, _898585] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_898577, _898579, _898581)), _898583), _898585)), 7686 ^ _773908 : [(7689 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898579), _898583), _898585)))], (7687 ^ _773908) ^ [] : [-(hBOOL(hAPP(_898577, _898583)))]], 7690 ^ _773908 : [(7693 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898581), _898583), _898585)))], (7691 ^ _773908) ^ [] : [hBOOL(hAPP(_898577, _898583))]]], (49328 ^ _773908) ^ [_1769163, _1769165, _1769167] : [-(hAPP(c_New__DSequence_Opos__single(_1769163, _1769165), _1769167) = hAPP(c_Lazy__Sequence_Osingle(_1769163), _1769165))], (37486 ^ _773908) ^ [_1483197, _1483199, _1483201, _1483203] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1483197, _1483199)), hAPP(hAPP(c_Product__Type_OSigma(_1483197, _1483199), hAPP(hAPP(c_Set_Oinsert(_1483197), _1483201), c_Orderings_Obot__class_Obot(tc_fun(_1483197, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1483199, tc_HOL_Obool), _1483197), _1483203))) = hAPP(c_Finite__Set_Ocard(_1483199), _1483203))], (47024 ^ _773908) ^ [_1717782, _1717784, _1717786, _1717788] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1717782, _1717782)), hAPP(hAPP(c_Product__Type_OPair(_1717782, _1717782), _1717784), _1717786)), c_Transitive__Closure_Ortrancl(_1717782, _1717788)))), 47025 ^ _773908 : [(47028 ^ _773908) ^ [] : [-(_1717784 = _1717786), hBOOL(hAPP(hAPP(c_member(tc_prod(_1717782, _1717782)), hAPP(hAPP(c_Product__Type_OPair(_1717782, _1717782), _1717784), _1717786)), c_Transitive__Closure_Otrancl(_1717782, _1717788)))], (47026 ^ _773908) ^ [] : [_1717784 = _1717786]]], (43533 ^ _773908) ^ [_1639001, _1639003, _1639005, _1639007, _1639009, _1639011] : [c_List_Olist__all2(_1639001, _1639003, _1639005, _1639007, _1639009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639011), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639001)), _1639007))), -(hBOOL(hAPP(hAPP(_1639005, hAPP(hAPP(c_List_Onth(_1639001), _1639007), _1639011)), hAPP(hAPP(c_List_Onth(_1639003), _1639009), _1639011))))], (35905 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (50699 ^ _773908) ^ [_1799651, _1799653, _1799655] : [c_Relation_Osym(_1799651, _1799653), c_Relation_Osym(_1799651, _1799655), -(c_Relation_Osym(_1799651, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1799651, _1799651), tc_HOL_Obool)), _1799653), _1799655)))], (5893 ^ _773908) ^ [_868228, _868230, _868232] : [hAPP(c_Com_Ocom_OBODY, _868228) = c_Com_Ocom_OSemi(_868230, _868232)], (40993 ^ _773908) ^ [_1581467, _1581469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581467)), _1581469)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1581467), _1581469) = _1581469)], (43803 ^ _773908) ^ [_1645214] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645214, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1645214, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1645214, tc_HOL_Obool)))], (45953 ^ _773908) ^ [_1692356, _1692358, _1692360, _1692362, _1692364] : [class_Groups_Omonoid__add(_1692356), 45959 ^ _773908 : [(45964 ^ _773908) ^ [] : [hAPP(_1692364, 45958 ^ [_1692356, _1692358, _1692360, _1692362, _1692364]) = c_Groups_Ozero__class_Ozero(_1692356)], (45962 ^ _773908) ^ [] : [hBOOL(hAPP(_1692362, 45958 ^ [_1692356, _1692358, _1692360, _1692362, _1692364]))], (45960 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692358), 45958 ^ [_1692356, _1692358, _1692360, _1692362, _1692364]), hAPP(c_List_Oset(_1692358), _1692360))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1692356), hAPP(hAPP(c_List_Omap(_1692358, _1692356), _1692364), hAPP(c_List_Ofilter(_1692358, _1692362), _1692360))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1692356), hAPP(hAPP(c_List_Omap(_1692358, _1692356), _1692364), _1692360)))], (38709 ^ _773908) ^ [_1521755, _1521757] : [c_Wellfounded_Owf(_1521755, _1521757), -(c_Wellfounded_Owf(_1521755, hAPP(hAPP(c_Relation_Orel__comp(_1521755, _1521755, _1521755), _1521757), _1521757)))], (47199 ^ _773908) ^ [_1721887, _1721889] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721887, _1721887), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1721887, _1721889)), c_Relation_OId(_1721887)) = c_Transitive__Closure_Ortrancl(_1721887, _1721889))], (23013 ^ _773908) ^ [_1173492, _1173494, _1173496, _1173498] : [class_Groups_Ouminus(_1173492), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173494, _1173492)), _1173496), _1173498) = hAPP(c_Groups_Ouminus__class_Ouminus(_1173492), hAPP(_1173496, _1173498)))], (5895 ^ _773908) ^ [_868282, _868284, _868286, _868288] : [c_Com_Ocom_OSemi(_868282, _868284) = c_Com_Ocom_OSemi(_868286, _868288), 5898 ^ _773908 : [(5901 ^ _773908) ^ [] : [-(_868284 = _868288)], (5899 ^ _773908) ^ [] : [-(_868282 = _868286)]]], (3270 ^ _773908) ^ [_822931, _822933, _822935, _822937, _822939, _822941, _822943, _822945] : [-(c_Recdef_Osame__fst(_822945, _822941, _822937, _822933) = c_Recdef_Osame__fst(_822943, _822939, _822935, _822931)), _822945 = _822943, _822941 = _822939, _822937 = _822935, _822933 = _822931], (31896 ^ _773908) ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125] : [c_Equiv__Relations_Oequiv(_1364113, _1364115, _1364117), c_Equiv__Relations_Ocongruent(_1364113, tc_fun(_1364119, tc_HOL_Obool), _1364117, _1364121), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364113, tc_fun(_1364119, tc_HOL_Obool)), _1364123), _1364121) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364113, tc_fun(_1364119, tc_HOL_Obool)), _1364125), _1364121), hBOOL(hAPP(hAPP(c_member(tc_fun(_1364113, tc_HOL_Obool)), _1364123), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1364113), _1364115), _1364117))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1364113, tc_HOL_Obool)), _1364125), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1364113), _1364115), _1364117))), 31918 ^ _773908 : [(31922 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364113), 31920 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125]), _1364115)))], (31924 ^ _773908) ^ [] : [-(hAPP(_1364121, 31917 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125]) = hAPP(_1364121, 31920 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125]))], (31926 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1364113, _1364113)), hAPP(hAPP(c_Product__Type_OPair(_1364113, _1364113), 31917 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125]), 31920 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125])), _1364117))], (31919 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364113), 31917 ^ [_1364113, _1364115, _1364117, _1364119, _1364121, _1364123, _1364125]), _1364115)))]], -(_1364123 = _1364125)], (44814 ^ _773908) ^ [_1669443, _1669445, _1669447] : [44815 ^ _773908 : [(44818 ^ _773908) ^ [] : [_1669447 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44816 ^ _773908) ^ [] : [-(_1669443 = c_List_Olist_ONil(tc_List_Olist(_1669445)))]], 44822 ^ _773908 : [(44825 ^ _773908) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669445)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1669445)), _1669443), 44821 ^ [_1669443, _1669445, _1669447])) = _1669447], (44823 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44821 ^ [_1669443, _1669445, _1669447]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1669445))), _1669443))))]], -(c_List_Otranspose(_1669445, _1669443) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1669445)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1669445)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1669445), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1669445)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1669445)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1669445), hAPP(hAPP(c_COMBB(tc_List_Olist(_1669445), tc_fun(tc_Nat_Onat, _1669445), tc_Nat_Onat), c_List_Onth(_1669445)), hAPP(c_List_Onth(tc_List_Olist(_1669445)), _1669443))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1669445))), _1669443)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1669447)))], (29819 ^ _773908) ^ [_1318303, _1318305, _1318307, _1318309, _1318311, _1318313, _1318315] : [c_Finite__Set_Ofolding__idem(_1318303, _1318305, _1318307, _1318309), -(hAPP(c_Fun_Ocomp(_1318305, _1318305, _1318311, hAPP(_1318307, _1318313)), hAPP(c_Fun_Ocomp(_1318305, _1318305, _1318311, hAPP(_1318307, _1318313)), _1318315)) = hAPP(c_Fun_Ocomp(_1318305, _1318305, _1318311, hAPP(_1318307, _1318313)), _1318315))], (11605 ^ _773908) ^ [_967758] : [11607 ^ _773908 : [(11610 ^ _773908) ^ [] : [hBOOL(hAPP(_967758, 11606 ^ [_967758]))], (11608 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11606 ^ [_967758])))]], 11611 ^ _773908 : [(11612 ^ _773908) ^ [_967885] : [-(hBOOL(hAPP(_967758, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _967885))))]]], (46833 ^ _773908) ^ [_1712497, _1712499, _1712501, _1712503, _1712505, _1712507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712497, _1712497)), hAPP(hAPP(c_Product__Type_OPair(_1712497, _1712497), _1712499), _1712501)), c_Transitive__Closure_Ortrancl(_1712497, _1712503))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712497), tc_List_Olist(_1712497))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712497), tc_List_Olist(_1712497)), _1712505), _1712507)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1712497), c_List_Olistrel1(_1712497, _1712503)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712497), tc_List_Olist(_1712497))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712497), tc_List_Olist(_1712497)), hAPP(hAPP(c_List_Olist_OCons(_1712497), _1712499), _1712505)), hAPP(hAPP(c_List_Olist_OCons(_1712497), _1712501), _1712507))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1712497), c_List_Olistrel1(_1712497, _1712503)))))], (47351 ^ _773908) ^ [_1725567, _1725569] : [-(hAPP(c_Relation_OField(_1725567), hAPP(c_Relation_Oconverse(_1725567, _1725567), _1725569)) = hAPP(c_Relation_OField(_1725567), _1725569))], (11385 ^ _773908) ^ [_963896, _963898] : [class_Groups_Oordered__ab__group__add(_963896), 11388 ^ _773908 : [(11395 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963896), _963898), c_Groups_Ozero__class_Ozero(_963896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963896), c_Groups_Ozero__class_Ozero(_963896)), hAPP(c_Groups_Ouminus__class_Ouminus(_963896), _963898))))], (11389 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963896), c_Groups_Ozero__class_Ozero(_963896)), hAPP(c_Groups_Ouminus__class_Ouminus(_963896), _963898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963896), _963898), c_Groups_Ozero__class_Ozero(_963896))))]]], (14659 ^ _773908) ^ [_1021790, _1021792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021790), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021792), _1021790)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021790), _1021792) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1604 ^ _773908) ^ [_796944, _796946] : [-(class_Rings_Oordered__cancel__semiring(_796944)), _796946 = _796944, class_Rings_Oordered__cancel__semiring(_796946)], (42403 ^ _773908) ^ [_1614068, _1614070, _1614072, _1614074] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614068, tc_fun(_1614070, tc_HOL_Obool)), _1614072), _1614074) = hAPP(c_Set_OCollect(_1614070), hAPP(hAPP(c_COMBB(tc_fun(_1614068, tc_HOL_Obool), tc_HOL_Obool, _1614070), c_HOL_OAll(_1614068)), hAPP(hAPP(c_COMBB(tc_fun(_1614068, tc_HOL_Obool), tc_fun(_1614068, tc_HOL_Obool), _1614070), hAPP(c_COMBS(_1614068, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1614068), c_fimplies), hAPP(hAPP(c_COMBC(_1614068, tc_fun(_1614068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1614068)), _1614072)))), hAPP(hAPP(c_COMBC(_1614070, tc_fun(_1614068, tc_fun(_1614070, tc_HOL_Obool)), tc_fun(_1614068, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1614070, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1614068, tc_fun(_1614070, tc_HOL_Obool)), tc_fun(_1614068, tc_HOL_Obool)), _1614070), c_COMBB(tc_fun(_1614070, tc_HOL_Obool), tc_HOL_Obool, _1614068)), c_member(_1614070))), _1614074)))))], (11924 ^ _773908) ^ [_973412, _973414, _973416, _973418] : [class_Rings_Olinordered__semiring(_973412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973412), _973414), _973416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973412), _973418), _973416))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973412), c_Groups_Ozero__class_Ozero(_973412)), _973416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973412), _973414), _973418)))], (51620 ^ _773908) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (35707 ^ _773908) ^ [_1443902, _1443904, _1443906, _1443908, _1443910] : [class_Groups_Ocomm__monoid__add(_1443902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443904), _1443906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443904, tc_HOL_Obool)), _1443908), _1443906)), 35721 ^ _773908 : [(35724 ^ _773908) ^ [] : [hAPP(_1443910, 35720 ^ [_1443902, _1443904, _1443906, _1443908, _1443910]) = c_Groups_Ozero__class_Ozero(_1443902)], (35722 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443904), 35720 ^ [_1443902, _1443904, _1443906, _1443908, _1443910]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443904, tc_HOL_Obool)), _1443906), _1443908))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443904, _1443902), _1443910), _1443906) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443904, _1443902), _1443910), _1443908))], (49244 ^ _773908) ^ [_1767110, _1767112, _1767114] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1767110), _1767112)), hBOOL(hAPP(_1767114, c_Orderings_Obot__class_Obot(tc_fun(_1767110, tc_HOL_Obool)))), 49255 ^ _773908 : [(49258 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1767110), 49253 ^ [_1767110, _1767112, _1767114]), 49254 ^ [_1767110, _1767112, _1767114]))], (49260 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1767114, 49254 ^ [_1767110, _1767112, _1767114])))], (49262 ^ _773908) ^ [] : [hBOOL(hAPP(_1767114, hAPP(hAPP(c_Set_Oinsert(_1767110), 49253 ^ [_1767110, _1767112, _1767114]), 49254 ^ [_1767110, _1767112, _1767114])))], (49256 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1767110), 49254 ^ [_1767110, _1767112, _1767114])))]], -(hBOOL(hAPP(_1767114, _1767112)))], (47269 ^ _773908) ^ [_1723480, _1723482] : [c_Wellfounded_Oacyclic(_1723480, hAPP(c_Relation_Oconverse(_1723480, _1723480), _1723482)), -(c_Wellfounded_Oacyclic(_1723480, _1723482))], (20097 ^ _773908) ^ [_1120683, _1120685] : [class_Int_Onumber__ring(_1120683), -(hAPP(c_Int_Onumber__class_Onumber__of(_1120683), c_Int_OBit0(_1120685)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120683), c_Groups_Ozero__class_Ozero(_1120683)), hAPP(c_Int_Onumber__class_Onumber__of(_1120683), _1120685))), hAPP(c_Int_Onumber__class_Onumber__of(_1120683), _1120685)))], (14601 ^ _773908) ^ [_1020741, _1020743, _1020745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020741), _1020743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020745), _1020743)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020745), _1020741))))], (46634 ^ _773908) ^ [_1707425, _1707427, _1707429, _1707431] : [46636 ^ _773908 : [(46639 ^ _773908) ^ [] : [hBOOL(hAPP(_1707429, 46635 ^ [_1707425, _1707427, _1707429, _1707431]))], (46637 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1707425), 46635 ^ [_1707425, _1707427, _1707429, _1707431]), hAPP(c_List_Oset(_1707425), _1707427))))]], -(c_List_OtakeWhile(_1707425, _1707429, hAPP(hAPP(c_List_Oappend(_1707425), _1707427), _1707431)) = hAPP(hAPP(c_List_Oappend(_1707425), _1707427), c_List_OtakeWhile(_1707425, _1707429, _1707431)))], (38514 ^ _773908) ^ [_1514684, _1514686, _1514688, _1514690] : [class_Groups_Ocomm__monoid__add(_1514684), c_Fun_Oinj__on(_1514686, _1514684, _1514688, _1514690), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514686, _1514684), _1514688), _1514690) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514684, _1514684), c_Fun_Oid(_1514684)), hAPP(c_Set_Oimage(_1514686, _1514684, _1514688), _1514690)))], (48063 ^ _773908) ^ [_1742304, _1742306] : [c_List_Olist__ex(_1742304, _1742306, c_List_Olist_ONil(_1742304))], (31844 ^ _773908) ^ [_1362832, _1362834, _1362836, _1362838, _1362840] : [_1362832 = c_Orderings_Obot__class_Obot(tc_fun(_1362834, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362836, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362834, tc_fun(_1362836, tc_HOL_Obool)), _1362832), _1362838)), _1362840) = _1362840)], (16481 ^ _773908) ^ [_1056579, _1056581] : [class_Rings_Olinordered__idom(_1056579), -(hAPP(c_Groups_Oabs__class_Oabs(_1056579), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056579), _1056581)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056579), _1056581))], (16959 ^ _773908) ^ [_1065934, _1065936, _1065938] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1065936), _1065938)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065934), _1065936)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065934), _1065938)))], (6488 ^ _773908) ^ [_879379, _879381, _879383, _879385, _879387, _879389] : [-(c_Com_Ocom_OCall(_879379, _879381, _879383) = c_Com_Ocom_OCall(_879385, _879387, _879389)), _879379 = _879385, _879381 = _879387, _879383 = _879389], (22831 ^ _773908) ^ [_1170021] : [class_Nat_Osize(_1170021), -(c_FunDef_Ois__measure(_1170021, c_Nat_Osize__class_Osize(_1170021)))], (47353 ^ _773908) ^ [_1725608, _1725610, _1725612, _1725614] : [-(hAPP(c_Relation_Oconverse(_1725608, _1725610), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1725608, _1725610), tc_HOL_Obool)), _1725612), _1725614)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1725610, _1725608), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1725608, _1725610), _1725612)), hAPP(c_Relation_Oconverse(_1725608, _1725610), _1725614)))], (10869 ^ _773908) ^ [_954446, _954448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _954446), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _954446), _954448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _954446))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _954448))))], (1934 ^ _773908) ^ [_801069, _801071] : [-(hBOOL(_801069)), _801071 = _801069, hBOOL(_801071)], (8581 ^ _773908) ^ [_915856, _915858] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _915856), _915858) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _915858), _915856))], (46476 ^ _773908) ^ [_1703394, _1703396, _1703398, _1703400, _1703402] : [46477 ^ _773908 : [(46480 ^ _773908) ^ [] : [hBOOL(hAPP(_1703402, hAPP(hAPP(c_List_Ozip(_1703394, _1703398), hAPP(hAPP(c_List_Otake(_1703394), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703394)), _1703396)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703398)), _1703400))), _1703396)), hAPP(hAPP(c_List_Otake(_1703398), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703394)), _1703396)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703398)), _1703400))), _1703400))))], (46478 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703394)), hAPP(hAPP(c_List_Otake(_1703394), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703394)), _1703396)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703398)), _1703400))), _1703396)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703398)), hAPP(hAPP(c_List_Otake(_1703398), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703394)), _1703396)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703398)), _1703400))), _1703400)))]], -(hBOOL(hAPP(_1703402, hAPP(hAPP(c_List_Ozip(_1703394, _1703398), _1703396), _1703400))))], (19761 ^ _773908) ^ [_1114759, _1114761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114759), 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)))), _1114761)), 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)))), _1114759)) = 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), _1114761), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1114759))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38631 ^ _773908) ^ [_1518507, _1518509, _1518511, _1518513, _1518515, _1518517, _1518519, _1518521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518507, _1518509), tc_HOL_Obool)), _1518511), hAPP(hAPP(c_Product__Type_OSigma(_1518507, _1518509), _1518513), hAPP(c_COMBK(tc_fun(_1518509, tc_HOL_Obool), _1518507), _1518515)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518509, _1518517), tc_HOL_Obool)), _1518519), hAPP(hAPP(c_Product__Type_OSigma(_1518509, _1518517), _1518515), hAPP(c_COMBK(tc_fun(_1518517, tc_HOL_Obool), _1518509), _1518521)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518507, _1518517), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518507, _1518509, _1518517), _1518511), _1518519)), hAPP(hAPP(c_Product__Type_OSigma(_1518507, _1518517), _1518513), hAPP(c_COMBK(tc_fun(_1518517, tc_HOL_Obool), _1518507), _1518521)))))], (15859 ^ _773908) ^ [_1044046, _1044048] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044046), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044046), _1044048))], (39039 ^ _773908) ^ [_1528916, _1528918, _1528920] : [-(hAPP(c_Relation_ORange(_1528916, _1528918), hAPP(c_Set_OCollect(tc_prod(_1528916, _1528918)), hAPP(c_Product__Type_Oprod_Oprod__case(_1528916, _1528918, tc_HOL_Obool), _1528920))) = hAPP(c_Set_OCollect(_1528918), hAPP(hAPP(c_COMBB(tc_fun(_1528916, tc_HOL_Obool), tc_HOL_Obool, _1528918), c_HOL_OEx(_1528916)), hAPP(c_COMBC(_1528916, _1528918, tc_HOL_Obool), _1528920))))], (8833 ^ _773908) ^ [_920141, _920143, _920145] : [class_Groups_Ogroup__add(_920141), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920141), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920141), _920143), _920145)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920141), hAPP(c_Groups_Ouminus__class_Ouminus(_920141), _920145)), hAPP(c_Groups_Ouminus__class_Ouminus(_920141), _920143)))], (7775 ^ _773908) ^ [_900696, _900698, _900700] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_900696, _900698, _900700)], (29281 ^ _773908) ^ [_1308142, _1308144, _1308146] : [class_Lattices_Olattice(_1308142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308142), _1308144)), -(_1308144 = c_Orderings_Obot__class_Obot(tc_fun(_1308142, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308142), _1308146)), -(_1308146 = c_Orderings_Obot__class_Obot(tc_fun(_1308142, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308142, tc_HOL_Obool)), _1308144), _1308146) = c_Orderings_Obot__class_Obot(tc_fun(_1308142, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1308142, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308142, tc_HOL_Obool)), _1308144), _1308146)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1308142), c_Big__Operators_Olattice__class_OSup__fin(_1308142, _1308144)), c_Big__Operators_Olattice__class_OSup__fin(_1308142, _1308146)))], (50054 ^ _773908) ^ [_1785427, _1785429] : [50055 ^ _773908 : [(50056 ^ _773908) ^ [_1785493] : [hBOOL(hAPP(_1785429, _1785493))]], 50058 ^ _773908 : [(50061 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1785429, 50057 ^ [_1785427, _1785429])))], (50059 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785427), 50057 ^ [_1785427, _1785429]), c_Orderings_Otop__class_Otop(tc_fun(_1785427, tc_HOL_Obool)))))]]], (12254 ^ _773908) ^ [_979153] : [-(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), _979153))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6716 ^ _773908) ^ [_882857, _882859, _882861] : [class_Orderings_Olinorder(_882857), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882857), _882859), _882861))), 6723 ^ _773908 : [(6730 ^ _773908) ^ [] : [_882861 = _882859, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882857), _882861), _882859))], (6724 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882857), _882861), _882859))), -(_882861 = _882859)]]], (15663 ^ _773908) ^ [_1040357, _1040359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040357), _1040359)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040357), _1040359)))], (49527 ^ _773908) ^ [_1773597, _1773599, _1773601, _1773603] : [49534 ^ _773908 : [(49537 ^ _773908) ^ [] : [_1773599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49535 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1773603, _1773601)))]], 49528 ^ _773908 : [(49529 ^ _773908) ^ [_1773669] : [hBOOL(hAPP(hAPP(c_member(_1773597), _1773669), hAPP(c_List_Oset(_1773597), c_List_Oreplicate(_1773597, _1773599, _1773601)))), hBOOL(hAPP(_1773603, _1773669))]]], (15511 ^ _773908) ^ [_1037199, _1037201, _1037203] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037201), _1037203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037199), _1037201)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037199), _1037203)))], (13769 ^ _773908) ^ [_1005847, _1005849] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005847, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005849)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005847, _1005849) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30722 ^ _773908) ^ [_1336594, _1336596, _1336598, _1336600] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336594), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336596, tc_Nat_Onat), _1336598), _1336600)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336596, _1336594), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1336594, _1336596), c_Nat_Osemiring__1__class_Oof__nat(_1336594)), _1336598)), _1336600)), class_Groups_Ocomm__monoid__mult(_1336594), class_Rings_Osemiring__1(_1336594)], (32626 ^ _773908) ^ [_1379464, _1379466, _1379468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379464, tc_HOL_Obool)), _1379466), _1379468)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1379464, tc_HOL_Obool)), _1379466), hAPP(c_Set_OPow(_1379464), _1379468))))], (5773 ^ _773908) ^ [_865413, _865415, _865417] : [hAPP(hAPP(c_Set_Oinsert(_865413), _865415), _865417) = c_Orderings_Obot__class_Obot(tc_fun(_865413, tc_HOL_Obool))], (51574 ^ _773908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (4556 ^ _773908) ^ [_843238, _843240] : [_843240 = _843238, -(c_List_Otake(_843240) = c_List_Otake(_843238))], (51634 ^ _773908) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (3862 ^ _773908) ^ [_832159, _832161, _832163, _832165] : [-(c_Big__Operators_Olattice__class_OSup__fin(_832165, _832161) = c_Big__Operators_Olattice__class_OSup__fin(_832163, _832159)), _832165 = _832163, _832161 = _832159], (29187 ^ _773908) ^ [_1306491, _1306493, _1306495] : [class_Lattices_Olattice(_1306491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306491), _1306493)), -(hBOOL(hAPP(hAPP(c_member(_1306491), _1306495), _1306493))), -(_1306493 = c_Orderings_Obot__class_Obot(tc_fun(_1306491, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1306491, hAPP(hAPP(c_Set_Oinsert(_1306491), _1306495), _1306493)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1306491), _1306495), c_Big__Operators_Olattice__class_OSup__fin(_1306491, _1306493)))], (51640 ^ _773908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (41922 ^ _773908) ^ [_1600362, _1600364, _1600366, _1600368] : [-(hAPP(hAPP(c_List_Omap(_1600362, _1600364), _1600366), c_List_Obutlast(_1600362, _1600368)) = c_List_Obutlast(_1600364, hAPP(hAPP(c_List_Omap(_1600362, _1600364), _1600366), _1600368)))], (39989 ^ _773908) ^ [_1554886, _1554888, _1554890, _1554892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1554886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554888)), _1554890))), -(hAPP(hAPP(c_List_Onth(_1554888), hAPP(hAPP(c_List_Oappend(_1554888), _1554890), _1554892)), _1554886) = hAPP(hAPP(c_List_Onth(_1554888), _1554890), _1554886))], (32193 ^ _773908) ^ [_1370897, _1370899, _1370901, _1370903, _1370905, _1370907, _1370909] : [c_Big__Operators_Ocomm__monoid__big(_1370897, _1370899, _1370901, _1370903, _1370905), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370899), _1370907))), -(hAPP(hAPP(_1370905, _1370909), _1370907) = _1370903)], (42261 ^ _773908) ^ [_1610855, _1610857, _1610859, _1610861, _1610863, _1610865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610855, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1610857, _1610855, _1610859), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610861, tc_fun(_1610857, tc_HOL_Obool)), _1610863), _1610865))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610861, tc_fun(_1610855, tc_HOL_Obool)), _1610863), hAPP(hAPP(c_COMBB(tc_fun(_1610857, tc_HOL_Obool), tc_fun(_1610855, tc_HOL_Obool), _1610861), c_Relation_OImage(_1610857, _1610855, _1610859)), _1610865)))))], (32191 ^ _773908) ^ [_1370856, _1370858] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1370856, _1370858)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1370858), _1370856)))], (46262 ^ _773908) ^ [_1699404] : [-(c_Wellfounded_OwfP(_1699404, hAPP(c_COMBK(tc_fun(_1699404, tc_HOL_Obool), _1699404), hAPP(c_COMBK(tc_HOL_Obool, _1699404), c_fFalse))))], (41930 ^ _773908) ^ [_1600620, _1600622, _1600624, _1600626, _1600628, _1600630] : [-(hAPP(hAPP(c_List_Omap(_1600620, _1600622), _1600624), hAPP(hAPP(c_List_Omap(_1600626, _1600620), _1600628), _1600630)) = hAPP(hAPP(c_List_Omap(_1600626, _1600622), hAPP(c_Fun_Ocomp(_1600620, _1600622, _1600626, _1600624), _1600628)), _1600630))], (45260 ^ _773908) ^ [_1677804, _1677806, _1677808, _1677810, _1677812, _1677814] : [class_Orderings_Olinorder(_1677804), c_List_Olinorder__class_Osorted(_1677804, hAPP(hAPP(c_List_Omap(_1677806, _1677804), _1677808), _1677810)), hBOOL(hAPP(_1677812, _1677814)), -(hAPP(c_List_Ofilter(_1677806, _1677812), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677806, _1677804, _1677808), _1677814), _1677810)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677806, _1677804, _1677808), _1677814), hAPP(c_List_Ofilter(_1677806, _1677812), _1677810)))], (19897 ^ _773908) ^ [_1117251] : [-(c_Int_OBit0(_1117251) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117251), _1117251))], (9191 ^ _773908) ^ [_926577, _926579, _926581, _926583] : [class_Rings_Olinordered__ring__strict(_926577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926577), c_Groups_Ozero__class_Ozero(_926577)), _926579)), 9198 ^ _773908 : [(9205 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926577), _926581), _926583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926577), _926579), _926581)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926577), _926579), _926583))))], (9199 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926577), _926579), _926581)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926577), _926579), _926583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926577), _926581), _926583)))]]], (36339 ^ _773908) ^ [_1456849, _1456851, _1456853, _1456855, _1456857, _1456859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456851, _1456853)), hAPP(hAPP(c_Product__Type_OPair(_1456851, _1456853), _1456857), _1456859)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456849, tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1456849, tc_HOL_Obool))), _1456855))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456849, tc_fun(_1456851, tc_fun(_1456853, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1456849, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_fun(_1456851, tc_fun(_1456853, tc_HOL_Obool)), _1456849), hAPP(c_COMBC(_1456851, tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_fun(_1456853, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456853, tc_fun(tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_fun(_1456853, tc_HOL_Obool)), _1456851), c_COMBC(_1456853, tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456853, tc_prod(_1456851, _1456853)), tc_fun(_1456853, tc_fun(tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_HOL_Obool)), _1456851), hAPP(c_COMBB(tc_prod(_1456851, _1456853), tc_fun(tc_fun(tc_prod(_1456851, _1456853), tc_HOL_Obool), tc_HOL_Obool), _1456853), c_member(tc_prod(_1456851, _1456853)))), c_Product__Type_OPair(_1456851, _1456853))))), _1456855)), _1456857), _1456859)))], (42698 ^ _773908) ^ [_1620658, _1620660] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1620658)), hAPP(c_Code__Numeral_Oof__nat, _1620660)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1620658), _1620660)))], (20183 ^ _773908) ^ [_1122270, _1122272] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1122270)), c_Int_OBit1(_1122272)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122270), c_Int_Osucc(_1122272))))], (11676 ^ _773908) ^ [_968922] : [11678 ^ _773908 : [(11681 ^ _773908) ^ [] : [hBOOL(hAPP(_968922, hAPP(c_Int_Onat, 11677 ^ [_968922])))], (11679 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11677 ^ [_968922])))]], 11682 ^ _773908 : [(11683 ^ _773908) ^ [_969055] : [-(hBOOL(hAPP(_968922, _969055)))]]], (13442 ^ _773908) ^ [_999679, _999681, _999683] : [_999679 = _999681, 13445 ^ _773908 : [(13448 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999683, tc_HOL_Obool)), _999681), _999679)))], (13446 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999683, tc_HOL_Obool)), _999679), _999681)))]]], (34402 ^ _773908) ^ [_1414444, _1414446, _1414448] : [class_Orderings_Oorder(_1414444), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414444, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1414444), _1414446)), c_SetInterval_Oord__class_OatLeastAtMost(_1414444, _1414446, _1414448)) = c_Orderings_Obot__class_Obot(tc_fun(_1414444, tc_HOL_Obool)))], (7809 ^ _773908) ^ [_901325, _901327, _901329, _901331] : [class_Rings_Ocomm__semiring__1(_901325), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901325), _901327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901325), _901329), _901331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901325), _901327), _901329)), _901331))], (8963 ^ _773908) ^ [_922447, _922449, _922451, _922453] : [class_Rings_Ocomm__semiring__1(_922447), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922447), _922449), _922451)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922447), _922453), _922451)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922447), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922447), _922449), _922453)), _922451))], (19013 ^ _773908) ^ [_1102389, _1102391, _1102393] : [class_Rings_Oring__1(_1102389), hBOOL(hAPP(hAPP(c_member(_1102389), _1102391), c_Int_Oring__1__class_OInts(_1102389))), -(hBOOL(hAPP(hAPP(c_member(_1102389), hAPP(hAPP(c_Power_Opower__class_Opower(_1102389), _1102391), _1102393)), c_Int_Oring__1__class_OInts(_1102389))))], (51772 ^ _773908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (25397 ^ _773908) ^ [_1222699, _1222701, _1222703, _1222705] : [class_Orderings_Olinorder(_1222699), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222699), _1222701), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222699), _1222703), _1222705)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222699), _1222703), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222699), _1222701), _1222705)))], (5769 ^ _773908) ^ [_865285, _865287, _865289, _865291, _865293, _865295] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_865285, _865287, _865289, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_865285), _865291), _865293), _865295)) = hAPP(hAPP(hAPP(_865289, _865291), _865293), _865295))], (39721 ^ _773908) ^ [_1547223, _1547225] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1547223), tc_List_Olist(_1547223), c_List_Olistrel(_1547223, _1547225)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1547223)), c_List_Olist_ONil(_1547223)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1547223), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1547223)), c_List_Olist_ONil(_1547223)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1547223), tc_HOL_Obool))))], (9961 ^ _773908) ^ [_939646] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939646), _939646)))], (41354 ^ _773908) ^ [_1588834, _1588836, _1588838] : [class_Orderings_Olinorder(_1588834), -(c_Big__Operators_Olattice_OInf__fin(_1588834, c_Orderings_Oord__class_Omin(_1588834), hAPP(c_List_Oset(_1588834), hAPP(hAPP(c_List_Olist_OCons(_1588834), _1588836), _1588838))) = hAPP(c_List_Ofoldl(_1588834, _1588834, c_Orderings_Oord__class_Omin(_1588834), _1588836), _1588838))], (19589 ^ _773908) ^ [_1111860] : [class_Rings_Osemiring__1(_1111860), -(hBOOL(hAPP(hAPP(c_member(_1111860), c_Groups_Ozero__class_Ozero(_1111860)), c_Nat_Osemiring__1__class_ONats(_1111860))))], (35118 ^ _773908) ^ [_1430802, _1430804, _1430806, _1430808, _1430810] : [class_Rings_Oring(_1430802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430804), _1430806)), hBOOL(hAPP(hAPP(c_member(_1430804), _1430808), _1430806)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430804, _1430802), _1430810), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430804, tc_HOL_Obool)), _1430806), hAPP(hAPP(c_Set_Oinsert(_1430804), _1430808), c_Orderings_Obot__class_Obot(tc_fun(_1430804, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430802), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430804, _1430802), _1430810), _1430806)), hAPP(_1430810, _1430808)))], (48643 ^ _773908) ^ [_1754090, _1754092, _1754094, _1754096, _1754098, _1754100] : [c_Finite__Set_Ofun__left__comm(_1754090, _1754092, _1754094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1754090), _1754096)), -(hAPP(hAPP(_1754094, _1754098), hAPP(hAPP(c_Finite__Set_Ofold(_1754090, _1754092, _1754094), _1754100), _1754096)) = hAPP(hAPP(c_Finite__Set_Ofold(_1754090, _1754092, _1754094), hAPP(hAPP(_1754094, _1754098), _1754100)), _1754096))], (51590 ^ _773908) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (35066 ^ _773908) ^ [_1429571, _1429573] : [class_Groups_Oordered__ab__group__add(_1429571), -(hAPP(c_Set_Oimage(_1429571, _1429571, c_Groups_Ouminus__class_Ouminus(_1429571)), hAPP(c_SetInterval_Oord__class_OatMost(_1429571), _1429573)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1429571), hAPP(c_Groups_Ouminus__class_Ouminus(_1429571), _1429573)))], (49420 ^ _773908) ^ [_1771667, _1771669] : [-(c_List_Oreplicate(_1771667, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1771669) = c_List_Olist_ONil(_1771667))], (3168 ^ _773908) ^ [_821388, _821390] : [_821390 = _821388, -(c_Int_OBit1(_821390) = c_Int_OBit1(_821388))], (44182 ^ _773908) ^ [_1654403, _1654405, _1654407, _1654409] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654403, tc_HOL_Obool), hAPP(c_Set_Oimage(_1654405, tc_fun(_1654403, tc_HOL_Obool), _1654407), _1654409)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654405, tc_fun(_1654403, tc_HOL_Obool)), _1654409), _1654407))], (6206 ^ _773908) ^ [_874604, _874606, _874608, _874610, _874612] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_874604, _874606), _874608, _874610, _874612), 6210 ^ _773908 : [(6213 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_874606, 6209 ^ [_874604, _874606, _874608, _874610, _874612], _874610, _874612))], (6211 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_874604, _874608, _874610, 6209 ^ [_874604, _874606, _874608, _874610, _874612]))]]], (26315 ^ _773908) ^ [_1242415, _1242417, _1242419, _1242421] : [c_FunDef_Oreduction__pair(_1242415, _1242417), -(c_FunDef_Oreduction__pair(_1242419, hAPP(hAPP(c_FunDef_Orp__inv__image(_1242415, _1242419), _1242417), _1242421)))], (11217 ^ _773908) ^ [_960796, _960798, _960800, _960802] : [class_Rings_Oordered__ring(_960796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960796), _960798), _960800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960796), _960802), c_Groups_Ozero__class_Ozero(_960796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960796), _960800), _960802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960796), _960798), _960802))))], (19347 ^ _773908) ^ [_1107964, _1107966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107964), _1107966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107964)), c_Int_OBit1(_1107966))))], (51758 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (17269 ^ _773908) ^ [_1071963, _1071965] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071963), _1071965) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1071965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1071963 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5700 ^ _773908) ^ [_861056, _861058] : [_861058 = _861056, -(tc_Hoare__Mirabelle_Otriple(_861058) = tc_Hoare__Mirabelle_Otriple(_861056))], (31708 ^ _773908) ^ [_1358682, _1358684, _1358686] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358682, tc_fun(_1358684, tc_HOL_Obool)), _1358686), hAPP(c_COMBK(tc_fun(_1358684, tc_HOL_Obool), _1358682), c_Orderings_Obot__class_Obot(tc_fun(_1358684, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1358684, tc_HOL_Obool)))], (48201 ^ _773908) ^ [_1745423, _1745425, _1745427, _1745429] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1745423, _1745425, _1745427), _1745429), c_Orderings_Obot__class_Obot(tc_fun(_1745423, tc_HOL_Obool))) = _1745429)], (42844 ^ _773908) ^ [_1624013] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1624013)) = _1624013)], (10733 ^ _773908) ^ [_951948, _951950, _951952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _951948), _951950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _951952), _951948)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _951952), _951950))))], (7771 ^ _773908) ^ [_900594, _900596, _900598, _900600, _900602, _900604] : [c_Com_Ocom_OCond(_900594, _900596, _900598) = c_Com_Ocom_OCall(_900600, _900602, _900604)], (42812 ^ _773908) ^ [_1623463, _1623465, _1623467, _1623469, _1623471] : [-(_1623463 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1623465, _1623467, _1623463, _1623469), _1623471) = hAPP(hAPP(c_Product__Type_Oscomp(_1623467, _1623465, _1623467, tc_prod(_1623465, _1623467)), hAPP(_1623469, _1623471)), c_Random_Oiterate(_1623465, _1623467, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1623463), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1623469)))], (42068 ^ _773908) ^ [_1605510, _1605512, _1605514, _1605516] : [42070 ^ _773908 : [(42073 ^ _773908) ^ [] : [hAPP(_1605516, 42069 ^ [_1605510, _1605512, _1605514, _1605516]) = c_Orderings_Otop__class_Otop(tc_fun(_1605510, tc_HOL_Obool))], (42071 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605512), 42069 ^ [_1605510, _1605512, _1605514, _1605516]), _1605514)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1605510, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605512, tc_fun(_1605510, tc_HOL_Obool)), _1605514), _1605516))], (1694 ^ _773908) ^ [_798069, _798071] : [-(class_Rings_Ono__zero__divisors(_798069)), _798071 = _798069, class_Rings_Ono__zero__divisors(_798071)], (32062 ^ _773908) ^ [_1368313, _1368315, _1368317, _1368319, _1368321, _1368323, _1368325] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368313, tc_fun(_1368315, tc_fun(_1368317, tc_HOL_Obool))), _1368319), _1368321), _1368323), _1368325)), 32066 ^ _773908 : [(32069 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1368321, 32065 ^ [_1368313, _1368315, _1368317, _1368319, _1368321, _1368323, _1368325]), _1368323), _1368325)))], (32067 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1368313), 32065 ^ [_1368313, _1368315, _1368317, _1368319, _1368321, _1368323, _1368325]), _1368319)))]]], (26625 ^ _773908) ^ [_1251698, _1251700, _1251702, _1251704, _1251706] : [hBOOL(hAPP(hAPP(c_member(_1251698), _1251700), hAPP(c_Relation_OImage(_1251702, _1251698, _1251704), hAPP(hAPP(c_Set_Oinsert(_1251702), _1251706), c_Orderings_Obot__class_Obot(tc_fun(_1251702, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1251702, _1251698)), hAPP(hAPP(c_Product__Type_OPair(_1251702, _1251698), _1251706), _1251700)), _1251704)))], (51414 ^ _773908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (48505 ^ _773908) ^ [_1751610, _1751612, _1751614] : [class_Lattices_Olattice(_1751610), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751610), _1751612)), -(hBOOL(hAPP(hAPP(c_member(_1751610), _1751614), _1751612))), -(c_Big__Operators_Olattice__class_OSup__fin(_1751610, hAPP(hAPP(c_Set_Oinsert(_1751610), _1751614), _1751612)) = hAPP(hAPP(c_Finite__Set_Ofold(_1751610, _1751610, c_Lattices_Osemilattice__sup__class_Osup(_1751610)), _1751614), _1751612))], (40791 ^ _773908) ^ [_1574732, _1574734, _1574736, _1574738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574732), tc_List_Olist(_1574732))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574732), tc_List_Olist(_1574732)), _1574734), _1574736)), c_List_Olistrel(_1574732, _1574738))), 40794 ^ _773908 : [(40797 ^ _773908) ^ [_1575068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574732, _1574732)), _1575068), hAPP(c_List_Oset(tc_prod(_1574732, _1574732)), hAPP(hAPP(c_List_Ozip(_1574732, _1574732), _1574734), _1574736)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1574732, _1574732, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1574732, tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_fun(_1574732, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574732, tc_fun(tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_fun(_1574732, tc_HOL_Obool)), _1574732), c_COMBC(_1574732, tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574732, tc_prod(_1574732, _1574732)), tc_fun(_1574732, tc_fun(tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_HOL_Obool)), _1574732), hAPP(c_COMBB(tc_prod(_1574732, _1574732), tc_fun(tc_fun(tc_prod(_1574732, _1574732), tc_HOL_Obool), tc_HOL_Obool), _1574732), c_member(tc_prod(_1574732, _1574732)))), c_Product__Type_OPair(_1574732, _1574732)))), _1574738)), _1575068)))], (40795 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574732)), _1574734) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574732)), _1574736))]]], (32346 ^ _773908) ^ [_1373931, _1373933, _1373935, _1373937, _1373939] : [class_Groups_Ocomm__monoid__mult(_1373931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373933), _1373935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373933, tc_HOL_Obool)), _1373937), _1373935)), 32360 ^ _773908 : [(32363 ^ _773908) ^ [] : [hAPP(_1373939, 32359 ^ [_1373931, _1373933, _1373935, _1373937, _1373939]) = c_Groups_Oone__class_Oone(_1373931)], (32361 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373933), 32359 ^ [_1373931, _1373933, _1373935, _1373937, _1373939]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373933, tc_HOL_Obool)), _1373935), _1373937))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373933, _1373931), _1373939), _1373935) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373933, _1373931), _1373939), _1373937))], (4284 ^ _773908) ^ [_838966, _838968, _838970, _838972, _838974, _838976, _838978, _838980] : [-(c_New__Random__Sequence_Opos__empty(_838980, _838976, _838972, _838968) = c_New__Random__Sequence_Opos__empty(_838978, _838974, _838970, _838966)), _838980 = _838978, _838976 = _838974, _838972 = _838970, _838968 = _838966], (17583 ^ _773908) ^ [_1077502, _1077504, _1077506, _1077508] : [class_Rings_Olinordered__semidom(_1077502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077502), hAPP(hAPP(c_Power_Opower__class_Opower(_1077502), _1077504), hAPP(c_Nat_OSuc, _1077506))), hAPP(hAPP(c_Power_Opower__class_Opower(_1077502), _1077508), hAPP(c_Nat_OSuc, _1077506)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077502), c_Groups_Ozero__class_Ozero(_1077502)), _1077508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077502), _1077504), _1077508)))], (51558 ^ _773908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (24361 ^ _773908) ^ [_1201433, _1201435, _1201437, _1201439] : [_1201433 = _1201435, 24364 ^ _773908 : [(24367 ^ _773908) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1201437, _1201439), _1201433) = hAPP(c_Product__Type_Osnd(_1201437, _1201439), _1201435))], (24365 ^ _773908) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1201437, _1201439), _1201433) = hAPP(c_Product__Type_Ofst(_1201437, _1201439), _1201435))]]], (38215 ^ _773908) ^ [_1502693, _1502695, _1502697] : [class_Orderings_Olinorder(_1502693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502693), _1502695)), -(_1502695 = c_Orderings_Obot__class_Obot(tc_fun(_1502693, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502693), _1502697)), -(_1502697 = c_Orderings_Obot__class_Obot(tc_fun(_1502693, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1502693), c_Big__Operators_Olattice_OSup__fin(_1502693, c_Orderings_Oord__class_Omax(_1502693), _1502695)), c_Big__Operators_Olattice_OSup__fin(_1502693, c_Orderings_Oord__class_Omax(_1502693), _1502697)) = c_Big__Operators_Olattice_OSup__fin(_1502693, c_Orderings_Oord__class_Omax(_1502693), hAPP(c_Set_OCollect(_1502693), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_HOL_Obool), tc_HOL_Obool, _1502693), c_HOL_OEx(_1502693)), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool)), tc_fun(_1502693, tc_HOL_Obool), _1502693), hAPP(c_COMBB(tc_fun(_1502693, tc_HOL_Obool), tc_HOL_Obool, _1502693), c_HOL_OEx(_1502693))), hAPP(hAPP(c_COMBC(_1502693, tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool)), tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_fun(tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool))), tc_fun(tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool)), tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool))), _1502693), c_COMBS(_1502693, tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_fun(_1502693, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1502693, tc_fun(tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool))), _1502693), hAPP(c_COMBB(tc_fun(_1502693, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool)), _1502693), c_COMBS(_1502693, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool)), tc_fun(_1502693, tc_fun(_1502693, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1502693), hAPP(c_COMBB(tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1502693), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1502693), c_fconj))), hAPP(hAPP(c_COMBC(_1502693, tc_fun(_1502693, tc_fun(_1502693, _1502693)), tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1502693, _1502693), tc_fun(_1502693, tc_HOL_Obool)), tc_fun(tc_fun(_1502693, tc_fun(_1502693, _1502693)), tc_fun(_1502693, tc_fun(_1502693, tc_HOL_Obool))), _1502693), c_COMBB(tc_fun(_1502693, _1502693), tc_fun(_1502693, tc_HOL_Obool), _1502693)), hAPP(hAPP(c_COMBB(tc_fun(_1502693, tc_HOL_Obool), tc_fun(tc_fun(_1502693, _1502693), tc_fun(_1502693, tc_HOL_Obool)), _1502693), c_COMBB(_1502693, tc_HOL_Obool, _1502693)), c_fequal))), c_Orderings_Oord__class_Omin(_1502693)))))), hAPP(hAPP(c_COMBC(_1502693, tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1502693, tc_HOL_Obool), tc_fun(_1502693, tc_HOL_Obool)), _1502693), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1502693)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1502693), c_fconj), hAPP(hAPP(c_COMBC(_1502693, tc_fun(_1502693, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502693)), _1502695)))), hAPP(hAPP(c_COMBC(_1502693, tc_fun(_1502693, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502693)), _1502697))))))))], (49266 ^ _773908) ^ [] : [-(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)))], (17041 ^ _773908) ^ [_1067675, _1067677] : [class_Groups_Oabs__if(_1067675), 17044 ^ _773908 : [(17051 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067675), _1067677), c_Groups_Ozero__class_Ozero(_1067675)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1067675), _1067677) = _1067677)], (17045 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067675), _1067677), c_Groups_Ozero__class_Ozero(_1067675))), -(hAPP(c_Groups_Oabs__class_Oabs(_1067675), _1067677) = hAPP(c_Groups_Ouminus__class_Ouminus(_1067675), _1067677))]]], (16799 ^ _773908) ^ [_1062456, _1062458, _1062460, _1062462] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062456), _1062458), _1062460)), hAPP(c_Int_Onumber__class_Onumber__of(_1062456), _1062462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062456), _1062458), hAPP(c_Int_Onumber__class_Onumber__of(_1062456), _1062462))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062456), _1062460), hAPP(c_Int_Onumber__class_Onumber__of(_1062456), _1062462)))), class_Int_Onumber(_1062456), class_Rings_Osemiring(_1062456)], (50808 ^ _773908) ^ [_1801285, _1801287] : [c_Equiv__Relations_Opart__equivp(_1801285, _1801287), 50812 ^ _773908 : [(50817 ^ _773908) ^ [] : [-(c_Predicate_Otransp(_1801285, _1801287))], (50815 ^ _773908) ^ [] : [-(c_Predicate_Osymp(_1801285, _1801287))], (50813 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1801287, 50811 ^ [_1801285, _1801287]), 50811 ^ [_1801285, _1801287])))]]], (38567 ^ _773908) ^ [_1516510, _1516512, _1516514, _1516516, _1516518, _1516520, _1516522, _1516524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516510, _1516512)), hAPP(hAPP(c_Product__Type_OPair(_1516510, _1516512), _1516514), _1516516)), _1516518)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516512, _1516520)), hAPP(hAPP(c_Product__Type_OPair(_1516512, _1516520), _1516516), _1516522)), _1516524)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516510, _1516520)), hAPP(hAPP(c_Product__Type_OPair(_1516510, _1516520), _1516514), _1516522)), hAPP(hAPP(c_Relation_Orel__comp(_1516510, _1516512, _1516520), _1516518), _1516524))))], (42325 ^ _773908) ^ [_1612407, _1612409, _1612411, _1612413, _1612415] : [c_Fun_Oinj__on(_1612407, _1612409, _1612411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1612407, tc_HOL_Obool)), hAPP(c_List_Oset(_1612407), _1612413)), hAPP(c_List_Oset(_1612407), _1612415))), 42328 ^ _773908 : [(42335 ^ _773908) ^ [] : [_1612413 = _1612415, -(hAPP(hAPP(c_List_Omap(_1612407, _1612409), _1612411), _1612413) = hAPP(hAPP(c_List_Omap(_1612407, _1612409), _1612411), _1612415))], (42329 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Omap(_1612407, _1612409), _1612411), _1612413) = hAPP(hAPP(c_List_Omap(_1612407, _1612409), _1612411), _1612415), -(_1612413 = _1612415)]]], (34049 ^ _773908) ^ [_1407546, _1407548, _1407550] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1407546, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1407548)), _1407550) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407546, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1407546, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1407548)), _1407550)), hAPP(_1407550, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22675 ^ _773908) ^ [_1167324, _1167326, _1167328, _1167330] : [class_Fields_Olinordered__field__inverse__zero(_1167324), class_Int_Onumber(_1167324), 22682 ^ _773908 : [(22683 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167324), _1167328), _1167330))), 22686 ^ _773908 : [(22693 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), c_Groups_Ozero__class_Ozero(_1167324)), _1167330))), 22696 ^ _773908 : [(22703 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), _1167330), c_Groups_Ozero__class_Ozero(_1167324)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), c_Groups_Ozero__class_Ozero(_1167324))))], (22697 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), _1167330), c_Groups_Ozero__class_Ozero(_1167324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), _1167328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), _1167330))))]]], (22687 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), c_Groups_Ozero__class_Ozero(_1167324)), _1167330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), _1167330)), _1167328)))]]], (22709 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167324), _1167328), _1167330)))), 22712 ^ _773908 : [(22715 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), _1167330)), _1167328))], (22713 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), c_Groups_Ozero__class_Ozero(_1167324)), _1167330)))]], 22716 ^ _773908 : [(22719 ^ _773908) ^ [] : [22720 ^ _773908 : [(22723 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), _1167328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), _1167330)))], (22721 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), _1167330), c_Groups_Ozero__class_Ozero(_1167324))))]], 22724 ^ _773908 : [(22727 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167324), hAPP(c_Int_Onumber__class_Onumber__of(_1167324), _1167326)), c_Groups_Ozero__class_Ozero(_1167324)))], (22725 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), _1167330), c_Groups_Ozero__class_Ozero(_1167324)))]]], (22717 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167324), c_Groups_Ozero__class_Ozero(_1167324)), _1167330))]]]]], (42886 ^ _773908) ^ [_1624727] : [-(c_Code__Numeral_OSuc__code__numeral(_1624727) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1624727))))], (51790 ^ _773908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (9459 ^ _773908) ^ [_931507, _931509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931507)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _931509))))], (42323 ^ _773908) ^ [_1612372] : [-(hAPP(c_List_Omap(_1612372, _1612372), c_Fun_Oid(_1612372)) = c_Fun_Oid(tc_List_Olist(_1612372)))], (43491 ^ _773908) ^ [_1637904, _1637906, _1637908, _1637910] : [_1637910 = c_List_Olist_ONil(_1637904), -(c_List_Olist__all2(_1637904, _1637906, _1637908, _1637910, c_List_Olist_ONil(_1637906)))], (15391 ^ _773908) ^ [_1035083, _1035085, _1035087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035083), _1035085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035083), _1035087)), _1035085)))], (51842 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (480 ^ _773908) ^ [_781322, _781324] : [-(c_List_Onat__list(_781322)), _781324 = _781322, c_List_Onat__list(_781324)], (49724 ^ _773908) ^ [_1777682, _1777684, _1777686, _1777688, _1777690] : [49726 ^ _773908 : [(49729 ^ _773908) ^ [] : [c_Relation_Orefl__on(_1777686, hAPP(_1777688, 49725 ^ [_1777682, _1777684, _1777686, _1777688, _1777690]), hAPP(_1777690, 49725 ^ [_1777682, _1777684, _1777686, _1777688, _1777690]))], (49727 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777682), 49725 ^ [_1777682, _1777684, _1777686, _1777688, _1777690]), _1777684)))]], -(c_Relation_Orefl__on(_1777686, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1777682, tc_fun(_1777686, tc_HOL_Obool)), _1777684), _1777688), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1777682, tc_fun(tc_prod(_1777686, _1777686), tc_HOL_Obool)), _1777684), _1777690)))], (21021 ^ _773908) ^ [_1137623, _1137625, _1137627] : [class_Fields_Olinordered__field__inverse__zero(_1137623), 21024 ^ _773908 : [(21039 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137623), _1137625), _1137627)), c_Groups_Ozero__class_Ozero(_1137623)))), 21040 ^ _773908 : [(21047 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), _1137625), c_Groups_Ozero__class_Ozero(_1137623))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), c_Groups_Ozero__class_Ozero(_1137623)), _1137627))], (21041 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), c_Groups_Ozero__class_Ozero(_1137623)), _1137625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), _1137627), c_Groups_Ozero__class_Ozero(_1137623)))]]], (21025 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137623), _1137625), _1137627)), c_Groups_Ozero__class_Ozero(_1137623))), 21030 ^ _773908 : [(21033 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), _1137627), c_Groups_Ozero__class_Ozero(_1137623))))], (21031 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), c_Groups_Ozero__class_Ozero(_1137623)), _1137625)))]], 21034 ^ _773908 : [(21037 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), c_Groups_Ozero__class_Ozero(_1137623)), _1137627)))], (21035 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137623), _1137625), c_Groups_Ozero__class_Ozero(_1137623))))]]]]], (39966 ^ _773908) ^ [_1554276, _1554278, _1554280] : [-(_1554276 = _1554278), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554280)), _1554276) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554280)), _1554278), 39972 ^ _773908 : [(39975 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Onth(_1554280), _1554276), 39971 ^ [_1554276, _1554278, _1554280]) = hAPP(hAPP(c_List_Onth(_1554280), _1554278), 39971 ^ [_1554276, _1554278, _1554280])], (39973 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39971 ^ [_1554276, _1554278, _1554280]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554280)), _1554276))))]]], (20547 ^ _773908) ^ [_1128850, _1128852] : [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), _1128850))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1128852))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128850))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128852)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128850)))], (35835 ^ _773908) ^ [_1446389, _1446391] : [-(hBOOL(hAPP(hAPP(c_member(_1446389), _1446391), c_Orderings_Otop__class_Otop(tc_fun(_1446389, tc_HOL_Obool)))))], (40971 ^ _773908) ^ [_1580991, _1580993] : [-(hAPP(c_List_Orotate1(_1580991), _1580993) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1580991), _1580991, c_List_Olist_ONil(_1580991), hAPP(hAPP(c_COMBB(tc_List_Olist(_1580991), tc_fun(tc_List_Olist(_1580991), tc_List_Olist(_1580991)), _1580991), hAPP(c_COMBC(tc_List_Olist(_1580991), tc_List_Olist(_1580991), tc_List_Olist(_1580991)), c_List_Oappend(_1580991))), hAPP(hAPP(c_COMBC(_1580991, tc_List_Olist(_1580991), tc_List_Olist(_1580991)), c_List_Olist_OCons(_1580991)), c_List_Olist_ONil(_1580991)))), _1580993))], (45896 ^ _773908) ^ [_1691071, _1691073, _1691075] : [45898 ^ _773908 : [(45901 ^ _773908) ^ [] : [hBOOL(hAPP(_1691073, 45897 ^ [_1691071, _1691073, _1691075]))], (45899 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1691071), 45897 ^ [_1691071, _1691073, _1691075]), hAPP(c_List_Oset(_1691071), _1691075))))]], -(c_List_OdropWhile(_1691071, _1691073, _1691075) = c_List_Olist_ONil(_1691071))], (23447 ^ _773908) ^ [_1182490, _1182492] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1182490, _1182492) = 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), _1182490), _1182492)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1182490, _1182492)))], (41458 ^ _773908) ^ [_1590588, _1590590, _1590592] : [-(c_List_Olast(_1590588, hAPP(hAPP(c_List_Oappend(_1590588), _1590590), hAPP(hAPP(c_List_Olist_OCons(_1590588), _1590592), c_List_Olist_ONil(_1590588)))) = _1590592)], (51660 ^ _773908) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (7577 ^ _773908) ^ [_896717, _896719, _896721, _896723, _896725, _896727] : [-(c_Com_Ocom_OCond(_896717, _896719, _896721) = c_Com_Ocom_OCond(_896723, _896725, _896727)), _896717 = _896723, _896719 = _896725, _896721 = _896727], (32163 ^ _773908) ^ [_1370282, _1370284, _1370286, _1370288] : [_1370282 = _1370284, hBOOL(hAPP(hAPP(c_member(_1370286), _1370282), _1370288)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1370286, _1370286)), hAPP(hAPP(c_Product__Type_OPair(_1370286, _1370286), _1370282), _1370284)), c_Relation_OId__on(_1370286, _1370288))))], (5642 ^ _773908) ^ [_860201, _860203, _860205, _860207, _860209, _860211] : [-(c_COMBS(_860211, _860207, _860203) = c_COMBS(_860209, _860205, _860201)), _860211 = _860209, _860207 = _860205, _860203 = _860201], (24329 ^ _773908) ^ [_1200726, _1200728, _1200730, _1200732] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1200726, _1200728)), hAPP(hAPP(c_Product__Type_OPair(_1200726, _1200728), _1200730), _1200732)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1200726, _1200728), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1200726, tc_fun(_1200728, tc_HOL_Obool))), _1200730), _1200732)))], (35435 ^ _773908) ^ [_1438094] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1438094)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1438094)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1438094)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (9085 ^ _773908) ^ [_924753, _924755] : [class_Groups_Ogroup__add(_924753), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924753), hAPP(c_Groups_Ouminus__class_Ouminus(_924753), _924755)), _924755) = c_Groups_Ozero__class_Ozero(_924753))], (41452 ^ _773908) ^ [_1590535, _1590537] : [-(_1590535 = c_List_Olist_ONil(_1590537)), -(hBOOL(hAPP(hAPP(c_member(_1590537), c_List_Olast(_1590537, _1590535)), hAPP(c_List_Oset(_1590537), _1590535))))], (30704 ^ _773908) ^ [_1336218, _1336220, _1336222] : [class_Groups_Ocomm__monoid__mult(_1336218), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336220, _1336218), hAPP(c_COMBK(_1336218, _1336220), c_Groups_Oone__class_Oone(_1336218))), _1336222) = c_Groups_Oone__class_Oone(_1336218))], (32083 ^ _773908) ^ [_1368878, _1368880, _1368882] : [class_Orderings_Oorder(_1368878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368878), _1368880), _1368882)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1368878, _1368882, _1368880) = c_Orderings_Obot__class_Obot(tc_fun(_1368878, tc_HOL_Obool)))], (43119 ^ _773908) ^ [_1630129, _1630131, _1630133, _1630135, _1630137, _1630139] : [class_Orderings_Olinorder(_1630129), 43122 ^ _773908 : [(43129 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630129), hAPP(_1630131, _1630133)), hAPP(_1630131, _1630135)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630137, _1630129, _1630131), _1630133), hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630135), _1630139)) = hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630135), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630137, _1630129, _1630131), _1630133), _1630139)))], (43123 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630129), hAPP(_1630131, _1630133)), hAPP(_1630131, _1630135))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630137, _1630129, _1630131), _1630133), hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630135), _1630139)) = hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630133), hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630135), _1630139)))]]], (34840 ^ _773908) ^ [_1424530, _1424532, _1424534, _1424536, _1424538] : [class_Groups_Ocomm__monoid__add(_1424530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424532), _1424534)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424532), _1424536)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424530), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424532, _1424530), _1424538), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424532, tc_HOL_Obool)), _1424534), _1424536))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424532, _1424530), _1424538), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424532, tc_HOL_Obool)), _1424534), _1424536))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424530), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424532, _1424530), _1424538), _1424534)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424532, _1424530), _1424538), _1424536)))], (18077 ^ _773908) ^ [_1085700, _1085702, _1085704] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085700)))), 18080 ^ _773908 : [(18087 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085702)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085700)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085702)), _1085704)) = 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), _1085700), _1085702))), _1085704))], (18081 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085702))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085700)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085702)), _1085704)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085700)), _1085704))]]], (10771 ^ _773908) ^ [_952717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952717)), -(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)), _952717))))], (4502 ^ _773908) ^ [_842451, _842453] : [_842453 = _842451, -(c_List_Orev(_842453) = c_List_Orev(_842451))], (20801 ^ _773908) ^ [_1133818] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133818)))], (39326 ^ _773908) ^ [_1537835, _1537837, _1537839] : [_1537837 = c_List_Olist_ONil(_1537835), -(hAPP(hAPP(c_List_Oappend(_1537835), _1537837), _1537839) = _1537839)], (35400 ^ _773908) ^ [_1437245, _1437247, _1437249, _1437251] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437245), _1437247)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437245), _1437249)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437245, tc_Nat_Onat), _1437251), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437245, tc_HOL_Obool)), _1437247), _1437249)) = 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(_1437245, tc_Nat_Onat), _1437251), _1437247)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437245, tc_Nat_Onat), _1437251), _1437249))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437245, tc_Nat_Onat), _1437251), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437245, tc_HOL_Obool)), _1437247), _1437249))))], (14683 ^ _773908) ^ [_1022196, _1022198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022196), 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)), _1022198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022196), _1022198)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40229 ^ _773908) ^ [_1560593, _1560595, _1560597] : [-(hAPP(hAPP(c_List_Odrop(_1560593), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1560593), _1560595), _1560597)) = _1560597)], (20571 ^ _773908) ^ [_1129264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1129264)), -(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), _1129264), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (1264 ^ _773908) ^ [_792694, _792696] : [-(class_Rings_Ocomm__ring__1(_792694)), _792696 = _792694, class_Rings_Ocomm__ring__1(_792696)], (25487 ^ _773908) ^ [_1224915, _1224917, _1224919, _1224921, _1224923, _1224925, _1224927] : [-(hAPP(c_Product__Type_Oapsnd(_1224915, _1224917, _1224919, _1224921), hAPP(c_Product__Type_Oapfst(_1224923, _1224919, _1224915, _1224925), _1224927)) = hAPP(hAPP(c_Product__Type_OPair(_1224919, _1224917), hAPP(_1224925, hAPP(c_Product__Type_Ofst(_1224923, _1224915), _1224927))), hAPP(_1224921, hAPP(c_Product__Type_Osnd(_1224923, _1224915), _1224927))))], (50225 ^ _773908) ^ [_1790812, _1790814] : [c_Relation_Otrans(_1790812, _1790814), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1790812, _1790812), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1790812, _1790812, _1790812), _1790814), _1790814)), _1790814)))], (51484 ^ _773908) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (25753 ^ _773908) ^ [_1230285, _1230287] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1230285, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1230285, tc_HOL_Obool))), _1230287) = _1230287)], (3384 ^ _773908) ^ [_824728, _824730] : [_824730 = _824728, -(c_Int_Onumber__class_Onumber__of(_824730) = c_Int_Onumber__class_Onumber__of(_824728))], (26253 ^ _773908) ^ [_1240174, _1240176, _1240178, _1240180] : [hBOOL(hAPP(hAPP(c_member(_1240174), _1240176), _1240178)), -(hBOOL(hAPP(hAPP(c_member(_1240174), _1240176), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240174, tc_HOL_Obool)), _1240178), _1240180))))], (13045 ^ _773908) ^ [_992757, _992759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992757), _992759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992757)), _992759)))], (19751 ^ _773908) ^ [_1114520, _1114522] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1114520, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1114522)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1114520, 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)))), _1114522)))], (39713 ^ _773908) ^ [_1546995, _1546997, _1546999, _1547001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1546995), tc_List_Olist(_1546995))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1546995), tc_List_Olist(_1546995)), _1546997), _1546999)), c_List_Olistrel(_1546995, _1547001))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1546995)), _1546997) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1546995)), _1546999))], (39432 ^ _773908) ^ [_1539737, _1539739, _1539741, _1539743, _1539745] : [-(hAPP(hAPP(c_List_Oappend(_1539737), _1539739), hAPP(hAPP(c_List_Olist_OCons(_1539737), _1539741), c_List_Olist_ONil(_1539737))) = hAPP(hAPP(c_List_Oappend(_1539737), _1539743), hAPP(hAPP(c_List_Olist_OCons(_1539737), _1539745), c_List_Olist_ONil(_1539737)))), _1539739 = _1539743, _1539741 = _1539745], (39795 ^ _773908) ^ [_1549743, _1549745, _1549747, _1549749, _1549751, _1549753] : [c_List_Olistrelp(_1549743, _1549745, hAPP(hAPP(c_List_Olist_OCons(_1549743), _1549747), _1549749), hAPP(hAPP(c_List_Olist_OCons(_1549743), _1549751), _1549753)), 39798 ^ _773908 : [(39801 ^ _773908) ^ [] : [-(c_List_Olistrelp(_1549743, _1549745, _1549749, _1549753))], (39799 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1549745, _1549747), _1549751)))]]], (44756 ^ _773908) ^ [_1668238, _1668240, _1668242, _1668244] : [-(c_List_Oupt(_1668238, _1668240) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1668242), _1668244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668238), _1668240)), _1668238 = _1668242, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668238), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1668240) = _1668244], (19315 ^ _773908) ^ [_1107387, _1107389] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1107387)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107389)) = 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)))), _1107387)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107389)))], (43393 ^ _773908) ^ [_1636003, _1636005, _1636007, _1636009, _1636011] : [c_List_Olist__all2(_1636003, _1636005, _1636007, _1636009, _1636011), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636003)), _1636009) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636005)), _1636011))], (28176 ^ _773908) ^ [_1284526, _1284528, _1284530] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284526, tc_HOL_Obool)), _1284528), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284526, tc_HOL_Obool)), _1284528), _1284530)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284526, tc_HOL_Obool)), _1284528), _1284530))], (19469 ^ _773908) ^ [_1109977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1109977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1109977)))], (32009 ^ _773908) ^ [_1367077, _1367079, _1367081, _1367083, _1367085, _1367087, _1367089] : [c_Big__Operators_Ocomm__monoid__big(_1367077, _1367079, _1367081, _1367083, _1367085), 32012 ^ _773908 : [(32019 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1367079), _1367087))), -(hAPP(hAPP(_1367085, _1367089), _1367087) = _1367083)], (32013 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1367079), _1367087)), -(hAPP(hAPP(_1367085, _1367089), _1367087) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1367077, _1367079, _1367081), _1367089), _1367083), _1367087))]]], (42720 ^ _773908) ^ [_1621172, _1621174, _1621176, _1621178, _1621180] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621172)), _1621174) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621176)), _1621178), 42723 ^ _773908 : [(42732 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1621172, _1621176), _1621174), _1621178) = _1621180), hAPP(hAPP(c_List_Omap(tc_prod(_1621172, _1621176), _1621172), c_Product__Type_Ofst(_1621172, _1621176)), _1621180) = _1621174, hAPP(hAPP(c_List_Omap(tc_prod(_1621172, _1621176), _1621176), c_Product__Type_Osnd(_1621172, _1621176)), _1621180) = _1621178], (42724 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Ozip(_1621172, _1621176), _1621174), _1621178) = _1621180, 42727 ^ _773908 : [(42730 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1621172, _1621176), _1621176), c_Product__Type_Osnd(_1621172, _1621176)), _1621180) = _1621178)], (42728 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1621172, _1621176), _1621172), c_Product__Type_Ofst(_1621172, _1621176)), _1621180) = _1621174)]]]]], (24381 ^ _773908) ^ [_1201822, _1201824, _1201826] : [-(hAPP(c_Product__Type_Ofst(_1201822, _1201824), _1201826) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201822, _1201824, _1201822), c_COMBK(_1201822, _1201824)), _1201826))], (9079 ^ _773908) ^ [_924648, _924650] : [class_Groups_Oab__group__add(_924648), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924648), hAPP(c_Groups_Ouminus__class_Ouminus(_924648), _924650)), _924650) = c_Groups_Ozero__class_Ozero(_924648))], (39901 ^ _773908) ^ [_1552329, _1552331, _1552333] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1552329)), _1552331), c_Wellfounded_Oacc(tc_List_Olist(_1552329), c_List_Olistrel1(_1552329, _1552333)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1552329)), _1552331), c_List_Olists(_1552329, c_Wellfounded_Oacc(_1552329, _1552333)))))], (33780 ^ _773908) ^ [_1401463, _1401465, _1401467, _1401469] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1401463, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1401465)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1401463, tc_HOL_Obool), tc_Nat_Onat), _1401467), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1401469))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1401463, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1401469, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1401465), _1401469))), _1401467))], (51628 ^ _773908) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (42275 ^ _773908) ^ [_1611451] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611451, tc_HOL_Obool) = c_Set_OBall(_1611451))], (25733 ^ _773908) ^ [_1229904, _1229906, _1229908] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229904, tc_HOL_Obool)), _1229906), _1229908) = c_Orderings_Obot__class_Obot(tc_fun(_1229904, tc_HOL_Obool)), 25736 ^ _773908 : [(25739 ^ _773908) ^ [] : [-(_1229908 = c_Orderings_Obot__class_Obot(tc_fun(_1229904, tc_HOL_Obool)))], (25737 ^ _773908) ^ [] : [-(_1229906 = c_Orderings_Obot__class_Obot(tc_fun(_1229904, tc_HOL_Obool)))]]], (29523 ^ _773908) ^ [_1313032, _1313034, _1313036] : [class_Orderings_Olinorder(_1313032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313032), _1313034)), hBOOL(hAPP(hAPP(c_member(_1313032), _1313036), _1313034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313032), c_Big__Operators_Olinorder__class_OMin(_1313032, _1313034)), _1313036)))], (23676 ^ _773908) ^ [_1187024, _1187026, _1187028, _1187030, _1187032] : [hBOOL(hAPP(hAPP(_1187024, _1187026), _1187028)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1187030, _1187032, tc_HOL_Obool), _1187024), hAPP(hAPP(c_Product__Type_OPair(_1187030, _1187032), _1187026), _1187028))))], (28903 ^ _773908) ^ [_1301895, _1301897] : [class_Lattices_Olattice(_1301895), -(c_Big__Operators_Olattice__class_OSup__fin(_1301895, hAPP(hAPP(c_Set_Oinsert(_1301895), _1301897), c_Orderings_Obot__class_Obot(tc_fun(_1301895, tc_HOL_Obool)))) = _1301897)], (38647 ^ _773908) ^ [_1519237, _1519239, _1519241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519237, _1519237), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519237, _1519237, _1519237), _1519239), _1519241)), _1519239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1519237, _1519239)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1519237, _1519241)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1519237, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1519237, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1519237, tc_HOL_Obool), tc_fun(_1519237, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1519237, _1519239))))], (10635 ^ _773908) ^ [_950196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _950196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43807 ^ _773908) ^ [_1645305, _1645307] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1645305), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1645305, tc_HOL_Obool), _1645307))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1645305, tc_HOL_Obool)), _1645307)))], (19517 ^ _773908) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (12292 ^ _773908) ^ [_979776, _979778] : [_979776 = hAPP(c_Int_Onat, _979778), 12295 ^ _773908 : [(12302 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979778))), -(_979776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12296 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979778)), -(_979778 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _979776))]]], (13021 ^ _773908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48411 ^ _773908) ^ [_1749715, _1749717, _1749719] : [class_Orderings_Olinorder(_1749715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749715), _1749717)), -(c_Big__Operators_Olinorder__class_OMin(_1749715, hAPP(hAPP(c_Set_Oinsert(_1749715), _1749719), _1749717)) = hAPP(hAPP(c_Finite__Set_Ofold(_1749715, _1749715, c_Orderings_Oord__class_Omin(_1749715)), _1749719), _1749717))], (49993 ^ _773908) ^ [_1784032, _1784034, _1784036, _1784038] : [-(hAPP(c_Relation_OImage(_1784032, _1784034, hAPP(c_Set_OCollect(tc_prod(_1784032, _1784034)), hAPP(c_Product__Type_Oprod_Oprod__case(_1784032, _1784034, tc_HOL_Obool), _1784036))), _1784038) = hAPP(c_Set_OCollect(_1784034), hAPP(hAPP(c_COMBB(tc_fun(_1784032, tc_HOL_Obool), tc_HOL_Obool, _1784034), c_HOL_OEx(_1784032)), hAPP(hAPP(c_COMBB(tc_fun(_1784032, tc_HOL_Obool), tc_fun(_1784032, tc_HOL_Obool), _1784034), hAPP(c_COMBS(_1784032, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784032), c_fconj), hAPP(hAPP(c_COMBC(_1784032, tc_fun(_1784032, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784032)), _1784038)))), hAPP(c_COMBC(_1784032, _1784034, tc_HOL_Obool), _1784036)))))], (956 ^ _773908) ^ [_788450, _788452, _788454, _788456] : [-(c_Equiv__Relations_Oequivp(_788454, _788450)), c_Equiv__Relations_Oequivp(_788456, _788452), _788456 = _788454, _788452 = _788450], (39827 ^ _773908) ^ [_1550592, _1550594, _1550596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550592, _1550592), tc_HOL_Obool)), _1550594), hAPP(hAPP(c_Product__Type_OSigma(_1550592, _1550592), _1550596), hAPP(c_COMBK(tc_fun(_1550592, tc_HOL_Obool), _1550592), _1550596)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1550592), tc_List_Olist(_1550592)), tc_HOL_Obool)), c_List_Olistrel(_1550592, _1550594)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1550592), tc_List_Olist(_1550592)), c_List_Olists(_1550592, _1550596)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1550592), tc_HOL_Obool), tc_List_Olist(_1550592)), c_List_Olists(_1550592, _1550596))))))], (13879 ^ _773908) ^ [_1007663, _1007665, _1007667] : [class_Lattices_Oboolean__algebra(_1007663), 13882 ^ _773908 : [(13889 ^ _773908) ^ [] : [_1007665 = _1007667, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007665) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007667))], (13883 ^ _773908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007665) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007667), -(_1007665 = _1007667)]]], (2564 ^ _773908) ^ [_811762, _811764, _811766, _811768] : [-(c_FunDef_Orp__inv__image(_811768, _811764) = c_FunDef_Orp__inv__image(_811766, _811762)), _811768 = _811766, _811764 = _811762], (36462 ^ _773908) ^ [_1460368, _1460370, _1460372, _1460374, _1460376] : [c_Equiv__Relations_Oequivp(_1460368, _1460370), hBOOL(hAPP(hAPP(_1460370, _1460372), _1460374)), hBOOL(hAPP(hAPP(_1460370, _1460374), _1460376)), -(hBOOL(hAPP(hAPP(_1460370, _1460372), _1460376)))], (42601 ^ _773908) ^ [_1618944, _1618946] : [42602 ^ _773908 : [(42603 ^ _773908) ^ [_1618990] : [hBOOL(hAPP(_1618944, _1618990))]], -(hBOOL(hAPP(_1618944, c_Hilbert__Choice_OEps(_1618946, _1618944))))], (47359 ^ _773908) ^ [_1725817, _1725819, _1725821] : [c_Relation_Orefl__on(_1725817, _1725819, hAPP(c_Relation_Oconverse(_1725817, _1725817), _1725821)), -(c_Relation_Orefl__on(_1725817, _1725819, _1725821))], (45559 ^ _773908) ^ [_1683930, _1683932, _1683934] : [hAPP(c_List_Orev(_1683930), _1683932) = hAPP(hAPP(c_List_Olist_OCons(_1683930), _1683934), c_List_Olist_ONil(_1683930)), -(_1683932 = hAPP(hAPP(c_List_Olist_OCons(_1683930), _1683934), c_List_Olist_ONil(_1683930)))], (2108 ^ _773908) ^ [_804516, _804518, _804520, _804522] : [-(c_SMT_Oz3div(_804522, _804518) = c_SMT_Oz3div(_804520, _804516)), _804522 = _804520, _804518 = _804516], (23741 ^ _773908) ^ [_1188591, _1188593, _1188595] : [hBOOL(hAPP(_1188591, hAPP(hAPP(c_Product__Type_OPair(_1188593, _1188595), 23742 ^ [_1188591, _1188593, _1188595]), 23743 ^ [_1188591, _1188593, _1188595]))), 23746 ^ _773908 : [(23747 ^ _773908) ^ [_1188738] : [-(hBOOL(hAPP(_1188591, _1188738)))]]], (50063 ^ _773908) ^ [_1785596, _1785598, _1785600, _1785602] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785596), _1785598)), 50066 ^ _773908 : [(50067 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785600), hAPP(c_Set_OCollect(_1785600), hAPP(hAPP(c_COMBB(tc_fun(_1785596, tc_HOL_Obool), tc_HOL_Obool, _1785600), c_HOL_OEx(_1785596)), hAPP(hAPP(c_COMBB(tc_fun(_1785596, tc_HOL_Obool), tc_fun(_1785596, tc_HOL_Obool), _1785600), hAPP(c_COMBS(_1785596, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785596), c_fconj), hAPP(hAPP(c_COMBC(_1785596, tc_fun(_1785596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785596)), _1785598)))), _1785602))))), 50070 ^ _773908 : [(50071 ^ _773908) ^ [_1785904] : [hBOOL(hAPP(hAPP(c_member(_1785596), _1785904), _1785598)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1785600), hAPP(c_Set_OCollect(_1785600), hAPP(hAPP(c_COMBC(_1785600, _1785596, tc_HOL_Obool), _1785602), _1785904)))))]]], (50077 ^ _773908) ^ [] : [50079 ^ _773908 : [(50082 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785600), hAPP(c_Set_OCollect(_1785600), hAPP(hAPP(c_COMBC(_1785600, _1785596, tc_HOL_Obool), _1785602), 50078 ^ [_1785596, _1785598, _1785600, _1785602]))))], (50080 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785596), 50078 ^ [_1785596, _1785598, _1785600, _1785602]), _1785598)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1785600), hAPP(c_Set_OCollect(_1785600), hAPP(hAPP(c_COMBB(tc_fun(_1785596, tc_HOL_Obool), tc_HOL_Obool, _1785600), c_HOL_OEx(_1785596)), hAPP(hAPP(c_COMBB(tc_fun(_1785596, tc_HOL_Obool), tc_fun(_1785596, tc_HOL_Obool), _1785600), hAPP(c_COMBS(_1785596, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785596), c_fconj), hAPP(hAPP(c_COMBC(_1785596, tc_fun(_1785596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785596)), _1785598)))), _1785602))))))]]], (24919 ^ _773908) ^ [_1213504, _1213506, _1213508, _1213510] : [class_Orderings_Olinorder(_1213504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213504), _1213506), _1213508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213504), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213504), _1213510), _1213506)), _1213508)))], (44297 ^ _773908) ^ [_1657081, _1657083, _1657085] : [-(hBOOL(hAPP(hAPP(c_member(_1657081), _1657083), hAPP(c_List_Oset(_1657081), _1657085)))), -(hAPP(c_List_OremoveAll(_1657081, _1657083), _1657085) = _1657085)], (30799 ^ _773908) ^ [_1338110, _1338112, _1338114] : [class_Groups_Ocomm__monoid__mult(_1338110), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338112, _1338110), _1338114), c_Orderings_Obot__class_Obot(tc_fun(_1338112, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1338110))], (37716 ^ _773908) ^ [_1489671, _1489673, _1489675, _1489677, _1489679, _1489681] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1489671, _1489673), _1489671, tc_prod(_1489675, _1489677), c_Product__Type_Ofst(_1489671, _1489673)), c_Product__Type_Omap__pair(_1489675, _1489671, _1489677, _1489673, _1489679, _1489681)) = hAPP(c_Fun_Ocomp(_1489675, _1489671, tc_prod(_1489675, _1489677), _1489679), c_Product__Type_Ofst(_1489675, _1489677)))], (28416 ^ _773908) ^ [_1290447, _1290449, _1290451, _1290453] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290447, tc_HOL_Obool)), _1290449), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290447, tc_HOL_Obool)), _1290451), _1290453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290447, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290447, tc_HOL_Obool)), _1290449), _1290451)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290447, tc_HOL_Obool)), _1290449), _1290453)))], (27304 ^ _773908) ^ [_1266914, _1266916] : [class_Finite__Set_Ofinite(_1266914), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266914), _1266916)))], (33042 ^ _773908) ^ [_1387564, _1387566, _1387568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1387564)), 33045 ^ _773908 : [(33046 ^ _773908) ^ [_1387698] : [33048 ^ _773908 : [(33054 ^ _773908) ^ [] : [-(_1387698 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33050 ^ [_1387564, _1387566, _1387568, _1387698]), 33047 ^ [_1387564, _1387566, _1387568, _1387698]))], (33052 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33050 ^ [_1387564, _1387566, _1387568, _1387698]), _1387566)))], (33049 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33047 ^ [_1387564, _1387566, _1387568, _1387698]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1387564))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387568), _1387698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1387568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1387698), _1387564))))]]], (27872 ^ _773908) ^ [_1278411, _1278413, _1278415] : [class_Lattices_Osemilattice__inf(_1278411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278411), _1278413), _1278415)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1278411), _1278415), _1278413) = _1278413)], (39627 ^ _773908) ^ [_1544582, _1544584, _1544586, _1544588, _1544590, _1544592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544582), tc_List_Olist(_1544582))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544582), tc_List_Olist(_1544582)), hAPP(hAPP(c_List_Olist_OCons(_1544582), _1544584), _1544586)), hAPP(hAPP(c_List_Olist_OCons(_1544582), _1544588), _1544590))), c_List_Olistrel1(_1544582, _1544592))), 39632 ^ _773908 : [(39635 ^ _773908) ^ [] : [-(_1544586 = _1544590)], (39633 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544582, _1544582)), hAPP(hAPP(c_Product__Type_OPair(_1544582, _1544582), _1544584), _1544588)), _1544592)))]], 39636 ^ _773908 : [(39639 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544582), tc_List_Olist(_1544582))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544582), tc_List_Olist(_1544582)), _1544586), _1544590)), c_List_Olistrel1(_1544582, _1544592))))], (39637 ^ _773908) ^ [] : [-(_1544584 = _1544588)]]], (51560 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (4200 ^ _773908) ^ [_837474, _837476, _837478, _837480, _837482, _837484, _837486, _837488] : [-(c_New__DSequence_Oneg__decr__bind(_837488, _837484, _837480, _837476) = c_New__DSequence_Oneg__decr__bind(_837486, _837482, _837478, _837474)), _837488 = _837486, _837484 = _837482, _837480 = _837478, _837476 = _837474], (22957 ^ _773908) ^ [_1172387, _1172389] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1172387), _1172389) = 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), _1172387)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1172389)))))], (24785 ^ _773908) ^ [_1211088, _1211090, _1211092, _1211094] : [class_Orderings_Olinorder(_1211088), 24788 ^ _773908 : [(24797 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211088), _1211092), _1211094)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), _1211092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), _1211094))], (24789 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1211088), _1211092), _1211094))), 24792 ^ _773908 : [(24795 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), _1211094)))], (24793 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211088), _1211090), _1211092)))]]]]], (42127 ^ _773908) ^ [_1606871, _1606873, _1606875, _1606877, _1606879] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606871, tc_fun(_1606873, tc_HOL_Obool)), _1606875), hAPP(hAPP(c_COMBB(tc_fun(_1606873, tc_HOL_Obool), tc_fun(_1606873, tc_HOL_Obool), _1606871), hAPP(c_Set_Oinsert(_1606873), _1606877)), _1606879)) = hAPP(hAPP(c_Set_Oinsert(_1606873), _1606877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606871, tc_fun(_1606873, tc_HOL_Obool)), _1606875), _1606879)))], (32662 ^ _773908) ^ [_1380219, _1380221, _1380223, _1380225, _1380227] : [class_Orderings_Oorder(_1380219), 32665 ^ _773908 : [(32686 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1380219, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1380219, _1380221, _1380223)), c_SetInterval_Oord__class_OatLeastAtMost(_1380219, _1380225, _1380227)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380225), _1380227)), 32689 ^ _773908 : [(32692 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380225), _1380221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380223), _1380227)), 32699 ^ _773908 : [(32702 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380219), _1380223), _1380227))], (32700 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380219), _1380225), _1380221))]]], (32690 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380221), _1380223)))]]], (32666 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1380219, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1380219, _1380221, _1380223)), c_SetInterval_Oord__class_OatLeastAtMost(_1380219, _1380225, _1380227))), 32669 ^ _773908 : [(32670 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380221), _1380223)), 32673 ^ _773908 : [(32678 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380219), _1380225), _1380221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380219), _1380223), _1380227)))], (32676 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380223), _1380227)))], (32674 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380225), _1380221)))]]], (32684 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380219), _1380225), _1380227)))]]]]], (29583 ^ _773908) ^ [_1313980, _1313982, _1313984] : [class_Orderings_Olinorder(_1313980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313980), _1313982)), -(_1313982 = c_Orderings_Obot__class_Obot(tc_fun(_1313980, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1313980, hAPP(hAPP(c_Set_Oinsert(_1313980), _1313984), _1313982)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313980), _1313984), c_Big__Operators_Olinorder__class_OMin(_1313980, _1313982)))], (26554 ^ _773908) ^ [_1249932, _1249934, _1249936, _1249938, _1249940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249932, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1249932, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1249934, _1249932, _1249936), _1249938)), hAPP(c_Set_Oimage(_1249934, _1249932, _1249936), _1249940))), hAPP(c_Set_Oimage(_1249934, _1249932, _1249936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1249934, tc_HOL_Obool)), _1249938), _1249940)))))], (12612 ^ _773908) ^ [_985279, _985281] : [12613 ^ _773908 : [(12616 ^ _773908) ^ [] : [_985279 = hAPP(c_Nat_OSuc, _985281)], (12614 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985279), _985281))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985279), hAPP(c_Nat_OSuc, _985281))))], (20923 ^ _773908) ^ [_1135796, _1135798, _1135800, _1135802] : [class_Fields_Olinordered__field__inverse__zero(_1135796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135796), _1135798), _1135800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135796), _1135802), c_Groups_Ozero__class_Ozero(_1135796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135796), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135796), _1135800), _1135802)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135796), _1135798), _1135802))))], (3986 ^ _773908) ^ [_834121, _834123, _834125, _834127, _834129, _834131] : [-(c_Finite__Set_Ofold(_834131, _834127, _834123) = c_Finite__Set_Ofold(_834129, _834125, _834121)), _834131 = _834129, _834127 = _834125, _834123 = _834121], (34612 ^ _773908) ^ [_1419552, _1419554, _1419556] : [class_Groups_Ocomm__monoid__add(_1419552), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419554, _1419552), _1419556), c_Orderings_Obot__class_Obot(tc_fun(_1419554, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1419552))], (11357 ^ _773908) ^ [_963474, _963476] : [class_Rings_Ocomm__ring__1(_963474), -(hAPP(c_Groups_Ouminus__class_Ouminus(_963474), _963476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963474), hAPP(c_Groups_Ouminus__class_Ouminus(_963474), c_Groups_Oone__class_Oone(_963474))), _963476))], (37143 ^ _773908) ^ [_1473963, _1473965, _1473967, _1473969, _1473971, _1473973] : [-(hAPP(c_Set_Ovimage(_1473963, _1473965, hAPP(c_Fun_Ocomp(_1473967, _1473965, _1473963, _1473969), _1473971)), _1473973) = hAPP(c_Set_Ovimage(_1473963, _1473967, _1473971), hAPP(c_Set_Ovimage(_1473967, _1473965, _1473969), _1473973)))], (5713 ^ _773908) ^ [_864092, _864094] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_864092, _864094, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_864092), tc_HOL_Obool))))], (44726 ^ _773908) ^ [_1667644, _1667646, _1667648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667644), _1667646)), -(c_List_Oupt(_1667644, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667646), _1667648)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1667644, _1667646)), c_List_Oupt(_1667646, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667646), _1667648))))], (42195 ^ _773908) ^ [_1609080, _1609082, _1609084, _1609086, _1609088, _1609090] : [class_Complete__Lattice_Ocomplete__lattice(_1609080), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609082, tc_fun(_1609084, _1609080)), _1609086), _1609088), _1609090) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609082, _1609080), _1609086), hAPP(hAPP(c_COMBC(_1609082, _1609084, _1609080), _1609088), _1609090)))], (48758 ^ _773908) ^ [_1756408, _1756410, _1756412, _1756414] : [class_Orderings_Olinorder(_1756408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1756408), _1756410)), 48768 ^ _773908 : [(48771 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756408), _1756412), 48767 ^ [_1756408, _1756410, _1756412, _1756414]))], (48769 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756408), 48767 ^ [_1756408, _1756410, _1756412, _1756414]), _1756410)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1756408), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1756408), _1756412), _1756414)), hAPP(hAPP(c_Finite__Set_Ofold(_1756408, _1756408, c_Orderings_Oord__class_Omin(_1756408)), _1756414), _1756410))))], (50951 ^ _773908) ^ [_1804746] : [-(c_Hilbert__Choice_Oinv__into(_1804746, _1804746, c_Orderings_Otop__class_Otop(tc_fun(_1804746, tc_HOL_Obool)), c_Fun_Oid(_1804746)) = c_Fun_Oid(_1804746))], (42646 ^ _773908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49358 ^ _773908) ^ [_1769890, _1769892, _1769894, _1769896, _1769898] : [hBOOL(hAPP(hAPP(_1769894, _1769898), _1769896)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769890, _1769892, _1769894), _1769896), _1769898)))], (35925 ^ _773908) ^ [_1447947, _1447949] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1447947, _1447949)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1447947, _1447949), tc_HOL_Obool)))), 35928 ^ _773908 : [(35931 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447949), c_Orderings_Otop__class_Otop(tc_fun(_1447949, tc_HOL_Obool)))))], (35929 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447947), c_Orderings_Otop__class_Otop(tc_fun(_1447947, tc_HOL_Obool)))))]]], (30273 ^ _773908) ^ [_1326947, _1326949] : [class_Orderings_Olinorder(_1326947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326947), _1326949)), -(_1326949 = c_Orderings_Obot__class_Obot(tc_fun(_1326947, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1326947), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326947), 30286 ^ [_1326947, _1326949]), 30287 ^ [_1326947, _1326949])), hAPP(hAPP(c_Set_Oinsert(_1326947), 30286 ^ [_1326947, _1326949]), hAPP(hAPP(c_Set_Oinsert(_1326947), 30287 ^ [_1326947, _1326949]), c_Orderings_Obot__class_Obot(tc_fun(_1326947, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1326947), c_Big__Operators_Olattice_OInf__fin(_1326947, c_Orderings_Oord__class_Omin(_1326947), _1326949)), _1326949)))], (15237 ^ _773908) ^ [_1032331, _1032333, _1032335, _1032337, _1032339] : [class_Groups_Oordered__ab__group__add(_1032331), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032331), _1032333), _1032335) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032331), _1032337), _1032339), 15244 ^ _773908 : [(15251 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032331), _1032337), _1032339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032331), _1032333), _1032335)))], (15245 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032331), _1032333), _1032335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032331), _1032337), _1032339)))]]], (51538 ^ _773908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (16393 ^ _773908) ^ [_1054942, _1054944] : [class_Int_Onumber__ring(_1054942), -(hAPP(c_Int_Oring__1__class_Oof__int(_1054942), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1054944)) = hAPP(c_Int_Onumber__class_Onumber__of(_1054942), _1054944))], (14496 ^ _773908) ^ [_1019062] : [-(_1019062 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019062), _1019062) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23670 ^ _773908) ^ [_1186895, _1186897, _1186899, _1186901, _1186903] : [hBOOL(hAPP(hAPP(_1186895, _1186897), _1186899)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186901, _1186903, tc_HOL_Obool), _1186895), hAPP(hAPP(c_Product__Type_OPair(_1186901, _1186903), _1186897), _1186899))))], (38653 ^ _773908) ^ [_1519638, _1519640, _1519642, _1519644, _1519646, _1519648, _1519650] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1519638, _1519640, _1519642, hAPP(hAPP(c_COMBC(_1519638, tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_fun(_1519640, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519640, tc_fun(tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_fun(_1519640, tc_HOL_Obool)), _1519638), c_COMBC(_1519640, tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519640, tc_prod(_1519638, _1519640)), tc_fun(_1519640, tc_fun(tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_HOL_Obool)), _1519638), hAPP(c_COMBB(tc_prod(_1519638, _1519640), tc_fun(tc_fun(tc_prod(_1519638, _1519640), tc_HOL_Obool), tc_HOL_Obool), _1519640), c_member(tc_prod(_1519638, _1519640)))), c_Product__Type_OPair(_1519638, _1519640)))), _1519644), hAPP(hAPP(c_COMBC(_1519640, tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_fun(_1519642, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519642, tc_fun(tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_fun(_1519642, tc_HOL_Obool)), _1519640), c_COMBC(_1519642, tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519642, tc_prod(_1519640, _1519642)), tc_fun(_1519642, tc_fun(tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_HOL_Obool)), _1519640), hAPP(c_COMBB(tc_prod(_1519640, _1519642), tc_fun(tc_fun(tc_prod(_1519640, _1519642), tc_HOL_Obool), tc_HOL_Obool), _1519642), c_member(tc_prod(_1519640, _1519642)))), c_Product__Type_OPair(_1519640, _1519642)))), _1519646)), _1519648), _1519650)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519638, _1519642)), hAPP(hAPP(c_Product__Type_OPair(_1519638, _1519642), _1519648), _1519650)), hAPP(hAPP(c_Relation_Orel__comp(_1519638, _1519640, _1519642), _1519644), _1519646))))], (34672 ^ _773908) ^ [_1420854, _1420856, _1420858, _1420860, _1420862] : [class_Groups_Ocomm__monoid__add(_1420854), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420854), _1420856), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1420858), _1420860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1420862), _1420860))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420854), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420854, tc_Nat_Onat), _1420856), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1420860))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1420858, _1420862)))], (17243 ^ _773908) ^ [_1071453, _1071455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071453), _1071455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071453)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071455))))], (41258 ^ _773908) ^ [_1586779, _1586781, _1586783] : [-(hAPP(c_List_Oset(_1586779), hAPP(c_List_Orotate(_1586779, _1586781), _1586783)) = hAPP(c_List_Oset(_1586779), _1586783))], (40211 ^ _773908) ^ [_1560217, _1560219] : [-(hAPP(hAPP(c_List_Odrop(_1560217), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1560219) = _1560219)], (20765 ^ _773908) ^ [_1133109, _1133111, _1133113] : [class_Fields_Ofield__inverse__zero(_1133109), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133109), hAPP(c_Groups_Ouminus__class_Ouminus(_1133109), _1133111)), hAPP(c_Groups_Ouminus__class_Ouminus(_1133109), _1133113)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133109), _1133111), _1133113))], (45935 ^ _773908) ^ [_1691905, _1691907, _1691909, _1691911, _1691913] : [-(c_List_OdropWhile(_1691905, _1691907, _1691909) = hAPP(hAPP(c_List_Olist_OCons(_1691905), _1691911), _1691913)), _1691909 = hAPP(hAPP(c_List_Oappend(_1691905), c_List_OtakeWhile(_1691905, _1691907, _1691909)), hAPP(hAPP(c_List_Olist_OCons(_1691905), _1691911), _1691913)), -(hBOOL(hAPP(_1691907, _1691911)))], (41276 ^ _773908) ^ [_1587219] : [-(c_List_Orotate(_1587219, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1587219)))], (43244 ^ _773908) ^ [_1632848, _1632850, _1632852, _1632854] : [-(hBOOL(hAPP(c_List_Olistsp(_1632848, _1632850), hAPP(hAPP(c_List_Olist_OCons(_1632848), _1632852), _1632854)))), hBOOL(hAPP(_1632850, _1632852)), hBOOL(hAPP(c_List_Olistsp(_1632848, _1632850), _1632854))], (44391 ^ _773908) ^ [_1658957, _1658959, _1658961] : [hAPP(c_List_Ofilter(_1658957, _1658959), _1658961) = c_List_Olist_ONil(_1658957), 44394 ^ _773908 : [(44395 ^ _773908) ^ [_1659054] : [hBOOL(hAPP(hAPP(c_member(_1658957), _1659054), hAPP(c_List_Oset(_1658957), _1658961))), hBOOL(hAPP(_1658959, _1659054))]]], (36331 ^ _773908) ^ [] : [-(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))))], (42393 ^ _773908) ^ [_1613859, _1613861, _1613863, _1613865, _1613867] : [class_Complete__Lattice_Ocomplete__lattice(_1613859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1613861, tc_HOL_Obool)), _1613863), _1613865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613859), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613861, _1613859), _1613865), _1613867)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613861, _1613859), _1613863), _1613867))))], (46183 ^ _773908) ^ [_1697392, _1697394] : [-(c_List_Omeasures(_1697392, _1697394) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1697392), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1697392, tc_List_Olist(tc_fun(_1697392, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1697392, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1697392, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1697392), c_List_Omap(tc_fun(_1697392, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1697392, tc_Nat_Onat), _1697392, tc_Nat_Onat), c_COMBI(tc_fun(_1697392, tc_Nat_Onat))))), _1697394)))], (41900 ^ _773908) ^ [_1599653, _1599655, _1599657, _1599659, _1599661] : [class_Rings_Osemiring__0(_1599653), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1599653), hAPP(hAPP(c_List_Omap(_1599655, _1599653), hAPP(hAPP(c_COMBC(_1599655, _1599653, _1599653), hAPP(hAPP(c_COMBB(_1599653, tc_fun(_1599653, _1599653), _1599655), c_Groups_Otimes__class_Otimes(_1599653)), _1599657)), _1599659)), _1599661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1599653), hAPP(c_List_Omonoid__add__class_Olistsum(_1599653), hAPP(hAPP(c_List_Omap(_1599655, _1599653), _1599657), _1599661))), _1599659))], (33824 ^ _773908) ^ [_1402349, _1402351, _1402353, _1402355, _1402357] : [class_Groups_Ocomm__monoid__mult(_1402349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402351), _1402353)), c_Fun_Oinj__on(_1402351, _1402351, _1402355, _1402353), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1402351, _1402349), _1402357), hAPP(c_Set_Oimage(_1402351, _1402351, _1402355), _1402353)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1402351, _1402349), hAPP(c_Fun_Ocomp(_1402351, _1402349, _1402351, _1402357), _1402355)), _1402353))], (43485 ^ _773908) ^ [_1637813, _1637815, _1637817, _1637819] : [c_List_Olist__all2(_1637813, _1637815, _1637817, _1637819, c_List_Olist_ONil(_1637815)), -(_1637819 = c_List_Olist_ONil(_1637813))], (8969 ^ _773908) ^ [_922606, _922608, _922610, _922612, _922614] : [class_Rings_Osemiring(_922606), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922606), _922608), _922610)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922606), _922612), _922610)), _922614)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922606), _922608), _922612)), _922610)), _922614))], (22955 ^ _773908) ^ [_1172344, _1172346] : [-(c_Nitpick_Onat__lcm(_1172344, _1172346) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172344), _1172346)), c_Nitpick_Onat__gcd(_1172344, _1172346)))], (20171 ^ _773908) ^ [_1122058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122058), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1122058)), c_Int_OMin)))], (13656 ^ _773908) ^ [_1003886] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003886, _1003886) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24429 ^ _773908) ^ [_1202887, _1202889, _1202891, _1202893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202887, tc_HOL_Obool)), _1202889), _1202891)), hBOOL(hAPP(_1202889, _1202893)), -(hBOOL(hAPP(_1202891, _1202893)))], (2996 ^ _773908) ^ [_818684, _818686, _818688, _818690, _818692, _818694, _818696, _818698] : [-(c_Nat_Onat_Onat__case(_818698, _818694, _818690, _818686) = c_Nat_Onat_Onat__case(_818696, _818692, _818688, _818684)), _818698 = _818696, _818694 = _818692, _818690 = _818688, _818686 = _818684], (50993 ^ _773908) ^ [_1805523, _1805525, _1805527, _1805529, _1805531] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1805523, _1805525, _1805527, _1805529), _1805531) = c_Hilbert__Choice_OEps(_1805523, hAPP(hAPP(c_COMBS(_1805523, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805523), c_fconj), hAPP(hAPP(c_COMBC(_1805523, tc_fun(_1805523, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805523)), _1805527))), hAPP(hAPP(c_COMBC(_1805523, _1805525, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1805525, tc_fun(_1805525, tc_HOL_Obool), _1805523), c_fequal), _1805529)), _1805531))))], (5859 ^ _773908) ^ [_867603, _867605, _867607, _867609] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_867603), _867605), _867607), _867609)), -(_867605 = _867609), -(hBOOL(hAPP(_867607, _867609)))], (44365 ^ _773908) ^ [_1658452, _1658454, _1658456] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1658452), tc_List_Olist(_1658452)), c_List_Opartition(_1658452, _1658454, _1658456)) = hAPP(c_List_Ofilter(_1658452, _1658454), _1658456))], (43582 ^ _773908) ^ [_1640217, _1640219, _1640221, _1640223, _1640225, _1640227, _1640229, _1640231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640217), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640219)), _1640221))), c_List_Olist__all2(_1640219, _1640223, _1640225, _1640221, _1640227), hBOOL(hAPP(hAPP(_1640225, _1640229), _1640231)), -(c_List_Olist__all2(_1640219, _1640223, _1640225, hAPP(hAPP(c_List_Olist__update(_1640219, _1640221), _1640217), _1640229), hAPP(hAPP(c_List_Olist__update(_1640223, _1640227), _1640217), _1640231)))], (22793 ^ _773908) ^ [_1169593, _1169595] : [-(_1169593 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1169593, _1169595) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1169593), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1169595)))], (1824 ^ _773908) ^ [_799694, _799696] : [-(class_Rings_Osemiring__0(_799694)), _799696 = _799694, class_Rings_Osemiring__0(_799696)], (32744 ^ _773908) ^ [_1381797, _1381799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381797), _1381799)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1381799, _1381797) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (45707 ^ _773908) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (10001 ^ _773908) ^ [] : [-(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))))], (44315 ^ _773908) ^ [_1657407, _1657409, _1657411] : [-(hAPP(c_List_Oset(_1657407), hAPP(c_List_OremoveAll(_1657407, _1657409), _1657411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1657407, tc_HOL_Obool)), hAPP(c_List_Oset(_1657407), _1657411)), hAPP(hAPP(c_Set_Oinsert(_1657407), _1657409), c_Orderings_Obot__class_Obot(tc_fun(_1657407, tc_HOL_Obool)))))], (51424 ^ _773908) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (48611 ^ _773908) ^ [_1753540, _1753542, _1753544, _1753546, _1753548, _1753550] : [c_Finite__Set_Ofun__left__comm(_1753540, _1753542, _1753544), -(hAPP(hAPP(_1753544, _1753546), hAPP(hAPP(_1753544, _1753548), _1753550)) = hAPP(hAPP(_1753544, _1753548), hAPP(hAPP(_1753544, _1753546), _1753550)))], (2630 ^ _773908) ^ [_812795, _812797, _812799, _812801, _812803, _812805, _812807, _812809, _812811, _812813] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_812813, _812809, _812805, _812801, _812797) = c_SetInterval_Oord_OgreaterThanAtMost(_812811, _812807, _812803, _812799, _812795)), _812813 = _812811, _812809 = _812807, _812805 = _812803, _812801 = _812799, _812797 = _812795], (6424 ^ _773908) ^ [_878225, _878227, _878229, _878231] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_878225), 6427 ^ _773908 : [(6434 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878225), _878227), _878231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878225), _878227), _878229)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878225), _878231), _878229))))], (6428 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878225), _878227), _878229)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878225), _878231), _878229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878225), _878227), _878231)))]]], (50201 ^ _773908) ^ [_1790439, _1790441, _1790443, _1790445] : [c_Relation_Otrans(_1790439, _1790441), c_Relation_Otrans(_1790443, _1790445), -(c_Relation_Otrans(tc_prod(_1790439, _1790443), c_Wellfounded_Olex__prod(_1790439, _1790443, _1790441, _1790445)))], (14935 ^ _773908) ^ [_1026655, _1026657, _1026659] : [hBOOL(hAPP(_1026655, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026657), _1026659))), 14938 ^ _773908 : [(14945 ^ _773908) ^ [] : [-(_1026659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14948 ^ _773908 : [(14949 ^ _773908) ^ [_1026907, _1026909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026907), _1026659)), _1026657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026659), _1026909)), _1026907), -(hBOOL(hAPP(_1026655, _1026909)))]]], (14939 ^ _773908) ^ [] : [_1026659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1026655, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (44780 ^ _773908) ^ [_1668668] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1668668) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1668668)))], (49851 ^ _773908) ^ [_1780732, _1780734, _1780736] : [-(c_FunDef_OTHE__default(_1780734, _1780736, _1780732) = c_HOL_OThe(_1780734, _1780732)), 49852 ^ _773908 : [(49853 ^ _773908) ^ [_1780796] : [hBOOL(hAPP(_1780732, _1780796)), 49857 ^ _773908 : [(49860 ^ _773908) ^ [] : [49856 ^ [_1780732, _1780734, _1780736, _1780796] = _1780796], (49858 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1780732, 49856 ^ [_1780732, _1780734, _1780736, _1780796])))]]]]], (13029 ^ _773908) ^ [_992516, _992518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992516), _992518)), 13032 ^ _773908 : [(13039 ^ _773908) ^ [] : [_992518 = _992516, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992518), hAPP(c_Nat_OSuc, _992516))))], (13033 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992518), hAPP(c_Nat_OSuc, _992516))), -(_992518 = _992516)]]], (33162 ^ _773908) ^ [_1389915] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1389915) = 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), _1389915))))], (7225 ^ _773908) ^ [_890744, _890746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890744), _890746)), -(hAPP(c_Nat_OSuc, _890744) = _890746), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890744)), _890746)))], (17079 ^ _773908) ^ [_1068272, _1068274, _1068276, _1068278] : [class_Int_Onumber__ring(_1068272), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068272), hAPP(c_Int_Onumber__class_Onumber__of(_1068272), _1068274)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068272), hAPP(c_Int_Onumber__class_Onumber__of(_1068272), _1068276)), _1068278)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068272), hAPP(c_Int_Onumber__class_Onumber__of(_1068272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068274), _1068276))), _1068278))], (16491 ^ _773908) ^ [_1056766, _1056768] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056766, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1056766, tc_HOL_Obool))), _1056768) = c_Orderings_Obot__class_Obot(tc_fun(_1056766, tc_HOL_Obool)))], (15863 ^ _773908) ^ [_1044126] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1044126)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1044126)], (18071 ^ _773908) ^ [_1085562, _1085564, _1085566] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085562))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085562)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085564)), _1085566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085564)), _1085566))], (18697 ^ _773908) ^ [_1097039, _1097041, _1097043] : [hBOOL(hAPP(hAPP(c_member(_1097039), _1097041), _1097043)), -(hAPP(hAPP(c_Set_Oinsert(_1097039), _1097041), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1097039, tc_HOL_Obool)), _1097043), hAPP(hAPP(c_Set_Oinsert(_1097039), _1097041), c_Orderings_Obot__class_Obot(tc_fun(_1097039, tc_HOL_Obool))))) = _1097043)], (20199 ^ _773908) ^ [_1122593, _1122595] : [class_Int_Onumber__ring(_1122593), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122593), hAPP(c_Int_Onumber__class_Onumber__of(_1122593), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1122595) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122593), _1122595), _1122595))], (38090 ^ _773908) ^ [_1498257, _1498259, _1498261] : [hBOOL(hAPP(_1498257, _1498259)), -(hAPP(c_Set_OCollect(_1498261), hAPP(hAPP(c_COMBS(_1498261, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498261), c_fconj), hAPP(hAPP(c_COMBC(_1498261, _1498261, tc_HOL_Obool), c_fequal), _1498259))), _1498257)) = hAPP(hAPP(c_Set_Oinsert(_1498261), _1498259), c_Orderings_Obot__class_Obot(tc_fun(_1498261, tc_HOL_Obool))))], (2554 ^ _773908) ^ [_811613, _811615, _811617, _811619] : [-(c_Orderings_Oord_Omax(_811619, _811615) = c_Orderings_Oord_Omax(_811617, _811613)), _811619 = _811617, _811615 = _811613], (37167 ^ _773908) ^ [_1474564, _1474566, _1474568] : [-(hAPP(c_Set_Ovimage(_1474564, _1474566, _1474568), c_Orderings_Otop__class_Otop(tc_fun(_1474566, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1474564, tc_HOL_Obool)))], (42714 ^ _773908) ^ [_1620981, _1620983, _1620985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1620981), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1620983), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1620983)), _1620985)))), -(hBOOL(hAPP(hAPP(c_member(_1620983), hAPP(c_Random_Opick(_1620983, _1620985), _1620981)), hAPP(c_List_Oset(_1620983), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1620983), _1620983), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1620983)), _1620985)))))], (30622 ^ _773908) ^ [_1334297, _1334299, _1334301] : [hAPP(c_Finite__Set_Ocard(_1334297), _1334299) = hAPP(c_Nat_OSuc, _1334301), 30627 ^ _773908 : [(30630 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1334297), 30625 ^ [_1334297, _1334299, _1334301]), 30626 ^ [_1334297, _1334299, _1334301]))], (30632 ^ _773908) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1334297), 30626 ^ [_1334297, _1334299, _1334301]) = _1334301)], (30634 ^ _773908) ^ [] : [_1334301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(30626 ^ [_1334297, _1334299, _1334301] = c_Orderings_Obot__class_Obot(tc_fun(_1334297, tc_HOL_Obool)))], (30628 ^ _773908) ^ [] : [-(_1334299 = hAPP(hAPP(c_Set_Oinsert(_1334297), 30625 ^ [_1334297, _1334299, _1334301]), 30626 ^ [_1334297, _1334299, _1334301]))]]], (47275 ^ _773908) ^ [_1723565, _1723567] : [c_Wellfounded_Oacyclic(_1723565, _1723567), -(c_Wellfounded_Oacyclic(_1723565, hAPP(c_Relation_Oconverse(_1723565, _1723565), _1723567)))], (38579 ^ _773908) ^ [_1516929, _1516931, _1516933, _1516935, _1516937, _1516939, _1516941] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1516929, _1516931, _1516933), _1516935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1516937, tc_fun(tc_prod(_1516931, _1516933), tc_HOL_Obool)), _1516939), _1516941)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1516937, tc_fun(tc_prod(_1516929, _1516933), tc_HOL_Obool)), _1516939), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1516931, _1516933), tc_HOL_Obool), tc_fun(tc_prod(_1516929, _1516933), tc_HOL_Obool), _1516937), hAPP(c_Relation_Orel__comp(_1516929, _1516931, _1516933), _1516935)), _1516941)))], (33471 ^ _773908) ^ [_1395658, _1395660] : [33479 ^ _773908 : [(33482 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1395660, 33478 ^ [_1395658, _1395660])))], (33480 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33478 ^ [_1395658, _1395660]), _1395658)))]], 33472 ^ _773908 : [(33473 ^ _773908) ^ [_1395726] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1395726), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1395658))), hBOOL(hAPP(_1395660, _1395726))]]], (27116 ^ _773908) ^ [_1262830, _1262832, _1262834, _1262836, _1262838] : [c_Equiv__Relations_Oequiv(_1262830, _1262832, _1262834), hBOOL(hAPP(hAPP(c_member(tc_prod(_1262830, _1262830)), hAPP(hAPP(c_Product__Type_OPair(_1262830, _1262830), _1262836), _1262838)), _1262834)), -(hAPP(c_Relation_OImage(_1262830, _1262830, _1262834), hAPP(hAPP(c_Set_Oinsert(_1262830), _1262836), c_Orderings_Obot__class_Obot(tc_fun(_1262830, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1262830, _1262830, _1262834), hAPP(hAPP(c_Set_Oinsert(_1262830), _1262838), c_Orderings_Obot__class_Obot(tc_fun(_1262830, tc_HOL_Obool)))))], (16290 ^ _773908) ^ [_1053077, _1053079, _1053081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1053079), 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), _1053079), _1053081))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1053077))), _1053081)))], (45947 ^ _773908) ^ [_1692169, _1692171, _1692173, _1692175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692169), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692171)), c_List_OdropWhile(_1692171, _1692173, _1692175)))), -(hAPP(hAPP(c_List_Onth(_1692171), c_List_OdropWhile(_1692171, _1692173, _1692175)), _1692169) = hAPP(hAPP(c_List_Onth(_1692171), _1692175), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692169), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692171)), c_List_OtakeWhile(_1692171, _1692173, _1692175)))))], (39096 ^ _773908) ^ [_1530345, _1530347, _1530349, _1530351] : [hBOOL(hAPP(c_Predicate_ORangeP(_1530345, _1530347, hAPP(hAPP(c_COMBC(_1530345, tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_fun(_1530347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530347, tc_fun(tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_fun(_1530347, tc_HOL_Obool)), _1530345), c_COMBC(_1530347, tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530347, tc_prod(_1530345, _1530347)), tc_fun(_1530347, tc_fun(tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_HOL_Obool)), _1530345), hAPP(c_COMBB(tc_prod(_1530345, _1530347), tc_fun(tc_fun(tc_prod(_1530345, _1530347), tc_HOL_Obool), tc_HOL_Obool), _1530347), c_member(tc_prod(_1530345, _1530347)))), c_Product__Type_OPair(_1530345, _1530347)))), _1530349)), _1530351)), -(hBOOL(hAPP(hAPP(c_member(_1530347), _1530351), hAPP(c_Relation_ORange(_1530345, _1530347), _1530349))))], (15897 ^ _773908) ^ [_1044932, _1044934, _1044936, _1044938, _1044940, _1044942] : [class_Rings_Oordered__ring(_1044932), 15900 ^ _773908 : [(15907 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044932), _1044934), _1044940)), _1044936)), _1044938)), _1044942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), _1044934), _1044936)), _1044938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), _1044940), _1044936)), _1044942))))], (15901 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), _1044934), _1044936)), _1044938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), _1044940), _1044936)), _1044942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044932), _1044934), _1044940)), _1044936)), _1044938)), _1044942)))]]], (8189 ^ _773908) ^ [_908382, _908384, _908386, _908388, _908390] : [c_Com_Ocom_OCond(_908382, _908384, _908386) = c_Com_Ocom_OWhile(_908388, _908390)], (28418 ^ _773908) ^ [_1290531, _1290533, _1290535, _1290537] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290531, tc_HOL_Obool)), _1290533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290531, tc_HOL_Obool)), _1290535), _1290537)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290531, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290531, tc_HOL_Obool)), _1290533), _1290535)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290531, tc_HOL_Obool)), _1290533), _1290537)))], (21289 ^ _773908) ^ [_1141982, _1141984] : [class_Rings_Odivision__ring(_1141982), -(_1141984 = c_Groups_Ozero__class_Ozero(_1141982)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141982), _1141984), _1141984) = c_Groups_Oone__class_Oone(_1141982))], (31211 ^ _773908) ^ [_1346908, _1346910, _1346912, _1346914, _1346916] : [class_Groups_Ocomm__monoid__mult(_1346908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346910), _1346912)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346910), _1346914)), 31225 ^ _773908 : [(31228 ^ _773908) ^ [] : [hAPP(_1346916, 31224 ^ [_1346908, _1346910, _1346912, _1346914, _1346916]) = c_Groups_Oone__class_Oone(_1346908)], (31226 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346910), 31224 ^ [_1346908, _1346910, _1346912, _1346914, _1346916]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346910, tc_HOL_Obool)), _1346912), _1346914))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346910, _1346908), _1346916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346910, tc_HOL_Obool)), _1346912), _1346914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346908), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346910, _1346908), _1346916), _1346912)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346910, _1346908), _1346916), _1346914)))], (45836 ^ _773908) ^ [_1689800, _1689802, _1689804] : [hBOOL(hAPP(c_List_Odistinct(_1689800), _1689802)), hBOOL(hAPP(hAPP(c_member(_1689800), _1689804), hAPP(c_List_Oset(_1689800), _1689802))), -(c_List_OtakeWhile(_1689800, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1689800), c_fNot), hAPP(hAPP(c_COMBC(_1689800, _1689800, tc_HOL_Obool), c_fequal), _1689804)), hAPP(c_List_Orev(_1689800), _1689802)) = hAPP(c_List_Orev(_1689800), hAPP(c_List_Otl(_1689800), c_List_OdropWhile(_1689800, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1689800), c_fNot), hAPP(hAPP(c_COMBC(_1689800, _1689800, tc_HOL_Obool), c_fequal), _1689804)), _1689802))))], (51217 ^ _773908) ^ [_1810733, _1810735, _1810737] : [c_Fun_Obij__betw(_1810733, _1810733, c_Fun_Oid(_1810733), _1810735, _1810737), -(_1810735 = _1810737)], (7493 ^ _773908) ^ [_895180, _895182, _895184] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_895180, _895182, _895184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_895184)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49930 ^ _773908) ^ [_1782416, _1782418, _1782420] : [c_List_Olist__ex(tc_Int_Oint, _1782416, c_List_Oupto(_1782418, _1782420)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1782416), _1782418, _1782420)], (30732 ^ _773908) ^ [_1336797, _1336799, _1336801] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336797, tc_Nat_Onat), _1336799), _1336801) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336797, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1336797), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1336799)), _1336801)))], (51756 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (33610 ^ _773908) ^ [_1398163, _1398165, _1398167, _1398169] : [class_Orderings_Oorder(_1398163), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398163, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1398163, _1398165), _1398167)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1398163, _1398167), _1398169)) = c_Orderings_Obot__class_Obot(tc_fun(_1398163, tc_HOL_Obool)))], (44712 ^ _773908) ^ [_1667476, _1667478] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667476), _1667478))), -(c_List_Oupt(_1667476, hAPP(c_Nat_OSuc, _1667478)) = c_List_Olist_ONil(tc_Nat_Onat))], (34123 ^ _773908) ^ [_1409059, _1409061, _1409063, _1409065, _1409067, _1409069, _1409071] : [c_Fun_Oinj__on(_1409059, _1409061, _1409063, hAPP(c_Set_Oimage(_1409065, _1409059, _1409067), _1409069)), c_Fun_Oinj__on(_1409065, _1409059, _1409067, _1409069), hBOOL(hAPP(hAPP(c_member(_1409061), _1409071), hAPP(c_Set_Oimage(_1409059, _1409061, _1409063), hAPP(c_Set_Oimage(_1409065, _1409059, _1409067), _1409069)))), -(hAPP(c_Fun_Othe__inv__into(_1409065, _1409061, _1409069, hAPP(c_Fun_Ocomp(_1409059, _1409061, _1409065, _1409063), _1409067)), _1409071) = hAPP(hAPP(c_Fun_Ocomp(_1409059, _1409065, _1409061, c_Fun_Othe__inv__into(_1409065, _1409059, _1409069, _1409067)), c_Fun_Othe__inv__into(_1409059, _1409061, hAPP(c_Set_Oimage(_1409065, _1409059, _1409067), _1409069), _1409063)), _1409071))], (18511 ^ _773908) ^ [_1093531, _1093533, _1093535, _1093537] : [hBOOL(hAPP(hAPP(c_member(_1093531), _1093533), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093531, tc_HOL_Obool)), _1093535), _1093537))), 18514 ^ _773908 : [(18517 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1093531), _1093533), _1093537))], (18515 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1093531), _1093533), _1093535)))]]], (12780 ^ _773908) ^ [_988170, _988172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988170), _988172)), -(_988172 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988170), 12783 ^ [_988170, _988172]))], (8507 ^ _773908) ^ [_914160, _914162, _914164, _914166, _914168] : [class_Rings_Ocomm__semiring__1(_914160), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), _914162), _914164)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), _914166), _914168)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), _914162), _914166)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914160), _914164), _914168)))], (18315 ^ _773908) ^ [_1090186, _1090188, _1090190, _1090192] : [hBOOL(hAPP(hAPP(c_member(_1090186), _1090188), _1090190)), -(hBOOL(hAPP(hAPP(c_member(_1090186), _1090188), _1090192))), -(hBOOL(hAPP(hAPP(c_member(_1090186), _1090188), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090186, tc_HOL_Obool)), _1090190), _1090192))))], (44401 ^ _773908) ^ [_1659162, _1659164, _1659166] : [44403 ^ _773908 : [(44406 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1659164, 44402 ^ [_1659162, _1659164, _1659166])))], (44404 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659162), 44402 ^ [_1659162, _1659164, _1659166]), hAPP(c_List_Oset(_1659162), _1659166))))]], -(hAPP(c_List_Ofilter(_1659162, _1659164), _1659166) = c_List_Olist_ONil(_1659162))], (9399 ^ _773908) ^ [_930469, _930471, _930473] : [class_Rings_Olinordered__ring__strict(_930469), 9402 ^ _773908 : [(9411 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930469), _930471), _930471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930469), _930473), _930473)) = c_Groups_Ozero__class_Ozero(_930469)), _930471 = c_Groups_Ozero__class_Ozero(_930469), _930473 = c_Groups_Ozero__class_Ozero(_930469)], (9403 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930469), _930471), _930471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930469), _930473), _930473)) = c_Groups_Ozero__class_Ozero(_930469), 9406 ^ _773908 : [(9409 ^ _773908) ^ [] : [-(_930473 = c_Groups_Ozero__class_Ozero(_930469))], (9407 ^ _773908) ^ [] : [-(_930471 = c_Groups_Ozero__class_Ozero(_930469))]]]]], (38102 ^ _773908) ^ [_1498512, _1498514, _1498516] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1498512, tc_HOL_Obool)), _1498514), _1498516) = hAPP(c_Set_OCollect(_1498512), hAPP(hAPP(c_COMBS(_1498512, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498512), c_fconj), hAPP(hAPP(c_COMBC(_1498512, tc_fun(_1498512, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498512)), _1498514))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498512), c_fNot), hAPP(hAPP(c_COMBC(_1498512, tc_fun(_1498512, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498512)), _1498516)))))], (10539 ^ _773908) ^ [_948625, _948627, _948629, _948631, _948633] : [class_Groups_Oordered__ab__semigroup__add(_948625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948625), _948627), _948629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948625), _948631), _948633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948625), _948627), _948631)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948625), _948629), _948633))))], (11147 ^ _773908) ^ [_959479, _959481, _959483] : [class_Rings_Oordered__cancel__semiring(_959479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959479), _959481), c_Groups_Ozero__class_Ozero(_959479))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959479), c_Groups_Ozero__class_Ozero(_959479)), _959483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959479), _959481), _959483)), c_Groups_Ozero__class_Ozero(_959479))))], (23634 ^ _773908) ^ [_1186198, _1186200] : [_1186198 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1186198, _1186200) = 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)))], (19855 ^ _773908) ^ [_1116607, _1116609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116607)), c_Int_OBit0(_1116609))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116607), _1116609)))], (46488 ^ _773908) ^ [_1703874, _1703876, _1703878, _1703880] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1703874), _1703876))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1703878), hAPP(c_Set_Oimage(_1703874, _1703878, _1703880), _1703876))), 46496 ^ _773908 : [(46499 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1703874), hAPP(c_Set_OCollect(_1703874), hAPP(hAPP(c_COMBS(_1703874, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1703874), c_fconj), hAPP(hAPP(c_COMBC(_1703874, tc_fun(_1703874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1703874)), _1703876))), hAPP(hAPP(c_COMBC(_1703874, _1703878, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1703878, tc_fun(_1703878, tc_HOL_Obool), _1703874), c_fequal), _1703880)), hAPP(_1703880, 46495 ^ [_1703874, _1703876, _1703878, _1703880]))))))], (46497 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703874), 46495 ^ [_1703874, _1703876, _1703878, _1703880]), _1703876)))]]], (43731 ^ _773908) ^ [_1643701, _1643703] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643701, tc_HOL_Obool), _1643703) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1643701, tc_HOL_Obool), tc_fun(_1643701, tc_HOL_Obool)), _1643703), c_COMBI(tc_fun(_1643701, tc_HOL_Obool))))], (38152 ^ _773908) ^ [_1500199, _1500201, _1500203, _1500205, _1500207] : [class_Groups_Ocomm__monoid__add(_1500199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500201), _1500203)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500201, _1500199), _1500205), hAPP(c_Set_OCollect(_1500201), hAPP(hAPP(c_COMBS(_1500201, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500201), c_fconj), hAPP(hAPP(c_COMBC(_1500201, tc_fun(_1500201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500201)), _1500203))), hAPP(hAPP(c_COMBC(_1500201, tc_fun(_1500201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500201)), _1500207)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500201, _1500199), hAPP(hAPP(c_COMBC(_1500201, _1500199, _1500199), hAPP(hAPP(c_COMBS(_1500201, _1500199, tc_fun(_1500199, _1500199)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1500199, tc_fun(_1500199, _1500199)), _1500201), c_If(_1500199)), hAPP(hAPP(c_COMBC(_1500201, tc_fun(_1500201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500201)), _1500207))), _1500205)), c_Groups_Ozero__class_Ozero(_1500199))), _1500203))], (21055 ^ _773908) ^ [_1138213, _1138215, _1138217] : [class_Fields_Olinordered__field__inverse__zero(_1138213), 21058 ^ _773908 : [(21073 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138213), _1138215), _1138217)))), 21074 ^ _773908 : [(21081 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), _1138215), c_Groups_Ozero__class_Ozero(_1138213))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), _1138217), c_Groups_Ozero__class_Ozero(_1138213)))], (21075 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), _1138215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), _1138217))]]], (21059 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138213), _1138215), _1138217))), 21064 ^ _773908 : [(21067 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), _1138217)))], (21065 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), c_Groups_Ozero__class_Ozero(_1138213)), _1138215)))]], 21068 ^ _773908 : [(21071 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), _1138217), c_Groups_Ozero__class_Ozero(_1138213))))], (21069 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138213), _1138215), c_Groups_Ozero__class_Ozero(_1138213))))]]]]], (32654 ^ _773908) ^ [_1380021, _1380023] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1380021), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1380023) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1380021, _1380023))], (28100 ^ _773908) ^ [_1282924, _1282926, _1282928, _1282930] : [class_Lattices_Osemilattice__inf(_1282924), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282924), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282924), _1282926), _1282928)), _1282930) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282924), _1282926), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282924), _1282928), _1282930)))], (17267 ^ _773908) ^ [_1071922] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1071922) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49224 ^ _773908) ^ [_1766654, _1766656, _1766658, _1766660] : [class_Rings_Olinordered__semidom(_1766654), 49230 ^ _773908 : [(49233 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1766654), c_Groups_Ozero__class_Ozero(_1766654)), hAPP(_1766660, 49229 ^ [_1766654, _1766656, _1766658, _1766660])))], (49231 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766656), 49229 ^ [_1766654, _1766656, _1766658, _1766660]), _1766658)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1766654), c_Groups_Ozero__class_Ozero(_1766654)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1766656, _1766654), _1766660), _1766658))))], (34558 ^ _773908) ^ [_1417885, _1417887, _1417889] : [class_Groups_Ocomm__monoid__add(_1417885), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417887, _1417885), hAPP(c_COMBK(_1417885, _1417887), c_Groups_Ozero__class_Ozero(_1417885))), _1417889) = c_Groups_Ozero__class_Ozero(_1417885))], (20541 ^ _773908) ^ [_1128726, _1128728] : [class_Rings_Oring__1(_1128726), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128726), hAPP(c_Groups_Ouminus__class_Ouminus(_1128726), c_Groups_Oone__class_Oone(_1128726))), 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)))), _1128728)) = c_Groups_Oone__class_Oone(_1128726))], (37444 ^ _773908) ^ [_1482071, _1482073, _1482075, _1482077, _1482079] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1482071, _1482073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482071, tc_HOL_Obool)), _1482075), _1482077)), _1482079) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1482071, _1482073), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1482071, _1482073), _1482075), _1482079)), hAPP(hAPP(c_Product__Type_OSigma(_1482071, _1482073), _1482077), _1482079)))], (51243 ^ _773908) ^ [_1811161, _1811163, _1811165, _1811167, _1811169] : [c_Fun_Obij__betw(_1811161, _1811163, _1811165, _1811167, _1811169), -(hAPP(c_Finite__Set_Ocard(_1811161), _1811167) = hAPP(c_Finite__Set_Ocard(_1811163), _1811169))], (51872 ^ _773908) ^ [_1818093] : [hBOOL(hAPP(c_fNot, _1818093)), hBOOL(_1818093)], (49237 ^ _773908) ^ [_1766950, _1766952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49238 ^ [_1766950, _1766952]), hAPP(_1766950, 49238 ^ [_1766950, _1766952]))), -(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)), _1766950)), _1766952)))))], (44790 ^ _773908) ^ [_1668872, _1668874] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1668872, _1668874) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1668872), _1668874)))], (37195 ^ _773908) ^ [_1475207, _1475209, _1475211, _1475213] : [hAPP(c_Set_Oimage(_1475207, _1475209, _1475211), c_Orderings_Otop__class_Otop(tc_fun(_1475207, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1475209, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1475207, _1475209, _1475211), hAPP(c_Set_Ovimage(_1475207, _1475209, _1475211), _1475213)) = _1475213)], (18883 ^ _773908) ^ [_1100350] : [class_Int_Onumber__ring(_1100350), -(c_Groups_Ozero__class_Ozero(_1100350) = hAPP(c_Int_Onumber__class_Onumber__of(_1100350), c_Int_OPls))], (6794 ^ _773908) ^ [_883755, _883757] : [class_Orderings_Opreorder(_883755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883755), _883757), _883757))], (28644 ^ _773908) ^ [_1295562, _1295564, _1295566, _1295568] : [hBOOL(hAPP(hAPP(c_member(_1295562), _1295564), c_SetInterval_Oord_OatLeast(_1295562, _1295566, _1295568))), -(hBOOL(hAPP(hAPP(_1295566, _1295568), _1295564)))], (44353 ^ _773908) ^ [_1658137, _1658139, _1658141] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658137)), hAPP(c_List_Ofilter(_1658137, _1658139), _1658141)) = 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(_1658137)), _1658141)))), hAPP(hAPP(c_COMBB(_1658137, tc_HOL_Obool, tc_Nat_Onat), _1658139), hAPP(c_List_Onth(_1658137), _1658141))))))], (1134 ^ _773908) ^ [_791069, _791071] : [-(class_Rings_Olinordered__semiring__1__strict(_791069)), _791071 = _791069, class_Rings_Olinordered__semiring__1__strict(_791071)], (47864 ^ _773908) ^ [_1738384, _1738386, _1738388] : [class_Orderings_Olinorder(_1738384), 47870 ^ _773908 : [(47873 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738384), _1738388), 47869 ^ [_1738384, _1738386, _1738388]))], (47871 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738384), 47869 ^ [_1738384, _1738386, _1738388]), hAPP(c_List_Oset(_1738384), _1738386))))]], c_List_Olinorder__class_Osorted(_1738384, _1738386), -(c_List_Olinorder__class_Osorted(_1738384, hAPP(hAPP(c_List_Olist_OCons(_1738384), _1738388), _1738386)))], (36255 ^ _773908) ^ [_1454462, _1454464, _1454466, _1454468, _1454470] : [c_Fun_Oinj__on(_1454462, _1454464, _1454466, c_Orderings_Otop__class_Otop(tc_fun(_1454462, tc_HOL_Obool))), 36258 ^ _773908 : [(36265 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454462, tc_HOL_Obool)), _1454468), _1454470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454464, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1454462, _1454464, _1454466), _1454468)), hAPP(c_Set_Oimage(_1454462, _1454464, _1454466), _1454470))))], (36259 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454464, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1454462, _1454464, _1454466), _1454468)), hAPP(c_Set_Oimage(_1454462, _1454464, _1454466), _1454470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454462, tc_HOL_Obool)), _1454468), _1454470)))]]], (43961 ^ _773908) ^ [_1649045, _1649047, _1649049, _1649051] : [hBOOL(hAPP(c_Predicate_ODomainP(_1649045, _1649047, hAPP(hAPP(c_COMBC(_1649045, tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_fun(_1649047, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649047, tc_fun(tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_fun(_1649047, tc_HOL_Obool)), _1649045), c_COMBC(_1649047, tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649047, tc_prod(_1649045, _1649047)), tc_fun(_1649047, tc_fun(tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_HOL_Obool)), _1649045), hAPP(c_COMBB(tc_prod(_1649045, _1649047), tc_fun(tc_fun(tc_prod(_1649045, _1649047), tc_HOL_Obool), tc_HOL_Obool), _1649047), c_member(tc_prod(_1649045, _1649047)))), c_Product__Type_OPair(_1649045, _1649047)))), _1649049)), _1649051)), -(hBOOL(hAPP(hAPP(c_member(_1649045), _1649051), hAPP(c_Relation_ODomain(_1649045, _1649047), _1649049))))], (10009 ^ _773908) ^ [_940324, _940326, _940328] : [class_Rings_Olinordered__semidom(_940324), 10012 ^ _773908 : [(10019 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940326), _940328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940324), _940326)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940324), _940328))))], (10013 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940324), _940326)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940324), _940328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940326), _940328)))]]], (36189 ^ _773908) ^ [_1453130, _1453132, _1453134, _1453136] : [c_Fun_Oinj__on(_1453130, _1453132, _1453134, c_Orderings_Otop__class_Otop(tc_fun(_1453130, tc_HOL_Obool))), 36192 ^ _773908 : [(36206 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1453132), _1453136), hAPP(c_Set_Oimage(_1453130, _1453132, _1453134), c_Orderings_Otop__class_Otop(tc_fun(_1453130, tc_HOL_Obool)))))), 36207 ^ _773908 : [(36208 ^ _773908) ^ [_1453533] : [_1453136 = hAPP(_1453134, _1453533), 36212 ^ _773908 : [(36215 ^ _773908) ^ [] : [36211 ^ [_1453130, _1453132, _1453134, _1453136, _1453533] = _1453533], (36213 ^ _773908) ^ [] : [-(_1453136 = hAPP(_1453134, 36211 ^ [_1453130, _1453132, _1453134, _1453136, _1453533]))]]]]], (36193 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1453132), _1453136), hAPP(c_Set_Oimage(_1453130, _1453132, _1453134), c_Orderings_Otop__class_Otop(tc_fun(_1453130, tc_HOL_Obool))))), 36197 ^ _773908 : [(36200 ^ _773908) ^ [_1453395] : [_1453136 = hAPP(_1453134, _1453395), -(_1453395 = 36196 ^ [_1453130, _1453132, _1453134, _1453136])], (36198 ^ _773908) ^ [] : [-(_1453136 = hAPP(_1453134, 36196 ^ [_1453130, _1453132, _1453134, _1453136]))]]]]], (51229 ^ _773908) ^ [_1810909] : [-(c_Fun_Obij__betw(_1810909, _1810909, c_Fun_Oid(_1810909), c_Orderings_Otop__class_Otop(tc_fun(_1810909, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810909, tc_HOL_Obool))))], (39895 ^ _773908) ^ [_1552186, _1552188, _1552190] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1552186)), _1552188), c_List_Olists(_1552186, c_Wellfounded_Oacc(_1552186, _1552190)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1552186)), _1552188), c_Wellfounded_Oacc(tc_List_Olist(_1552186), c_List_Olistrel1(_1552186, _1552190)))))], (7089 ^ _773908) ^ [_888744] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _888744) = _888744)], (51466 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (12875 ^ _773908) ^ [_989789, _989791, _989793, _989795] : [class_Orderings_Oord(_989789), 12878 ^ _773908 : [(12887 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989791, _989789)), _989793), _989795))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989791, _989789)), _989793), _989795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989791, _989789)), _989795), _989793)))], (12879 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989791, _989789)), _989793), _989795)), 12882 ^ _773908 : [(12885 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989791, _989789)), _989795), _989793))], (12883 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989791, _989789)), _989793), _989795)))]]]]], (45107 ^ _773908) ^ [_1675135, _1675137, _1675139] : [-(c_List_Oinsert(_1675135, _1675137, c_List_Oremdups(_1675135, _1675139)) = c_List_Oremdups(_1675135, c_List_Oinsert(_1675135, _1675137, _1675139)))], (20461 ^ _773908) ^ [_1127014, _1127016, _1127018] : [class_Rings_Olinordered__idom(_1127014), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127014), c_Groups_Ozero__class_Ozero(_1127014)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127014), hAPP(hAPP(c_Power_Opower__class_Opower(_1127014), _1127016), 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(_1127014), _1127018), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (26880 ^ _773908) ^ [_1258182, _1258184] : [c_Nat__Transfer_Onat__set(_1258182), c_Nat__Transfer_Onat__set(_1258184), 26887 ^ _773908 : [(26894 ^ _773908) ^ [] : [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), _1258182)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258182), _1258184)))], (26888 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258182), _1258184)), -(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), _1258182)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258184))))]]], (47140 ^ _773908) ^ [_1720393, _1720395, _1720397, _1720399, _1720401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1720393, _1720393)), hAPP(hAPP(c_Product__Type_OPair(_1720393, _1720393), _1720395), _1720397)), _1720399)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1720393, _1720393)), hAPP(hAPP(c_Product__Type_OPair(_1720393, _1720393), _1720397), _1720401)), _1720399)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1720393, _1720393)), hAPP(hAPP(c_Product__Type_OPair(_1720393, _1720393), _1720395), _1720401)), c_Transitive__Closure_Otrancl(_1720393, _1720399))))], (12516 ^ _773908) ^ [_983588, _983590, _983592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983588), _983590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983590), _983592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983588), _983592)))], (3302 ^ _773908) ^ [_823453, _823455, _823457, _823459] : [-(c_List_OremoveAll(_823459, _823455) = c_List_OremoveAll(_823457, _823453)), _823459 = _823457, _823455 = _823453], (20285 ^ _773908) ^ [] : [-(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)))))], (3174 ^ _773908) ^ [_821473, _821475, _821477, _821479] : [-(c_List_Olistsp(_821479, _821475) = c_List_Olistsp(_821477, _821473)), _821479 = _821477, _821475 = _821473], (36045 ^ _773908) ^ [_1450186, _1450188] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450186), c_Orderings_Otop__class_Otop(tc_fun(_1450186, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1450186), _1450188) = hAPP(c_Finite__Set_Ocard(_1450186), c_Orderings_Otop__class_Otop(tc_fun(_1450186, tc_HOL_Obool))), -(_1450188 = c_Orderings_Otop__class_Otop(tc_fun(_1450186, tc_HOL_Obool)))], (41260 ^ _773908) ^ [_1586822, _1586824, _1586826] : [class_Groups_Omonoid__add(_1586822), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1586822), _1586824), hAPP(c_List_Ofoldl(_1586822, _1586822, c_Groups_Oplus__class_Oplus(_1586822), c_Groups_Ozero__class_Ozero(_1586822)), _1586826)) = hAPP(c_List_Ofoldl(_1586822, _1586822, c_Groups_Oplus__class_Oplus(_1586822), _1586824), _1586826))], (46923 ^ _773908) ^ [_1714941, _1714943, _1714945, _1714947] : [c_Wellfounded_Oacyclic(_1714941, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1714941, _1714941)), hAPP(hAPP(c_Product__Type_OPair(_1714941, _1714941), _1714943), _1714945)), _1714947)), 46926 ^ _773908 : [(46929 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714941, _1714941)), hAPP(hAPP(c_Product__Type_OPair(_1714941, _1714941), _1714945), _1714943)), c_Transitive__Closure_Ortrancl(_1714941, _1714947)))], (46927 ^ _773908) ^ [] : [-(c_Wellfounded_Oacyclic(_1714941, _1714947))]]], (30441 ^ _773908) ^ [_1330195, _1330197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330195), _1330197))), 30444 ^ _773908 : [(30447 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330195), _1330197)))], (30445 ^ _773908) ^ [] : [_1330197 = c_Orderings_Obot__class_Obot(tc_fun(_1330195, tc_HOL_Obool))]]], (51276 ^ _773908) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (49298 ^ _773908) ^ [_1768294, _1768296] : [-(hAPP(c_New__DSequence_Opos__empty(_1768294), _1768296) = c_Lazy__Sequence_Oempty(_1768294))], (42027 ^ _773908) ^ [_1604336, _1604338, _1604340, _1604342] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604336, tc_fun(_1604338, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604336, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1604338, tc_HOL_Obool), tc_fun(_1604338, tc_HOL_Obool), _1604336), hAPP(c_COMBC(_1604338, tc_fun(_1604338, tc_HOL_Obool), tc_HOL_Obool), c_member(_1604338))), _1604340)), _1604342)), -(hBOOL(hAPP(hAPP(c_member(_1604338), _1604342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604336, tc_fun(_1604338, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604336, tc_HOL_Obool))), _1604340))))], (35967 ^ _773908) ^ [_1448778, _1448780] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448778, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1448778, tc_HOL_Obool))), _1448780) = c_Orderings_Otop__class_Otop(tc_fun(_1448778, tc_HOL_Obool)))], (49352 ^ _773908) ^ [_1769783, _1769785, _1769787, _1769789, _1769791] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769783, _1769785, _1769787), _1769789), _1769791)), -(hBOOL(hAPP(hAPP(_1769787, _1769791), _1769789)))], (30894 ^ _773908) ^ [_1339742, _1339744, _1339746] : [class_Groups_Ocomm__monoid__add(_1339742), class_Groups_Ocomm__monoid__mult(_1339742), c_Nat__Transfer_Onat__set(_1339744), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1339742), _1339746), _1339744) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1339742), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1339742, tc_Nat_Onat), _1339746), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1339744)))], (51630 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (10881 ^ _773908) ^ [_954696, _954698, _954700] : [class_Rings_Olinordered__semidom(_954696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954696), c_Groups_Oone__class_Oone(_954696)), _954698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954696), c_Groups_Oone__class_Oone(_954696)), _954700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954696), c_Groups_Oone__class_Oone(_954696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954696), _954698), _954700))))], (11343 ^ _773908) ^ [_963203, _963205, _963207, _963209, _963211] : [class_Groups_Oordered__cancel__ab__semigroup__add(_963203), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963203), _963205), _963207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963203), _963209), _963211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963203), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963203), _963205), _963209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963203), _963207), _963211))))], (43153 ^ _773908) ^ [_1630924, _1630926, _1630928] : [hBOOL(hAPP(c_List_Olistsp(_1630924, _1630926), _1630928)), 43156 ^ _773908 : [(43157 ^ _773908) ^ [_1631013] : [hBOOL(hAPP(hAPP(c_member(_1630924), _1631013), hAPP(c_List_Oset(_1630924), _1630928))), -(hBOOL(hAPP(_1630926, _1631013)))]]], (26705 ^ _773908) ^ [_1254286, _1254288] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254286) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254288), -(_1254286 = _1254288)], (46576 ^ _773908) ^ [_1706092, _1706094, _1706096, _1706098, _1706100, _1706102] : [46579 ^ _773908 : [(46582 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1706098), _1706100), hAPP(hAPP(_1706102, 46577 ^ [_1706092, _1706094, _1706096, _1706098, _1706100, _1706102]), 46578 ^ [_1706092, _1706094, _1706096, _1706098, _1706100, _1706102])))], (46580 ^ _773908) ^ [] : [-(_1706092 = hAPP(hAPP(c_Product__Type_OPair(_1706094, _1706096), 46577 ^ [_1706092, _1706094, _1706096, _1706098, _1706100, _1706102]), 46578 ^ [_1706092, _1706094, _1706096, _1706098, _1706100, _1706102]))]], -(hBOOL(hAPP(hAPP(c_member(_1706098), _1706100), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1706094, _1706096, tc_fun(_1706098, tc_HOL_Obool)), _1706102), _1706092))))], (38278 ^ _773908) ^ [_1505444, _1505446] : [-(c_Fun_Oinj__on(tc_fun(_1505444, _1505446), tc_fun(tc_prod(_1505444, _1505446), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1505444, _1505446), tc_HOL_Obool), tc_fun(tc_prod(_1505444, _1505446), tc_HOL_Obool), tc_fun(_1505444, _1505446)), c_Set_OCollect(tc_prod(_1505444, _1505446))), hAPP(hAPP(c_COMBB(tc_fun(_1505444, tc_fun(_1505446, tc_HOL_Obool)), tc_fun(tc_prod(_1505444, _1505446), tc_HOL_Obool), tc_fun(_1505444, _1505446)), c_Product__Type_Oprod_Oprod__case(_1505444, _1505446, tc_HOL_Obool)), hAPP(c_COMBB(_1505446, tc_fun(_1505446, tc_HOL_Obool), _1505444), hAPP(c_COMBC(_1505446, _1505446, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1505444, _1505446), tc_HOL_Obool))))], (16961 ^ _773908) ^ [_1065991, _1065993] : [class_Int_Onumber__ring(_1065991), -(hAPP(c_Int_Onumber__class_Onumber__of(_1065991), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065993)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1065991), hAPP(c_Int_Onumber__class_Onumber__of(_1065991), _1065993)))], (19365 ^ _773908) ^ [_1108309, _1108311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108309)), c_Int_OBit1(_1108311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108309), _1108311)))], (51534 ^ _773908) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11654 ^ _773908) ^ [_968546] : [-(hBOOL(hAPP(_968546, 11661 ^ [_968546]))), 11655 ^ _773908 : [(11656 ^ _773908) ^ [_968598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _968598)), hBOOL(hAPP(_968546, hAPP(c_Int_Onat, _968598)))]]], (28426 ^ _773908) ^ [_1290759, _1290761, _1290763, _1290765, _1290767] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290759, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1290761, _1290759, _1290763), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290761, tc_HOL_Obool)), _1290765), _1290767))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290759, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1290761, _1290759, _1290763), _1290765)), hAPP(c_Relation_OImage(_1290761, _1290759, _1290763), _1290767)))))], (18797 ^ _773908) ^ [_1099103, _1099105] : [class_Int_Oring__char__0(_1099103), hBOOL(hAPP(hAPP(c_member(_1099103), _1099105), c_Int_Oring__1__class_OInts(_1099103))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099103), c_Groups_Oone__class_Oone(_1099103)), _1099105)), _1099105) = c_Groups_Ozero__class_Ozero(_1099103)], (28082 ^ _773908) ^ [_1282501, _1282503, _1282505, _1282507, _1282509] : [class_Lattices_Olattice(_1282501), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1282503, _1282501)), _1282505), _1282507), _1282509) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282501), hAPP(_1282505, _1282509)), hAPP(_1282507, _1282509)))], (40265 ^ _773908) ^ [_1561469, _1561471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1561469), hAPP(c_List_Oset(_1561469), _1561471))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561469)), _1561471))))], (7962 ^ _773908) ^ [_904196, _904198, _904200, _904202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904196, tc_HOL_Obool)), _904198), _904200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904196, tc_HOL_Obool)), _904200), _904202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_904196, tc_HOL_Obool)), _904198), _904202)))], (22829 ^ _773908) ^ [_1169996, _1169998] : [-(c_FunDef_Ois__measure(_1169996, _1169998))], (8481 ^ _773908) ^ [_913715, _913717, _913719, _913721] : [-(hAPP(hAPP(c_Nat_Ocompow(_913715, _913715), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913717), _913719)), _913721) = hAPP(c_Fun_Ocomp(_913715, _913715, _913715, hAPP(hAPP(c_Nat_Ocompow(_913715, _913715), _913717), _913721)), hAPP(hAPP(c_Nat_Ocompow(_913715, _913715), _913719), _913721)))], (19183 ^ _773908) ^ [_1105146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1105146)), -(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), _1105146))))], (31930 ^ _773908) ^ [_1365083, _1365085, _1365087, _1365089, _1365091, _1365093, _1365095, _1365097, _1365099, _1365101, _1365103] : [c_Equiv__Relations_Oequiv(_1365083, _1365085, _1365087), c_Equiv__Relations_Oequiv(_1365089, _1365091, _1365093), c_Equiv__Relations_Ocongruent2(_1365083, _1365089, tc_fun(_1365095, tc_HOL_Obool), _1365087, _1365093, _1365097), hBOOL(hAPP(hAPP(c_member(tc_fun(_1365083, tc_HOL_Obool)), _1365099), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1365083), _1365085), _1365087))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1365089, tc_HOL_Obool)), _1365101), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1365089), _1365091), _1365093))), 31952 ^ _773908 : [(31958 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1365095, tc_HOL_Obool)), hAPP(hAPP(_1365097, 31951 ^ [_1365083, _1365085, _1365087, _1365089, _1365091, _1365093, _1365095, _1365097, _1365099, _1365101, _1365103]), 31954 ^ [_1365083, _1365085, _1365087, _1365089, _1365091, _1365093, _1365095, _1365097, _1365099, _1365101, _1365103])), _1365103))], (31956 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365089), 31954 ^ [_1365083, _1365085, _1365087, _1365089, _1365091, _1365093, _1365095, _1365097, _1365099, _1365101, _1365103]), _1365091)))], (31953 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365083), 31951 ^ [_1365083, _1365085, _1365087, _1365089, _1365091, _1365093, _1365095, _1365097, _1365099, _1365101, _1365103]), _1365085)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1365095, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365083, tc_fun(_1365095, tc_HOL_Obool)), _1365099), hAPP(hAPP(c_COMBB(tc_fun(_1365089, tc_fun(_1365095, tc_HOL_Obool)), tc_fun(_1365095, tc_HOL_Obool), _1365083), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365089, tc_fun(_1365095, tc_HOL_Obool)), _1365101)), _1365097))), _1365103)))], (13795 ^ _773908) ^ [_1006258, _1006260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006258), _1006260)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006258, _1006260) = _1006258)], (14959 ^ _773908) ^ [_1027092, _1027094, _1027096] : [-(hBOOL(hAPP(_1027092, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027094), _1027096)))), 14962 ^ _773908 : [(14965 ^ _773908) ^ [] : [hBOOL(hAPP(_1027092, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14963 ^ _773908) ^ [] : [-(_1027096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14966 ^ _773908 : [(14971 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14969 ^ [_1027092, _1027094, _1027096]), _1027096)))], (14973 ^ _773908) ^ [] : [-(_1027094 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027096), 14968 ^ [_1027092, _1027094, _1027096])), 14969 ^ [_1027092, _1027094, _1027096]))], (14975 ^ _773908) ^ [] : [hBOOL(hAPP(_1027092, 14968 ^ [_1027092, _1027094, _1027096]))], (14967 ^ _773908) ^ [] : [_1027096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25289 ^ _773908) ^ [_1220705, _1220707] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220705)), hAPP(c_Nat_OSuc, _1220707)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1220705), _1220707)))], (6894 ^ _773908) ^ [_885418, _885420, _885422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885420), _885422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885418), _885420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885418), _885422))))], (36085 ^ _773908) ^ [_1450935, _1450937] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450935), _1450937)), 36088 ^ _773908 : [(36095 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450935), c_Orderings_Otop__class_Otop(tc_fun(_1450935, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1450935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450935, tc_HOL_Obool)), _1450937))))], (36089 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450935, tc_HOL_Obool)), _1450937))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1450935), c_Orderings_Otop__class_Otop(tc_fun(_1450935, tc_HOL_Obool)))))]]], (34628 ^ _773908) ^ [_1419785, _1419787, _1419789, _1419791] : [class_Groups_Ocomm__monoid__add(_1419785), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1419787), _1419789))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419787, _1419785), _1419791), _1419789) = c_Groups_Ozero__class_Ozero(_1419785))], (2652 ^ _773908) ^ [_813184, _813186, _813188, _813190, _813192, _813194, _813196, _813198, _813200, _813202] : [-(c_SetInterval_Oord_OatLeastLessThan(_813202, _813198, _813194, _813190, _813186) = c_SetInterval_Oord_OatLeastLessThan(_813200, _813196, _813192, _813188, _813184)), _813202 = _813200, _813198 = _813196, _813194 = _813192, _813190 = _813188, _813186 = _813184], (1444 ^ _773908) ^ [_794944, _794946] : [-(class_Lattices_Oboolean__algebra(_794944)), _794946 = _794944, class_Lattices_Oboolean__algebra(_794946)], (49991 ^ _773908) ^ [_1783961, _1783963, _1783965, _1783967] : [-(c_Random__Sequence_Omap(_1783961, _1783963, _1783965, _1783967) = c_Random__Sequence_Obind(_1783961, _1783963, _1783967, hAPP(c_Fun_Ocomp(_1783963, 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(_1783963)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1783961, c_Random__Sequence_Osingle(_1783963)), _1783965)))], (45103 ^ _773908) ^ [_1675052, _1675054, _1675056] : [-(c_List_Oremdups(_1675052, hAPP(c_List_Ofilter(_1675052, _1675054), _1675056)) = hAPP(c_List_Ofilter(_1675052, _1675054), c_List_Oremdups(_1675052, _1675056)))], (34187 ^ _773908) ^ [_1410396, _1410398, _1410400, _1410402] : [c_Fun_Oinj__on(_1410396, _1410398, _1410400, _1410402), -(hAPP(c_Set_Oimage(_1410398, _1410396, c_Fun_Othe__inv__into(_1410396, _1410398, _1410402, _1410400)), hAPP(c_Set_Oimage(_1410396, _1410398, _1410400), _1410402)) = _1410402)], (39102 ^ _773908) ^ [_1530696, _1530698, _1530700, _1530702] : [hBOOL(hAPP(hAPP(c_member(_1530698), _1530702), hAPP(c_Relation_ORange(_1530696, _1530698), _1530700))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1530696, _1530698, hAPP(hAPP(c_COMBC(_1530696, tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_fun(_1530698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530698, tc_fun(tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_fun(_1530698, tc_HOL_Obool)), _1530696), c_COMBC(_1530698, tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530698, tc_prod(_1530696, _1530698)), tc_fun(_1530698, tc_fun(tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_HOL_Obool)), _1530696), hAPP(c_COMBB(tc_prod(_1530696, _1530698), tc_fun(tc_fun(tc_prod(_1530696, _1530698), tc_HOL_Obool), tc_HOL_Obool), _1530698), c_member(tc_prod(_1530696, _1530698)))), c_Product__Type_OPair(_1530696, _1530698)))), _1530700)), _1530702)))], (2200 ^ _773908) ^ [_805894, _805896, _805898, _805900, _805902, _805904, _805906, _805908] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_805908, _805904, _805900, _805896) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_805906, _805902, _805898, _805894)), _805908 = _805906, _805904 = _805902, _805900 = _805898, _805896 = _805894], (892 ^ _773908) ^ [_787518, _787520, _787522, _787524, _787526, _787528, _787530, _787532] : [-(c_Wellfounded_Omax__extp(_787530, _787526, _787522, _787518)), c_Wellfounded_Omax__extp(_787532, _787528, _787524, _787520), _787532 = _787530, _787528 = _787526, _787524 = _787522, _787520 = _787518], (41750 ^ _773908) ^ [_1596448, _1596450] : [-(c_List_Obutlast(_1596448, _1596450) = hAPP(hAPP(c_List_Otake(_1596448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596448)), _1596450)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1596450))], (19525 ^ _773908) ^ [_1110903, _1110905] : [class_Int_Onumber__ring(_1110903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110903), _1110905), hAPP(c_Int_Onumber__class_Onumber__of(_1110903), c_Int_OBit1(c_Int_OPls))) = _1110905)], (26231 ^ _773908) ^ [_1239680, _1239682, _1239684, _1239686] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239680, tc_HOL_Obool)), _1239682), hAPP(hAPP(c_Set_Oinsert(_1239680), _1239684), _1239686)) = hAPP(hAPP(c_Set_Oinsert(_1239680), _1239684), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239680, tc_HOL_Obool)), _1239682), _1239686)))], (39332 ^ _773908) ^ [_1537954, _1537956, _1537958] : [hAPP(hAPP(c_List_Oappend(_1537954), _1537956), _1537958) = _1537956, -(_1537958 = c_List_Olist_ONil(_1537954))], (39833 ^ _773908) ^ [_1550837, _1550839] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1550837)), c_List_Olist_ONil(_1550837)), c_List_Olists(_1550837, _1550839))))], (34918 ^ _773908) ^ [_1426139, _1426141, _1426143, _1426145] : [class_Groups_Ocomm__monoid__add(_1426139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1426141), _1426143)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1426139), _1426145), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1426141), _1426143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426139), hAPP(_1426145, _1426141)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1426139), _1426145), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1426141)), _1426143))))], (40019 ^ _773908) ^ [_1555452, _1555454, _1555456, _1555458] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1555452) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1555454), hAPP(hAPP(c_List_Olist_OCons(_1555454), _1555456), _1555458)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1555452)) = hAPP(hAPP(c_List_Onth(_1555454), _1555458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1555452)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (8289 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8533 ^ _773908) ^ [_914885, _914887, _914889, _914891] : [class_Rings_Ocomm__semiring__1(_914885), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914885), _914887), _914889)), _914891) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914885), _914887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914885), _914889), _914891)))], (46293 ^ _773908) ^ [_1699915, _1699917] : [c_Wellfounded_Owf(_1699915, _1699917), -(c_Wellfounded_OwfP(_1699915, c_FunDef_Oin__rel(_1699915, _1699915, _1699917)))], (26653 ^ _773908) ^ [_1252890, _1252892, _1252894, _1252896] : [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), _1252890), _1252892)), 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), _1252894), _1252896)), 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), _1252890), _1252896)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252894), _1252892))))], (32954 ^ _773908) ^ [_1385873, _1385875, _1385877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385873)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1385875), _1385877)), 32961 ^ _773908 : [(32962 ^ _773908) ^ [_1386069] : [32964 ^ _773908 : [(32970 ^ _773908) ^ [] : [-(_1386069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32966 ^ [_1385873, _1385875, _1385877, _1386069]), 32963 ^ [_1385873, _1385875, _1385877, _1386069]))], (32968 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32966 ^ [_1385873, _1385875, _1385877, _1386069]), _1385877)))], (32965 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32963 ^ [_1385873, _1385875, _1385877, _1386069]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1385873))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385875), _1386069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1386069), _1385873))))]]], (42900 ^ _773908) ^ [_1624996, _1624998] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1624996), _1624998) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624996)), hAPP(c_Code__Numeral_Onat__of, _1624998))))], (16065 ^ _773908) ^ [_1048766, _1048768, _1048770, _1048772, _1048774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048766), _1048768)), 16068 ^ _773908 : [(16075 ^ _773908) ^ [] : [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), _1048768), _1048766)), _1048770)), _1048772) = _1048774, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048768), _1048770)), _1048772) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048766), _1048770)), _1048774))], (16069 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048768), _1048770)), _1048772) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048766), _1048770)), _1048774), -(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), _1048768), _1048766)), _1048770)), _1048772) = _1048774)]]], (15515 ^ _773908) ^ [_1037313, _1037315, _1037317] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037313), _1037315)), _1037317) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037313), _1037317)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037315), _1037317)))], (8653 ^ _773908) ^ [_917160, _917162, _917164] : [class_Groups_Ogroup__add(_917160), 8656 ^ _773908 : [(8663 ^ _773908) ^ [] : [_917164 = hAPP(c_Groups_Ouminus__class_Ouminus(_917160), _917162), -(_917162 = hAPP(c_Groups_Ouminus__class_Ouminus(_917160), _917164))], (8657 ^ _773908) ^ [] : [_917162 = hAPP(c_Groups_Ouminus__class_Ouminus(_917160), _917164), -(_917164 = hAPP(c_Groups_Ouminus__class_Ouminus(_917160), _917162))]]], (11731 ^ _773908) ^ [_969850, _969852] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969850)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _969852)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969850), _969852)))], (408 ^ _773908) ^ [_780214, _780216, _780218, _780220, _780222, _780224] : [-(c_Hoare__Mirabelle_Ohoare__valids(_780222, _780218, _780214)), c_Hoare__Mirabelle_Ohoare__valids(_780224, _780220, _780216), _780224 = _780222, _780220 = _780218, _780216 = _780214], (12212 ^ _773908) ^ [_978516, _978518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978516)), 12215 ^ _773908 : [(12224 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _978516), _978518) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _978516 = c_Groups_Oone__class_Oone(tc_Int_Oint), _978518 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (12216 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _978516), _978518) = c_Groups_Oone__class_Oone(tc_Int_Oint), 12219 ^ _773908 : [(12222 ^ _773908) ^ [] : [-(_978518 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (12220 ^ _773908) ^ [] : [-(_978516 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (20109 ^ _773908) ^ [_1120944, _1120946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120944), _1120946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1120944)), c_Int_OBit1(_1120946))))], (24439 ^ _773908) ^ [_1203052, _1203054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203052), 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)), _1203054)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203052), _1203054) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1203052, _1203054)))], (49895 ^ _773908) ^ [_1781735, _1781737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1781735)), _1781737)), 49899 ^ _773908 : [(49900 ^ _773908) ^ [_1781836] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1781735)), _1781836), _1781737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781735)), _1781836)), 49898 ^ [_1781735, _1781737])))]]], (30449 ^ _773908) ^ [_1330336, _1330338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330336), _1330338)))), -(_1330338 = c_Orderings_Obot__class_Obot(tc_fun(_1330336, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330336), _1330338))], (15823 ^ _773908) ^ [_1043276, _1043278, _1043280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043276), _1043278)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043278), _1043276)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043280), _1043278)), _1043276))], (45577 ^ _773908) ^ [_1684329, _1684331, _1684333] : [_1684333 = hAPP(hAPP(c_List_Olist_OCons(_1684329), _1684331), c_List_Olist_ONil(_1684329)), -(hAPP(hAPP(c_List_Olist_OCons(_1684329), _1684331), c_List_Olist_ONil(_1684329)) = hAPP(c_List_Orev(_1684329), _1684333))], (15003 ^ _773908) ^ [_1027965, _1027967, _1027969] : [-(hBOOL(hAPP(_1027965, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027967, _1027969)))), 15006 ^ _773908 : [(15009 ^ _773908) ^ [] : [hBOOL(hAPP(_1027965, _1027967))], (15007 ^ _773908) ^ [] : [-(_1027969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15010 ^ _773908 : [(15015 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15013 ^ [_1027965, _1027967, _1027969]), _1027969)))], (15017 ^ _773908) ^ [] : [-(_1027967 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027969), 15012 ^ [_1027965, _1027967, _1027969])), 15013 ^ [_1027965, _1027967, _1027969]))], (15019 ^ _773908) ^ [] : [hBOOL(hAPP(_1027965, 15013 ^ [_1027965, _1027967, _1027969]))], (15011 ^ _773908) ^ [] : [_1027969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (49773 ^ _773908) ^ [_1778724, _1778726, _1778728] : [hBOOL(hAPP(hAPP(c_List_Omember(_1778724), _1778728), _1778726)), -(hBOOL(hAPP(hAPP(c_member(_1778724), _1778726), hAPP(c_List_Oset(_1778724), _1778728))))], (18005 ^ _773908) ^ [_1084465] : [-(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, _1084465))))))], (50243 ^ _773908) ^ [_1791124, _1791126] : [c_Relation_Otrans(_1791124, _1791126), -(c_Relation_Otrans(tc_List_Olist(_1791124), c_List_Olexord(_1791124, _1791126)))], (17899 ^ _773908) ^ [_1082912] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082912)), -(hAPP(c_Int_Onat, _1082912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16747 ^ _773908) ^ [_1061508, _1061510, _1061512] : [class_Rings_Olinordered__idom(_1061508), 16750 ^ _773908 : [(16759 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), hAPP(c_Groups_Oabs__class_Oabs(_1061508), _1061510)), _1061512))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), _1061510), _1061512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), hAPP(c_Groups_Ouminus__class_Ouminus(_1061508), _1061510)), _1061512))], (16751 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), hAPP(c_Groups_Oabs__class_Oabs(_1061508), _1061510)), _1061512)), 16754 ^ _773908 : [(16757 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), hAPP(c_Groups_Ouminus__class_Ouminus(_1061508), _1061510)), _1061512)))], (16755 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061508), _1061510), _1061512)))]]]]], (38458 ^ _773908) ^ [_1513675, _1513677, _1513679] : [-(hAPP(c_Fun_Ocomp(_1513675, _1513675, _1513677, c_Fun_Oid(_1513675)), _1513679) = _1513679)], (47740 ^ _773908) ^ [_1735793, _1735795] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1735793), _1735795)), 47746 ^ _773908 : [(47749 ^ _773908) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47747 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735793), 47745 ^ [_1735793, _1735795]), _1735795)))]], -(hAPP(c_Finite__Set_Ocard(_1735793), _1735795) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40427 ^ _773908) ^ [_1565267, _1565269, _1565271, _1565273, _1565275] : [hAPP(hAPP(c_List_Oappend(_1565267), _1565269), _1565271) = hAPP(hAPP(c_List_Oappend(_1565267), _1565273), _1565275), 40430 ^ _773908 : [(40439 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565269)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565273)))), 40442 ^ _773908 : [(40445 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1565267), hAPP(hAPP(c_List_Odrop(_1565267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565273)), _1565269)), _1565271) = _1565275)], (40443 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1565267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565273)), _1565269) = _1565273)]]], (40431 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565269)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565273))), 40434 ^ _773908 : [(40437 ^ _773908) ^ [] : [-(_1565271 = hAPP(hAPP(c_List_Oappend(_1565267), hAPP(hAPP(c_List_Odrop(_1565267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565269)), _1565273)), _1565275))], (40435 ^ _773908) ^ [] : [-(_1565269 = hAPP(hAPP(c_List_Otake(_1565267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1565267)), _1565269)), _1565273))]]]]], (10529 ^ _773908) ^ [_948430, _948432, _948434, _948436] : [class_Groups_Oordered__ab__semigroup__add(_948430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948430), _948432), _948434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948430), _948436), _948432)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948430), _948436), _948434))))], (19895 ^ _773908) ^ [_1117222, _1117224] : [c_Int_OBit0(_1117222) = c_Int_OBit1(_1117224)], (39174 ^ _773908) ^ [_1533300, _1533302, _1533304, _1533306] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533300), tc_List_Olist(_1533300))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533300), tc_List_Olist(_1533300)), _1533302), _1533304)), c_List_Olex(_1533300, _1533306)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533300), tc_List_Olist(_1533300))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533300), tc_List_Olist(_1533300)), _1533302), _1533304)), c_List_Olexord(_1533300, _1533306))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533300)), _1533302) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533300)), _1533304)], (43850 ^ _773908) ^ [_1646439, _1646441, _1646443] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646439, tc_HOL_Obool)), _1646441), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646439, tc_HOL_Obool), _1646443)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646439, tc_HOL_Obool), tc_fun(_1646439, tc_HOL_Obool)), _1646443), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646439, tc_HOL_Obool)), _1646441)))], (31493 ^ _773908) ^ [_1353598, _1353600] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1353598, _1353600))))], (5392 ^ _773908) ^ [_856348, _856350, _856352, _856354, _856356, _856358] : [-(c_Set_Oimage(_856358, _856354, _856350) = c_Set_Oimage(_856356, _856352, _856348)), _856358 = _856356, _856354 = _856352, _856350 = _856348], (12626 ^ _773908) ^ [_985548, _985550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985548), _985550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985548)), hAPP(c_Nat_OSuc, _985550))))], (39719 ^ _773908) ^ [_1547164, _1547166] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1547164), tc_List_Olist(_1547164))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1547164), tc_List_Olist(_1547164)), c_List_Olist_ONil(_1547164)), c_List_Olist_ONil(_1547164))), c_List_Olistrel(_1547164, _1547166))))], (37980 ^ _773908) ^ [_1495798, _1495800, _1495802] : [hBOOL(hAPP(hAPP(c_member(_1495798), _1495800), hAPP(c_Set_OCollect(_1495798), _1495802))), -(hBOOL(hAPP(_1495802, _1495800)))], (22425 ^ _773908) ^ [_1162475, _1162477, _1162479, _1162481] : [class_Fields_Olinordered__field__inverse__zero(_1162475), class_Int_Onumber(_1162475), 22432 ^ _773908 : [(22433 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162475), _1162477), _1162479)), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481))), 22436 ^ _773908 : [(22443 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), _1162479))), 22446 ^ _773908 : [(22453 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162479), c_Groups_Ozero__class_Ozero(_1162475)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481))))], (22447 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162479), c_Groups_Ozero__class_Ozero(_1162475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162475), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)), _1162479)), _1162477)))]]], (22437 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), _1162479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162475), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)), _1162479))))]]], (22459 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162475), _1162477), _1162479)), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)))), 22462 ^ _773908 : [(22465 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162475), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)), _1162479)))], (22463 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), _1162479)))]], 22466 ^ _773908 : [(22469 ^ _773908) ^ [] : [22470 ^ _773908 : [(22473 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162475), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)), _1162479)), _1162477))], (22471 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162479), c_Groups_Ozero__class_Ozero(_1162475))))]], 22474 ^ _773908 : [(22477 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), hAPP(c_Int_Onumber__class_Onumber__of(_1162475), _1162481)))], (22475 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), _1162479), c_Groups_Ozero__class_Ozero(_1162475)))]]], (22467 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162475), c_Groups_Ozero__class_Ozero(_1162475)), _1162479))]]]]], (14338 ^ _773908) ^ [_1016359, _1016361, _1016363] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016359), _1016361)), _1016363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016359), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016361), _1016363))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016359), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016361, _1016363))), _1016363)))], (6642 ^ _773908) ^ [_881804, _881806, _881808] : [class_Orderings_Opreorder(_881804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881804), _881806), _881808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881804), _881808), _881806))], (48431 ^ _773908) ^ [_1750085, _1750087, _1750089] : [class_Orderings_Olinorder(_1750085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750085), _1750087)), -(c_Big__Operators_Olattice_OInf__fin(_1750085, c_Orderings_Oord__class_Omin(_1750085), hAPP(hAPP(c_Set_Oinsert(_1750085), _1750089), _1750087)) = hAPP(hAPP(c_Finite__Set_Ofold(_1750085, _1750085, c_Orderings_Oord__class_Omin(_1750085)), _1750089), _1750087))], (15513 ^ _773908) ^ [_1037256, _1037258, _1037260] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037256), _1037258)), _1037260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037256), _1037260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037258), _1037260)))], (28320 ^ _773908) ^ [_1288211, _1288213] : [class_Lattices_Oboolean__algebra(_1288211), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288211), hAPP(c_Groups_Ouminus__class_Ouminus(_1288211), _1288213)), _1288213) = c_Orderings_Obot__class_Obot(_1288211))], (51360 ^ _773908) ^ [_1812824, _1812826] : [class_Orderings_Oord(_1812824), -(class_Orderings_Oord(tc_fun(_1812826, _1812824)))], (50253 ^ _773908) ^ [_1791264, _1791266] : [c_Relation_Otrans(_1791264, _1791266), -(c_Relation_Otrans(tc_List_Olist(_1791264), c_List_Olistrel(_1791264, _1791266)))], (39457 ^ _773908) ^ [_1540269, _1540271, _1540273, _1540275, _1540277] : [-(hAPP(hAPP(c_List_Olist_OCons(_1540269), _1540271), _1540273) = hAPP(hAPP(c_List_Oappend(_1540269), _1540275), _1540277)), 39458 ^ _773908 : [(39465 ^ _773908) ^ [_1540452] : [hAPP(hAPP(c_List_Olist_OCons(_1540269), _1540271), _1540452) = _1540275, _1540273 = hAPP(hAPP(c_List_Oappend(_1540269), _1540452), _1540277)], (39459 ^ _773908) ^ [] : [_1540275 = c_List_Olist_ONil(_1540269), hAPP(hAPP(c_List_Olist_OCons(_1540269), _1540271), _1540273) = _1540277]]], (8287 ^ _773908) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19653 ^ _773908) ^ [_1112911, _1112913] : [class_Int_Onumber__ring(_1112911), class_Rings_Olinordered__idom(_1112911), 19660 ^ _773908 : [(19667 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1112913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112911), c_Groups_Oone__class_Oone(_1112911)), hAPP(c_Int_Onumber__class_Onumber__of(_1112911), _1112913))))], (19661 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112911), c_Groups_Oone__class_Oone(_1112911)), hAPP(c_Int_Onumber__class_Onumber__of(_1112911), _1112913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1112913)))]]], (2728 ^ _773908) ^ [_814476, _814478] : [_814478 = _814476, -(c_SetInterval_Oord__class_OatLeast(_814478) = c_SetInterval_Oord__class_OatLeast(_814476))], (38468 ^ _773908) ^ [_1513890, _1513892] : [-(c_Product__Type_Oapfst(_1513890, _1513890, _1513892, c_Fun_Oid(_1513890)) = c_Fun_Oid(tc_prod(_1513890, _1513892)))], (40643 ^ _773908) ^ [_1570694, _1570696, _1570698, _1570700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570694, tc_HOL_Obool)), hAPP(c_List_Oset(_1570694), hAPP(hAPP(c_List_Olist__update(_1570694, _1570696), _1570698), _1570700))), hAPP(hAPP(c_Set_Oinsert(_1570694), _1570700), hAPP(c_List_Oset(_1570694), _1570696)))))], (30495 ^ _773908) ^ [_1331436, _1331438, _1331440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331436), _1331438)), -(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(_1331436), _1331440)), hAPP(c_Finite__Set_Ocard(_1331436), _1331438))), hAPP(c_Finite__Set_Ocard(_1331436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331436, tc_HOL_Obool)), _1331440), _1331438)))))], (28034 ^ _773908) ^ [_1281507, _1281509, _1281511, _1281513] : [hBOOL(hAPP(hAPP(c_member(_1281507), _1281509), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281507, tc_HOL_Obool)), _1281511), _1281513))), -(hBOOL(hAPP(hAPP(c_member(_1281507), _1281509), _1281513)))], (31580 ^ _773908) ^ [_1355928, _1355930, _1355932, _1355934, _1355936, _1355938, _1355940, _1355942, _1355944] : [c_Equiv__Relations_Oequiv(_1355928, _1355930, _1355932), c_Equiv__Relations_Oequiv(_1355934, _1355936, _1355938), c_Equiv__Relations_Ocongruent2(_1355928, _1355934, tc_fun(_1355940, tc_HOL_Obool), _1355932, _1355938, _1355942), hBOOL(hAPP(hAPP(c_member(_1355934), _1355944), _1355936)), -(c_Equiv__Relations_Ocongruent(_1355928, tc_fun(_1355940, tc_HOL_Obool), _1355932, hAPP(hAPP(c_COMBB(tc_fun(_1355934, tc_fun(_1355940, tc_HOL_Obool)), tc_fun(_1355940, tc_HOL_Obool), _1355928), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1355934, tc_fun(_1355940, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1355934, _1355934, _1355938), hAPP(hAPP(c_Set_Oinsert(_1355934), _1355944), c_Orderings_Obot__class_Obot(tc_fun(_1355934, tc_HOL_Obool)))))), _1355942)))], (40777 ^ _773908) ^ [_1574278, _1574280, _1574282, _1574284] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574278), tc_List_Olist(_1574278))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574278), tc_List_Olist(_1574278)), _1574280), _1574282)), c_List_Olistrel1(_1574278, _1574284)))), 40778 ^ _773908 : [(40779 ^ _773908) ^ [_1574411, _1574413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574278, _1574278)), hAPP(hAPP(c_Product__Type_OPair(_1574278, _1574278), hAPP(hAPP(c_List_Onth(_1574278), _1574280), _1574411)), _1574413)), _1574284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1574411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574278)), _1574280))), _1574282 = hAPP(hAPP(c_List_Olist__update(_1574278, _1574280), _1574411), _1574413)]]], (20825 ^ _773908) ^ [_1134127, _1134129] : [c_Nat__Transfer_Ois__nat(_1134127), c_Nat__Transfer_Ois__nat(_1134129), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1134127), _1134129)))], (20303 ^ _773908) ^ [_1124344] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1124344))), 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), _1124344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (50486 ^ _773908) ^ [_1795761, _1795763] : [-(c_Equiv__Relations_Oequivp(_1795761, _1795763)), c_Predicate_Oreflp(_1795761, _1795763), c_Predicate_Osymp(_1795761, _1795763), c_Predicate_Otransp(_1795761, _1795763)], (18367 ^ _773908) ^ [_1091052, _1091054, _1091056, _1091058] : [_1091052 = _1091054, 18370 ^ _773908 : [(18377 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1091056), _1091054), _1091058)), -(hBOOL(hAPP(hAPP(c_member(_1091056), _1091052), _1091058)))], (18371 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1091056), _1091052), _1091058)), -(hBOOL(hAPP(hAPP(c_member(_1091056), _1091054), _1091058)))]]], (24201 ^ _773908) ^ [_1197180, _1197182, _1197184, _1197186, _1197188, _1197190] : [hAPP(c_Product__Type_Oapsnd(_1197180, _1197182, _1197184, _1197186), _1197188) = hAPP(c_Product__Type_Oapsnd(_1197180, _1197182, _1197184, _1197190), _1197188), -(hAPP(_1197186, hAPP(c_Product__Type_Osnd(_1197184, _1197180), _1197188)) = hAPP(_1197190, hAPP(c_Product__Type_Osnd(_1197184, _1197180), _1197188)))], (49400 ^ _773908) ^ [_1770721, _1770723, _1770725, _1770727, _1770729] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1770721, _1770723, hAPP(hAPP(c_COMBC(_1770721, tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_fun(_1770723, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1770723, tc_fun(tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_fun(_1770723, tc_HOL_Obool)), _1770721), c_COMBC(_1770723, tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1770723, tc_prod(_1770721, _1770723)), tc_fun(_1770723, tc_fun(tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_HOL_Obool)), _1770721), hAPP(c_COMBB(tc_prod(_1770721, _1770723), tc_fun(tc_fun(tc_prod(_1770721, _1770723), tc_HOL_Obool), tc_HOL_Obool), _1770723), c_member(tc_prod(_1770721, _1770723)))), c_Product__Type_OPair(_1770721, _1770723)))), _1770725)), _1770727), _1770729)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1770723, _1770721)), hAPP(hAPP(c_Product__Type_OPair(_1770723, _1770721), _1770727), _1770729)), hAPP(c_Relation_Oconverse(_1770721, _1770723), _1770725))))], (36848 ^ _773908) ^ [_1468165, _1468167, _1468169] : [class_Orderings_Olinorder(_1468165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468165), _1468167)), hBOOL(hAPP(hAPP(c_member(_1468165), _1468169), _1468167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468165), hAPP(c_Finite__Set_Ofold1(_1468165, c_Orderings_Oord__class_Omin(_1468165)), _1468167)), _1468169)))], (40123 ^ _773908) ^ [_1558184, _1558186, _1558188, _1558190] : [_1558184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1558186), _1558184), hAPP(hAPP(c_List_Olist_OCons(_1558186), _1558188), _1558190)) = c_List_Olist_ONil(_1558186))], (19759 ^ _773908) ^ [_1114710, _1114712] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1114710)))), _1114712) = 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)))), _1114710)), _1114712))], (42896 ^ _773908) ^ [_1624904, _1624906] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1624904), _1624906) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624904)), hAPP(c_Code__Numeral_Onat__of, _1624906))))], (22189 ^ _773908) ^ [_1158005, _1158007, _1158009, _1158011] : [class_Fields_Olinordered__field(_1158005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158005), c_Groups_Ozero__class_Ozero(_1158005)), _1158007)), 22196 ^ _773908 : [(22203 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158005), _1158009), _1158007)), _1158011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158005), _1158009), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158005), _1158011), _1158007))))], (22197 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158005), _1158009), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158005), _1158011), _1158007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158005), _1158009), _1158007)), _1158011)))]]], (15685 ^ _773908) ^ [_1040741, _1040743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040743), _1040741)), -(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), _1040741), _1040743))))], (43927 ^ _773908) ^ [_1648311, _1648313, _1648315, _1648317] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648311, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1648311, _1648313), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1648311, _1648313), tc_HOL_Obool)), _1648315), _1648317))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648311, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1648311, _1648313), _1648315)), hAPP(c_Relation_ODomain(_1648311, _1648313), _1648317)))))], (24335 ^ _773908) ^ [_1200907, _1200909, _1200911, _1200913] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1200907, tc_fun(_1200909, tc_HOL_Obool))), _1200911), _1200913))], (30001 ^ _773908) ^ [_1321699, _1321701, _1321703, _1321705, _1321707, _1321709] : [c_Finite__Set_Ofolding__idem(_1321699, _1321701, _1321703, _1321705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321699), _1321707)), hBOOL(hAPP(hAPP(c_member(_1321699), _1321709), _1321707)), -(hAPP(c_Fun_Ocomp(_1321701, _1321701, _1321701, hAPP(_1321705, _1321707)), hAPP(_1321703, _1321709)) = hAPP(_1321705, _1321707))], (32460 ^ _773908) ^ [_1376393, _1376395, _1376397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376393, tc_HOL_Obool)), _1376395), _1376397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1376393, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1376393), _1376395)), hAPP(c_Set_OPow(_1376393), _1376397))))], (16815 ^ _773908) ^ [_1062830, _1062832, _1062834] : [class_Rings_Ocomm__semiring__1(_1062830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062830), _1062832), hAPP(hAPP(c_Power_Opower__class_Opower(_1062830), _1062832), _1062834)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1062830), _1062832), hAPP(c_Nat_OSuc, _1062834)))], (37916 ^ _773908) ^ [_1494323] : [class_Orderings_Olinorder(_1494323), -(c_Finite__Set_Ofun__left__comm__idem(_1494323, _1494323, c_Orderings_Oord__class_Omax(_1494323)))], (37213 ^ _773908) ^ [_1475658, _1475660, _1475662, _1475664, _1475666] : [-(hAPP(c_Set_Ovimage(_1475658, _1475660, _1475662), hAPP(hAPP(c_Set_Oinsert(_1475660), _1475664), _1475666)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475658, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1475658, _1475660, _1475662), hAPP(hAPP(c_Set_Oinsert(_1475660), _1475664), c_Orderings_Obot__class_Obot(tc_fun(_1475660, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1475658, _1475660, _1475662), _1475666)))], (24753 ^ _773908) ^ [_1210530, _1210532, _1210534] : [class_Orderings_Olinorder(_1210530), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210530), _1210532), _1210534) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210530), _1210534), _1210532))], (27344 ^ _773908) ^ [_1267605, _1267607, _1267609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267605), _1267607)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267605), _1267609)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267605, tc_HOL_Obool)), _1267607), _1267609))))], (37193 ^ _773908) ^ [_1475154, _1475156, _1475158, _1475160] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475154, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1475156, _1475154, _1475158), hAPP(c_Set_Ovimage(_1475156, _1475154, _1475158), _1475160))), _1475160)))], (19755 ^ _773908) ^ [_1114610, _1114612] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1114610))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114612)) = 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)))), _1114610), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114612)))], (44851 ^ _773908) ^ [_1670504, _1670506, _1670508] : [class_Groups_Omonoid__add(_1670504), -(hAPP(c_List_Ofoldl(_1670504, _1670504, c_Groups_Oplus__class_Oplus(_1670504), _1670506), _1670508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1670504), _1670506), c_List_Ofoldr(_1670504, _1670504, c_Groups_Oplus__class_Oplus(_1670504), _1670508, c_Groups_Ozero__class_Ozero(_1670504))))], (30059 ^ _773908) ^ [_1322819, _1322821, _1322823] : [class_Orderings_Olinorder(_1322819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322819), _1322821)), hBOOL(hAPP(hAPP(c_member(_1322819), _1322823), _1322821)), 30070 ^ _773908 : [(30077 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322819, tc_HOL_Obool)), _1322821), hAPP(hAPP(c_Set_Oinsert(_1322819), _1322823), c_Orderings_Obot__class_Obot(tc_fun(_1322819, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322819, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1322819, c_Orderings_Oord__class_Omin(_1322819), _1322821) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1322819), _1322823), c_Big__Operators_Olattice_OInf__fin(_1322819, c_Orderings_Oord__class_Omin(_1322819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322819, tc_HOL_Obool)), _1322821), hAPP(hAPP(c_Set_Oinsert(_1322819), _1322823), c_Orderings_Obot__class_Obot(tc_fun(_1322819, tc_HOL_Obool)))))))], (30071 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322819, tc_HOL_Obool)), _1322821), hAPP(hAPP(c_Set_Oinsert(_1322819), _1322823), c_Orderings_Obot__class_Obot(tc_fun(_1322819, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322819, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1322819, c_Orderings_Oord__class_Omin(_1322819), _1322821) = _1322823)]]], (40007 ^ _773908) ^ [_1555246, _1555248, _1555250, _1555252] : [-(_1555246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1555248), hAPP(hAPP(c_List_Olist_OCons(_1555248), _1555250), _1555252)), _1555246) = hAPP(hAPP(c_List_Onth(_1555248), _1555252), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1555246), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24407 ^ _773908) ^ [_1202526, _1202528, _1202530] : [hBOOL(hAPP(hAPP(c_member(_1202526), _1202528), hAPP(c_fequal, _1202530))), -(_1202528 = _1202530)], (35388 ^ _773908) ^ [_1436963, _1436965, _1436967, _1436969] : [hBOOL(hAPP(hAPP(c_member(_1436963), _1436965), _1436967)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436963, tc_Nat_Onat), _1436969), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1436963, tc_HOL_Obool)), _1436967), hAPP(hAPP(c_Set_Oinsert(_1436963), _1436965), c_Orderings_Obot__class_Obot(tc_fun(_1436963, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436963, tc_Nat_Onat), _1436969), _1436967)), hAPP(_1436969, _1436965)))], (47379 ^ _773908) ^ [_1726193, _1726195, _1726197] : [-(hAPP(c_Relation_ORange(_1726193, _1726195), _1726197) = hAPP(c_Relation_ODomain(_1726195, _1726193), hAPP(c_Relation_Oconverse(_1726193, _1726195), _1726197)))], (45917 ^ _773908) ^ [_1691526, _1691528, _1691530, _1691532, _1691534] : [hBOOL(hAPP(hAPP(c_member(_1691526), _1691528), hAPP(c_List_Oset(_1691526), _1691530))), -(hBOOL(hAPP(_1691532, _1691528))), -(c_List_OdropWhile(_1691526, _1691532, hAPP(hAPP(c_List_Oappend(_1691526), _1691530), _1691534)) = hAPP(hAPP(c_List_Oappend(_1691526), c_List_OdropWhile(_1691526, _1691532, _1691530)), _1691534))], (8997 ^ _773908) ^ [_923211, _923213] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923211), _923213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _923211)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _923213)))], (18105 ^ _773908) ^ [_1086172, _1086174] : [class_Int_Onumber__ring(_1086172), 18108 ^ _773908 : [(18115 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086174)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1086172), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086174)) = hAPP(c_Int_Onumber__class_Onumber__of(_1086172), _1086174))], (18109 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086174))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1086172), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086174)) = c_Groups_Ozero__class_Ozero(_1086172))]]], (50566 ^ _773908) ^ [_1797297, _1797299] : [c_Relation_Osym(_1797297, _1797299), -(hAPP(c_Relation_Oconverse(_1797297, _1797297), _1797299) = _1797299)], (51354 ^ _773908) ^ [_1812745, _1812747] : [class_Orderings_Otop(_1812745), -(class_Orderings_Otop(tc_fun(_1812747, _1812745)))], (49936 ^ _773908) ^ [_1782506, _1782508, _1782510] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1782506), _1782508, _1782510)), -(c_List_Olist__ex(tc_Int_Oint, _1782506, c_List_Oupto(_1782508, _1782510)))], (49942 ^ _773908) ^ [_1782572, _1782574, _1782576] : [c_List_Oall__interval__int(_1782572, _1782574, _1782576), 49945 ^ _773908 : [(49946 ^ _773908) ^ [_1782650] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1782650), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1782574, _1782576))), -(hBOOL(hAPP(_1782572, _1782650)))]]], (31758 ^ _773908) ^ [_1360213, _1360215, _1360217, _1360219, _1360221] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360213, tc_fun(_1360215, tc_HOL_Obool)), _1360217), hAPP(hAPP(c_COMBB(tc_fun(_1360215, tc_HOL_Obool), tc_fun(_1360215, tc_HOL_Obool), _1360213), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360215, tc_HOL_Obool)), _1360219)), _1360221)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360215, tc_HOL_Obool)), _1360219), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360213, tc_fun(_1360215, tc_HOL_Obool)), _1360217), _1360221)))], (11543 ^ _773908) ^ [_966655, _966657] : [-(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), _966655), _966657)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966657))], (36003 ^ _773908) ^ [_1449374, _1449376] : [class_Lattices_Obounded__lattice__top(_1449374), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449374), c_Orderings_Otop__class_Otop(_1449374)), _1449376) = _1449376)], (42870 ^ _773908) ^ [_1624445, _1624447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1624445), _1624447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624445)), hAPP(c_Code__Numeral_Onat__of, _1624447))))], (38665 ^ _773908) ^ [_1520914, _1520916, _1520918] : [c_Wellfounded_Owf(_1520914, _1520916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520914, _1520914), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520914, _1520914, _1520914), _1520916), _1520918)), _1520916)), -(c_FunDef_Oreduction__pair(_1520914, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1520914, _1520914), tc_HOL_Obool), tc_fun(tc_prod(_1520914, _1520914), tc_HOL_Obool)), _1520916), _1520918)))], (18575 ^ _773908) ^ [_1094806, _1094808] : [class_Rings_Osemiring__1(_1094806), 18578 ^ _773908 : [(18585 ^ _773908) ^ [] : [_1094808 = c_Groups_Ozero__class_Ozero(_1094806), -(c_Int_Oiszero(_1094806, _1094808))], (18579 ^ _773908) ^ [] : [c_Int_Oiszero(_1094806, _1094808), -(_1094808 = c_Groups_Ozero__class_Ozero(_1094806))]]], (12756 ^ _773908) ^ [_987671, _987673, _987675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987671), _987673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987671), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987675), _987673))))], (31343 ^ _773908) ^ [_1349986, _1349988, _1349990] : [class_Groups_Oordered__ab__group__add(_1349986), -(hAPP(c_Set_Oimage(_1349986, _1349986, c_Groups_Ouminus__class_Ouminus(_1349986)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1349986, _1349988, _1349990)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1349986, hAPP(c_Groups_Ouminus__class_Ouminus(_1349986), _1349990), hAPP(c_Groups_Ouminus__class_Ouminus(_1349986), _1349988)))], (1574 ^ _773908) ^ [_796569, _796571] : [-(class_Groups_Oordered__ab__semigroup__add(_796569)), _796571 = _796569, class_Groups_Oordered__ab__semigroup__add(_796571)], (47088 ^ _773908) ^ [_1719390, _1719392] : [-(c_Transitive__Closure_Ortrancl(_1719390, c_Transitive__Closure_Otrancl(_1719390, _1719392)) = c_Transitive__Closure_Ortrancl(_1719390, _1719392))], (23117 ^ _773908) ^ [_1175644, _1175646] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1175644) = hAPP(c_Nat_OSuc, _1175646), -(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(_1175644))), 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)), _1175646))))))], (3958 ^ _773908) ^ [_833647, _833649, _833651, _833653, _833655, _833657, _833659, _833661, _833663, _833665] : [-(c_Finite__Set_Ofold__graph(_833665, _833661, _833657, _833653, _833649) = c_Finite__Set_Ofold__graph(_833663, _833659, _833655, _833651, _833647)), _833665 = _833663, _833661 = _833659, _833657 = _833655, _833653 = _833651, _833649 = _833647], (41973 ^ _773908) ^ [_1602640, _1602642, _1602644, _1602646, _1602648, _1602650] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602642, _1602644)), hAPP(hAPP(c_Product__Type_OPair(_1602642, _1602644), _1602648), _1602650)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602640, tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1602640, tc_HOL_Obool))), _1602646))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602640, tc_fun(_1602642, tc_fun(_1602644, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1602640, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_fun(_1602642, tc_fun(_1602644, tc_HOL_Obool)), _1602640), hAPP(c_COMBC(_1602642, tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_fun(_1602644, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602644, tc_fun(tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_fun(_1602644, tc_HOL_Obool)), _1602642), c_COMBC(_1602644, tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602644, tc_prod(_1602642, _1602644)), tc_fun(_1602644, tc_fun(tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_HOL_Obool)), _1602642), hAPP(c_COMBB(tc_prod(_1602642, _1602644), tc_fun(tc_fun(tc_prod(_1602642, _1602644), tc_HOL_Obool), tc_HOL_Obool), _1602644), c_member(tc_prod(_1602642, _1602644)))), c_Product__Type_OPair(_1602642, _1602644))))), _1602646)), _1602648), _1602650)))], (36055 ^ _773908) ^ [_1450373, _1450375, _1450377, _1450379, _1450381] : [c_Fun_Oinj__on(_1450373, _1450375, _1450377, c_Orderings_Otop__class_Otop(tc_fun(_1450373, tc_HOL_Obool))), 36058 ^ _773908 : [(36065 ^ _773908) ^ [] : [_1450379 = _1450381, -(hAPP(c_Set_Oimage(_1450373, _1450375, _1450377), _1450379) = hAPP(c_Set_Oimage(_1450373, _1450375, _1450377), _1450381))], (36059 ^ _773908) ^ [] : [hAPP(c_Set_Oimage(_1450373, _1450375, _1450377), _1450379) = hAPP(c_Set_Oimage(_1450373, _1450375, _1450377), _1450381), -(_1450379 = _1450381)]]], (19583 ^ _773908) ^ [_1111776] : [class_Int_Onumber__ring(_1111776), c_Int_Oiszero(_1111776, hAPP(c_Int_Onumber__class_Onumber__of(_1111776), c_Int_OBit1(c_Int_OPls)))], (11705 ^ _773908) ^ [_969373, _969375, _969377, _969379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _969373), _969375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _969377), _969379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _969373), _969377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _969375), _969379))))], (41005 ^ _773908) ^ [_1581645, _1581647, _1581649, _1581651] : [hBOOL(hAPP(c_List_Odistinct(_1581645), _1581647)), -(hBOOL(hAPP(hAPP(c_member(_1581645), _1581649), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1581645, tc_HOL_Obool)), hAPP(c_List_Oset(_1581645), _1581647)), hAPP(hAPP(c_Set_Oinsert(_1581645), hAPP(hAPP(c_List_Onth(_1581645), _1581647), _1581651)), c_Orderings_Obot__class_Obot(tc_fun(_1581645, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1581645), hAPP(hAPP(c_List_Olist__update(_1581645, _1581647), _1581651), _1581649))))], (39234 ^ _773908) ^ [_1534869, _1534871, _1534873] : [_1534869 = hAPP(hAPP(c_List_Olist_OCons(_1534871), _1534873), _1534869)], (5965 ^ _773908) ^ [_869597] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _869597), _869597)))], (37814 ^ _773908) ^ [_1492249, _1492251, _1492253, _1492255, _1492257] : [c_Relation_Orefl__on(_1492249, _1492251, _1492253), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492249, _1492249)), hAPP(hAPP(c_Product__Type_OPair(_1492249, _1492249), _1492255), _1492257)), _1492253)), -(hBOOL(hAPP(hAPP(c_member(_1492249), _1492255), _1492251)))], (4828 ^ _773908) ^ [_847536, _847538, _847540, _847542] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_847542, _847538) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_847540, _847536)), _847542 = _847540, _847538 = _847536], (3902 ^ _773908) ^ [_832755, _832757, _832759, _832761, _832763, _832765] : [-(c_Big__Operators_Olattice_OInf__fin(_832765, _832761, _832757) = c_Big__Operators_Olattice_OInf__fin(_832763, _832759, _832755)), _832765 = _832763, _832761 = _832759, _832757 = _832755], (34794 ^ _773908) ^ [_1423649, _1423651, _1423653] : [class_Groups_Ocomm__monoid__add(_1423649), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1423649), _1423651), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423653))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423649), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1423649), _1423651), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1423653))), hAPP(_1423651, hAPP(c_Nat_OSuc, _1423653))))], (32646 ^ _773908) ^ [_1379847, _1379849] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1379847, _1379849)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379849)), _1379847))], (20301 ^ _773908) ^ [_1124307] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1124307)), 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, _1124307, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (41366 ^ _773908) ^ [_1589104, _1589106, _1589108, _1589110] : [class_Complete__Lattice_Ocomplete__lattice(_1589104), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1589106, _1589104), hAPP(c_List_Oset(_1589106), _1589108)), _1589110) = hAPP(c_List_Ofoldl(_1589104, _1589106, hAPP(c_COMBC(_1589106, _1589104, _1589104), hAPP(hAPP(c_COMBB(_1589104, tc_fun(_1589104, _1589104), _1589106), c_Lattices_Osemilattice__sup__class_Osup(_1589104)), _1589110)), c_Orderings_Obot__class_Obot(_1589104)), _1589108))], (3818 ^ _773908) ^ [_831491, _831493, _831495, _831497] : [-(c_Wellfounded_Omax__ext(_831497, _831493) = c_Wellfounded_Omax__ext(_831495, _831491)), _831497 = _831495, _831493 = _831491], (45909 ^ _773908) ^ [_1691355, _1691357, _1691359] : [-(c_List_OdropWhile(_1691355, _1691357, _1691359) = c_List_Olist_ONil(_1691355)), hBOOL(hAPP(_1691357, hAPP(c_List_Ohd(_1691355), c_List_OdropWhile(_1691355, _1691357, _1691359))))], (5026 ^ _773908) ^ [_850645, _850647, _850649, _850651, _850653, _850655, _850657, _850659] : [-(c_Random__Sequence_Omap(_850659, _850655, _850651, _850647) = c_Random__Sequence_Omap(_850657, _850653, _850649, _850645)), _850659 = _850657, _850655 = _850653, _850651 = _850649, _850647 = _850645], (46625 ^ _773908) ^ [_1707243, _1707245, _1707247, _1707249] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1707243, tc_Nat_Onat), _1707245), _1707247) = hAPP(c_Nat_OSuc, _1707249), 46629 ^ _773908 : [(46632 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1707245, 46628 ^ [_1707243, _1707245, _1707247, _1707249]))))], (46630 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1707243), 46628 ^ [_1707243, _1707245, _1707247, _1707249]), _1707247)))]]], (28721 ^ _773908) ^ [_1298269, _1298271, _1298273, _1298275, _1298277, _1298279] : [hBOOL(hAPP(hAPP(c_member(_1298269), _1298271), c_SetInterval_Oord_OatLeastLessThan(_1298269, _1298273, _1298275, _1298277, _1298279))), 28724 ^ _773908 : [(28727 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298275, _1298271), _1298279)))], (28725 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1298273, _1298277), _1298271)))]]], (14833 ^ _773908) ^ [_1024536, _1024538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024538, _1024536)), _1024536)))], (19463 ^ _773908) ^ [_1109876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1109876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1109876))))], (36735 ^ _773908) ^ [_1466078, _1466080, _1466082, _1466084] : [-(c_HOL_OThe(tc_prod(_1466078, _1466080), hAPP(c_Product__Type_Oprod_Oprod__case(_1466078, _1466080, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1466078, tc_fun(_1466080, tc_HOL_Obool), tc_fun(_1466080, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1466080, tc_HOL_Obool), tc_fun(_1466080, tc_HOL_Obool)), _1466078), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1466080)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1466078), c_fconj), hAPP(c_fequal, _1466082)))), hAPP(c_fequal, _1466084)))) = hAPP(hAPP(c_Product__Type_OPair(_1466078, _1466080), _1466082), _1466084))], (42700 ^ _773908) ^ [_1620719, _1620721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1620719)), hAPP(c_Code__Numeral_Oof__nat, _1620721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620719), _1620721)))], (44829 ^ _773908) ^ [_1669953, _1669955] : [-(c_List_Ofoldr(tc_List_Olist(_1669953), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1669953)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1669953))), c_List_Otranspose(_1669953, _1669955), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1669953))), hAPP(c_List_Ofilter(tc_List_Olist(_1669953), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1669953)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669953), tc_List_Olist(_1669953), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1669953)))), _1669955)))], (51332 ^ _773908) ^ [_1812458, _1812460] : [-(class_Finite__Set_Ofinite(tc_fun(_1812458, _1812460))), class_Finite__Set_Ofinite(_1812458), class_Finite__Set_Ofinite(_1812460)], (45655 ^ _773908) ^ [_1686133, _1686135, _1686137] : [class_Orderings_Olinorder(_1686133), c_List_Olinorder__class_Osorted(_1686133, hAPP(c_List_Orev(_1686133), _1686135)), 45662 ^ _773908 : [(45669 ^ _773908) ^ [] : [-(_1686135 = c_List_Olist_ONil(_1686133)), -(c_List_Ofoldr(_1686133, _1686133, c_Orderings_Oord__class_Omax(_1686133), _1686135, _1686137) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1686133), hAPP(hAPP(c_List_Onth(_1686133), _1686135), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1686137))], (45663 ^ _773908) ^ [] : [_1686135 = c_List_Olist_ONil(_1686133), -(c_List_Ofoldr(_1686133, _1686133, c_Orderings_Oord__class_Omax(_1686133), _1686135, _1686137) = _1686137)]]], (19519 ^ _773908) ^ [_1110758, _1110760] : [class_Int_Onumber__ring(_1110758), -(hAPP(c_Int_Onumber__class_Onumber__of(_1110758), c_Int_OBit1(_1110760)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110758), c_Groups_Oone__class_Oone(_1110758)), hAPP(c_Int_Onumber__class_Onumber__of(_1110758), _1110760))), hAPP(c_Int_Onumber__class_Onumber__of(_1110758), _1110760)))], (18285 ^ _773908) ^ [_1089659, _1089661] : [hBOOL(hAPP(hAPP(c_member(_1089659), _1089661), c_Orderings_Obot__class_Obot(tc_fun(_1089659, tc_HOL_Obool))))], (1154 ^ _773908) ^ [_791319, _791321] : [-(class_Groups_Olinordered__ab__group__add(_791319)), _791321 = _791319, class_Groups_Olinordered__ab__group__add(_791321)], (41274 ^ _773908) ^ [_1587163, _1587165, _1587167] : [-(c_List_Orotate(_1587163, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1587165), _1587167)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1587163), tc_List_Olist(_1587163), tc_List_Olist(_1587163), c_List_Orotate(_1587163, _1587165)), c_List_Orotate(_1587163, _1587167)))], (50761 ^ _773908) ^ [_1800548, _1800550, _1800552] : [c_Equiv__Relations_Oequiv(_1800548, _1800550, _1800552), 50764 ^ _773908 : [(50769 ^ _773908) ^ [] : [-(c_Relation_Otrans(_1800548, _1800552))], (50767 ^ _773908) ^ [] : [-(c_Relation_Osym(_1800548, _1800552))], (50765 ^ _773908) ^ [] : [-(c_Relation_Orefl__on(_1800548, _1800550, _1800552))]]], (20615 ^ _773908) ^ [_1130206, _1130208] : [class_Int_Onumber__ring(_1130206), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1130206), hAPP(c_Int_Onumber__class_Onumber__of(_1130206), 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)))), _1130208))) = hAPP(c_Int_Onumber__class_Onumber__of(_1130206), c_Int_OMin))], (42944 ^ _773908) ^ [_1626044, _1626046] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1626044), _1626046) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1626044, 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)))), _1626046))))], (40535 ^ _773908) ^ [_1568092, _1568094] : [-(_1568092 = c_List_Olist_ONil(_1568094)), -(hBOOL(hAPP(hAPP(c_member(_1568094), hAPP(c_List_Ohd(_1568094), _1568092)), hAPP(c_List_Oset(_1568094), _1568092))))], (2062 ^ _773908) ^ [_803827, _803829, _803831, _803833, _803835, _803837] : [-(c_Com_Ocom_OLocal(_803837, _803833, _803829) = c_Com_Ocom_OLocal(_803835, _803831, _803827)), _803837 = _803835, _803833 = _803831, _803829 = _803827], (39286 ^ _773908) ^ [_1536341, _1536343, _1536345, _1536347, _1536349] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1536341), tc_List_Olist(_1536341))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1536341), tc_List_Olist(_1536341)), _1536343), _1536345)), c_List_Olexord(_1536341, _1536347))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1536341), tc_List_Olist(_1536341))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1536341), tc_List_Olist(_1536341)), hAPP(hAPP(c_List_Oappend(_1536341), _1536349), _1536343)), hAPP(hAPP(c_List_Oappend(_1536341), _1536349), _1536345))), c_List_Olexord(_1536341, _1536347))))], (22893 ^ _773908) ^ [_1171026] : [c_Code__Numeral_OSuc__code__numeral(_1171026) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (24899 ^ _773908) ^ [_1213182, _1213184, _1213186] : [class_Orderings_Olinorder(_1213182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213182), _1213184), _1213186)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213182), _1213186), _1213184) = _1213184)], (26011 ^ _773908) ^ [_1234949, _1234951, _1234953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1234949, tc_HOL_Obool)), _1234951), _1234953)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1234949, tc_HOL_Obool)), _1234951), _1234953) = _1234953)], (1048 ^ _773908) ^ [_789760, _789762, _789764, _789766] : [-(c_Predicate_Otransp(_789764, _789760)), c_Predicate_Otransp(_789766, _789762), _789766 = _789764, _789762 = _789760], (37962 ^ _773908) ^ [_1495414, _1495416] : [-(hAPP(c_Set_OCollect(_1495414), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1495414), c_fNot), _1495416)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1495414, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1495414), _1495416)))], (26333 ^ _773908) ^ [_1242981, _1242983, _1242985, _1242987, _1242989, _1242991] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242981, tc_fun(_1242983, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1242981, tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_fun(_1242983, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1242983, tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_fun(_1242983, tc_HOL_Obool)), _1242981), c_COMBC(_1242983, tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1242983, tc_prod(_1242981, _1242983)), tc_fun(_1242983, tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), _1242981), hAPP(c_COMBB(tc_prod(_1242981, _1242983), tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool), _1242983), c_member(tc_prod(_1242981, _1242983)))), c_Product__Type_OPair(_1242981, _1242983)))), _1242985)), hAPP(hAPP(c_COMBC(_1242981, tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_fun(_1242983, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1242983, tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_fun(_1242983, tc_HOL_Obool)), _1242981), c_COMBC(_1242983, tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1242983, tc_prod(_1242981, _1242983)), tc_fun(_1242983, tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool)), _1242981), hAPP(c_COMBB(tc_prod(_1242981, _1242983), tc_fun(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool), tc_HOL_Obool), _1242983), c_member(tc_prod(_1242981, _1242983)))), c_Product__Type_OPair(_1242981, _1242983)))), _1242987)), _1242989), _1242991)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1242981, _1242983)), hAPP(hAPP(c_Product__Type_OPair(_1242981, _1242983), _1242989), _1242991)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1242981, _1242983), tc_HOL_Obool)), _1242985), _1242987))))], (15081 ^ _773908) ^ [_1029421, _1029423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029421)), -(c_SMT_Oz3div(_1029423, _1029421) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029423), _1029421))], (7563 ^ _773908) ^ [_896437, _896439, _896441, _896443, _896445, _896447] : [c_Com_Ocom_OCond(_896437, _896439, _896441) = c_Com_Ocom_OLocal(_896443, _896445, _896447)], (20159 ^ _773908) ^ [_1121862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1121862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1121862))))], (17465 ^ _773908) ^ [_1075413, _1075415, _1075417] : [class_Power_Opower(_1075413), class_Rings_Omult__zero(_1075413), class_Rings_Ono__zero__divisors(_1075413), class_Rings_Ozero__neq__one(_1075413), 17480 ^ _773908 : [(17489 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1075413), _1075415), _1075417) = c_Groups_Ozero__class_Ozero(_1075413)), _1075415 = c_Groups_Ozero__class_Ozero(_1075413), -(_1075417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17481 ^ _773908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1075413), _1075415), _1075417) = c_Groups_Ozero__class_Ozero(_1075413), 17484 ^ _773908 : [(17487 ^ _773908) ^ [] : [_1075417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17485 ^ _773908) ^ [] : [-(_1075415 = c_Groups_Ozero__class_Ozero(_1075413))]]]]], (7777 ^ _773908) ^ [_900727, _900729, _900731] : [class_Rings_Olinordered__idom(_900727), -(_900729 = _900731), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900727), _900729), _900731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900727), _900731), _900729)))], (31232 ^ _773908) ^ [_1347403, _1347405, _1347407] : [31234 ^ _773908 : [(31237 ^ _773908) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1347407, 31233 ^ [_1347403, _1347405, _1347407]))], (31235 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347403), 31233 ^ [_1347403, _1347405, _1347407]), _1347405)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347403, tc_Int_Oint), _1347407), _1347405) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347403, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1347403), c_Int_Onat), _1347407)), _1347405)))], (44361 ^ _773908) ^ [_1658324, _1658326, _1658328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658324)), hAPP(c_List_Ofilter(_1658324, _1658326), _1658328))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658324)), _1658328))))], (49131 ^ _773908) ^ [_1764664, _1764666, _1764668] : [c_List_Olist__all(_1764664, _1764666, _1764668), 49134 ^ _773908 : [(49135 ^ _773908) ^ [_1764745] : [hBOOL(hAPP(hAPP(c_member(_1764664), _1764745), hAPP(c_List_Oset(_1764664), _1764668))), -(hBOOL(hAPP(_1764666, _1764745)))]]], (5370 ^ _773908) ^ [_855959, _855961, _855963, _855965, _855967, _855969, _855971, _855973, _855975, _855977] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_855977, _855973, _855969, _855965, _855961) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_855975, _855971, _855967, _855963, _855959)), _855977 = _855975, _855973 = _855971, _855969 = _855967, _855965 = _855963, _855961 = _855959], (6800 ^ _773908) ^ [_883845, _883847, _883849] : [6801 ^ _773908 : [(6804 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_883849, _883847), _883845))], (6802 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883845), _883847)))]], 6807 ^ _773908 : [(6810 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_883849, _883847), _883845))], (6808 ^ _773908) ^ [] : [-(_883845 = _883847)]], 6813 ^ _773908 : [(6816 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_883849, _883847), _883845))], (6814 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883847), _883845)))]], -(hBOOL(hAPP(hAPP(_883849, _883847), _883845)))], (25563 ^ _773908) ^ [_1226551, _1226553, _1226555, _1226557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1226551), _1226553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1226555), _1226557)), -(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), _1226551), _1226555)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1226553), _1226557))), c_FunDef_Opair__leq)))], (4170 ^ _773908) ^ [_836885, _836887, _836889, _836891, _836893, _836895, _836897, _836899, _836901, _836903, _836905, _836907, _836909, _836911] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836911, _836907, _836903, _836899, _836895, _836891, _836887) = c_New__Random__Sequence_Oneg__decr__bind(_836909, _836905, _836901, _836897, _836893, _836889, _836885)), _836911 = _836909, _836907 = _836905, _836903 = _836901, _836899 = _836897, _836895 = _836893, _836891 = _836889, _836887 = _836885], (45800 ^ _773908) ^ [_1689052, _1689054, _1689056, _1689058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689052), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689054)), c_List_OtakeWhile(_1689054, _1689056, _1689058)))), -(hAPP(hAPP(c_List_Onth(_1689054), c_List_OtakeWhile(_1689054, _1689056, _1689058)), _1689052) = hAPP(hAPP(c_List_Onth(_1689054), _1689058), _1689052))], (35078 ^ _773908) ^ [_1429817] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1429817)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1429817)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1429817), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (25823 ^ _773908) ^ [_1231481, _1231483, _1231485] : [class_Lattices_Olattice(_1231481), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231481), _1231483), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231481), _1231485), _1231483))))], (41568 ^ _773908) ^ [_1592781, _1592783, _1592785] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1592781)), _1592783), c_List_Olists(_1592781, _1592785))), -(_1592783 = c_List_Olist_ONil(_1592781)), 41577 ^ _773908 : [(41582 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1592781)), 41576 ^ [_1592781, _1592783, _1592785]), c_List_Olists(_1592781, _1592785))))], (41580 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592781), 41575 ^ [_1592781, _1592783, _1592785]), _1592785)))], (41578 ^ _773908) ^ [] : [-(_1592783 = hAPP(hAPP(c_List_Olist_OCons(_1592781), 41575 ^ [_1592781, _1592783, _1592785]), 41576 ^ [_1592781, _1592783, _1592785]))]]], (3162 ^ _773908) ^ [_821303, _821305] : [_821305 = _821303, -(c_Lazy__Sequence_Ohb__not__seq(_821305) = c_Lazy__Sequence_Ohb__not__seq(_821303))], (40407 ^ _773908) ^ [_1564778, _1564780] : [-(c_List_Olists(_1564778, _1564780) = hAPP(c_Set_OCollect(tc_List_Olist(_1564778)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1564778), tc_fun(_1564778, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1564778, tc_HOL_Obool), tc_fun(tc_fun(_1564778, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1564778)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1564778, tc_HOL_Obool))), c_List_Oset(_1564778))), _1564780)))], (41770 ^ _773908) ^ [_1596801, _1596803, _1596805, _1596807] : [hAPP(hAPP(c_List_Oappend(_1596801), _1596803), hAPP(hAPP(c_List_Olist_OCons(_1596801), _1596805), c_List_Olist_ONil(_1596801))) = _1596807, 41773 ^ _773908 : [(41778 ^ _773908) ^ [] : [-(c_List_Olast(_1596801, _1596807) = _1596805)], (41776 ^ _773908) ^ [] : [-(c_List_Obutlast(_1596801, _1596807) = _1596803)], (41774 ^ _773908) ^ [] : [_1596807 = c_List_Olist_ONil(_1596801)]]], (18685 ^ _773908) ^ [_1096876] : [-(c_Int_Opred(_1096876) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1096876), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (2458 ^ _773908) ^ [_810069, _810071, _810073, _810075] : [-(c_Divides_OnegDivAlg(_810075, _810071) = c_Divides_OnegDivAlg(_810073, _810069)), _810075 = _810073, _810071 = _810069], (27990 ^ _773908) ^ [_1280676, _1280678, _1280680] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280676, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280676, tc_HOL_Obool)), _1280678), _1280680)), _1280678)))], (51622 ^ _773908) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (47012 ^ _773908) ^ [_1717524, _1717526, _1717528, _1717530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717524, _1717524)), hAPP(hAPP(c_Product__Type_OPair(_1717524, _1717524), _1717526), _1717528)), c_Transitive__Closure_Ortrancl(_1717524, _1717530))), -(_1717526 = _1717528), 47019 ^ _773908 : [(47022 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1717524, _1717524)), hAPP(hAPP(c_Product__Type_OPair(_1717524, _1717524), _1717526), _1717528)), c_Transitive__Closure_Otrancl(_1717524, _1717530))))], (47020 ^ _773908) ^ [] : [_1717526 = _1717528]]], (19137 ^ _773908) ^ [_1104430, _1104432] : [class_Int_Onumber__ring(_1104430), class_Rings_Olinordered__idom(_1104430), 19144 ^ _773908 : [(19151 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104430), c_Groups_Ozero__class_Ozero(_1104430)), hAPP(c_Int_Onumber__class_Onumber__of(_1104430), _1104432))))], (19145 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104430), c_Groups_Ozero__class_Ozero(_1104430)), hAPP(c_Int_Onumber__class_Onumber__of(_1104430), _1104432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104432)))]]], (27442 ^ _773908) ^ [_1269687, _1269689, _1269691, _1269693, _1269695] : [c_Finite__Set_Ofolding__one(_1269687, _1269689, _1269691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269687), _1269693)), hBOOL(hAPP(hAPP(c_member(_1269687), _1269695), _1269693)), 27453 ^ _773908 : [(27460 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269687, tc_HOL_Obool)), _1269693), hAPP(hAPP(c_Set_Oinsert(_1269687), _1269695), c_Orderings_Obot__class_Obot(tc_fun(_1269687, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1269687, tc_HOL_Obool))), -(hAPP(_1269691, _1269693) = hAPP(hAPP(_1269689, _1269695), hAPP(_1269691, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269687, tc_HOL_Obool)), _1269693), hAPP(hAPP(c_Set_Oinsert(_1269687), _1269695), c_Orderings_Obot__class_Obot(tc_fun(_1269687, tc_HOL_Obool)))))))], (27454 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269687, tc_HOL_Obool)), _1269693), hAPP(hAPP(c_Set_Oinsert(_1269687), _1269695), c_Orderings_Obot__class_Obot(tc_fun(_1269687, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1269687, tc_HOL_Obool)), -(hAPP(_1269691, _1269693) = _1269695)]]], (22169 ^ _773908) ^ [_1157624, _1157626, _1157628, _1157630] : [class_Fields_Olinordered__field(_1157624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157624), c_Groups_Ozero__class_Ozero(_1157624)), _1157626)), 22176 ^ _773908 : [(22183 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157624), _1157628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157624), _1157630), _1157626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157624), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157624), _1157628), _1157626)), _1157630)))], (22177 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157624), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157624), _1157628), _1157626)), _1157630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157624), _1157628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157624), _1157630), _1157626))))]]], (48024 ^ _773908) ^ [_1741579, _1741581, _1741583, _1741585] : [48025 ^ _773908 : [(48028 ^ _773908) ^ [] : [c_List_Olist__ex(_1741579, _1741581, _1741585)], (48026 ^ _773908) ^ [] : [c_List_Olist__ex(_1741579, _1741581, _1741583)]], -(c_List_Olist__ex(_1741579, _1741581, hAPP(hAPP(c_List_Oappend(_1741579), _1741583), _1741585)))], (14569 ^ _773908) ^ [_1020216, _1020218, _1020220, _1020222] : [class_Divides_Osemiring__div(_1020216), 14572 ^ _773908 : [(14579 ^ _773908) ^ [] : [-(_1020218 = c_Groups_Ozero__class_Ozero(_1020216)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020216), _1020218), _1020220)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020216), _1020218), _1020222)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020216), _1020220), _1020222))], (14573 ^ _773908) ^ [] : [_1020218 = c_Groups_Ozero__class_Ozero(_1020216), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020216), _1020218), _1020220)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020216), _1020218), _1020222)) = c_Groups_Ozero__class_Ozero(_1020216))]]], (29693 ^ _773908) ^ [_1315906, _1315908, _1315910] : [class_Orderings_Olinorder(_1315906), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315906), _1315908)), -(_1315908 = c_Orderings_Obot__class_Obot(tc_fun(_1315906, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315906), _1315910)), -(_1315910 = c_Orderings_Obot__class_Obot(tc_fun(_1315906, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315906, tc_HOL_Obool)), _1315908), _1315910) = c_Orderings_Obot__class_Obot(tc_fun(_1315906, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1315906, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315906, tc_HOL_Obool)), _1315908), _1315910)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315906), c_Big__Operators_Olinorder__class_OMin(_1315906, _1315908)), c_Big__Operators_Olinorder__class_OMin(_1315906, _1315910)))], (17149 ^ _773908) ^ [_1069668, _1069670, _1069672, _1069674] : [class_Rings_Olinordered__semidom(_1069668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069668), c_Groups_Oone__class_Oone(_1069668)), _1069670)), 17156 ^ _773908 : [(17163 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069672), _1069674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069668), hAPP(hAPP(c_Power_Opower__class_Opower(_1069668), _1069670), _1069672)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069668), _1069670), _1069674))))], (17157 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069668), hAPP(hAPP(c_Power_Opower__class_Opower(_1069668), _1069670), _1069672)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069668), _1069670), _1069674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069672), _1069674)))]]], (26339 ^ _773908) ^ [_1243638, _1243640, _1243642, _1243644, _1243646, _1243648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1243638, _1243640)), hAPP(hAPP(c_Product__Type_OPair(_1243638, _1243640), _1243646), _1243648)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool)), _1243642), _1243644))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1243638, tc_fun(_1243640, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1243638, tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_fun(_1243640, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1243640, tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_fun(_1243640, tc_HOL_Obool)), _1243638), c_COMBC(_1243640, tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1243640, tc_prod(_1243638, _1243640)), tc_fun(_1243640, tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), _1243638), hAPP(c_COMBB(tc_prod(_1243638, _1243640), tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool), _1243640), c_member(tc_prod(_1243638, _1243640)))), c_Product__Type_OPair(_1243638, _1243640)))), _1243642)), hAPP(hAPP(c_COMBC(_1243638, tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_fun(_1243640, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1243640, tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_fun(_1243640, tc_HOL_Obool)), _1243638), c_COMBC(_1243640, tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1243640, tc_prod(_1243638, _1243640)), tc_fun(_1243640, tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool)), _1243638), hAPP(c_COMBB(tc_prod(_1243638, _1243640), tc_fun(tc_fun(tc_prod(_1243638, _1243640), tc_HOL_Obool), tc_HOL_Obool), _1243640), c_member(tc_prod(_1243638, _1243640)))), c_Product__Type_OPair(_1243638, _1243640)))), _1243644)), _1243646), _1243648)))], (20789 ^ _773908) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (49166 ^ _773908) ^ [_1765333, _1765335, _1765337, _1765339] : [-(c_List_Olist__ex1(_1765333, _1765335, hAPP(hAPP(c_List_Olist_OCons(_1765333), _1765337), _1765339))), 49169 ^ _773908 : [(49172 ^ _773908) ^ [] : [c_List_Olist__all(_1765333, hAPP(hAPP(c_COMBS(_1765333, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765333), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765333), c_fNot), _1765335))), hAPP(c_fequal, _1765337)), _1765339)], (49170 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1765335, _1765337)))]], 49173 ^ _773908 : [(49176 ^ _773908) ^ [] : [c_List_Olist__ex1(_1765333, _1765335, _1765339)], (49174 ^ _773908) ^ [] : [hBOOL(hAPP(_1765335, _1765337))]]], (9371 ^ _773908) ^ [_929931, _929933, _929935, _929937] : [class_Rings_Olinordered__ring__strict(_929931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929931), _929933), _929935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929931), _929937), c_Groups_Ozero__class_Ozero(_929931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929931), _929935), _929937)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929931), _929933), _929937))))], (7791 ^ _773908) ^ [_900862, _900864, _900866, _900868, _900870] : [class_Rings_Ocomm__semiring__1(_900862), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), _900864), _900866)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), _900868), _900870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), _900864), _900868)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900862), _900866), _900870)))], (37488 ^ _773908) ^ [_1483270, _1483272, _1483274, _1483276, _1483278, _1483280] : [hBOOL(hAPP(hAPP(c_member(_1483270), _1483272), _1483274)), 37491 ^ _773908 : [(37498 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483276, tc_HOL_Obool)), _1483278), _1483280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1483276, _1483270), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1483276, _1483270), _1483278), hAPP(c_COMBK(tc_fun(_1483270, tc_HOL_Obool), _1483276), _1483274))), hAPP(hAPP(c_Product__Type_OSigma(_1483276, _1483270), _1483280), hAPP(c_COMBK(tc_fun(_1483270, tc_HOL_Obool), _1483276), _1483274)))))], (37492 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1483276, _1483270), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1483276, _1483270), _1483278), hAPP(c_COMBK(tc_fun(_1483270, tc_HOL_Obool), _1483276), _1483274))), hAPP(hAPP(c_Product__Type_OSigma(_1483276, _1483270), _1483280), hAPP(c_COMBK(tc_fun(_1483270, tc_HOL_Obool), _1483276), _1483274)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483276, tc_HOL_Obool)), _1483278), _1483280)))]]], (8285 ^ _773908) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17519 ^ _773908) ^ [_1076243, _1076245, _1076247, _1076249] : [class_Rings_Olinordered__semidom(_1076243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076243), c_Groups_Oone__class_Oone(_1076243)), _1076245)), 17526 ^ _773908 : [(17533 ^ _773908) ^ [] : [_1076247 = _1076249, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076243), _1076245), _1076247) = hAPP(hAPP(c_Power_Opower__class_Opower(_1076243), _1076245), _1076249))], (17527 ^ _773908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1076243), _1076245), _1076247) = hAPP(hAPP(c_Power_Opower__class_Opower(_1076243), _1076245), _1076249), -(_1076247 = _1076249)]]], (2962 ^ _773908) ^ [_818165, _818167, _818169, _818171] : [-(c_List_Olexn(_818171, _818167) = c_List_Olexn(_818169, _818165)), _818171 = _818169, _818167 = _818165], (33616 ^ _773908) ^ [_1398298, _1398300] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398298)), _1398300) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1398298, _1398300))], (29831 ^ _773908) ^ [_1318581, _1318583, _1318585] : [class_Orderings_Olinorder(_1318581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318581), _1318583)), hBOOL(hAPP(hAPP(c_member(_1318581), _1318585), _1318583)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318581), _1318585), c_Big__Operators_Olattice_OSup__fin(_1318581, c_Orderings_Oord__class_Omax(_1318581), _1318583)) = c_Big__Operators_Olattice_OSup__fin(_1318581, c_Orderings_Oord__class_Omax(_1318581), _1318583))], (48547 ^ _773908) ^ [_1752252, _1752254, _1752256] : [class_Orderings_Olinorder(_1752252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752252), _1752254)), -(hBOOL(hAPP(hAPP(c_member(_1752252), _1752256), _1752254))), -(c_Big__Operators_Olinorder__class_OMax(_1752252, hAPP(hAPP(c_Set_Oinsert(_1752252), _1752256), _1752254)) = hAPP(hAPP(c_Finite__Set_Ofold(_1752252, _1752252, c_Orderings_Oord__class_Omax(_1752252)), _1752256), _1752254))], (46806 ^ _773908) ^ [_1711825, _1711827] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1711825, _1711825), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1711825, _1711827)), c_Relation_OId(_1711825)) = c_Transitive__Closure_Ortrancl(_1711825, _1711827))], (19923 ^ _773908) ^ [_1117730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1117730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1117730)))], (2884 ^ _773908) ^ [_816906, _816908] : [_816908 = _816906, -(c_Wellfounded_Omeasure(_816908) = c_Wellfounded_Omeasure(_816906))], (46730 ^ _773908) ^ [_1709961, _1709963, _1709965, _1709967, _1709969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1709961, _1709961)), hAPP(hAPP(c_Product__Type_OPair(_1709961, _1709961), _1709963), _1709965)), c_Transitive__Closure_Ortrancl(_1709961, _1709967))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1709961, _1709961)), hAPP(hAPP(c_Product__Type_OPair(_1709961, _1709961), _1709965), _1709969)), _1709967)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1709961, _1709961)), hAPP(hAPP(c_Product__Type_OPair(_1709961, _1709961), _1709963), _1709969)), c_Transitive__Closure_Ortrancl(_1709961, _1709967))))], (32007 ^ _773908) ^ [_1367039] : [-(hAPP(c_Int_Onat, _1367039) = 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, _1367039)), 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)))))))], (20715 ^ _773908) ^ [] : [-(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))], (44967 ^ _773908) ^ [_1672711, _1672713] : [c_List_Oremdups(_1672711, _1672713) = c_List_Olist_ONil(_1672711), -(_1672713 = c_List_Olist_ONil(_1672711))], (38577 ^ _773908) ^ [_1516797, _1516799, _1516801, _1516803, _1516805, _1516807, _1516809] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1516797, _1516799, _1516801), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1516803, tc_fun(tc_prod(_1516797, _1516799), tc_HOL_Obool)), _1516805), _1516807)), _1516809) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1516803, tc_fun(tc_prod(_1516797, _1516801), tc_HOL_Obool)), _1516805), hAPP(hAPP(c_COMBC(_1516803, tc_fun(tc_prod(_1516799, _1516801), tc_HOL_Obool), tc_fun(tc_prod(_1516797, _1516801), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1516797, _1516799), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1516799, _1516801), tc_HOL_Obool), tc_fun(tc_prod(_1516797, _1516801), tc_HOL_Obool)), _1516803), c_Relation_Orel__comp(_1516797, _1516799, _1516801)), _1516807)), _1516809)))], (39679 ^ _773908) ^ [_1546022, _1546024, _1546026, _1546028] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1546022), tc_List_Olist(_1546022), c_List_Olistrel(_1546022, _1546024)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1546022)), hAPP(hAPP(c_List_Olist_OCons(_1546022), _1546026), _1546028)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1546022), tc_HOL_Obool)))) = c_List_Oset__Cons(_1546022, hAPP(c_Relation_OImage(_1546022, _1546022, _1546024), hAPP(hAPP(c_Set_Oinsert(_1546022), _1546026), c_Orderings_Obot__class_Obot(tc_fun(_1546022, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1546022), tc_List_Olist(_1546022), c_List_Olistrel(_1546022, _1546024)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1546022)), _1546028), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1546022), tc_HOL_Obool))))))], (22619 ^ _773908) ^ [_1166255, _1166257, _1166259, _1166261] : [class_Fields_Olinordered__field__inverse__zero(_1166255), class_Int_Onumber(_1166255), 22626 ^ _773908 : [(22627 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166255), _1166257), _1166259)), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261))), 22630 ^ _773908 : [(22637 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), _1166259))), 22640 ^ _773908 : [(22647 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), _1166259), c_Groups_Ozero__class_Ozero(_1166255)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261))))], (22641 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), _1166259), c_Groups_Ozero__class_Ozero(_1166255))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166255), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)), _1166259)), _1166257)))]]], (22631 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), _1166259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), _1166257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166255), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)), _1166259))))]]], (22653 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166255), _1166257), _1166259)), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)))), 22656 ^ _773908 : [(22659 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), _1166257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166255), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)), _1166259)))], (22657 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), _1166259)))]], 22660 ^ _773908 : [(22663 ^ _773908) ^ [] : [22664 ^ _773908 : [(22667 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166255), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)), _1166259)), _1166257))], (22665 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), _1166259), c_Groups_Ozero__class_Ozero(_1166255))))]], 22668 ^ _773908 : [(22671 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), hAPP(c_Int_Onumber__class_Onumber__of(_1166255), _1166261)))], (22669 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), _1166259), c_Groups_Ozero__class_Ozero(_1166255)))]]], (22661 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166255), c_Groups_Ozero__class_Ozero(_1166255)), _1166259))]]]]], (3194 ^ _773908) ^ [_821771, _821773, _821775, _821777, _821779, _821781, _821783, _821785] : [-(c_Enum_Oproduct(_821785, _821781, _821777, _821773) = c_Enum_Oproduct(_821783, _821779, _821775, _821771)), _821785 = _821783, _821781 = _821779, _821777 = _821775, _821773 = _821771], (40075 ^ _773908) ^ [_1557122, _1557124, _1557126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557122)), _1557124)), _1557126)), -(hAPP(hAPP(c_List_Otake(_1557122), _1557126), _1557124) = _1557124)], (7835 ^ _773908) ^ [_901877, _901879] : [class_Rings_Olinordered__semidom(_901877), 7838 ^ _773908 : [(7845 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901877), c_Groups_Ozero__class_Ozero(_901877)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_901877), _901879))))], (7839 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901877), c_Groups_Ozero__class_Ozero(_901877)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_901877), _901879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901879)))]]], (35458 ^ _773908) ^ [_1438636, _1438638, _1438640] : [class_Orderings_Olinorder(_1438636), 35461 ^ _773908 : [(35468 ^ _773908) ^ [] : [_1438638 = _1438640, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438636), _1438638) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438636), _1438640))], (35462 ^ _773908) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438636), _1438638) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1438636), _1438640), -(_1438638 = _1438640)]]], (33764 ^ _773908) ^ [_1401171, _1401173, _1401175] : [class_Orderings_Oorder(_1401171), 33767 ^ _773908 : [(33774 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401171), _1401173), _1401175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401171, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1401171), _1401173)), hAPP(c_SetInterval_Oord__class_OatMost(_1401171), _1401175))))], (33768 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401171, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1401171), _1401173)), hAPP(c_SetInterval_Oord__class_OatMost(_1401171), _1401175))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401171), _1401173), _1401175)))]]], (26739 ^ _773908) ^ [_1254875, _1254877] : [-(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), _1254875), _1254877)), 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), _1254877), _1254875)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (8195 ^ _773908) ^ [_908550, _908552, _908554, _908556] : [c_Com_Ocom_OAss(_908550, _908552) = c_Com_Ocom_OWhile(_908554, _908556)], (28488 ^ _773908) ^ [_1292325, _1292327, _1292329, _1292331, _1292333, _1292335, _1292337, _1292339] : [c_Finite__Set_Ofolding__image__simple(_1292325, _1292327, _1292329, _1292331, _1292333, _1292335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292327), _1292337)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292327), _1292339)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292327, tc_HOL_Obool)), _1292337), _1292339) = c_Orderings_Obot__class_Obot(tc_fun(_1292327, tc_HOL_Obool)), -(hAPP(_1292335, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292327, tc_HOL_Obool)), _1292337), _1292339)) = hAPP(hAPP(_1292329, hAPP(_1292335, _1292337)), hAPP(_1292335, _1292339)))], (28344 ^ _773908) ^ [_1288713, _1288715, _1288717, _1288719] : [hBOOL(hAPP(hAPP(c_member(_1288713), _1288715), _1288717)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288713, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1288713), _1288715), _1288719)), _1288717) = hAPP(hAPP(c_Set_Oinsert(_1288713), _1288715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288713, tc_HOL_Obool)), _1288719), _1288717)))], (25279 ^ _773908) ^ [_1220491, _1220493, _1220495, _1220497] : [class_Groups_Oordered__ab__group__add(_1220491), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220491), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220491), _1220493), _1220495)), _1220497) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220491), _1220493), _1220497)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220491), _1220495), _1220497)))], (44180 ^ _773908) ^ [_1654346, _1654348, _1654350, _1654352] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654346, tc_fun(_1654348, tc_HOL_Obool)), _1654350), _1654352) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654348, tc_HOL_Obool), hAPP(c_Set_Oimage(_1654346, tc_fun(_1654348, tc_HOL_Obool), _1654352), _1654350)))], (4054 ^ _773908) ^ [_835167, _835169] : [_835169 = _835167, -(c_Rings_Oinverse__class_Odivide(_835169) = c_Rings_Oinverse__class_Odivide(_835167))], (39757 ^ _773908) ^ [_1548681, _1548683, _1548685, _1548687, _1548689] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1548681), tc_List_Olist(_1548681))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1548681), tc_List_Olist(_1548681)), hAPP(hAPP(c_List_Olist_OCons(_1548681), _1548683), _1548685)), _1548687)), c_List_Olistrel(_1548681, _1548689))), 39762 ^ _773908 : [(39767 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1548681), tc_List_Olist(_1548681))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1548681), tc_List_Olist(_1548681)), _1548685), 39761 ^ [_1548681, _1548683, _1548685, _1548687, _1548689])), c_List_Olistrel(_1548681, _1548689))))], (39765 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548681, _1548681)), hAPP(hAPP(c_Product__Type_OPair(_1548681, _1548681), _1548683), 39760 ^ [_1548681, _1548683, _1548685, _1548687, _1548689])), _1548689)))], (39763 ^ _773908) ^ [] : [-(_1548687 = hAPP(hAPP(c_List_Olist_OCons(_1548681), 39760 ^ [_1548681, _1548683, _1548685, _1548687, _1548689]), 39761 ^ [_1548681, _1548683, _1548685, _1548687, _1548689]))]]], (29937 ^ _773908) ^ [_1320344, _1320346, _1320348] : [class_Orderings_Olinorder(_1320344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320344), _1320346)), 29944 ^ _773908 : [(29951 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320344, tc_HOL_Obool)), _1320346), hAPP(hAPP(c_Set_Oinsert(_1320344), _1320348), c_Orderings_Obot__class_Obot(tc_fun(_1320344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320344, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1320344, c_Orderings_Oord__class_Omax(_1320344), hAPP(hAPP(c_Set_Oinsert(_1320344), _1320348), _1320346)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320344), _1320348), c_Big__Operators_Olattice_OSup__fin(_1320344, c_Orderings_Oord__class_Omax(_1320344), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320344, tc_HOL_Obool)), _1320346), hAPP(hAPP(c_Set_Oinsert(_1320344), _1320348), c_Orderings_Obot__class_Obot(tc_fun(_1320344, tc_HOL_Obool)))))))], (29945 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320344, tc_HOL_Obool)), _1320346), hAPP(hAPP(c_Set_Oinsert(_1320344), _1320348), c_Orderings_Obot__class_Obot(tc_fun(_1320344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320344, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1320344, c_Orderings_Oord__class_Omax(_1320344), hAPP(hAPP(c_Set_Oinsert(_1320344), _1320348), _1320346)) = _1320348)]]], (9979 ^ _773908) ^ [_939879, _939881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939879), _939881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _939881), _939879)), -(_939879 = _939881)], (1254 ^ _773908) ^ [_792569, _792571] : [-(class_Rings_Oordered__ring(_792569)), _792571 = _792569, class_Rings_Oordered__ring(_792571)], (26528 ^ _773908) ^ [_1249375, _1249377, _1249379, _1249381] : [_1249381 = c_Orderings_Obot__class_Obot(tc_fun(_1249377, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1249375, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1249377, _1249375, _1249379), _1249381))], (43913 ^ _773908) ^ [_1647797, _1647799, _1647801, _1647803] : [43914 ^ _773908 : [(43915 ^ _773908) ^ [_1647872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1647797, _1647801)), hAPP(hAPP(c_Product__Type_OPair(_1647797, _1647801), _1647799), _1647872)), _1647803))]], -(hBOOL(hAPP(hAPP(c_member(_1647797), _1647799), hAPP(c_Relation_ODomain(_1647797, _1647801), _1647803))))], (39055 ^ _773908) ^ [_1529303, _1529305, _1529307] : [_1529307 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529303, _1529305), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1529303, _1529305), _1529307) = c_Orderings_Obot__class_Obot(tc_fun(_1529305, tc_HOL_Obool)))], (50086 ^ _773908) ^ [_1786300, _1786302] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1786300, tc_HOL_Obool), _1786302) = hAPP(c_Set_OCollect(_1786300), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786300, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1786300), c_HOL_OEx(tc_fun(_1786300, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786300, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1786300, tc_HOL_Obool), tc_HOL_Obool), _1786300), hAPP(c_COMBS(tc_fun(_1786300, 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(_1786300, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1786300, tc_HOL_Obool), tc_fun(tc_fun(_1786300, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1786300, tc_HOL_Obool))), _1786302)))), c_member(_1786300)))))], (25677 ^ _773908) ^ [] : [-(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)))], (29565 ^ _773908) ^ [_1313674, _1313676, _1313678] : [class_Orderings_Olinorder(_1313674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313674, tc_HOL_Obool)), _1313676), _1313678)), -(_1313676 = c_Orderings_Obot__class_Obot(tc_fun(_1313674, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313674), _1313678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313674), c_Big__Operators_Olinorder__class_OMin(_1313674, _1313678)), c_Big__Operators_Olinorder__class_OMin(_1313674, _1313676))))], (4106 ^ _773908) ^ [_835941, _835943, _835945, _835947] : [-(c_Nitpick_Ouminus__frac(_835947, _835943) = c_Nitpick_Ouminus__frac(_835945, _835941)), _835947 = _835945, _835943 = _835941], (3156 ^ _773908) ^ [_821218, _821220] : [_821220 = _821218, -(c_Code__Numeral_OSuc__code__numeral(_821220) = c_Code__Numeral_OSuc__code__numeral(_821218))], (14857 ^ _773908) ^ [_1024978, _1024980, _1024982] : [-(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), _1024978), _1024980)), _1024980)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024978, _1024980))), _1024982) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024978), _1024982))], (22825 ^ _773908) ^ [_1169946, _1169948] : [-(c_FunDef_Ois__measure(_1169946, _1169948))], (39873 ^ _773908) ^ [_1551686, _1551688] : [-(c_List_Olist_Olist__size(_1551686, _1551688, c_List_Olist_ONil(_1551686)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5877 ^ _773908) ^ [_867862, _867864, _867866, _867868] : [-(hAPP(hAPP(c_Set_Oinsert(_867862), _867864), hAPP(hAPP(c_Set_Oinsert(_867862), _867866), _867868)) = hAPP(hAPP(c_Set_Oinsert(_867862), _867866), hAPP(hAPP(c_Set_Oinsert(_867862), _867864), _867868)))], (25373 ^ _773908) ^ [_1222197, _1222199, _1222201] : [class_Orderings_Olinorder(_1222197), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222197), _1222199), _1222201) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222197), _1222201), _1222199))], (46241 ^ _773908) ^ [_1698808, _1698810, _1698812, _1698814, _1698816, _1698818, _1698820, _1698822] : [46243 ^ _773908 : [(46246 ^ _773908) ^ [] : [hAPP(c_Fun_Ocomp(_1698812, _1698812, _1698814, hAPP(_1698816, 46242 ^ [_1698808, _1698810, _1698812, _1698814, _1698816, _1698818, _1698820, _1698822])), _1698818) = hAPP(c_Fun_Ocomp(_1698814, _1698812, _1698814, _1698818), hAPP(_1698820, 46242 ^ [_1698808, _1698810, _1698812, _1698814, _1698816, _1698818, _1698820, _1698822]))], (46244 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1698808), 46242 ^ [_1698808, _1698810, _1698812, _1698814, _1698816, _1698818, _1698820, _1698822]), hAPP(c_List_Oset(_1698808), _1698810))))]], -(hAPP(c_List_Ofoldl(_1698812, _1698808, hAPP(c_COMBC(_1698808, _1698812, _1698812), _1698816), hAPP(_1698818, _1698822)), _1698810) = hAPP(_1698818, hAPP(c_List_Ofoldl(_1698814, _1698808, hAPP(c_COMBC(_1698808, _1698814, _1698814), _1698820), _1698822), _1698810)))], (18673 ^ _773908) ^ [_1096676, _1096678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096676), _1096678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1096676)), _1096678)))], (46439 ^ _773908) ^ [_1702806, _1702808] : [c_Nitpick_Owf_H(_1702806, _1702808), 46442 ^ _773908 : [(46445 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1702806, _1702806)), _1702808))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (46443 ^ _773908) ^ [] : [-(c_Wellfounded_Oacyclic(_1702806, _1702808))]]], (30117 ^ _773908) ^ [_1324076, _1324078] : [class_Orderings_Olinorder(_1324076), -(c_Big__Operators_Olattice_OInf__fin(_1324076, c_Orderings_Oord__class_Omin(_1324076), hAPP(hAPP(c_Set_Oinsert(_1324076), _1324078), c_Orderings_Obot__class_Obot(tc_fun(_1324076, tc_HOL_Obool)))) = _1324078)], (17861 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (14611 ^ _773908) ^ [_1020922, _1020924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020922)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020924), _1020922)), _1020922) = _1020924)], (18402 ^ _773908) ^ [_1091565, _1091567] : [_1091567 = c_Orderings_Obot__class_Obot(tc_fun(_1091565, tc_HOL_Obool)), 18405 ^ _773908 : [(18406 ^ _773908) ^ [_1091645] : [hBOOL(hAPP(hAPP(c_member(_1091565), _1091645), _1091567))]]], (36135 ^ _773908) ^ [_1452205, _1452207, _1452209, _1452211] : [c_Fun_Oinj__on(_1452205, _1452207, _1452209, c_Orderings_Otop__class_Otop(tc_fun(_1452205, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1452205, _1452207, c_Orderings_Otop__class_Otop(tc_fun(_1452205, tc_HOL_Obool)), _1452209), hAPP(_1452209, _1452211)) = _1452211)], (48099 ^ _773908) ^ [_1743121, _1743123, _1743125] : [hBOOL(hAPP(hAPP(c_member(_1743121), _1743123), hAPP(c_List_Oset(_1743121), _1743125))), 48104 ^ _773908 : [(48107 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1743121), _1743123), hAPP(c_List_Oset(_1743121), 48102 ^ [_1743121, _1743123, _1743125])))], (48105 ^ _773908) ^ [] : [-(_1743125 = hAPP(hAPP(c_List_Oappend(_1743121), 48102 ^ [_1743121, _1743123, _1743125]), hAPP(hAPP(c_List_Olist_OCons(_1743121), _1743123), 48103 ^ [_1743121, _1743123, _1743125])))]]], (41035 ^ _773908) ^ [_1582246, _1582248, _1582250] : [-(hAPP(c_List_Otl(_1582246), hAPP(hAPP(c_List_Odrop(_1582246), _1582248), _1582250)) = hAPP(hAPP(c_List_Odrop(_1582246), _1582248), hAPP(c_List_Otl(_1582246), _1582250)))], (49274 ^ _773908) ^ [_1767730, _1767732, _1767734, _1767736, _1767738] : [-(_1767730 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1767732, _1767734, _1767736, _1767738), _1767730) = c_Lazy__Sequence_Ohb__bind(_1767732, _1767734, hAPP(_1767736, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1767730), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1767732, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1767734))), _1767738), _1767730)))], (42999 ^ _773908) ^ [_1627239, _1627241] : [-(c_List_Oremove1(_1627239, _1627241, c_List_Olist_ONil(_1627239)) = c_List_Olist_ONil(_1627239))], (2710 ^ _773908) ^ [_814175, _814177, _814179, _814181, _814183, _814185, _814187, _814189] : [-(c_Sum__Type_OPlus(_814189, _814185, _814181, _814177) = c_Sum__Type_OPlus(_814187, _814183, _814179, _814175)), _814189 = _814187, _814185 = _814183, _814181 = _814179, _814177 = _814175], (28130 ^ _773908) ^ [_1283621, _1283623, _1283625] : [class_Lattices_Olattice(_1283621), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283621), _1283623), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283621), _1283623), _1283625)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1283621), _1283623), _1283625))], (17105 ^ _773908) ^ [_1068782, _1068784, _1068786] : [class_Int_Onumber__ring(_1068782), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068782), hAPP(c_Int_Onumber__class_Onumber__of(_1068782), _1068784)), hAPP(c_Int_Onumber__class_Onumber__of(_1068782), _1068786)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068784), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068786))))], (41306 ^ _773908) ^ [_1587841, _1587843] : [-(c_List_Orotate(_1587841, _1587843) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1587841), tc_List_Olist(_1587841)), _1587843), c_List_Orotate1(_1587841)))], (17733 ^ _773908) ^ [_1080274, _1080276, _1080278] : [class_Rings_Oring__1(_1080274), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1080274), hAPP(c_Groups_Ouminus__class_Ouminus(_1080274), _1080276)), _1080278) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080274), hAPP(hAPP(c_Power_Opower__class_Opower(_1080274), hAPP(c_Groups_Ouminus__class_Ouminus(_1080274), c_Groups_Oone__class_Oone(_1080274))), _1080278)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080274), _1080276), _1080278)))], (26578 ^ _773908) ^ [_1250464, _1250466, _1250468, _1250470, _1250472] : [-(hAPP(c_Relation_OImage(_1250464, _1250466, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1250464, _1250466), tc_HOL_Obool)), _1250468), _1250470)), _1250472) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250466, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1250464, _1250466, _1250468), _1250472)), hAPP(c_Relation_OImage(_1250464, _1250466, _1250470), _1250472)))], (26359 ^ _773908) ^ [_1244764, _1244766, _1244768, _1244770] : [c_Wellfounded_Omax__extp(_1244764, hAPP(hAPP(c_COMBC(_1244764, tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_fun(_1244764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1244764, tc_fun(tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_fun(_1244764, tc_HOL_Obool)), _1244764), c_COMBC(_1244764, tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1244764, tc_prod(_1244764, _1244764)), tc_fun(_1244764, tc_fun(tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_HOL_Obool)), _1244764), hAPP(c_COMBB(tc_prod(_1244764, _1244764), tc_fun(tc_fun(tc_prod(_1244764, _1244764), tc_HOL_Obool), tc_HOL_Obool), _1244764), c_member(tc_prod(_1244764, _1244764)))), c_Product__Type_OPair(_1244764, _1244764)))), _1244766), _1244768, _1244770), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1244764, tc_HOL_Obool), tc_fun(_1244764, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1244764, tc_HOL_Obool), tc_fun(_1244764, tc_HOL_Obool)), _1244768), _1244770)), c_Wellfounded_Omax__ext(_1244764, _1244766))))], (22003 ^ _773908) ^ [_1154554, _1154556, _1154558] : [class_Fields_Olinordered__field(_1154554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154554), _1154556), _1154558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154554), _1154556), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154554), _1154556), _1154558)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154554), c_Groups_Oone__class_Oone(_1154554)), c_Groups_Oone__class_Oone(_1154554))))))], (40013 ^ _773908) ^ [_1555333, _1555335, _1555337, _1555339] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1555333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1555335), hAPP(hAPP(c_List_Olist_OCons(_1555335), _1555337), _1555339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1555333)) = _1555337)], (41083 ^ _773908) ^ [_1583146, _1583148, _1583150] : [hBOOL(hAPP(c_List_Odistinct(_1583146), hAPP(hAPP(c_List_Olist_OCons(_1583146), _1583148), _1583150))), 41086 ^ _773908 : [(41089 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1583146), _1583150)))], (41087 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1583146), _1583148), hAPP(c_List_Oset(_1583146), _1583150)))]]], (20185 ^ _773908) ^ [_1122315, _1122317] : [class_Int_Onumber__ring(_1122315), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122315), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122315), c_Groups_Oone__class_Oone(_1122315)), c_Groups_Oone__class_Oone(_1122315))), hAPP(c_Int_Onumber__class_Onumber__of(_1122315), _1122317)) = hAPP(c_Int_Onumber__class_Onumber__of(_1122315), c_Int_OBit0(_1122317)))], (28200 ^ _773908) ^ [_1284984, _1284986] : [c_Nat__Transfer_Onat__set(_1284984), c_Nat__Transfer_Onat__set(_1284986), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1284984), _1284986)))], (16307 ^ _773908) ^ [_1053421, _1053423, _1053425] : [16309 ^ _773908 : [(16314 ^ _773908) ^ [] : [hBOOL(hAPP(_1053423, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16308 ^ [_1053421, _1053423, _1053425]), _1053421)))], (16312 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1053423, 16308 ^ [_1053421, _1053423, _1053425])))], (16310 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16308 ^ [_1053421, _1053423, _1053425]), _1053421)))]], hBOOL(hAPP(_1053423, _1053425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053425), _1053421)), -(hBOOL(hAPP(_1053423, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25037 ^ _773908) ^ [_1215593, _1215595] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1215593), hAPP(c_Nat_OSuc, _1215595)) = 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)), _1215595)), _1215593))], (9995 ^ _773908) ^ [_940124] : [class_Rings_Olinordered__semidom(_940124), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940124), c_Groups_Ozero__class_Ozero(_940124)), c_Groups_Oone__class_Oone(_940124))))], (24573 ^ _773908) ^ [_1206766, _1206768, _1206770] : [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), _1206766), _1206768))), -(hBOOL(hAPP(hAPP(_1206770, _1206766), _1206768))), 24580 ^ _773908 : [(24583 ^ _773908) ^ [] : [-(24579 ^ [_1206766, _1206768, _1206770] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1206770, 24579 ^ [_1206766, _1206768, _1206770]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 24578 ^ [_1206766, _1206768, _1206770], 24579 ^ [_1206766, _1206768, _1206770]))))], (24589 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1206770, 24578 ^ [_1206766, _1206768, _1206770]), 24579 ^ [_1206766, _1206768, _1206770]))], (24581 ^ _773908) ^ [] : [-(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), 24578 ^ [_1206766, _1206768, _1206770]), 24579 ^ [_1206766, _1206768, _1206770]))))]]], (28432 ^ _773908) ^ [_1290989, _1290991, _1290993] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290989, tc_HOL_Obool)), _1290991), _1290993) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290989, tc_HOL_Obool)), _1290991), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290989, tc_HOL_Obool)), _1290993)))], (3396 ^ _773908) ^ [_824898, _824900, _824902, _824904, _824906, _824908] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_824908, _824904, _824900) = c_SetInterval_Oord__class_OgreaterThanAtMost(_824906, _824902, _824898)), _824908 = _824906, _824904 = _824902, _824900 = _824898], (26677 ^ _773908) ^ [_1253695, _1253697, _1253699, _1253701, _1253703, _1253705, _1253707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1253695, _1253697)), hAPP(hAPP(c_Product__Type_OPair(_1253695, _1253697), _1253699), _1253701)), _1253703)), -(hBOOL(hAPP(hAPP(c_member(_1253705), hAPP(hAPP(_1253707, _1253699), _1253701)), hAPP(c_Set_Oimage(tc_prod(_1253695, _1253697), _1253705, hAPP(c_Product__Type_Oprod_Oprod__case(_1253695, _1253697, _1253705), _1253707)), _1253703))))], (5250 ^ _773908) ^ [_854177, _854179, _854181, _854183] : [-(c_Transitive__Closure_Otrancl(_854183, _854179) = c_Transitive__Closure_Otrancl(_854181, _854177)), _854183 = _854181, _854179 = _854177], (26866 ^ _773908) ^ [_1257958, _1257960] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1257958, _1257958), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257960) = c_Relation_OId(_1257958))], (45601 ^ _773908) ^ [_1684957, _1684959, _1684961] : [-(hAPP(c_List_Orev(_1684957), hAPP(hAPP(c_List_Olist_OCons(_1684957), _1684959), _1684961)) = hAPP(hAPP(c_List_Oappend(_1684957), hAPP(c_List_Orev(_1684957), _1684961)), hAPP(hAPP(c_List_Olist_OCons(_1684957), _1684959), c_List_Olist_ONil(_1684957))))], (23682 ^ _773908) ^ [_1187153, _1187155, _1187157, _1187159, _1187161, _1187163] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1187153, _1187153)), hAPP(hAPP(c_Product__Type_OPair(_1187153, _1187153), _1187155), _1187157)), _1187159)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1187153, _1187153)), hAPP(hAPP(c_Product__Type_OPair(_1187153, _1187153), _1187157), _1187161)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1187153, _1187153), tc_HOL_Obool), _1187163), _1187159))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1187153, _1187153)), hAPP(hAPP(c_Product__Type_OPair(_1187153, _1187153), _1187155), _1187161)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1187153, _1187153), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1187163)), _1187159))))], (17255 ^ _773908) ^ [_1071684, _1071686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071684), _1071686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071686))))], (47281 ^ _773908) ^ [_1723656, _1723658, _1723660, _1723662] : [-(hAPP(c_Relation_Oconverse(_1723656, _1723656), hAPP(hAPP(c_Relation_Oinv__image(_1723658, _1723656), _1723660), _1723662)) = hAPP(hAPP(c_Relation_Oinv__image(_1723658, _1723656), hAPP(c_Relation_Oconverse(_1723658, _1723658), _1723660)), _1723662))], (19425 ^ _773908) ^ [_1109242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1109242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1109242))))], (31868 ^ _773908) ^ [_1363369, _1363371, _1363373, _1363375, _1363377] : [_1363369 = c_Orderings_Obot__class_Obot(tc_fun(_1363371, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363371, tc_fun(_1363373, tc_HOL_Obool)), _1363369), hAPP(hAPP(c_COMBC(_1363371, tc_fun(_1363373, tc_HOL_Obool), tc_fun(_1363373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363373, tc_HOL_Obool), tc_fun(tc_fun(_1363373, tc_HOL_Obool), tc_fun(_1363373, tc_HOL_Obool)), _1363371), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363373, tc_HOL_Obool))), _1363375)), _1363377)) = c_Orderings_Obot__class_Obot(tc_fun(_1363373, tc_HOL_Obool)))], (8197 ^ _773908) ^ [_908606, _908608, _908610, _908612, _908614] : [c_Com_Ocom_OCall(_908606, _908608, _908610) = c_Com_Ocom_OWhile(_908612, _908614)], (22799 ^ _773908) ^ [] : [-(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))], (37478 ^ _773908) ^ [_1482992, _1482994, _1482996, _1482998, _1483000, _1483002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482992, _1482994)), hAPP(hAPP(c_Product__Type_OPair(_1482992, _1482994), _1482996), _1482998)), hAPP(hAPP(c_Product__Type_OSigma(_1482992, _1482994), _1483000), _1483002))), 37481 ^ _773908 : [(37484 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482994), _1482998), hAPP(_1483002, _1482996))))], (37482 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482992), _1482996), _1483000)))]]], (18541 ^ _773908) ^ [_1094193, _1094195, _1094197] : [hBOOL(hAPP(hAPP(c_member(_1094193), _1094195), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1094193, tc_HOL_Obool)), _1094197))), hBOOL(hAPP(hAPP(c_member(_1094193), _1094195), _1094197))], (51532 ^ _773908) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (35959 ^ _773908) ^ [_1448629, _1448631, _1448633, _1448635, _1448637, _1448639] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1448629, _1448631, _1448633, _1448635, _1448637), _1448639)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448629), _1448637)))], (49098 ^ _773908) ^ [_1764044, _1764046, _1764048] : [c_List_Olist__all(_1764044, _1764046, hAPP(c_List_Orev(_1764044), _1764048)), -(c_List_Olist__all(_1764044, _1764046, _1764048))], (16927 ^ _773908) ^ [_1065176, _1065178, _1065180, _1065182] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065176, tc_HOL_Obool)), _1065178), hAPP(hAPP(c_Set_Oinsert(_1065176), _1065180), _1065182)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065176, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065176, tc_HOL_Obool)), _1065178), _1065182)), hAPP(hAPP(c_Set_Oinsert(_1065176), _1065180), c_Orderings_Obot__class_Obot(tc_fun(_1065176, tc_HOL_Obool)))))], (31800 ^ _773908) ^ [_1361673, _1361675, _1361677, _1361679, _1361681, _1361683] : [hBOOL(hAPP(hAPP(c_member(_1361673), _1361675), _1361677)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361673, tc_fun(_1361679, tc_HOL_Obool)), _1361677), hAPP(hAPP(c_COMBB(tc_fun(_1361679, tc_HOL_Obool), tc_fun(_1361679, tc_HOL_Obool), _1361673), hAPP(c_Set_Oinsert(_1361679), _1361681)), _1361683)) = hAPP(hAPP(c_Set_Oinsert(_1361679), _1361681), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361673, tc_fun(_1361679, tc_HOL_Obool)), _1361677), _1361683)))], (41649 ^ _773908) ^ [_1594379, _1594381, _1594383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1594379), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1594381))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1594381), _1594379), _1594383)) = 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), _1594381)), _1594383)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1594381), _1594379)))], (40529 ^ _773908) ^ [_1568036, _1568038, _1568040] : [-(_1568036 = c_List_Olist_ONil(_1568038)), -(hAPP(c_List_Ohd(_1568038), hAPP(hAPP(c_List_Oappend(_1568038), _1568036), _1568040)) = hAPP(c_List_Ohd(_1568038), _1568036))], (37782 ^ _773908) ^ [_1491633, _1491635, _1491637, _1491639, _1491641] : [c_Relation_Orefl__on(_1491633, _1491635, _1491637), c_Relation_Orefl__on(_1491633, _1491639, _1491641), -(c_Relation_Orefl__on(_1491633, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491633, tc_HOL_Obool)), _1491635), _1491639), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491633, _1491633), tc_HOL_Obool)), _1491637), _1491641)))], (8436 ^ _773908) ^ [_912959, _912961] : [hBOOL(hAPP(_912959, hAPP(c_Int_Onat, _912961))), 8439 ^ _773908 : [(8446 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912961), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_912959, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8440 ^ _773908) ^ [_913059] : [_912961 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913059), -(hBOOL(hAPP(_912959, _913059)))]]], (20803 ^ _773908) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8699 ^ _773908) ^ [_917952, _917954, _917956, _917958] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_917952, _917954), tc_fun(_917952, _917954)), _917956), c_Fun_Ocomp(_917954, _917954, _917952, _917958)) = c_Fun_Ocomp(_917954, _917954, _917952, hAPP(hAPP(c_Nat_Ocompow(_917954, _917954), _917956), _917958)))], (24471 ^ _773908) ^ [_1203704, _1203706, _1203708, _1203710, _1203712, _1203714] : [hBOOL(hAPP(hAPP(_1203704, _1203706), _1203708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203710, tc_fun(_1203712, tc_HOL_Obool))), _1203704), _1203714)), -(hBOOL(hAPP(hAPP(_1203714, _1203706), _1203708)))], (51065 ^ _773908) ^ [_1807662, _1807664] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807662), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1807664, hAPP(c_Code__Numeral_Onat__of, 51070 ^ [_1807662, _1807664]))), -(hBOOL(hAPP(_1807664, _1807662)))], (40153 ^ _773908) ^ [_1558905, _1558907, _1558909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558905), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558907)), _1558909))), -(_1558909 = hAPP(hAPP(c_List_Oappend(_1558907), hAPP(hAPP(c_List_Otake(_1558907), _1558905), _1558909)), hAPP(hAPP(c_List_Olist_OCons(_1558907), hAPP(hAPP(c_List_Onth(_1558907), _1558909), _1558905)), hAPP(hAPP(c_List_Odrop(_1558907), hAPP(c_Nat_OSuc, _1558905)), _1558909))))], (23769 ^ _773908) ^ [_1189238, _1189240, _1189242, _1189244, _1189246, _1189248, _1189250] : [-(hAPP(c_Product__Type_Oapsnd(_1189238, _1189240, _1189242, _1189244), hAPP(c_Product__Type_Oapsnd(_1189246, _1189238, _1189242, _1189248), _1189250)) = hAPP(c_Product__Type_Oapsnd(_1189246, _1189240, _1189242, hAPP(c_Fun_Ocomp(_1189238, _1189240, _1189246, _1189244), _1189248)), _1189250))], (29407 ^ _773908) ^ [_1310610, _1310612, _1310614] : [class_Orderings_Olinorder(_1310610), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310610), _1310612)), -(_1310612 = c_Orderings_Obot__class_Obot(tc_fun(_1310610, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310610), _1310614)), -(_1310614 = c_Orderings_Obot__class_Obot(tc_fun(_1310610, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310610, tc_HOL_Obool)), _1310612), _1310614) = c_Orderings_Obot__class_Obot(tc_fun(_1310610, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1310610, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310610, tc_HOL_Obool)), _1310612), _1310614)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310610), c_Big__Operators_Olinorder__class_OMax(_1310610, _1310612)), c_Big__Operators_Olinorder__class_OMax(_1310610, _1310614)))], (44720 ^ _773908) ^ [_1667551, _1667553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667551), _1667553)), -(c_List_Oupt(_1667553, _1667551) = c_List_Olist_ONil(tc_Nat_Onat))], (46299 ^ _773908) ^ [_1700015, _1700017] : [c_Wellfounded_OwfP(_1700015, hAPP(hAPP(c_COMBC(_1700015, tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_fun(_1700015, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700015, tc_fun(tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_fun(_1700015, tc_HOL_Obool)), _1700015), c_COMBC(_1700015, tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700015, tc_prod(_1700015, _1700015)), tc_fun(_1700015, tc_fun(tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_HOL_Obool)), _1700015), hAPP(c_COMBB(tc_prod(_1700015, _1700015), tc_fun(tc_fun(tc_prod(_1700015, _1700015), tc_HOL_Obool), tc_HOL_Obool), _1700015), c_member(tc_prod(_1700015, _1700015)))), c_Product__Type_OPair(_1700015, _1700015)))), _1700017)), -(c_Wellfounded_Owf(_1700015, _1700017))], (7403 ^ _773908) ^ [_893649, _893651] : [class_Rings_Olinordered__idom(_893649), 7406 ^ _773908 : [(7413 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893649), _893651), c_Groups_Ozero__class_Ozero(_893649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893649), _893651), _893651)), c_Groups_Ozero__class_Ozero(_893649))))], (7407 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893649), _893651), _893651)), c_Groups_Ozero__class_Ozero(_893649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893649), _893651), c_Groups_Ozero__class_Ozero(_893649))))]]], (45491 ^ _773908) ^ [_1682595, _1682597, _1682599] : [hAPP(c_List_Orev(_1682595), _1682597) = _1682599, -(_1682597 = hAPP(c_List_Orev(_1682595), _1682599))], (39769 ^ _773908) ^ [_1549070, _1549072, _1549074, _1549076, _1549078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1549070), tc_List_Olist(_1549070))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1549070), tc_List_Olist(_1549070)), _1549072), hAPP(hAPP(c_List_Olist_OCons(_1549070), _1549074), _1549076))), c_List_Olistrel(_1549070, _1549078))), 39774 ^ _773908 : [(39779 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1549070), tc_List_Olist(_1549070))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1549070), tc_List_Olist(_1549070)), 39773 ^ [_1549070, _1549072, _1549074, _1549076, _1549078]), _1549076)), c_List_Olistrel(_1549070, _1549078))))], (39777 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549070, _1549070)), hAPP(hAPP(c_Product__Type_OPair(_1549070, _1549070), 39772 ^ [_1549070, _1549072, _1549074, _1549076, _1549078]), _1549074)), _1549078)))], (39775 ^ _773908) ^ [] : [-(_1549072 = hAPP(hAPP(c_List_Olist_OCons(_1549070), 39772 ^ [_1549070, _1549072, _1549074, _1549076, _1549078]), 39773 ^ [_1549070, _1549072, _1549074, _1549076, _1549078]))]]], (36651 ^ _773908) ^ [_1464306, _1464308, _1464310, _1464312, _1464314] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1464306, _1464308, hAPP(hAPP(c_Set_Oinsert(_1464306), _1464310), _1464312)), _1464314)), 36656 ^ _773908 : [(36661 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464306), 36654 ^ [_1464306, _1464308, _1464310, _1464312, _1464314]), 36655 ^ [_1464306, _1464308, _1464310, _1464312, _1464314]))], (36659 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1464306, _1464306, _1464308, 36654 ^ [_1464306, _1464308, _1464310, _1464312, _1464314], 36655 ^ [_1464306, _1464308, _1464310, _1464312, _1464314]), _1464314)))], (36657 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1464306), _1464310), _1464312) = hAPP(hAPP(c_Set_Oinsert(_1464306), 36654 ^ [_1464306, _1464308, _1464310, _1464312, _1464314]), 36655 ^ [_1464306, _1464308, _1464310, _1464312, _1464314]))]]], (29767 ^ _773908) ^ [_1317227, _1317229, _1317231, _1317233, _1317235, _1317237] : [c_Finite__Set_Ofolding__idem(_1317227, _1317229, _1317231, _1317233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317227), _1317235)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317227), _1317237)), -(hAPP(_1317233, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317227, tc_HOL_Obool)), _1317235), _1317237)) = hAPP(c_Fun_Ocomp(_1317229, _1317229, _1317229, hAPP(_1317233, _1317235)), hAPP(_1317233, _1317237)))], (7695 ^ _773908) ^ [_898835, _898837, _898839, _898841, _898843] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_898835, _898837, _898839)), _898841), _898843))), 7696 ^ _773908 : [(7703 ^ _773908) ^ [] : [-(hBOOL(hAPP(_898835, _898841))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898839), _898841), _898843))], (7697 ^ _773908) ^ [] : [hBOOL(hAPP(_898835, _898841)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898837), _898841), _898843))]]], (34928 ^ _773908) ^ [_1426372, _1426374, _1426376, _1426378] : [class_Groups_Ocomm__monoid__add(_1426372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1426374), _1426376)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1426372), _1426378), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1426374, _1426376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426372), hAPP(_1426378, _1426374)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1426372), _1426378), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1426374), _1426376))))], (29957 ^ _773908) ^ [_1320832, _1320834, _1320836] : [class_Orderings_Olinorder(_1320832), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320832), _1320834)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320832), _1320836)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320832, tc_HOL_Obool)), _1320834), _1320836) = c_Orderings_Obot__class_Obot(tc_fun(_1320832, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320832), c_Big__Operators_Olattice_OSup__fin(_1320832, c_Orderings_Oord__class_Omax(_1320832), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320832, tc_HOL_Obool)), _1320834), _1320836))), c_Big__Operators_Olattice_OSup__fin(_1320832, c_Orderings_Oord__class_Omax(_1320832), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320832, tc_HOL_Obool)), _1320834), _1320836))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320832), c_Big__Operators_Olattice_OSup__fin(_1320832, c_Orderings_Oord__class_Omax(_1320832), _1320834)), c_Big__Operators_Olattice_OSup__fin(_1320832, c_Orderings_Oord__class_Omax(_1320832), _1320836)))], (1434 ^ _773908) ^ [_794819, _794821] : [-(class_Lattices_Odistrib__lattice(_794819)), _794821 = _794819, class_Lattices_Odistrib__lattice(_794821)], (4302 ^ _773908) ^ [_839267, _839269] : [_839269 = _839267, -(c_New__DSequence_Opos__empty(_839269) = c_New__DSequence_Opos__empty(_839267))], (49454 ^ _773908) ^ [_1772254, _1772256, _1772258, _1772260] : [-(hBOOL(hAPP(_1772254, _1772256))), -(hAPP(c_List_Ofilter(_1772258, _1772254), c_List_Oreplicate(_1772258, _1772260, _1772256)) = c_List_Olist_ONil(_1772258))], (48989 ^ _773908) ^ [_1761849, _1761851, _1761853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1761849), c_Nitpick_Oplus__frac(_1761849, _1761851, c_Nitpick_Ouminus__frac(_1761849, _1761853)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1761849, _1761851, _1761853))], (30103 ^ _773908) ^ [_1323829, _1323831, _1323833] : [class_Orderings_Olinorder(_1323829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323829), _1323831)), hBOOL(hAPP(hAPP(c_member(_1323829), _1323833), _1323831)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323829), _1323833), c_Big__Operators_Olattice_OInf__fin(_1323829, c_Orderings_Oord__class_Omin(_1323829), _1323831)) = c_Big__Operators_Olattice_OInf__fin(_1323829, c_Orderings_Oord__class_Omin(_1323829), _1323831))], (49326 ^ _773908) ^ [_1769114, _1769116, _1769118] : [-(c_List_Osplice(_1769114, hAPP(hAPP(c_List_Olist_OCons(_1769114), _1769116), _1769118), c_List_Olist_ONil(_1769114)) = hAPP(hAPP(c_List_Olist_OCons(_1769114), _1769116), _1769118))], (49572 ^ _773908) ^ [_1774376, _1774378, _1774380, _1774382] : [-(hAPP(hAPP(c_List_Oappend(_1774376), c_List_Oreplicate(_1774376, _1774378, _1774380)), hAPP(hAPP(c_List_Olist_OCons(_1774376), _1774380), _1774382)) = hAPP(hAPP(c_List_Olist_OCons(_1774376), _1774380), hAPP(hAPP(c_List_Oappend(_1774376), c_List_Oreplicate(_1774376, _1774378, _1774380)), _1774382)))], (38054 ^ _773908) ^ [_1497437, _1497439, _1497441, _1497443] : [hBOOL(hAPP(hAPP(c_member(_1497437), _1497439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497437, tc_HOL_Obool)), _1497441), hAPP(c_Set_OCollect(_1497437), _1497443)))), 38057 ^ _773908 : [(38060 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1497443, _1497439)))], (38058 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497437), _1497439), _1497441)))]]], (23961 ^ _773908) ^ [_1192735, _1192737, _1192739] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192735, _1192735), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192737), _1192739))), -(_1192735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1192737 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18971 ^ _773908) ^ [_1101660, _1101662, _1101664] : [class_Rings_Oring__1(_1101660), hBOOL(hAPP(hAPP(c_member(_1101660), _1101662), c_Int_Oring__1__class_OInts(_1101660))), hBOOL(hAPP(hAPP(c_member(_1101660), _1101664), c_Int_Oring__1__class_OInts(_1101660))), -(hBOOL(hAPP(hAPP(c_member(_1101660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101660), _1101662), _1101664)), c_Int_Oring__1__class_OInts(_1101660))))], (17991 ^ _773908) ^ [_1084249] : [class_Int_Onumber__ring(_1084249), -(hAPP(c_Int_Oring__1__class_Oof__int(_1084249), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1084249), c_Int_OMin))], (18137 ^ _773908) ^ [_1086699, _1086701] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086699)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086699)), _1086701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1086699))), _1086701))], (3892 ^ _773908) ^ [_832606, _832608, _832610, _832612] : [-(c_Big__Operators_Olinorder__class_OMax(_832612, _832608) = c_Big__Operators_Olinorder__class_OMax(_832610, _832606)), _832612 = _832610, _832608 = _832606], (5598 ^ _773908) ^ [_859525, _859527] : [_859527 = _859525, -(c_COMBI(_859527) = c_COMBI(_859525))], (44539 ^ _773908) ^ [_1662484, _1662486, _1662488] : [hBOOL(hAPP(c_List_Odistinct(_1662484), _1662486)), -(hAPP(c_List_Ofilter(_1662484, hAPP(hAPP(c_COMBC(_1662484, tc_fun(_1662484, tc_HOL_Obool), tc_HOL_Obool), c_member(_1662484)), hAPP(c_List_Oset(_1662484), c_List_Osublist(_1662484, _1662486, _1662488)))), _1662486) = c_List_Osublist(_1662484, _1662486, _1662488))], (41113 ^ _773908) ^ [_1583760, _1583762] : [hBOOL(hAPP(c_List_Odistinct(_1583760), _1583762)), 41116 ^ _773908 : [(41117 ^ _773908) ^ [_1583892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1583892), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583760)), _1583762))), 41120 ^ _773908 : [(41121 ^ _773908) ^ [_1584019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1584019), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583760)), _1583762))), -(_1583892 = _1584019), hAPP(hAPP(c_List_Onth(_1583760), _1583762), _1583892) = hAPP(hAPP(c_List_Onth(_1583760), _1583762), _1584019)]]]]], (13261 ^ _773908) ^ [] : [-(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))))], (47439 ^ _773908) ^ [_1727898, _1727900] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1727898, _1727898)), _1727900)), c_Wellfounded_Oacyclic(_1727898, _1727900), -(c_Wellfounded_Owf(_1727898, hAPP(c_Relation_Oconverse(_1727898, _1727898), _1727900)))], (30293 ^ _773908) ^ [_1327397, _1327399, _1327401] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327397), _1327399)), 30296 ^ _773908 : [(30303 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327397), _1327401), _1327399))), -(hAPP(c_Finite__Set_Ocard(_1327397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327397, tc_HOL_Obool)), _1327399), hAPP(hAPP(c_Set_Oinsert(_1327397), _1327401), c_Orderings_Obot__class_Obot(tc_fun(_1327397, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1327397), _1327399))], (30297 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327397), _1327401), _1327399)), -(hAPP(c_Finite__Set_Ocard(_1327397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327397, tc_HOL_Obool)), _1327399), hAPP(hAPP(c_Set_Oinsert(_1327397), _1327401), c_Orderings_Obot__class_Obot(tc_fun(_1327397, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327397), _1327399)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (51157 ^ _773908) ^ [_1809421, _1809423, _1809425] : [c_Fun_Obij__betw(_1809421, _1809423, _1809425, c_Orderings_Otop__class_Otop(tc_fun(_1809421, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1809423, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1809423, _1809421, c_Orderings_Otop__class_Otop(tc_fun(_1809423, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1809421, _1809423, c_Orderings_Otop__class_Otop(tc_fun(_1809421, tc_HOL_Obool)), _1809425)) = _1809425)], (38851 ^ _773908) ^ [_1524580] : [-(c_Wellfounded_Owf(tc_fun(_1524580, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1524580)))], (38286 ^ _773908) ^ [_1505993] : [-(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)))), _1505993)) = 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), _1505993), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (20771 ^ _773908) ^ [_1133238, _1133240, _1133242] : [class_Rings_Odivision__ring(_1133238), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133238), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133238), _1133240), _1133242)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133238), hAPP(c_Groups_Ouminus__class_Ouminus(_1133238), _1133240)), _1133242))], (6217 ^ _773908) ^ [_874784] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _874784)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17863 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15595 ^ _773908) ^ [_1038862, _1038864, _1038866, _1038868, _1038870, _1038872] : [class_Rings_Oring(_1038862), 15598 ^ _773908 : [(15605 ^ _773908) ^ [] : [_1038868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038862), _1038870), _1038864)), _1038866)), _1038872), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), _1038864), _1038866)), _1038868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), _1038870), _1038866)), _1038872))], (15599 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), _1038864), _1038866)), _1038868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), _1038870), _1038866)), _1038872), -(_1038868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038862), _1038870), _1038864)), _1038866)), _1038872))]]], (28775 ^ _773908) ^ [_1299351, _1299353, _1299355, _1299357, _1299359, _1299361] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299351, tc_fun(_1299353, tc_HOL_Obool))), _1299355), _1299357), _1299359), _1299361)), -(hBOOL(hAPP(hAPP(_1299357, _1299359), _1299361)))], (20805 ^ _773908) ^ [_1133861, _1133863] : [c_Nat__Transfer_Ois__nat(_1133861), c_Nat__Transfer_Ois__nat(_1133863), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133861), _1133863)))], (23421 ^ _773908) ^ [_1181577, _1181579] : [class_Rings_Oring__1(_1181577), 23424 ^ _773908 : [(23431 ^ _773908) ^ [] : [-(_1181579 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23434 ^ _773908 : [(23441 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181579), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1181577), _1181579) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1181577), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1181577, _1181577)), tc_fun(tc_Int_Oint, _1181577)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1181577, _1181577), _1181577), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1181577, _1181577)), tc_fun(tc_Int_Oint, _1181577)), tc_Int_Oint), c_COMBB(tc_fun(_1181577, _1181577), _1181577, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1181577, tc_fun(tc_fun(_1181577, _1181577), _1181577), tc_Int_Oint), c_HOL_OLet(_1181577, _1181577)), c_Int_Oring__1__class_Oof__int(_1181577)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1181577, _1181577), tc_fun(_1181577, _1181577)), hAPP(hAPP(c_COMBB(tc_fun(_1181577, tc_fun(_1181577, _1181577)), tc_fun(tc_fun(_1181577, _1181577), tc_fun(_1181577, _1181577)), tc_Int_Oint), c_COMBS(_1181577, _1181577, _1181577)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1181577, _1181577), tc_fun(_1181577, tc_fun(_1181577, _1181577))), hAPP(hAPP(c_COMBB(tc_fun(_1181577, tc_fun(_1181577, _1181577)), tc_fun(tc_fun(_1181577, _1181577), tc_fun(_1181577, tc_fun(_1181577, _1181577))), tc_Int_Oint), c_COMBB(_1181577, tc_fun(_1181577, _1181577), _1181577)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1181577, tc_fun(_1181577, _1181577)), tc_Int_Oint), c_If(_1181577)), 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(_1181577, _1181577, _1181577), c_Groups_Oplus__class_Oplus(_1181577)), c_COMBI(_1181577))))), hAPP(hAPP(c_COMBC(_1181577, _1181577, _1181577), hAPP(hAPP(c_COMBB(_1181577, tc_fun(_1181577, _1181577), _1181577), c_Groups_Oplus__class_Oplus(_1181577)), hAPP(hAPP(c_COMBS(_1181577, _1181577, _1181577), c_Groups_Oplus__class_Oplus(_1181577)), c_COMBI(_1181577)))), c_Groups_Oone__class_Oone(_1181577))))), c_Divides_Odivmod__int(_1181579, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (23435 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181579), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1181577), _1181579) = hAPP(c_Groups_Ouminus__class_Ouminus(_1181577), hAPP(c_Int_Oring__1__class_Oof__int(_1181577), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181579))))]]], (23425 ^ _773908) ^ [] : [_1181579 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1181577), _1181579) = c_Groups_Ozero__class_Ozero(_1181577))]]], (8485 ^ _773908) ^ [_913841, _913843, _913845] : [class_Rings_Oidom(_913841), 8488 ^ _773908 : [(8489 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913841), _913843), _913843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913841), _913845), _913845), -(_913843 = _913845), -(_913843 = hAPP(c_Groups_Ouminus__class_Ouminus(_913841), _913845))], (8499 ^ _773908) ^ [] : [8500 ^ _773908 : [(8503 ^ _773908) ^ [] : [_913843 = hAPP(c_Groups_Ouminus__class_Ouminus(_913841), _913845)], (8501 ^ _773908) ^ [] : [_913843 = _913845]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913841), _913843), _913843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913841), _913845), _913845))]]], (43473 ^ _773908) ^ [_1637604, _1637606, _1637608, _1637610] : [c_List_Olist__all2(_1637604, _1637606, _1637608, c_List_Olist_ONil(_1637604), _1637610), -(_1637610 = c_List_Olist_ONil(_1637606))], (19177 ^ _773908) ^ [_1105061] : [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), _1105061))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1105061)))], (50937 ^ _773908) ^ [_1804453, _1804455, _1804457, _1804459, _1804461, _1804463] : [hAPP(c_Hilbert__Choice_Oinv__into(_1804453, _1804455, _1804457, _1804459), _1804461) = hAPP(c_Hilbert__Choice_Oinv__into(_1804453, _1804455, _1804457, _1804459), _1804463), hBOOL(hAPP(hAPP(c_member(_1804455), _1804461), hAPP(c_Set_Oimage(_1804453, _1804455, _1804459), _1804457))), hBOOL(hAPP(hAPP(c_member(_1804455), _1804463), hAPP(c_Set_Oimage(_1804453, _1804455, _1804459), _1804457))), -(_1804461 = _1804463)], (47645 ^ _773908) ^ [_1733375, _1733377, _1733379, _1733381, _1733383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1733375, _1733375)), hAPP(hAPP(c_Product__Type_OPair(_1733375, _1733375), _1733377), _1733379)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1733375, _1733375), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1733381)), _1733383))), 47649 ^ _773908 : [(47652 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733375, _1733375)), hAPP(hAPP(c_Product__Type_OPair(_1733375, _1733375), 47648 ^ [_1733375, _1733377, _1733379, _1733381, _1733383]), _1733379)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1733375, _1733375), tc_HOL_Obool), _1733381), _1733383))))], (47650 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733375, _1733375)), hAPP(hAPP(c_Product__Type_OPair(_1733375, _1733375), _1733377), 47648 ^ [_1733375, _1733377, _1733379, _1733381, _1733383])), _1733383)))]]], (43095 ^ _773908) ^ [_1629162, _1629164, _1629166, _1629168] : [-(c_List_Opartition(_1629162, _1629164, hAPP(hAPP(c_List_Olist_OCons(_1629162), _1629166), _1629168)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1629162), tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1629162), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1629162), tc_fun(tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), tc_fun(tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), tc_List_Olist(_1629162)), c_COMBS(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_fun(tc_List_Olist(_1629162), tc_fun(tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), tc_List_Olist(_1629162)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_fun(tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_List_Olist(_1629162)), hAPP(c_If(tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), hAPP(_1629164, _1629166)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1629162), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_List_Olist(_1629162)), c_Product__Type_OPair(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), hAPP(c_List_Olist_OCons(_1629162), _1629166))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1629162), tc_fun(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162))), tc_fun(tc_fun(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_fun(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), tc_List_Olist(_1629162)), c_COMBB(tc_List_Olist(_1629162), tc_prod(tc_List_Olist(_1629162), tc_List_Olist(_1629162)), tc_List_Olist(_1629162))), c_Product__Type_OPair(tc_List_Olist(_1629162), tc_List_Olist(_1629162)))), hAPP(c_List_Olist_OCons(_1629162), _1629166)))), c_List_Opartition(_1629162, _1629164, _1629168)))], (18441 ^ _773908) ^ [_1092212, _1092214, _1092216, _1092218] : [18442 ^ _773908 : [(18445 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1092212), _1092214), _1092218))], (18443 ^ _773908) ^ [] : [_1092214 = _1092216]], -(hBOOL(hAPP(hAPP(c_member(_1092212), _1092214), hAPP(hAPP(c_Set_Oinsert(_1092212), _1092216), _1092218))))], (5234 ^ _773908) ^ [_853943, _853945] : [_853945 = _853943, -(c_Relation_OId(_853945) = c_Relation_OId(_853943))], (20467 ^ _773908) ^ [_1127157, _1127159, _1127161] : [class_Rings_Olinordered__idom(_1127157), 20470 ^ _773908 : [(20479 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127157), hAPP(hAPP(c_Power_Opower__class_Opower(_1127157), _1127159), 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(_1127157), _1127161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1127157)))), _1127159 = c_Groups_Ozero__class_Ozero(_1127157), _1127161 = c_Groups_Ozero__class_Ozero(_1127157)], (20471 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127157), hAPP(hAPP(c_Power_Opower__class_Opower(_1127157), _1127159), 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(_1127157), _1127161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1127157))), 20474 ^ _773908 : [(20477 ^ _773908) ^ [] : [-(_1127161 = c_Groups_Ozero__class_Ozero(_1127157))], (20475 ^ _773908) ^ [] : [-(_1127159 = c_Groups_Ozero__class_Ozero(_1127157))]]]]], (6662 ^ _773908) ^ [_882110, _882112, _882114] : [class_Orderings_Oorder(_882110), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882110), _882112), _882114)), _882112 = _882114], (4762 ^ _773908) ^ [_846501, _846503, _846505, _846507, _846509, _846511, _846513, _846515, _846517, _846519] : [-(c_Option_Ooption_Ooption__case(_846519, _846515, _846511, _846507, _846503) = c_Option_Ooption_Ooption__case(_846517, _846513, _846509, _846505, _846501)), _846519 = _846517, _846515 = _846513, _846511 = _846509, _846507 = _846505, _846503 = _846501], (47224 ^ _773908) ^ [_1722537, _1722539, _1722541] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1722537, _1722537)), _1722539), c_Transitive__Closure_Otrancl(_1722537, _1722541)))), 47225 ^ _773908 : [(47226 ^ _773908) ^ [_1722616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1722616)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1722537, _1722537)), _1722539), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1722537, _1722537), tc_HOL_Obool), _1722616), _1722541)))]]], (9239 ^ _773908) ^ [_927468, _927470, _927472] : [class_Rings_Olinordered__semiring__strict(_927468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927468), c_Groups_Ozero__class_Ozero(_927468)), _927470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927468), _927472), c_Groups_Ozero__class_Ozero(_927468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927468), _927472), _927470)), c_Groups_Ozero__class_Ozero(_927468))))], (5276 ^ _773908) ^ [_854560, _854562] : [_854562 = _854560, -(c_Orderings_Oord__class_Oless__eq(_854562) = c_Orderings_Oord__class_Oless__eq(_854560))], (38641 ^ _773908) ^ [_1518866, _1518868, _1518870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518866, _1518866), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518866, _1518866, _1518866), _1518868), _1518870)), _1518868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1518866, _1518868)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1518866, _1518870)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1518866, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1518866, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1518866, tc_HOL_Obool), tc_fun(_1518866, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1518866, _1518868))))], (9783 ^ _773908) ^ [_936871, _936873, _936875, _936877, _936879] : [class_Orderings_Oord(_936871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936873, _936871)), _936875), _936877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936871), hAPP(_936875, _936879)), hAPP(_936877, _936879))))], (37331 ^ _773908) ^ [_1478726, _1478728] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1478726), c_Int_OInteg)), hBOOL(hAPP(_1478728, hAPP(c_Int_ORep__Integ, 37336 ^ [_1478726, _1478728]))), -(hBOOL(hAPP(_1478728, _1478726)))], (14448 ^ _773908) ^ [_1018287, _1018289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1018287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018289, _1018287)), _1018287)))], (45527 ^ _773908) ^ [_1683369, _1683371] : [hBOOL(hAPP(c_List_Odistinct(_1683369), _1683371)), -(hBOOL(hAPP(c_List_Odistinct(_1683369), hAPP(c_List_Orev(_1683369), _1683371))))], (42547 ^ _773908) ^ [_1617713, _1617715, _1617717, _1617719, _1617721] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617713, tc_fun(_1617715, tc_HOL_Obool)), _1617717), _1617719), _1617721)), 42550 ^ _773908 : [(42551 ^ _773908) ^ [_1617822] : [hBOOL(hAPP(hAPP(c_member(_1617713), _1617822), _1617717)), -(hBOOL(hAPP(hAPP(_1617719, _1617822), _1617721)))]]], (45165 ^ _773908) ^ [_1676041, _1676043, _1676045] : [class_Orderings_Olinorder(_1676041), 45168 ^ _773908 : [(45175 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1676041, _1676045), -(c_List_Olinorder__class_Osorted(_1676041, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676041, _1676041, c_COMBI(_1676041)), _1676043), _1676045)))], (45169 ^ _773908) ^ [] : [c_List_Olinorder__class_Osorted(_1676041, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676041, _1676041, c_COMBI(_1676041)), _1676043), _1676045)), -(c_List_Olinorder__class_Osorted(_1676041, _1676045))]]], (3390 ^ _773908) ^ [_824813, _824815] : [_824815 = _824813, -(c_SetInterval_Oord__class_OlessThan(_824815) = c_SetInterval_Oord__class_OlessThan(_824813))], (42981 ^ _773908) ^ [_1626956, _1626958, _1626960] : [hBOOL(hAPP(c_List_Odistinct(_1626956), _1626958)), -(hBOOL(hAPP(c_List_Odistinct(_1626956), c_List_Oremove1(_1626956, _1626960, _1626958))))], (18421 ^ _773908) ^ [_1091874, _1091876] : [hBOOL(hAPP(hAPP(c_member(_1091874), _1091876), c_Orderings_Obot__class_Obot(tc_fun(_1091874, tc_HOL_Obool))))], (24605 ^ _773908) ^ [_1207490, _1207492, _1207494] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1207490, _1207492), _1207494)), 24608 ^ _773908 : [(24617 ^ _773908) ^ [] : [-(_1207492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24620 ^ _773908 : [(24629 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1207492))), 24632 ^ _773908 : [(24635 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1207494)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24633 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207492), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1207494))))]]], (24621 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1207492)), 24624 ^ _773908 : [(24627 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1207494)), _1207492)))], (24625 ^ _773908) ^ [] : [-(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), _1207494))))]]]]], (24611 ^ _773908) ^ [] : [_1207492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1207494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24609 ^ _773908) ^ [] : [-(_1207490 = 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), _1207494)), _1207492)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1207494)))]]], (19893 ^ _773908) ^ [_1117181, _1117183] : [c_Int_OBit1(_1117181) = c_Int_OBit0(_1117183)], (38972 ^ _773908) ^ [_1527112] : [class_Orderings_Owellorder(_1527112), -(c_Wellfounded_Owf(_1527112, hAPP(c_Set_OCollect(tc_prod(_1527112, _1527112)), hAPP(c_Product__Type_Oprod_Oprod__case(_1527112, _1527112, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1527112)))))], (51814 ^ _773908) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (27992 ^ _773908) ^ [_1280724, _1280726] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280724, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1280724, tc_HOL_Obool))), _1280726) = c_Orderings_Obot__class_Obot(tc_fun(_1280724, tc_HOL_Obool)))], (33600 ^ _773908) ^ [_1397956, _1397958, _1397960, _1397962] : [class_Orderings_Olinorder(_1397956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397956), _1397958), _1397960)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1397956, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397956, _1397958), _1397962)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397956, _1397958), _1397960)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397956, _1397960), _1397962))], (42295 ^ _773908) ^ [_1611902, _1611904, _1611906, _1611908] : [hAPP(hAPP(c_List_Omap(_1611902, _1611904), _1611906), _1611908) = c_List_Olist_ONil(_1611904), -(_1611908 = c_List_Olist_ONil(_1611902))], (19797 ^ _773908) ^ [_1115539, _1115541] : [class_Rings_Osemiring__1(_1115539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115541)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1115539), 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)))), _1115541))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115539), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1115539), hAPP(c_Int_Onat, _1115541))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1115539), hAPP(c_Int_Onat, _1115541))))], (47753 ^ _773908) ^ [_1735993, _1735995] : [class_Enum_Oenum(_1735993), 47756 ^ _773908 : [(47764 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1735993), _1735995)), 47767 ^ _773908 : [(47768 ^ _773908) ^ [_1736211] : [-(hBOOL(hAPP(_1735995, _1736211)))]]], (47757 ^ _773908) ^ [] : [hBOOL(hAPP(_1735995, 47758 ^ [_1735993, _1735995])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1735993), _1735995)))]]], (37928 ^ _773908) ^ [_1494579, _1494581] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1494579)), 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)), _1494579))), 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, _1494581))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35174 ^ _773908) ^ [_1432323, _1432325, _1432327, _1432329] : [class_Groups_Oab__group__add(_1432323), 35177 ^ _773908 : [(35184 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1432325), _1432327))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1432323), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1432323, _1432323), hAPP(hAPP(c_COMBB(_1432323, tc_fun(_1432323, _1432323), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1432323)), _1432329)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1432323, tc_Nat_Onat), _1432329), 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, _1432325, _1432327)) = c_Groups_Ozero__class_Ozero(_1432323))], (35178 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1432325), _1432327)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1432323), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1432323, _1432323), hAPP(hAPP(c_COMBB(_1432323, tc_fun(_1432323, _1432323), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1432323)), _1432329)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1432323, tc_Nat_Onat), _1432329), 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, _1432325, _1432327)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1432323), hAPP(_1432329, _1432325)), hAPP(_1432329, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1432327), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (16296 ^ _773908) ^ [_1053224, _1053226, _1053228] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1053224, _1053226) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1053228, _1053226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053228), _1053224)), -(_1053224 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053226), 16303 ^ [_1053224, _1053226, _1053228])))], (44833 ^ _773908) ^ [_1670109, _1670111, _1670113, _1670115, _1670117, _1670119] : [-(c_List_Ofoldr(_1670109, _1670111, _1670113, hAPP(hAPP(c_List_Olist_OCons(_1670109), _1670115), _1670117), _1670119) = hAPP(hAPP(_1670113, _1670115), c_List_Ofoldr(_1670109, _1670111, _1670113, _1670117, _1670119)))], (47807 ^ _773908) ^ [_1736959, _1736961, _1736963, _1736965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1736959, tc_HOL_Obool), tc_fun(_1736959, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1736959, tc_HOL_Obool), tc_fun(_1736959, tc_HOL_Obool)), _1736961), _1736963)), c_Wellfounded_Omax__ext(_1736959, _1736965))), 47810 ^ _773908 : [(47813 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1736959), _1736963)))], (47815 ^ _773908) ^ [] : [_1736963 = c_Orderings_Obot__class_Obot(tc_fun(_1736959, tc_HOL_Obool))], (47817 ^ _773908) ^ [_1737253] : [hBOOL(hAPP(hAPP(c_member(_1736959), _1737253), _1736961)), 47821 ^ _773908 : [(47824 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1736959, _1736959)), hAPP(hAPP(c_Product__Type_OPair(_1736959, _1736959), _1737253), 47820 ^ [_1736959, _1736961, _1736963, _1736965, _1737253])), _1736965)))], (47822 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736959), 47820 ^ [_1736959, _1736961, _1736963, _1736965, _1737253]), _1736963)))]]], (47811 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1736959), _1736961)))]]], (8243 ^ _773908) ^ [_909613, _909615, _909617] : [class_Rings_Olinordered__semidom(_909613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909613), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909613), _909615)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909613), _909617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909615), _909617)))], (51794 ^ _773908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (6836 ^ _773908) ^ [_884483, _884485, _884487, _884489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884483), _884485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884487), _884489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884483), _884487)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884485), _884489))))], (21465 ^ _773908) ^ [_1145007, _1145009, _1145011] : [class_Fields_Olinordered__field(_1145007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145007), c_Groups_Ozero__class_Ozero(_1145007)), _1145009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145007), _1145011), c_Groups_Ozero__class_Ozero(_1145007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145007), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145007), _1145009), _1145011)), c_Groups_Ozero__class_Ozero(_1145007))))], (12422 ^ _773908) ^ [_981970, _981972, _981974, _981976, _981978] : [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), _981970), _981972)), _981974)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _981970), _981976)), _981978))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981978), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981970), _981978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981970), _981974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981976), _981972)))], (20411 ^ _773908) ^ [] : [-(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))))], (6524 ^ _773908) ^ [_880007, _880009, _880011] : [class_Orderings_Olinorder(_880007), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880007), _880009), _880011))), -(_880009 = _880011), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880007), _880011), _880009)))], (42756 ^ _773908) ^ [_1621796, _1621798, _1621800, _1621802] : [class_Groups_Ocomm__monoid__add(_1621796), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1621796), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1621796), _1621798), c_List_Oupto(_1621800, _1621802))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1621796), _1621798), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1621800, _1621802))))], (44911 ^ _773908) ^ [_1671755, _1671757, _1671759, _1671761] : [class_Orderings_Olinorder(_1671755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671755), _1671757), _1671759)), c_List_Olinorder__class_Osorted(_1671755, hAPP(hAPP(c_List_Olist_OCons(_1671755), _1671759), _1671761)), -(c_List_Olinorder__class_Osorted(_1671755, hAPP(hAPP(c_List_Olist_OCons(_1671755), _1671757), hAPP(hAPP(c_List_Olist_OCons(_1671755), _1671759), _1671761))))], (11119 ^ _773908) ^ [_958969, _958971, _958973] : [class_Rings_Oordered__cancel__semiring(_958969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958969), c_Groups_Ozero__class_Ozero(_958969)), _958971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958969), _958973), c_Groups_Ozero__class_Ozero(_958969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958969), _958971), _958973)), c_Groups_Ozero__class_Ozero(_958969))))], (12985 ^ _773908) ^ [_991760, _991762, _991764] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991760, tc_HOL_Obool)), _991762), _991764))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991760, tc_HOL_Obool)), _991762), _991764)), -(_991762 = _991764)], (34472 ^ _773908) ^ [_1415814, _1415816, _1415818, _1415820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1415814), _1415816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415814, tc_HOL_Obool)), _1415816), _1415818)), hBOOL(hAPP(_1415820, c_Orderings_Obot__class_Obot(tc_fun(_1415814, tc_HOL_Obool)))), 34487 ^ _773908 : [(34488 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1415814), 34486 ^ [_1415814, _1415816, _1415818, _1415820])))], (34492 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1415814), 34485 ^ [_1415814, _1415816, _1415818, _1415820]), 34486 ^ [_1415814, _1415816, _1415818, _1415820]))], (34496 ^ _773908) ^ [] : [hBOOL(hAPP(_1415820, hAPP(hAPP(c_Set_Oinsert(_1415814), 34485 ^ [_1415814, _1415816, _1415818, _1415820]), 34486 ^ [_1415814, _1415816, _1415818, _1415820])))], (34494 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1415820, 34486 ^ [_1415814, _1415816, _1415818, _1415820])))], (34490 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415814), 34485 ^ [_1415814, _1415816, _1415818, _1415820]), _1415818)))]], -(hBOOL(hAPP(_1415820, _1415816)))], (42459 ^ _773908) ^ [_1615687, _1615689, _1615691] : [c_Fun_Oinj__on(_1615687, _1615689, _1615691, c_Orderings_Otop__class_Otop(tc_fun(_1615687, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1615687), tc_List_Olist(_1615689), hAPP(c_List_Omap(_1615687, _1615689), _1615691), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1615687), tc_HOL_Obool))))], (12466 ^ _773908) ^ [_982830, _982832, _982834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982830)), 12469 ^ _773908 : [(12476 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982832), _982834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982830), _982832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982830), _982834))))], (12470 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982830), _982832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982830), _982834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982832), _982834)))]]], (30535 ^ _773908) ^ [_1332338, _1332340, _1332342] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332338), _1332340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332338, tc_HOL_Obool)), _1332340), hAPP(hAPP(c_Set_Oinsert(_1332338), _1332342), c_Orderings_Obot__class_Obot(tc_fun(_1332338, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1332338), _1332340))))], (44734 ^ _773908) ^ [_1667833, _1667835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667833)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667835))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667833), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667835)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667833)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667833)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667835))))], (43862 ^ _773908) ^ [_1646824, _1646826, _1646828, _1646830] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646824, tc_HOL_Obool), hAPP(c_Set_Oimage(_1646826, tc_fun(_1646824, tc_HOL_Obool), _1646828), _1646830)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646826, tc_fun(_1646824, tc_HOL_Obool)), _1646830), _1646828))], (51498 ^ _773908) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (29719 ^ _773908) ^ [_1316383, _1316385] : [class_Groups_Olinordered__ab__group__add(_1316383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316383), _1316385)), -(_1316385 = c_Orderings_Obot__class_Obot(tc_fun(_1316383, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1316383), c_Big__Operators_Olinorder__class_OMin(_1316383, _1316385)) = c_Big__Operators_Olinorder__class_OMax(_1316383, hAPP(c_Set_Oimage(_1316383, _1316383, c_Groups_Ouminus__class_Ouminus(_1316383)), _1316385)))], (41073 ^ _773908) ^ [_1582955, _1582957, _1582959] : [-(_1582955 = c_List_Olist_ONil(_1582957)), -(hAPP(c_List_Otl(_1582957), hAPP(hAPP(c_List_Oappend(_1582957), _1582955), _1582959)) = hAPP(hAPP(c_List_Oappend(_1582957), hAPP(c_List_Otl(_1582957), _1582955)), _1582959))], (41342 ^ _773908) ^ [_1588576, _1588578, _1588580] : [class_Orderings_Olinorder(_1588576), -(c_Big__Operators_Olinorder__class_OMin(_1588576, hAPP(c_List_Oset(_1588576), hAPP(hAPP(c_List_Olist_OCons(_1588576), _1588578), _1588580))) = hAPP(c_List_Ofoldl(_1588576, _1588576, c_Orderings_Oord__class_Omin(_1588576), _1588578), _1588580))], (9911 ^ _773908) ^ [_938891, _938893, _938895, _938897] : [class_Orderings_Oorder(_938891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938891), _938893), _938895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938891), _938897), _938893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938891), _938897), _938895)))], (35897 ^ _773908) ^ [_1447452, _1447454] : [class_Orderings_Otop(_1447452), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1447452), _1447454), c_Orderings_Otop__class_Otop(_1447452))))], (14293 ^ _773908) ^ [_1015419, _1015421, _1015423] : [hBOOL(hAPP(_1015419, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015421), _1015423))), 14298 ^ _773908 : [(14301 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1015419, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14299 ^ _773908) ^ [] : [-(_1015423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14303 ^ _773908 : [(14308 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1015419, 14302 ^ [_1015419, _1015421, _1015423])))], (14306 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015423), hAPP(c_Nat_OSuc, 14302 ^ [_1015419, _1015421, _1015423])))))], (14304 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015423), 14302 ^ [_1015419, _1015421, _1015423])), _1015421)))]]], (33174 ^ _773908) ^ [_1390300, _1390302, _1390304] : [-(c_Fun_Oinj__on(_1390300, _1390302, _1390304, c_Orderings_Obot__class_Obot(tc_fun(_1390300, tc_HOL_Obool))))], (37400 ^ _773908) ^ [_1480387, _1480389, _1480391] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1480387, _1480389), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1480387, _1480389), c_Orderings_Otop__class_Otop(tc_fun(_1480387, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1480389, tc_HOL_Obool), _1480387), _1480391))) = hAPP(hAPP(c_Product__Type_OSigma(_1480387, _1480389), c_Orderings_Otop__class_Otop(tc_fun(_1480387, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1480389, tc_HOL_Obool), _1480387), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1480389, tc_HOL_Obool)), _1480391))))], (26426 ^ _773908) ^ [_1246994, _1246996, _1246998, _1247000, _1247002, _1247004] : [_1246994 = hAPP(_1246996, _1246998), hBOOL(hAPP(hAPP(c_member(_1247000), _1246998), _1247002)), -(hBOOL(hAPP(hAPP(c_member(_1247004), _1246994), hAPP(c_Set_Oimage(_1247000, _1247004, _1246996), _1247002))))], (14585 ^ _773908) ^ [_1020522, _1020524] : [class_Divides_Osemiring__div(_1020522), -(_1020524 = c_Groups_Ozero__class_Ozero(_1020522)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020522), _1020524), _1020524) = c_Groups_Oone__class_Oone(_1020522))], (23845 ^ _773908) ^ [_1190784, _1190786, _1190788, _1190790] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1190784, _1190786), _1190788)), hBOOL(hAPP(hAPP(_1190786, _1190790), _1190788)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1190784, _1190786), _1190790)))], (51576 ^ _773908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (23241 ^ _773908) ^ [_1178451, _1178453] : [-(c_Divides_OnegDivAlg(_1178451, _1178453) = hAPP(c_Divides_Oadjust(_1178453), c_Divides_OnegDivAlg(_1178451, 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)))), _1178453)))), -(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), _1178451), _1178453)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178453), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16867 ^ _773908) ^ [_1063909, _1063911] : [class_Rings_Ocomm__semiring__1(_1063909), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1063909), _1063911), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1063909))], (40213 ^ _773908) ^ [_1560250, _1560252, _1560254] : [-(hAPP(c_List_Oset(_1560250), hAPP(hAPP(c_List_Olist_OCons(_1560250), _1560252), _1560254)) = hAPP(hAPP(c_Set_Oinsert(_1560250), _1560252), hAPP(c_List_Oset(_1560250), _1560254)))], (28182 ^ _773908) ^ [_1284671, _1284673, _1284675, _1284677] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284671, tc_HOL_Obool)), _1284673), _1284675), _1284677)), -(hBOOL(hAPP(_1284675, _1284677)))], (44424 ^ _773908) ^ [_1659528, _1659530, _1659532, _1659534] : [-(hAPP(c_List_Ofilter(_1659528, _1659530), hAPP(hAPP(c_List_Oappend(_1659528), _1659532), _1659534)) = hAPP(hAPP(c_List_Oappend(_1659528), hAPP(c_List_Ofilter(_1659528, _1659530), _1659532)), hAPP(c_List_Ofilter(_1659528, _1659530), _1659534)))], (6144 ^ _773908) ^ [_873492] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _873492)], (20965 ^ _773908) ^ [_1136603, _1136605, _1136607] : [class_Fields_Olinordered__field(_1136603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136603), _1136605), c_Groups_Ozero__class_Ozero(_1136603))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136603), _1136607), c_Groups_Ozero__class_Ozero(_1136603))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136603), c_Groups_Ozero__class_Ozero(_1136603)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136603), _1136605), _1136607))))], (9053 ^ _773908) ^ [_924219, _924221] : [class_Rings_Olinordered__idom(_924219), 9056 ^ _773908 : [(9063 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924219), _924221), c_Groups_Ozero__class_Ozero(_924219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924219), _924221), hAPP(c_Groups_Ouminus__class_Ouminus(_924219), _924221))))], (9057 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924219), _924221), hAPP(c_Groups_Ouminus__class_Ouminus(_924219), _924221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924219), _924221), c_Groups_Ozero__class_Ozero(_924219))))]]], (3064 ^ _773908) ^ [_819778, _819780] : [_819780 = _819778, -(c_SetInterval_Oord__class_OgreaterThan(_819780) = c_SetInterval_Oord__class_OgreaterThan(_819778))], (13692 ^ _773908) ^ [_1004482, _1004484, _1004486] : [class_Rings_Olinordered__idom(_1004482), -(c_Groups_Osgn__class_Osgn(_1004482, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004482), _1004484), _1004486)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004482), c_Groups_Osgn__class_Osgn(_1004482, _1004484)), c_Groups_Osgn__class_Osgn(_1004482, _1004486)))], (32578 ^ _773908) ^ [_1378495, _1378497, _1378499, _1378501] : [class_Orderings_Oorder(_1378495), 32581 ^ _773908 : [(32590 ^ _773908) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1378495, _1378497, _1378499) = hAPP(hAPP(c_Set_Oinsert(_1378495), _1378501), c_Orderings_Obot__class_Obot(tc_fun(_1378495, tc_HOL_Obool)))), _1378497 = _1378499, _1378499 = _1378501], (32582 ^ _773908) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1378495, _1378497, _1378499) = hAPP(hAPP(c_Set_Oinsert(_1378495), _1378501), c_Orderings_Obot__class_Obot(tc_fun(_1378495, tc_HOL_Obool))), 32585 ^ _773908 : [(32588 ^ _773908) ^ [] : [-(_1378499 = _1378501)], (32586 ^ _773908) ^ [] : [-(_1378497 = _1378499)]]]]], (19157 ^ _773908) ^ [_1104735, _1104737] : [class_Int_Onumber__ring(_1104735), class_Rings_Olinordered__idom(_1104735), 19164 ^ _773908 : [(19171 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104737), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104735), hAPP(c_Int_Onumber__class_Onumber__of(_1104735), _1104737)), c_Groups_Ozero__class_Ozero(_1104735))))], (19165 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104735), hAPP(c_Int_Onumber__class_Onumber__of(_1104735), _1104737)), c_Groups_Ozero__class_Ozero(_1104735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104737), c_Int_OPls)))]]], (36991 ^ _773908) ^ [_1470729, _1470731, _1470733] : [class_Orderings_Olinorder(_1470729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470729), _1470731)), -(_1470731 = c_Orderings_Obot__class_Obot(tc_fun(_1470729, tc_HOL_Obool))), 37002 ^ _773908 : [(37003 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470729), _1470733), hAPP(c_Finite__Set_Ofold1(_1470729, c_Orderings_Oord__class_Omin(_1470729)), _1470731))), 37006 ^ _773908 : [(37007 ^ _773908) ^ [_1471022] : [hBOOL(hAPP(hAPP(c_member(_1470729), _1471022), _1470731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470729), _1470733), _1471022)))]]], (37013 ^ _773908) ^ [] : [37015 ^ _773908 : [(37018 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470729), _1470733), 37014 ^ [_1470729, _1470731, _1470733]))], (37016 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470729), 37014 ^ [_1470729, _1470731, _1470733]), _1470731)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470729), _1470733), hAPP(c_Finite__Set_Ofold1(_1470729, c_Orderings_Oord__class_Omin(_1470729)), _1470731))))]]], (6260 ^ _773908) ^ [_875434, _875436] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_875434, _875436)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_875434)), c_Com_Ocom_Ocom__size(_875436))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8317 ^ _773908) ^ [_911047, _911049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911047)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911047), _911049)))], (42820 ^ _773908) ^ [_1623646, _1623648] : [hAPP(c_Code__Numeral_Onat__of, _1623646) = hAPP(c_Code__Numeral_Onat__of, _1623648), -(_1623646 = _1623648)], (5292 ^ _773908) ^ [_854794, _854796, _854798, _854800] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854800, _854796) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854798, _854794)), _854800 = _854798, _854796 = _854794], (28188 ^ _773908) ^ [_1284782, _1284784, _1284786, _1284788] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1284782, tc_HOL_Obool)), _1284784), _1284786), _1284788)), -(hBOOL(hAPP(_1284784, _1284788)))], (47393 ^ _773908) ^ [_1726601, _1726603, _1726605, _1726607] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1726601, _1726601)), hAPP(hAPP(c_Product__Type_OPair(_1726601, _1726601), _1726603), _1726605)), c_Transitive__Closure_Ortrancl(_1726601, hAPP(c_Relation_Oconverse(_1726601, _1726601), _1726607)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1726601, _1726601)), hAPP(hAPP(c_Product__Type_OPair(_1726601, _1726601), _1726605), _1726603)), c_Transitive__Closure_Ortrancl(_1726601, _1726607))))], (41298 ^ _773908) ^ [_1587617, _1587619, _1587621] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587617)), hAPP(c_List_Orotate(_1587617, _1587619), _1587621)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587617)), _1587621))], (15351 ^ _773908) ^ [_1034320, _1034322, _1034324, _1034326] : [class_Divides_Oring__div(_1034320), -(c_Divides_Odiv__class_Omod(_1034320, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034320), _1034322), _1034324), _1034326) = c_Divides_Odiv__class_Omod(_1034320, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034320), c_Divides_Odiv__class_Omod(_1034320, _1034322, _1034326)), c_Divides_Odiv__class_Omod(_1034320, _1034324, _1034326)), _1034326))], (39198 ^ _773908) ^ [_1534012, _1534014, _1534016, _1534018, _1534020, _1534022] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1534012), tc_List_Olist(_1534012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1534012), tc_List_Olist(_1534012)), hAPP(hAPP(c_List_Olist_OCons(_1534012), _1534014), _1534016)), hAPP(hAPP(c_List_Olist_OCons(_1534012), _1534018), _1534020))), c_List_Olex(_1534012, _1534022)))), 39199 ^ _773908 : [(39206 ^ _773908) ^ [] : [_1534014 = _1534018, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1534012), tc_List_Olist(_1534012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1534012), tc_List_Olist(_1534012)), _1534016), _1534020)), c_List_Olex(_1534012, _1534022)))], (39200 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534012, _1534012)), hAPP(hAPP(c_Product__Type_OPair(_1534012, _1534012), _1534014), _1534018)), _1534022)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1534012)), _1534016) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1534012)), _1534020)]]], (49886 ^ _773908) ^ [_1781509, _1781511, _1781513, _1781515, _1781517, _1781519, _1781521] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1781509, tc_fun(_1781511, tc_fun(_1781513, tc_HOL_Obool))), _1781515), _1781517), _1781519), _1781521)), 49890 ^ _773908 : [(49893 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1781517, 49889 ^ [_1781509, _1781511, _1781513, _1781515, _1781517, _1781519, _1781521]), _1781519), _1781521)))], (49891 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781509), 49889 ^ [_1781509, _1781511, _1781513, _1781515, _1781517, _1781519, _1781521]), _1781515)))]]], (46831 ^ _773908) ^ [_1712458, _1712460] : [-(hAPP(c_Relation_ODomain(_1712458, _1712458), c_Transitive__Closure_Ortrancl(_1712458, _1712460)) = c_Orderings_Otop__class_Otop(tc_fun(_1712458, tc_HOL_Obool)))], (14515 ^ _773908) ^ [_1019332] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019332), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43543 ^ _773908) ^ [_1639242, _1639244, _1639246, _1639248, _1639250] : [c_List_Olist__all2(_1639242, _1639244, _1639246, _1639248, _1639250), 43546 ^ _773908 : [(43549 ^ _773908) ^ [_1639405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639405), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639242)), _1639248))), -(hBOOL(hAPP(hAPP(_1639246, hAPP(hAPP(c_List_Onth(_1639242), _1639248), _1639405)), hAPP(hAPP(c_List_Onth(_1639244), _1639250), _1639405))))], (43547 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639242)), _1639248) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639244)), _1639250))]]], (49864 ^ _773908) ^ [_1780990, _1780992, _1780994] : [-(c_FunDef_OTHE__default(_1780992, _1780994, _1780990) = _1780994), 49866 ^ _773908 : [(49869 ^ _773908) ^ [_1781112] : [hBOOL(hAPP(_1780990, _1781112)), -(_1781112 = 49865 ^ [_1780990, _1780992, _1780994])], (49867 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1780990, 49865 ^ [_1780990, _1780992, _1780994])))]]], (32466 ^ _773908) ^ [_1376538, _1376540, _1376542, _1376544, _1376546] : [hAPP(c_Set_Oimage(_1376538, _1376540, _1376542), _1376544) = _1376546, -(hAPP(c_Set_Oimage(tc_fun(_1376538, tc_HOL_Obool), tc_fun(_1376540, tc_HOL_Obool), c_Set_Oimage(_1376538, _1376540, _1376542)), hAPP(c_Set_OPow(_1376538), _1376544)) = hAPP(c_Set_OPow(_1376540), _1376546))], (17287 ^ _773908) ^ [_1072190, _1072192, _1072194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072190), _1072192)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1072190), _1072194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072192), _1072194)))], (39861 ^ _773908) ^ [_1551488, _1551490, _1551492] : [c_Equiv__Relations_Oequiv(_1551488, _1551490, _1551492), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1551488), c_List_Olists(_1551488, _1551490), c_List_Olistrel(_1551488, _1551492)))], (26522 ^ _773908) ^ [_1249264, _1249266, _1249268, _1249270] : [c_Orderings_Obot__class_Obot(tc_fun(_1249264, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1249266, _1249264, _1249268), _1249270), -(_1249270 = c_Orderings_Obot__class_Obot(tc_fun(_1249266, tc_HOL_Obool)))], (37247 ^ _773908) ^ [_1476433, _1476435, _1476437, _1476439] : [c_Fun_Oinj__on(_1476433, _1476435, _1476437, c_Orderings_Otop__class_Otop(tc_fun(_1476433, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1476433, _1476435, _1476437), hAPP(c_Set_Oimage(_1476433, _1476435, _1476437), _1476439)) = _1476439)], (1414 ^ _773908) ^ [_794569, _794571] : [-(class_Lattices_Osemilattice__sup(_794569)), _794571 = _794569, class_Lattices_Osemilattice__sup(_794571)], (5190 ^ _773908) ^ [_853275, _853277, _853279, _853281, _853283, _853285] : [-(c_Relation_Orel__comp(_853285, _853281, _853277) = c_Relation_Orel__comp(_853283, _853279, _853275)), _853285 = _853283, _853281 = _853279, _853277 = _853275], (6181 ^ _773908) ^ [_874148, _874150, _874152, _874154, _874156] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_874148, _874150), _874152, _874154, _874156), 6185 ^ _773908 : [(6188 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_874150, 6184 ^ [_874148, _874150, _874152, _874154, _874156], _874154, _874156))], (6186 ^ _773908) ^ [] : [-(c_Natural_Oevaln(_874148, _874152, _874154, 6184 ^ [_874148, _874150, _874152, _874154, _874156]))]]], (15679 ^ _773908) ^ [_1040642, _1040644] : [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), _1040642), _1040644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040644), _1040642)))], (45545 ^ _773908) ^ [_1683692, _1683694] : [c_List_Olist_ONil(_1683692) = hAPP(c_List_Orev(_1683692), _1683694), -(_1683694 = c_List_Olist_ONil(_1683692))], (2538 ^ _773908) ^ [_811379, _811381] : [_811381 = _811379, -(c_Int_Opred(_811381) = c_Int_Opred(_811379))], (604 ^ _773908) ^ [_783134, _783136, _783138, _783140, _783142, _783144, _783146, _783148] : [-(c_Finite__Set_Ofolding(_783146, _783142, _783138, _783134)), c_Finite__Set_Ofolding(_783148, _783144, _783140, _783136), _783148 = _783146, _783144 = _783142, _783140 = _783138, _783136 = _783134], (47417 ^ _773908) ^ [_1727383, _1727385, _1727387, _1727389, _1727391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1727385, tc_HOL_Obool)), _1727389), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1727385, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1727383, _1727385, hAPP(c_Relation_Oconverse(_1727385, _1727383), _1727387)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1727383, tc_HOL_Obool)), _1727391))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1727383, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1727385, _1727383, _1727387), _1727389)), _1727391)))], (25421 ^ _773908) ^ [_1223338, _1223340, _1223342, _1223344, _1223346, _1223348] : [hAPP(c_Product__Type_Oapfst(_1223338, _1223340, _1223342, _1223344), _1223346) = hAPP(c_Product__Type_Oapfst(_1223338, _1223340, _1223342, _1223348), _1223346), -(hAPP(_1223344, hAPP(c_Product__Type_Ofst(_1223338, _1223342), _1223346)) = hAPP(_1223348, hAPP(c_Product__Type_Ofst(_1223338, _1223342), _1223346)))], (43854 ^ _773908) ^ [_1646589, _1646591, _1646593] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646589, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1646589, tc_HOL_Obool), tc_HOL_Obool)), _1646591), _1646593)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1646589, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646589, tc_HOL_Obool), _1646591)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646589, tc_HOL_Obool), _1646593)))], (51516 ^ _773908) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (33977 ^ _773908) ^ [_1405764, _1405766, _1405768, _1405770] : [class_Orderings_Olinorder(_1405764), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405764, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1405764, _1405766, _1405768)), hAPP(c_SetInterval_Oord__class_OatMost(_1405764), _1405770)) = c_SetInterval_Oord__class_OatLeastAtMost(_1405764, _1405766, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1405764), _1405768), _1405770)))], (48189 ^ _773908) ^ [_1745181, _1745183, _1745185, _1745187, _1745189, _1745191] : [c_Finite__Set_Ofolding(_1745181, _1745183, _1745185, _1745187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745181), _1745189)), -(hAPP(hAPP(_1745187, _1745189), _1745191) = hAPP(hAPP(c_Finite__Set_Ofold(_1745181, _1745183, _1745185), _1745191), _1745189))], (8669 ^ _773908) ^ [_917401, _917403] : [class_Groups_Ogroup__add(_917401), -(hAPP(c_Groups_Ouminus__class_Ouminus(_917401), hAPP(c_Groups_Ouminus__class_Ouminus(_917401), _917403)) = _917403)], (39135 ^ _773908) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (15517 ^ _773908) ^ [_1037370, _1037372, _1037374] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037372), _1037374)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037370), _1037372)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037370), _1037374)))], (50777 ^ _773908) ^ [_1800803, _1800805] : [c_Relation_Osym(_1800803, hAPP(c_Set_OCollect(tc_prod(_1800803, _1800803)), hAPP(c_Product__Type_Oprod_Oprod__case(_1800803, _1800803, tc_HOL_Obool), _1800805))), -(c_Predicate_Osymp(_1800803, _1800805))], (10573 ^ _773908) ^ [_949286, _949288] : [class_Orderings_Obot(_949286), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949286), c_Orderings_Obot__class_Obot(_949286)), _949288)))], (47399 ^ _773908) ^ [_1726782, _1726784, _1726786, _1726788] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1726782, _1726782)), hAPP(hAPP(c_Product__Type_OPair(_1726782, _1726782), _1726784), _1726786)), hAPP(c_Relation_Oconverse(_1726782, _1726782), c_Transitive__Closure_Otrancl(_1726782, _1726788)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1726782, _1726782)), hAPP(hAPP(c_Product__Type_OPair(_1726782, _1726782), _1726784), _1726786)), c_Transitive__Closure_Otrancl(_1726782, hAPP(c_Relation_Oconverse(_1726782, _1726782), _1726788)))))], (18865 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (1594 ^ _773908) ^ [_796819, _796821] : [-(class_Groups_Ocancel__ab__semigroup__add(_796819)), _796821 = _796819, class_Groups_Ocancel__ab__semigroup__add(_796821)], (9021 ^ _773908) ^ [_923671, _923673] : [class_Groups_Oordered__ab__group__add(_923671), 9024 ^ _773908 : [(9031 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923671), c_Groups_Ozero__class_Ozero(_923671)), _923673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923671), hAPP(c_Groups_Ouminus__class_Ouminus(_923671), _923673)), c_Groups_Ozero__class_Ozero(_923671))))], (9025 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923671), hAPP(c_Groups_Ouminus__class_Ouminus(_923671), _923673)), c_Groups_Ozero__class_Ozero(_923671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923671), c_Groups_Ozero__class_Ozero(_923671)), _923673)))]]], (5614 ^ _773908) ^ [_859759, _859761, _859763, _859765, _859767, _859769] : [-(c_COMBB(_859769, _859765, _859761) = c_COMBB(_859767, _859763, _859759)), _859769 = _859767, _859765 = _859763, _859761 = _859759], (30425 ^ _773908) ^ [_1329886, _1329888, _1329890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329886), _1329888)), 30428 ^ _773908 : [(30435 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329886), _1329890), _1329888))), -(hAPP(c_Finite__Set_Ocard(_1329886), hAPP(hAPP(c_Set_Oinsert(_1329886), _1329890), _1329888)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1329886), _1329888)))], (30429 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329886), _1329890), _1329888)), -(hAPP(c_Finite__Set_Ocard(_1329886), hAPP(hAPP(c_Set_Oinsert(_1329886), _1329890), _1329888)) = hAPP(c_Finite__Set_Ocard(_1329886), _1329888))]]], (8863 ^ _773908) ^ [_920716, _920718] : [class_Rings_Ocomm__semiring__1(_920716), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920716), _920718), c_Groups_Ozero__class_Ozero(_920716)) = c_Groups_Ozero__class_Ozero(_920716))], (39611 ^ _773908) ^ [_1544107, _1544109, _1544111, _1544113, _1544115, _1544117] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544107), tc_List_Olist(_1544107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544107), tc_List_Olist(_1544107)), hAPP(hAPP(c_List_Oappend(_1544107), _1544109), _1544115)), hAPP(hAPP(c_List_Oappend(_1544107), _1544111), _1544117))), c_List_Olistrel1(_1544107, _1544113)))), 39612 ^ _773908 : [(39619 ^ _773908) ^ [] : [_1544109 = _1544111, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544107), tc_List_Olist(_1544107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544107), tc_List_Olist(_1544107)), _1544115), _1544117)), c_List_Olistrel1(_1544107, _1544113)))], (39613 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1544107), tc_List_Olist(_1544107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1544107), tc_List_Olist(_1544107)), _1544109), _1544111)), c_List_Olistrel1(_1544107, _1544113))), _1544115 = _1544117]]], (20023 ^ _773908) ^ [_1119480] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1119480)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1119480)))], (13704 ^ _773908) ^ [_1004714, _1004716, _1004718] : [class_Divides_Osemiring__div(_1004714), -(c_Divides_Odiv__class_Omod(_1004714, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004714), _1004716), _1004718), _1004716) = c_Groups_Ozero__class_Ozero(_1004714))], (26371 ^ _773908) ^ [_1245555, _1245557] : [c_Relation_Oirrefl(_1245555, _1245557), 26374 ^ _773908 : [(26375 ^ _773908) ^ [_1245637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1245555, _1245555)), hAPP(hAPP(c_Product__Type_OPair(_1245555, _1245555), _1245637), _1245637)), _1245557))]]], (20759 ^ _773908) ^ [_1132980, _1132982, _1132984] : [class_Fields_Ofield__inverse__zero(_1132980), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132980), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132980), _1132982), _1132984)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132980), _1132982), hAPP(c_Groups_Ouminus__class_Ouminus(_1132980), _1132984)))], (30385 ^ _773908) ^ [_1329159, _1329161, _1329163] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329159), _1329161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329159, tc_HOL_Obool)), _1329163), _1329161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329159), _1329161)), hAPP(c_Finite__Set_Ocard(_1329159), _1329163))), -(_1329163 = _1329161)], (17455 ^ _773908) ^ [_1075230, _1075232, _1075234] : [class_Rings_Olinordered__semidom(_1075230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075230), c_Groups_Ozero__class_Ozero(_1075230)), _1075232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075230), c_Groups_Ozero__class_Ozero(_1075230)), hAPP(hAPP(c_Power_Opower__class_Opower(_1075230), _1075232), _1075234))))], (48631 ^ _773908) ^ [_1753920] : [class_Groups_Oab__semigroup__mult(_1753920), -(c_Finite__Set_Ofun__left__comm(_1753920, _1753920, c_Groups_Otimes__class_Otimes(_1753920)))], (10519 ^ _773908) ^ [_948235, _948237, _948239, _948241] : [class_Groups_Oordered__ab__semigroup__add(_948235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948235), _948237), _948239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948235), _948237), _948241)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948235), _948239), _948241))))], (28218 ^ _773908) ^ [_1285444, _1285446, _1285448, _1285450] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285444, tc_HOL_Obool)), _1285446), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285444, tc_HOL_Obool)), _1285448), _1285450)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285444, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285444, tc_HOL_Obool)), _1285446), _1285448)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285444, tc_HOL_Obool)), _1285446), _1285450)))], (24989 ^ _773908) ^ [_1214712, _1214714, _1214716, _1214718] : [class_Orderings_Olinorder(_1214712), 24992 ^ _773908 : [(24993 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214712), _1214714), _1214716)), _1214718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), _1214714), _1214718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), _1214716), _1214718)))], (25003 ^ _773908) ^ [] : [25004 ^ _773908 : [(25007 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), _1214716), _1214718))], (25005 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), _1214714), _1214718))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214712), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214712), _1214714), _1214716)), _1214718)))]]], (7631 ^ _773908) ^ [_897648, _897650, _897652, _897654, _897656, _897658] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_897648, _897650, _897652), _897654, _897656, _897658)), 7632 ^ _773908 : [(7639 ^ _773908) ^ [] : [-(hBOOL(hAPP(_897648, _897654))), c_Natural_Oevaln(_897652, _897654, _897656, _897658)], (7633 ^ _773908) ^ [] : [hBOOL(hAPP(_897648, _897654)), c_Natural_Oevaln(_897650, _897654, _897656, _897658)]]], (46353 ^ _773908) ^ [_1701425, _1701427] : [c_Wellfounded_Owf(_1701425, _1701427), -(c_Wellfounded_Oacyclic(_1701425, _1701427))], (46857 ^ _773908) ^ [_1713306, _1713308, _1713310, _1713312] : [-(hBOOL(hAPP(hAPP(c_member(_1713306), _1713308), hAPP(c_Relation_ODomain(_1713306, _1713306), _1713310)))), 46860 ^ _773908 : [(46867 ^ _773908) ^ [] : [_1713308 = _1713312, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713306, _1713306)), hAPP(hAPP(c_Product__Type_OPair(_1713306, _1713306), _1713308), _1713312)), c_Transitive__Closure_Ortrancl(_1713306, _1713310))))], (46861 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713306, _1713306)), hAPP(hAPP(c_Product__Type_OPair(_1713306, _1713306), _1713308), _1713312)), c_Transitive__Closure_Ortrancl(_1713306, _1713310))), -(_1713308 = _1713312)]]], (40647 ^ _773908) ^ [_1570847, _1570849, _1570851, _1570853, _1570855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1570847), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570849)), _1570851))), -(hAPP(hAPP(c_List_Olist__update(_1570849, hAPP(hAPP(c_List_Oappend(_1570849), _1570851), _1570853)), _1570847), _1570855) = hAPP(hAPP(c_List_Oappend(_1570849), hAPP(hAPP(c_List_Olist__update(_1570849, _1570851), _1570847), _1570855)), _1570853))], (32724 ^ _773908) ^ [_1381350, _1381352, _1381354, _1381356] : [class_Orderings_Oorder(_1381350), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381350, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1381350, _1381352, _1381354)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1381350, _1381354, _1381356)) = c_Orderings_Obot__class_Obot(tc_fun(_1381350, tc_HOL_Obool)))], (7173 ^ _773908) ^ [_889887, _889889] : [7174 ^ _773908 : [(7177 ^ _773908) ^ [] : [_889887 = _889889], (7175 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889887), _889889))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889887), hAPP(c_Nat_OSuc, _889889))))], (38438 ^ _773908) ^ [_1512182, _1512184] : [c_Relation_Orefl__on(_1512182, c_Orderings_Otop__class_Otop(tc_fun(_1512182, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1512182, _1512182)), hAPP(c_Product__Type_Oprod_Oprod__case(_1512182, _1512182, tc_HOL_Obool), _1512184))), -(c_Predicate_Oreflp(_1512182, _1512184))], (24683 ^ _773908) ^ [_1208893, _1208895] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1208893)), hAPP(c_Nat_OSuc, _1208895)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1208893))), 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)), _1208895)))))], (32149 ^ _773908) ^ [_1369948, _1369950, _1369952] : [-(hAPP(c_Relation_OImage(_1369948, _1369948, c_Relation_OId__on(_1369948, _1369950)), _1369952) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369948, tc_HOL_Obool)), _1369950), _1369952))], (15273 ^ _773908) ^ [_1032927, _1032929, _1032931] : [class_Groups_Oab__group__add(_1032927), 15276 ^ _773908 : [(15283 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032927), _1032929), _1032931) = c_Groups_Ozero__class_Ozero(_1032927), -(_1032929 = _1032931)], (15277 ^ _773908) ^ [] : [_1032929 = _1032931, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032927), _1032929), _1032931) = c_Groups_Ozero__class_Ozero(_1032927))]]], (22313 ^ _773908) ^ [_1160292, _1160294, _1160296, _1160298] : [class_Fields_Olinordered__field__inverse__zero(_1160292), class_Int_Onumber(_1160292), 22320 ^ _773908 : [(22321 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160294), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160292), _1160296), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)))), 22324 ^ _773908 : [(22331 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), c_Groups_Ozero__class_Ozero(_1160292)), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)))), 22334 ^ _773908 : [(22341 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)), c_Groups_Ozero__class_Ozero(_1160292)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160294), c_Groups_Ozero__class_Ozero(_1160292))))], (22335 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)), c_Groups_Ozero__class_Ozero(_1160292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160292), _1160294), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)))))]]], (22325 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), c_Groups_Ozero__class_Ozero(_1160292)), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160292), _1160294), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))), _1160296)))]]], (22347 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160294), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160292), _1160296), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))))), 22350 ^ _773908 : [(22353 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160292), _1160294), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))), _1160296))], (22351 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), c_Groups_Ozero__class_Ozero(_1160292)), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))))]], 22354 ^ _773908 : [(22357 ^ _773908) ^ [] : [22358 ^ _773908 : [(22361 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160292), _1160294), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298))))], (22359 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)), c_Groups_Ozero__class_Ozero(_1160292))))]], 22362 ^ _773908 : [(22365 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), _1160294), c_Groups_Ozero__class_Ozero(_1160292)))], (22363 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)), c_Groups_Ozero__class_Ozero(_1160292)))]]], (22355 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160292), c_Groups_Ozero__class_Ozero(_1160292)), hAPP(c_Int_Onumber__class_Onumber__of(_1160292), _1160298)))]]]]], (12857 ^ _773908) ^ [_989535, _989537] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989535), _989537) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12860 ^ _773908 : [(12863 ^ _773908) ^ [] : [-(_989537 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12861 ^ _773908) ^ [] : [-(_989535 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (43399 ^ _773908) ^ [_1636120, _1636122, _1636124, _1636126, _1636128, _1636130, _1636132] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636120)), _1636122) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636124)), _1636126), 43402 ^ _773908 : [(43411 ^ _773908) ^ [] : [-(c_List_Olist__all2(_1636120, _1636124, _1636128, hAPP(hAPP(c_List_Oappend(_1636120), _1636122), _1636130), hAPP(hAPP(c_List_Oappend(_1636124), _1636126), _1636132))), c_List_Olist__all2(_1636120, _1636124, _1636128, _1636122, _1636126), c_List_Olist__all2(_1636120, _1636124, _1636128, _1636130, _1636132)], (43403 ^ _773908) ^ [] : [c_List_Olist__all2(_1636120, _1636124, _1636128, hAPP(hAPP(c_List_Oappend(_1636120), _1636122), _1636130), hAPP(hAPP(c_List_Oappend(_1636124), _1636126), _1636132)), 43406 ^ _773908 : [(43409 ^ _773908) ^ [] : [-(c_List_Olist__all2(_1636120, _1636124, _1636128, _1636130, _1636132))], (43407 ^ _773908) ^ [] : [-(c_List_Olist__all2(_1636120, _1636124, _1636128, _1636122, _1636126))]]]]], (44134 ^ _773908) ^ [_1653473, _1653475, _1653477] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1653473, tc_HOL_Obool)), _1653475), _1653477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653473, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653473, tc_HOL_Obool), _1653477)), _1653475)))], (31776 ^ _773908) ^ [_1361055, _1361057, _1361059, _1361061, _1361063] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361055, tc_fun(_1361057, tc_HOL_Obool)), _1361059), hAPP(hAPP(c_COMBC(_1361055, tc_fun(_1361057, tc_HOL_Obool), tc_fun(_1361057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361057, tc_HOL_Obool), tc_fun(tc_fun(_1361057, tc_HOL_Obool), tc_fun(_1361057, tc_HOL_Obool)), _1361055), c_Groups_Ominus__class_Ominus(tc_fun(_1361057, tc_HOL_Obool))), _1361061)), _1361063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361057, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361055, tc_fun(_1361057, tc_HOL_Obool)), _1361059), _1361061)), _1361063))], (51105 ^ _773908) ^ [_1808312, _1808314] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1808312), _1808314))), -(c_Quickcheck_Obeyond(_1808312, _1808314) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (34422 ^ _773908) ^ [_1414883, _1414885, _1414887, _1414889, _1414891] : [c_Finite__Set_Ofolding__one__idem(_1414883, _1414885, _1414887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414883), _1414889)), -(_1414889 = c_Orderings_Obot__class_Obot(tc_fun(_1414883, tc_HOL_Obool))), -(hAPP(_1414887, hAPP(hAPP(c_Set_Oinsert(_1414883), _1414891), _1414889)) = hAPP(hAPP(_1414885, _1414891), hAPP(_1414887, _1414889)))], (5931 ^ _773908) ^ [_868864, _868866, _868868] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _868864)), _868866), _868868)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _868864))), _868866), _868868)))], (46563 ^ _773908) ^ [_1705734, _1705736, _1705738, _1705740, _1705742] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705734)), _1705736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705738)), _1705740), 46569 ^ _773908 : [(46572 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1705742, hAPP(hAPP(c_List_Onth(_1705734), _1705736), 46568 ^ [_1705734, _1705736, _1705738, _1705740, _1705742])), hAPP(hAPP(c_List_Onth(_1705738), _1705740), 46568 ^ [_1705734, _1705736, _1705738, _1705740, _1705742])))], (46570 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46568 ^ [_1705734, _1705736, _1705738, _1705740, _1705742]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705734)), _1705736))))]], -(c_List_Olist__all2(_1705734, _1705738, _1705742, _1705736, _1705740))], (12110 ^ _773908) ^ [_976954, _976956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _976954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _976956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976954), _976956))))], (33526 ^ _773908) ^ [_1396735, _1396737] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1396735), _1396737)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1396735)), hAPP(c_Nat_OSuc, _1396737)))], (38585 ^ _773908) ^ [_1517143, _1517145, _1517147] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517143, _1517143, _1517145), c_Relation_OId(_1517143)), _1517147) = _1517147)], (8293 ^ _773908) ^ [_910447, _910449, _910451, _910453, _910455, _910457, _910459] : [-(hAPP(c_Fun_Ocomp(_910447, _910449, _910451, _910453), hAPP(c_Fun_Ocomp(_910455, _910447, _910451, _910457), _910459)) = hAPP(c_Fun_Ocomp(_910455, _910449, _910451, hAPP(c_Fun_Ocomp(_910447, _910449, _910455, _910453), _910457)), _910459))], (40337 ^ _773908) ^ [_1563209, _1563211, _1563213, _1563215, _1563217] : [hBOOL(hAPP(hAPP(c_member(_1563209), _1563211), hAPP(c_List_Oset(_1563209), _1563213))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1563215), hAPP(_1563217, _1563211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1563215), c_List_Olist_Olist__size(_1563209, _1563217, _1563213))))], (51824 ^ _773908) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (25811 ^ _773908) ^ [_1231267, _1231269, _1231271] : [class_Lattices_Olattice(_1231267), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231267), _1231269), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1231267), _1231269), _1231271))))], (51626 ^ _773908) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (12234 ^ _773908) ^ [_978817] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _978817)) = 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), _978817)))], (37956 ^ _773908) ^ [_1495137] : [-(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)), _1495137)))))], (44351 ^ _773908) ^ [_1658017, _1658019, _1658021] : [-(c_Enum_On__lists(_1658017, hAPP(c_Nat_OSuc, _1658019), _1658021) = c_List_Oconcat(tc_List_Olist(_1658017), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1658017), tc_List_Olist(tc_List_Olist(_1658017))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658017), tc_List_Olist(_1658017), tc_List_Olist(tc_List_Olist(_1658017))), hAPP(hAPP(c_COMBB(tc_fun(_1658017, tc_List_Olist(_1658017)), tc_fun(tc_List_Olist(_1658017), tc_List_Olist(tc_List_Olist(_1658017))), tc_List_Olist(_1658017)), c_List_Omap(_1658017, tc_List_Olist(_1658017))), hAPP(c_COMBC(_1658017, tc_List_Olist(_1658017), tc_List_Olist(_1658017)), c_List_Olist_OCons(_1658017)))), _1658021)), c_Enum_On__lists(_1658017, _1658019, _1658021))))], (23817 ^ _773908) ^ [_1190290, _1190292] : [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), _1190290), _1190292))), 23820 ^ _773908 : [(23829 ^ _773908) ^ [] : [-(c_Divides_OposDivAlg(_1190290, _1190292) = hAPP(c_Divides_Oadjust(_1190292), c_Divides_OposDivAlg(_1190290, 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)))), _1190292)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190290), _1190292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1190292), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23821 ^ _773908) ^ [] : [23822 ^ _773908 : [(23825 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1190292), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23823 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190290), _1190292))]], -(c_Divides_OposDivAlg(_1190290, _1190292) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190290))]]], (1204 ^ _773908) ^ [_791944, _791946] : [-(class_Groups_Oordered__ab__group__add(_791944)), _791946 = _791944, class_Groups_Oordered__ab__group__add(_791946)], (12750 ^ _773908) ^ [_987548, _987550, _987552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987548), _987550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987548), _987552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987550), _987552))))], (37570 ^ _773908) ^ [_1485161, _1485163, _1485165, _1485167, _1485169, _1485171] : [-(hAPP(c_Set_Ovimage(_1485161, tc_prod(_1485163, _1485165), _1485167), hAPP(hAPP(c_Product__Type_OSigma(_1485163, _1485165), _1485169), hAPP(c_COMBK(tc_fun(_1485165, tc_HOL_Obool), _1485163), _1485171))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485161, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1485161, _1485163, hAPP(c_Fun_Ocomp(tc_prod(_1485163, _1485165), _1485163, _1485161, c_Product__Type_Ofst(_1485163, _1485165)), _1485167)), _1485169)), hAPP(c_Set_Ovimage(_1485161, _1485165, hAPP(c_Fun_Ocomp(tc_prod(_1485163, _1485165), _1485165, _1485161, c_Product__Type_Osnd(_1485163, _1485165)), _1485167)), _1485171)))], (1474 ^ _773908) ^ [_795319, _795321] : [-(class_Orderings_Obot(_795319)), _795321 = _795319, class_Orderings_Obot(_795321)], (51828 ^ _773908) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (13289 ^ _773908) ^ [_997031, _997033] : [-(hBOOL(hAPP(_997031, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_997031, _997033)), 13297 ^ _773908 : [(13300 ^ _773908) ^ [_997269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997269), 13296 ^ [_997031, _997033])), hBOOL(hAPP(_997031, _997269))], (13306 ^ _773908) ^ [] : [-(hBOOL(hAPP(_997031, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13296 ^ [_997031, _997033]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13298 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13296 ^ [_997031, _997033]), _997033)))]]], (8359 ^ _773908) ^ [_911681, _911683] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911681) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911683), -(_911681 = _911683)], (19249 ^ _773908) ^ [_1106251, _1106253, _1106255] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106251), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106253)), _1106255)) = 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), _1106251), _1106253))), _1106255))], (18935 ^ _773908) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (38124 ^ _773908) ^ [_1499048, _1499050, _1499052, _1499054] : [-(hAPP(c_Set_Ovimage(_1499048, _1499050, _1499052), _1499054) = hAPP(c_Set_OCollect(_1499048), hAPP(hAPP(c_COMBC(_1499048, tc_fun(_1499050, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1499050, tc_fun(tc_fun(_1499050, tc_HOL_Obool), tc_HOL_Obool), _1499048), c_member(_1499050)), _1499052)), _1499054)))], (44375 ^ _773908) ^ [_1658620, _1658622, _1658624, _1658626] : [-(hAPP(c_List_Ofilter(_1658620, _1658622), c_List_Oremove1(_1658620, _1658624, _1658626)) = c_List_Oremove1(_1658620, _1658624, hAPP(c_List_Ofilter(_1658620, _1658622), _1658626)))], (12803 ^ _773908) ^ [_988574, _988576, _988578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988574), _988576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988578), _988576))))], (43986 ^ _773908) ^ [_1650012, _1650014, _1650016, _1650018, _1650020] : [hBOOL(hAPP(hAPP(_1650012, _1650014), _1650016)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1650018, _1650020, _1650012), _1650014)))], (21597 ^ _773908) ^ [_1147535, _1147537, _1147539, _1147541] : [class_Fields_Olinordered__field(_1147535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147535), c_Groups_Ozero__class_Ozero(_1147535)), _1147537)), 21604 ^ _773908 : [(21611 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147535), _1147539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147535), _1147541), _1147537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147535), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147535), _1147539), _1147537)), _1147541)))], (21605 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147535), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147535), _1147539), _1147537)), _1147541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147535), _1147539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147535), _1147541), _1147537))))]]], (42441 ^ _773908) ^ [_1615208, _1615210, _1615212, _1615214, _1615216] : [_1615208 = c_Orderings_Obot__class_Obot(tc_fun(_1615210, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615210, tc_fun(_1615212, tc_HOL_Obool)), _1615208), hAPP(hAPP(c_COMBC(_1615210, tc_fun(_1615212, tc_HOL_Obool), tc_fun(_1615212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615212, tc_HOL_Obool), tc_fun(tc_fun(_1615212, tc_HOL_Obool), tc_fun(_1615212, tc_HOL_Obool)), _1615210), c_Groups_Ominus__class_Ominus(tc_fun(_1615212, tc_HOL_Obool))), _1615214)), _1615216)) = c_Orderings_Otop__class_Otop(tc_fun(_1615212, tc_HOL_Obool)))], (12130 ^ _773908) ^ [_977278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977278)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_977278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50592 ^ _773908) ^ [_1797700, _1797702] : [c_Relation_Osym(_1797700, _1797702), -(c_Relation_Osym(tc_List_Olist(_1797700), c_List_Olistrel(_1797700, _1797702)))], (13558 ^ _773908) ^ [_1001765, _1001767, _1001769, _1001771] : [class_Divides_Osemiring__div(_1001765), -(c_Divides_Odiv__class_Omod(_1001765, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001765), _1001767), _1001769), _1001771) = c_Divides_Odiv__class_Omod(_1001765, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001765), c_Divides_Odiv__class_Omod(_1001765, _1001767, _1001771)), c_Divides_Odiv__class_Omod(_1001765, _1001769, _1001771)), _1001771))], (33838 ^ _773908) ^ [_1402624, _1402626, _1402628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1402624), _1402626)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1402624), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1402626), _1402628)) = 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, _1402624), _1402626)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1402626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1402626), _1402628))))], (29493 ^ _773908) ^ [_1312419, _1312421, _1312423] : [class_Orderings_Olinorder(_1312419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312419), _1312421)), hBOOL(hAPP(hAPP(c_member(_1312419), _1312423), _1312421)), 29504 ^ _773908 : [(29511 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312419, tc_HOL_Obool)), _1312421), hAPP(hAPP(c_Set_Oinsert(_1312419), _1312423), c_Orderings_Obot__class_Obot(tc_fun(_1312419, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1312419, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1312419, _1312421) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312419), _1312423), c_Big__Operators_Olinorder__class_OMin(_1312419, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312419, tc_HOL_Obool)), _1312421), hAPP(hAPP(c_Set_Oinsert(_1312419), _1312423), c_Orderings_Obot__class_Obot(tc_fun(_1312419, tc_HOL_Obool)))))))], (29505 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312419, tc_HOL_Obool)), _1312421), hAPP(hAPP(c_Set_Oinsert(_1312419), _1312423), c_Orderings_Obot__class_Obot(tc_fun(_1312419, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1312419, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1312419, _1312421) = _1312423)]]], (16241 ^ _773908) ^ [_1052188, _1052190] : [_1052188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052188), _1052190) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12504 ^ _773908) ^ [_983455, _983457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983455), _983457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983457), _983455)))], (10481 ^ _773908) ^ [_947526, _947528] : [class_Rings_Ocomm__semiring__1(_947526), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947526), _947528), c_Groups_Oone__class_Oone(_947526)) = _947528)], (23874 ^ _773908) ^ [_1191359, _1191361, _1191363] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1191359, _1191361), _1191363)), 23877 ^ _773908 : [(23878 ^ _773908) ^ [_1191444] : [hBOOL(hAPP(hAPP(_1191361, _1191444), _1191363)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1191359, _1191361), _1191444)))]]], (44074 ^ _773908) ^ [_1652260, _1652262] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652260, tc_HOL_Obool), _1652262) = hAPP(c_Set_OCollect(_1652260), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1652260, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1652260), c_HOL_OAll(tc_fun(_1652260, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1652260, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1652260, tc_HOL_Obool), tc_HOL_Obool), _1652260), hAPP(c_COMBS(tc_fun(_1652260, 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(_1652260, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1652260, tc_HOL_Obool), tc_fun(tc_fun(_1652260, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1652260, tc_HOL_Obool))), _1652262)))), c_member(_1652260)))))], (7765 ^ _773908) ^ [_900408, _900410, _900412, _900414, _900416] : [c_Com_Ocom_OCond(_900408, _900410, _900412) = c_Com_Ocom_OSemi(_900414, _900416)], (18553 ^ _773908) ^ [_1094373, _1094375, _1094377] : [hBOOL(hAPP(hAPP(c_member(_1094373), _1094375), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1094373, tc_HOL_Obool)), _1094377))), hBOOL(hAPP(hAPP(c_member(_1094373), _1094375), _1094377))], (3562 ^ _773908) ^ [_827547, _827549] : [_827549 = _827547, -(c_List_Oembed__list(_827549) = c_List_Oembed__list(_827547))], (17169 ^ _773908) ^ [_1070043, _1070045, _1070047, _1070049] : [class_Rings_Olinordered__semidom(_1070043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070043), c_Groups_Oone__class_Oone(_1070043)), _1070045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070043), hAPP(hAPP(c_Power_Opower__class_Opower(_1070043), _1070045), _1070047)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070043), _1070045), _1070049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070047), _1070049)))], (16521 ^ _773908) ^ [_1057449, _1057451, _1057453] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1057449, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057449, tc_HOL_Obool)), _1057451), _1057453)), _1057451)))], (256 ^ _773908) ^ [_777806, _777808, _777810, _777812, _777814, _777816, _777818, _777820, _777822, _777824] : [-(c_Finite__Set_Ofolding__image(_777822, _777818, _777814, _777810, _777806)), c_Finite__Set_Ofolding__image(_777824, _777820, _777816, _777812, _777808), _777824 = _777822, _777820 = _777818, _777816 = _777814, _777812 = _777810, _777808 = _777806], (24037 ^ _773908) ^ [_1194018, _1194020] : [24038 ^ _773908 : [(24041 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194020), _1194018))], (24039 ^ _773908) ^ [] : [_1194018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1194020, _1194018) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1194020))], (5869 ^ _773908) ^ [_867717, _867719, _867721, _867723] : [5870 ^ _773908 : [(5873 ^ _773908) ^ [] : [hBOOL(hAPP(_867721, _867723))], (5871 ^ _773908) ^ [] : [_867719 = _867723]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_867717), _867719), _867721), _867723)))], (33676 ^ _773908) ^ [_1399472, _1399474, _1399476, _1399478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399472), _1399474)), hAPP(c_Finite__Set_Ocard(_1399476), hAPP(c_Set_Oimage(_1399472, _1399476, _1399478), _1399474)) = hAPP(c_Finite__Set_Ocard(_1399472), _1399474), -(c_Fun_Oinj__on(_1399472, _1399476, _1399478, _1399474))], (8467 ^ _773908) ^ [_913497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _913497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913497)))], (50410 ^ _773908) ^ [_1794571, _1794573, _1794575, _1794577] : [c_Relation_Oantisym(_1794571, _1794573), hBOOL(hAPP(hAPP(c_member(tc_prod(_1794571, _1794571)), hAPP(hAPP(c_Product__Type_OPair(_1794571, _1794571), _1794575), _1794577)), _1794573)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1794571, _1794571)), hAPP(hAPP(c_Product__Type_OPair(_1794571, _1794571), _1794577), _1794575)), _1794573)), -(_1794575 = _1794577)], (46804 ^ _773908) ^ [_1711769, _1711771] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1711769), tc_List_Olist(_1711769)), tc_HOL_Obool)), c_List_Olistrel1(_1711769, c_Transitive__Closure_Ortrancl(_1711769, _1711771))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1711769), c_List_Olistrel1(_1711769, _1711771)))))], (6156 ^ _773908) ^ [_873693, _873695, _873697, _873699] : [c_Natural_Oevaln(_873693, _873695, _873697, _873699), -(c_Natural_Oevaln(_873693, _873695, hAPP(c_Nat_OSuc, _873697), _873699))], (41894 ^ _773908) ^ [_1599470, _1599472, _1599474, _1599476, _1599478] : [class_Rings_Osemiring__0(_1599470), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1599470), hAPP(hAPP(c_List_Omap(_1599472, _1599470), hAPP(hAPP(c_COMBB(_1599470, _1599470, _1599472), hAPP(c_Groups_Otimes__class_Otimes(_1599470), _1599474)), _1599476)), _1599478)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1599470), _1599474), hAPP(c_List_Omonoid__add__class_Olistsum(_1599470), hAPP(hAPP(c_List_Omap(_1599472, _1599470), _1599476), _1599478))))], (26711 ^ _773908) ^ [_1254392, _1254394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254392), _1254394)), -(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)), _1254392)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254394))))], (41394 ^ _773908) ^ [_1589720, _1589722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1589720), _1589722)), -(c_List_Oupto(_1589722, _1589720) = c_List_Olist_ONil(tc_Int_Oint))], (31812 ^ _773908) ^ [_1362025, _1362027, _1362029, _1362031, _1362033] : [hBOOL(hAPP(hAPP(c_member(_1362025), _1362027), _1362029)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362031, tc_HOL_Obool)), hAPP(_1362033, _1362027)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362025, tc_fun(_1362031, tc_HOL_Obool)), _1362029), _1362033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362025, tc_fun(_1362031, tc_HOL_Obool)), _1362029), _1362033))], (44484 ^ _773908) ^ [_1660815, _1660817] : [c_List_Olist_ONil(_1660815) = c_List_Oconcat(_1660815, _1660817), 44487 ^ _773908 : [(44488 ^ _773908) ^ [_1660906] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1660815)), _1660906), hAPP(c_List_Oset(tc_List_Olist(_1660815)), _1660817))), -(_1660906 = c_List_Olist_ONil(_1660815))]]], (35943 ^ _773908) ^ [_1448309, _1448311] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1448309, _1448311)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1448309, _1448311), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448311), c_Orderings_Otop__class_Otop(tc_fun(_1448311, tc_HOL_Obool)))))], (1334 ^ _773908) ^ [_793569, _793571] : [-(class_Rings_Oring__1(_793569)), _793571 = _793569, class_Rings_Oring__1(_793571)], (37237 ^ _773908) ^ [_1476252, _1476254, _1476256, _1476258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476252), _1476254)), c_Fun_Oinj__on(_1476256, _1476252, _1476258, c_Orderings_Otop__class_Otop(tc_fun(_1476256, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476256), hAPP(c_Set_Ovimage(_1476256, _1476252, _1476258), _1476254))))], (17509 ^ _773908) ^ [_1076088, _1076090] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1076088), c_Groups_Ozero__class_Ozero(_1076088)), hAPP(c_Nat_OSuc, _1076090)) = c_Groups_Ozero__class_Ozero(_1076088)), class_Power_Opower(_1076088), class_Rings_Osemiring__0(_1076088)], (1980 ^ _773908) ^ [_802544, _802546, _802548, _802550, _802552, _802554, _802556, _802558] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_802558, _802554, _802550, _802546) = c_Hoare__Mirabelle_Otriple_Otriple__case(_802556, _802552, _802548, _802544)), _802558 = _802556, _802554 = _802552, _802550 = _802548, _802546 = _802544], (17945 ^ _773908) ^ [_1083596] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1083596, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34324 ^ _773908) ^ [_1412987, _1412989, _1412991] : [class_Orderings_Oord(_1412987), 34327 ^ _773908 : [(34334 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412987), _1412989), _1412991)), -(hBOOL(hAPP(hAPP(c_member(_1412987), _1412989), hAPP(c_SetInterval_Oord__class_OlessThan(_1412987), _1412991))))], (34328 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1412987), _1412989), hAPP(c_SetInterval_Oord__class_OlessThan(_1412987), _1412991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412987), _1412989), _1412991)))]]], (14310 ^ _773908) ^ [_1015723, _1015725, _1015727] : [-(hBOOL(hAPP(_1015723, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015725), _1015727)))), 14311 ^ _773908 : [(14318 ^ _773908) ^ [_1015891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015727), _1015891)), _1015725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015727), hAPP(c_Nat_OSuc, _1015891)))), hBOOL(hAPP(_1015723, _1015891))], (14312 ^ _773908) ^ [] : [_1015727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1015723, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (12977 ^ _773908) ^ [_991611, _991613, _991615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991611, tc_HOL_Obool)), _991613), _991615)), 12980 ^ _773908 : [(12983 ^ _773908) ^ [] : [_991613 = _991615], (12981 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991611, tc_HOL_Obool)), _991613), _991615)))]]], (6388 ^ _773908) ^ [_877528, _877530, _877532, _877534] : [class_Groups_Oordered__cancel__ab__semigroup__add(_877528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877528), _877530), _877532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877528), _877534), _877530)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877528), _877534), _877532))))], (45905 ^ _773908) ^ [_1691263, _1691265, _1691267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691263)), c_List_OdropWhile(_1691263, _1691265, _1691267))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691263)), _1691267))))], (16695 ^ _773908) ^ [_1060595, _1060597] : [class_Groups_Oordered__ab__group__add__abs(_1060595), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060595), hAPP(c_Groups_Ouminus__class_Ouminus(_1060595), _1060597)), hAPP(c_Groups_Oabs__class_Oabs(_1060595), _1060597))))], (39707 ^ _773908) ^ [_1546844, _1546846, _1546848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1546844, _1546844), tc_HOL_Obool)), _1546846), _1546848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1546844), tc_List_Olist(_1546844)), tc_HOL_Obool)), c_List_Olistrel(_1546844, _1546846)), c_List_Olistrel(_1546844, _1546848))))], (13350 ^ _773908) ^ [_998080, _998082] : [class_Rings_Olinordered__idom(_998080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998080), _998082), c_Groups_Ozero__class_Ozero(_998080))), -(c_Groups_Osgn__class_Osgn(_998080, _998082) = hAPP(c_Groups_Ouminus__class_Ouminus(_998080), c_Groups_Oone__class_Oone(_998080)))], (37215 ^ _773908) ^ [_1475742, _1475744, _1475746, _1475748] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475742), hAPP(c_Set_Ovimage(_1475742, _1475744, _1475746), _1475748))), hAPP(c_Set_Oimage(_1475742, _1475744, _1475746), c_Orderings_Otop__class_Otop(tc_fun(_1475742, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1475744, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1475744), _1475748)))], (43568 ^ _773908) ^ [_1639918, _1639920, _1639922, _1639924, _1639926, _1639928, _1639930, _1639932] : [c_List_Olist__all2(_1639918, _1639920, _1639922, _1639924, _1639926), hBOOL(hAPP(hAPP(_1639922, _1639928), _1639930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639932), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639920)), _1639926))), -(c_List_Olist__all2(_1639918, _1639920, _1639922, hAPP(hAPP(c_List_Olist__update(_1639918, _1639924), _1639932), _1639928), hAPP(hAPP(c_List_Olist__update(_1639920, _1639926), _1639932), _1639930)))], (2692 ^ _773908) ^ [_813874, _813876, _813878, _813880, _813882, _813884, _813886, _813888] : [-(c_SetInterval_Oord_OatLeastAtMost(_813888, _813884, _813880, _813876) = c_SetInterval_Oord_OatLeastAtMost(_813886, _813882, _813878, _813874)), _813888 = _813886, _813884 = _813882, _813880 = _813878, _813876 = _813874], (33660 ^ _773908) ^ [_1399188, _1399190, _1399192, _1399194] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399188), _1399190)), 33663 ^ _773908 : [(33670 ^ _773908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1399192), hAPP(c_Set_Oimage(_1399188, _1399192, _1399194), _1399190)) = hAPP(c_Finite__Set_Ocard(_1399188), _1399190), -(c_Fun_Oinj__on(_1399188, _1399192, _1399194, _1399190))], (33664 ^ _773908) ^ [] : [c_Fun_Oinj__on(_1399188, _1399192, _1399194, _1399190), -(hAPP(c_Finite__Set_Ocard(_1399192), hAPP(c_Set_Oimage(_1399188, _1399192, _1399194), _1399190)) = hAPP(c_Finite__Set_Ocard(_1399188), _1399190))]]], (13137 ^ _773908) ^ [_994420, _994422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994420), _994422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994420)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994422))))], (28711 ^ _773908) ^ [_1298049, _1298051, _1298053, _1298055, _1298057, _1298059] : [-(hBOOL(hAPP(hAPP(c_member(_1298049), _1298051), c_SetInterval_Oord_OgreaterThanAtMost(_1298049, _1298053, _1298055, _1298057, _1298059)))), hBOOL(hAPP(hAPP(_1298055, _1298057), _1298051)), hBOOL(hAPP(hAPP(_1298053, _1298051), _1298059))], (19791 ^ _773908) ^ [_1115412, _1115414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115412)), -(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)))), _1115414)), 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)))), _1115412)) = 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, _1115414, _1115412))))], (28022 ^ _773908) ^ [_1281309, _1281311] : [class_Lattices_Obounded__lattice__bot(_1281309), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1281309), _1281311), c_Orderings_Obot__class_Obot(_1281309)) = c_Orderings_Obot__class_Obot(_1281309))], (6702 ^ _773908) ^ [_882722, _882724, _882726] : [class_Orderings_Olinorder(_882722), -(_882724 = _882726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882722), _882724), _882726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882722), _882726), _882724)))], (48918 ^ _773908) ^ [_1760006, _1760008, _1760010, _1760012, _1760014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1760006, tc_HOL_Obool)), _1760008), _1760010)), 48924 ^ _773908 : [(48929 ^ _773908) ^ [] : [hBOOL(hAPP(_1760014, 48923 ^ [_1760006, _1760008, _1760010, _1760012, _1760014]))], (48927 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1760012, 48923 ^ [_1760006, _1760008, _1760010, _1760012, _1760014])))], (48925 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760006), 48923 ^ [_1760006, _1760008, _1760010, _1760012, _1760014]), _1760008)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1760006, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1760006, tc_HOL_Obool)), _1760008), hAPP(c_Set_OCollect(_1760006), _1760012))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1760006, tc_HOL_Obool)), _1760010), hAPP(c_Set_OCollect(_1760006), _1760014)))))], (39222 ^ _773908) ^ [_1534629, _1534631, _1534633, _1534635, _1534637] : [-(hAPP(hAPP(c_List_Olist_OCons(_1534629), _1534631), _1534633) = hAPP(hAPP(c_List_Olist_OCons(_1534629), _1534635), _1534637)), _1534631 = _1534635, _1534633 = _1534637], (13450 ^ _773908) ^ [_999820, _999822, _999824] : [-(_999820 = _999822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999824, tc_HOL_Obool)), _999820), _999822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999824, tc_HOL_Obool)), _999822), _999820))], (6912 ^ _773908) ^ [_885783, _885785, _885787] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885783), _885785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885783), _885787), -(_885785 = _885787)], (40327 ^ _773908) ^ [_1562994, _1562996, _1562998, _1563000] : [-(hAPP(hAPP(c_List_Oappend(_1562994), _1562996), _1562998) = _1563000), _1562996 = hAPP(hAPP(c_List_Otake(_1562994), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562994)), _1562996)), _1563000), _1562998 = hAPP(hAPP(c_List_Odrop(_1562994), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562994)), _1562996)), _1563000)], (19287 ^ _773908) ^ [_1106874, _1106876] : [class_Int_Onumber__ring(_1106874), 19290 ^ _773908 : [(19297 ^ _773908) ^ [] : [c_Int_Oiszero(_1106874, hAPP(c_Int_Onumber__class_Onumber__of(_1106874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106876), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1106874), _1106876) = c_Groups_Oone__class_Oone(_1106874))], (19291 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1106874), _1106876) = c_Groups_Oone__class_Oone(_1106874), -(c_Int_Oiszero(_1106874, hAPP(c_Int_Onumber__class_Onumber__of(_1106874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106876), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (33632 ^ _773908) ^ [_1398583, _1398585, _1398587] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398583), _1398585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398583, tc_HOL_Obool)), _1398585), hAPP(c_Set_Oimage(_1398583, _1398583, _1398587), _1398585))), -(c_Fun_Oinj__on(_1398583, _1398583, _1398587, _1398585))], (10101 ^ _773908) ^ [_941907, _941909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941907), _941909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _941907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _941909), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50424 ^ _773908) ^ [_1794855, _1794857] : [c_Relation_Oantisym(_1794855, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1794855, _1794855), tc_HOL_Obool)), _1794857), c_Relation_OId(_1794855))), -(c_Relation_Oantisym(_1794855, _1794857))], (40103 ^ _773908) ^ [_1557668, _1557670, _1557672] : [40104 ^ _773908 : [(40107 ^ _773908) ^ [] : [_1557672 = c_List_Olist_ONil(_1557668)], (40105 ^ _773908) ^ [] : [_1557670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1557668), _1557670), _1557672) = c_List_Olist_ONil(_1557668))], (15231 ^ _773908) ^ [_1032202, _1032204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032202), _1032204)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032204)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032202)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032204), _1032202)))], (39601 ^ _773908) ^ [_1543790, _1543792, _1543794, _1543796] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1543790), tc_List_Olist(_1543790))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1543790), tc_List_Olist(_1543790)), _1543792), _1543794)), c_List_Olistrel1(_1543790, _1543796))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1543790)), _1543792) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1543790)), _1543794))], (37293 ^ _773908) ^ [_1477589, _1477591, _1477593, _1477595, _1477597, _1477599] : [-(hBOOL(hAPP(hAPP(c_member(_1477589), _1477591), _1477593))), 37296 ^ _773908 : [(37303 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477589), _1477595), _1477593))), -(hAPP(c_Set_Ovimage(_1477597, _1477589, hAPP(hAPP(c_COMBC(_1477597, _1477589, _1477589), hAPP(hAPP(c_COMBC(_1477597, _1477589, tc_fun(_1477589, _1477589)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477589, tc_fun(_1477589, _1477589)), _1477597), c_If(_1477589)), hAPP(hAPP(c_COMBC(_1477597, tc_fun(_1477597, tc_HOL_Obool), tc_HOL_Obool), c_member(_1477597)), _1477599))), _1477591)), _1477595)), _1477593) = c_Orderings_Obot__class_Obot(tc_fun(_1477597, tc_HOL_Obool)))], (37297 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1477589), _1477595), _1477593)), -(hAPP(c_Set_Ovimage(_1477597, _1477589, hAPP(hAPP(c_COMBC(_1477597, _1477589, _1477589), hAPP(hAPP(c_COMBC(_1477597, _1477589, tc_fun(_1477589, _1477589)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477589, tc_fun(_1477589, _1477589)), _1477597), c_If(_1477589)), hAPP(hAPP(c_COMBC(_1477597, tc_fun(_1477597, tc_HOL_Obool), tc_HOL_Obool), c_member(_1477597)), _1477599))), _1477591)), _1477595)), _1477593) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1477597, tc_HOL_Obool)), _1477599))]]], (3882 ^ _773908) ^ [_832457, _832459, _832461, _832463] : [-(c_Big__Operators_Olinorder__class_OMin(_832463, _832459) = c_Big__Operators_Olinorder__class_OMin(_832461, _832457)), _832463 = _832461, _832459 = _832457], (37058 ^ _773908) ^ [_1471991, _1471993, _1471995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471991, tc_HOL_Obool)), _1471993), hAPP(hAPP(c_Set_Oinsert(_1471991), _1471995), c_Orderings_Obot__class_Obot(tc_fun(_1471991, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1471991, _1471995, _1471993) = c_HOL_OThe(_1471991, hAPP(hAPP(c_COMBC(_1471991, tc_fun(_1471991, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471991)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471991, tc_HOL_Obool)), _1471993), hAPP(hAPP(c_Set_Oinsert(_1471991), _1471995), c_Orderings_Obot__class_Obot(tc_fun(_1471991, tc_HOL_Obool)))))))], (37135 ^ _773908) ^ [_1473738, _1473740, _1473742, _1473744, _1473746] : [-(hAPP(c_Set_Ovimage(_1473738, _1473740, _1473742), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473740, tc_HOL_Obool)), _1473744), _1473746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473738, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473738, _1473740, _1473742), _1473744)), hAPP(c_Set_Ovimage(_1473738, _1473740, _1473742), _1473746)))], (22837 ^ _773908) ^ [_1170110, _1170112, _1170114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1170110), _1170112)), -(c_Random_Ominus__shift(_1170114, _1170110, _1170112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1170114), _1170110)), _1170112))], (19211 ^ _773908) ^ [_1105631, _1105633] : [class_Int_Oring__char__0(_1105631), hBOOL(hAPP(hAPP(c_member(_1105631), _1105633), c_Int_Oring__1__class_OInts(_1105631))), 19218 ^ _773908 : [(19225 ^ _773908) ^ [] : [_1105633 = c_Groups_Ozero__class_Ozero(_1105631), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105631), _1105633), _1105633) = c_Groups_Ozero__class_Ozero(_1105631))], (19219 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105631), _1105633), _1105633) = c_Groups_Ozero__class_Ozero(_1105631), -(_1105633 = c_Groups_Ozero__class_Ozero(_1105631))]]], (41758 ^ _773908) ^ [_1596643, _1596645, _1596647, _1596649] : [-(_1596643 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596645)), _1596647)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1596645, hAPP(hAPP(c_List_Olist__update(_1596645, _1596647), _1596643), _1596649)) = hAPP(hAPP(c_List_Olist__update(_1596645, c_List_Obutlast(_1596645, _1596647)), _1596643), _1596649))], (50850 ^ _773908) ^ [_1802370, _1802372, _1802374, _1802376, _1802378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802370, tc_HOL_Obool)), _1802372), hAPP(c_Set_Oimage(_1802374, _1802370, _1802376), _1802378))), -(c_Fun_Oinj__on(_1802370, _1802374, c_Hilbert__Choice_Oinv__into(_1802374, _1802370, _1802378, _1802376), _1802372))], (15785 ^ _773908) ^ [_1042617, _1042619, _1042621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042617), _1042619)), 15788 ^ _773908 : [(15795 ^ _773908) ^ [] : [_1042619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042621), _1042617), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042619), _1042617) = _1042621)], (15789 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042619), _1042617) = _1042621, -(_1042619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042621), _1042617))]]], (42848 ^ _773908) ^ [_1624071] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1624071)) = _1624071)], (38144 ^ _773908) ^ [_1499936, _1499938, _1499940, _1499942, _1499944, _1499946] : [-(hAPP(c_Set_Oimage(_1499936, _1499938, hAPP(hAPP(c_COMBS(_1499936, _1499938, _1499938), hAPP(hAPP(c_COMBS(_1499936, _1499938, tc_fun(_1499938, _1499938)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1499938, tc_fun(_1499938, _1499938)), _1499936), c_If(_1499938)), _1499940)), _1499942)), _1499944)), _1499946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499938, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1499936, _1499938, _1499942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499936, tc_HOL_Obool)), _1499946), hAPP(c_Set_OCollect(_1499936), _1499940)))), hAPP(c_Set_Oimage(_1499936, _1499938, _1499944), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499936, tc_HOL_Obool)), _1499946), hAPP(c_Set_OCollect(_1499936), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1499936), c_fNot), _1499940))))))], (6472 ^ _773908) ^ [_879062, _879064, _879066, _879068] : [class_Groups_Oab__semigroup__add(_879062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879062), _879064), _879066)), _879068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879062), _879064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879062), _879066), _879068)))], (41740 ^ _773908) ^ [_1596211, _1596213, _1596215] : [-(c_List_Obutlast(_1596211, hAPP(hAPP(c_List_Oappend(_1596211), _1596213), hAPP(hAPP(c_List_Olist_OCons(_1596211), _1596215), c_List_Olist_ONil(_1596211)))) = _1596213)], (30640 ^ _773908) ^ [_1334715, _1334717, _1334719] : [-(hAPP(c_Finite__Set_Ocard(_1334715), _1334717) = hAPP(c_Nat_OSuc, _1334719)), 30641 ^ _773908 : [(30642 ^ _773908) ^ [_1334815, _1334817] : [_1334717 = hAPP(hAPP(c_Set_Oinsert(_1334715), _1334817), _1334815), -(hBOOL(hAPP(hAPP(c_member(_1334715), _1334817), _1334815))), hAPP(c_Finite__Set_Ocard(_1334715), _1334815) = _1334719, 30653 ^ _773908 : [(30656 ^ _773908) ^ [] : [_1334815 = c_Orderings_Obot__class_Obot(tc_fun(_1334715, tc_HOL_Obool))], (30654 ^ _773908) ^ [] : [-(_1334719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (21123 ^ _773908) ^ [_1139297, _1139299, _1139301, _1139303] : [class_Fields_Ofield__inverse__zero(_1139297), 21126 ^ _773908 : [(21127 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139297), _1139299), _1139301) = _1139303, 21130 ^ _773908 : [(21137 ^ _773908) ^ [] : [_1139301 = c_Groups_Ozero__class_Ozero(_1139297), -(_1139303 = c_Groups_Ozero__class_Ozero(_1139297))], (21131 ^ _773908) ^ [] : [-(_1139301 = c_Groups_Ozero__class_Ozero(_1139297)), -(_1139299 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139297), _1139303), _1139301))]]], (21143 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139297), _1139299), _1139301) = _1139303), 21146 ^ _773908 : [(21149 ^ _773908) ^ [] : [_1139299 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139297), _1139303), _1139301)], (21147 ^ _773908) ^ [] : [_1139301 = c_Groups_Ozero__class_Ozero(_1139297)]], 21150 ^ _773908 : [(21153 ^ _773908) ^ [] : [_1139303 = c_Groups_Ozero__class_Ozero(_1139297)], (21151 ^ _773908) ^ [] : [-(_1139301 = c_Groups_Ozero__class_Ozero(_1139297))]]]]], (23656 ^ _773908) ^ [_1186588, _1186590, _1186592, _1186594, _1186596] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1186588, _1186590), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1186592), _1186594))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186596)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1186588, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186590), _1186596)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1186592), _1186596)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186590), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1186592, _1186596))), _1186594)))))], (37368 ^ _773908) ^ [_1479496, _1479498, _1479500] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1479496, _1479498), c_Orderings_Obot__class_Obot(tc_fun(_1479496, tc_HOL_Obool))), _1479500) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479496, _1479498), tc_HOL_Obool)))], (18615 ^ _773908) ^ [_1095426, _1095428, _1095430] : [hBOOL(hAPP(hAPP(c_member(_1095426), _1095428), hAPP(hAPP(c_Set_Oinsert(_1095426), _1095430), c_Orderings_Obot__class_Obot(tc_fun(_1095426, tc_HOL_Obool))))), -(_1095428 = _1095430)], (21355 ^ _773908) ^ [_1142950, _1142952, _1142954] : [class_Fields_Ofield__inverse__zero(_1142950), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142950), c_Groups_Oone__class_Oone(_1142950)), hAPP(hAPP(c_Power_Opower__class_Opower(_1142950), _1142952), _1142954)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1142950), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142950), c_Groups_Oone__class_Oone(_1142950)), _1142952)), _1142954))], (34258 ^ _773908) ^ [_1411917, _1411919, _1411921] : [class_Orderings_Olinorder(_1411917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411917), _1411919), _1411921)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411917, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1411917), _1411919)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1411917, _1411919, _1411921)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1411917), _1411921))], (40231 ^ _773908) ^ [_1560636, _1560638, _1560640] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1560636, tc_HOL_Obool)), hAPP(c_List_Oset(_1560636), _1560638)), hAPP(c_List_Oset(_1560636), hAPP(hAPP(c_List_Olist_OCons(_1560636), _1560640), _1560638)))))], (19231 ^ _773908) ^ [_1105951, _1105953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105951), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105951)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105953)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21167 ^ _773908) ^ [_1139953, _1139955, _1139957, _1139959] : [class_Fields_Ofield__inverse__zero(_1139953), -(_1139955 = c_Groups_Ozero__class_Ozero(_1139953)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139953), _1139955), _1139957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139953), _1139955), _1139959)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139953), _1139957), _1139959))], (25075 ^ _773908) ^ [_1216688, _1216690, _1216692, _1216694, _1216696, _1216698, _1216700] : [-(hAPP(c_Product__Type_Oapfst(_1216688, _1216690, _1216692, _1216694), hAPP(c_Product__Type_Oapsnd(_1216696, _1216692, _1216688, _1216698), _1216700)) = hAPP(hAPP(c_Product__Type_OPair(_1216690, _1216692), hAPP(_1216694, hAPP(c_Product__Type_Ofst(_1216688, _1216696), _1216700))), hAPP(_1216698, hAPP(c_Product__Type_Osnd(_1216688, _1216696), _1216700))))], (30821 ^ _773908) ^ [_1338452, _1338454, _1338456, _1338458] : [class_Groups_Ocomm__monoid__mult(_1338452), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338454), _1338456))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338454, _1338452), _1338458), _1338456) = c_Groups_Oone__class_Oone(_1338452))], (36779 ^ _773908) ^ [_1466890, _1466892] : [class_Orderings_Olinorder(_1466890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466890), _1466892)), -(c_Big__Operators_Olattice_OInf__fin(_1466890, c_Orderings_Oord__class_Omin(_1466890), _1466892) = hAPP(c_Finite__Set_Ofold1(_1466890, c_Orderings_Oord__class_Omin(_1466890)), _1466892))], (42525 ^ _773908) ^ [_1617128, _1617130, _1617132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617128), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617130)), _1617132))), -(hAPP(c_Random_Opick(_1617130, hAPP(hAPP(c_List_Omap(_1617130, tc_prod(tc_Code__Numeral_Ocode__numeral, _1617130)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1617130), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1617132)), hAPP(c_Code__Numeral_Oof__nat, _1617128)) = hAPP(hAPP(c_List_Onth(_1617130), _1617132), _1617128))], (32474 ^ _773908) ^ [_1376785, _1376787, _1376789] : [hAPP(c_Set_Oimage(_1376787, tc_fun(_1376787, tc_HOL_Obool), _1376785), _1376789) = hAPP(c_Set_OPow(_1376787), _1376789)], (25675 ^ _773908) ^ [] : [-(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)))], (49296 ^ _773908) ^ [_1768233, _1768235, _1768237, _1768239, _1768241] : [-(hAPP(c_New__DSequence_Oneg__bind(_1768233, _1768235, _1768237, _1768239), _1768241) = c_Lazy__Sequence_Ohb__bind(_1768233, _1768235, hAPP(_1768237, _1768241), hAPP(hAPP(c_COMBC(_1768233, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1768235))), _1768239), _1768241)))], (10463 ^ _773908) ^ [_947241, _947243] : [class_Groups_Omonoid__mult(_947241), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947241), _947243), c_Groups_Oone__class_Oone(_947241)) = _947243)], (44247 ^ _773908) ^ [_1656020, _1656022, _1656024, _1656026] : [44249 ^ _773908 : [(44252 ^ _773908) ^ [] : [c_Wellfounded_Owf(_1656022, hAPP(_1656024, 44248 ^ [_1656020, _1656022, _1656024, _1656026]))], (44250 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1656020, 44248 ^ [_1656020, _1656022, _1656024, _1656026])))]], -(c_Wellfounded_Owf(tc_prod(_1656026, _1656022), c_Recdef_Osame__fst(_1656026, _1656022, _1656020, _1656024)))], (13943 ^ _773908) ^ [_1008711, _1008713, _1008715] : [hBOOL(hAPP(_1008711, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008713, _1008715))), 13946 ^ _773908 : [(13971 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008715), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13974 ^ _773908 : [(13975 ^ _773908) ^ [_1009333, _1009335] : [-(hBOOL(hAPP(_1008711, _1009333))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008715), _1009333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1009333), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1008713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008715), _1009335)), _1009333)]]], (13953 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008715)), 13956 ^ _773908 : [(13957 ^ _773908) ^ [_1009041, _1009043] : [-(hBOOL(hAPP(_1008711, _1009041))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009041), _1008715)), _1008713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008715), _1009043)), _1009041)]]], (13947 ^ _773908) ^ [] : [_1008715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1008711, _1008713)))]]], (39294 ^ _773908) ^ [_1537126, _1537128, _1537130, _1537132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1537126), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1537128), _1537130))), -(hAPP(c_Random_Opick(_1537128, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1537128)), _1537130), _1537132)), _1537126) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1537128), _1537130))], (14067 ^ _773908) ^ [_1011083, _1011085, _1011087, _1011089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011085), _1011087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1011087), 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), _1011085), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011089, _1011083))), _1011087)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17987 ^ _773908) ^ [_1084150, _1084152, _1084154, _1084156] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1084150, _1084152, _1084154), _1084156), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1084152)], (27492 ^ _773908) ^ [_1270842, _1270844, _1270846, _1270848, _1270850, _1270852, _1270854, _1270856] : [c_Finite__Set_Ofolding(_1270842, _1270844, _1270846, _1270848), -(hAPP(c_Fun_Ocomp(_1270844, _1270844, _1270850, hAPP(_1270846, _1270852)), hAPP(c_Fun_Ocomp(_1270844, _1270844, _1270850, hAPP(_1270846, _1270854)), _1270856)) = hAPP(c_Fun_Ocomp(_1270844, _1270844, _1270850, hAPP(_1270846, _1270854)), hAPP(c_Fun_Ocomp(_1270844, _1270844, _1270850, hAPP(_1270846, _1270852)), _1270856)))], (40091 ^ _773908) ^ [_1557503, _1557505] : [-(hAPP(hAPP(c_List_Otake(_1557503), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1557505) = c_List_Olist_ONil(_1557503))], (4134 ^ _773908) ^ [_836345, _836347, _836349, _836351, _836353, _836355] : [-(c_Product__Type_Ointernal__split(_836355, _836351, _836347) = c_Product__Type_Ointernal__split(_836353, _836349, _836345)), _836355 = _836353, _836351 = _836349, _836347 = _836345], (40515 ^ _773908) ^ [_1567817, _1567819, _1567821] : [-(hAPP(c_List_Ohd(_1567817), hAPP(hAPP(c_List_Olist_OCons(_1567817), _1567819), _1567821)) = _1567819)], (36303 ^ _773908) ^ [_1455604, _1455606] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455604, 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(_1455604, tc_HOL_Obool)), tc_fun(_1455604, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1455604, tc_HOL_Obool)), tc_fun(_1455604, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455604, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1455606)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455604, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455606))], (50023 ^ _773908) ^ [_1784698, _1784700, _1784702] : [-(c_List_Olist__ex(_1784698, _1784700, _1784702)), 50024 ^ _773908 : [(50025 ^ _773908) ^ [_1784755] : [hBOOL(hAPP(hAPP(c_member(_1784698), _1784755), hAPP(c_List_Oset(_1784698), _1784702))), hBOOL(hAPP(_1784700, _1784755))]]], (50158 ^ _773908) ^ [_1789316, _1789318, _1789320, _1789322] : [-(c_Wellfounded_Omax__extp(_1789316, _1789318, _1789320, _1789322)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789316), _1789320)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789316), _1789322)), -(_1789322 = c_Orderings_Obot__class_Obot(tc_fun(_1789316, tc_HOL_Obool))), 50172 ^ _773908 : [(50175 ^ _773908) ^ [_1789661] : [hBOOL(hAPP(hAPP(c_member(_1789316), _1789661), _1789322)), hBOOL(hAPP(hAPP(_1789318, 50171 ^ [_1789316, _1789318, _1789320, _1789322]), _1789661))], (50173 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789316), 50171 ^ [_1789316, _1789318, _1789320, _1789322]), _1789320)))]]], (11938 ^ _773908) ^ [_973681, _973683, _973685, _973687, _973689] : [class_Rings_Olinordered__semiring__strict(_973681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973681), _973683), _973685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973681), _973687), _973689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973681), c_Groups_Ozero__class_Ozero(_973681)), _973683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973681), c_Groups_Ozero__class_Ozero(_973681)), _973687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973681), _973683), _973687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973681), _973685), _973689))))], (45617 ^ _773908) ^ [_1685160, _1685162] : [-(hAPP(c_List_Orev(_1685160), _1685162) = hAPP(c_List_Ofoldl(tc_List_Olist(_1685160), _1685160, hAPP(c_COMBC(_1685160, tc_List_Olist(_1685160), tc_List_Olist(_1685160)), c_List_Olist_OCons(_1685160)), c_List_Olist_ONil(_1685160)), _1685162))], (15327 ^ _773908) ^ [_1033822, _1033824, _1033826] : [class_Groups_Ogroup__add(_1033822), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033822), _1033824), _1033826)), _1033826) = _1033824)], (48203 ^ _773908) ^ [_1745467, _1745469, _1745471, _1745473] : [class_Lattices_Osemilattice__inf(_1745467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745467), _1745469)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1745467, _1745467, c_Lattices_Osemilattice__inf__class_Oinf(_1745467)), _1745471), hAPP(hAPP(c_Set_Oinsert(_1745467), _1745473), _1745469)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1745467), _1745473), hAPP(hAPP(c_Finite__Set_Ofold(_1745467, _1745467, c_Lattices_Osemilattice__inf__class_Oinf(_1745467)), _1745471), _1745469)))], (12720 ^ _773908) ^ [_986984, _986986, _986988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986984), _986986)), _986988)), 12723 ^ _773908 : [(12726 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986986), _986988)))], (12724 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986984), _986988)))]]], (13546 ^ _773908) ^ [_1001495, _1001497, _1001499, _1001501] : [class_Divides_Osemiring__div(_1001495), -(c_Divides_Odiv__class_Omod(_1001495, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001495), _1001497), _1001499), _1001501) = c_Divides_Odiv__class_Omod(_1001495, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001495), _1001497), c_Divides_Odiv__class_Omod(_1001495, _1001499, _1001501)), _1001501))], (18879 ^ _773908) ^ [] : [c_Int_OPls = c_Int_OMin], (33528 ^ _773908) ^ [_1396781, _1396783, _1396785] : [class_Orderings_Oorder(_1396781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396781), _1396783), _1396785)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1396781, _1396785), _1396783) = c_Orderings_Obot__class_Obot(tc_fun(_1396781, tc_HOL_Obool)))], (10423 ^ _773908) ^ [_946585, _946587, _946589, _946591] : [class_Orderings_Opreorder(_946585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946585), _946587), _946589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946585), _946589), _946591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946585), _946587), _946591)))], (28362 ^ _773908) ^ [_1289124, _1289126, _1289128, _1289130] : [-(hBOOL(hAPP(hAPP(c_member(_1289124), _1289126), _1289128))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289124, tc_HOL_Obool)), _1289128), hAPP(hAPP(c_Set_Oinsert(_1289124), _1289126), _1289130)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289124, tc_HOL_Obool)), _1289128), _1289130))], (18408 ^ _773908) ^ [_1091696, _1091698] : [18409 ^ _773908 : [(18410 ^ _773908) ^ [_1091749] : [hBOOL(hAPP(hAPP(c_member(_1091696), _1091749), _1091698))]], _1091698 = c_Orderings_Obot__class_Obot(tc_fun(_1091696, tc_HOL_Obool))], (36245 ^ _773908) ^ [_1454267, _1454269] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1454267), c_Orderings_Otop__class_Otop(tc_fun(_1454267, tc_HOL_Obool)))), c_Fun_Oinj__on(_1454267, _1454267, _1454269, c_Orderings_Otop__class_Otop(tc_fun(_1454267, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1454267, _1454267, _1454269), c_Orderings_Otop__class_Otop(tc_fun(_1454267, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1454267, tc_HOL_Obool)))], (50687 ^ _773908) ^ [_1799462, _1799464] : [-(c_Relation_Osym(_1799462, c_Relation_OId__on(_1799462, _1799464)))], (50037 ^ _773908) ^ [_1785106, _1785108, _1785110] : [hBOOL(hAPP(hAPP(c_member(_1785108), _1785106), c_Orderings_Obot__class_Obot(tc_fun(_1785108, tc_HOL_Obool)))), hBOOL(hAPP(_1785110, _1785106))], (46033 ^ _773908) ^ [_1693951, _1693953, _1693955, _1693957] : [class_Orderings_Olinorder(_1693951), -(hAPP(c_List_Oset(_1693953), c_List_Olinorder__class_Osort__key(_1693953, _1693951, _1693955, _1693957)) = hAPP(c_List_Oset(_1693953), _1693957))], (42890 ^ _773908) ^ [_1624807] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1624807), 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, _1624807)) = _1624807)], (51422 ^ _773908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (43515 ^ _773908) ^ [_1638542, _1638544, _1638546, _1638548, _1638550, _1638552, _1638554] : [c_List_Olist__all2(_1638542, _1638550, hAPP(hAPP(c_COMBC(_1638542, tc_fun(_1638550, _1638544), tc_fun(_1638550, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638544, tc_HOL_Obool), tc_fun(tc_fun(_1638550, _1638544), tc_fun(_1638550, tc_HOL_Obool)), _1638542), c_COMBB(_1638544, tc_HOL_Obool, _1638550)), _1638546)), _1638552), _1638548, _1638554), -(c_List_Olist__all2(_1638542, _1638544, _1638546, _1638548, hAPP(hAPP(c_List_Omap(_1638550, _1638544), _1638552), _1638554)))], (34292 ^ _773908) ^ [_1412505] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412505)) = _1412505)], (23329 ^ _773908) ^ [_1179978] : [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), _1179978))), 23332 ^ _773908 : [(23339 ^ _773908) ^ [] : [-(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), _1179978)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179978)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179978)), 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), _1179978)))))], (23333 ^ _773908) ^ [] : [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), _1179978))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179978)) = 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)))]]], (49912 ^ _773908) ^ [_1782077, _1782079] : [-(c_Lazy__Sequence_Oappend(_1782077, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1782077), _1782079) = _1782079)], (12943 ^ _773908) ^ [_990972, _990974, _990976, _990978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990972, tc_HOL_Obool)), _990974), _990976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990972, tc_HOL_Obool)), _990976), _990978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990972, tc_HOL_Obool)), _990974), _990978)))], (23492 ^ _773908) ^ [] : [-(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)))))], (32736 ^ _773908) ^ [_1381604, _1381606, _1381608, _1381610] : [class_Orderings_Oorder(_1381604), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381604, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1381604, _1381606, _1381608)), c_SetInterval_Oord__class_OatLeastAtMost(_1381604, _1381608, _1381610)) = c_Orderings_Obot__class_Obot(tc_fun(_1381604, tc_HOL_Obool)))], (1314 ^ _773908) ^ [_793319, _793321] : [-(class_Groups_Osgn__if(_793319)), _793321 = _793319, class_Groups_Osgn__if(_793321)], (15221 ^ _773908) ^ [_1032003, _1032005, _1032007] : [class_Rings_Oring__1(_1032003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032005), _1032007)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032003), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032007), _1032005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032003), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032003), _1032007)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032003), _1032005)))], (38500 ^ _773908) ^ [_1514414, _1514416] : [-(hAPP(hAPP(c_Nat_Ocompow(_1514414, _1514414), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1514416) = c_Fun_Oid(_1514414))], (28614 ^ _773908) ^ [_1294923, _1294925, _1294927, _1294929, _1294931, _1294933] : [c_Finite__Set_Ofolding(_1294923, _1294925, _1294927, _1294929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294923), _1294931)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294923), _1294933)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294923, tc_HOL_Obool)), _1294931), _1294933) = c_Orderings_Obot__class_Obot(tc_fun(_1294923, tc_HOL_Obool)), -(hAPP(_1294929, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294923, tc_HOL_Obool)), _1294931), _1294933)) = hAPP(c_Fun_Ocomp(_1294925, _1294925, _1294925, hAPP(_1294929, _1294931)), hAPP(_1294929, _1294933)))], (6316 ^ _773908) ^ [_876226] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876226), hAPP(c_Nat_OSuc, _876226))))], (20609 ^ _773908) ^ [_1130095, _1130097] : [class_Int_Onumber__ring(_1130095), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1130095), hAPP(c_Int_Onumber__class_Onumber__of(_1130095), 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)))), _1130097)) = c_Groups_Oone__class_Oone(_1130095))], (45886 ^ _773908) ^ [_1690871, _1690873, _1690875] : [c_List_OdropWhile(_1690871, _1690873, _1690875) = c_List_Olist_ONil(_1690871), 45889 ^ _773908 : [(45890 ^ _773908) ^ [_1690962] : [hBOOL(hAPP(hAPP(c_member(_1690871), _1690962), hAPP(c_List_Oset(_1690871), _1690875))), -(hBOOL(hAPP(_1690873, _1690962)))]]], (4804 ^ _773908) ^ [_847196, _847198] : [_847198 = _847196, -(c_Lazy__Sequence_Oyield(_847198) = c_Lazy__Sequence_Oyield(_847196))], (22369 ^ _773908) ^ [_1161406, _1161408, _1161410, _1161412] : [class_Fields_Olinordered__field__inverse__zero(_1161406), class_Int_Onumber(_1161406), 22376 ^ _773908 : [(22377 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161406), _1161410), _1161412))), 22380 ^ _773908 : [(22387 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), c_Groups_Ozero__class_Ozero(_1161406)), _1161412))), 22390 ^ _773908 : [(22397 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161412), c_Groups_Ozero__class_Ozero(_1161406)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), c_Groups_Ozero__class_Ozero(_1161406))))], (22391 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161412), c_Groups_Ozero__class_Ozero(_1161406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), _1161412))))]]], (22381 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), c_Groups_Ozero__class_Ozero(_1161406)), _1161412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), _1161412)), _1161410)))]]], (22403 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161406), _1161410), _1161412)))), 22406 ^ _773908 : [(22409 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), _1161412)), _1161410))], (22407 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), c_Groups_Ozero__class_Ozero(_1161406)), _1161412)))]], 22410 ^ _773908 : [(22413 ^ _773908) ^ [] : [22414 ^ _773908 : [(22417 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), _1161412)))], (22415 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161412), c_Groups_Ozero__class_Ozero(_1161406))))]], 22418 ^ _773908 : [(22421 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), hAPP(c_Int_Onumber__class_Onumber__of(_1161406), _1161408)), c_Groups_Ozero__class_Ozero(_1161406)))], (22419 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), _1161412), c_Groups_Ozero__class_Ozero(_1161406)))]]], (22411 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161406), c_Groups_Ozero__class_Ozero(_1161406)), _1161412))]]]]], (43973 ^ _773908) ^ [_1649753, _1649755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1649753, tc_HOL_Obool)), _1649755)), 43979 ^ _773908 : [(43982 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649753), 43978 ^ [_1649753, _1649755]))], (43980 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1649753, tc_HOL_Obool)), 43978 ^ [_1649753, _1649755]), _1649755)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1649753), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649753, tc_HOL_Obool), _1649755))))], (41630 ^ _773908) ^ [_1594055] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1594055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 41633 ^ _773908 : [(41634 ^ _773908) ^ [_1594130] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1594130), hAPP(c_List_Oset(tc_Nat_Onat), _1594055))), -(_1594130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44156 ^ _773908) ^ [_1653932, _1653934] : [class_Complete__Lattice_Ocomplete__lattice(_1653932), -(c_Complete__Lattice_OInf__class_OInf(_1653932, hAPP(hAPP(c_Set_Oinsert(_1653932), _1653934), c_Orderings_Obot__class_Obot(tc_fun(_1653932, tc_HOL_Obool)))) = _1653934)], (7287 ^ _773908) ^ [_891890, _891892, _891894] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_891890, _891892, _891894)], (47170 ^ _773908) ^ [_1721188, _1721190, _1721192, _1721194, _1721196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1721188, _1721188)), hAPP(hAPP(c_Product__Type_OPair(_1721188, _1721188), _1721190), _1721192)), c_Transitive__Closure_Otrancl(_1721188, _1721194))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1721188, _1721188)), hAPP(hAPP(c_Product__Type_OPair(_1721188, _1721188), _1721192), _1721196)), c_Transitive__Closure_Otrancl(_1721188, _1721194))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1721188, _1721188)), hAPP(hAPP(c_Product__Type_OPair(_1721188, _1721188), _1721190), _1721196)), c_Transitive__Closure_Otrancl(_1721188, _1721194))))], (28795 ^ _773908) ^ [_1299790, _1299792, _1299794, _1299796, _1299798] : [-(hBOOL(hAPP(hAPP(c_member(_1299790), _1299792), c_SetInterval_Oord_OatLeastAtMost(_1299790, _1299794, _1299796, _1299798)))), hBOOL(hAPP(hAPP(_1299794, _1299796), _1299792)), hBOOL(hAPP(hAPP(_1299794, _1299792), _1299798))], (9571 ^ _773908) ^ [_933370, _933372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933370), hAPP(c_Int_Onat, _933372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933370)), _933372)))], (37884 ^ _773908) ^ [_1493861] : [-(c_Finite__Set_Ofun__left__comm__idem(_1493861, tc_fun(_1493861, tc_HOL_Obool), c_Set_Oinsert(_1493861)))], (40936 ^ _773908) ^ [_1580143, _1580145, _1580147, _1580149] : [-(hAPP(c_List_Olist_Olist__case(_1580143, _1580145, _1580147, _1580149), c_List_Olist_ONil(_1580145)) = _1580147)], (47114 ^ _773908) ^ [_1719895, _1719897] : [c_Wellfounded_Owf(_1719895, _1719897), -(c_Wellfounded_Owf(_1719895, c_Transitive__Closure_Otrancl(_1719895, _1719897)))], (25379 ^ _773908) ^ [_1222306, _1222308, _1222310] : [class_Orderings_Olinorder(_1222306), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222306), _1222308), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222306), _1222308), _1222310)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222306), _1222308), _1222310))], (17739 ^ _773908) ^ [_1080439, _1080441, _1080443] : [class_Rings_Olinordered__semidom(_1080439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080439), c_Groups_Ozero__class_Ozero(_1080439)), _1080441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080439), _1080441), c_Groups_Oone__class_Oone(_1080439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080439), _1080441), hAPP(hAPP(c_Power_Opower__class_Opower(_1080439), _1080441), _1080443))), hAPP(hAPP(c_Power_Opower__class_Opower(_1080439), _1080441), _1080443))))], (26408 ^ _773908) ^ [_1246653, _1246655, _1246657, _1246659, _1246661, _1246663] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246653, tc_fun(_1246655, tc_HOL_Obool))), _1246657), _1246659), _1246661), _1246663)), -(hBOOL(hAPP(hAPP(_1246657, _1246661), _1246663))), -(hBOOL(hAPP(hAPP(_1246659, _1246661), _1246663)))], (43029 ^ _773908) ^ [_1627745, _1627747, _1627749] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627745, tc_HOL_Obool)), hAPP(c_List_Oset(_1627745), c_List_Oremove1(_1627745, _1627747, _1627749))), hAPP(c_List_Oset(_1627745), _1627749))))], (3232 ^ _773908) ^ [_822370, _822372] : [_822372 = _822370, -(c_Power_Opower__class_Opower(_822372) = c_Power_Opower__class_Opower(_822370))], (5977 ^ _773908) ^ [_869790, _869792, _869794] : [c_Hoare__Mirabelle_Otriple__valid(_869790, hAPP(c_Nat_OSuc, _869792), _869794), -(c_Hoare__Mirabelle_Otriple__valid(_869790, _869792, _869794))], (22953 ^ _773908) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (2806 ^ _773908) ^ [_815633, _815635, _815637, _815639] : [-(c_Divides_Odivmod__nat__rel(_815639, _815635) = c_Divides_Odivmod__nat__rel(_815637, _815633)), _815639 = _815637, _815635 = _815633], (32620 ^ _773908) ^ [_1379339, _1379341, _1379343] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1379339, tc_HOL_Obool)), _1379341), hAPP(c_Set_OPow(_1379339), _1379343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379339, tc_HOL_Obool)), _1379341), _1379343)))], (16145 ^ _773908) ^ [_1050449, _1050451] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050449), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1050451), _1050449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050451), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050451, _1050449)))], (43031 ^ _773908) ^ [_1627811, _1627813, _1627815, _1627817] : [hBOOL(hAPP(hAPP(c_member(_1627811), _1627813), hAPP(c_List_Oset(_1627811), _1627815))), -(c_List_Oremove1(_1627811, _1627813, hAPP(hAPP(c_List_Oappend(_1627811), _1627815), _1627817)) = hAPP(hAPP(c_List_Oappend(_1627811), c_List_Oremove1(_1627811, _1627813, _1627815)), _1627817))], (33570 ^ _773908) ^ [_1397398, _1397400, _1397402, _1397404, _1397406] : [class_Orderings_Olinorder(_1397398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397398, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397398, _1397400), _1397402)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1397398, _1397404), _1397406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397398), _1397402), _1397400))), 33581 ^ _773908 : [(33584 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397398), _1397402), _1397406)))], (33582 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397398), _1397404), _1397400)))]]], (28264 ^ _773908) ^ [_1286773, _1286775] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1286773), c_Orderings_Obot__class_Obot(tc_fun(_1286773, tc_HOL_Obool))), _1286775) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286773, tc_HOL_Obool), tc_HOL_Obool)))], (8575 ^ _773908) ^ [_915713, _915715, _915717, _915719] : [class_Rings_Ocomm__semiring__1(_915713), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915713), _915715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915713), _915717), _915719)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915713), _915717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915713), _915715), _915719)))], (32217 ^ _773908) ^ [_1371290, _1371292, _1371294] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1371290, _1371290)), _1371292), c_Relation_OId__on(_1371290, _1371294))), 32221 ^ _773908 : [(32224 ^ _773908) ^ [] : [-(_1371292 = hAPP(hAPP(c_Product__Type_OPair(_1371290, _1371290), 32220 ^ [_1371290, _1371292, _1371294]), 32220 ^ [_1371290, _1371292, _1371294]))], (32222 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1371290), 32220 ^ [_1371290, _1371292, _1371294]), _1371294)))]]], (32147 ^ _773908) ^ [_1369909] : [-(c_Relation_OId__on(_1369909, c_Orderings_Obot__class_Obot(tc_fun(_1369909, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1369909, _1369909), tc_HOL_Obool)))], (3948 ^ _773908) ^ [_833498, _833500, _833502, _833504] : [-(c_List_Oremdups(_833504, _833500) = c_List_Oremdups(_833502, _833498)), _833504 = _833502, _833500 = _833498], (12170 ^ _773908) ^ [_977898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _977898), 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)), _977898)), _977898)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9069 ^ _773908) ^ [_924487, _924489, _924491] : [class_Groups_Ogroup__add(_924487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924487), _924489), _924491) = c_Groups_Ozero__class_Ozero(_924487), -(hAPP(c_Groups_Ouminus__class_Ouminus(_924487), _924489) = _924491)], (37163 ^ _773908) ^ [_1474406, _1474408, _1474410, _1474412, _1474414] : [-(hAPP(c_Set_Ovimage(_1474406, _1474408, _1474410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474408, tc_HOL_Obool)), _1474412), _1474414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474406, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1474406, _1474408, _1474410), _1474412)), hAPP(c_Set_Ovimage(_1474406, _1474408, _1474410), _1474414)))], (1854 ^ _773908) ^ [_800069, _800071] : [-(class_Rings_Osemiring(_800069)), _800071 = _800069, class_Rings_Osemiring(_800071)], (18559 ^ _773908) ^ [_1094497, _1094499, _1094501] : [hBOOL(hAPP(hAPP(c_member(_1094497), _1094499), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1094497, tc_HOL_Obool)), _1094501))), hBOOL(hAPP(hAPP(c_member(_1094497), _1094499), _1094501))], (17811 ^ _773908) ^ [_1081642, _1081644] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081642)))), 17814 ^ _773908 : [(17821 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081644)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081642), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081644)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081642), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081644))))], (17815 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081644))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081642), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081644)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081642))]]], (19303 ^ _773908) ^ [_1107133, _1107135] : [class_Int_Onumber__ring(_1107133), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1107133), c_Groups_Oone__class_Oone(_1107133)), hAPP(c_Int_Onumber__class_Onumber__of(_1107133), _1107135)) = hAPP(c_Int_Onumber__class_Onumber__of(_1107133), 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), _1107135))))], (23269 ^ _773908) ^ [_1178953, _1178955] : [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), _1178953))), 23272 ^ _773908 : [(23279 ^ _773908) ^ [] : [-(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), _1178955)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178955), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178955), 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), _1178953)))))], (23273 ^ _773908) ^ [] : [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), _1178955)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178955), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953)) = 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), _1178955)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178953))))]]], (28747 ^ _773908) ^ [_1298788, _1298790, _1298792, _1298794, _1298796] : [-(hBOOL(hAPP(hAPP(c_member(_1298788), _1298790), c_SetInterval_Oord_OgreaterThanLessThan(_1298788, _1298792, _1298794, _1298796)))), hBOOL(hAPP(hAPP(_1298792, _1298794), _1298790)), hBOOL(hAPP(hAPP(_1298792, _1298790), _1298796))], (50844 ^ _773908) ^ [_1802221, _1802223, _1802225, _1802227, _1802229] : [c_Fun_Oinj__on(_1802221, _1802223, _1802225, c_Orderings_Otop__class_Otop(tc_fun(_1802221, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1802223, _1802227, _1802221, hAPP(c_Fun_Ocomp(_1802221, _1802227, _1802223, _1802229), c_Hilbert__Choice_Oinv__into(_1802221, _1802223, c_Orderings_Otop__class_Otop(tc_fun(_1802221, tc_HOL_Obool)), _1802225))), _1802225) = _1802229)], (38551 ^ _773908) ^ [_1515795, _1515797] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515795), _1515797)), -(_1515797 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1515795, 38555 ^ [_1515795, _1515797]), 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)), 38554 ^ [_1515795, _1515797]))))], (25697 ^ _773908) ^ [_1229256, _1229258, _1229260, _1229262] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229256, tc_HOL_Obool)), _1229258), _1229260), _1229262)), -(hBOOL(hAPP(_1229258, _1229262))), -(hBOOL(hAPP(_1229260, _1229262)))], (49716 ^ _773908) ^ [_1777345, _1777347, _1777349] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1777345, _1777347), _1777349) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1777345, tc_Lazy__Sequence_Olazy__sequence(_1777345)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1777345, tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1777345, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat)), _1777345), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1777345), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1777345)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1777345, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1777345), tc_Nat_Onat)), _1777345), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1777345))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1777345), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1777347))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1777345, _1777347))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1777345), _1777349)))], (32708 ^ _773908) ^ [_1380990, _1380992, _1380994, _1380996] : [class_Orderings_Olinorder(_1380990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380990), _1380992), _1380994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380990), _1380994), _1380996)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380990, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1380990, _1380992, _1380994)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1380990, _1380994, _1380996)) = c_SetInterval_Oord__class_OatLeastAtMost(_1380990, _1380992, _1380996))], (32780 ^ _773908) ^ [_1382519, _1382521, _1382523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1382519)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1382521), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1382523)), 32787 ^ _773908 : [(32788 ^ _773908) ^ [_1382727] : [32790 ^ _773908 : [(32796 ^ _773908) ^ [] : [-(_1382727 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32792 ^ [_1382519, _1382521, _1382523, _1382727]), 32789 ^ [_1382519, _1382521, _1382523, _1382727]))], (32794 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32792 ^ [_1382519, _1382521, _1382523, _1382727]), _1382523)))], (32791 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32789 ^ [_1382519, _1382521, _1382523, _1382727]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1382519))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382521), _1382727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1382727), _1382519))))]]], (25663 ^ _773908) ^ [_1228549, _1228551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228549), _1228551)), -(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), _1228549), _1228551)), c_Wellfounded_Oless__than)))], (25205 ^ _773908) ^ [_1219177, _1219179, _1219181] : [class_Orderings_Olinorder(_1219177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219177), _1219179), _1219181)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219177), _1219179), _1219181) = _1219181)], (44341 ^ _773908) ^ [_1657816, _1657818, _1657820] : [hBOOL(hAPP(hAPP(c_member(_1657816), _1657818), hAPP(c_List_Oset(_1657816), _1657820))), -(c_List_Oinsert(_1657816, _1657818, _1657820) = _1657820)], (31806 ^ _773908) ^ [_1361878, _1361880, _1361882, _1361884, _1361886] : [hBOOL(hAPP(hAPP(c_member(_1361878), _1361880), _1361882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1361884, tc_HOL_Obool)), hAPP(_1361886, _1361880)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361878, tc_fun(_1361884, tc_HOL_Obool)), _1361882), _1361886))))], (8675 ^ _773908) ^ [_917496, _917498, _917500, _917502] : [-(hAPP(_917496, hAPP(hAPP(hAPP(c_Nat_Ocompow(_917498, _917498), _917500), _917496), _917502)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_917498, _917498), _917500), _917496), hAPP(_917496, _917502)))], (32858 ^ _773908) ^ [_1384089, _1384091] : [32866 ^ _773908 : [(32869 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1384091, 32865 ^ [_1384089, _1384091])))], (32867 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 32865 ^ [_1384089, _1384091]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1384089))))]], 32859 ^ _773908 : [(32860 ^ _773908) ^ [_1384158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1384158), _1384089)), hBOOL(hAPP(_1384091, _1384158))]]], (41472 ^ _773908) ^ [_1590893, _1590895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1590893), _1590895))), -(c_List_Oupto(_1590893, _1590895) = c_List_Olist_ONil(tc_Int_Oint))], (8869 ^ _773908) ^ [_920815, _920817, _920819] : [class_Rings_Oring__no__zero__divisors(_920815), 8872 ^ _773908 : [(8873 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920815), _920817), _920819) = c_Groups_Ozero__class_Ozero(_920815), -(_920817 = c_Groups_Ozero__class_Ozero(_920815)), -(_920819 = c_Groups_Ozero__class_Ozero(_920815))], (8883 ^ _773908) ^ [] : [8884 ^ _773908 : [(8887 ^ _773908) ^ [] : [_920819 = c_Groups_Ozero__class_Ozero(_920815)], (8885 ^ _773908) ^ [] : [_920817 = c_Groups_Ozero__class_Ozero(_920815)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920815), _920817), _920819) = c_Groups_Ozero__class_Ozero(_920815))]]], (31850 ^ _773908) ^ [_1362965, _1362967, _1362969, _1362971, _1362973] : [-(_1362965 = c_Orderings_Obot__class_Obot(tc_fun(_1362967, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362969, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362967, tc_fun(_1362969, tc_HOL_Obool)), _1362965), _1362971)), _1362973) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362967, tc_fun(_1362969, tc_HOL_Obool)), _1362965), hAPP(hAPP(c_COMBC(_1362967, tc_fun(_1362969, tc_HOL_Obool), tc_fun(_1362969, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362969, tc_HOL_Obool), tc_fun(tc_fun(_1362969, tc_HOL_Obool), tc_fun(_1362969, tc_HOL_Obool)), _1362967), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362969, tc_HOL_Obool))), _1362971)), _1362973)))], (51398 ^ _773908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (19867 ^ _773908) ^ [_1116827] : [c_Int_OBit0(_1116827) = c_Int_OPls, -(_1116827 = c_Int_OPls)], (21089 ^ _773908) ^ [_1138803, _1138805, _1138807, _1138809] : [class_Fields_Ofield__inverse__zero(_1138803), 21092 ^ _773908 : [(21093 ^ _773908) ^ [] : [_1138805 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138803), _1138807), _1138809), 21096 ^ _773908 : [(21103 ^ _773908) ^ [] : [_1138809 = c_Groups_Ozero__class_Ozero(_1138803), -(_1138805 = c_Groups_Ozero__class_Ozero(_1138803))], (21097 ^ _773908) ^ [] : [-(_1138809 = c_Groups_Ozero__class_Ozero(_1138803)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138803), _1138805), _1138809) = _1138807)]]], (21109 ^ _773908) ^ [] : [-(_1138805 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138803), _1138807), _1138809)), 21112 ^ _773908 : [(21115 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138803), _1138805), _1138809) = _1138807], (21113 ^ _773908) ^ [] : [_1138809 = c_Groups_Ozero__class_Ozero(_1138803)]], 21116 ^ _773908 : [(21119 ^ _773908) ^ [] : [_1138805 = c_Groups_Ozero__class_Ozero(_1138803)], (21117 ^ _773908) ^ [] : [-(_1138809 = c_Groups_Ozero__class_Ozero(_1138803))]]]]], (35318 ^ _773908) ^ [_1435489, _1435491, _1435493] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435489), _1435491)), 35321 ^ _773908 : [(35341 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435489, tc_Nat_Onat), _1435493), _1435491) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 35342 ^ _773908 : [(35343 ^ _773908) ^ [_1435970] : [hBOOL(hAPP(hAPP(c_member(_1435489), _1435970), _1435491)), hAPP(_1435493, _1435970) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 35351 ^ _773908 : [(35356 ^ _773908) ^ [] : [hAPP(_1435493, 35350 ^ [_1435489, _1435491, _1435493, _1435970]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35354 ^ _773908) ^ [] : [_1435970 = 35350 ^ [_1435489, _1435491, _1435493, _1435970]], (35352 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435489), 35350 ^ [_1435489, _1435491, _1435493, _1435970]), _1435491)))]]]]], (35322 ^ _773908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435489, tc_Nat_Onat), _1435493), _1435491) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 35326 ^ _773908 : [(35331 ^ _773908) ^ [_1435809] : [hBOOL(hAPP(hAPP(c_member(_1435489), _1435809), _1435491)), -(35325 ^ [_1435489, _1435491, _1435493] = _1435809), -(hAPP(_1435493, _1435809) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35329 ^ _773908) ^ [] : [-(hAPP(_1435493, 35325 ^ [_1435489, _1435491, _1435493]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (35327 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435489), 35325 ^ [_1435489, _1435491, _1435493]), _1435491)))]]]]], (23075 ^ _773908) ^ [_1174699, _1174701, _1174703] : [class_Int_Onumber__ring(_1174699), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1174699), hAPP(c_Int_Onumber__class_Onumber__of(_1174699), _1174701)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1174703))) = hAPP(hAPP(c_HOL_OLet(_1174699, _1174699), hAPP(hAPP(c_Power_Opower__class_Opower(_1174699), hAPP(c_Int_Onumber__class_Onumber__of(_1174699), _1174701)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174703))), hAPP(hAPP(c_COMBS(_1174699, _1174699, _1174699), c_Groups_Otimes__class_Otimes(_1174699)), c_COMBI(_1174699))))], (28424 ^ _773908) ^ [_1290710, _1290712] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290710, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290710, tc_HOL_Obool)), _1290712)), _1290712) = c_Orderings_Obot__class_Obot(tc_fun(_1290710, tc_HOL_Obool)))], (23472 ^ _773908) ^ [_1183047, _1183049, _1183051, _1183053, _1183055] : [-(hAPP(c_Nat_Onat_Onat__rec(_1183047, _1183049, _1183051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1183053)), _1183055)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1183047), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1183053))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183047, _1183047), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1183047, tc_fun(_1183047, _1183047)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1183047, tc_fun(_1183047, _1183047)), tc_Int_Oint), c_If(_1183047)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1183047, _1183049, _1183051), _1183055))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183047, _1183047), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1183047, _1183047), tc_Int_Oint), _1183051), 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)), _1183055))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1183047, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1183047, _1183049, _1183051)), 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)), _1183055))))))], (44794 ^ _773908) ^ [_1668945, _1668947] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1668945), hAPP(c_List_Onth(_1668945), _1668947)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668945)), _1668947))) = _1668947)], (34137 ^ _773908) ^ [_1409422, _1409424] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1409422), _1409424))))], (32540 ^ _773908) ^ [_1377827, _1377829, _1377831, _1377833, _1377835] : [class_Orderings_Oorder(_1377827), 32543 ^ _773908 : [(32556 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377827, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1377827, _1377829, _1377831)), c_SetInterval_Oord__class_OatLeastAtMost(_1377827, _1377833, _1377835)))), 32557 ^ _773908 : [(32560 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377833), _1377829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377831), _1377835))], (32558 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377829), _1377831)))]]], (32544 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377827, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1377827, _1377829, _1377831)), c_SetInterval_Oord__class_OatLeastAtMost(_1377827, _1377833, _1377835))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377829), _1377831)), 32551 ^ _773908 : [(32554 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377831), _1377835)))], (32552 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377827), _1377833), _1377829)))]]]]], (41446 ^ _773908) ^ [_1590428, _1590430, _1590432] : [_1590428 = c_List_Olist_ONil(_1590430), -(c_List_Olast(_1590430, hAPP(hAPP(c_List_Oappend(_1590430), _1590432), _1590428)) = c_List_Olast(_1590430, _1590432))], (13664 ^ _773908) ^ [_1004042, _1004044] : [-(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, _1004042, _1004044)), _1004044) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1004042), _1004044))], (3238 ^ _773908) ^ [_822455, _822457] : [_822457 = _822455, -(c_Equiv__Relations_Oquotient(_822457) = c_Equiv__Relations_Oquotient(_822455))], (44052 ^ _773908) ^ [_1651805, _1651807, _1651809, _1651811] : [hBOOL(hAPP(hAPP(c_member(_1651805), _1651807), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651805, tc_HOL_Obool), _1651809))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1651805, tc_HOL_Obool)), _1651811), _1651809)), -(hBOOL(hAPP(hAPP(c_member(_1651805), _1651807), _1651811)))], (3480 ^ _773908) ^ [_826256, _826258, _826260, _826262] : [-(c_List_Orotate(_826262, _826258) = c_List_Orotate(_826260, _826256)), _826262 = _826260, _826258 = _826256], (42884 ^ _773908) ^ [_1624690, _1624692] : [-(c_Code__Numeral_Onat__of__aux(_1624690, _1624692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1624690)), _1624692))], (51436 ^ _773908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (33886 ^ _773908) ^ [_1403767, _1403769] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1403767), _1403769))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1403767), hAPP(c_Nat_OSuc, _1403769)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (528 ^ _773908) ^ [_781958, _781960, _781962, _781964, _781966, _781968, _781970, _781972, _781974, _781976] : [-(c_List_Olist__all2(_781974, _781970, _781966, _781962, _781958)), c_List_Olist__all2(_781976, _781972, _781968, _781964, _781960), _781976 = _781974, _781972 = _781970, _781968 = _781966, _781964 = _781962, _781960 = _781958], (6268 ^ _773908) ^ [_875578, _875580] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_875578, _875580)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25291 ^ _773908) ^ [_1220751, _1220753, _1220755, _1220757] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1220751), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220751), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220751), _1220753), _1220755)), _1220757) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220751), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220751), _1220753), _1220757)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220751), _1220755), _1220757)))], (37608 ^ _773908) ^ [_1486757, _1486759, _1486761, _1486763] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486757), _1486759)), 37614 ^ _773908 : [(37617 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486761), hAPP(_1486763, 37613 ^ [_1486757, _1486759, _1486761, _1486763])))], (37615 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486757), 37613 ^ [_1486757, _1486759, _1486761, _1486763]), _1486759)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1486757, _1486761)), hAPP(hAPP(c_Product__Type_OSigma(_1486757, _1486761), _1486759), _1486763))))], (41906 ^ _773908) ^ [_1599856, _1599858, _1599860, _1599862, _1599864] : [class_Groups_Ocomm__monoid__add(_1599856), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1599856), hAPP(hAPP(c_List_Omap(_1599858, _1599856), hAPP(hAPP(c_COMBS(_1599858, _1599856, _1599856), hAPP(hAPP(c_COMBB(_1599856, tc_fun(_1599856, _1599856), _1599858), c_Groups_Oplus__class_Oplus(_1599856)), _1599860)), _1599862)), _1599864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1599856), hAPP(c_List_Omonoid__add__class_Olistsum(_1599856), hAPP(hAPP(c_List_Omap(_1599858, _1599856), _1599860), _1599864))), hAPP(c_List_Omonoid__add__class_Olistsum(_1599856), hAPP(hAPP(c_List_Omap(_1599858, _1599856), _1599862), _1599864))))], (37372 ^ _773908) ^ [_1479616, _1479618, _1479620, _1479622, _1479624, _1479626] : [class_Groups_Ocomm__monoid__add(_1479616), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479618, _1479616), hAPP(hAPP(c_COMBC(_1479618, tc_fun(_1479620, tc_HOL_Obool), _1479616), hAPP(hAPP(c_COMBB(tc_fun(_1479620, _1479616), tc_fun(tc_fun(_1479620, tc_HOL_Obool), _1479616), _1479618), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479620, _1479616)), _1479622)), _1479624)), _1479626) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1479618, _1479620), _1479616), hAPP(c_Product__Type_Oprod_Oprod__case(_1479618, _1479620, _1479616), _1479622)), hAPP(hAPP(c_Product__Type_OSigma(_1479618, _1479620), _1479626), hAPP(c_COMBK(tc_fun(_1479620, tc_HOL_Obool), _1479618), _1479624))))], (51796 ^ _773908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (47636 ^ _773908) ^ [_1733063, _1733065, _1733067, _1733069, _1733071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1733063, _1733063)), hAPP(hAPP(c_Product__Type_OPair(_1733063, _1733063), _1733065), _1733067)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1733063, _1733063), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1733069)), _1733071))), 47640 ^ _773908 : [(47643 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733063, _1733063)), hAPP(hAPP(c_Product__Type_OPair(_1733063, _1733063), 47639 ^ [_1733063, _1733065, _1733067, _1733069, _1733071]), _1733067)), _1733071)))], (47641 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733063, _1733063)), hAPP(hAPP(c_Product__Type_OPair(_1733063, _1733063), _1733065), 47639 ^ [_1733063, _1733065, _1733067, _1733069, _1733071])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1733063, _1733063), tc_HOL_Obool), _1733069), _1733071))))]]], (41107 ^ _773908) ^ [_1583626, _1583628] : [hBOOL(hAPP(c_List_Odistinct(_1583626), _1583628)), -(hAPP(c_Finite__Set_Ocard(_1583626), hAPP(c_List_Oset(_1583626), _1583628)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583626)), _1583628))], (44831 ^ _773908) ^ [_1670050, _1670052, _1670054, _1670056, _1670058, _1670060] : [-(c_List_Ofoldr(_1670050, _1670052, _1670054, hAPP(hAPP(c_List_Oappend(_1670050), _1670056), _1670058), _1670060) = c_List_Ofoldr(_1670050, _1670052, _1670054, _1670056, c_List_Ofoldr(_1670050, _1670052, _1670054, _1670058, _1670060)))], (24193 ^ _773908) ^ [_1196986, _1196988, _1196990, _1196992, _1196994] : [hAPP(c_Product__Type_Osnd(_1196986, _1196988), hAPP(hAPP(c_Product__Type_OPair(_1196986, _1196988), _1196990), _1196992)) = _1196994, -(_1196992 = _1196994)], (38472 ^ _773908) ^ [_1513957, _1513959] : [-(hAPP(c_Fun_Oid(_1513957), _1513959) = _1513959)], (2320 ^ _773908) ^ [_807854, _807856, _807858, _807860, _807862, _807864] : [-(c_Nat_Onat_Onat__rec(_807864, _807860, _807856) = c_Nat_Onat_Onat__rec(_807862, _807858, _807854)), _807864 = _807862, _807860 = _807858, _807856 = _807854], (43449 ^ _773908) ^ [_1637056, _1637058, _1637060, _1637062, _1637064, _1637066] : [c_List_Olist__all2(_1637056, _1637058, _1637060, _1637062, _1637064), -(c_List_Olist__all2(_1637056, _1637058, _1637060, hAPP(hAPP(c_List_Odrop(_1637056), _1637066), _1637062), hAPP(hAPP(c_List_Odrop(_1637058), _1637066), _1637064)))], (39284 ^ _773908) ^ [_1536286, _1536288, _1536290] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1536286)), hAPP(hAPP(c_List_Olist_OCons(_1536286), _1536288), _1536290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1536286)), _1536290)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46027 ^ _773908) ^ [_1693826, _1693828, _1693830, _1693832, _1693834] : [class_Orderings_Olinorder(_1693826), -(hAPP(c_List_Ofilter(_1693828, _1693830), c_List_Olinorder__class_Osort__key(_1693828, _1693826, _1693832, _1693834)) = c_List_Olinorder__class_Osort__key(_1693828, _1693826, _1693832, hAPP(c_List_Ofilter(_1693828, _1693830), _1693834)))], (6239 ^ _773908) ^ [_875076, _875078, _875080, _875082] : [class_Rings_Osemiring__1(_875076), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_875076, _875078, hAPP(c_Nat_OSuc, _875080), _875082) = c_Nat_Osemiring__1__class_Oof__nat__aux(_875076, _875078, _875080, hAPP(_875078, _875082)))], (25419 ^ _773908) ^ [_1223257, _1223259, _1223261, _1223263, _1223265] : [-(hAPP(c_Product__Type_Ofst(_1223257, _1223259), hAPP(c_Product__Type_Oapfst(_1223261, _1223257, _1223259, _1223263), _1223265)) = hAPP(_1223263, hAPP(c_Product__Type_Ofst(_1223261, _1223259), _1223265)))], (8789 ^ _773908) ^ [_919337, _919339, _919341] : [class_Groups_Oordered__ab__group__add(_919337), 8792 ^ _773908 : [(8799 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919337), hAPP(c_Groups_Ouminus__class_Ouminus(_919337), _919341)), _919339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919337), hAPP(c_Groups_Ouminus__class_Ouminus(_919337), _919339)), _919341)))], (8793 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919337), hAPP(c_Groups_Ouminus__class_Ouminus(_919337), _919339)), _919341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919337), hAPP(c_Groups_Ouminus__class_Ouminus(_919337), _919341)), _919339)))]]], (35152 ^ _773908) ^ [_1431597, _1431599, _1431601, _1431603] : [class_Rings_Ocomm__semiring__1(_1431597), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431597), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431597), c_Groups_Oone__class_Oone(_1431597)), c_Groups_Oone__class_Oone(_1431597))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1431597), hAPP(hAPP(c_COMBB(_1431597, _1431597, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1431597), _1431599)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1431597, _1431597), hAPP(hAPP(c_COMBB(_1431597, tc_fun(_1431597, _1431597), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1431597)), c_Nat_Osemiring__1__class_Oof__nat(_1431597))), _1431601))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1431603))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431597), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1431597), _1431603)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431597), _1431599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431597), _1431599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431597), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1431597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1431603), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1431601)))))], (49312 ^ _773908) ^ [_1768776, _1768778, _1768780] : [-(hAPP(c_New__DSequence_Oneg__single(_1768776, _1768778), _1768780) = c_Lazy__Sequence_Ohb__single(_1768776, _1768778))], (51141 ^ _773908) ^ [_1809119, _1809121, _1809123, _1809125, _1809127, _1809129] : [c_Fun_Obij__betw(_1809119, _1809121, _1809123, _1809125, _1809127), hBOOL(hAPP(hAPP(c_member(_1809119), _1809129), _1809125)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1809121, _1809119, _1809127, c_Hilbert__Choice_Oinv__into(_1809119, _1809121, _1809125, _1809123)), _1809129) = hAPP(_1809123, _1809129))], (14424 ^ _773908) ^ [_1017949, _1017951] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017949, _1017951)) = _1017951, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1017949), _1017951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37958 ^ _773908) ^ [_1495168, _1495170, _1495172, _1495174] : [-(hAPP(c_Set_OCollect(tc_prod(_1495168, _1495170)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495168, _1495170, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1495168, tc_fun(_1495170, tc_HOL_Obool), tc_fun(_1495170, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1495170, tc_HOL_Obool), tc_fun(_1495170, tc_HOL_Obool)), _1495168), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1495170)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495168), c_fconj), _1495172))), _1495174))) = hAPP(hAPP(c_Product__Type_OSigma(_1495168, _1495170), hAPP(c_Set_OCollect(_1495168), _1495172)), hAPP(c_COMBK(tc_fun(_1495170, tc_HOL_Obool), _1495168), hAPP(c_Set_OCollect(_1495170), _1495174))))], (44788 ^ _773908) ^ [_1668831, _1668833] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1668831, _1668833) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1668831), hAPP(c_Nat_OSuc, _1668833))))], (4020 ^ _773908) ^ [_834640, _834642] : [_834642 = _834640, -(c_Divides_Odiv__class_Odiv(_834642) = c_Divides_Odiv__class_Odiv(_834640))], (51868 ^ _773908) ^ [] : [hBOOL(c_fFalse)], (5538 ^ _773908) ^ [_858653, _858655] : [_858655 = _858653, -(c_Finite__Set_Ofinite(_858655) = c_Finite__Set_Ofinite(_858653))], (19543 ^ _773908) ^ [_1111192] : [class_Int_Onumber__ring(_1111192), -(hAPP(c_Int_Onumber__class_Onumber__of(_1111192), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1111192))], (18943 ^ _773908) ^ [_1101150, _1101152, _1101154] : [class_Rings_Oring__1(_1101150), hBOOL(hAPP(hAPP(c_member(_1101150), _1101152), c_Int_Oring__1__class_OInts(_1101150))), hBOOL(hAPP(hAPP(c_member(_1101150), _1101154), c_Int_Oring__1__class_OInts(_1101150))), -(hBOOL(hAPP(hAPP(c_member(_1101150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101150), _1101152), _1101154)), c_Int_Oring__1__class_OInts(_1101150))))], (42802 ^ _773908) ^ [_1623186, _1623188, _1623190, _1623192, _1623194, _1623196, _1623198] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1623186, _1623188, _1623190, _1623192), _1623194), _1623196), _1623198) = hAPP(hAPP(_1623196, hAPP(c_Product__Type_Ofst(_1623188, _1623190), hAPP(_1623194, _1623198))), hAPP(c_Product__Type_Osnd(_1623188, _1623190), hAPP(_1623194, _1623198))))], (37390 ^ _773908) ^ [_1480102, _1480104, _1480106, _1480108] : [37391 ^ _773908 : [(37394 ^ _773908) ^ [] : [_1480108 = c_Orderings_Obot__class_Obot(tc_fun(_1480104, tc_HOL_Obool))], (37392 ^ _773908) ^ [] : [_1480106 = c_Orderings_Obot__class_Obot(tc_fun(_1480102, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1480102, _1480104), _1480106), hAPP(c_COMBK(tc_fun(_1480104, tc_HOL_Obool), _1480102), _1480108)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480102, _1480104), tc_HOL_Obool)))], (32060 ^ _773908) ^ [_1368252, _1368254] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1368252, _1368254))))], (34806 ^ _773908) ^ [_1423919, _1423921] : [class_Orderings_Olinorder(_1423919), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423919, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1423919), _1423921)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1423919), _1423921))], (32884 ^ _773908) ^ [_1384574, _1384576] : [32886 ^ _773908 : [(32889 ^ _773908) ^ [] : [hBOOL(hAPP(_1384576, 32885 ^ [_1384574, _1384576]))], (32887 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32885 ^ [_1384574, _1384576]), _1384574)))]], 32890 ^ _773908 : [(32891 ^ _773908) ^ [_1384725] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1384725), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1384574))), -(hBOOL(hAPP(_1384576, _1384725)))]]], (9698 ^ _773908) ^ [_935495, _935497] : [-(hAPP(c_Int_Onat, _935495) = _935497), 9701 ^ _773908 : [(9704 ^ _773908) ^ [] : [_935495 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935497)], (9702 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935495)))]], 9705 ^ _773908 : [(9708 ^ _773908) ^ [] : [_935497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9706 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935495))]]], (51522 ^ _773908) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (8921 ^ _773908) ^ [_921523] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921523)) = _921523)], (47881 ^ _773908) ^ [_1738700, _1738702, _1738704] : [47883 ^ _773908 : [(47886 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1738700), _1738704), 47882 ^ [_1738700, _1738702, _1738704]))], (47884 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1738700, tc_HOL_Obool)), 47882 ^ [_1738700, _1738702, _1738704]), _1738702)))]], -(hBOOL(hAPP(hAPP(c_member(_1738700), _1738704), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1738700, tc_HOL_Obool), _1738702))))], (13145 ^ _773908) ^ [] : [-(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))], (39473 ^ _773908) ^ [_1540640, _1540642, _1540644, _1540646, _1540648] : [hAPP(hAPP(c_List_Oappend(_1540640), _1540642), _1540644) = hAPP(hAPP(c_List_Olist_OCons(_1540640), _1540646), _1540648), 39478 ^ _773908 : [(39481 ^ _773908) ^ [] : [-(_1540644 = hAPP(hAPP(c_List_Olist_OCons(_1540640), _1540646), _1540648))], (39479 ^ _773908) ^ [] : [-(_1540642 = c_List_Olist_ONil(_1540640))]], 39483 ^ _773908 : [(39486 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1540640), 39482 ^ [_1540640, _1540642, _1540644, _1540646, _1540648]), _1540644) = _1540648)], (39484 ^ _773908) ^ [] : [-(_1540642 = hAPP(hAPP(c_List_Olist_OCons(_1540640), _1540646), 39482 ^ [_1540640, _1540642, _1540644, _1540646, _1540648]))]]], (46181 ^ _773908) ^ [_1697338, _1697340, _1697342] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1697338, _1697338)), hAPP(hAPP(c_Product__Type_OPair(_1697338, _1697338), _1697340), _1697342)), c_List_Omeasures(_1697338, c_List_Olist_ONil(tc_fun(_1697338, tc_Nat_Onat)))))], (38476 ^ _773908) ^ [_1514024, _1514026, _1514028] : [c_Predicate_Oreflp(_1514024, _1514026), -(hBOOL(hAPP(hAPP(_1514026, _1514028), _1514028)))], (34197 ^ _773908) ^ [_1410610] : [-(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)), _1410610)) = hAPP(c_Int_Onat, _1410610))], (6682 ^ _773908) ^ [_882416, _882418, _882420] : [class_Orderings_Opreorder(_882416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882416), _882418), _882420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882416), _882420), _882418))], (1998 ^ _773908) ^ [_802845, _802847, _802849, _802851, _802853, _802855] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_802855, _802851, _802847) = c_Hoare__Mirabelle_Otriple_Otriple__size(_802853, _802849, _802845)), _802855 = _802853, _802851 = _802849, _802847 = _802845], (46788 ^ _773908) ^ [_1711417, _1711419, _1711421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711417, _1711417), tc_HOL_Obool)), _1711419), _1711421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1711417, _1711417), tc_HOL_Obool)), _1711421), c_Transitive__Closure_Ortrancl(_1711417, _1711419))), -(c_Transitive__Closure_Ortrancl(_1711417, _1711421) = c_Transitive__Closure_Ortrancl(_1711417, _1711419))], (5690 ^ _773908) ^ [_860911, _860913, _860915, _860917] : [-(tc_fun(_860917, _860913) = tc_fun(_860915, _860911)), _860917 = _860915, _860913 = _860911], (23905 ^ _773908) ^ [_1192019, _1192021, _1192023, _1192025, _1192027, _1192029] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192019, _1192021), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192023), _1192025))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192019, _1192021), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192027), _1192029))), -(_1192021 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1192025 = _1192029)], (44881 ^ _773908) ^ [_1671312] : [class_Orderings_Olinorder(_1671312), -(c_List_Olinorder__class_Osorted(_1671312, c_List_Olist_ONil(_1671312)))], (4550 ^ _773908) ^ [_843153, _843155] : [_843155 = _843153, -(c_List_Ohd(_843155) = c_List_Ohd(_843153))], (30469 ^ _773908) ^ [_1330759, _1330761, _1330763] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330759), _1330761)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330759), _1330763)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330759), _1330761)), hAPP(c_Finite__Set_Ocard(_1330759), _1330763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330759), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330759, tc_HOL_Obool)), _1330761), _1330763))), hAPP(c_Finite__Set_Ocard(_1330759), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330759, tc_HOL_Obool)), _1330761), _1330763))))], (46953 ^ _773908) ^ [_1715780, _1715782] : [-(c_Transitive__Closure_Ortrancl(_1715780, _1715782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1715780, _1715780), 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(_1715780, _1715780), tc_HOL_Obool), tc_fun(tc_prod(_1715780, _1715780), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1715780, _1715780), tc_HOL_Obool)), _1715782)))], (31556 ^ _773908) ^ [_1355392, _1355394, _1355396, _1355398, _1355400, _1355402, _1355404, _1355406, _1355408, _1355410] : [c_Equiv__Relations_Ocongruent2(_1355392, _1355394, _1355396, _1355398, _1355400, _1355402), hBOOL(hAPP(hAPP(c_member(tc_prod(_1355392, _1355392)), hAPP(hAPP(c_Product__Type_OPair(_1355392, _1355392), _1355404), _1355406)), _1355398)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1355394, _1355394)), hAPP(hAPP(c_Product__Type_OPair(_1355394, _1355394), _1355408), _1355410)), _1355400)), -(hAPP(hAPP(_1355402, _1355404), _1355408) = hAPP(hAPP(_1355402, _1355406), _1355410))], (27558 ^ _773908) ^ [_1272319, _1272321, _1272323, _1272325, _1272327, _1272329, _1272331, _1272333] : [c_Finite__Set_Ofolding__image__simple(_1272319, _1272321, _1272323, _1272325, _1272327, _1272329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272321), _1272331)), -(hBOOL(hAPP(hAPP(c_member(_1272321), _1272333), _1272331))), -(hAPP(_1272329, hAPP(hAPP(c_Set_Oinsert(_1272321), _1272333), _1272331)) = hAPP(hAPP(_1272323, hAPP(_1272327, _1272333)), hAPP(_1272329, _1272331)))], (43135 ^ _773908) ^ [_1630511, _1630513, _1630515, _1630517, _1630519] : [class_Orderings_Olinorder(_1630511), -(hAPP(c_List_Oset(_1630513), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1630513, _1630511, _1630515), _1630517), _1630519)) = hAPP(hAPP(c_Set_Oinsert(_1630513), _1630517), hAPP(c_List_Oset(_1630513), _1630519)))], (9091 ^ _773908) ^ [_924858, _924860, _924862] : [class_Groups_Ogroup__add(_924858), 9094 ^ _773908 : [(9101 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924858), _924860), _924862) = c_Groups_Ozero__class_Ozero(_924858), -(_924860 = hAPP(c_Groups_Ouminus__class_Ouminus(_924858), _924862))], (9095 ^ _773908) ^ [] : [_924860 = hAPP(c_Groups_Ouminus__class_Ouminus(_924858), _924862), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924858), _924860), _924862) = c_Groups_Ozero__class_Ozero(_924858))]]], (11569 ^ _773908) ^ [_967188, _967190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _967188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _967190)), -(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), _967188), _967190))))], (9117 ^ _773908) ^ [_925255, _925257] : [class_Rings_Olinordered__ring(_925255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925255), _925257), _925257)), c_Groups_Ozero__class_Ozero(_925255)))], (23520 ^ _773908) ^ [_1184029, _1184031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184029))), 23523 ^ _773908 : [(23530 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184031))), -(c_Divides_Odivmod__int(_1184029, _1184031) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1184029), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1184031))))], (23524 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184031)), -(c_Divides_Odivmod__int(_1184029, _1184031) = c_Divides_OnegDivAlg(_1184029, _1184031))]]], (10223 ^ _773908) ^ [_943751, _943753, _943755] : [class_Orderings_Oorder(_943751), 10226 ^ _773908 : [(10227 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943751), _943753), _943755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943751), _943753), _943755))), -(_943753 = _943755)], (10237 ^ _773908) ^ [] : [10238 ^ _773908 : [(10241 ^ _773908) ^ [] : [_943753 = _943755], (10239 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943751), _943753), _943755))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943751), _943753), _943755)))]]], (43172 ^ _773908) ^ [_1631312, _1631314, _1631316, _1631318] : [hBOOL(hAPP(c_List_Olistsp(_1631312, _1631314), _1631316)), hBOOL(hAPP(c_List_Olistsp(_1631312, _1631318), _1631316)), -(hBOOL(hAPP(c_List_Olistsp(_1631312, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1631312, tc_HOL_Obool)), _1631314), _1631318)), _1631316)))], (6478 ^ _773908) ^ [_879232, _879234, _879236, _879238, _879240, _879242] : [c_Com_Ocom_OCall(_879232, _879234, _879236) = c_Com_Ocom_OCall(_879238, _879240, _879242), 6481 ^ _773908 : [(6486 ^ _773908) ^ [] : [-(_879236 = _879242)], (6484 ^ _773908) ^ [] : [-(_879234 = _879240)], (6482 ^ _773908) ^ [] : [-(_879232 = _879238)]]], (36769 ^ _773908) ^ [_1466733, _1466735] : [class_Orderings_Olinorder(_1466733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466733), _1466735)), -(c_Big__Operators_Olinorder__class_OMax(_1466733, _1466735) = hAPP(c_Finite__Set_Ofold1(_1466733, c_Orderings_Oord__class_Omax(_1466733)), _1466735))], (13251 ^ _773908) ^ [_996338, _996340, _996342] : [13252 ^ _773908 : [(13255 ^ _773908) ^ [] : [_996340 = _996342], (13253 ^ _773908) ^ [] : [_996338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996338), _996340) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996338), _996342))], (34958 ^ _773908) ^ [_1427187, _1427189, _1427191, _1427193, _1427195] : [class_Groups_Ocomm__monoid__add(_1427187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427189), _1427191)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427189), _1427193)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427189, tc_HOL_Obool)), _1427191), _1427193) = c_Orderings_Obot__class_Obot(tc_fun(_1427189, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427189, _1427187), _1427195), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427189, tc_HOL_Obool)), _1427191), _1427193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427187), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427189, _1427187), _1427195), _1427191)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427189, _1427187), _1427195), _1427193)))], (34660 ^ _773908) ^ [_1420500, _1420502, _1420504, _1420506, _1420508] : [class_Groups_Ocomm__monoid__add(_1420500), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420500), _1420502), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1420504), _1420506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1420508), _1420506))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420500), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420500, tc_Nat_Onat), _1420502), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1420506))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1420504), _1420508)))], (8919 ^ _773908) ^ [] : [-(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))], (26394 ^ _773908) ^ [_1246279, _1246281, _1246283, _1246285] : [-(hAPP(c_Relation_OField(_1246279), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1246279, _1246279)), hAPP(hAPP(c_Product__Type_OPair(_1246279, _1246279), _1246281), _1246283)), _1246285)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246279, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1246279), _1246281), hAPP(hAPP(c_Set_Oinsert(_1246279), _1246283), c_Orderings_Obot__class_Obot(tc_fun(_1246279, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1246279), _1246285)))], (32442 ^ _773908) ^ [_1376038, _1376040] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1376038, tc_HOL_Obool)), hAPP(c_Set_OPow(_1376038), _1376040))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376038), _1376040)))], (35871 ^ _773908) ^ [] : [-(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))], (16284 ^ _773908) ^ [_1052930, _1052932, _1052934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052934), 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), _1052934), _1052932))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1052930)))))], (15871 ^ _773908) ^ [_1044298, _1044300] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044298, _1044300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044298), _1044300)), _1044300)))], (17419 ^ _773908) ^ [_1074558, _1074560, _1074562] : [class_Rings_Olinordered__idom(_1074558), -(hAPP(c_Groups_Oabs__class_Oabs(_1074558), hAPP(hAPP(c_Power_Opower__class_Opower(_1074558), _1074560), _1074562)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074558), hAPP(c_Groups_Oabs__class_Oabs(_1074558), _1074560)), _1074562))], (19651 ^ _773908) ^ [] : [-(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)))))], (42750 ^ _773908) ^ [_1621714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1621714)), _1621714 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18907 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4000 ^ _773908) ^ [_834342, _834344, _834346, _834348] : [-(c_HOL_OLet(_834348, _834344) = c_HOL_OLet(_834346, _834342)), _834348 = _834346, _834344 = _834342], (28054 ^ _773908) ^ [_1281957, _1281959, _1281961, _1281963] : [-(hBOOL(hAPP(hAPP(c_member(_1281957), _1281959), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281957, tc_HOL_Obool)), _1281961), _1281963)))), hBOOL(hAPP(hAPP(c_member(_1281957), _1281959), _1281961)), hBOOL(hAPP(hAPP(c_member(_1281957), _1281959), _1281963))], (9385 ^ _773908) ^ [_930200, _930202, _930204, _930206] : [class_Rings_Olinordered__ring__strict(_930200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930200), _930202), _930204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930200), _930206), c_Groups_Ozero__class_Ozero(_930200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930200), _930206), _930204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930200), _930206), _930202))))], (45423 ^ _773908) ^ [_1680971, _1680973, _1680975] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1680971), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1680971))), _1680973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1680971))), _1680973))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1680971), _1680971), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680971), tc_Nat_Onat, _1680971), c_List_Onth(_1680971)), _1680975)), hAPP(c_List_Ofilter(tc_List_Olist(_1680971), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1680971)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680975)), c_Nat_Osize__class_Osize(tc_List_Olist(_1680971)))), c_List_Otranspose(_1680971, _1680973))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1680971)), _1680973), _1680975))], (51099 ^ _773908) ^ [_1808225, _1808227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1808225), _1808227)), -(c_Quickcheck_Obeyond(_1808225, _1808227) = _1808227)], (12026 ^ _773908) ^ [_975373, _975375, _975377, _975379] : [class_Rings_Olinordered__ring__strict(_975373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975373), _975375), c_Groups_Ozero__class_Ozero(_975373))), 12033 ^ _773908 : [(12040 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975373), _975379), _975377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975373), _975375), _975377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975373), _975375), _975379))))], (12034 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975373), _975375), _975377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975373), _975375), _975379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975373), _975379), _975377)))]]], (1344 ^ _773908) ^ [_793694, _793696] : [-(class_Rings_Oring(_793694)), _793696 = _793694, class_Rings_Oring(_793696)], (23371 ^ _773908) ^ [_1180677, _1180679, _1180681, _1180683, _1180685] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1180677, _1180679)), hAPP(hAPP(c_Product__Type_OPair(_1180677, _1180679), _1180683), _1180685)), _1180681)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1180677, _1180679, _1180681), _1180683), _1180685)))], (38162 ^ _773908) ^ [_1500608, _1500610, _1500612, _1500614, _1500616, _1500618] : [class_Groups_Ocomm__monoid__add(_1500608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500610), _1500612)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500610, _1500608), _1500614), _1500612) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500616, _1500608), hAPP(hAPP(c_COMBB(tc_fun(_1500610, tc_HOL_Obool), _1500608, _1500616), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500610, _1500608), _1500614)), hAPP(hAPP(c_COMBB(tc_fun(_1500610, tc_HOL_Obool), tc_fun(_1500610, tc_HOL_Obool), _1500616), c_Set_OCollect(_1500610)), hAPP(hAPP(c_COMBB(tc_fun(_1500610, tc_HOL_Obool), tc_fun(_1500610, tc_HOL_Obool), _1500616), hAPP(c_COMBS(_1500610, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500610), c_fconj), hAPP(hAPP(c_COMBC(_1500610, tc_fun(_1500610, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500610)), _1500612)))), hAPP(c_COMBC(_1500610, _1500616, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1500616, tc_fun(_1500616, tc_HOL_Obool), _1500610), c_fequal), _1500618)))))), hAPP(c_Set_Oimage(_1500610, _1500616, _1500618), _1500612)))], (31790 ^ _773908) ^ [_1361482, _1361484, _1361486, _1361488, _1361490] : [class_Complete__Lattice_Ocomplete__lattice(_1361482), hBOOL(hAPP(hAPP(c_member(_1361484), _1361486), _1361488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361482), hAPP(_1361490, _1361486)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361484, _1361482), _1361488), _1361490))))], (5316 ^ _773908) ^ [_855164, _855166] : [_855166 = _855164, -(c_Groups_Otimes__class_Otimes(_855166) = c_Groups_Otimes__class_Otimes(_855164))], (45631 ^ _773908) ^ [_1685597, _1685599, _1685601, _1685603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685597), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685599)), _1685601))), -(hAPP(c_List_Orev(_1685599), hAPP(hAPP(c_List_Olist__update(_1685599, _1685601), _1685597), _1685603)) = hAPP(hAPP(c_List_Olist__update(_1685599, hAPP(c_List_Orev(_1685599), _1685601)), 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(_1685599)), _1685601)), _1685597)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1685603))], (37510 ^ _773908) ^ [_1483873, _1483875, _1483877, _1483879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1483873, _1483875)), hAPP(hAPP(c_Product__Type_OSigma(_1483873, _1483875), _1483877), hAPP(c_COMBK(tc_fun(_1483875, tc_HOL_Obool), _1483873), _1483879)))), -(_1483879 = c_Orderings_Obot__class_Obot(tc_fun(_1483875, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1483873), _1483877)))], (51850 ^ _773908) ^ [_1817714, _1817716, _1817718, _1817720, _1817722, _1817724] : [-(hAPP(hAPP(hAPP(c_COMBB(_1817714, _1817716, _1817718), _1817720), _1817722), _1817724) = hAPP(_1817720, hAPP(_1817722, _1817724)))], (37436 ^ _773908) ^ [_1481704, _1481706, _1481708, _1481710, _1481712] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1481704, _1481706), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481704, tc_HOL_Obool)), _1481708), _1481710)), _1481712) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1481704, _1481706), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1481704, _1481706), _1481708), _1481712)), hAPP(hAPP(c_Product__Type_OSigma(_1481704, _1481706), _1481710), _1481712)))], (48109 ^ _773908) ^ [_1743376, _1743378, _1743380] : [-(hBOOL(hAPP(hAPP(c_member(_1743376), _1743378), hAPP(c_List_Oset(_1743376), _1743380)))), 48110 ^ _773908 : [(48111 ^ _773908) ^ [_1743465] : [48112 ^ _773908 : [(48113 ^ _773908) ^ [_1743538] : [_1743380 = hAPP(hAPP(c_List_Oappend(_1743376), _1743465), hAPP(hAPP(c_List_Olist_OCons(_1743376), _1743378), _1743538))]], -(hBOOL(hAPP(hAPP(c_member(_1743376), _1743378), hAPP(c_List_Oset(_1743376), _1743465))))]]], (33458 ^ _773908) ^ [_1395430, _1395432] : [33466 ^ _773908 : [(33469 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1395432, 33465 ^ [_1395430, _1395432])))], (33467 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33465 ^ [_1395430, _1395432]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1395430))))]], 33459 ^ _773908 : [(33460 ^ _773908) ^ [_1395498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1395498), _1395430)), hBOOL(hAPP(_1395432, _1395498))]]], (5903 ^ _773908) ^ [_868397, _868399, _868401, _868403] : [-(c_Com_Ocom_OSemi(_868397, _868399) = c_Com_Ocom_OSemi(_868401, _868403)), _868397 = _868401, _868399 = _868403], (15295 ^ _773908) ^ [_1033263, _1033265] : [class_Groups_Ogroup__add(_1033263), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033263), _1033265), c_Groups_Ozero__class_Ozero(_1033263)) = _1033265)], (15503 ^ _773908) ^ [_1037048, _1037050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037048), _1037050)), _1037048)))], (40171 ^ _773908) ^ [_1559395] : [-(hAPP(c_List_Oset(_1559395), c_List_Olist_ONil(_1559395)) = c_Orderings_Obot__class_Obot(tc_fun(_1559395, tc_HOL_Obool)))], (32750 ^ _773908) ^ [_1381886, _1381888] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381886), _1381888))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1381888, _1381886) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1381888), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1381888), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1381886)))], (18017 ^ _773908) ^ [_1084664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084664)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1084664) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (26271 ^ _773908) ^ [_1240656, _1240658, _1240660, _1240662] : [hBOOL(hAPP(hAPP(c_member(_1240656), _1240662), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240656, tc_HOL_Obool)), _1240658), _1240660))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240656, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1240656, tc_fun(_1240656, tc_HOL_Obool), tc_HOL_Obool), c_member(_1240656)), _1240658)), hAPP(hAPP(c_COMBC(_1240656, tc_fun(_1240656, tc_HOL_Obool), tc_HOL_Obool), c_member(_1240656)), _1240660)), _1240662)))], (22951 ^ _773908) ^ [_1172289, _1172291] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1172289), _1172291) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1172289), _1172291))], (51800 ^ _773908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (26952 ^ _773908) ^ [_1259256] : [c_Nat__Transfer_Onat__set(_1259256), 26955 ^ _773908 : [(26956 ^ _773908) ^ [_1259322] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259322), _1259256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259322)))]]], (17365 ^ _773908) ^ [_1073464, _1073466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1073464)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1073464), _1073466)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1073464)), _1073466))], (14911 ^ _773908) ^ [_1026071, _1026073, _1026075, _1026077] : [class_Divides_Osemiring__div(_1026071), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026071), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026071), _1026073), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026071), _1026075), _1026073))), c_Divides_Odiv__class_Omod(_1026071, _1026075, _1026073))), _1026077) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026071), _1026075), _1026077))], (38607 ^ _773908) ^ [_1517816, _1517818, _1517820] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517816, _1517816), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1517818)), _1517820) = hAPP(hAPP(c_Relation_Orel__comp(_1517816, _1517816, _1517816), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1517816, _1517816), tc_HOL_Obool), _1517818), _1517820)), _1517820))], (37378 ^ _773908) ^ [_1479861, _1479863, _1479865] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1479861, _1479863), _1479865), hAPP(c_COMBK(tc_fun(_1479863, tc_HOL_Obool), _1479861), c_Orderings_Obot__class_Obot(tc_fun(_1479863, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479861, _1479863), tc_HOL_Obool)))], (29795 ^ _773908) ^ [_1317779, _1317781, _1317783] : [class_Orderings_Olinorder(_1317779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317779), _1317781)), hBOOL(hAPP(hAPP(c_member(_1317779), _1317783), _1317781)), 29806 ^ _773908 : [(29813 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317779, tc_HOL_Obool)), _1317781), hAPP(hAPP(c_Set_Oinsert(_1317779), _1317783), c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1317779, c_Orderings_Oord__class_Omax(_1317779), _1317781) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317779), _1317783), c_Big__Operators_Olattice_OSup__fin(_1317779, c_Orderings_Oord__class_Omax(_1317779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317779, tc_HOL_Obool)), _1317781), hAPP(hAPP(c_Set_Oinsert(_1317779), _1317783), c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool)))))))], (29807 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317779, tc_HOL_Obool)), _1317781), hAPP(hAPP(c_Set_Oinsert(_1317779), _1317783), c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1317779, c_Orderings_Oord__class_Omax(_1317779), _1317781) = _1317783)]]], (23933 ^ _773908) ^ [_1192427, _1192429, _1192431] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192427, _1192427), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192429), _1192431))), -(_1192427 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1192431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39312 ^ _773908) ^ [_1537548, _1537550] : [-(c_List_Oset__Cons(_1537548, _1537550, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1537548)), c_List_Olist_ONil(_1537548)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1537548), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1537548, tc_List_Olist(_1537548), hAPP(hAPP(c_COMBC(_1537548, tc_List_Olist(_1537548), tc_List_Olist(_1537548)), c_List_Olist_OCons(_1537548)), c_List_Olist_ONil(_1537548))), _1537550))], (26115 ^ _773908) ^ [_1237200, _1237202, _1237204, _1237206] : [26119 ^ _773908 : [(26122 ^ _773908) ^ [] : [hBOOL(hAPP(_1237206, 26118 ^ [_1237200, _1237202, _1237204, _1237206]))], (26120 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1237200), 26118 ^ [_1237200, _1237202, _1237204, _1237206]), _1237202)))]], 26124 ^ _773908 : [(26127 ^ _773908) ^ [] : [hBOOL(hAPP(_1237206, 26123 ^ [_1237200, _1237202, _1237204, _1237206]))], (26125 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1237200), 26123 ^ [_1237200, _1237202, _1237204, _1237206]), _1237204)))]], 26128 ^ _773908 : [(26129 ^ _773908) ^ [_1237533] : [hBOOL(hAPP(hAPP(c_member(_1237200), _1237533), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1237200, tc_HOL_Obool)), _1237202), _1237204))), -(hBOOL(hAPP(_1237206, _1237533)))]]], (5741 ^ _773908) ^ [_864622, _864624, _864626, _864628] : [c_Hoare__Mirabelle_Ohoare__derivs(_864622, _864624, _864626), c_Hoare__Mirabelle_Ohoare__derivs(_864622, _864628, _864624), -(c_Hoare__Mirabelle_Ohoare__derivs(_864622, _864628, _864626))], (23129 ^ _773908) ^ [_1175911, _1175913] : [hAPP(c_Nat_OSuc, _1175911) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1175913), -(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(_1175913))), 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)), _1175911))))))], (3024 ^ _773908) ^ [_819134, _819136] : [_819136 = _819134, -(c_List_Orotate1(_819136) = c_List_Orotate1(_819134))], (708 ^ _773908) ^ [_784688, _784690, _784692, _784694] : [-(c_Wellfounded_Owf(_784692, _784688)), c_Wellfounded_Owf(_784694, _784690), _784694 = _784692, _784690 = _784688], (44494 ^ _773908) ^ [_1661021, _1661023] : [44496 ^ _773908 : [(44499 ^ _773908) ^ [] : [44495 ^ [_1661021, _1661023] = c_List_Olist_ONil(_1661021)], (44497 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1661021)), 44495 ^ [_1661021, _1661023]), hAPP(c_List_Oset(tc_List_Olist(_1661021)), _1661023))))]], -(c_List_Olist_ONil(_1661021) = c_List_Oconcat(_1661021, _1661023))], (13005 ^ _773908) ^ [_992112, _992114, _992116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992112)), 13008 ^ _773908 : [(13015 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992114), _992116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992112), _992114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992112), _992116))))], (13009 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992112), _992114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992112), _992116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992114), _992116)))]]], (39141 ^ _773908) ^ [_1532231, _1532233, _1532235] : [c_Wellfounded_Owf(_1532231, _1532233), -(c_Wellfounded_Owf(tc_List_Olist(_1532231), hAPP(c_List_Olexn(_1532231, _1532233), _1532235)))], (14559 ^ _773908) ^ [_1020088, _1020090, _1020092] : [class_Divides_Osemiring__div(_1020088), -(_1020090 = c_Groups_Ozero__class_Ozero(_1020088)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020088), _1020092), _1020090)), _1020090) = _1020092)], (16935 ^ _773908) ^ [_1065428, _1065430, _1065432] : [class_Int_Onumber__ring(_1065428), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065428), hAPP(c_Int_Onumber__class_Onumber__of(_1065428), _1065430)), hAPP(c_Int_Onumber__class_Onumber__of(_1065428), _1065432)) = hAPP(c_Int_Onumber__class_Onumber__of(_1065428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065430), _1065432)))], (28332 ^ _773908) ^ [_1288435, _1288437, _1288439] : [class_Lattices_Oboolean__algebra(_1288435), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1288435), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288435), _1288437), _1288439)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1288435), hAPP(c_Groups_Ouminus__class_Ouminus(_1288435), _1288437)), hAPP(c_Groups_Ouminus__class_Ouminus(_1288435), _1288439)))], (37556 ^ _773908) ^ [_1484854, _1484856, _1484858, _1484860] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1484854), _1484856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1484854, _1484854), tc_HOL_Obool)), _1484858), hAPP(hAPP(c_Product__Type_OSigma(_1484854, _1484854), _1484856), hAPP(c_COMBK(tc_fun(_1484854, tc_HOL_Obool), _1484854), _1484856)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1484854, tc_HOL_Obool)), _1484860), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1484854), _1484856), _1484858))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1484854), _1484860)))], (31830 ^ _773908) ^ [_1362471, _1362473] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362471, tc_fun(_1362471, tc_HOL_Obool)), _1362473), hAPP(hAPP(c_COMBC(_1362471, tc_fun(_1362471, tc_HOL_Obool), tc_fun(_1362471, tc_HOL_Obool)), c_Set_Oinsert(_1362471)), c_Orderings_Obot__class_Obot(tc_fun(_1362471, tc_HOL_Obool)))) = _1362473)], (38078 ^ _773908) ^ [_1498011, _1498013, _1498015] : [hBOOL(hAPP(_1498011, _1498013)), -(hAPP(c_Set_OCollect(_1498015), hAPP(hAPP(c_COMBS(_1498015, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498015), c_fconj), hAPP(c_fequal, _1498013))), _1498011)) = hAPP(hAPP(c_Set_Oinsert(_1498015), _1498013), c_Orderings_Obot__class_Obot(tc_fun(_1498015, tc_HOL_Obool))))], (18957 ^ _773908) ^ [_1101405, _1101407, _1101409] : [class_Rings_Oring__1(_1101405), hBOOL(hAPP(hAPP(c_member(_1101405), _1101407), c_Int_Oring__1__class_OInts(_1101405))), hBOOL(hAPP(hAPP(c_member(_1101405), _1101409), c_Int_Oring__1__class_OInts(_1101405))), -(hBOOL(hAPP(hAPP(c_member(_1101405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101405), _1101407), _1101409)), c_Int_Oring__1__class_OInts(_1101405))))], (25573 ^ _773908) ^ [_1226754, _1226756, _1226758, _1226760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1226754), _1226756)), 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)), _1226758), _1226754)), 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)), _1226760), _1226756)), 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)), _1226758), _1226760)), _1226756)), c_FunDef_Omax__strict)))], (2194 ^ _773908) ^ [_805809, _805811] : [_805811 = _805809, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_805811) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_805809))], (46413 ^ _773908) ^ [_1702427, _1702429] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1702427, _1702427)), _1702429)), 46416 ^ _773908 : [(46423 ^ _773908) ^ [] : [c_Wellfounded_Oacyclic(_1702427, _1702429), -(c_Wellfounded_Owf(_1702427, _1702429))], (46417 ^ _773908) ^ [] : [c_Wellfounded_Owf(_1702427, _1702429), -(c_Wellfounded_Oacyclic(_1702427, _1702429))]]], (50267 ^ _773908) ^ [_1791493, _1791495] : [c_Relation_Otrans(_1791493, hAPP(c_Relation_Oconverse(_1791493, _1791493), _1791495)), -(c_Relation_Otrans(_1791493, _1791495))], (49570 ^ _773908) ^ [_1774321, _1774323, _1774325, _1774327] : [-(c_List_Oreplicate(_1774321, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774323), _1774325), _1774327) = hAPP(hAPP(c_List_Oappend(_1774321), c_List_Oreplicate(_1774321, _1774323, _1774327)), c_List_Oreplicate(_1774321, _1774325, _1774327)))], (13069 ^ _773908) ^ [_993197, _993199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993197), hAPP(c_Nat_OSuc, _993199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993197), _993199)))], (49616 ^ _773908) ^ [_1775170, _1775172, _1775174] : [-(hAPP(c_List_Oset(_1775170), c_List_Oreplicate(_1775170, hAPP(c_Nat_OSuc, _1775172), _1775174)) = hAPP(hAPP(c_Set_Oinsert(_1775170), _1775174), c_Orderings_Obot__class_Obot(tc_fun(_1775170, tc_HOL_Obool))))], (7121 ^ _773908) ^ [_889243, _889245] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889243)), _889245) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _889243), hAPP(c_Nat_OSuc, _889245)))], (49952 ^ _773908) ^ [_1782753, _1782755, _1782757] : [49954 ^ _773908 : [(49957 ^ _773908) ^ [] : [hBOOL(hAPP(_1782753, 49953 ^ [_1782753, _1782755, _1782757]))], (49955 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49953 ^ [_1782753, _1782755, _1782757]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1782755, _1782757))))]], -(c_List_Oall__interval__int(_1782753, _1782755, _1782757))], (20435 ^ _773908) ^ [_1126473, _1126475, _1126477] : [class_Rings_Ocomm__semiring__1(_1126473), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126473), _1126475), 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)))), _1126477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126473), hAPP(hAPP(c_Power_Opower__class_Opower(_1126473), _1126475), _1126477)), hAPP(hAPP(c_Power_Opower__class_Opower(_1126473), _1126475), _1126477)))], (31862 ^ _773908) ^ [_1363243, _1363245, _1363247, _1363249, _1363251] : [-(_1363243 = c_Orderings_Obot__class_Obot(tc_fun(_1363245, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363247, tc_HOL_Obool)), _1363249), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363245, tc_fun(_1363247, tc_HOL_Obool)), _1363243), _1363251)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363245, tc_fun(_1363247, tc_HOL_Obool)), _1363243), hAPP(hAPP(c_COMBB(tc_fun(_1363247, tc_HOL_Obool), tc_fun(_1363247, tc_HOL_Obool), _1363245), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363247, tc_HOL_Obool)), _1363249)), _1363251)))], (7457 ^ _773908) ^ [_894597, _894599, _894601] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_894597), 7460 ^ _773908 : [(7467 ^ _773908) ^ [] : [_894601 = c_Groups_Ozero__class_Ozero(_894597), -(_894599 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894597), _894599), _894601))], (7461 ^ _773908) ^ [] : [_894599 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894597), _894599), _894601), -(_894601 = c_Groups_Ozero__class_Ozero(_894597))]]], (38941 ^ _773908) ^ [_1526573, _1526575] : [38943 ^ _773908 : [(38944 ^ _773908) ^ [_1526598] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526573, _1526573)), hAPP(hAPP(c_Product__Type_OPair(_1526573, _1526573), hAPP(38942 ^ [_1526573, _1526575], hAPP(c_Nat_OSuc, _1526598))), hAPP(38942 ^ [_1526573, _1526575], _1526598))), _1526575)))]], -(c_Wellfounded_Owf(_1526573, _1526575))], (31983 ^ _773908) ^ [_1366596, _1366598, _1366600, _1366602, _1366604, _1366606, _1366608, _1366610] : [hBOOL(hAPP(hAPP(c_member(_1366596), _1366598), _1366600)), hBOOL(hAPP(hAPP(hAPP(_1366602, _1366598), _1366604), _1366606)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1366596, tc_fun(_1366608, tc_fun(_1366610, tc_HOL_Obool))), _1366600), _1366602), _1366604), _1366606)))], (6134 ^ _773908) ^ [_873355, _873357] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _873355, _873357, _873355))], (14181 ^ _773908) ^ [_1013258, _1013260, _1013262] : [hBOOL(hAPP(_1013258, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013260), _1013262))), 14184 ^ _773908 : [(14209 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013262), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14212 ^ _773908 : [(14213 ^ _773908) ^ [_1013922] : [-(hBOOL(hAPP(_1013258, _1013922))), 14214 ^ _773908 : [(14215 ^ _773908) ^ [_1013996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013262), _1013996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1013996), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1013260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013262), _1013922)), _1013996)]]]]], (14191 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013262)), 14194 ^ _773908 : [(14195 ^ _773908) ^ [_1013592] : [-(hBOOL(hAPP(_1013258, _1013592))), 14196 ^ _773908 : [(14197 ^ _773908) ^ [_1013663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013663), _1013262)), _1013260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013262), _1013592)), _1013663)]]]]], (14185 ^ _773908) ^ [] : [_1013262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1013258, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37886 ^ _773908) ^ [_1493890] : [class_Lattices_Oab__semigroup__idem__mult(_1493890), -(c_Finite__Set_Ofun__left__comm__idem(_1493890, _1493890, c_Groups_Otimes__class_Otimes(_1493890)))], (8613 ^ _773908) ^ [_916506] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _916506)) = _916506)], (38290 ^ _773908) ^ [_1506075, _1506077, _1506079] : [class_Groups_Olinordered__ab__semigroup__add(_1506075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506075), _1506077)), -(_1506077 = c_Orderings_Obot__class_Obot(tc_fun(_1506075, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1506075), _1506079), c_Big__Operators_Olinorder__class_OMin(_1506075, _1506077)) = c_Big__Operators_Olinorder__class_OMin(_1506075, hAPP(c_Set_OCollect(_1506075), hAPP(hAPP(c_COMBB(tc_fun(_1506075, tc_HOL_Obool), tc_HOL_Obool, _1506075), c_HOL_OEx(_1506075)), hAPP(hAPP(c_COMBC(_1506075, tc_fun(_1506075, tc_HOL_Obool), tc_fun(_1506075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506075, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506075, tc_HOL_Obool), tc_fun(_1506075, tc_HOL_Obool)), _1506075), c_COMBS(_1506075, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506075, tc_HOL_Obool), tc_fun(_1506075, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506075), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506075), c_fconj)), hAPP(hAPP(c_COMBC(_1506075, tc_fun(_1506075, _1506075), tc_fun(_1506075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506075, tc_HOL_Obool), tc_fun(tc_fun(_1506075, _1506075), tc_fun(_1506075, tc_HOL_Obool)), _1506075), c_COMBB(_1506075, tc_HOL_Obool, _1506075)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1506075), _1506079))))), hAPP(hAPP(c_COMBC(_1506075, tc_fun(_1506075, tc_HOL_Obool), tc_HOL_Obool), c_member(_1506075)), _1506077))))))], (5302 ^ _773908) ^ [_854943, _854945, _854947, _854949, _854951, _854953] : [-(c_Finite__Set_Ofold__image(_854953, _854949, _854945) = c_Finite__Set_Ofold__image(_854951, _854947, _854943)), _854953 = _854951, _854949 = _854947, _854945 = _854943], (39813 ^ _773908) ^ [_1550115, _1550117, _1550119, _1550121, _1550123] : [_1550115 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1550117, _1550119, _1550121), _1550115), _1550123) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1550119), _1550117), c_List_Olist_ONil(_1550119)), _1550123))], (12586 ^ _773908) ^ [_984901, _984903, _984905] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984901, tc_HOL_Obool)), _984903), hAPP(hAPP(c_Set_Oinsert(_984901), _984905), _984903))))], (14669 ^ _773908) ^ [_1021951, _1021953, _1021955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021951), 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)), _1021953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021953), _1021955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021951), _1021953)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021951), _1021955))))], (49877 ^ _773908) ^ [_1781251, _1781253, _1781255, _1781257, _1781259, _1781261, _1781263] : [49879 ^ _773908 : [(49882 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1781255, 49878 ^ [_1781251, _1781253, _1781255, _1781257, _1781259, _1781261, _1781263]), _1781257), _1781259))], (49880 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781251), 49878 ^ [_1781251, _1781253, _1781255, _1781257, _1781259, _1781261, _1781263]), _1781253)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1781251, tc_fun(_1781261, tc_fun(_1781263, tc_HOL_Obool))), _1781253), _1781255), _1781257), _1781259)))], (50580 ^ _773908) ^ [_1797518, _1797520] : [c_Relation_Osym(_1797518, _1797520), -(c_Relation_Osym(_1797518, c_Transitive__Closure_Ortrancl(_1797518, _1797520)))], (10381 ^ _773908) ^ [_945945, _945947, _945949] : [class_Orderings_Oorder(_945945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945945), _945947), _945949)), -(_945949 = _945947), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945945), _945947), _945949)))], (13279 ^ _773908) ^ [_996853, _996855, _996857] : [class_Lattices_Oboolean__algebra(_996853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996853), _996855), _996857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996853), hAPP(c_Groups_Ouminus__class_Ouminus(_996853), _996857)), hAPP(c_Groups_Ouminus__class_Ouminus(_996853), _996855))))], (41522 ^ _773908) ^ [_1591646] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1591646)), -(c_List_Onat__list(_1591646))], (41284 ^ _773908) ^ [_1587364, _1587366, _1587368, _1587370] : [-(hAPP(c_List_Ofoldl(_1587364, _1587366, _1587368, _1587370), c_List_Olist_ONil(_1587366)) = _1587370)], (26201 ^ _773908) ^ [_1238977, _1238979, _1238981, _1238983] : [class_Lattices_Osemilattice__sup(_1238977), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238977), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238977), _1238979), _1238981)), _1238983) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238977), _1238979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238977), _1238981), _1238983)))], (48995 ^ _773908) ^ [_1761984, _1761986, _1761988] : [c_Nitpick_Oless__eq__frac(_1761984, _1761986, _1761988), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1761984), c_Nitpick_Oplus__frac(_1761984, _1761986, c_Nitpick_Ouminus__frac(_1761984, _1761988)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8187 ^ _773908) ^ [_908328, _908330, _908332] : [hAPP(c_Com_Ocom_OBODY, _908328) = c_Com_Ocom_OWhile(_908330, _908332)], (6221 ^ _773908) ^ [_874830] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _874830)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35490 ^ _773908) ^ [_1439145, _1439147, _1439149] : [class_Orderings_Olinorder(_1439145), 35493 ^ _773908 : [(35500 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439145), _1439149), _1439147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439145, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439145), _1439147)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439145), _1439149))))], (35494 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439145, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439145), _1439147)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1439145), _1439149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439145), _1439149), _1439147)))]]], (30678 ^ _773908) ^ [_1335457, _1335459, _1335461, _1335463, _1335465, _1335467] : [class_Groups_Ocomm__monoid__mult(_1335457), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335459), _1335461)), 30685 ^ _773908 : [(30692 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335459), _1335463), _1335461))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335459, _1335457), hAPP(hAPP(c_COMBC(_1335459, _1335457, _1335457), hAPP(hAPP(c_COMBS(_1335459, _1335457, tc_fun(_1335457, _1335457)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1335457, tc_fun(_1335457, _1335457)), _1335459), c_If(_1335457)), hAPP(hAPP(c_COMBC(_1335459, _1335459, tc_HOL_Obool), c_fequal), _1335463))), _1335465)), _1335467)), _1335461) = hAPP(hAPP(c_Power_Opower__class_Opower(_1335457), _1335467), hAPP(c_Finite__Set_Ocard(_1335459), _1335461)))], (30686 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1335459), _1335463), _1335461)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335459, _1335457), hAPP(hAPP(c_COMBC(_1335459, _1335457, _1335457), hAPP(hAPP(c_COMBS(_1335459, _1335457, tc_fun(_1335457, _1335457)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1335457, tc_fun(_1335457, _1335457)), _1335459), c_If(_1335457)), hAPP(hAPP(c_COMBC(_1335459, _1335459, tc_HOL_Obool), c_fequal), _1335463))), _1335465)), _1335467)), _1335461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335457), hAPP(_1335465, _1335463)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335457), _1335467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1335459), _1335461)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (20309 ^ _773908) ^ [_1124475, _1124477] : [class_Rings_Olinordered__idom(_1124475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124475), c_Groups_Ozero__class_Ozero(_1124475)), hAPP(hAPP(c_Power_Opower__class_Opower(_1124475), _1124477), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (38677 ^ _773908) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (36391 ^ _773908) ^ [] : [-(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))], (48687 ^ _773908) ^ [_1754931, _1754933, _1754935, _1754937, _1754939, _1754941] : [c_Finite__Set_Ofun__left__comm(_1754931, _1754933, _1754935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1754931), _1754937)), -(hBOOL(hAPP(hAPP(c_member(_1754931), _1754939), _1754937))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1754931, _1754933, _1754935), _1754941), hAPP(hAPP(c_Set_Oinsert(_1754931), _1754939), _1754937)) = hAPP(hAPP(_1754935, _1754939), hAPP(hAPP(c_Finite__Set_Ofold(_1754931, _1754933, _1754935), _1754941), _1754937)))], (48471 ^ _773908) ^ [_1750956, _1750958, _1750960, _1750962] : [class_Complete__Lattice_Ocomplete__lattice(_1750956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750958), _1750960)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1750958, _1750956), _1750960), _1750962) = hAPP(hAPP(c_Finite__Set_Ofold(_1750958, _1750956, hAPP(hAPP(c_COMBB(_1750956, tc_fun(_1750956, _1750956), _1750958), c_Lattices_Osemilattice__sup__class_Osup(_1750956)), _1750962)), c_Orderings_Obot__class_Obot(_1750956)), _1750960))], (5913 ^ _773908) ^ [_868563, _868565] : [hAPP(c_Com_Ocom_OBODY, _868563) = hAPP(c_Com_Ocom_OBODY, _868565), -(_868563 = _868565)], (40587 ^ _773908) ^ [_1569465, _1569467, _1569469, _1569471] : [_1569467 = c_List_Olist_ONil(_1569465), -(hAPP(hAPP(c_List_Olist__update(_1569465, _1569467), _1569469), _1569471) = c_List_Olist_ONil(_1569465))], (25511 ^ _773908) ^ [_1225486, _1225488, _1225490, _1225492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225486), _1225488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225490), _1225492)), -(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), _1225486), _1225490)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1225488), _1225492))), c_FunDef_Opair__less)))], (40661 ^ _773908) ^ [_1571240, _1571242, _1571244, _1571246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1571240), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571242)), _1571244))), 40664 ^ _773908 : [(40671 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Onth(_1571242), _1571244), _1571240) = _1571246, -(hAPP(hAPP(c_List_Olist__update(_1571242, _1571244), _1571240), _1571246) = _1571244)], (40665 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1571242, _1571244), _1571240), _1571246) = _1571244, -(hAPP(hAPP(c_List_Onth(_1571242), _1571244), _1571240) = _1571246)]]], (18297 ^ _773908) ^ [_1089836, _1089838, _1089840, _1089842] : [18298 ^ _773908 : [(18301 ^ _773908) ^ [] : [_1089838 = _1089842], (18299 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1089836), _1089838), _1089840))]], -(hBOOL(hAPP(hAPP(c_member(_1089836), _1089838), hAPP(hAPP(c_Set_Oinsert(_1089836), _1089842), _1089840))))], (5919 ^ _773908) ^ [_868648, _868650] : [_868648 = _868650, -(hAPP(c_Com_Ocom_OBODY, _868648) = hAPP(c_Com_Ocom_OBODY, _868650))], (8375 ^ _773908) ^ [_911959, _911961] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911959), _911961) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _911961), _911959))], (40042 ^ _773908) ^ [_1556094, _1556096, _1556098, _1556100] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1556094), tc_List_Olist(_1556094))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1556094), tc_List_Olist(_1556094)), _1556096), _1556098)), c_List_Olexord(_1556094, _1556100)))), 40043 ^ _773908 : [(40050 ^ _773908) ^ [_1556401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1556401), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556094)), _1556096)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556094)), _1556098)))), hAPP(hAPP(c_List_Otake(_1556094), _1556401), _1556096) = hAPP(hAPP(c_List_Otake(_1556094), _1556401), _1556098), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556094, _1556094)), hAPP(hAPP(c_Product__Type_OPair(_1556094, _1556094), hAPP(hAPP(c_List_Onth(_1556094), _1556096), _1556401)), hAPP(hAPP(c_List_Onth(_1556094), _1556098), _1556401))), _1556100))], (40044 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556094)), _1556096)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556094)), _1556098))), hAPP(hAPP(c_List_Otake(_1556094), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556094)), _1556096)), _1556098) = _1556096]]], (28252 ^ _773908) ^ [_1286455, _1286457, _1286459, _1286461] : [class_Lattices_Odistrib__lattice(_1286455), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286455), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286455), _1286457), _1286459)), _1286461) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286455), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286455), _1286457), _1286461)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1286455), _1286459), _1286461)))], (37448 ^ _773908) ^ [_1482242, _1482244, _1482246, _1482248, _1482250, _1482252] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482242, _1482244)), hAPP(hAPP(c_Product__Type_OPair(_1482242, _1482244), _1482246), _1482248)), hAPP(hAPP(c_Product__Type_OSigma(_1482242, _1482244), _1482250), _1482252))), 37451 ^ _773908 : [(37454 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482244), _1482248), hAPP(_1482252, _1482246))))], (37452 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482242), _1482246), _1482250)))]]], (8203 ^ _773908) ^ [_908774, _908776, _908778, _908780] : [c_Com_Ocom_OWhile(_908774, _908776) = c_Com_Ocom_OSemi(_908778, _908780)], (24711 ^ _773908) ^ [_1209599, _1209601, _1209603, _1209605] : [class_Orderings_Olinorder(_1209599), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209599), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209599), _1209601), _1209603)), _1209605) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209599), _1209601), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209599), _1209603), _1209605)))], (8331 ^ _773908) ^ [_911299, _911301] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _911299), _911301))), -(_911299 = _911301), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _911301), _911299)))], (25089 ^ _773908) ^ [_1217084, _1217086, _1217088, _1217090] : [class_Orderings_Olinorder(_1217084), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217084), _1217086), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217084), _1217088), _1217090)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217084), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217084), _1217086), _1217088)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217084), _1217086), _1217090)))], (38759 ^ _773908) ^ [_1522578, _1522580, _1522582, _1522584, _1522586, _1522588, _1522590] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1522578, _1522580, _1522582, _1522584, _1522586), _1522588), _1522590)), 38763 ^ _773908 : [(38766 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1522586, 38762 ^ [_1522578, _1522580, _1522582, _1522584, _1522586, _1522588, _1522590]), _1522590)))], (38764 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1522584, _1522588), 38762 ^ [_1522578, _1522580, _1522582, _1522584, _1522586, _1522588, _1522590])))]]], (42979 ^ _773908) ^ [_1626911, _1626913, _1626915, _1626917] : [-(c_List_Oremove1(_1626911, _1626913, c_List_Oremove1(_1626911, _1626915, _1626917)) = c_List_Oremove1(_1626911, _1626915, c_List_Oremove1(_1626911, _1626913, _1626917)))], (16469 ^ _773908) ^ [_1056315, _1056317] : [class_Groups_Oordered__ab__group__add__abs(_1056315), -(hAPP(c_Groups_Oabs__class_Oabs(_1056315), hAPP(c_Groups_Ouminus__class_Ouminus(_1056315), _1056317)) = hAPP(c_Groups_Oabs__class_Oabs(_1056315), _1056317))], (24179 ^ _773908) ^ [_1196642, _1196644, _1196646, _1196648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1196642, _1196642)), hAPP(hAPP(c_Product__Type_OPair(_1196642, _1196642), _1196644), _1196646)), hAPP(c_Wellfounded_Omeasure(_1196642), _1196648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1196648, _1196644)), hAPP(_1196648, _1196646))))], (40119 ^ _773908) ^ [_1558034, _1558036, _1558038, _1558040] : [-(hAPP(hAPP(c_List_Otake(_1558034), _1558036), hAPP(hAPP(c_List_Oappend(_1558034), _1558038), _1558040)) = hAPP(hAPP(c_List_Oappend(_1558034), hAPP(hAPP(c_List_Otake(_1558034), _1558036), _1558038)), hAPP(hAPP(c_List_Otake(_1558034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1558036), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558034)), _1558038))), _1558040)))], (49624 ^ _773908) ^ [_1775583, _1775585] : [-(c_Predicate_Opred__comp(_1775583, _1775583, _1775583, c_fequal, c_Predicate_Opred__comp(_1775583, _1775583, _1775583, _1775585, c_fequal)) = _1775585)], (45826 ^ _773908) ^ [_1689648] : [c_List_Onat__list(_1689648), -(c_List_Oembed__list(c_List_Oreturn__list(_1689648)) = _1689648)], (21807 ^ _773908) ^ [_1151326, _1151328, _1151330, _1151332, _1151334] : [class_Fields_Ofield(_1151326), -(_1151328 = c_Groups_Ozero__class_Ozero(_1151326)), -(_1151330 = c_Groups_Ozero__class_Ozero(_1151326)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151326), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151326), _1151332), _1151328)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151326), _1151334), _1151330)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1151326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151326), _1151332), _1151330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151326), _1151334), _1151328))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151326), _1151328), _1151330)))], (41671 ^ _773908) ^ [_1594812, _1594814, _1594816, _1594818] : [41673 ^ _773908 : [(41676 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1594816, 41672 ^ [_1594812, _1594814, _1594816, _1594818])), hAPP(_1594818, 41672 ^ [_1594812, _1594814, _1594816, _1594818])))], (41674 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1594812), 41672 ^ [_1594812, _1594814, _1594816, _1594818]), hAPP(c_List_Oset(_1594812), _1594814))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1594812, _1594816, _1594814)), c_List_Olist_Olist__size(_1594812, _1594818, _1594814))))], (35728 ^ _773908) ^ [_1444353, _1444355, _1444357, _1444359, _1444361] : [class_Groups_Ocomm__monoid__add(_1444353), class_Groups_Oordered__cancel__ab__semigroup__add(_1444353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444355), _1444357)), -(_1444357 = c_Orderings_Obot__class_Obot(tc_fun(_1444355, tc_HOL_Obool))), 35746 ^ _773908 : [(35749 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444353), hAPP(_1444359, 35745 ^ [_1444353, _1444355, _1444357, _1444359, _1444361])), hAPP(_1444361, 35745 ^ [_1444353, _1444355, _1444357, _1444359, _1444361])))], (35747 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444355), 35745 ^ [_1444353, _1444355, _1444357, _1444359, _1444361]), _1444357)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444353), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444355, _1444353), _1444359), _1444357)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444355, _1444353), _1444361), _1444357))))], (44644 ^ _773908) ^ [_1666297, _1666299] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1666297, _1666299)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1666297), _1666299))], (30415 ^ _773908) ^ [_1329728, _1329730, _1329732] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329728), _1329730)), -(hBOOL(hAPP(hAPP(c_member(_1329728), _1329732), _1329730))), -(hAPP(c_Finite__Set_Ocard(_1329728), hAPP(hAPP(c_Set_Oinsert(_1329728), _1329732), _1329730)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1329728), _1329730)))], (12774 ^ _773908) ^ [_988030, _988032, _988034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988032), _988034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988030), _988032)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988030), _988034))))], (21201 ^ _773908) ^ [_1140564, _1140566, _1140568, _1140570] : [class_Rings_Odivision__ring(_1140564), -(_1140566 = c_Groups_Ozero__class_Ozero(_1140564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140564), _1140568), _1140566) = _1140570, -(_1140568 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140564), _1140570), _1140566))], (39657 ^ _773908) ^ [_1545380, _1545382, _1545384, _1545386, _1545388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545380, _1545380)), hAPP(hAPP(c_Product__Type_OPair(_1545380, _1545380), _1545382), _1545384)), _1545386)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1545380), tc_List_Olist(_1545380))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1545380), tc_List_Olist(_1545380)), hAPP(hAPP(c_List_Olist_OCons(_1545380), _1545382), _1545388)), hAPP(hAPP(c_List_Olist_OCons(_1545380), _1545384), _1545388))), c_List_Olistrel1(_1545380, _1545386))))], (51670 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Com_Ovname))], (43596 ^ _773908) ^ [_1640516, _1640518, _1640520, _1640522] : [hBOOL(hAPP(c_List_Odistinct(_1640516), _1640518)), hBOOL(hAPP(c_List_Odistinct(_1640520), _1640522)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1640516, _1640520)), c_Enum_Oproduct(_1640516, _1640520, _1640518, _1640522))))], (46768 ^ _773908) ^ [_1710955] : [-(c_Transitive__Closure_Ortrancl(_1710955, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1710955, _1710955), tc_HOL_Obool))) = c_Relation_OId(_1710955))], (6374 ^ _773908) ^ [_877257, _877259, _877261, _877263, _877265] : [class_Groups_Oordered__cancel__ab__semigroup__add(_877257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877257), _877259), _877261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877257), _877263), _877265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877257), _877259), _877263)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877257), _877261), _877265))))], (8473 ^ _773908) ^ [_913582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _913582))))], (45145 ^ _773908) ^ [_1675769, _1675771] : [class_Orderings_Olinorder(_1675769), c_List_Olinorder__class_Osorted(_1675769, _1675771), -(c_List_Olinorder__class_Osorted(_1675769, c_List_Oremdups(_1675769, _1675771)))], (28909 ^ _773908) ^ [_1302002, _1302004, _1302006] : [class_Orderings_Olinorder(_1302002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302002), _1302004)), hBOOL(hAPP(hAPP(c_member(_1302002), _1302006), _1302004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302002), _1302006), c_Big__Operators_Olinorder__class_OMax(_1302002, _1302004))))], (40165 ^ _773908) ^ [_1559250, _1559252, _1559254, _1559256] : [hBOOL(hAPP(hAPP(c_member(_1559250), _1559252), hAPP(c_List_Oset(_1559250), hAPP(hAPP(c_List_Otake(_1559250), _1559254), _1559256)))), -(hBOOL(hAPP(hAPP(c_member(_1559250), _1559252), hAPP(c_List_Oset(_1559250), _1559256))))], (40832 ^ _773908) ^ [_1576507, _1576509, _1576511] : [40834 ^ _773908 : [(40837 ^ _773908) ^ [] : [hBOOL(hAPP(_1576509, 40833 ^ [_1576507, _1576509, _1576511]))], (40835 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576507), 40833 ^ [_1576507, _1576509, _1576511]), _1576511)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1576507, _1576509), _1576511)))], (39184 ^ _773908) ^ [_1533614, _1533616, _1533618, _1533620, _1533622, _1533624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533614), tc_List_Olist(_1533614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533614), tc_List_Olist(_1533614)), hAPP(hAPP(c_List_Olist_OCons(_1533614), _1533616), _1533618)), hAPP(hAPP(c_List_Olist_OCons(_1533614), _1533620), _1533622))), c_List_Olex(_1533614, _1533624))), 39189 ^ _773908 : [(39192 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533614)), _1533618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1533614)), _1533622))], (39190 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533614, _1533614)), hAPP(hAPP(c_Product__Type_OPair(_1533614, _1533614), _1533616), _1533620)), _1533624)))]], 39193 ^ _773908 : [(39196 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1533614), tc_List_Olist(_1533614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1533614), tc_List_Olist(_1533614)), _1533618), _1533622)), c_List_Olex(_1533614, _1533624))))], (39194 ^ _773908) ^ [] : [-(_1533616 = _1533620)]]], (27071 ^ _773908) ^ [_1261760, _1261762, _1261764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1261760, _1261760), tc_HOL_Obool)), _1261762), _1261764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261760, tc_HOL_Obool)), c_Wellfounded_Oacc(_1261760, _1261764)), c_Wellfounded_Oacc(_1261760, _1261762))))], (9301 ^ _773908) ^ [_928614, _928616, _928618] : [class_Rings_Olinordered__semiring__strict(_928614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928614), _928616), c_Groups_Ozero__class_Ozero(_928614))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928614), c_Groups_Ozero__class_Ozero(_928614)), _928618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928614), _928616), _928618)), c_Groups_Ozero__class_Ozero(_928614))))], (7305 ^ _773908) ^ [_892166, _892168] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892166), _892168) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7306 ^ _773908 : [(7313 ^ _773908) ^ [] : [_892166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _892168 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7307 ^ _773908) ^ [] : [_892166 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _892168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (26848 ^ _773908) ^ [_1257559, _1257561, _1257563, _1257565, _1257567, _1257569, _1257571] : [-(hAPP(c_Fun_Ocomp(_1257559, _1257561, _1257563, _1257565), c_Fun_Ofun__upd(_1257563, _1257559, _1257567, _1257569, _1257571)) = c_Fun_Ofun__upd(_1257563, _1257561, hAPP(c_Fun_Ocomp(_1257559, _1257561, _1257563, _1257565), _1257567), _1257569, hAPP(_1257565, _1257571)))], (31103 ^ _773908) ^ [_1344485, _1344487, _1344489, _1344491] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1344485), _1344487)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344489), _1344491)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1344485, _1344489)), c_Sum__Type_OPlus(_1344485, _1344489, _1344487, _1344491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1344485), _1344487)), hAPP(c_Finite__Set_Ocard(_1344489), _1344491)))], (36313 ^ _773908) ^ [] : [-(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))))], (5761 ^ _773908) ^ [_864962, _864964, _864966, _864968, _864970] : [c_Hoare__Mirabelle_Ohoare__derivs(_864962, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_864962)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864962), _864964), hAPP(c_Com_Ocom_OBODY, _864966)), _864968)), _864970), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_864962)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864962), _864964), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _864966))), _864968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_864962), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_864962, _864970, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_864962)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_864962), _864964), hAPP(c_Com_Ocom_OBODY, _864966)), _864968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_864962), tc_HOL_Obool)))))], (25707 ^ _773908) ^ [_1229386, _1229388, _1229390, _1229392] : [25708 ^ _773908 : [(25711 ^ _773908) ^ [] : [hBOOL(hAPP(_1229390, _1229388))], (25709 ^ _773908) ^ [] : [hBOOL(hAPP(_1229386, _1229388))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229392, tc_HOL_Obool)), _1229390), _1229386), _1229388)))], (42696 ^ _773908) ^ [_1620592, _1620594, _1620596] : [-(hAPP(hAPP(c_List_Ozip(_1620592, _1620594), hAPP(hAPP(c_List_Omap(tc_prod(_1620592, _1620594), _1620592), c_Product__Type_Ofst(_1620592, _1620594)), _1620596)), hAPP(hAPP(c_List_Omap(tc_prod(_1620592, _1620594), _1620594), c_Product__Type_Osnd(_1620592, _1620594)), _1620596)) = _1620596)], (12688 ^ _773908) ^ [_986454, _986456] : [12689 ^ _773908 : [(12692 ^ _773908) ^ [] : [_986454 = _986456], (12690 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986454), _986456))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986454), _986456)))], (51508 ^ _773908) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51928 ^ _773908) ^ [_1818785, _1818787] : [-(hBOOL(_1818785)), -(hBOOL(hAPP(hAPP(c_fimplies, _1818785), _1818787)))], (45615 ^ _773908) ^ [_1685114, _1685116] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1685114), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1685114))), c_List_Otranspose(_1685114, _1685116)))))], (14917 ^ _773908) ^ [_1026238, _1026240, _1026242] : [class_Divides_Osemiring__div(_1026238), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026238), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026238), _1026240), _1026242)), _1026242)), c_Divides_Odiv__class_Omod(_1026238, _1026240, _1026242)) = _1026240)], (23123 ^ _773908) ^ [_1175767, _1175769] : [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(_1175767))), 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)), _1175769))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1175767) = hAPP(c_Nat_OSuc, _1175769))], (40247 ^ _773908) ^ [_1561040, _1561042, _1561044, _1561046] : [-(hAPP(hAPP(c_List_Odrop(_1561040), _1561042), hAPP(hAPP(c_List_Otake(_1561040), _1561044), _1561046)) = hAPP(hAPP(c_List_Otake(_1561040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1561044), _1561042)), hAPP(hAPP(c_List_Odrop(_1561040), _1561042), _1561046)))], (35907 ^ _773908) ^ [_1447593] : [class_Finite__Set_Ofinite(_1447593), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447593), c_Orderings_Otop__class_Otop(tc_fun(_1447593, tc_HOL_Obool)))))], (1364 ^ _773908) ^ [_793944, _793946] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_793944)), _793946 = _793944, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_793946)], (18345 ^ _773908) ^ [_1090692, _1090694, _1090696] : [hBOOL(hAPP(_1090696, _1090694)), -(hBOOL(hAPP(hAPP(c_member(_1090692), _1090694), _1090696)))], (38247 ^ _773908) ^ [_1504376, _1504378] : [-(hAPP(c_Set_OPow(_1504376), _1504378) = hAPP(c_Set_OCollect(tc_fun(_1504376, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1504376, tc_HOL_Obool), tc_fun(_1504376, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1504376, tc_HOL_Obool))), _1504378)))], (45984 ^ _773908) ^ [_1693122, _1693124] : [class_Orderings_Olinorder(_1693122), -(c_List_Olinorder__class_Osort__key(_1693122, _1693122, c_COMBI(_1693122), _1693124) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693122), _1693122, hAPP(c_COMBC(_1693122, tc_List_Olist(_1693122), tc_List_Olist(_1693122)), c_List_Olinorder__class_Oinsort__key(_1693122, _1693122, c_COMBI(_1693122))), c_List_Olist_ONil(_1693122)), _1693124))], (32448 ^ _773908) ^ [_1376143, _1376145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376143), _1376145)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1376143, tc_HOL_Obool)), hAPP(c_Set_OPow(_1376143), _1376145))))], (42230 ^ _773908) ^ [_1609868, _1609870, _1609872, _1609874, _1609876, _1609878] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609868, tc_fun(_1609870, tc_HOL_Obool)), _1609872), hAPP(hAPP(c_COMBC(_1609868, tc_fun(_1609874, tc_fun(_1609870, tc_HOL_Obool)), tc_fun(_1609870, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609874, tc_HOL_Obool), tc_fun(tc_fun(_1609874, tc_fun(_1609870, tc_HOL_Obool)), tc_fun(_1609870, tc_HOL_Obool)), _1609868), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609874, tc_fun(_1609870, tc_HOL_Obool))), _1609876)), _1609878)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609874, tc_fun(_1609870, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609868, tc_fun(_1609874, tc_HOL_Obool)), _1609872), _1609876)), _1609878))], (48333 ^ _773908) ^ [_1748278, _1748280, _1748282, _1748284] : [class_Orderings_Olinorder(_1748278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748278), _1748280)), hBOOL(hAPP(hAPP(c_member(_1748278), _1748282), _1748280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748278), hAPP(hAPP(c_Finite__Set_Ofold(_1748278, _1748278, c_Orderings_Oord__class_Omin(_1748278)), _1748284), _1748280)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1748278), _1748282), _1748284))))], (51658 ^ _773908) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (13775 ^ _773908) ^ [_1005937, _1005939] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005937), _1005939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005937, _1005939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (40357 ^ _773908) ^ [_1563625, _1563627, _1563629] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1563625)), _1563627), c_List_Olists(_1563625, _1563629))), 40360 ^ _773908 : [(40361 ^ _773908) ^ [_1563733] : [hBOOL(hAPP(hAPP(c_member(_1563625), _1563733), hAPP(c_List_Oset(_1563625), _1563627))), -(hBOOL(hAPP(hAPP(c_member(_1563625), _1563733), _1563629)))]]], (31445 ^ _773908) ^ [_1352407, _1352409, _1352411, _1352413, _1352415, _1352417] : [hBOOL(hAPP(hAPP(c_member(_1352407), _1352409), _1352411)), hBOOL(hAPP(hAPP(c_member(_1352413), _1352415), hAPP(_1352417, _1352409))), -(hBOOL(hAPP(hAPP(c_member(_1352413), _1352415), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1352407, tc_fun(_1352413, tc_HOL_Obool)), _1352411), _1352417))))], (6002 ^ _773908) ^ [_870296] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _870296), _870296)))], (30991 ^ _773908) ^ [_1342005, _1342007, _1342009, _1342011] : [class_Groups_Ocomm__monoid__mult(_1342005), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342007), _1342009)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342007, _1342005), hAPP(c_COMBK(_1342005, _1342007), _1342011)), _1342009) = hAPP(hAPP(c_Power_Opower__class_Opower(_1342005), _1342011), hAPP(c_Finite__Set_Ocard(_1342007), _1342009)))], (13522 ^ _773908) ^ [_1001103, _1001105] : [class_Divides_Osemiring__div(_1001103), -(c_Divides_Odiv__class_Omod(_1001103, _1001105, c_Groups_Ozero__class_Ozero(_1001103)) = _1001105)], (12256 ^ _773908) ^ [_979187, _979189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979189)), 12263 ^ _773908 : [(12270 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979187), _979189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _979187)), hAPP(c_Int_Onat, _979189))))], (12264 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _979187)), hAPP(c_Int_Onat, _979189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979187), _979189)))]]], (24839 ^ _773908) ^ [_1212031, _1212033, _1212035, _1212037] : [class_Groups_Oordered__ab__group__add(_1212031), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212031), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212031), _1212033), _1212035)), _1212037) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212031), _1212033), _1212037)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212031), _1212035), _1212037)))], (38922 ^ _773908) ^ [_1525951, _1525953, _1525955] : [c_Wellfounded_Owf(_1525951, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525951, _1525951), tc_HOL_Obool)), _1525953), _1525955)), -(c_Wellfounded_Owf(_1525951, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525951, _1525951), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525951, _1525951), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1525951, _1525951, _1525951), _1525953), _1525953)), hAPP(hAPP(c_Relation_Orel__comp(_1525951, _1525951, _1525951), _1525955), _1525953))), _1525955)))], (51618 ^ _773908) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (5464 ^ _773908) ^ [_857490, _857492, _857494, _857496, _857498, _857500, _857502, _857504] : [-(c_Product__Type_Ocurry(_857504, _857500, _857496, _857492) = c_Product__Type_Ocurry(_857502, _857498, _857494, _857490)), _857504 = _857502, _857500 = _857498, _857496 = _857494, _857492 = _857490], (14839 ^ _773908) ^ [_1024635, _1024637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1024637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024635), _1024637)), _1024635)))], (27256 ^ _773908) ^ [_1266169, _1266171, _1266173, _1266175] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266169), _1266171)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266173), hAPP(c_Set_Oimage(_1266169, _1266173, _1266175), _1266171))))], (44642 ^ _773908) ^ [_1666260, _1666262] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1666260), _1666262) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1666260, _1666262)))], (18895 ^ _773908) ^ [_1100524, _1100526] : [class_Int_Onumber__ring(_1100524), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100524), _1100526), hAPP(c_Int_Onumber__class_Onumber__of(_1100524), c_Int_OPls)) = _1100526)], (26301 ^ _773908) ^ [_1241495, _1241497] : [-(c_FunDef_Orp__inv__image(_1241495, _1241497) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))))), tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))), tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)), tc_fun(tc_fun(_1241497, _1241495), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool)), c_COMBS(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)), tc_fun(tc_fun(_1241497, _1241495), tc_fun(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), tc_fun(tc_prod(_1241495, _1241495), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool))), tc_fun(_1241497, _1241495)), c_Product__Type_OPair(tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool), tc_fun(tc_prod(_1241497, _1241497), tc_HOL_Obool)))), c_Relation_Oinv__image(_1241495, _1241497))))), c_Relation_Oinv__image(_1241495, _1241497))))], (16332 ^ _773908) ^ [_1053898, _1053900, _1053902] : [class_Fields_Olinordered__field(_1053898), 16338 ^ _773908 : [(16341 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053898), _1053900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053898), _1053902), 16337 ^ [_1053898, _1053900, _1053902])))], (16339 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053898), c_Groups_Ozero__class_Ozero(_1053898)), 16337 ^ [_1053898, _1053900, _1053902])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053898), _1053900), _1053902)))], (37718 ^ _773908) ^ [_1489742, _1489744, _1489746, _1489748, _1489750, _1489752, _1489754, _1489756, _1489758, _1489760, _1489762] : [-(hAPP(c_Product__Type_Omap__pair(_1489742, _1489744, _1489746, _1489748, _1489750, _1489752), hAPP(c_Product__Type_Omap__pair(_1489754, _1489742, _1489756, _1489746, _1489758, _1489760), _1489762)) = hAPP(c_Product__Type_Omap__pair(_1489754, _1489744, _1489756, _1489748, hAPP(c_Fun_Ocomp(_1489742, _1489744, _1489754, _1489750), _1489758), hAPP(c_Fun_Ocomp(_1489746, _1489748, _1489756, _1489752), _1489760)), _1489762))], (38559 ^ _773908) ^ [_1515926, _1515928] : [38560 ^ _773908 : [(38561 ^ _773908) ^ [_1515990, _1515992] : [_1515928 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1515926, _1515990), 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)), _1515992)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515926), _1515928)))], (19561 ^ _773908) ^ [_1111499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1111499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1111499)))], (49763 ^ _773908) ^ [_1778520] : [-(c_List_Omember(_1778520) = c_List_Oset(_1778520))], (11417 ^ _773908) ^ [_964438, _964440] : [class_Groups_Oordered__ab__group__add(_964438), 11420 ^ _773908 : [(11427 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964438), c_Groups_Ozero__class_Ozero(_964438)), _964440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964438), hAPP(c_Groups_Ouminus__class_Ouminus(_964438), _964440)), c_Groups_Ozero__class_Ozero(_964438))))], (11421 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964438), hAPP(c_Groups_Ouminus__class_Ouminus(_964438), _964440)), c_Groups_Ozero__class_Ozero(_964438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964438), c_Groups_Ozero__class_Ozero(_964438)), _964440)))]]], (13640 ^ _773908) ^ [_1003578, _1003580, _1003582, _1003584] : [class_Divides_Oring__div(_1003578), c_Divides_Odiv__class_Omod(_1003578, _1003580, _1003582) = c_Divides_Odiv__class_Omod(_1003578, _1003584, _1003582), -(c_Divides_Odiv__class_Omod(_1003578, hAPP(c_Groups_Ouminus__class_Ouminus(_1003578), _1003580), _1003582) = c_Divides_Odiv__class_Omod(_1003578, hAPP(c_Groups_Ouminus__class_Ouminus(_1003578), _1003584), _1003582))], (49462 ^ _773908) ^ [_1772365, _1772367, _1772369, _1772371, _1772373] : [-(hAPP(hAPP(c_List_Omap(_1772365, _1772367), _1772369), c_List_Oreplicate(_1772365, _1772371, _1772373)) = c_List_Oreplicate(_1772367, _1772371, hAPP(_1772369, _1772373)))], (18221 ^ _773908) ^ [_1088362, _1088364, _1088366, _1088368] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1088362, tc_HOL_Obool)), _1088364), hAPP(hAPP(c_Set_Oinsert(_1088362), _1088366), _1088368)))), 18224 ^ _773908 : [(18227 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1088362, tc_HOL_Obool)), _1088364), _1088368))], (18225 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1088362), _1088366), _1088368)))]], 18228 ^ _773908 : [(18231 ^ _773908) ^ [] : [18232 ^ _773908 : [(18235 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1088362, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088362, tc_HOL_Obool)), _1088364), hAPP(hAPP(c_Set_Oinsert(_1088362), _1088366), c_Orderings_Obot__class_Obot(tc_fun(_1088362, tc_HOL_Obool))))), _1088368))], (18233 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1088362), _1088366), _1088364)))]], 18236 ^ _773908 : [(18239 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1088362, tc_HOL_Obool)), _1088364), _1088368))], (18237 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1088362), _1088366), _1088364))]]], (18229 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1088362), _1088366), _1088368))]]], (51518 ^ _773908) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (40477 ^ _773908) ^ [_1566682, _1566684, _1566686, _1566688] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1566682) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1566684), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1566682)), hAPP(hAPP(c_List_Olist_OCons(_1566684), _1566686), _1566688)) = hAPP(hAPP(c_List_Olist_OCons(_1566684), _1566686), _1566688))], (2782 ^ _773908) ^ [_815263, _815265, _815267, _815269, _815271, _815273] : [-(c_Finite__Set_Ofold1Set(_815273, _815269, _815265) = c_Finite__Set_Ofold1Set(_815271, _815267, _815263)), _815273 = _815271, _815269 = _815267, _815265 = _815263], (40263 ^ _773908) ^ [_1561418, _1561420, _1561422] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1561418, tc_HOL_Obool)), hAPP(c_List_Oset(_1561418), c_List_Osublist(_1561418, _1561420, _1561422))), hAPP(c_List_Oset(_1561418), _1561420))))], (41488 ^ _773908) ^ [_1591191, _1591193] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591193)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591191), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1591193)) = c_List_Olist_ONil(tc_Int_Oint))], (8519 ^ _773908) ^ [_914514, _914516, _914518, _914520, _914522] : [class_Rings_Ocomm__semiring__1(_914514), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), _914516), _914518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), _914520), _914522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), _914516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), _914518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914514), _914520), _914522))))], (35050 ^ _773908) ^ [_1429225, _1429227, _1429229, _1429231] : [class_Groups_Ocomm__monoid__add(_1429225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1429227), _1429229)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429225), _1429231), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1429227, _1429229)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429225), hAPP(_1429231, _1429227)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429225), _1429231), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1429227, _1429229))))], (51428 ^ _773908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (18023 ^ _773908) ^ [_1084764, _1084766] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084764) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084766), 18026 ^ _773908 : [(18033 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084764)))), 18036 ^ _773908 : [(18043 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084766)))), -(_1084764 = _1084766)], (18037 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084766))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084764) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (18027 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084766)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14354 ^ _773908) ^ [_1016711, _1016713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016711), _1016713)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016711, _1016713) = _1016711)], (15801 ^ _773908) ^ [_1042876, _1042878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042876), _1042878)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042878), _1042876)), _1042876) = _1042878)], (30337 ^ _773908) ^ [_1328348] : [-(hAPP(c_Finite__Set_Ocard(_1328348), c_Orderings_Obot__class_Obot(tc_fun(_1328348, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20529 ^ _773908) ^ [_1128404, _1128406, _1128408] : [class_Rings_Ocomm__semiring__1(_1128404), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128404), _1128406), 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)))), _1128408))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128404), _1128406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128404), hAPP(hAPP(c_Power_Opower__class_Opower(_1128404), _1128406), _1128408)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128404), _1128406), _1128408))))], (46051 ^ _773908) ^ [_1694284, _1694286, _1694288, _1694290, _1694292] : [class_Orderings_Olinorder(_1694284), -(c_List_Olinorder__class_Osort__key(_1694286, _1694284, _1694288, hAPP(hAPP(c_List_Olist_OCons(_1694286), _1694290), _1694292)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694286, _1694284, _1694288), _1694290), c_List_Olinorder__class_Osort__key(_1694286, _1694284, _1694288, _1694292)))], (20027 ^ _773908) ^ [_1119556, _1119558] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1119556)), c_Int_OBit1(_1119558)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1119556), _1119558)))], (49330 ^ _773908) ^ [_1769216, _1769218] : [c_Wellfounded_Oacyclic(_1769216, hAPP(c_Set_OCollect(tc_prod(_1769216, _1769216)), hAPP(c_Product__Type_Oprod_Oprod__case(_1769216, _1769216, tc_HOL_Obool), c_Predicate_Oconversep(_1769216, _1769216, _1769218)))), -(c_Wellfounded_Oacyclic(_1769216, hAPP(c_Set_OCollect(tc_prod(_1769216, _1769216)), hAPP(c_Product__Type_Oprod_Oprod__case(_1769216, _1769216, tc_HOL_Obool), _1769218))))], (33892 ^ _773908) ^ [] : [-(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))))], (42049 ^ _773908) ^ [_1605030, _1605032, _1605034, _1605036] : [42051 ^ _773908 : [(42054 ^ _773908) ^ [] : [hAPP(_1605036, 42050 ^ [_1605030, _1605032, _1605034, _1605036]) = c_Orderings_Otop__class_Otop(tc_fun(_1605032, tc_HOL_Obool))], (42052 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605030), 42050 ^ [_1605030, _1605032, _1605034, _1605036]), _1605034)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605030, tc_fun(_1605032, tc_HOL_Obool)), _1605034), _1605036) = c_Orderings_Otop__class_Otop(tc_fun(_1605032, tc_HOL_Obool)))], (36737 ^ _773908) ^ [_1466184, _1466186, _1466188] : [-(c_HOL_OThe(tc_prod(_1466184, _1466186), _1466188) = c_HOL_OThe(tc_prod(_1466184, _1466186), hAPP(c_Product__Type_Oprod_Oprod__case(_1466184, _1466186, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1466186, tc_prod(_1466184, _1466186)), tc_fun(_1466186, tc_HOL_Obool), _1466184), hAPP(c_COMBB(tc_prod(_1466184, _1466186), tc_HOL_Obool, _1466186), _1466188)), c_Product__Type_OPair(_1466184, _1466186)))))], (46515 ^ _773908) ^ [_1704569, _1704571, _1704573, _1704575] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1704569), _1704571)), 46521 ^ _773908 : [(46524 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1704573), hAPP(_1704575, 46520 ^ [_1704569, _1704571, _1704573, _1704575])))], (46522 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1704569), 46520 ^ [_1704569, _1704571, _1704573, _1704575]), _1704571)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1704573), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1704569, tc_fun(_1704573, tc_HOL_Obool)), _1704571), _1704575))))], (3410 ^ _773908) ^ [_825119, _825121, _825123, _825125, _825127, _825129] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_825129, _825125, _825121) = c_SetInterval_Oord__class_OgreaterThanLessThan(_825127, _825123, _825119)), _825129 = _825127, _825125 = _825123, _825121 = _825119], (4406 ^ _773908) ^ [_840939, _840941, _840943, _840945, _840947, _840949, _840951, _840953] : [-(c_New__Random__Sequence_Opos__map(_840953, _840949, _840945, _840941) = c_New__Random__Sequence_Opos__map(_840951, _840947, _840943, _840939)), _840953 = _840951, _840949 = _840947, _840945 = _840943, _840941 = _840939], (4594 ^ _773908) ^ [_843791, _843793, _843795, _843797, _843799, _843801] : [-(c_List_Oreplicate(_843801, _843797, _843793) = c_List_Oreplicate(_843799, _843795, _843791)), _843801 = _843799, _843797 = _843795, _843793 = _843791], (44545 ^ _773908) ^ [_1662639, _1662641, _1662643] : [44547 ^ _773908 : [(44550 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1662639), tc_List_Olist(_1662639), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1662639), tc_fun(tc_List_Olist(_1662639), tc_Nat_Onat), tc_fun(tc_List_Olist(_1662639), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1662639), tc_Nat_Onat), tc_fun(tc_List_Olist(_1662639), tc_HOL_Obool)), tc_List_Olist(_1662639)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1662639))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1662639)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1662639))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1662639)))), 44546 ^ [_1662639, _1662641, _1662643]))], (44548 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662639), tc_List_Olist(_1662639))), 44546 ^ [_1662639, _1662641, _1662643]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1662639), tc_List_Olist(_1662639))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1662639), tc_List_Olist(_1662639)), _1662641), _1662643)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1662639))), _1662641) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1662639))), _1662643), 44555 ^ _773908 : [(44562 ^ _773908) ^ [] : [_1662641 = _1662643, -(c_List_Oconcat(_1662639, _1662641) = c_List_Oconcat(_1662639, _1662643))], (44556 ^ _773908) ^ [] : [c_List_Oconcat(_1662639, _1662641) = c_List_Oconcat(_1662639, _1662643), -(_1662641 = _1662643)]]], (25341 ^ _773908) ^ [_1221639, _1221641, _1221643, _1221645] : [class_Orderings_Olinorder(_1221639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221639), _1221641), _1221643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221639), _1221641), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221639), _1221645), _1221643))))], (8999 ^ _773908) ^ [_923257, _923259, _923261] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923259), _923261)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923257), _923259)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923257), _923261)))], (34139 ^ _773908) ^ [_1409455] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1409455))], (39913 ^ _773908) ^ [_1552686, _1552688, _1552690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1552686), tc_List_Olist(_1552686))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1552686), tc_List_Olist(_1552686)), c_List_Olist_ONil(_1552686)), _1552688)), c_List_Olexord(_1552686, _1552690))), -(_1552688 = hAPP(hAPP(c_List_Olist_OCons(_1552686), 39916 ^ [_1552686, _1552688, _1552690]), 39917 ^ [_1552686, _1552688, _1552690]))], (27754 ^ _773908) ^ [_1276347, _1276349, _1276351] : [27755 ^ _773908 : [(27758 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276347), _1276351))], (27756 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276347), _1276349))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276347), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1276347, tc_HOL_Obool)), _1276349), _1276351))))], (3430 ^ _773908) ^ [_825425, _825427, _825429, _825431, _825433, _825435] : [-(c_List_Oinsert(_825435, _825431, _825427) = c_List_Oinsert(_825433, _825429, _825425)), _825435 = _825433, _825431 = _825429, _825427 = _825425], (48032 ^ _773908) ^ [_1741740, _1741742, _1741744] : [c_List_Olist__ex(_1741740, _1741742, _1741744), 48036 ^ _773908 : [(48039 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1741742, 48035 ^ [_1741740, _1741742, _1741744])))], (48037 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741740), 48035 ^ [_1741740, _1741742, _1741744]), hAPP(c_List_Oset(_1741740), _1741744))))]]], (46718 ^ _773908) ^ [_1709628, _1709630, _1709632] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709628), tc_List_Olist(_1709628))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709628), tc_List_Olist(_1709628)), _1709630), _1709630)), c_List_Olistrel(_1709628, c_Transitive__Closure_Ortrancl(_1709628, _1709632)))))], (36430 ^ _773908) ^ [_1459793, _1459795] : [-(c_Equiv__Relations_Oequivp(_1459793, _1459795)), 36435 ^ _773908 : [(36438 ^ _773908) ^ [] : [hAPP(_1459795, 36431 ^ [_1459793, _1459795]) = hAPP(_1459795, 36432 ^ [_1459793, _1459795])], (36436 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1459795, 36431 ^ [_1459793, _1459795]), 36432 ^ [_1459793, _1459795])))]], 36439 ^ _773908 : [(36442 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1459795, 36431 ^ [_1459793, _1459795]), 36432 ^ [_1459793, _1459795]))], (36440 ^ _773908) ^ [] : [-(hAPP(_1459795, 36431 ^ [_1459793, _1459795]) = hAPP(_1459795, 36432 ^ [_1459793, _1459795]))]]], (37910 ^ _773908) ^ [_1494244] : [class_Orderings_Olinorder(_1494244), -(c_Finite__Set_Ofun__left__comm__idem(_1494244, _1494244, c_Orderings_Oord__class_Omin(_1494244)))], (40415 ^ _773908) ^ [_1564994, _1564996, _1564998, _1565000] : [-(_1564994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1564996), _1564994), hAPP(hAPP(c_List_Olist_OCons(_1564996), _1564998), _1565000)) = hAPP(hAPP(c_List_Odrop(_1564996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1564994), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1565000))], (51097 ^ _773908) ^ [_1808179, _1808181, _1808183, _1808185] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1808179, _1808181, _1808183, _1808185, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1808181)) = _1808183)], (16525 ^ _773908) ^ [_1057548, _1057550] : [class_Rings_Ocomm__semiring__1(_1057548), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057548), _1057550), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1057550)], (6950 ^ _773908) ^ [_886382, _886384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886382), _886384)), _886382))], (25625 ^ _773908) ^ [_1227815, _1227817, _1227819, _1227821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1227815), _1227817)), 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)), _1227815), _1227819)), 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)), _1227817), _1227821)), 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)), _1227817), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1227819), _1227821))), c_FunDef_Omin__weak)))], (3802 ^ _773908) ^ [_831257, _831259, _831261, _831263] : [-(c_Wellfounded_Oacc(_831263, _831259) = c_Wellfounded_Oacc(_831261, _831257)), _831263 = _831261, _831259 = _831257], (14693 ^ _773908) ^ [_1022361, _1022363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022361), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14696 ^ _773908 : [(14703 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022363), 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), _1022363), _1022361))))], (14697 ^ _773908) ^ [] : [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), _1022363), _1022361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022363), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (49767 ^ _773908) ^ [_1778611, _1778613, _1778615] : [hBOOL(hAPP(hAPP(c_member(_1778611), _1778613), hAPP(c_List_Oset(_1778611), _1778615))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1778611), _1778615), _1778613)))], (24449 ^ _773908) ^ [_1203237, _1203239, _1203241] : [hAPP(hAPP(c_COMBC(_1203237, tc_fun(_1203237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1203237)), _1203239) = hAPP(hAPP(c_COMBC(_1203237, tc_fun(_1203237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1203237)), _1203241), -(_1203239 = _1203241)], (42087 ^ _773908) ^ [_1605931, _1605933, _1605935, _1605937, _1605939] : [c_Fun_Oinj__on(_1605931, _1605933, _1605935, c_Orderings_Otop__class_Otop(tc_fun(_1605931, tc_HOL_Obool))), 42090 ^ _773908 : [(42097 ^ _773908) ^ [] : [_1605937 = _1605939, -(hAPP(hAPP(c_List_Omap(_1605931, _1605933), _1605935), _1605937) = hAPP(hAPP(c_List_Omap(_1605931, _1605933), _1605935), _1605939))], (42091 ^ _773908) ^ [] : [hAPP(hAPP(c_List_Omap(_1605931, _1605933), _1605935), _1605937) = hAPP(hAPP(c_List_Omap(_1605931, _1605933), _1605935), _1605939), -(_1605937 = _1605939)]]], (10825 ^ _773908) ^ [_953623, _953625, _953627, _953629, _953631, _953633] : [class_Rings_Olinordered__semiring__1__strict(_953623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953623), _953625), _953627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953623), _953629), _953627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953623), c_Groups_Ozero__class_Ozero(_953623)), _953631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953623), c_Groups_Ozero__class_Ozero(_953623)), _953633)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953623), _953631), _953633) = c_Groups_Oone__class_Oone(_953623), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953623), _953631), _953625)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953623), _953633), _953629))), _953627)))], (11433 ^ _773908) ^ [_964712, _964714] : [class_Groups_Olinordered__ab__group__add(_964712), 11436 ^ _773908 : [(11443 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964712), c_Groups_Ozero__class_Ozero(_964712)), _964714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964712), hAPP(c_Groups_Ouminus__class_Ouminus(_964712), _964714)), _964714)))], (11437 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964712), hAPP(c_Groups_Ouminus__class_Ouminus(_964712), _964714)), _964714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964712), c_Groups_Ozero__class_Ozero(_964712)), _964714)))]]], (7489 ^ _773908) ^ [_895079, _895081, _895083] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_895079, _895081, _895083)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_895081)), c_Com_Ocom_Ocom__size(_895083))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50709 ^ _773908) ^ [_1799812, _1799814] : [c_Equiv__Relations_Oequivp(_1799812, _1799814), -(c_Equiv__Relations_Opart__equivp(_1799812, _1799814))], (46772 ^ _773908) ^ [_1711025, _1711027] : [-(hAPP(c_Relation_ORange(_1711025, _1711025), c_Transitive__Closure_Ortrancl(_1711025, _1711027)) = c_Orderings_Otop__class_Otop(tc_fun(_1711025, tc_HOL_Obool)))], (51163 ^ _773908) ^ [_1809566, _1809568, _1809570] : [c_Fun_Obij__betw(_1809566, _1809568, _1809570, c_Orderings_Otop__class_Otop(tc_fun(_1809566, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1809568, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1809568, _1809566, c_Hilbert__Choice_Oinv__into(_1809566, _1809568, c_Orderings_Otop__class_Otop(tc_fun(_1809566, tc_HOL_Obool)), _1809570), c_Orderings_Otop__class_Otop(tc_fun(_1809568, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1809566, tc_HOL_Obool))))], (20979 ^ _773908) ^ [_1136858, _1136860, _1136862] : [class_Fields_Olinordered__field(_1136858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136858), _1136860), c_Groups_Ozero__class_Ozero(_1136858))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136858), c_Groups_Ozero__class_Ozero(_1136858)), _1136862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136858), _1136860), _1136862)), c_Groups_Ozero__class_Ozero(_1136858))))], (14388 ^ _773908) ^ [_1017325, _1017327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017325)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017325), _1017327)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1017325)), hAPP(c_Int_Onat, _1017327)))], (38512 ^ _773908) ^ [_1514641, _1514643] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1514641, _1514643, tc_prod(_1514641, _1514643)), c_Product__Type_OPair(_1514641, _1514643)) = c_Fun_Oid(tc_prod(_1514641, _1514643)))], (18535 ^ _773908) ^ [_1094043, _1094045, _1094047, _1094049] : [hBOOL(hAPP(hAPP(c_member(_1094043), _1094045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1094043, tc_HOL_Obool)), _1094047), _1094049))), hBOOL(hAPP(hAPP(c_member(_1094043), _1094045), _1094049))], (10607 ^ _773908) ^ [_949782, _949784, _949786] : [10608 ^ _773908 : [(10611 ^ _773908) ^ [] : [_949782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10609 ^ _773908) ^ [] : [_949784 = _949786]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949782), _949784) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949782), _949786))], (31433 ^ _773908) ^ [_1352233, _1352235] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1352233), _1352235)), -(hAPP(c_Finite__Set_Ocard(_1352233), _1352235) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1352233, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1352233), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352235))], (1144 ^ _773908) ^ [_791194, _791196] : [-(class_Groups_Oordered__ab__group__add__abs(_791194)), _791196 = _791194, class_Groups_Oordered__ab__group__add__abs(_791196)], (36725 ^ _773908) ^ [_1465913, _1465915, _1465917, _1465919] : [c_Finite__Set_Ofolding__one(_1465913, _1465915, _1465917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465913), _1465919)), -(hAPP(_1465917, _1465919) = hAPP(c_Finite__Set_Ofold1(_1465913, _1465915), _1465919))], (10255 ^ _773908) ^ [_944169, _944171, _944173] : [class_Orderings_Olinorder(_944169), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944169), _944171), _944173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944169), _944173), _944171)))], (38280 ^ _773908) ^ [_1505564] : [-(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)))), _1505564))))], (33644 ^ _773908) ^ [_1398792, _1398794, _1398796] : [-(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)), _1398792)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1398794), _1398796)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398794), _1398792)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398796), _1398792)))], (4362 ^ _773908) ^ [_840255, _840257] : [_840257 = _840255, -(c_New__Random__Sequence_Oneg__single(_840257) = c_New__Random__Sequence_Oneg__single(_840255))], (18863 ^ _773908) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40803 ^ _773908) ^ [_1575461, _1575463, _1575465, _1575467] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1575461), tc_List_Olist(_1575461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1575461), tc_List_Olist(_1575461)), _1575463), _1575465)), c_List_Olistrel(_1575461, _1575467)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1575461)), _1575463) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1575461)), _1575465), 40809 ^ _773908 : [(40812 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1575461, _1575461, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1575461, tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_fun(_1575461, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575461, tc_fun(tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_fun(_1575461, tc_HOL_Obool)), _1575461), c_COMBC(_1575461, tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575461, tc_prod(_1575461, _1575461)), tc_fun(_1575461, tc_fun(tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_HOL_Obool)), _1575461), hAPP(c_COMBB(tc_prod(_1575461, _1575461), tc_fun(tc_fun(tc_prod(_1575461, _1575461), tc_HOL_Obool), tc_HOL_Obool), _1575461), c_member(tc_prod(_1575461, _1575461)))), c_Product__Type_OPair(_1575461, _1575461)))), _1575467)), 40808 ^ [_1575461, _1575463, _1575465, _1575467]))], (40810 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575461, _1575461)), 40808 ^ [_1575461, _1575463, _1575465, _1575467]), hAPP(c_List_Oset(tc_prod(_1575461, _1575461)), hAPP(hAPP(c_List_Ozip(_1575461, _1575461), _1575463), _1575465)))))]]], (26737 ^ _773908) ^ [] : [-(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))))], (51614 ^ _773908) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (8821 ^ _773908) ^ [_919903, _919905, _919907] : [class_Groups_Ogroup__add(_919903), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919903), hAPP(c_Groups_Ouminus__class_Ouminus(_919903), _919905)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919903), _919905), _919907)) = _919907)], (26649 ^ _773908) ^ [] : [-(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))))))], (27604 ^ _773908) ^ [_1273044, _1273046, _1273048, _1273050, _1273052] : [c_Finite__Set_Ofolding__one(_1273044, _1273046, _1273048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273044), _1273050)), 27611 ^ _773908 : [(27618 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273044, tc_HOL_Obool)), _1273050), hAPP(hAPP(c_Set_Oinsert(_1273044), _1273052), c_Orderings_Obot__class_Obot(tc_fun(_1273044, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1273044, tc_HOL_Obool))), -(hAPP(_1273048, hAPP(hAPP(c_Set_Oinsert(_1273044), _1273052), _1273050)) = hAPP(hAPP(_1273046, _1273052), hAPP(_1273048, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273044, tc_HOL_Obool)), _1273050), hAPP(hAPP(c_Set_Oinsert(_1273044), _1273052), c_Orderings_Obot__class_Obot(tc_fun(_1273044, tc_HOL_Obool)))))))], (27612 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273044, tc_HOL_Obool)), _1273050), hAPP(hAPP(c_Set_Oinsert(_1273044), _1273052), c_Orderings_Obot__class_Obot(tc_fun(_1273044, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1273044, tc_HOL_Obool)), -(hAPP(_1273048, hAPP(hAPP(c_Set_Oinsert(_1273044), _1273052), _1273050)) = _1273052)]]], (36307 ^ _773908) ^ [_1455756] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1455756), c_Orderings_Otop__class_Otop(tc_fun(_1455756, 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(_1455756), c_Orderings_Otop__class_Otop(tc_fun(_1455756, tc_HOL_Obool))))))], (45115 ^ _773908) ^ [_1675304, _1675306] : [c_List_Oremdups(_1675304, _1675306) = _1675306, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675304)), c_List_Oremdups(_1675304, _1675306)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675304)), _1675306))], (9672 ^ _773908) ^ [_935109, _935111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935111)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _935109)), hAPP(c_Int_Onat, _935111)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935109), _935111)))], (13650 ^ _773908) ^ [_1003765, _1003767, _1003769] : [class_Divides_Oring__div(_1003765), -(c_Divides_Odiv__class_Omod(_1003765, hAPP(c_Groups_Ouminus__class_Ouminus(_1003765), _1003767), _1003769) = c_Divides_Odiv__class_Omod(_1003765, hAPP(c_Groups_Ouminus__class_Ouminus(_1003765), c_Divides_Odiv__class_Omod(_1003765, _1003767, _1003769)), _1003769))], (15141 ^ _773908) ^ [_1030433, _1030435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030435)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1030433)), hAPP(c_Int_Onat, _1030435)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1030433, _1030435)))], (47975 ^ _773908) ^ [_1740674, _1740676, _1740678, _1740680, _1740682, _1740684, _1740686, _1740688] : [class_Groups_Ocomm__monoid__add(_1740674), c_Fun_Oinj__on(_1740676, _1740678, _1740680, _1740682), _1740684 = hAPP(c_Set_Oimage(_1740676, _1740678, _1740680), _1740682), 47989 ^ _773908 : [(47992 ^ _773908) ^ [] : [hAPP(_1740686, 47988 ^ [_1740674, _1740676, _1740678, _1740680, _1740682, _1740684, _1740686, _1740688]) = hAPP(_1740688, hAPP(_1740680, 47988 ^ [_1740674, _1740676, _1740678, _1740680, _1740682, _1740684, _1740686, _1740688]))], (47990 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740676), 47988 ^ [_1740674, _1740676, _1740678, _1740680, _1740682, _1740684, _1740686, _1740688]), _1740682)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1740678, _1740674), _1740688), _1740684) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1740676, _1740674), _1740686), _1740682))], (18881 ^ _773908) ^ [] : [c_Int_OMin = c_Int_OPls], (10633 ^ _773908) ^ [_950167] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _950167), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40575 ^ _773908) ^ [_1569169, _1569171, _1569173, _1569175, _1569177, _1569179, _1569181] : [-(hAPP(hAPP(c_List_Ozip(_1569169, _1569171), hAPP(hAPP(c_List_Olist__update(_1569169, _1569173), _1569175), _1569177)), hAPP(hAPP(c_List_Olist__update(_1569171, _1569179), _1569175), _1569181)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1569169, _1569171), hAPP(hAPP(c_List_Ozip(_1569169, _1569171), _1569173), _1569179)), _1569175), hAPP(hAPP(c_Product__Type_OPair(_1569169, _1569171), _1569177), _1569181)))], (5556 ^ _773908) ^ [_858908, _858910, _858912, _858914] : [-(tc_sum(_858914, _858910) = tc_sum(_858912, _858908)), _858914 = _858912, _858910 = _858908], (15691 ^ _773908) ^ [_1040846, _1040848] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040846), _1040848)), hAPP(c_Nat_OSuc, _1040846))))], (12046 ^ _773908) ^ [_975754, _975756, _975758, _975760] : [class_Rings_Olinordered__ring__strict(_975754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975754), c_Groups_Ozero__class_Ozero(_975754)), _975756)), 12053 ^ _773908 : [(12060 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975754), _975758), _975760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975754), _975756), _975758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975754), _975756), _975760))))], (12054 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975754), _975756), _975758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975754), _975756), _975760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975754), _975758), _975760)))]]], (38120 ^ _773908) ^ [_1498924, _1498926, _1498928] : [-(hAPP(hAPP(c_Set_Oinsert(_1498924), _1498926), _1498928) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498924, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1498924), hAPP(hAPP(c_COMBC(_1498924, _1498924, tc_HOL_Obool), c_fequal), _1498926))), _1498928))], (2024 ^ _773908) ^ [_803236, _803238, _803240, _803242, _803244, _803246] : [-(c_Com_Ocom_OCond(_803246, _803242, _803238) = c_Com_Ocom_OCond(_803244, _803240, _803236)), _803246 = _803244, _803242 = _803240, _803238 = _803236], (43929 ^ _773908) ^ [_1648393, _1648395, _1648397, _1648399] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648393, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648393, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1648393, _1648395), _1648397)), hAPP(c_Relation_ODomain(_1648393, _1648395), _1648399))), hAPP(c_Relation_ODomain(_1648393, _1648395), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1648393, _1648395), tc_HOL_Obool)), _1648397), _1648399)))))], (28356 ^ _773908) ^ [_1289051, _1289053, _1289055, _1289057] : [-(hBOOL(hAPP(hAPP(c_member(_1289051), _1289053), _1289055))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289051, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1289051), _1289053), _1289057)), _1289055) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289051, tc_HOL_Obool)), _1289057), _1289055))], (49422 ^ _773908) ^ [_1771716, _1771718, _1771720] : [c_List_Olist_ONil(_1771716) = c_List_Oreplicate(_1771716, _1771718, _1771720), -(_1771718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24291 ^ _773908) ^ [_1199335, _1199337, _1199339, _1199341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool)), _1199339), _1199341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199335, tc_fun(_1199337, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1199335, tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_fun(_1199337, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199337, tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_fun(_1199337, tc_HOL_Obool)), _1199335), c_COMBC(_1199337, tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199337, tc_prod(_1199335, _1199337)), tc_fun(_1199337, tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), _1199335), hAPP(c_COMBB(tc_prod(_1199335, _1199337), tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool), _1199337), c_member(tc_prod(_1199335, _1199337)))), c_Product__Type_OPair(_1199335, _1199337)))), _1199339)), hAPP(hAPP(c_COMBC(_1199335, tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_fun(_1199337, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199337, tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_fun(_1199337, tc_HOL_Obool)), _1199335), c_COMBC(_1199337, tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1199337, tc_prod(_1199335, _1199337)), tc_fun(_1199337, tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool)), _1199335), hAPP(c_COMBB(tc_prod(_1199335, _1199337), tc_fun(tc_fun(tc_prod(_1199335, _1199337), tc_HOL_Obool), tc_HOL_Obool), _1199337), c_member(tc_prod(_1199335, _1199337)))), c_Product__Type_OPair(_1199335, _1199337)))), _1199341))))], (28350 ^ _773908) ^ [_1288884, _1288886, _1288888, _1288890] : [hBOOL(hAPP(hAPP(c_member(_1288884), _1288886), _1288888)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288884, tc_HOL_Obool)), _1288888), hAPP(hAPP(c_Set_Oinsert(_1288884), _1288886), _1288890)) = hAPP(hAPP(c_Set_Oinsert(_1288884), _1288886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288884, tc_HOL_Obool)), _1288888), _1288890)))], (37904 ^ _773908) ^ [_1494127, _1494129, _1494131, _1494133] : [c_Finite__Set_Ofun__left__comm__idem(_1494127, _1494129, _1494131), -(hAPP(c_Fun_Ocomp(_1494129, _1494129, _1494129, hAPP(_1494131, _1494133)), hAPP(_1494131, _1494133)) = hAPP(_1494131, _1494133))], (3706 ^ _773908) ^ [_829815, _829817] : [_829817 = _829815, -(c_New__DSequence_Opos__not__seq(_829817) = c_New__DSequence_Opos__not__seq(_829815))], (15869 ^ _773908) ^ [_1044251, _1044253] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044251), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044253), _1044251)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044253), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044253, _1044251)))], (24461 ^ _773908) ^ [_1203513, _1203515, _1203517, _1203519, _1203521, _1203523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203513, tc_fun(_1203515, tc_HOL_Obool))), _1203517), _1203519)), hBOOL(hAPP(hAPP(_1203517, _1203521), _1203523)), -(hBOOL(hAPP(hAPP(_1203519, _1203521), _1203523)))], (37589 ^ _773908) ^ [_1486114, _1486116, _1486118, _1486120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1486116, _1486114), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1486114, tc_prod(_1486116, _1486114), 37585 ^ [_1486114, _1486116, _1486118, _1486120]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486116, tc_fun(_1486114, tc_HOL_Obool)), _1486118), _1486120))), hAPP(hAPP(c_Product__Type_OSigma(_1486116, _1486114), _1486118), _1486120))))], (35548 ^ _773908) ^ [_1440259, _1440261, _1440263] : [class_Orderings_Oorder(_1440259), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440259, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1440259, _1440261, _1440263)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1440259), _1440263)) = c_Orderings_Obot__class_Obot(tc_fun(_1440259, tc_HOL_Obool)))], (10901 ^ _773908) ^ [_955096, _955098, _955100] : [class_Rings_Ocomm__semiring__1(_955096), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955096), _955098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955096), _955100), _955098)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955096), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955096), _955100), c_Groups_Oone__class_Oone(_955096))), _955098))], (28891 ^ _773908) ^ [_1301681, _1301683] : [class_Orderings_Olinorder(_1301681), -(c_Big__Operators_Olinorder__class_OMax(_1301681, hAPP(hAPP(c_Set_Oinsert(_1301681), _1301683), c_Orderings_Obot__class_Obot(tc_fun(_1301681, tc_HOL_Obool)))) = _1301683)], (6162 ^ _773908) ^ [_873806, _873808, _873810] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_873806), _873808), _873810)), -(c_Natural_Oevaln(_873806, _873808, 6165 ^ [_873806, _873808, _873810], _873810))], (12638 ^ _773908) ^ [_985762, _985764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985762), hAPP(c_Nat_OSuc, _985764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985762), _985764))), -(_985762 = hAPP(c_Nat_OSuc, _985764))], (43218 ^ _773908) ^ [_1632350, _1632352, _1632354, _1632356] : [hBOOL(hAPP(c_List_Olistsp(_1632350, _1632352), hAPP(hAPP(c_List_Oappend(_1632350), _1632354), _1632356))), 43221 ^ _773908 : [(43224 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1632350, _1632352), _1632356)))], (43222 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1632350, _1632352), _1632354)))]]], (7193 ^ _773908) ^ [_890260, _890262] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890260), _890262))), 7196 ^ _773908 : [(7203 ^ _773908) ^ [] : [_890260 = _890262, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890260), hAPP(c_Nat_OSuc, _890262))))], (7197 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890260), hAPP(c_Nat_OSuc, _890262))), -(_890260 = _890262)]]], (42167 ^ _773908) ^ [_1607780, _1607782, _1607784, _1607786, _1607788] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607780, tc_fun(_1607782, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1607780), _1607784), _1607786)), _1607788) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1607782, tc_HOL_Obool)), hAPP(_1607788, _1607784)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607780, tc_fun(_1607782, tc_HOL_Obool)), _1607786), _1607788)))], (43608 ^ _773908) ^ [_1640763, _1640765] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1640763))), c_Enum_Osublists(_1640763, _1640765)) = 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(_1640763)), _1640765)))], (4720 ^ _773908) ^ [_845884, _845886, _845888, _845890] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845890, _845886) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845888, _845884)), _845890 = _845888, _845886 = _845884], (50139 ^ _773908) ^ [_1788916, _1788918, _1788920, _1788922] : [c_Wellfounded_Omax__extp(_1788916, _1788918, _1788920, _1788922), 50142 ^ _773908 : [(50145 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1788916), _1788922)))], (50147 ^ _773908) ^ [] : [_1788922 = c_Orderings_Obot__class_Obot(tc_fun(_1788916, tc_HOL_Obool))], (50149 ^ _773908) ^ [_1789132] : [hBOOL(hAPP(hAPP(c_member(_1788916), _1789132), _1788920)), 50153 ^ _773908 : [(50156 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1788918, _1789132), 50152 ^ [_1788916, _1788918, _1788920, _1788922, _1789132])))], (50154 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788916), 50152 ^ [_1788916, _1788918, _1788920, _1788922, _1789132]), _1788922)))]]], (50143 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1788916), _1788920)))]]], (42682 ^ _773908) ^ [_1620260, _1620262, _1620264, _1620266] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620260)), _1620262) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620264)), _1620266), -(hAPP(hAPP(c_List_Omap(tc_prod(_1620260, _1620264), _1620260), c_Product__Type_Ofst(_1620260, _1620264)), hAPP(hAPP(c_List_Ozip(_1620260, _1620264), _1620262), _1620266)) = _1620262)], (36177 ^ _773908) ^ [_1452920, _1452922] : [class_Lattices_Oboolean__algebra(_1452920), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1452920), hAPP(c_Groups_Ouminus__class_Ouminus(_1452920), _1452922)), _1452922) = c_Orderings_Otop__class_Otop(_1452920))], (38062 ^ _773908) ^ [_1497604, _1497606, _1497608, _1497610] : [-(hBOOL(hAPP(hAPP(c_member(_1497604), _1497606), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497604, tc_HOL_Obool)), _1497608), hAPP(c_Set_OCollect(_1497604), _1497610))))), hBOOL(hAPP(hAPP(c_member(_1497604), _1497606), _1497608)), hBOOL(hAPP(_1497610, _1497606))], (42363 ^ _773908) ^ [_1613215, _1613217, _1613219, _1613221] : [hBOOL(hAPP(c_List_Odistinct(_1613215), hAPP(hAPP(c_List_Omap(_1613217, _1613215), _1613219), _1613221))), 42366 ^ _773908 : [(42369 ^ _773908) ^ [] : [-(c_Fun_Oinj__on(_1613217, _1613215, _1613219, hAPP(c_List_Oset(_1613217), _1613221)))], (42367 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1613217), _1613221)))]]], (43856 ^ _773908) ^ [_1646659, _1646661, _1646663, _1646665] : [-(hAPP(c_Relation_ODomain(_1646659, _1646661), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1646659, _1646661), tc_HOL_Obool)), _1646663), _1646665)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1646659, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1646659, _1646661), _1646663)), hAPP(c_Relation_ODomain(_1646659, _1646661), _1646665)))], (51826 ^ _773908) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (50747 ^ _773908) ^ [_1800357, _1800359, _1800361] : [c_Relation_Orefl__on(_1800357, _1800359, _1800361), c_Relation_Osym(_1800357, _1800361), c_Relation_Otrans(_1800357, _1800361), -(c_Equiv__Relations_Oequiv(_1800357, _1800359, _1800361))], (27988 ^ _773908) ^ [_1280628, _1280630, _1280632] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280628, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280628, tc_HOL_Obool)), _1280630), _1280632)), _1280632)))], (34716 ^ _773908) ^ [_1421896, _1421898, _1421900] : [class_Orderings_Oord(_1421896), 34719 ^ _773908 : [(34726 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421896), _1421900), _1421898)), -(hBOOL(hAPP(hAPP(c_member(_1421896), _1421898), hAPP(c_SetInterval_Oord__class_OatLeast(_1421896), _1421900))))], (34720 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1421896), _1421898), hAPP(c_SetInterval_Oord__class_OatLeast(_1421896), _1421900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421896), _1421900), _1421898)))]]], (35080 ^ _773908) ^ [_1429861, _1429863, _1429865, _1429867, _1429869] : [class_Groups_Ocomm__monoid__add(_1429861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1429863), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1429865), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429861), _1429867), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1429863, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1429865), _1429869))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429861), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429861), _1429867), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1429863, _1429865))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429861), _1429867), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1429865), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1429865), _1429869)))))], (8525 ^ _773908) ^ [_914691, _914693, _914695, _914697] : [class_Rings_Ocomm__semiring__1(_914691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914691), _914693), _914695)), _914697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914691), _914693), _914697)), _914695))], (44646 ^ _773908) ^ [_1666334, _1666336] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1666334, _1666336))))], (25461 ^ _773908) ^ [_1224258, _1224260, _1224262, _1224264] : [class_Orderings_Olinorder(_1224258), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224258), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224258), _1224260), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224258), _1224262), _1224264))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224258), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224258), _1224260), _1224262)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224258), _1224260), _1224264)))))], (28680 ^ _773908) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (5668 ^ _773908) ^ [_860592, _860594] : [_860594 = _860592, -(c_Option_Othe(_860594) = c_Option_Othe(_860592))], (3584 ^ _773908) ^ [_827866, _827868, _827870, _827872, _827874, _827876, _827878, _827880] : [-(c_List_Olinorder__class_Osort__key(_827880, _827876, _827872, _827868) = c_List_Olinorder__class_Osort__key(_827878, _827874, _827870, _827866)), _827880 = _827878, _827876 = _827874, _827872 = _827870, _827868 = _827866], (8561 ^ _773908) ^ [_915398, _915400, _915402] : [class_Rings_Oring(_915398), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915398), hAPP(c_Groups_Ouminus__class_Ouminus(_915398), _915400)), _915402) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915398), _915400), hAPP(c_Groups_Ouminus__class_Ouminus(_915398), _915402)))], (43350 ^ _773908) ^ [_1634911, _1634913, _1634915] : [class_Orderings_Olinorder(_1634911), -(hAPP(c_List_Oset(_1634911), c_List_Olinorder__class_Oinsort__insert__key(_1634911, _1634911, c_COMBI(_1634911), _1634913, _1634915)) = hAPP(hAPP(c_Set_Oinsert(_1634911), _1634913), hAPP(c_List_Oset(_1634911), _1634915)))], (44449 ^ _773908) ^ [_1660106, _1660108] : [-(c_List_Oconcat(_1660106, _1660108) = hAPP(c_List_Ofoldl(tc_List_Olist(_1660106), tc_List_Olist(_1660106), c_List_Oappend(_1660106), c_List_Olist_ONil(_1660106)), _1660108))], (19271 ^ _773908) ^ [_1106615, _1106617] : [class_Int_Onumber__ring(_1106615), 19274 ^ _773908 : [(19281 ^ _773908) ^ [] : [c_Int_Oiszero(_1106615, hAPP(c_Int_Onumber__class_Onumber__of(_1106615), 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), _1106617)))), -(c_Groups_Oone__class_Oone(_1106615) = hAPP(c_Int_Onumber__class_Onumber__of(_1106615), _1106617))], (19275 ^ _773908) ^ [] : [c_Groups_Oone__class_Oone(_1106615) = hAPP(c_Int_Onumber__class_Onumber__of(_1106615), _1106617), -(c_Int_Oiszero(_1106615, hAPP(c_Int_Onumber__class_Onumber__of(_1106615), 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), _1106617)))))]]], (36663 ^ _773908) ^ [_1464699] : [-(c_Nitpick_Oone__frac(_1464699) = c_Nitpick_OAbs__Frac(_1464699, 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))))], (33646 ^ _773908) ^ [_1398853, _1398855, _1398857, _1398859, _1398861, _1398863] : [c_Fun_Oinj__on(_1398853, _1398855, _1398857, _1398859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398853, tc_HOL_Obool)), _1398861), _1398859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398853, tc_HOL_Obool)), _1398863), _1398859)), -(hAPP(c_Set_Oimage(_1398853, _1398855, _1398857), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398853, tc_HOL_Obool)), _1398861), _1398863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398855, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398853, _1398855, _1398857), _1398861)), hAPP(c_Set_Oimage(_1398853, _1398855, _1398857), _1398863)))], (12536 ^ _773908) ^ [_983915, _983917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983915, tc_HOL_Obool)), _983917), c_Orderings_Obot__class_Obot(tc_fun(_983915, tc_HOL_Obool)))), -(_983917 = c_Orderings_Obot__class_Obot(tc_fun(_983915, tc_HOL_Obool)))], (13516 ^ _773908) ^ [_1001012, _1001014] : [class_Divides_Osemiring__div(_1001012), -(c_Divides_Odiv__class_Omod(_1001012, c_Groups_Ozero__class_Ozero(_1001012), _1001014) = c_Groups_Ozero__class_Ozero(_1001012))], (16203 ^ _773908) ^ [_1051635, _1051637] : [_1051635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051635), _1051637) = _1051637)], (7291 ^ _773908) ^ [_891982, _891984] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _891982), _891984) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7296 ^ _773908 : [(7299 ^ _773908) ^ [] : [-(_891984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7297 ^ _773908) ^ [] : [-(_891982 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7300 ^ _773908 : [(7303 ^ _773908) ^ [] : [-(_891984 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7301 ^ _773908) ^ [] : [-(_891982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19819 ^ _773908) ^ [_1115938, _1115940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1115938)), c_Int_OBit0(_1115940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115938), _1115940)))], (6245 ^ _773908) ^ [_875187, _875189, _875191] : [class_Rings_Osemiring__1(_875187), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_875187, _875189, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _875191) = _875191)], (38818 ^ _773908) ^ [_1523800, _1523802, _1523804, _1523806, _1523808] : [hAPP(hAPP(c_List_Oappend(_1523800), _1523802), _1523804) = hAPP(hAPP(c_List_Oappend(_1523800), _1523806), _1523808), 38824 ^ _773908 : [(38827 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1523800), 38821 ^ [_1523800, _1523802, _1523804, _1523806, _1523808]), _1523804) = _1523808)], (38825 ^ _773908) ^ [] : [-(_1523802 = hAPP(hAPP(c_List_Oappend(_1523800), _1523806), 38821 ^ [_1523800, _1523802, _1523804, _1523806, _1523808]))]], 38828 ^ _773908 : [(38831 ^ _773908) ^ [] : [-(_1523804 = hAPP(hAPP(c_List_Oappend(_1523800), 38821 ^ [_1523800, _1523802, _1523804, _1523806, _1523808]), _1523808))], (38829 ^ _773908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1523800), _1523802), 38821 ^ [_1523800, _1523802, _1523804, _1523806, _1523808]) = _1523806)]]], (49554 ^ _773908) ^ [_1774121, _1774123, _1774125] : [-(_1774121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1774123, c_List_Oreplicate(_1774123, _1774121, _1774125)) = _1774125)], (36023 ^ _773908) ^ [_1449685, _1449687, _1449689, _1449691, _1449693] : [_1449685 = hAPP(_1449687, _1449689), -(hBOOL(hAPP(hAPP(c_member(_1449691), _1449685), hAPP(c_Set_Oimage(_1449693, _1449691, _1449687), c_Orderings_Otop__class_Otop(tc_fun(_1449693, tc_HOL_Obool))))))], (41998 ^ _773908) ^ [_1603674, _1603676, _1603678, _1603680, _1603682] : [class_Complete__Lattice_Ocomplete__lattice(_1603674), 42001 ^ _773908 : [(42002 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1603674), _1603676), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603678, _1603674), _1603680), _1603682))), 42005 ^ _773908 : [(42006 ^ _773908) ^ [_1603855] : [hBOOL(hAPP(hAPP(c_member(_1603678), _1603855), _1603680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1603674), _1603676), hAPP(_1603682, _1603855))))]]], (42012 ^ _773908) ^ [] : [42014 ^ _773908 : [(42017 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1603674), _1603676), hAPP(_1603682, 42013 ^ [_1603674, _1603676, _1603678, _1603680, _1603682])))], (42015 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603678), 42013 ^ [_1603674, _1603676, _1603678, _1603680, _1603682]), _1603680)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1603674), _1603676), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603678, _1603674), _1603680), _1603682))))]]], (51752 ^ _773908) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (50872 ^ _773908) ^ [_1802851, _1802853, _1802855, _1802857] : [c_Fun_Oinj__on(_1802851, _1802853, _1802855, c_Orderings_Otop__class_Otop(tc_fun(_1802851, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1802853, _1802851, c_Hilbert__Choice_Oinv__into(_1802851, _1802853, c_Orderings_Otop__class_Otop(tc_fun(_1802851, tc_HOL_Obool)), _1802855)), hAPP(c_Set_Oimage(_1802851, _1802853, _1802855), _1802857)) = _1802857)], (46991 ^ _773908) ^ [_1716631, _1716633, _1716635, _1716637] : [-(c_Transitive__Closure_Otrancl(_1716631, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1716631, _1716631)), hAPP(hAPP(c_Product__Type_OPair(_1716631, _1716631), _1716633), _1716635)), _1716637)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1716631, _1716631), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1716631, _1716637)), hAPP(c_Set_OCollect(tc_prod(_1716631, _1716631)), hAPP(c_Product__Type_Oprod_Oprod__case(_1716631, _1716631, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1716631, tc_fun(_1716631, tc_HOL_Obool), tc_fun(_1716631, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1716631, tc_HOL_Obool), tc_fun(_1716631, tc_HOL_Obool)), _1716631), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1716631)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1716631), c_fconj), hAPP(hAPP(c_COMBC(_1716631, tc_fun(tc_prod(_1716631, _1716631), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1716631, _1716631), tc_fun(tc_fun(tc_prod(_1716631, _1716631), tc_HOL_Obool), tc_HOL_Obool), _1716631), c_member(tc_prod(_1716631, _1716631))), hAPP(hAPP(c_COMBC(_1716631, _1716631, tc_prod(_1716631, _1716631)), c_Product__Type_OPair(_1716631, _1716631)), _1716633))), c_Transitive__Closure_Ortrancl(_1716631, _1716637))))), hAPP(hAPP(c_COMBC(_1716631, tc_fun(tc_prod(_1716631, _1716631), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1716631, _1716631), tc_fun(tc_fun(tc_prod(_1716631, _1716631), tc_HOL_Obool), tc_HOL_Obool), _1716631), c_member(tc_prod(_1716631, _1716631))), hAPP(c_Product__Type_OPair(_1716631, _1716631), _1716635))), c_Transitive__Closure_Ortrancl(_1716631, _1716637)))))))], (19067 ^ _773908) ^ [_1103295, _1103297] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103295)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103297)))), 19070 ^ _773908 : [(19073 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1103297))], (19071 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103295), _1103297)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103295), _1103297))], (44107 ^ _773908) ^ [_1653013, _1653015, _1653017] : [class_Complete__Lattice_Ocomplete__lattice(_1653013), class_Orderings_Olinorder(_1653013), 44114 ^ _773908 : [(44124 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1653013), c_Complete__Lattice_OInf__class_OInf(_1653013, _1653015)), _1653017))), 44125 ^ _773908 : [(44126 ^ _773908) ^ [_1653319] : [hBOOL(hAPP(hAPP(c_member(_1653013), _1653319), _1653015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1653013), _1653319), _1653017))]]], (44115 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1653013), c_Complete__Lattice_OInf__class_OInf(_1653013, _1653015)), _1653017)), 44119 ^ _773908 : [(44122 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1653013), 44118 ^ [_1653013, _1653015, _1653017]), _1653017)))], (44120 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653013), 44118 ^ [_1653013, _1653015, _1653017]), _1653015)))]]]]], (44283 ^ _773908) ^ [_1656837, _1656839, _1656841, _1656843] : [_1656837 = _1656839, -(hAPP(c_List_OremoveAll(_1656841, _1656837), hAPP(hAPP(c_List_Olist_OCons(_1656841), _1656839), _1656843)) = hAPP(c_List_OremoveAll(_1656841, _1656837), _1656843))], (51816 ^ _773908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (44154 ^ _773908) ^ [_1653862, _1653864, _1653866] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653862, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1653862, tc_HOL_Obool), tc_HOL_Obool)), _1653864), _1653866)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1653862, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653862, tc_HOL_Obool), _1653864)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1653862, tc_HOL_Obool), _1653866)))], (47303 ^ _773908) ^ [_1724340, _1724342, _1724344, _1724346, _1724348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1724342, _1724340)), hAPP(hAPP(c_Product__Type_OPair(_1724342, _1724340), _1724346), _1724344)), _1724348)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1724340, _1724342)), hAPP(hAPP(c_Product__Type_OPair(_1724340, _1724342), _1724344), _1724346)), hAPP(c_Relation_Oconverse(_1724342, _1724340), _1724348))))], (17235 ^ _773908) ^ [_1071307] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071307) = _1071307)], (24845 ^ _773908) ^ [_1212190, _1212192, _1212194, _1212196] : [class_Orderings_Olinorder(_1212190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212190), _1212192), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212190), _1212194), _1212196))), 24852 ^ _773908 : [(24855 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212190), _1212192), _1212196)))], (24853 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212190), _1212192), _1212194)))]]], (47283 ^ _773908) ^ [_1723715, _1723717, _1723719, _1723721, _1723723] : [-(hAPP(c_Relation_Oconverse(_1723715, _1723717), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1723719, tc_fun(tc_prod(_1723715, _1723717), tc_HOL_Obool)), _1723721), _1723723)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1723719, tc_fun(tc_prod(_1723717, _1723715), tc_HOL_Obool)), _1723721), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1723715, _1723717), tc_HOL_Obool), tc_fun(tc_prod(_1723717, _1723715), tc_HOL_Obool), _1723719), c_Relation_Oconverse(_1723715, _1723717)), _1723723)))], (38201 ^ _773908) ^ [_1502195, _1502197, _1502199] : [class_Orderings_Olinorder(_1502195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502195), _1502197)), -(_1502197 = c_Orderings_Obot__class_Obot(tc_fun(_1502195, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1502195), _1502199), c_Big__Operators_Olattice_OSup__fin(_1502195, c_Orderings_Oord__class_Omax(_1502195), _1502197)) = c_Big__Operators_Olattice_OSup__fin(_1502195, c_Orderings_Oord__class_Omax(_1502195), hAPP(c_Set_OCollect(_1502195), hAPP(hAPP(c_COMBB(tc_fun(_1502195, tc_HOL_Obool), tc_HOL_Obool, _1502195), c_HOL_OEx(_1502195)), hAPP(hAPP(c_COMBC(_1502195, tc_fun(_1502195, tc_HOL_Obool), tc_fun(_1502195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502195, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1502195, tc_HOL_Obool), tc_fun(_1502195, tc_HOL_Obool)), _1502195), c_COMBS(_1502195, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502195, tc_HOL_Obool), tc_fun(_1502195, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1502195), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1502195), c_fconj)), hAPP(hAPP(c_COMBC(_1502195, tc_fun(_1502195, _1502195), tc_fun(_1502195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502195, tc_HOL_Obool), tc_fun(tc_fun(_1502195, _1502195), tc_fun(_1502195, tc_HOL_Obool)), _1502195), c_COMBB(_1502195, tc_HOL_Obool, _1502195)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1502195), _1502199))))), hAPP(hAPP(c_COMBC(_1502195, tc_fun(_1502195, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502195)), _1502197))))))], (13867 ^ _773908) ^ [_1007481, _1007483] : [class_Lattices_Oab__semigroup__idem__mult(_1007481), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007481), _1007483), _1007483) = _1007483)], (3772 ^ _773908) ^ [_830810, _830812, _830814, _830816] : [-(c_Relation_ODomain(_830816, _830812) = c_Relation_ODomain(_830814, _830810)), _830816 = _830814, _830812 = _830810], (10265 ^ _773908) ^ [_944289, _944291, _944293] : [class_Orderings_Olinorder(_944289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944289), _944291), _944293))), 10272 ^ _773908 : [(10279 ^ _773908) ^ [] : [_944291 = _944293, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944289), _944291), _944293)))], (10273 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944289), _944291), _944293)), -(_944291 = _944293)]]], (25587 ^ _773908) ^ [_1227035, _1227037, _1227039, _1227041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1227035), _1227037)), 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)), _1227035), _1227039)), 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)), _1227037), _1227041)), 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)), _1227037), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1227039), _1227041))), c_FunDef_Omin__strict)))], (3504 ^ _773908) ^ [_826626, _826628, _826630, _826632] : [-(c_List_Olist__update(_826632, _826628) = c_List_Olist__update(_826630, _826626)), _826632 = _826630, _826628 = _826626], (190 ^ _773908) ^ [_776691, _776693] : [-(class_Fields_Ofield__inverse__zero(_776691)), _776693 = _776691, class_Fields_Ofield__inverse__zero(_776693)], (7289 ^ _773908) ^ [_891936, _891938, _891940] : [c_Com_Ocom_OCall(_891936, _891938, _891940) = c_Com_Ocom_OSKIP], (40695 ^ _773908) ^ [_1571927, _1571929, _1571931, _1571933, _1571935, _1571937] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571927, _1571929)), hAPP(hAPP(c_Product__Type_OPair(_1571927, _1571929), _1571931), _1571933)), hAPP(c_List_Oset(tc_prod(_1571927, _1571929)), hAPP(hAPP(c_List_Ozip(_1571927, _1571929), _1571935), _1571937)))), 40698 ^ _773908 : [(40701 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571929), _1571933), hAPP(c_List_Oset(_1571929), _1571937))))], (40699 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571927), _1571931), hAPP(c_List_Oset(_1571927), _1571935))))]]], (18393 ^ _773908) ^ [_1091478] : [-(c_Int_Osucc(c_Int_Opred(_1091478)) = _1091478)], (44517 ^ _773908) ^ [_1661836, _1661838, _1661840, _1661842] : [hBOOL(hAPP(hAPP(c_member(_1661836), _1661838), hAPP(c_List_Oset(_1661836), _1661840))), -(hBOOL(hAPP(_1661842, _1661838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661836)), hAPP(c_List_Ofilter(_1661836, _1661842), _1661840))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661836)), _1661840))))], (46931 ^ _773908) ^ [_1715136, _1715138, _1715140, _1715142] : [-(c_Wellfounded_Oacyclic(_1715136, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1715136, _1715136)), hAPP(hAPP(c_Product__Type_OPair(_1715136, _1715136), _1715138), _1715140)), _1715142))), c_Wellfounded_Oacyclic(_1715136, _1715142), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1715136, _1715136)), hAPP(hAPP(c_Product__Type_OPair(_1715136, _1715136), _1715140), _1715138)), c_Transitive__Closure_Ortrancl(_1715136, _1715142))))], (37960 ^ _773908) ^ [_1495289, _1495291, _1495293, _1495295] : [-(hAPP(c_Set_OCollect(tc_prod(_1495289, _1495291)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495289, _1495291, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1495289, tc_fun(_1495291, tc_HOL_Obool), tc_fun(_1495291, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1495291, tc_HOL_Obool), tc_fun(_1495291, tc_HOL_Obool)), _1495289), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1495291)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495289), c_fconj), _1495293))), _1495295))) = hAPP(hAPP(c_Product__Type_OSigma(_1495289, _1495291), hAPP(c_Set_OCollect(_1495289), _1495293)), hAPP(hAPP(c_COMBB(tc_fun(_1495291, tc_HOL_Obool), tc_fun(_1495291, tc_HOL_Obool), _1495289), c_Set_OCollect(_1495291)), _1495295)))], (37851 ^ _773908) ^ [_1493126, _1493128, _1493130, _1493132, _1493134, _1493136, _1493138, _1493140] : [c_Finite__Set_Ofolding__image__simple(_1493126, _1493128, _1493130, _1493132, _1493134, _1493136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493128), _1493138)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493128), _1493140)), 37865 ^ _773908 : [(37868 ^ _773908) ^ [] : [hAPP(_1493134, 37864 ^ [_1493126, _1493128, _1493130, _1493132, _1493134, _1493136, _1493138, _1493140]) = _1493132], (37866 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493128), 37864 ^ [_1493126, _1493128, _1493130, _1493132, _1493134, _1493136, _1493138, _1493140]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493128, tc_HOL_Obool)), _1493138), _1493140))))]], -(hAPP(_1493136, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493128, tc_HOL_Obool)), _1493138), _1493140)) = hAPP(hAPP(_1493130, hAPP(_1493136, _1493138)), hAPP(_1493136, _1493140)))], (20241 ^ _773908) ^ [] : [-(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))))], (22261 ^ _773908) ^ [_1159339, _1159341, _1159343, _1159345] : [class_Fields_Olinordered__field__inverse__zero(_1159339), 22264 ^ _773908 : [(22265 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159341), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159339), _1159343), _1159345))), 22268 ^ _773908 : [(22275 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), c_Groups_Ozero__class_Ozero(_1159339)), _1159345))), 22278 ^ _773908 : [(22285 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), _1159345), c_Groups_Ozero__class_Ozero(_1159339)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159341), c_Groups_Ozero__class_Ozero(_1159339))))], (22279 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), _1159345), c_Groups_Ozero__class_Ozero(_1159339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159339), _1159341), _1159345))))]]], (22269 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), c_Groups_Ozero__class_Ozero(_1159339)), _1159345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159339), _1159341), _1159345)), _1159343)))]]], (22291 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159341), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159339), _1159343), _1159345)))), 22294 ^ _773908 : [(22297 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159339), _1159341), _1159345)), _1159343))], (22295 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), c_Groups_Ozero__class_Ozero(_1159339)), _1159345)))]], 22298 ^ _773908 : [(22301 ^ _773908) ^ [] : [22302 ^ _773908 : [(22305 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159339), _1159341), _1159345)))], (22303 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), _1159345), c_Groups_Ozero__class_Ozero(_1159339))))]], 22306 ^ _773908 : [(22309 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159339), _1159341), c_Groups_Ozero__class_Ozero(_1159339)))], (22307 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), _1159345), c_Groups_Ozero__class_Ozero(_1159339)))]]], (22299 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159339), c_Groups_Ozero__class_Ozero(_1159339)), _1159345))]]]]], (36561 ^ _773908) ^ [_1462437, _1462439, _1462441, _1462443, _1462445, _1462447] : [c_Typedef_Otype__definition(_1462437, _1462439, _1462441, _1462443, _1462445), -(hBOOL(hAPP(hAPP(c_member(_1462439), hAPP(_1462441, _1462447)), _1462445)))], (5943 ^ _773908) ^ [_869164, _869166, _869168, _869170, _869172] : [c_Hoare__Mirabelle_Otriple__valid(_869164, hAPP(c_Nat_OSuc, _869166), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869164), _869168), hAPP(c_Com_Ocom_OBODY, _869170)), _869172)), -(c_Hoare__Mirabelle_Otriple__valid(_869164, _869166, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869164), _869168), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _869170))), _869172)))], (24093 ^ _773908) ^ [_1195013, _1195015] : [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), _1195013), _1195015))), 24096 ^ _773908 : [(24103 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195015), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24106 ^ _773908 : [(24115 ^ _773908) ^ [] : [-(c_Nitpick_Onorm__frac(_1195013, _1195015) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1195013), _1195015)), 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), _1195013))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195015)))), -(_1195013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1195015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24107 ^ _773908) ^ [] : [24108 ^ _773908 : [(24111 ^ _773908) ^ [] : [_1195015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24109 ^ _773908) ^ [] : [_1195013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1195013, _1195015) = 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)))]]], (24097 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195015), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1195013, _1195015) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195013), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195015)))]]], (24337 ^ _773908) ^ [_1200949, _1200951, _1200953] : [_1200949 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1200951, _1200951), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1200951, _1200951), tc_HOL_Obool)), _1200949), _1200953)))], (26153 ^ _773908) ^ [_1237955, _1237957, _1237959] : [class_Lattices_Olattice(_1237955), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237955), _1237957), _1237959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1237955), _1237959), _1237957))], (3102 ^ _773908) ^ [_820385, _820387, _820389, _820391] : [-(c_Nitpick_Ocard_H(_820391, _820387) = c_Nitpick_Ocard_H(_820389, _820385)), _820391 = _820389, _820387 = _820385], (23560 ^ _773908) ^ [_1184737, _1184739, _1184741, _1184743, _1184745] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1184737, _1184739), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1184741), _1184743))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184739)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184745), _1184737), _1184739), 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), _1184745), _1184741)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184745), _1184743)), _1184739))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184745), _1184743), _1184739)))))], (28787 ^ _773908) ^ [_1299641, _1299643, _1299645, _1299647, _1299649] : [hBOOL(hAPP(hAPP(c_member(_1299641), _1299643), c_SetInterval_Oord_OatLeastAtMost(_1299641, _1299645, _1299647, _1299649))), 28790 ^ _773908 : [(28793 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1299645, _1299643), _1299649)))], (28791 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1299645, _1299647), _1299643)))]]], (35849 ^ _773908) ^ [_1446611, _1446613, _1446615, _1446617, _1446619] : [c_Fun_Oinj__on(_1446611, _1446613, _1446615, c_Orderings_Otop__class_Otop(tc_fun(_1446611, tc_HOL_Obool))), 35852 ^ _773908 : [(35859 ^ _773908) ^ [] : [_1446617 = _1446619, -(hAPP(_1446615, _1446617) = hAPP(_1446615, _1446619))], (35853 ^ _773908) ^ [] : [hAPP(_1446615, _1446617) = hAPP(_1446615, _1446619), -(_1446617 = _1446619)]]], (44461 ^ _773908) ^ [_1660282, _1660284, _1660286] : [-(c_List_Oconcat(_1660282, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1660282)), _1660284), _1660286)) = hAPP(hAPP(c_List_Oappend(_1660282), _1660284), c_List_Oconcat(_1660282, _1660286)))], (40991 ^ _773908) ^ [_1581405, _1581407, _1581409, _1581411] : [-(hAPP(c_List_Orotate1(_1581407), hAPP(hAPP(c_List_Olist_OCons(_1581407), _1581409), _1581411)) = hAPP(hAPP(c_List_Oappend(_1581407), _1581411), hAPP(hAPP(c_List_Olist_OCons(_1581407), _1581409), c_List_Olist_ONil(_1581407))))], (35518 ^ _773908) ^ [_1439659] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1439659)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1439659))], (42780 ^ _773908) ^ [_1622525, _1622527] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1622525), _1622527))), -(c_Nitpick_Ocard_H(_1622525, _1622527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42139 ^ _773908) ^ [_1607089, _1607091, _1607093, _1607095, _1607097, _1607099] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607089, tc_fun(_1607091, tc_HOL_Obool)), _1607093), hAPP(hAPP(c_COMBB(_1607095, tc_fun(_1607091, tc_HOL_Obool), _1607089), _1607097), _1607099)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607095, tc_fun(_1607091, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1607089, _1607095, _1607099), _1607093)), _1607097))], (25715 ^ _773908) ^ [_1229541, _1229543, _1229545, _1229547] : [hBOOL(hAPP(hAPP(c_member(_1229541), _1229543), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229541, tc_HOL_Obool)), _1229545), _1229547))), -(hBOOL(hAPP(hAPP(c_member(_1229541), _1229543), _1229545))), -(hBOOL(hAPP(hAPP(c_member(_1229541), _1229543), _1229547)))], (24885 ^ _773908) ^ [_1212933, _1212935, _1212937, _1212939] : [class_Orderings_Olinorder(_1212933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212933), _1212935), _1212937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212933), _1212935), _1212939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212933), _1212935), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212933), _1212937), _1212939))))], (38172 ^ _773908) ^ [_1501019, _1501021, _1501023, _1501025] : [-(hAPP(c_Relation_OImage(_1501019, _1501021, _1501023), hAPP(hAPP(c_Set_Oinsert(_1501019), _1501025), c_Orderings_Obot__class_Obot(tc_fun(_1501019, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1501021), hAPP(hAPP(c_COMBC(_1501021, tc_fun(tc_prod(_1501019, _1501021), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1501019, _1501021), tc_fun(tc_fun(tc_prod(_1501019, _1501021), tc_HOL_Obool), tc_HOL_Obool), _1501021), c_member(tc_prod(_1501019, _1501021))), hAPP(c_Product__Type_OPair(_1501019, _1501021), _1501025))), _1501023)))], (18049 ^ _773908) ^ [_1085149, _1085151] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085149) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085151)), 18052 ^ _773908 : [(18055 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085151)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18053 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085149))))]], 18056 ^ _773908 : [(18059 ^ _773908) ^ [] : [18060 ^ _773908 : [(18063 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085149) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18061 ^ _773908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085151))))]], 18064 ^ _773908 : [(18067 ^ _773908) ^ [] : [_1085149 = _1085151], (18065 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085151)))]]], (18057 ^ _773908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085149)))]]], (17873 ^ _773908) ^ [_1082569] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1082569) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1082569))], (16209 ^ _773908) ^ [_1051718, _1051720] : [-(_1051718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051718), _1051720) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051718), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1051720)))], (51900 ^ _773908) ^ [_1818430, _1818432] : [hBOOL(hAPP(hAPP(c_fconj, _1818430), _1818432)), -(hBOOL(_1818432))], (17893 ^ _773908) ^ [_1082821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082821), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082821)))], (14263 ^ _773908) ^ [_1014932, _1014934, _1014936, _1014938] : [_1014932 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014934), _1014936)), _1014938), -(_1014934 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1014932), _1014934) = _1014936), 14270 ^ _773908 : [(14273 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014938)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014938), _1014934))], (14271 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014934)))]], 14278 ^ _773908 : [(14281 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014934), _1014938)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014938), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14279 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014934))]]], (10179 ^ _773908) ^ [_943058, _943060, _943062] : [class_Orderings_Oorder(_943058), 10182 ^ _773908 : [(10191 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943058), _943060), _943062))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943058), _943060), _943062)), -(_943060 = _943062)], (10183 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943058), _943060), _943062)), 10186 ^ _773908 : [(10189 ^ _773908) ^ [] : [_943060 = _943062], (10187 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943058), _943060), _943062)))]]]]], (3568 ^ _773908) ^ [_827632, _827634] : [_827634 = _827632, -(c_List_Omonoid__add__class_Olistsum(_827634) = c_List_Omonoid__add__class_Olistsum(_827632))], (5706 ^ _773908) ^ [_863966, _863968] : [hAPP(_863966, 5707 ^ [_863966, _863968]) = hAPP(_863968, 5707 ^ [_863966, _863968]), -(_863966 = _863968)], (51480 ^ _773908) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (12696 ^ _773908) ^ [_986606, _986608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986606), _986608)), 12699 ^ _773908 : [(12702 ^ _773908) ^ [] : [_986606 = _986608], (12700 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986606), _986608)))]]], (44746 ^ _773908) ^ [_1668065, _1668067, _1668069, _1668071] : [c_List_Oupt(_1668065, _1668067) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1668069), _1668071), 44749 ^ _773908 : [(44754 ^ _773908) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668065), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1668067) = _1668071)], (44752 ^ _773908) ^ [] : [-(_1668065 = _1668069)], (44750 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668065), _1668067)))]]], (51550 ^ _773908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (45571 ^ _773908) ^ [_1684204, _1684206, _1684208] : [hAPP(hAPP(c_List_Olist_OCons(_1684204), _1684206), c_List_Olist_ONil(_1684204)) = hAPP(c_List_Orev(_1684204), _1684208), -(_1684208 = hAPP(hAPP(c_List_Olist_OCons(_1684204), _1684206), c_List_Olist_ONil(_1684204)))], (39338 ^ _773908) ^ [_1538049, _1538051, _1538053] : [_1538053 = c_List_Olist_ONil(_1538049), -(hAPP(hAPP(c_List_Oappend(_1538049), _1538051), _1538053) = _1538051)], (31180 ^ _773908) ^ [_1346228, _1346230, _1346232, _1346234] : [-(c_Sum__Type_OPlus(_1346228, _1346230, _1346232, _1346234) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1346228, _1346230), tc_HOL_Obool))), _1346232 = c_Orderings_Obot__class_Obot(tc_fun(_1346228, tc_HOL_Obool)), _1346234 = c_Orderings_Obot__class_Obot(tc_fun(_1346230, tc_HOL_Obool))], (41480 ^ _773908) ^ [_1590982, _1590984] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1590982, _1590984) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1590982), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1590984)))], (23205 ^ _773908) ^ [_1177705, _1177707, _1177709] : [class_Int_Onumber__ring(_1177705), 23208 ^ _773908 : [(23215 ^ _773908) ^ [] : [-(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), _1177707)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1177705), _1177709), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1177707))) = c_Groups_Oone__class_Oone(_1177705))], (23209 ^ _773908) ^ [] : [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), _1177707))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1177705), _1177709), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1177707))) = hAPP(hAPP(c_HOL_OLet(_1177705, _1177705), hAPP(hAPP(c_Power_Opower__class_Opower(_1177705), _1177709), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177707))), hAPP(hAPP(c_COMBS(_1177705, _1177705, _1177705), hAPP(hAPP(c_COMBB(_1177705, tc_fun(_1177705, _1177705), _1177705), c_Groups_Otimes__class_Otimes(_1177705)), hAPP(c_Groups_Otimes__class_Otimes(_1177705), _1177709))), c_COMBI(_1177705))))]]], (49733 ^ _773908) ^ [_1777968, _1777970, _1777972] : [hBOOL(hAPP(hAPP(c_List_Omember(_1777968), _1777970), _1777972)), -(hBOOL(hAPP(hAPP(c_member(_1777968), _1777972), hAPP(c_List_Oset(_1777968), _1777970))))], (20071 ^ _773908) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (19901 ^ _773908) ^ [_1117325, _1117327] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1117325)), _1117327) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117325), _1117327)))], (24317 ^ _773908) ^ [_1200415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200415)), 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), _1200415)) = 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), _1200415))))))], (3030 ^ _773908) ^ [_819219, _819221] : [_819221 = _819219, -(c_Set_OBall(_819221) = c_Set_OBall(_819219))], (43260 ^ _773908) ^ [_1633133, _1633135] : [-(hBOOL(hAPP(c_List_Olistsp(_1633133, _1633135), c_List_Olist_ONil(_1633133))))], (16263 ^ _773908) ^ [_1052518, _1052520, _1052522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052518)), 16269 ^ _773908 : [(16272 ^ _773908) ^ [] : [hBOOL(hAPP(_1052520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16268 ^ [_1052518, _1052520, _1052522]), _1052518)))], (16270 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1052520, 16268 ^ [_1052518, _1052520, _1052522])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052522)), 16277 ^ _773908 : [(16278 ^ _773908) ^ [_1052807] : [hBOOL(hAPP(_1052520, _1052807)), -(hBOOL(hAPP(_1052520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052522), _1052518)))))]]], (10003 ^ _773908) ^ [_940237] : [class_Rings_Osemiring__1(_940237), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940237), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_940237))], (38508 ^ _773908) ^ [_1514555, _1514557, _1514559, _1514561] : [-(c_Product__Type_Oapfst(_1514555, _1514557, _1514559, _1514561) = c_Product__Type_Omap__pair(_1514555, _1514557, _1514559, _1514559, _1514561, c_Fun_Oid(_1514559)))], (6900 ^ _773908) ^ [_885561, _885563, _885565] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885561), _885563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885565), _885563), -(_885561 = _885565)], (47627 ^ _773908) ^ [_1732755, _1732757, _1732759, _1732761, _1732763] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1732755, _1732755)), hAPP(hAPP(c_Product__Type_OPair(_1732755, _1732755), _1732757), _1732759)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1732755, _1732755), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1732761)), _1732763))), 47631 ^ _773908 : [(47634 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1732755, _1732755)), hAPP(hAPP(c_Product__Type_OPair(_1732755, _1732755), 47630 ^ [_1732755, _1732757, _1732759, _1732761, _1732763]), _1732759)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1732755, _1732755), tc_HOL_Obool), _1732761), _1732763))))], (47632 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1732755, _1732755)), hAPP(hAPP(c_Product__Type_OPair(_1732755, _1732755), _1732757), 47630 ^ [_1732755, _1732757, _1732759, _1732761, _1732763])), _1732763)))]]], (41360 ^ _773908) ^ [_1588969, _1588971, _1588973] : [class_Orderings_Olinorder(_1588969), -(c_Big__Operators_Olattice_OSup__fin(_1588969, c_Orderings_Oord__class_Omax(_1588969), hAPP(c_List_Oset(_1588969), hAPP(hAPP(c_List_Olist_OCons(_1588969), _1588971), _1588973))) = hAPP(c_List_Ofoldl(_1588969, _1588969, c_Orderings_Oord__class_Omax(_1588969), _1588971), _1588973))], (44062 ^ _773908) ^ [_1652002, _1652004, _1652006, _1652008] : [hBOOL(hAPP(hAPP(c_member(_1652002), _1652004), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1652002, tc_HOL_Obool), _1652006))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1652002, tc_HOL_Obool)), _1652008), _1652006)), -(hBOOL(hAPP(hAPP(c_member(_1652002), _1652004), _1652008)))], (16995 ^ _773908) ^ [_1066628, _1066630, _1066632] : [class_Rings_Oordered__ring__abs(_1066628), -(hAPP(c_Groups_Oabs__class_Oabs(_1066628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066628), _1066630), _1066632)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066628), hAPP(c_Groups_Oabs__class_Oabs(_1066628), _1066630)), hAPP(c_Groups_Oabs__class_Oabs(_1066628), _1066632))), 17002 ^ _773908 : [(17005 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066628), _1066630), c_Groups_Ozero__class_Ozero(_1066628)))], (17003 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066628), c_Groups_Ozero__class_Ozero(_1066628)), _1066630))]], 17006 ^ _773908 : [(17009 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066628), _1066632), c_Groups_Ozero__class_Ozero(_1066628)))], (17007 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066628), c_Groups_Ozero__class_Ozero(_1066628)), _1066632))]]], (46250 ^ _773908) ^ [_1699192, _1699194] : [c_Wellfounded_OwfP(_1699192, _1699194), -(c_Wellfounded_Owf(_1699192, hAPP(c_Set_OCollect(tc_prod(_1699192, _1699192)), hAPP(c_Product__Type_Oprod_Oprod__case(_1699192, _1699192, tc_HOL_Obool), _1699194))))], (43366 ^ _773908) ^ [_1635235, _1635237, _1635239, _1635241, _1635243] : [-(c_Enum_Oproduct(_1635235, _1635237, hAPP(hAPP(c_List_Olist_OCons(_1635235), _1635239), _1635241), _1635243) = hAPP(hAPP(c_List_Oappend(tc_prod(_1635235, _1635237)), hAPP(hAPP(c_List_Omap(_1635237, tc_prod(_1635235, _1635237)), hAPP(c_Product__Type_OPair(_1635235, _1635237), _1635239)), _1635243)), c_Enum_Oproduct(_1635235, _1635237, _1635241, _1635243)))], (51668 ^ _773908) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (23197 ^ _773908) ^ [_1177454, _1177456] : [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(_1177454))), 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)), _1177456)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1177454)), hAPP(c_Nat_OSuc, _1177456))))], (5260 ^ _773908) ^ [_854326, _854328, _854330, _854332] : [-(c_Relation_Oconverse(_854332, _854328) = c_Relation_Oconverse(_854330, _854326)), _854332 = _854330, _854328 = _854326], (44463 ^ _773908) ^ [_1660333, _1660335, _1660337] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1660333), tc_List_Olist(_1660333)), c_List_Opartition(_1660333, _1660335, _1660337)) = hAPP(c_List_Ofilter(_1660333, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1660333, c_fNot), _1660335)), _1660337))], (51314 ^ _773908) ^ [_1812221, _1812223] : [class_Lattices_Odistrib__lattice(_1812221), -(class_Lattices_Odistrib__lattice(tc_fun(_1812223, _1812221)))], (24199 ^ _773908) ^ [_1197099, _1197101, _1197103, _1197105, _1197107] : [-(hAPP(c_Product__Type_Osnd(_1197099, _1197101), hAPP(c_Product__Type_Oapsnd(_1197103, _1197101, _1197099, _1197105), _1197107)) = hAPP(_1197105, hAPP(c_Product__Type_Osnd(_1197099, _1197103), _1197107)))], (33746 ^ _773908) ^ [_1400862] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1400862)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1400862)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1400862)))], (28392 ^ _773908) ^ [_1289719, _1289721, _1289723, _1289725, _1289727] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289719, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1289721, _1289719, _1289723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289721, tc_HOL_Obool)), _1289725), _1289727))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289719, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1289721, _1289719, _1289723), _1289725)), hAPP(c_Set_Oimage(_1289721, _1289719, _1289723), _1289727)))))], (51606 ^ _773908) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (19911 ^ _773908) ^ [_1117522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1117522)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117522), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4060 ^ _773908) ^ [_835252, _835254] : [_835254 = _835252, -(c_Int_Oring__1__class_Oof__int(_835254) = c_Int_Oring__1__class_Oof__int(_835252))], (48575 ^ _773908) ^ [_1752686, _1752688, _1752690, _1752692, _1752694, _1752696] : [c_Finite__Set_Ofun__left__comm(_1752686, _1752688, _1752690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752686), _1752692)), hBOOL(hAPP(hAPP(c_member(_1752686), _1752694), _1752692)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1752686, _1752688, _1752690), _1752696), _1752692) = hAPP(hAPP(_1752690, _1752694), hAPP(hAPP(c_Finite__Set_Ofold(_1752686, _1752688, _1752690), _1752696), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1752686, tc_HOL_Obool)), _1752692), hAPP(hAPP(c_Set_Oinsert(_1752686), _1752694), c_Orderings_Obot__class_Obot(tc_fun(_1752686, tc_HOL_Obool)))))))], (29143 ^ _773908) ^ [_1305793, _1305795, _1305797] : [class_Lattices_Olattice(_1305793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305793), _1305795)), -(_1305795 = c_Orderings_Obot__class_Obot(tc_fun(_1305793, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305793), _1305797)), -(_1305797 = c_Orderings_Obot__class_Obot(tc_fun(_1305793, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1305793, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305793, tc_HOL_Obool)), _1305795), _1305797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305793), c_Big__Operators_Olattice__class_OInf__fin(_1305793, _1305795)), c_Big__Operators_Olattice__class_OInf__fin(_1305793, _1305797)))], (48006 ^ _773908) ^ [_1741301, _1741303, _1741305, _1741307] : [48007 ^ _773908 : [(48010 ^ _773908) ^ [] : [c_List_Olist__ex(_1741301, _1741303, _1741307)], (48008 ^ _773908) ^ [] : [hBOOL(hAPP(_1741303, _1741305))]], -(c_List_Olist__ex(_1741301, _1741303, hAPP(hAPP(c_List_Olist_OCons(_1741301), _1741305), _1741307)))], (37621 ^ _773908) ^ [_1487044, _1487046, _1487048, _1487050, _1487052, _1487054] : [class_Groups_Ocomm__monoid__mult(_1487044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487046), _1487048)), 37631 ^ _773908 : [(37634 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487050), hAPP(_1487052, 37630 ^ [_1487044, _1487046, _1487048, _1487050, _1487052, _1487054])))], (37632 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487046), 37630 ^ [_1487044, _1487046, _1487048, _1487050, _1487052, _1487054]), _1487048)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487046, _1487044), hAPP(hAPP(c_COMBS(_1487046, tc_fun(_1487050, tc_HOL_Obool), _1487044), hAPP(hAPP(c_COMBB(tc_fun(_1487050, _1487044), tc_fun(tc_fun(_1487050, tc_HOL_Obool), _1487044), _1487046), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1487050, _1487044)), _1487054)), _1487052)), _1487048) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1487046, _1487050), _1487044), hAPP(c_Product__Type_Oprod_Oprod__case(_1487046, _1487050, _1487044), _1487054)), hAPP(hAPP(c_Product__Type_OSigma(_1487046, _1487050), _1487048), _1487052)))], (38689 ^ _773908) ^ [_1521427] : [-(c_Wellfounded_Owf(_1521427, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521427, _1521427), tc_HOL_Obool))))], (19381 ^ _773908) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (38174 ^ _773908) ^ [_1501122, _1501124, _1501126, _1501128, _1501130, _1501132] : [class_Groups_Ocomm__monoid__add(_1501122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501124), _1501126)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501124, _1501122), hAPP(hAPP(c_COMBS(_1501124, _1501122, _1501122), hAPP(hAPP(c_COMBS(_1501124, _1501122, tc_fun(_1501122, _1501122)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1501122, tc_fun(_1501122, _1501122)), _1501124), c_If(_1501122)), _1501128)), _1501130)), _1501132)), _1501126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1501122), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501124, _1501122), _1501130), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501124, tc_HOL_Obool)), _1501126), hAPP(c_Set_OCollect(_1501124), _1501128)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1501124, _1501122), _1501132), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501124, tc_HOL_Obool)), _1501126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1501124, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1501124), _1501128))))))], (14087 ^ _773908) ^ [_1011440, _1011442] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011440))), -(c_SMT_Oz3mod(_1011442, _1011440) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011442, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011440)))], (42846 ^ _773908) ^ [_1624042] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1624042)) = _1624042)], (44084 ^ _773908) ^ [_1652579, _1652581, _1652583] : [class_Complete__Lattice_Ocomplete__lattice(_1652579), 44087 ^ _773908 : [(44088 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1652579), _1652581), c_Complete__Lattice_OInf__class_OInf(_1652579, _1652583))), 44091 ^ _773908 : [(44092 ^ _773908) ^ [_1652737] : [hBOOL(hAPP(hAPP(c_member(_1652579), _1652737), _1652583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1652579), _1652581), _1652737)))]]], (44098 ^ _773908) ^ [] : [44100 ^ _773908 : [(44103 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1652579), _1652581), 44099 ^ [_1652579, _1652581, _1652583]))], (44101 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652579), 44099 ^ [_1652579, _1652581, _1652583]), _1652583)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1652579), _1652581), c_Complete__Lattice_OInf__class_OInf(_1652579, _1652583))))]]], (21569 ^ _773908) ^ [_1146997, _1146999, _1147001, _1147003] : [class_Fields_Olinordered__field(_1146997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146997), c_Groups_Ozero__class_Ozero(_1146997)), _1146999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146997), _1147001), _1146999)), _1147003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146997), _1147001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146997), _1147003), _1146999))))], (9123 ^ _773908) ^ [_925365, _925367, _925369, _925371] : [class_Rings_Olinordered__ring__strict(_925365), 9126 ^ _773908 : [(9141 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925365), _925367), _925369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925365), _925371), _925369)))), 9142 ^ _773908 : [(9149 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925369), c_Groups_Ozero__class_Ozero(_925365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925371), _925367))], (9143 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), c_Groups_Ozero__class_Ozero(_925365)), _925369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925367), _925371))]]], (9127 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925365), _925367), _925369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925365), _925371), _925369))), 9132 ^ _773908 : [(9135 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925367), _925371)))], (9133 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), c_Groups_Ozero__class_Ozero(_925365)), _925369)))]], 9136 ^ _773908 : [(9139 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925371), _925367)))], (9137 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925365), _925369), c_Groups_Ozero__class_Ozero(_925365))))]]]]], (33164 ^ _773908) ^ [_1389951, _1389953, _1389955] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1389951), _1389953)), c_Fun_Oinj__on(_1389951, tc_fun(tc_fun(_1389951, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1389951, tc_fun(tc_prod(_1389951, _1389951), tc_HOL_Obool), tc_fun(tc_fun(_1389951, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1389951, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1389951, _1389951), tc_HOL_Obool), tc_fun(tc_fun(_1389951, tc_HOL_Obool), tc_HOL_Obool)), _1389951), c_Equiv__Relations_Oquotient(_1389951)), hAPP(hAPP(c_COMBC(_1389951, tc_fun(_1389951, tc_HOL_Obool), tc_fun(_1389951, tc_HOL_Obool)), c_Set_Oinsert(_1389951)), c_Orderings_Obot__class_Obot(tc_fun(_1389951, tc_HOL_Obool))))), _1389955), _1389953), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1389951, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1389951), _1389953), _1389955)) = hAPP(c_Finite__Set_Ocard(_1389951), _1389953))], (16941 ^ _773908) ^ [_1065563, _1065565, _1065567] : [class_Int_Onumber__ring(_1065563), -(hAPP(c_Int_Onumber__class_Onumber__of(_1065563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065565), _1065567)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065563), hAPP(c_Int_Onumber__class_Onumber__of(_1065563), _1065565)), hAPP(c_Int_Onumber__class_Onumber__of(_1065563), _1065567)))], (34025 ^ _773908) ^ [_1406810, _1406812, _1406814, _1406816] : [class_Orderings_Olinorder(_1406810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406810), _1406812), _1406814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406810), _1406814), _1406816)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406810, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1406810, _1406812, _1406814)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406810, _1406814), _1406816)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1406810, _1406812, _1406816))], (5514 ^ _773908) ^ [_858267, _858269] : [_858269 = _858267, -(c_Orderings_Otop__class_Otop(_858269) = c_Orderings_Otop__class_Otop(_858267))], (26942 ^ _773908) ^ [_1259109, _1259111] : [c_Nat__Transfer_Onat__set(_1259109), c_Nat__Transfer_Onat__set(_1259111), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1259109), _1259111)))], (38865 ^ _773908) ^ [_1524813, _1524815, _1524817, _1524819] : [c_Wellfounded_Owf(_1524813, _1524815), hBOOL(hAPP(hAPP(c_member(tc_prod(_1524813, _1524813)), hAPP(hAPP(c_Product__Type_OPair(_1524813, _1524813), _1524817), _1524819)), _1524815)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1524813, _1524813)), hAPP(hAPP(c_Product__Type_OPair(_1524813, _1524813), _1524819), _1524817)), _1524815))], (11203 ^ _773908) ^ [_960527, _960529, _960531, _960533] : [class_Rings_Oordered__comm__semiring(_960527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960527), _960529), _960531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960527), c_Groups_Ozero__class_Ozero(_960527)), _960533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960527), _960533), _960529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960527), _960533), _960531))))], (36035 ^ _773908) ^ [_1449927, _1449929, _1449931, _1449933, _1449935] : [hAPP(c_Set_Oimage(_1449927, _1449929, _1449931), c_Orderings_Otop__class_Otop(tc_fun(_1449927, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1449929, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449929, _1449933, _1449935), c_Orderings_Otop__class_Otop(tc_fun(_1449929, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1449933, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1449927, _1449933, hAPP(c_Fun_Ocomp(_1449929, _1449933, _1449927, _1449935), _1449931)), c_Orderings_Otop__class_Otop(tc_fun(_1449927, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1449933, tc_HOL_Obool)))], (8615 ^ _773908) ^ [_916535, _916537, _916539, _916541] : [class_Groups_Oab__semigroup__mult(_916535), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916535), _916537), _916539)), _916541) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916535), _916537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916535), _916539), _916541)))], (26743 ^ _773908) ^ [_1254957] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254957) = 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), _1254957), 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))))))], (30025 ^ _773908) ^ [_1322171, _1322173] : [class_Orderings_Olinorder(_1322171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322171), _1322173)), -(_1322173 = c_Orderings_Obot__class_Obot(tc_fun(_1322171, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1322171), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322171), 30038 ^ [_1322171, _1322173]), 30039 ^ [_1322171, _1322173])), hAPP(hAPP(c_Set_Oinsert(_1322171), 30038 ^ [_1322171, _1322173]), hAPP(hAPP(c_Set_Oinsert(_1322171), 30039 ^ [_1322171, _1322173]), c_Orderings_Obot__class_Obot(tc_fun(_1322171, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1322171), c_Big__Operators_Olattice_OSup__fin(_1322171, c_Orderings_Oord__class_Omax(_1322171), _1322173)), _1322173)))], (15385 ^ _773908) ^ [_1034957] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034957) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26444 ^ _773908) ^ [_1247364, _1247366, _1247368, _1247370, _1247372, _1247374] : [hBOOL(hAPP(hAPP(_1247364, _1247366), _1247368)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247370, tc_fun(_1247372, tc_HOL_Obool))), _1247374), _1247364), _1247366), _1247368)))], (46138 ^ _773908) ^ [_1696161, _1696163, _1696165] : [-(c_List_Omaps(_1696161, _1696163, _1696165, c_List_Olist_ONil(_1696161)) = c_List_Olist_ONil(_1696163))], (47473 ^ _773908) ^ [_1728745, _1728747] : [-(c_Relation_Osingle__valued(_1728745, _1728745, c_Relation_OId__on(_1728745, _1728747)))], (47387 ^ _773908) ^ [_1726420, _1726422, _1726424, _1726426] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1726420, _1726420)), hAPP(hAPP(c_Product__Type_OPair(_1726420, _1726420), _1726422), _1726424)), c_Transitive__Closure_Ortrancl(_1726420, _1726426))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1726420, _1726420)), hAPP(hAPP(c_Product__Type_OPair(_1726420, _1726420), _1726424), _1726422)), c_Transitive__Closure_Ortrancl(_1726420, hAPP(c_Relation_Oconverse(_1726420, _1726420), _1726426)))))], (7988 ^ _773908) ^ [_904718, _904720, _904722, _904724] : [-(c_Com_Ocom_OWhile(_904718, _904720) = c_Com_Ocom_OWhile(_904722, _904724)), _904718 = _904722, _904720 = _904724], (26345 ^ _773908) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (25285 ^ _773908) ^ [_1220650] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220650) = _1220650)], (15707 ^ _773908) ^ [_1041131, _1041133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041131), _1041133)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041131), _1041133) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25031 ^ _773908) ^ [_1215453, _1215455, _1215457, _1215459] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_1215453, _1215455), _1215457, _1215459, hAPP(hAPP(hAPP(c_Natural_Oupdate, _1215457), _1215453), hAPP(_1215455, _1215457))))], (34071 ^ _773908) ^ [_1408044, _1408046, _1408048, _1408050] : [class_Orderings_Olinorder(_1408044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408044), _1408046), _1408048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408044), _1408048), _1408050)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408044, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1408044, _1408046, _1408048)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1408044, _1408048, _1408050)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408044, _1408046), _1408050))], (41979 ^ _773908) ^ [_1603153, _1603155, _1603157, _1603159, _1603161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603153, tc_HOL_Obool)), _1603155), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603157, tc_fun(_1603153, tc_HOL_Obool)), _1603159), _1603161))), 41982 ^ _773908 : [(41983 ^ _773908) ^ [_1603286] : [hBOOL(hAPP(hAPP(c_member(_1603157), _1603286), _1603159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603153, tc_HOL_Obool)), _1603155), hAPP(_1603161, _1603286))))]]], (11910 ^ _773908) ^ [_973143, _973145, _973147, _973149] : [class_Rings_Olinordered__semiring__strict(_973143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973143), _973145), _973147)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973143), _973149), _973147))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973143), c_Groups_Ozero__class_Ozero(_973143)), _973147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973143), _973145), _973149)))], (10553 ^ _773908) ^ [_948896, _948898, _948900, _948902] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_948896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948896), _948898), _948900)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948896), _948902), _948900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948896), _948898), _948902)))], (23149 ^ _773908) ^ [_1176360] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176360)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1176360)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176360)), 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)))))], (39663 ^ _773908) ^ [_1545593, _1545595, _1545597, _1545599, _1545601, _1545603, _1545605, _1545607] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545593, _1545593)), hAPP(hAPP(c_Product__Type_OPair(_1545593, _1545593), _1545595), _1545597)), _1545599)), _1545601 = hAPP(hAPP(c_List_Oappend(_1545593), _1545603), hAPP(hAPP(c_List_Olist_OCons(_1545593), _1545595), _1545605)), _1545607 = hAPP(hAPP(c_List_Oappend(_1545593), _1545603), hAPP(hAPP(c_List_Olist_OCons(_1545593), _1545597), _1545605)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1545593), tc_List_Olist(_1545593))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1545593), tc_List_Olist(_1545593)), _1545601), _1545607)), c_List_Olistrel1(_1545593, _1545599))))], (18707 ^ _773908) ^ [_1097258] : [class_Int_Onumber__ring(_1097258), c_Int_Oiszero(_1097258, hAPP(c_Int_Onumber__class_Onumber__of(_1097258), c_Int_OMin))], (6219 ^ _773908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51123 ^ _773908) ^ [_1808679, _1808681, _1808683, _1808685, _1808687] : [hBOOL(hAPP(_1808679, hAPP(hAPP(c_Product__Type_OPair(_1808681, _1808683), _1808685), _1808687))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1808681, _1808683, tc_HOL_Obool, _1808679), _1808685), _1808687)))], (13460 ^ _773908) ^ [_999995, _999997, _999999] : [_999995 = _999997, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999999, tc_HOL_Obool)), _999995), _999997)))], (48289 ^ _773908) ^ [_1747406, _1747408, _1747410, _1747412, _1747414] : [c_Finite__Set_Ofolding__one__idem(_1747406, _1747408, _1747410), hBOOL(hAPP(c_Finite__Set_Ofinite(_1747406), _1747412)), -(hAPP(_1747410, hAPP(hAPP(c_Set_Oinsert(_1747406), _1747414), _1747412)) = hAPP(hAPP(c_Finite__Set_Ofold(_1747406, _1747406, _1747408), _1747414), _1747412))], (49596 ^ _773908) ^ [_1774890, _1774892, _1774894] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1774890), hAPP(c_COMBK(_1774890, tc_Nat_Onat), _1774892)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1774894)) = c_List_Oreplicate(_1774890, _1774894, _1774892))], (8193 ^ _773908) ^ [_908497, _908499, _908501, _908503] : [c_Com_Ocom_OWhile(_908497, _908499) = c_Com_Ocom_OAss(_908501, _908503)], (33452 ^ _773908) ^ [_1395296, _1395298, _1395300, _1395302] : [c_Fun_Oinj__on(_1395296, _1395298, _1395300, _1395302), -(hAPP(c_Finite__Set_Ocard(_1395298), hAPP(c_Set_Oimage(_1395296, _1395298, _1395300), _1395302)) = hAPP(c_Finite__Set_Ocard(_1395296), _1395302))], (1904 ^ _773908) ^ [_800694, _800696] : [-(class_Int_Onumber(_800694)), _800696 = _800694, class_Int_Onumber(_800696)], (3782 ^ _773908) ^ [_830959, _830961, _830963, _830965] : [-(c_Nat_Ocompow(_830965, _830961) = c_Nat_Ocompow(_830963, _830959)), _830965 = _830963, _830961 = _830959], (1194 ^ _773908) ^ [_791819, _791821] : [-(class_Rings_Olinordered__semiring__1(_791819)), _791821 = _791819, class_Rings_Olinordered__semiring__1(_791821)], (24383 ^ _773908) ^ [_1201868, _1201870, _1201872] : [c_FunDef_Ois__measure(_1201868, _1201870), -(c_FunDef_Ois__measure(tc_prod(_1201868, _1201872), hAPP(hAPP(c_COMBB(_1201868, tc_Nat_Onat, tc_prod(_1201868, _1201872)), _1201870), c_Product__Type_Ofst(_1201868, _1201872))))], (2138 ^ _773908) ^ [_804971, _804973] : [_804973 = _804971, -(c_Nat_Osemiring__1__class_ONats(_804973) = c_Nat_Osemiring__1__class_ONats(_804971))], (20401 ^ _773908) ^ [_1126050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1126050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1126050 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6154 ^ _773908) ^ [_873667] : [hAPP(c_Nat_OSuc, _873667) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27216 ^ _773908) ^ [_1265328, _1265330, _1265332, _1265334, _1265336] : [hAPP(c_Relation_OImage(_1265328, _1265328, _1265330), hAPP(hAPP(c_Set_Oinsert(_1265328), _1265332), c_Orderings_Obot__class_Obot(tc_fun(_1265328, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1265328, _1265328, _1265330), hAPP(hAPP(c_Set_Oinsert(_1265328), _1265334), c_Orderings_Obot__class_Obot(tc_fun(_1265328, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1265328, _1265336, _1265330), hBOOL(hAPP(hAPP(c_member(_1265328), _1265334), _1265336)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1265328, _1265328)), hAPP(hAPP(c_Product__Type_OPair(_1265328, _1265328), _1265332), _1265334)), _1265330)))], (46484 ^ _773908) ^ [_1703806, _1703808] : [-(c_HOL_OThe(_1703806, hAPP(c_fequal, _1703808)) = _1703808)], (39041 ^ _773908) ^ [_1528991, _1528993, _1528995, _1528997, _1528999] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528991, _1528993)), hAPP(hAPP(c_Product__Type_OPair(_1528991, _1528993), _1528995), _1528997)), _1528999)), -(hBOOL(hAPP(hAPP(c_member(_1528993), _1528997), hAPP(c_Relation_ORange(_1528991, _1528993), _1528999))))], (13626 ^ _773908) ^ [_1003295, _1003297, _1003299, _1003301, _1003303, _1003305] : [class_Divides_Osemiring__div(_1003295), c_Divides_Odiv__class_Omod(_1003295, _1003297, _1003299) = c_Divides_Odiv__class_Omod(_1003295, _1003301, _1003299), c_Divides_Odiv__class_Omod(_1003295, _1003303, _1003299) = c_Divides_Odiv__class_Omod(_1003295, _1003305, _1003299), -(c_Divides_Odiv__class_Omod(_1003295, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003295), _1003297), _1003303), _1003299) = c_Divides_Odiv__class_Omod(_1003295, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003295), _1003301), _1003305), _1003299))], (15737 ^ _773908) ^ [_1041666, _1041668, _1041670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041666), _1041668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041666), _1041670)), 15744 ^ _773908 : [(15751 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041668), _1041670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041668), _1041666)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041670), _1041666))))], (15745 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041668), _1041666)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041670), _1041666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041668), _1041670)))]]], (32048 ^ _773908) ^ [_1368012, _1368014, _1368016] : [class_Orderings_Olinorder(_1368012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368012), _1368014), _1368016)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1368012, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1368012, _1368014, _1368016)), hAPP(hAPP(c_Set_Oinsert(_1368012), _1368016), c_Orderings_Obot__class_Obot(tc_fun(_1368012, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1368012, _1368014, _1368016))], (49468 ^ _773908) ^ [_1772512, _1772514, _1772516, _1772518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772512), _1772514)), -(hAPP(hAPP(c_List_Onth(_1772516), c_List_Oreplicate(_1772516, _1772514, _1772518)), _1772512) = _1772518)], (45485 ^ _773908) ^ [_1682476, _1682478, _1682480] : [_1682478 = _1682480, -(hAPP(c_List_Orev(_1682476), _1682478) = hAPP(c_List_Orev(_1682476), _1682480))], (28272 ^ _773908) ^ [_1286954, _1286956, _1286958] : [_1286956 = c_Orderings_Obot__class_Obot(tc_fun(_1286954, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286954, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1286954), _1286956), _1286958))], (7024 ^ _773908) ^ [_887656, _887658] : [7025 ^ _773908 : [(7028 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887658))], (7026 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887656))]], -(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), _887656), _887658))))], (49320 ^ _773908) ^ [_1768981, _1768983] : [-(c_List_Osplice(_1768981, c_List_Olist_ONil(_1768981), _1768983) = _1768983)], (13422 ^ _773908) ^ [_999157, _999159, _999161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999157, tc_HOL_Obool)), _999159), _999161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999157, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999157, tc_HOL_Obool)), _999161)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999157, tc_HOL_Obool)), _999159))))], (3620 ^ _773908) ^ [_828468, _828470, _828472, _828474] : [-(c_List_Olex(_828474, _828470) = c_List_Olex(_828472, _828468)), _828474 = _828472, _828470 = _828468], (40001 ^ _773908) ^ [_1555139, _1555141, _1555143, _1555145] : [_1555139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1555141), hAPP(hAPP(c_List_Olist_OCons(_1555141), _1555143), _1555145)), _1555139) = _1555143)], (25495 ^ _773908) ^ [_1225094, _1225096, _1225098, _1225100, _1225102, _1225104, _1225106] : [hBOOL(hAPP(_1225094, _1225096)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1225098, _1225098)), hAPP(hAPP(c_Product__Type_OPair(_1225098, _1225098), _1225100), _1225102)), hAPP(_1225104, _1225096))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1225106, _1225098), tc_prod(_1225106, _1225098))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1225106, _1225098), tc_prod(_1225106, _1225098)), hAPP(hAPP(c_Product__Type_OPair(_1225106, _1225098), _1225096), _1225100)), hAPP(hAPP(c_Product__Type_OPair(_1225106, _1225098), _1225096), _1225102))), c_Recdef_Osame__fst(_1225106, _1225098, _1225094, _1225104))))], (41101 ^ _773908) ^ [_1583507, _1583509] : [hAPP(c_Finite__Set_Ocard(_1583507), hAPP(c_List_Oset(_1583507), _1583509)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583507)), _1583509), -(hBOOL(hAPP(c_List_Odistinct(_1583507), _1583509)))], (47383 ^ _773908) ^ [_1726283, _1726285, _1726287] : [-(hAPP(c_Relation_ORange(_1726283, _1726285), hAPP(c_Relation_Oconverse(_1726285, _1726283), _1726287)) = hAPP(c_Relation_ODomain(_1726285, _1726283), _1726287))], (51223 ^ _773908) ^ [_1810818, _1810820, _1810822] : [_1810820 = _1810822, -(c_Fun_Obij__betw(_1810818, _1810818, c_Fun_Oid(_1810818), _1810820, _1810822))], (35368 ^ _773908) ^ [_1436504, _1436506, _1436508, _1436510] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436504), _1436506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1436504, tc_HOL_Obool)), _1436506), _1436508)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436504, tc_Nat_Onat), _1436510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1436504, tc_HOL_Obool)), _1436508), _1436506)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436504, tc_Nat_Onat), _1436510), _1436508)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436504, tc_Nat_Onat), _1436510), _1436506)))], (798 ^ _773908) ^ [_786089, _786091, _786093, _786095, _786097, _786099, _786101, _786103] : [-(c_Nat__Transfer_Otransfer__morphism(_786101, _786097, _786093, _786089)), c_Nat__Transfer_Otransfer__morphism(_786103, _786099, _786095, _786091), _786103 = _786101, _786099 = _786097, _786095 = _786093, _786091 = _786089], (49765 ^ _773908) ^ [_1778559, _1778561] : [hBOOL(hAPP(hAPP(c_List_Omember(_1778559), c_List_Olist_ONil(_1778559)), _1778561))], (24297 ^ _773908) ^ [_1199942, _1199944, _1199946] : [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), _1199942), _1199944))), -(hBOOL(hAPP(hAPP(_1199946, _1199942), _1199944))), 24304 ^ _773908 : [(24307 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24303 ^ [_1199942, _1199944, _1199946]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1199946, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24302 ^ [_1199942, _1199944, _1199946])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24303 ^ [_1199942, _1199944, _1199946]))))], (24313 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1199946, 24302 ^ [_1199942, _1199944, _1199946]), 24303 ^ [_1199942, _1199944, _1199946]))], (24305 ^ _773908) ^ [] : [-(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), 24302 ^ [_1199942, _1199944, _1199946]), 24303 ^ [_1199942, _1199944, _1199946]))))]]], (12440 ^ _773908) ^ [_982325, _982327, _982329, _982331, _982333, _982335] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982325), _982327)), _982329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982331), _982333)), _982335), 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), _982331), _982333)), _982335)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982329), _982325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _982331), _982325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _982333), _982327)))], (31127 ^ _773908) ^ [_1345021, _1345023, _1345025, _1345027, _1345029] : [class_Fields_Ofield(_1345021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345023), _1345025)), -(hAPP(_1345027, _1345029) = c_Groups_Ozero__class_Ozero(_1345021)), 31138 ^ _773908 : [(31145 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345023), _1345029), _1345025))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345023, _1345021), _1345027), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345023, tc_HOL_Obool)), _1345025), hAPP(hAPP(c_Set_Oinsert(_1345023), _1345029), c_Orderings_Obot__class_Obot(tc_fun(_1345023, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345023, _1345021), _1345027), _1345025))], (31139 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1345023), _1345029), _1345025)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345023, _1345021), _1345027), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345023, tc_HOL_Obool)), _1345025), hAPP(hAPP(c_Set_Oinsert(_1345023), _1345029), c_Orderings_Obot__class_Obot(tc_fun(_1345023, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345021), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345023, _1345021), _1345027), _1345025)), hAPP(_1345027, _1345029)))]]], (14765 ^ _773908) ^ [_1023504, _1023506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023504)), 14768 ^ _773908 : [(14775 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023504), _1023506)), -(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), _1023506), _1023504))))], (14769 ^ _773908) ^ [] : [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), _1023506), _1023504))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023504), _1023506)))]]], (13428 ^ _773908) ^ [_999326, _999328, _999330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999326, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999326, tc_HOL_Obool)), _999328)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_999326, tc_HOL_Obool)), _999330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999326, tc_HOL_Obool)), _999330), _999328)))], (40569 ^ _773908) ^ [_1568957, _1568959, _1568961, _1568963, _1568965] : [-(hAPP(hAPP(c_List_Olist__update(_1568957, hAPP(hAPP(c_List_Olist_OCons(_1568957), _1568959), _1568961)), hAPP(c_Nat_OSuc, _1568963)), _1568965) = hAPP(hAPP(c_List_Olist_OCons(_1568957), _1568959), hAPP(hAPP(c_List_Olist__update(_1568957, _1568961), _1568963), _1568965)))], (41661 ^ _773908) ^ [_1594635, _1594637] : [class_Groups_Ocomm__monoid__add(_1594635), hBOOL(hAPP(c_List_Odistinct(_1594635), _1594637)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1594635), _1594637) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1594635, _1594635), c_COMBI(_1594635)), hAPP(c_List_Oset(_1594635), _1594637)))], (7181 ^ _773908) ^ [_890045, _890047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890045)), hAPP(c_Nat_OSuc, _890047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890045), _890047)))], (10715 ^ _773908) ^ [_951667, _951669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951667), _951669)), 10718 ^ _773908 : [(10721 ^ _773908) ^ [] : [_951667 = _951669], (10719 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _951667), _951669)))]]], (17387 ^ _773908) ^ [_1073857, _1073859, _1073861] : [class_Groups_Omonoid__mult(_1073857), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073857), hAPP(hAPP(c_Power_Opower__class_Opower(_1073857), _1073859), _1073861)), _1073859) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073857), _1073859), hAPP(hAPP(c_Power_Opower__class_Opower(_1073857), _1073859), _1073861)))], (45927 ^ _773908) ^ [_1691724, _1691726, _1691728, _1691730, _1691732] : [c_List_OdropWhile(_1691724, _1691726, _1691728) = hAPP(hAPP(c_List_Olist_OCons(_1691724), _1691730), _1691732), 45930 ^ _773908 : [(45933 ^ _773908) ^ [] : [hBOOL(hAPP(_1691726, _1691730))], (45931 ^ _773908) ^ [] : [-(_1691728 = hAPP(hAPP(c_List_Oappend(_1691724), c_List_OtakeWhile(_1691724, _1691726, _1691728)), hAPP(hAPP(c_List_Olist_OCons(_1691724), _1691730), _1691732)))]]], (41764 ^ _773908) ^ [_1596718, _1596720] : [-(_1596718 = c_List_Olist_ONil(_1596720)), -(hAPP(hAPP(c_List_Oappend(_1596720), c_List_Obutlast(_1596720, _1596718)), hAPP(hAPP(c_List_Olist_OCons(_1596720), c_List_Olast(_1596720, _1596718)), c_List_Olist_ONil(_1596720))) = _1596718)], (10025 ^ _773908) ^ [_940601, _940603, _940605] : [class_Rings_Olinordered__idom(_940601), 10028 ^ _773908 : [(10035 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _940603), _940605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940601), hAPP(c_Int_Oring__1__class_Oof__int(_940601), _940603)), hAPP(c_Int_Oring__1__class_Oof__int(_940601), _940605))))], (10029 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940601), hAPP(c_Int_Oring__1__class_Oof__int(_940601), _940603)), hAPP(c_Int_Oring__1__class_Oof__int(_940601), _940605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _940603), _940605)))]]], (26189 ^ _773908) ^ [_1238691, _1238693, _1238695, _1238697] : [class_Lattices_Olattice(_1238691), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238691), _1238693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238691), _1238695), _1238697)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238691), _1238695), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1238691), _1238693), _1238697)))], (17317 ^ _773908) ^ [_1072658, _1072660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1072658)), -(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), _1072658), _1072660))))], (20841 ^ _773908) ^ [_1134347, _1134349, _1134351] : [class_Fields_Olinordered__field__inverse__zero(_1134347), 20844 ^ _773908 : [(20859 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134347), _1134349), _1134351)))), 20860 ^ _773908 : [(20867 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), _1134349), c_Groups_Ozero__class_Ozero(_1134347))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), _1134351), c_Groups_Ozero__class_Ozero(_1134347)))], (20861 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), _1134349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), _1134351))]]], (20845 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134347), _1134349), _1134351))), 20850 ^ _773908 : [(20853 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), _1134351)))], (20851 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), c_Groups_Ozero__class_Ozero(_1134347)), _1134349)))]], 20854 ^ _773908 : [(20857 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), _1134351), c_Groups_Ozero__class_Ozero(_1134347))))], (20855 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134347), _1134349), c_Groups_Ozero__class_Ozero(_1134347))))]]]]], (12276 ^ _773908) ^ [_979502, _979504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _979502)), 12279 ^ _773908 : [(12286 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979502), _979504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _979502)), hAPP(c_Int_Onat, _979504))))], (12280 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _979502)), hAPP(c_Int_Onat, _979504))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979502), _979504)))]]], (6045 ^ _773908) ^ [_871178, _871180] : [hAPP(c_Nat_OSuc, _871178) = hAPP(c_Nat_OSuc, _871180), -(_871178 = _871180)], (988 ^ _773908) ^ [_788912, _788914, _788916, _788918, _788920, _788922] : [-(c_Relation_Orefl__on(_788920, _788916, _788912)), c_Relation_Orefl__on(_788922, _788918, _788914), _788922 = _788920, _788918 = _788916, _788914 = _788912], (50655 ^ _773908) ^ [_1798794, _1798796] : [-(c_Equiv__Relations_Opart__equivp(_1798794, _1798796)), 50658 ^ _773908 : [(50659 ^ _773908) ^ [_1798914] : [hBOOL(hAPP(hAPP(_1798796, _1798914), _1798914))]], 50676 ^ _773908 : [(50679 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798796, 50661 ^ [_1798794, _1798796]), 50661 ^ [_1798794, _1798796])))], (50681 ^ _773908) ^ [] : [-(hAPP(_1798796, 50660 ^ [_1798794, _1798796]) = hAPP(_1798796, 50661 ^ [_1798794, _1798796]))], (50683 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1798796, 50660 ^ [_1798794, _1798796]), 50661 ^ [_1798794, _1798796]))], (50677 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798796, 50660 ^ [_1798794, _1798796]), 50660 ^ [_1798794, _1798796])))]], 50664 ^ _773908 : [(50667 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(_1798796, 50660 ^ [_1798794, _1798796]), 50660 ^ [_1798794, _1798796])), hBOOL(hAPP(hAPP(_1798796, 50661 ^ [_1798794, _1798796]), 50661 ^ [_1798794, _1798796])), hAPP(_1798796, 50660 ^ [_1798794, _1798796]) = hAPP(_1798796, 50661 ^ [_1798794, _1798796])], (50665 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1798796, 50660 ^ [_1798794, _1798796]), 50661 ^ [_1798794, _1798796])))]]], (11764 ^ _773908) ^ [_970426] : [class_Rings_Olinordered__semidom(_970426), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970426), c_Groups_Ozero__class_Ozero(_970426)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970426), c_Groups_Oone__class_Oone(_970426)), c_Groups_Oone__class_Oone(_970426)))))], (32458 ^ _773908) ^ [_1376353, _1376355] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1376353, tc_HOL_Obool)), _1376355), hAPP(c_Set_OPow(_1376353), _1376355))))], (51468 ^ _773908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (22989 ^ _773908) ^ [_1172981, _1172983, _1172985, _1172987] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1172981, _1172983, _1172985, c_Code__Numeral_OSuc__code__numeral(_1172987)) = hAPP(hAPP(_1172985, _1172987), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1172981, _1172983, _1172985, _1172987)))], (39568 ^ _773908) ^ [_1542844, _1542846, _1542848, _1542850, _1542852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1542844), tc_List_Olist(_1542844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1542844), tc_List_Olist(_1542844)), hAPP(hAPP(c_List_Oappend(_1542844), _1542846), _1542848)), hAPP(hAPP(c_List_Oappend(_1542844), _1542846), _1542850))), c_List_Olexord(_1542844, _1542852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542844, _1542844)), hAPP(hAPP(c_Product__Type_OPair(_1542844, _1542844), 39573 ^ [_1542844, _1542846, _1542848, _1542850, _1542852]), 39573 ^ [_1542844, _1542846, _1542848, _1542850, _1542852])), _1542852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1542844), tc_List_Olist(_1542844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1542844), tc_List_Olist(_1542844)), _1542848), _1542850)), c_List_Olexord(_1542844, _1542852))))], (49817 ^ _773908) ^ [_1779723, _1779725, _1779727, _1779729] : [class_Groups_Ocomm__monoid__add(_1779723), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1779725, tc_HOL_Obool)), _1779727)), 49827 ^ _773908 : [(49830 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1779725), 49826 ^ [_1779723, _1779725, _1779727, _1779729]))], (49828 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1779725, tc_HOL_Obool)), 49826 ^ [_1779723, _1779725, _1779727, _1779729]), _1779727)))]], 49834 ^ _773908 : [(49838 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1779725, tc_HOL_Obool)), 49836 ^ [_1779723, _1779725, _1779727, _1779729]), _1779727)))], (49835 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1779725, tc_HOL_Obool)), 49833 ^ [_1779723, _1779725, _1779727, _1779729]), _1779727)))], (49847 ^ _773908) ^ [] : [hAPP(_1779729, 49841 ^ [_1779723, _1779725, _1779727, _1779729]) = c_Groups_Ozero__class_Ozero(_1779723)], (49843 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779725), 49841 ^ [_1779723, _1779725, _1779727, _1779729]), 49833 ^ [_1779723, _1779725, _1779727, _1779729])))], (49845 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779725), 49841 ^ [_1779723, _1779725, _1779727, _1779729]), 49836 ^ [_1779723, _1779725, _1779727, _1779729])))], (49840 ^ _773908) ^ [] : [49833 ^ [_1779723, _1779725, _1779727, _1779729] = 49836 ^ [_1779723, _1779725, _1779727, _1779729]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1779725, _1779723), _1779729), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1779725, tc_HOL_Obool), _1779727)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1779725, tc_HOL_Obool), _1779723), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1779725, _1779723), _1779729)), _1779727))], (41410 ^ _773908) ^ [_1589994, _1589996, _1589998] : [-(_1589994 = c_List_Olist_ONil(_1589996)), -(c_List_Olast(_1589996, hAPP(hAPP(c_List_Olist_OCons(_1589996), _1589998), _1589994)) = c_List_Olast(_1589996, _1589994))], (44465 ^ _773908) ^ [_1660403, _1660405] : [c_List_Oconcat(_1660403, _1660405) = c_List_Olist_ONil(_1660403), 44468 ^ _773908 : [(44469 ^ _773908) ^ [_1660494] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1660403)), _1660494), hAPP(c_List_Oset(tc_List_Olist(_1660403)), _1660405))), -(_1660494 = c_List_Olist_ONil(_1660403))]]], (46486 ^ _773908) ^ [_1703837, _1703839] : [-(c_HOL_OThe(_1703837, hAPP(hAPP(c_COMBC(_1703837, _1703837, tc_HOL_Obool), c_fequal), _1703839)) = _1703839)], (32286 ^ _773908) ^ [_1372722, _1372724, _1372726] : [class_Orderings_Olinorder(_1372722), hAPP(_1372724, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372722), 32291 ^ [_1372722, _1372724, _1372726]), 32292 ^ [_1372722, _1372724, _1372726])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372722), hAPP(_1372724, 32291 ^ [_1372722, _1372724, _1372726])), hAPP(_1372724, 32292 ^ [_1372722, _1372724, _1372726])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372722), _1372726)), -(_1372726 = c_Orderings_Obot__class_Obot(tc_fun(_1372722, tc_HOL_Obool))), -(hAPP(_1372724, c_Big__Operators_Olinorder__class_OMin(_1372722, _1372726)) = c_Big__Operators_Olinorder__class_OMin(_1372722, hAPP(c_Set_Oimage(_1372722, _1372722, _1372724), _1372726)))], (26017 ^ _773908) ^ [_1235066, _1235068, _1235070] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1235066, tc_HOL_Obool)), _1235068), _1235070) = _1235070, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1235066, tc_HOL_Obool)), _1235068), _1235070)))], (51854 ^ _773908) ^ [_1817818, _1817820, _1817822, _1817824, _1817826, _1817828] : [-(hAPP(hAPP(hAPP(c_COMBS(_1817818, _1817820, _1817822), _1817824), _1817826), _1817828) = hAPP(hAPP(_1817824, _1817828), hAPP(_1817826, _1817828)))], (47309 ^ _773908) ^ [_1724534, _1724536, _1724538, _1724540] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724534), tc_List_Olist(_1724534))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724534), tc_List_Olist(_1724534)), _1724536), _1724538)), c_List_Olistrel1(_1724534, hAPP(c_Relation_Oconverse(_1724534, _1724534), _1724540)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724534), tc_List_Olist(_1724534))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724534), tc_List_Olist(_1724534)), _1724536), _1724538)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1724534), tc_List_Olist(_1724534)), c_List_Olistrel1(_1724534, _1724540)))))], (26291 ^ _773908) ^ [_1241269, _1241271, _1241273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241269, tc_HOL_Obool)), _1241271), _1241273)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241269, tc_HOL_Obool)), _1241271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241269, tc_HOL_Obool)), _1241273), _1241271)) = _1241273)], (12004 ^ _773908) ^ [_974950, _974952, _974954, _974956, _974958] : [class_Rings_Olinordered__semiring__strict(_974950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974950), _974952), _974954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974950), _974956), _974958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974950), c_Groups_Ozero__class_Ozero(_974950)), _974954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974950), c_Groups_Ozero__class_Ozero(_974950)), _974956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974950), _974952), _974956)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974950), _974954), _974958))))], (17111 ^ _773908) ^ [_1068923, _1068925, _1068927, _1068929] : [class_Int_Onumber__ring(_1068923), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068923), hAPP(c_Int_Onumber__class_Onumber__of(_1068923), _1068925)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068923), _1068927), hAPP(c_Int_Onumber__class_Onumber__of(_1068923), _1068929))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068923), hAPP(c_Int_Onumber__class_Onumber__of(_1068923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068925), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068929)))), _1068927))], (19907 ^ _773908) ^ [_1117451] : [c_Int_OBit0(_1117451) = c_Int_OMin], (15301 ^ _773908) ^ [_1033358, _1033360, _1033362, _1033364, _1033366] : [class_Groups_Oordered__ab__group__add(_1033358), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033358), _1033360), _1033362) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033358), _1033364), _1033366), 15308 ^ _773908 : [(15315 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033358), _1033364), _1033366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033358), _1033360), _1033362)))], (15309 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033358), _1033360), _1033362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033358), _1033364), _1033366)))]]], (17569 ^ _773908) ^ [_1077233, _1077235, _1077237, _1077239] : [class_Rings_Olinordered__semidom(_1077233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077233), hAPP(hAPP(c_Power_Opower__class_Opower(_1077233), _1077235), _1077237)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077233), _1077239), _1077237))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077233), c_Groups_Ozero__class_Ozero(_1077233)), _1077239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077233), _1077235), _1077239)))], (20287 ^ _773908) ^ [_1124055, _1124057] : [class_Rings_Olinordered__idom(_1124055), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124055), hAPP(c_Groups_Oabs__class_Oabs(_1124055), _1124057)), 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(_1124055), _1124057), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (23865 ^ _773908) ^ [_1191155, _1191157, _1191159] : [23867 ^ _773908 : [(23870 ^ _773908) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1191155, _1191157), 23866 ^ [_1191155, _1191157, _1191159]))], (23868 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1191157, 23866 ^ [_1191155, _1191157, _1191159]), _1191159)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1191155, _1191157), _1191159)))], (51036 ^ _773908) ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712] : [class_Groups_Ocomm__monoid__mult(_1806702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1806704), _1806706)), 51046 ^ _773908 : [(51049 ^ _773908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806708), hAPP(_1806710, 51045 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712])))], (51047 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806704), 51045 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712]), _1806706)))]], 51053 ^ _773908 : [(51057 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806704), 51055 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712]), _1806706)))], (51059 ^ _773908) ^ [] : [51052 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712] = 51055 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712]], (51061 ^ _773908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1806708, tc_HOL_Obool)), hAPP(_1806710, 51052 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712])), hAPP(_1806710, 51055 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712])) = c_Orderings_Obot__class_Obot(tc_fun(_1806708, tc_HOL_Obool))], (51054 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806704), 51052 ^ [_1806702, _1806704, _1806706, _1806708, _1806710, _1806712]), _1806706)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1806702, _1806708, c_Groups_Otimes__class_Otimes(_1806702)), _1806712), c_Groups_Oone__class_Oone(_1806702)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1806704, tc_fun(_1806708, tc_HOL_Obool)), _1806706), _1806710)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1806702, _1806704, c_Groups_Otimes__class_Otimes(_1806702)), hAPP(hAPP(c_COMBB(tc_fun(_1806708, tc_HOL_Obool), _1806702, _1806704), hAPP(hAPP(c_Finite__Set_Ofold__image(_1806702, _1806708, c_Groups_Otimes__class_Otimes(_1806702)), _1806712), c_Groups_Oone__class_Oone(_1806702))), _1806710)), c_Groups_Oone__class_Oone(_1806702)), _1806706))], (39306 ^ _773908) ^ [_1537357, _1537359, _1537361, _1537363] : [-(c_List_Osublist(_1537357, hAPP(hAPP(c_List_Olist_OCons(_1537357), _1537359), _1537361), _1537363) = hAPP(hAPP(c_List_Oappend(_1537357), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1537357)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1537363)), hAPP(hAPP(c_List_Olist_OCons(_1537357), _1537359), c_List_Olist_ONil(_1537357))), c_List_Olist_ONil(_1537357))), c_List_Osublist(_1537357, _1537361, 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)), _1537363)))))], (5811 ^ _773908) ^ [_866186, _866188, _866190] : [class_Orderings_Obot(_866186), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_866188, _866186)), _866190) = c_Orderings_Obot__class_Obot(_866186))], (1674 ^ _773908) ^ [_797819, _797821] : [-(class_Groups_Oab__semigroup__add(_797819)), _797821 = _797819, class_Groups_Oab__semigroup__add(_797821)], (49150 ^ _773908) ^ [_1765057, _1765059, _1765061, _1765063] : [c_List_Olist__ex1(_1765057, _1765059, hAPP(hAPP(c_List_Olist_OCons(_1765057), _1765061), _1765063)), 49153 ^ _773908 : [(49160 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1765059, _1765061))), -(c_List_Olist__ex1(_1765057, _1765059, _1765063))], (49154 ^ _773908) ^ [] : [hBOOL(hAPP(_1765059, _1765061)), -(c_List_Olist__all(_1765057, hAPP(hAPP(c_COMBS(_1765057, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765057), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765057), c_fNot), _1765059))), hAPP(c_fequal, _1765061)), _1765063))]]], (26438 ^ _773908) ^ [_1247231, _1247233, _1247235, _1247237, _1247239, _1247241] : [hBOOL(hAPP(hAPP(_1247231, _1247233), _1247235)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247237, tc_fun(_1247239, tc_HOL_Obool))), _1247231), _1247241), _1247233), _1247235)))], (43192 ^ _773908) ^ [_1631755, _1631757, _1631759, _1631761] : [-(hBOOL(hAPP(c_List_Olistsp(_1631755, hAPP(hAPP(c_COMBS(_1631755, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631755), c_fconj), _1631757)), _1631759)), _1631761))), hBOOL(hAPP(c_List_Olistsp(_1631755, _1631757), _1631761)), hBOOL(hAPP(c_List_Olistsp(_1631755, _1631759), _1631761))], (26485 ^ _773908) ^ [_1248429, _1248431, _1248433, _1248435, _1248437, _1248439] : [hBOOL(hAPP(hAPP(c_member(_1248429), _1248431), _1248433)), _1248435 = hAPP(_1248437, _1248431), -(hBOOL(hAPP(hAPP(c_member(_1248439), _1248435), hAPP(c_Set_Oimage(_1248429, _1248439, _1248437), _1248433))))], (15151 ^ _773908) ^ [_1030606, _1030608, _1030610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030606)), 15157 ^ _773908 : [(15160 ^ _773908) ^ [] : [hBOOL(hAPP(_1030608, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15156 ^ [_1030606, _1030608, _1030610]), _1030606)))], (15158 ^ _773908) ^ [] : [-(hBOOL(hAPP(_1030608, 15156 ^ [_1030606, _1030608, _1030610])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030610)), 15165 ^ _773908 : [(15166 ^ _773908) ^ [_1030895] : [hBOOL(hAPP(_1030608, _1030895)), -(hBOOL(hAPP(_1030608, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030610), _1030606)))))]]], (19377 ^ _773908) ^ [_1108526] : [c_Int_OPls = c_Int_OBit1(_1108526)], (46965 ^ _773908) ^ [_1716141, _1716143] : [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), _1716141), _1716143)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1716141), _1716143)))], (7505 ^ _773908) ^ [_895381, _895383, _895385, _895387, _895389, _895391] : [hBOOL(hAPP(_895381, _895383)), c_Natural_Oevaln(_895385, _895383, _895387, _895389), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_895381, _895385, _895391), _895383, _895387, _895389))], (32203 ^ _773908) ^ [_1371025, _1371027, _1371029, _1371031] : [class_Orderings_Olinorder(_1371025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371025), _1371027), _1371029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371025), _1371029), _1371031)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1371025, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1371025, _1371027, _1371029)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1371025, _1371029, _1371031)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1371025, _1371027, _1371031))], (48269 ^ _773908) ^ [_1746944, _1746946, _1746948, _1746950, _1746952] : [class_Complete__Lattice_Ocomplete__lattice(_1746944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1746946), _1746948)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1746944), _1746950), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1746946, _1746944), _1746948), _1746952)) = hAPP(hAPP(c_Finite__Set_Ofold(_1746946, _1746944, hAPP(hAPP(c_COMBB(_1746944, tc_fun(_1746944, _1746944), _1746946), c_Lattices_Osemilattice__sup__class_Osup(_1746944)), _1746952)), _1746950), _1746948))], (51716 ^ _773908) ^ [_1816329, _1816331] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1816329, _1816331)))], (4568 ^ _773908) ^ [_843408, _843410] : [_843410 = _843408, -(c_List_Oappend(_843410) = c_List_Oappend(_843408))], (43906 ^ _773908) ^ [_1647640, _1647642, _1647644, _1647646] : [hBOOL(hAPP(hAPP(c_member(_1647640), _1647642), hAPP(c_Relation_ODomain(_1647640, _1647644), _1647646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647640, _1647644)), hAPP(hAPP(c_Product__Type_OPair(_1647640, _1647644), _1647642), 43909 ^ [_1647640, _1647642, _1647644, _1647646])), _1647646)))], (44585 ^ _773908) ^ [_1664007, _1664009, _1664011, _1664013] : [-(c_List_Oconcat(_1664007, hAPP(hAPP(c_List_Omap(_1664009, tc_List_Olist(_1664007)), hAPP(hAPP(c_COMBC(_1664009, tc_List_Olist(_1664007), tc_List_Olist(_1664007)), hAPP(hAPP(c_COMBB(_1664007, tc_fun(tc_List_Olist(_1664007), tc_List_Olist(_1664007)), _1664009), c_List_Olist_OCons(_1664007)), _1664011)), c_List_Olist_ONil(_1664007))), _1664013)) = hAPP(hAPP(c_List_Omap(_1664009, _1664007), _1664011), _1664013))], (7273 ^ _773908) ^ [_891535, _891537, _891539, _891541] : [hAPP(c_Com_Ocom_OBODY, _891535) = c_Com_Ocom_OCall(_891537, _891539, _891541)], (64 ^ _773908) ^ [_774736, _774738, _774740, _774742, _774744, _774746, _774748, _774750, _774752, _774754, _774756, _774758] : [-(c_Nitpick_Ofold__graph_H(_774756, _774752, _774748, _774744, _774740, _774736)), c_Nitpick_Ofold__graph_H(_774758, _774754, _774750, _774746, _774742, _774738), _774758 = _774756, _774754 = _774752, _774750 = _774748, _774746 = _774744, _774742 = _774740, _774738 = _774736], (20019 ^ _773908) ^ [_1119394, _1119396] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1119394)), c_Int_OBit0(_1119396)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1119394), _1119396)))], (47720 ^ _773908) ^ [_1735403, _1735405, _1735407, _1735409] : [class_Orderings_Oorder(_1735403), class_Enum_Oenum(_1735405), 47727 ^ _773908 : [(47734 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1735405), hAPP(hAPP(c_COMBS(_1735405, _1735403, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1735403, tc_fun(_1735403, tc_HOL_Obool), _1735405), c_Orderings_Oord__class_Oless__eq(_1735403)), _1735407)), _1735409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1735405, _1735403)), _1735407), _1735409)))], (47728 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1735405, _1735403)), _1735407), _1735409)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1735405), hAPP(hAPP(c_COMBS(_1735405, _1735403, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1735403, tc_fun(_1735403, tc_HOL_Obool), _1735405), c_Orderings_Oord__class_Oless__eq(_1735403)), _1735407)), _1735409))))]]], (50035 ^ _773908) ^ [_1785078] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785078, tc_HOL_Obool) = c_Set_OBex(_1785078))], (26299 ^ _773908) ^ [] : [-(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)))))], (14454 ^ _773908) ^ [_1018386, _1018388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018386), 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)), _1018388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018386), _1018388)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25041 ^ _773908) ^ [_1215730] : [class_Orderings_Oord(_1215730), -(c_Orderings_Oord__class_Omin(_1215730) = c_Orderings_Oord_Omin(_1215730, c_Orderings_Oord__class_Oless__eq(_1215730)))], (5340 ^ _773908) ^ [_855504, _855506, _855508, _855510] : [-(c_Quickcheck_Obeyond(_855510, _855506) = c_Quickcheck_Obeyond(_855508, _855504)), _855510 = _855508, _855506 = _855504], (2746 ^ _773908) ^ [_814731, _814733] : [_814733 = _814731, -(c_Nitpick_Oone__frac(_814733) = c_Nitpick_Oone__frac(_814731))], (10959 ^ _773908) ^ [_956193, _956195, _956197] : [class_Groups_Oordered__comm__monoid__add(_956193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956193), c_Groups_Ozero__class_Ozero(_956193)), _956195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956193), c_Groups_Ozero__class_Ozero(_956193)), _956197)), 10970 ^ _773908 : [(10979 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956193), _956195), _956197) = c_Groups_Ozero__class_Ozero(_956193)), _956195 = c_Groups_Ozero__class_Ozero(_956193), _956197 = c_Groups_Ozero__class_Ozero(_956193)], (10971 ^ _773908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956193), _956195), _956197) = c_Groups_Ozero__class_Ozero(_956193), 10974 ^ _773908 : [(10977 ^ _773908) ^ [] : [-(_956197 = c_Groups_Ozero__class_Ozero(_956193))], (10975 ^ _773908) ^ [] : [-(_956195 = c_Groups_Ozero__class_Ozero(_956193))]]]]], (14438 ^ _773908) ^ [_1018134, _1018136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018136)), -(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), _1018134), _1018136))))], (3288 ^ _773908) ^ [_823232, _823234, _823236, _823238, _823240, _823242] : [-(c_Enum_On__lists(_823242, _823238, _823234) = c_Enum_On__lists(_823240, _823236, _823232)), _823242 = _823240, _823238 = _823236, _823234 = _823232], (16457 ^ _773908) ^ [_1056095, _1056097, _1056099] : [class_Groups_Oordered__ab__group__add__abs(_1056095), -(hAPP(c_Groups_Oabs__class_Oabs(_1056095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056095), _1056097), _1056099)) = hAPP(c_Groups_Oabs__class_Oabs(_1056095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056095), _1056099), _1056097)))], (2772 ^ _773908) ^ [_815114, _815116, _815118, _815120] : [-(c_Set_Othe__elem(_815120, _815116) = c_Set_Othe__elem(_815118, _815114)), _815120 = _815118, _815116 = _815114], (47092 ^ _773908) ^ [_1719458, _1719460] : [-(c_Transitive__Closure_Otrancl(_1719458, _1719460) = hAPP(hAPP(c_Relation_Orel__comp(_1719458, _1719458, _1719458), c_Transitive__Closure_Ortrancl(_1719458, _1719460)), _1719460))], (43262 ^ _773908) ^ [_1633165, _1633167, _1633169] : [class_Orderings_Olinorder(_1633165), -(c_List_Oremove1(_1633165, _1633167, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1633165, _1633165, c_COMBI(_1633165)), _1633167), _1633169)) = _1633169)], (6632 ^ _773908) ^ [_881644, _881646, _881648] : [class_Orderings_Oorder(_881644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881644), _881646), _881648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881644), _881648), _881646))], (32109 ^ _773908) ^ [_1369260, _1369262, _1369264] : [class_Orderings_Oorder(_1369260), 32112 ^ _773908 : [(32119 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369260), _1369262), _1369264))), -(c_Orderings_Obot__class_Obot(tc_fun(_1369260, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1369260, _1369262, _1369264))], (32113 ^ _773908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1369260, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1369260, _1369262, _1369264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1369260), _1369262), _1369264))]]], (47770 ^ _773908) ^ [_1736246, _1736248] : [class_Enum_Oenum(_1736246), 47773 ^ _773908 : [(47780 ^ _773908) ^ [] : [hBOOL(hAPP(_1736248, 47781 ^ [_1736246, _1736248])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736246), _1736248)))], (47774 ^ _773908) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736246), _1736248)), 47777 ^ _773908 : [(47778 ^ _773908) ^ [_1736372] : [-(hBOOL(hAPP(_1736248, _1736372)))]]]]], (25613 ^ _773908) ^ [_1227621, _1227623, _1227625, _1227627] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227621), _1227627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227625), _1227623), -(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), _1227621), _1227623)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1227625), _1227627))), c_Int_Ointrel)))], (33784 ^ _773908) ^ [_1401583, _1401585, _1401587, _1401589, _1401591, _1401593] : [c_Fun_Oinj__on(_1401583, _1401585, _1401587, _1401589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401585, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1401583, _1401585, _1401587), _1401589)), _1401591)), c_Fun_Oinj__on(_1401585, _1401583, _1401593, _1401591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401583, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1401585, _1401583, _1401593), _1401591)), _1401589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401583), _1401589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401585), _1401591)), -(hAPP(c_Finite__Set_Ocard(_1401583), _1401589) = hAPP(c_Finite__Set_Ocard(_1401585), _1401591))], (4980 ^ _773908) ^ [_849956, _849958, _849960, _849962] : [-(c_Product__Type_Osnd(_849962, _849958) = c_Product__Type_Osnd(_849960, _849956)), _849962 = _849960, _849958 = _849956], (22551 ^ _773908) ^ [_1164942, _1164944] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164942), hAPP(c_Int_Onumber__class_Onumber__of(_1164942), c_Int_OMin)), _1164944) = hAPP(c_Groups_Ouminus__class_Ouminus(_1164942), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164942), c_Groups_Oone__class_Oone(_1164942)), _1164944))), class_Fields_Ofield__inverse__zero(_1164942), class_Int_Onumber__ring(_1164942)], (41953 ^ _773908) ^ [_1601268, _1601270, _1601272, _1601274] : [-(hAPP(hAPP(c_List_Omap(_1601268, _1601270), _1601272), hAPP(c_List_Otl(_1601268), _1601274)) = hAPP(c_List_Otl(_1601270), hAPP(hAPP(c_List_Omap(_1601268, _1601270), _1601272), _1601274)))], (42242 ^ _773908) ^ [_1610254, _1610256, _1610258, _1610260, _1610262] : [42244 ^ _773908 : [(42247 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1610254), _1610256), hAPP(_1610262, 42243 ^ [_1610254, _1610256, _1610258, _1610260, _1610262])))], (42245 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610258), 42243 ^ [_1610254, _1610256, _1610258, _1610260, _1610262]), _1610260)))]], -(hBOOL(hAPP(hAPP(c_member(_1610254), _1610256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610258, tc_fun(_1610254, tc_HOL_Obool)), _1610260), _1610262))))], (11559 ^ _773908) ^ [_966959, _966961, _966963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966961), _966963)), -(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, _966959)), _966961)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _966959)), _966963))))], (47371 ^ _773908) ^ [_1726005, _1726007, _1726009] : [c_Equiv__Relations_Oequiv(_1726005, _1726007, _1726009), -(hAPP(hAPP(c_Relation_Orel__comp(_1726005, _1726005, _1726005), hAPP(c_Relation_Oconverse(_1726005, _1726005), _1726009)), _1726009) = _1726009)], (15945 ^ _773908) ^ [_1046249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046249)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046249), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1046249)], (9935 ^ _773908) ^ [_939309, _939311, _939313] : [class_Orderings_Olinorder(_939309), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939309), _939311), _939313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939309), _939313), _939311)))], (722 ^ _773908) ^ [_784881, _784883, _784885, _784887, _784889, _784891, _784893, _784895, _784897, _784899, _784901, _784903] : [-(c_Finite__Set_Ofolding__image__simple__idem(_784901, _784897, _784893, _784889, _784885, _784881)), c_Finite__Set_Ofolding__image__simple__idem(_784903, _784899, _784895, _784891, _784887, _784883), _784903 = _784901, _784899 = _784897, _784895 = _784893, _784891 = _784889, _784887 = _784885, _784883 = _784881], (6876 ^ _773908) ^ [_885204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885204), _885204))], (36938 ^ _773908) ^ [_1469800, _1469802, _1469804] : [class_Lattices_Oab__semigroup__idem__mult(_1469800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469800), _1469802)), -(_1469802 = c_Orderings_Obot__class_Obot(tc_fun(_1469800, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469800), _1469804)), -(_1469804 = c_Orderings_Obot__class_Obot(tc_fun(_1469800, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1469800, c_Groups_Otimes__class_Otimes(_1469800)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469800, tc_HOL_Obool)), _1469802), _1469804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469800), hAPP(c_Finite__Set_Ofold1(_1469800, c_Groups_Otimes__class_Otimes(_1469800)), _1469802)), hAPP(c_Finite__Set_Ofold1(_1469800, c_Groups_Otimes__class_Otimes(_1469800)), _1469804)))], (9925 ^ _773908) ^ [_939124, _939126, _939128, _939130, _939132] : [class_Orderings_Oord(_939124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939126, _939124)), _939128), _939130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939124), hAPP(_939128, _939132)), hAPP(_939130, _939132))))], (48533 ^ _773908) ^ [_1752038, _1752040, _1752042] : [class_Orderings_Olinorder(_1752038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752038), _1752040)), -(hBOOL(hAPP(hAPP(c_member(_1752038), _1752042), _1752040))), -(c_Big__Operators_Olinorder__class_OMin(_1752038, hAPP(hAPP(c_Set_Oinsert(_1752038), _1752042), _1752040)) = hAPP(hAPP(c_Finite__Set_Ofold(_1752038, _1752038, c_Orderings_Oord__class_Omin(_1752038)), _1752042), _1752040))], (43521 ^ _773908) ^ [_1638745, _1638747, _1638749] : [-(c_Enum_Oproduct(_1638745, _1638747, c_List_Olist_ONil(_1638745), _1638749) = c_List_Olist_ONil(tc_prod(_1638745, _1638747)))], (38243 ^ _773908) ^ [_1503967, _1503969] : [-(hAPP(c_Set_OPow(_1503967), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1503967, tc_HOL_Obool)), _1503969)) = hAPP(c_Set_OCollect(tc_fun(_1503967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1503967, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1503967, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1503967, tc_HOL_Obool), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1503967, tc_HOL_Obool)), c_COMBS(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1503967, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1503967, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1503967, tc_HOL_Obool), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_fun(_1503967, tc_HOL_Obool)), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_fun(_1503967, tc_HOL_Obool)), tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1503967, tc_HOL_Obool)), c_COMBB(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1503967, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1503967, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503967, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1503967, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1503967, tc_HOL_Obool)), _1503969)), c_Set_OPow(_1503967))))))], (39266 ^ _773908) ^ [_1535664, _1535666, _1535668, _1535670, _1535672, _1535674] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1535664), tc_List_Olist(_1535664))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1535664), tc_List_Olist(_1535664)), hAPP(hAPP(c_List_Olist_OCons(_1535664), _1535666), _1535668)), hAPP(hAPP(c_List_Olist_OCons(_1535664), _1535670), _1535672))), c_List_Olexord(_1535664, _1535674)))), 39267 ^ _773908 : [(39270 ^ _773908) ^ [] : [_1535666 = _1535670, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1535664), tc_List_Olist(_1535664))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1535664), tc_List_Olist(_1535664)), _1535668), _1535672)), c_List_Olexord(_1535664, _1535674)))], (39268 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535664, _1535664)), hAPP(hAPP(c_Product__Type_OPair(_1535664, _1535664), _1535666), _1535670)), _1535674))]]], (8701 ^ _773908) ^ [_918015] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918015))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29883 ^ _773908) ^ [_1319493, _1319495, _1319497] : [class_Orderings_Olinorder(_1319493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319493), _1319495)), hBOOL(hAPP(hAPP(c_member(_1319493), _1319497), _1319495)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319493), _1319497), c_Big__Operators_Olattice_OSup__fin(_1319493, c_Orderings_Oord__class_Omax(_1319493), _1319495)) = _1319497)], (7565 ^ _773908) ^ [_896502, _896504, _896506, _896508, _896510, _896512] : [c_Com_Ocom_OLocal(_896502, _896504, _896506) = c_Com_Ocom_OCond(_896508, _896510, _896512)], (2264 ^ _773908) ^ [_806954, _806956, _806958, _806960, _806962, _806964, _806966, _806968] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_806968, _806964, _806960, _806956) = c_Nat_Osemiring__1__class_Oof__nat__aux(_806966, _806962, _806958, _806954)), _806968 = _806966, _806964 = _806962, _806960 = _806958, _806956 = _806954], (27107 ^ _773908) ^ [_1262590, _1262592, _1262594] : [27109 ^ _773908 : [(27112 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1262590), 27108 ^ [_1262590, _1262592, _1262594]), c_Wellfounded_Oacc(_1262590, _1262594)))], (27110 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1262590, _1262590)), hAPP(hAPP(c_Product__Type_OPair(_1262590, _1262590), 27108 ^ [_1262590, _1262592, _1262594]), _1262592)), _1262594)))]], -(hBOOL(hAPP(hAPP(c_member(_1262590), _1262592), c_Wellfounded_Oacc(_1262590, _1262594))))], (6692 ^ _773908) ^ [_882576, _882578, _882580] : [class_Orderings_Oorder(_882576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882576), _882578), _882580)), _882578 = _882580], (17887 ^ _773908) ^ [_1082736] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1082736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11882 ^ _773908) ^ [_972605, _972607, _972609, _972611] : [class_Rings_Olinordered__semiring__strict(_972605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972605), _972607), _972609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972605), _972607), _972611))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972605), c_Groups_Ozero__class_Ozero(_972605)), _972607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972605), _972609), _972611)))], (49987 ^ _773908) ^ [_1783851, _1783853, _1783855] : [-(c_Random__Sequence_Oempty(_1783851, _1783853, _1783855) = 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(_1783851)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1783851)))], (44144 ^ _773908) ^ [_1653697, _1653699, _1653701] : [class_Complete__Lattice_Ocomplete__lattice(_1653697), hBOOL(hAPP(hAPP(c_member(_1653697), _1653699), _1653701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653697), c_Complete__Lattice_OInf__class_OInf(_1653697, _1653701)), _1653699)))], (43709 ^ _773908) ^ [_1643141, _1643143, _1643145, _1643147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1643141, _1643143), tc_HOL_Obool)), _1643145), _1643147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643141, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1643141, _1643143), _1643145)), hAPP(c_Relation_ODomain(_1643141, _1643143), _1643147))))], (48041 ^ _773908) ^ [_1741894, _1741896, _1741898] : [-(c_List_Olist__ex(_1741894, _1741896, _1741898)), 48042 ^ _773908 : [(48043 ^ _773908) ^ [_1741951] : [hBOOL(hAPP(hAPP(c_member(_1741894), _1741951), hAPP(c_List_Oset(_1741894), _1741898))), hBOOL(hAPP(_1741896, _1741951))]]], (12620 ^ _773908) ^ [_985443, _985445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985443)), hAPP(c_Nat_OSuc, _985445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985443), _985445)))], (23379 ^ _773908) ^ [_1180844, _1180846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180846)), -(c_Divides_OposDivAlg(_1180844, _1180846) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180844), _1180846)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1180844, _1180846)))], (14081 ^ _773908) ^ [_1011351, _1011353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011351)), -(c_SMT_Oz3mod(_1011353, _1011351) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011353, _1011351))], (3688 ^ _773908) ^ [_829514, _829516, _829518, _829520, _829522, _829524, _829526, _829528] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_829528, _829524, _829520, _829516) = c_New__Random__Sequence_Opos__not__random__dseq(_829526, _829522, _829518, _829514)), _829528 = _829526, _829524 = _829522, _829520 = _829518, _829516 = _829514], (32005 ^ _773908) ^ [_1367010] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1367010)) = _1367010)], (8231 ^ _773908) ^ [_909422, _909424] : [class_Rings_Olinordered__semidom(_909422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909422), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909422), _909424)), c_Groups_Ozero__class_Ozero(_909422)))], (5789 ^ _773908) ^ [_865739, _865741, _865743, _865745, _865747] : [-(hAPP(hAPP(c_Set_Oinsert(_865739), _865741), hAPP(hAPP(c_Set_Oinsert(_865739), _865743), c_Orderings_Obot__class_Obot(tc_fun(_865739, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_865739), _865745), hAPP(hAPP(c_Set_Oinsert(_865739), _865747), c_Orderings_Obot__class_Obot(tc_fun(_865739, tc_HOL_Obool))))), 5790 ^ _773908 : [(5797 ^ _773908) ^ [] : [_865741 = _865747, _865743 = _865745], (5791 ^ _773908) ^ [] : [_865741 = _865745, _865743 = _865747]]], (38488 ^ _773908) ^ [_1514204, _1514206] : [-(hAPP(c_Set_Ovimage(_1514204, _1514204, c_Fun_Oid(_1514204)), _1514206) = _1514206)], (28632 ^ _773908) ^ [_1295317, _1295319, _1295321, _1295323] : [hBOOL(hAPP(hAPP(c_member(_1295317), _1295319), c_SetInterval_Oord_OatMost(_1295317, _1295321, _1295323))), -(hBOOL(hAPP(hAPP(_1295321, _1295319), _1295323)))], (14480 ^ _773908) ^ [_1018807, _1018809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018807)), 14483 ^ _773908 : [(14490 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018809), 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), _1018809), _1018807)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14484 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018809), _1018807)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018809), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (16979 ^ _773908) ^ [_1066320, _1066322] : [class_Rings_Olinordered__idom(_1066320), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066320), c_Groups_Osgn__class_Osgn(_1066320, _1066322)), hAPP(c_Groups_Oabs__class_Oabs(_1066320), _1066322)) = _1066322)], (50524 ^ _773908) ^ [_1796350, _1796352] : [c_Relation_Osym(_1796350, _1796352), 50527 ^ _773908 : [(50528 ^ _773908) ^ [_1796456, _1796458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796350, _1796350)), hAPP(hAPP(c_Product__Type_OPair(_1796350, _1796350), _1796458), _1796456)), _1796352)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796350, _1796350)), hAPP(hAPP(c_Product__Type_OPair(_1796350, _1796350), _1796456), _1796458)), _1796352)))]]], (16925 ^ _773908) ^ [_1065093, _1065095, _1065097, _1065099] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065093, tc_HOL_Obool)), _1065095), hAPP(hAPP(c_Set_Oinsert(_1065093), _1065097), _1065099)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065093, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065093, tc_HOL_Obool)), _1065095), hAPP(hAPP(c_Set_Oinsert(_1065093), _1065097), c_Orderings_Obot__class_Obot(tc_fun(_1065093, tc_HOL_Obool))))), _1065099))], (46045 ^ _773908) ^ [_1694177, _1694179, _1694181, _1694183] : [class_Orderings_Olinorder(_1694177), -(c_List_Olinorder__class_Osorted(_1694177, hAPP(hAPP(c_List_Omap(_1694179, _1694177), _1694181), c_List_Olinorder__class_Osort__key(_1694179, _1694177, _1694181, _1694183))))], (5817 ^ _773908) ^ [_866283, _866285, _866287] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_866283, _866285, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_866283)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866283), _866287), c_Com_Ocom_OSKIP), _866287)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_866283), tc_HOL_Obool)))))], (47381 ^ _773908) ^ [_1726238, _1726240, _1726242] : [-(hAPP(c_Relation_ODomain(_1726238, _1726240), hAPP(c_Relation_Oconverse(_1726240, _1726238), _1726242)) = hAPP(c_Relation_ORange(_1726240, _1726238), _1726242))], (23301 ^ _773908) ^ [_1179574, _1179576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179574), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1179576, _1179574) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179576), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179574)))], (386 ^ _773908) ^ [_779861, _779863, _779865, _779867, _779869, _779871, _779873, _779875] : [-(c_Equiv__Relations_Ocongruent(_779873, _779869, _779865, _779861)), c_Equiv__Relations_Ocongruent(_779875, _779871, _779867, _779863), _779875 = _779873, _779871 = _779869, _779867 = _779865, _779863 = _779861], (35778 ^ _773908) ^ [_1445347, _1445349, _1445351, _1445353, _1445355] : [class_Groups_Oab__semigroup__mult(_1445347), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1445347, _1445347, c_Groups_Otimes__class_Otimes(_1445347), _1445349, _1445351), _1445353)), hBOOL(hAPP(hAPP(c_member(_1445347), _1445355), _1445351)), -(hBOOL(hAPP(hAPP(c_member(_1445347), _1445349), _1445351))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1445347, _1445347, c_Groups_Otimes__class_Otimes(_1445347), _1445355, hAPP(hAPP(c_Set_Oinsert(_1445347), _1445349), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1445347, tc_HOL_Obool)), _1445351), hAPP(hAPP(c_Set_Oinsert(_1445347), _1445355), c_Orderings_Obot__class_Obot(tc_fun(_1445347, tc_HOL_Obool)))))), _1445353)))], (4974 ^ _773908) ^ [_849871, _849873] : [_849873 = _849871, -(c_DSequence_Ounion(_849873) = c_DSequence_Ounion(_849871))], (18713 ^ _773908) ^ [_1097363, _1097365, _1097367, _1097369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097363, tc_HOL_Obool)), _1097365), hAPP(hAPP(c_Set_Oinsert(_1097363), _1097367), _1097369))), 18716 ^ _773908 : [(18723 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097363), _1097367), _1097365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097363, tc_HOL_Obool)), _1097365), _1097369)))], (18717 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1097363), _1097367), _1097365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097363, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1097363, tc_HOL_Obool)), _1097365), hAPP(hAPP(c_Set_Oinsert(_1097363), _1097367), c_Orderings_Obot__class_Obot(tc_fun(_1097363, tc_HOL_Obool))))), _1097369)))]]], (23087 ^ _773908) ^ [_1175004, _1175006] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1175004))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1175006)), hAPP(c_Int_Onat, _1175004)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175006), _1175004)), 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)))], (21841 ^ _773908) ^ [_1151929, _1151931, _1151933, _1151935] : [class_Fields_Ofield__inverse__zero(_1151929), class_Int_Onumber(_1151929), 21848 ^ _773908 : [(21849 ^ _773908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151929), _1151931), hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933)) = _1151935, 21852 ^ _773908 : [(21859 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933) = c_Groups_Ozero__class_Ozero(_1151929), -(_1151935 = c_Groups_Ozero__class_Ozero(_1151929))], (21853 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933) = c_Groups_Ozero__class_Ozero(_1151929)), -(_1151931 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151929), _1151935), hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933)))]]], (21865 ^ _773908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151929), _1151931), hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933)) = _1151935), 21868 ^ _773908 : [(21871 ^ _773908) ^ [] : [_1151931 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151929), _1151935), hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933))], (21869 ^ _773908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933) = c_Groups_Ozero__class_Ozero(_1151929)]], 21872 ^ _773908 : [(21875 ^ _773908) ^ [] : [_1151935 = c_Groups_Ozero__class_Ozero(_1151929)], (21873 ^ _773908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1151929), _1151933) = c_Groups_Ozero__class_Ozero(_1151929))]]]]], (30369 ^ _773908) ^ [_1328835, _1328837, _1328839] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1328835), _1328837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1328835), _1328837)), hAPP(c_Finite__Set_Ocard(_1328835), hAPP(hAPP(c_Set_Oinsert(_1328835), _1328839), _1328837)))))], (41466 ^ _773908) ^ [_1590776, _1590778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1590776), _1590778)), -(c_List_Oupto(_1590776, _1590778) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1590776), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1590776), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1590778)))], (4040 ^ _773908) ^ [_834946, _834948, _834950, _834952, _834954, _834956] : [-(c_Nitpick_Oof__frac(_834956, _834952, _834948) = c_Nitpick_Oof__frac(_834954, _834950, _834946)), _834956 = _834954, _834952 = _834950, _834948 = _834946], (16585 ^ _773908) ^ [_1058541, _1058543] : [16586 ^ _773908 : [(16589 ^ _773908) ^ [] : [_1058543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16587 ^ _773908) ^ [] : [-(_1058541 = 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), _1058541)), _1058543))))], (28212 ^ _773908) ^ [_1285203, _1285205, _1285207, _1285209] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285203, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285203, tc_HOL_Obool)), _1285205), _1285207)), _1285209) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285203, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285203, tc_HOL_Obool)), _1285205), _1285209)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285203, tc_HOL_Obool)), _1285207), _1285209)))], (43774 ^ _773908) ^ [_1644649, _1644651, _1644653] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1644649, tc_HOL_Obool)), _1644651), _1644653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1644649, tc_HOL_Obool)), _1644651), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1644649, tc_HOL_Obool), _1644653))))], (40547 ^ _773908) ^ [_1568193, _1568195, _1568197] : [-(_1568193 = c_List_Olist_ONil(_1568195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568197), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1568195)), _1568193))), -(hAPP(c_List_Ohd(_1568195), hAPP(hAPP(c_List_Odrop(_1568195), _1568197), _1568193)) = hAPP(hAPP(c_List_Onth(_1568195), _1568193), _1568197))], (28394 ^ _773908) ^ [_1289803, _1289805, _1289807] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289803, tc_HOL_Obool)), _1289805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289803, tc_HOL_Obool)), _1289807), _1289805)) = c_Orderings_Obot__class_Obot(tc_fun(_1289803, tc_HOL_Obool)))], (28374 ^ _773908) ^ [_1289381, _1289383, _1289385, _1289387] : [-(hBOOL(hAPP(hAPP(c_member(_1289381), _1289383), _1289385))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289381, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1289381), _1289383), _1289387)), _1289385) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1289381, tc_HOL_Obool)), _1289387), _1289385))], (45155 ^ _773908) ^ [_1675902, _1675904, _1675906] : [class_Orderings_Olinorder(_1675902), c_List_Olinorder__class_Osorted(_1675902, _1675904), -(c_List_Olinorder__class_Osorted(_1675902, c_List_Oremove1(_1675902, _1675906, _1675904)))], (31015 ^ _773908) ^ [_1342454, _1342456, _1342458, _1342460, _1342462] : [class_Groups_Ocomm__monoid__mult(_1342454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342456), _1342458)), -(hBOOL(hAPP(hAPP(c_member(_1342456), _1342460), _1342458))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342456, _1342454), _1342462), hAPP(hAPP(c_Set_Oinsert(_1342456), _1342460), _1342458)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342454), hAPP(_1342462, _1342460)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342456, _1342454), _1342462), _1342458)))], (11565 ^ _773908) ^ [_967096, _967098] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967096), hAPP(c_Nat_OSuc, _967098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967096), _967098)))], (22063 ^ _773908) ^ [] : [-(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))], (17871 ^ _773908) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15289 ^ _773908) ^ [_1033168, _1033170] : [class_Groups_Ogroup__add(_1033168), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033168), _1033170), _1033170) = c_Groups_Ozero__class_Ozero(_1033168))], (39595 ^ _773908) ^ [_1543555, _1543557, _1543559, _1543561, _1543563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1543555), tc_List_Olist(_1543555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1543555), tc_List_Olist(_1543555)), _1543557), _1543559)), c_List_Olistrel1(_1543555, _1543561))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1543555), tc_List_Olist(_1543555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1543555), tc_List_Olist(_1543555)), hAPP(hAPP(c_List_Olist_OCons(_1543555), _1543563), _1543557)), hAPP(hAPP(c_List_Olist_OCons(_1543555), _1543563), _1543559))), c_List_Olistrel1(_1543555, _1543561))))], (50783 ^ _773908) ^ [_1800927, _1800929] : [c_Equiv__Relations_Opart__equivp(_1800927, _1800929), 50787 ^ _773908 : [(50792 ^ _773908) ^ [] : [-(c_Predicate_Otransp(_1800927, _1800929))], (50790 ^ _773908) ^ [] : [-(c_Predicate_Osymp(_1800927, _1800929))], (50788 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(_1800929, 50786 ^ [_1800927, _1800929]), 50786 ^ [_1800927, _1800929])))]]], (22563 ^ _773908) ^ [_1165141, _1165143, _1165145, _1165147] : [class_Fields_Olinordered__field__inverse__zero(_1165141), class_Int_Onumber(_1165141), 22570 ^ _773908 : [(22571 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165141), _1165143), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))), _1165147)), 22574 ^ _773908 : [(22581 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)))), 22584 ^ _773908 : [(22591 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)), c_Groups_Ozero__class_Ozero(_1165141)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), _1165147)))], (22585 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)), c_Groups_Ozero__class_Ozero(_1165141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165141), _1165147), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))), _1165143)))]]], (22575 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), _1165143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165141), _1165147), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)))))]]], (22597 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165141), _1165143), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))), _1165147))), 22600 ^ _773908 : [(22603 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), _1165143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165141), _1165147), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))))], (22601 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))))]], 22604 ^ _773908 : [(22607 ^ _773908) ^ [] : [22608 ^ _773908 : [(22611 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165141), _1165147), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145))), _1165143))], (22609 ^ _773908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)), c_Groups_Ozero__class_Ozero(_1165141))))]], 22612 ^ _773908 : [(22615 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), _1165147))], (22613 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)), c_Groups_Ozero__class_Ozero(_1165141)))]]], (22605 ^ _773908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165141), c_Groups_Ozero__class_Ozero(_1165141)), hAPP(c_Int_Onumber__class_Onumber__of(_1165141), _1165145)))]]]]], (41233 ^ _773908) ^ [_1586342, _1586344] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1586342), _1586344) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 41236 ^ _773908 : [(41239 ^ _773908) ^ [_1586456] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1586456), hAPP(c_List_Oset(tc_Nat_Onat), _1586344))), -(_1586456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41237 ^ _773908) ^ [] : [-(_1586342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19395 ^ _773908) ^ [_1108783] : [c_Int_OBit1(_1108783) = c_Int_OMin, -(_1108783 = c_Int_OMin)], (17929 ^ _773908) ^ [_1083354] : [class_Int_Onumber__ring(_1083354), -(hAPP(c_Int_Onumber__class_Onumber__of(_1083354), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083354), c_Groups_Oone__class_Oone(_1083354)))]], input).
% 48.55/47.23  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))],start(51952 ^ 0)).
% 48.55/47.23  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G)))],extension(12907 ^ 1,bind([[_990340, _990342, _990344, _990346], [t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G)]]))).
% 48.55/47.23  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn))), v_Q)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))],extension(51950 ^ 2)).
% 48.55/47.23  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)), v_G))))],extension(12586 ^ 2,bind([[_984901, _984903, _984905], [tc_Hoare__Mirabelle_Otriple(t_a), v_G, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), v_P), hAPP(c_Com_Ocom_OBODY, v_pn)), v_Q)]]))).
% 48.55/47.23  %-----------------------------------------------------
% 48.55/47.23  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------